CDPL::ForceField Namespace Reference

Contains classes and functions related to molecular force fields. More...

Namespaces
	AtomProperty
	Provides keys for built-in Chem::Atom properties.
	BondProperty
	Provides keys for built-in Chem::Bond properties.
	InteractionType
	Provides flags for the specification of a set of force field interaction types.
	MMFF94ParameterSet
	Provides flags for the specification of the MMFF94 parameter set to use.
	MolecularGraphProperty
	Provides keys for built-in Chem::MolecularGraph properties.
	UFFAtomType
	Provides constants for the specification of Universal Force Field (UFF) atom types.

Classes
class	ElasticPotential
	Stores parameters for an elastic potential (harmonic distance restraint) between a pair of atoms. More...
class	Error
	Base class of the ForceField subsystem exception hierarchy. More...
class	ParameterizationFailed
	Thrown when force field parameterization has failed. More...
struct	GradientVectorTraits
	Generic primary traits template providing zero-initialization for a 3D gradient vector container of type GV. More...
struct	GradientVectorTraits< Math::VectorArray< V > >
	ForceField::GradientVectorTraits specialization for containers of type Math::VectorArray. More...
struct	GradientVectorTraits< std::vector< V > >
	ForceField::GradientVectorTraits specialization for containers of type std::vector. More...
class	MMFF94AngleBendingInteraction
	Stores parameters for a single MMFF94 angle-bending interaction defined over an atom triplet. More...
class	MMFF94AngleBendingInteractionParameterizer
	Detects and parameterizes the MMFF94 angle-bending interactions of a molecular graph. More...
class	MMFF94AngleBendingParameterTable
	Data structure for the storage and lookup of MMFF94 angle-bending interaction parameters. More...
class	MMFF94AromaticAtomTypeDefinitionTable
	Definitions for the second-stage MMFF94 aromatic atom typing. More...
class	MMFF94AromaticSSSRSubset
	Implements the extraction of all rings in the SSSR of a molecular graph that are aromatic according to MMFF94 conventions. More...
class	MMFF94AtomTypePropertyTable
	Lookup table mapping numeric MMFF94 atom types to per-atom-type structural and chemical property data used during MMFF94 atom and bond typing. More...
class	MMFF94AtomTyper
	Assigns MMFF94 symbolic and numeric atom types to the atoms of a molecular graph. More...
class	MMFF94BondChargeIncrementTable
	Lookup table mapping (bond type, atom-type 1, atom-type 2) triples to MMFF94 bond charge increments. More...
class	MMFF94BondStretchingInteraction
	Stores parameters for a single MMFF94 bond-stretching interaction between two bonded atoms. More...
class	MMFF94BondStretchingInteractionParameterizer
	Detects and parameterizes the MMFF94 bond-stretching interactions of a molecular graph. More...
class	MMFF94BondStretchingParameterTable
	Data structure for the storage and lookup of MMFF94 bond-stretching interaction parameters. More...
class	MMFF94BondStretchingRuleParameterTable
	Lookup table mapping (atomic-number 1, atomic-number 2) pairs to fallback MMFF94 bond-stretching parameters used when no atom-type-specific entry is available. More...
class	MMFF94BondTyper
	Assigns MMFF94 bond type indices to the bonds of a molecular graph. More...
class	MMFF94ChargeCalculator
	Calculator for the MMFF94 partial atomic charges of a molecular graph. More...
class	MMFF94DefaultStretchBendParameterTable
	Lookup table mapping (terminal-atom-1 PTE row, center-atom PTE row, terminal-atom-2 PTE row) triples to fallback MMFF94 stretch-bend coupling force constants used when no atom-type-specific entry is available. More...
class	MMFF94ElectrostaticInteraction
	Stores parameters for a single MMFF94 electrostatic interaction between two non-bonded atoms. More...
class	MMFF94ElectrostaticInteractionParameterizer
	Detects and parameterizes the MMFF94 electrostatic interactions of a molecular graph. More...
class	MMFF94EnergyCalculator
	Calculates the total MMFF94 force field energy for a set of atom 3D coordinates. More...
class	MMFF94FormalAtomChargeDefinitionTable
	Lookup table mapping symbolic MMFF94 atom types to their formal-charge definitions used by the MMFF94 charge model. More...
class	MMFF94GradientCalculator
	Calculates the total MMFF94 force field energy and its gradient for a set of atom 3D coordinates. More...
class	MMFF94HeavyToHydrogenAtomTypeMap
	Lookup table mapping each heavy atom symbolic MMFF94 type to the symbolic MMFF94 type used for hydrogen atoms bonded to it. More...
class	MMFF94InteractionData
	Container holding the full set of MMFF94 interaction parameters for a molecular graph. More...
class	MMFF94InteractionParameterizer
	One-stop MMFF94 parameterizer that combines atom typing, bond typing, partial-charge assignment and per-interaction-type parameter look-up into a single parameterize() call. More...
class	MMFF94OutOfPlaneBendingInteraction
	Stores parameters for a single MMFF94 out-of-plane bending interaction at a trigonal center. More...
class	MMFF94OutOfPlaneBendingInteractionParameterizer
	Detects and parameterizes the MMFF94 out-of-plane bending interactions of a molecular graph. More...
class	MMFF94OutOfPlaneBendingParameterTable
	Lookup table mapping (terminal-atom-1 type, center-atom type, terminal-atom-2 type, out-of-plane-atom type) quadruples to MMFF94 out-of-plane bending force constants. More...
class	MMFF94PartialBondChargeIncrementTable
	Lookup table mapping numeric MMFF94 atom types to per-atom partial bond charge increments and formal-charge adjustment factors used by the MMFF94 charge model. More...
class	MMFF94PrimaryToParameterAtomTypeMap
	Lookup table mapping each primary numeric MMFF94 atom type to the ordered list of fallback numeric atom types used when looking up missing interaction parameters. More...
class	MMFF94StretchBendInteraction
	Stores paramters for a single MMFF94 stretch-bend coupling interaction. More...
class	MMFF94StretchBendInteractionParameterizer
class	MMFF94StretchBendParameterTable
	Lookup table mapping (stretch-bend type, terminal-atom-1 type, center-atom type, terminal-atom-2 type) quadruples to MMFF94 stretch-bend coupling force constants. More...
class	MMFF94SymbolicAtomTypePatternTable
	Ordered list of SMARTS-style substructure patterns used to assign symbolic MMFF94 atom types during atom typing. More...
class	MMFF94SymbolicToNumericAtomTypeMap
	Lookup table mapping each symbolic MMFF94 atom type to its corresponding numeric MMFF94 atom type. More...
class	MMFF94TorsionInteraction
	Stores parameters for a single MMFF94 torsion interaction over an atom quadruplet i-j-k-l. More...
class	MMFF94TorsionInteractionParameterizer
	Detects and parameterizes the MMFF94 torsion interactions of a molecular graph. More...
class	MMFF94TorsionParameterTable
	Lookup table mapping (torsion type, terminal-atom-1 type, center-atom-1 type, center-atom-2 type, terminal-atom-2 type) quintuples to the three MMFF94 torsion-energy Fourier-series parameters (V1, V2, V3). More...
class	MMFF94VanDerWaalsInteraction
	Stores parameters for a single MMFF94 Van der Waals interaction between two non-bonded atoms. More...
class	MMFF94VanDerWaalsInteractionParameterizer
	Detects and parameterizes the MMFF94 Van der Waals interactions of a molecular graph. More...
class	MMFF94VanDerWaalsParameterTable
	Lookup table mapping numeric MMFF94 atom types to per-atom-type Van der Waals parameters (atomic polarizability, effective electron number, scaling factors A/G, and H-donor/-acceptor classification). More...
class	UFFAtomTypePropertyTable
	Lookup table mapping numeric UFF atom types to the per-atom-type parameters used by the Universal Force Field (UFF). More...

Typedefs
typedef Util::Array< ElasticPotential >	ElasticPotentialList
	Data structure for the storage of elastic potential parameter set records. More...
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction2
	Generic wrapper for storing user-defined two-atom interaction filtering functions (see [FUNWRP]). More...
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction3
	Generic wrapper for storing user-defined three-atom interaction filtering functions (see [FUNWRP]). More...
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction4
	Generic wrapper for storing user-defined four-atom interaction filtering functions (see [FUNWRP]). More...
typedef Util::Array< MMFF94AngleBendingInteraction >	MMFF94AngleBendingInteractionList
	Data structure for the storage of MMFF94 angle-bending interaction parameter set records. More...
typedef Util::Array< MMFF94BondStretchingInteraction >	MMFF94BondStretchingInteractionList
	Data structure for the storage of MMFF94 bond-stretching interaction parameter set records. More...
typedef Util::Array< MMFF94ElectrostaticInteraction >	MMFF94ElectrostaticInteractionList
	Data structure for the storage of MMFF94 electrostatic interaction parameter set records. More...
typedef Util::Array< MMFF94OutOfPlaneBendingInteraction >	MMFF94OutOfPlaneBendingInteractionList
	Data structure for the storage of MMFF94 out-of-plane bending interaction parameter set records. More...
typedef std::function< unsigned int(const Chem::Atom &)>	MMFF94NumericAtomTypeFunction
	Generic wrapper class used to store a user-defined numeric MMFF94 atom type function. More...
typedef std::function< const std::string &(const Chem::Atom &)>	MMFF94SymbolicAtomTypeFunction
	Generic wrapper class used to store a user-defined symbolic MMFF94 atom type function. More...
typedef std::function< double(const Chem::Atom &)>	MMFF94AtomChargeFunction
	Generic wrapper class used to store a user-defined MMFF94 partial atom charge function. More...
typedef std::function< unsigned int(const Chem::Bond &)>	MMFF94BondTypeIndexFunction
	Generic wrapper class used to store a user-defined MMFF94 bond type index function. More...
typedef std::function< const Chem::FragmentList::SharedPointer &(const Chem::MolecularGraph &)>	MMFF94RingSetFunction
	Generic wrapper class used to store a user-defined MMFF94 ring set function. More...
typedef Util::Array< MMFF94StretchBendInteraction >	MMFF94StretchBendInteractionList
	Data structure for the storage of MMFF94 stretch-bend coupling interaction parameter set records. More...
typedef Util::Array< MMFF94TorsionInteraction >	MMFF94TorsionInteractionList
	Data structure for the storage of MMFF94 torsion interaction parameter set records. More...
typedef Util::Array< MMFF94VanDerWaalsInteraction >	MMFF94VanDerWaalsInteractionList
	Data structure for the storage of MMFF94 Van der Waals interaction parameter set records. More...
typedef std::function< std::size_t(const Chem::Atom &, const Chem::Atom &, const Chem::MolecularGraph &)>	TopologicalAtomDistanceFunction
	Generic wrapper class used to store a user-defined topological atom-pair distance function. More...

Functions
CDPL_FORCEFIELD_API const std::string &	getMMFF94SymbolicType (const Chem::Atom &atom)
	Returns the value of the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property of atom. More...
CDPL_FORCEFIELD_API void	setMMFF94SymbolicType (Chem::Atom &atom, const std::string &type)
	Sets the value of the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property of atom to type. More...
CDPL_FORCEFIELD_API void	clearMMFF94SymbolicType (Chem::Atom &atom)
	Removes the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property from atom. More...
CDPL_FORCEFIELD_API bool	hasMMFF94SymbolicType (const Chem::Atom &atom)
	Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property. More...
CDPL_FORCEFIELD_API unsigned int	getMMFF94NumericType (const Chem::Atom &atom)
	Returns the value of the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property of atom. More...
CDPL_FORCEFIELD_API void	setMMFF94NumericType (Chem::Atom &atom, unsigned int type)
	Sets the value of the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property of atom to type. More...
CDPL_FORCEFIELD_API void	clearMMFF94NumericType (Chem::Atom &atom)
	Removes the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property from atom. More...
CDPL_FORCEFIELD_API bool	hasMMFF94NumericType (const Chem::Atom &atom)
	Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property. More...
CDPL_FORCEFIELD_API double	getMMFF94Charge (const Chem::Atom &atom)
	Returns the value of the ForceField::AtomProperty::MMFF94_CHARGE property of atom. More...
CDPL_FORCEFIELD_API void	setMMFF94Charge (Chem::Atom &atom, double charge)
	Sets the value of the ForceField::AtomProperty::MMFF94_CHARGE property of atom to charge. More...
CDPL_FORCEFIELD_API void	clearMMFF94Charge (Chem::Atom &atom)
	Removes the ForceField::AtomProperty::MMFF94_CHARGE property from atom. More...
CDPL_FORCEFIELD_API bool	hasMMFF94Charge (const Chem::Atom &atom)
	Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_CHARGE property. More...
CDPL_FORCEFIELD_API unsigned int	getUFFType (const Chem::Atom &atom)
	Returns the value of the ForceField::AtomProperty::UFF_TYPE property of atom. More...
CDPL_FORCEFIELD_API void	setUFFType (Chem::Atom &atom, unsigned int type)
	Sets the value of the ForceField::AtomProperty::UFF_TYPE property of atom to type. More...
CDPL_FORCEFIELD_API void	clearUFFType (Chem::Atom &atom)
	Removes the ForceField::AtomProperty::UFF_TYPE property from atom. More...
CDPL_FORCEFIELD_API bool	hasUFFType (const Chem::Atom &atom)
	Tells whether atom carries an explicit ForceField::AtomProperty::UFF_TYPE property. More...
CDPL_FORCEFIELD_API unsigned int	perceiveUFFType (const Chem::Atom &atom, const Chem::MolecularGraph &molgraph)
	Perceives the UFF atom type of atom in the context of the molecular graph molgraph. More...
CDPL_FORCEFIELD_API unsigned int	getMMFF94TypeIndex (const Chem::Bond &bond)
	Returns the value of the ForceField::BondProperty::MMFF94_TYPE_INDEX property of bond. More...
CDPL_FORCEFIELD_API void	setMMFF94TypeIndex (Chem::Bond &bond, unsigned int type_idx)
	Sets the value of the ForceField::BondProperty::MMFF94_TYPE_INDEX property of bond to type_idx. More...
CDPL_FORCEFIELD_API void	clearMMFF94TypeIndex (Chem::Bond &bond)
	Removes the ForceField::BondProperty::MMFF94_TYPE_INDEX property from bond. More...
CDPL_FORCEFIELD_API bool	hasMMFF94TypeIndex (const Chem::Bond &bond)
	Tells whether bond carries an explicit ForceField::BondProperty::MMFF94_TYPE_INDEX property. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcElasticPotentialEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Accumulates the energies calculated for the elastic potentials specified by the iterators in the given range. More...
template<typename ValueType , typename CoordsArray >
ValueType	calcElasticPotentialEnergy (const ElasticPotential &pot, const CoordsArray &coords)
	Calculates the energy of a single elastic potential pot for the supplied atom coordinates coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcElasticPotentialEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &force_const, const ValueType &ref_length)
	Calculates the energy \( E_{ij} \) of an elastic potential applied on a pair of atoms i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcElasticPotentialGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Accumulates the energies and gradient contributions calculated for the elastic potentials specified by the iterators in the given range. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcElasticPotentialGradient (const ElasticPotential &pot, const CoordsArray &coords, GradVector &grad)
	Calculates the energy and gradient contribution of a single elastic potential pot for the supplied atom coordinates coords. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcElasticPotentialGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &force_const, const ValueType &ref_length)
	Calculates the elastic potential energy gradient \( \nabla E_{ij} \) for a pair of atoms i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94BondStretchingEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the bond-stretching interaction energies of all MMFF94 bond-stretching interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94BondStretchingEnergy (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords)
	Calculates the bond-stretching interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94BondStretchingEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &force_const, const ValueType &ref_length)
	Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More...
template<typename ValueType >
ValueType	calcMMFF94BondStretchingEnergy (const ValueType &r_ij, const ValueType &force_const, const ValueType &ref_length)
	Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94AngleBendingEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the angle-bending interaction energies of all MMFF94 angle-bending interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94AngleBendingEnergy (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords)
	Calculates the angle-bending interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94AngleBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, bool linear, const ValueType &force_const, const ValueType &ref_angle)
	Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94AngleBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk, bool linear, const ValueType &force_const, const ValueType &ref_angle)
	Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94StretchBendEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the stretch-bend coupling interaction energies of all MMFF94 stretch-bend interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94StretchBendEnergy (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords)
	Calculates the stretch-bend coupling interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94StretchBendEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2)
	Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94StretchBendEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2)
	Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94OutOfPlaneBendingEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the out-of-plane bending interaction energies of all MMFF94 out-of-plane bending interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94OutOfPlaneBendingEnergy (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords)
	Calculates the out-of-plane bending interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94OutOfPlaneBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &force_const)
	Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94OutOfPlaneBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &r_jl, const ValueType &force_const)
	Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94TorsionEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the torsion interaction energies of all MMFF94 torsion interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94TorsionEnergy (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords)
	Calculates the torsion interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94TorsionEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, const ValueType &tor_param1, const ValueType &tor_param2, const ValueType &tor_param3)
	Calculates the torsion interaction energy \( ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94ElectrostaticEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the electrostatic interaction energies of all MMFF94 electrostatic interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94ElectrostaticEnergy (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords)
	Calculates the electrostatic interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94ElectrostaticEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo)
	Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More...
template<typename ValueType >
ValueType	calcMMFF94ElectrostaticEnergy (const ValueType &r_ij, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo)
	Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcMMFF94VanDerWaalsEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
	Sums the Van der Waals interaction energies of all MMFF94 Van der Waals interactions in the iterator range [beg, end). More...
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94VanDerWaalsEnergy (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords)
	Calculates the Van der Waals interaction energy of iaction using the geometry from coords. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcMMFF94VanDerWaalsEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7)
	Calculates the Van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More...
template<typename ValueType >
ValueType	calcMMFF94VanDerWaalsEnergy (const ValueType &r_ij, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7)
	Calculates the Van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94BondStretchingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 bond-stretching interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94BondStretchingGradient (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the bond-stretching interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94BondStretchingGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &force_const, const ValueType &ref_length)
	Calculates the bond stretching interaction energy gradient \( \nabla EB_{ij} \) for the bond i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94AngleBendingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 angle-bending interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94AngleBendingGradient (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the angle-bending interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94AngleBendingGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, bool linear, const ValueType &force_const, const ValueType &ref_angle)
	Calculates the angle bending interaction energy gradient \( \nabla EA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94StretchBendGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 stretch-bend coupling interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94StretchBendGradient (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the stretch-bend coupling interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94StretchBendGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2)
	Calculates the stretch-bend interaction energy gradient \( \nabla EBA_{ijk} \) for two bonds i-j and j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94OutOfPlaneBendingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 out-of-plane bending interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94OutOfPlaneBendingGradient (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the out-of-plane bending interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94OutOfPlaneBendingGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, GradVec &oop_atom_grad, const ValueType &force_const)
	Calculates the out-of-plane bending interaction energy gradient \( \nabla EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94TorsionGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 torsion interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94TorsionGradient (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the torsion interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94TorsionGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom1_grad, GradVec &ctr_atom2_grad, GradVec &term_atom2_grad, const ValueType &tor_param1, const ValueType &tor_param2, const ValueType &tor_param3)
	Calculates the torsion interaction energy gradient \( \nabla ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94ElectrostaticGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 electrostatic interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94ElectrostaticGradient (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the electrostatic interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94ElectrostaticGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo)
	Calculates the electrostatic interaction energy gradient \( \nabla EQ_{ij} \) for the atom pair i-j. More...
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94VanDerWaalsGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad)
	Sums the MMFF94 Van der Waals interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad. More...
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94VanDerWaalsGradient (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords, GradVector &grad)
	Calculates the Van der Waals interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcMMFF94VanDerWaalsGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7)
	Calculates the Van der Waals interaction energy gradient \( \nabla E_{vdW_{ij}} \) for the atom pair i-j. More...
CDPL_FORCEFIELD_API const Chem::FragmentList::SharedPointer &	getMMFF94AromaticRings (const Chem::MolecularGraph &molgraph)
	Returns the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property of molgraph. More...
CDPL_FORCEFIELD_API void	setMMFF94AromaticRings (Chem::MolecularGraph &molgraph, const Chem::FragmentList::SharedPointer &rings)
	Sets the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property of molgraph to rings. More...
CDPL_FORCEFIELD_API void	clearMMFF94AromaticRings (Chem::MolecularGraph &molgraph)
	Removes the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property from molgraph. More...
CDPL_FORCEFIELD_API bool	hasMMFF94AromaticRings (const Chem::MolecularGraph &molgraph)
	Tells whether molgraph carries an explicit ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property. More...
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer	perceiveMMFF94AromaticRings (const Chem::MolecularGraph &molgraph)
	Perceives the list of MMFF94 aromatic rings of the molecular graph molgraph without storing the result. More...
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer	perceiveMMFF94AromaticRings (Chem::MolecularGraph &molgraph, bool overwrite)
	Perceives the list of MMFF94 aromatic rings of molgraph and stores the result as the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property. More...
CDPL_FORCEFIELD_API void	assignMMFF94AtomTypes (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
	Assigns MMFF94 atom types to the atoms of molgraph. More...
CDPL_FORCEFIELD_API void	assignMMFF94BondTypeIndices (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
	Assigns MMFF94 bond type indices to the bonds of molgraph. More...
CDPL_FORCEFIELD_API void	calcMMFF94AtomCharges (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
	Calculates and assigns MMFF94 partial atomic charges to the atoms of molgraph. More...
CDPL_FORCEFIELD_API void	assignUFFAtomTypes (Chem::MolecularGraph &molgraph, bool overwrite)
	Assigns UFF atom types to the atoms of molgraph. More...
CDPL_FORCEFIELD_API void	filterInteractions (const MMFF94InteractionData &ia_data, MMFF94InteractionData &filtered_ia_data, const Util::BitSet &inc_atom_mask)
	Filters an MMFF94 interaction-data set, retaining only those interactions that exclusively reference atoms in inc_atom_mask. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcSquaredDistance (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos)
	Calculates the squared distance \( r_{ij}^2 \) between two atoms i and j. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcDistance (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos)
	Calculates the distance \( r_{ij} \) between two atoms i and j. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondLengthsAndAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, ValueType &bond_length1, ValueType &bond_length2)
	Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondLengthsAndAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, ValueType &bond_length1, ValueType &bond_length2)
	Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos)
	Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk)
	Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos)
	Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcBondAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk)
	Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcOutOfPlaneAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos)
	Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcOutOfPlaneAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &r_jl)
	Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k. More...
template<typename ValueType , typename CoordsVec >
ValueType	calcDihedralAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos)
	Calculates the cosine of the dihedral angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcDistanceDerivatives (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_deriv, GradVec &atom2_deriv)
	Calculates the partial derivatives \( \frac{\partial r_{ij}}{\partial \vec{p_x}} \) of the distance \( r_{ij} \) between two atoms i and j. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcBondAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom_deriv, GradVec &term_atom2_deriv)
	Calculates the partial derivatives \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_x}} \) of the of the cosine of the angle \( \vartheta_{ijk} \) between the bonds i-j and j-k. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcDihedralAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom1_deriv, GradVec &ctr_atom2_deriv, GradVec &term_atom2_deriv)
	Calculates the partial derivatives \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_x}} \) of the cosine of the angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l. More...
template<typename ValueType , typename CoordsVec , typename GradVec >
ValueType	calcOutOfPlaneAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom_deriv, GradVec &term_atom2_deriv, GradVec &oop_atom_deriv)
	Calculates the partial derivatives \( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_x}} \) of the cosine of the angle \( \omega_{ijk;l} \) between the bond j-l and the normal of the plane defined by the atoms i-j-k. More...

Detailed Description

Contains classes and functions related to molecular force fields.

Typedef Documentation

ElasticPotentialList

typedef Util::Array<ElasticPotential> CDPL::ForceField::ElasticPotentialList

Data structure for the storage of elastic potential parameter set records.

Since

1.1

InteractionFilterFunction2

typedef std::function<bool(const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction2

Generic wrapper for storing user-defined two-atom interaction filtering functions (see [FUNWRP]).

The function is invoked with the two interacting atoms and is expected to return true if the interaction should be considered, and false if it should be skipped.

InteractionFilterFunction3

typedef std::function<bool(const Chem::Atom&, const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction3

Generic wrapper for storing user-defined three-atom interaction filtering functions (see [FUNWRP]).

The function is invoked with the three interacting atoms (typically used for angle-bending and stretch-bend interactions) and is expected to return true if the interaction should be considered, and false if it should be skipped.

InteractionFilterFunction4

typedef std::function<bool(const Chem::Atom&, const Chem::Atom&, const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction4

Generic wrapper for storing user-defined four-atom interaction filtering functions (see [FUNWRP]).

The function is invoked with the four interacting atoms (typically used for torsion and out-of-plane bending interactions) and is expected to return true if the interaction should be considered, and false if it should be skipped.

MMFF94AngleBendingInteractionList

typedef Util::Array<MMFF94AngleBendingInteraction> CDPL::ForceField::MMFF94AngleBendingInteractionList

Data structure for the storage of MMFF94 angle-bending interaction parameter set records.

MMFF94BondStretchingInteractionList

typedef Util::Array<MMFF94BondStretchingInteraction> CDPL::ForceField::MMFF94BondStretchingInteractionList

Data structure for the storage of MMFF94 bond-stretching interaction parameter set records.

MMFF94ElectrostaticInteractionList

typedef Util::Array<MMFF94ElectrostaticInteraction> CDPL::ForceField::MMFF94ElectrostaticInteractionList

Data structure for the storage of MMFF94 electrostatic interaction parameter set records.

MMFF94OutOfPlaneBendingInteractionList

typedef Util::Array<MMFF94OutOfPlaneBendingInteraction> CDPL::ForceField::MMFF94OutOfPlaneBendingInteractionList

Data structure for the storage of MMFF94 out-of-plane bending interaction parameter set records.

MMFF94NumericAtomTypeFunction

typedef std::function<unsigned int(const Chem::Atom&)> CDPL::ForceField::MMFF94NumericAtomTypeFunction

Generic wrapper class used to store a user-defined numeric MMFF94 atom type function.

MMFF94SymbolicAtomTypeFunction

typedef std::function<const std::string&(const Chem::Atom&)> CDPL::ForceField::MMFF94SymbolicAtomTypeFunction

Generic wrapper class used to store a user-defined symbolic MMFF94 atom type function.

MMFF94AtomChargeFunction

typedef std::function<double(const Chem::Atom&)> CDPL::ForceField::MMFF94AtomChargeFunction

Generic wrapper class used to store a user-defined MMFF94 partial atom charge function.

MMFF94BondTypeIndexFunction

typedef std::function<unsigned int(const Chem::Bond&)> CDPL::ForceField::MMFF94BondTypeIndexFunction

Generic wrapper class used to store a user-defined MMFF94 bond type index function.

MMFF94RingSetFunction

typedef std::function<const Chem::FragmentList::SharedPointer&(const Chem::MolecularGraph&)> CDPL::ForceField::MMFF94RingSetFunction

Generic wrapper class used to store a user-defined MMFF94 ring set function.

MMFF94StretchBendInteractionList

typedef Util::Array<MMFF94StretchBendInteraction> CDPL::ForceField::MMFF94StretchBendInteractionList

Data structure for the storage of MMFF94 stretch-bend coupling interaction parameter set records.

MMFF94TorsionInteractionList

typedef Util::Array<MMFF94TorsionInteraction> CDPL::ForceField::MMFF94TorsionInteractionList

Data structure for the storage of MMFF94 torsion interaction parameter set records.

MMFF94VanDerWaalsInteractionList

typedef Util::Array<MMFF94VanDerWaalsInteraction> CDPL::ForceField::MMFF94VanDerWaalsInteractionList

Data structure for the storage of MMFF94 Van der Waals interaction parameter set records.

TopologicalAtomDistanceFunction

typedef std::function<std::size_t(const Chem::Atom&, const Chem::Atom&, const Chem::MolecularGraph&)> CDPL::ForceField::TopologicalAtomDistanceFunction

Generic wrapper class used to store a user-defined topological atom-pair distance function.

Function Documentation

getMMFF94SymbolicType()

CDPL_FORCEFIELD_API const std::string& CDPL::ForceField::getMMFF94SymbolicType

(

const Chem::Atom &

atom

)

Returns the value of the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property of atom.

Parameters

atom

The atom.

Returns

The symbolic MMFF94 atom type.

setMMFF94SymbolicType()

CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94SymbolicType	(	Chem::Atom &	atom,
		const std::string &	type
	)

Sets the value of the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property of atom to type.

Parameters

atom	The atom.
type	The new symbolic MMFF94 atom type.

clearMMFF94SymbolicType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94SymbolicType

(

Chem::Atom &

atom

)

Removes the ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property from atom.

Parameters

atom

The atom.

hasMMFF94SymbolicType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94SymbolicType

(

const Chem::Atom &

atom

)

Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_SYMBOLIC_TYPE property.

Parameters

atom

The atom.

Returns

true if the symbolic MMFF94 atom type is set, and false otherwise.

getMMFF94NumericType()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94NumericType

(

const Chem::Atom &

atom

)

Returns the value of the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property of atom.

Parameters

atom

The atom.

Returns

The numeric MMFF94 atom type.

setMMFF94NumericType()

CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94NumericType	(	Chem::Atom &	atom,
		unsigned int	type
	)

Sets the value of the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property of atom to type.

Parameters

atom	The atom.
type	The new numeric MMFF94 atom type.

clearMMFF94NumericType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94NumericType

(

Chem::Atom &

atom

)

Removes the ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property from atom.

Parameters

atom

The atom.

hasMMFF94NumericType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94NumericType

(

const Chem::Atom &

atom

)

Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_NUMERIC_TYPE property.

Parameters

atom

The atom.

Returns

true if the numeric MMFF94 atom type is set, and false otherwise.

getMMFF94Charge()

CDPL_FORCEFIELD_API double CDPL::ForceField::getMMFF94Charge

(

const Chem::Atom &

atom

)

Returns the value of the ForceField::AtomProperty::MMFF94_CHARGE property of atom.

Parameters

atom

The atom.

Returns

The MMFF94 partial atomic charge.

setMMFF94Charge()

CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94Charge	(	Chem::Atom &	atom,
		double	charge
	)

Sets the value of the ForceField::AtomProperty::MMFF94_CHARGE property of atom to charge.

Parameters

atom	The atom.
charge	The new MMFF94 partial atomic charge.

clearMMFF94Charge()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94Charge

(

Chem::Atom &

atom

)

Removes the ForceField::AtomProperty::MMFF94_CHARGE property from atom.

Parameters

atom

The atom.

hasMMFF94Charge()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94Charge

(

const Chem::Atom &

atom

)

Tells whether atom carries an explicit ForceField::AtomProperty::MMFF94_CHARGE property.

Parameters

atom

The atom.

Returns

true if the MMFF94 partial atomic charge is set, and false otherwise.

getUFFType()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getUFFType

(

const Chem::Atom &

atom

)

Returns the value of the ForceField::AtomProperty::UFF_TYPE property of atom.

Parameters

atom

The atom.

Returns

The numeric UFF atom type.

setUFFType()

CDPL_FORCEFIELD_API void CDPL::ForceField::setUFFType	(	Chem::Atom &	atom,
		unsigned int	type
	)

Sets the value of the ForceField::AtomProperty::UFF_TYPE property of atom to type.

Parameters

atom	The atom.
type	The new numeric UFF atom type.

clearUFFType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearUFFType

(

Chem::Atom &

atom

)

Removes the ForceField::AtomProperty::UFF_TYPE property from atom.

Parameters

atom

The atom.

hasUFFType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasUFFType

(

const Chem::Atom &

atom

)

Tells whether atom carries an explicit ForceField::AtomProperty::UFF_TYPE property.

Parameters

atom

The atom.

Returns

true if the numeric UFF atom type is set, and false otherwise.

perceiveUFFType()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::perceiveUFFType	(	const Chem::Atom &	atom,
		const Chem::MolecularGraph &	molgraph
	)

Perceives the UFF atom type of atom in the context of the molecular graph molgraph.

Parameters

atom	The atom whose UFF type is to be perceived.
molgraph	The molecular graph providing the atom environment for type perception.

Returns

The perceived numeric UFF atom type.

getMMFF94TypeIndex()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94TypeIndex

(

const Chem::Bond &

bond

)

Returns the value of the ForceField::BondProperty::MMFF94_TYPE_INDEX property of bond.

Parameters

bond

The bond.

Returns

The MMFF94 bond type index.

setMMFF94TypeIndex()

CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94TypeIndex	(	Chem::Bond &	bond,
		unsigned int	type_idx
	)

Sets the value of the ForceField::BondProperty::MMFF94_TYPE_INDEX property of bond to type_idx.

Parameters

bond	The bond.
type_idx	The new MMFF94 bond type index.

clearMMFF94TypeIndex()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94TypeIndex

(

Chem::Bond &

bond

)

Removes the ForceField::BondProperty::MMFF94_TYPE_INDEX property from bond.

Parameters

bond

The bond.

hasMMFF94TypeIndex()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94TypeIndex

(

const Chem::Bond &

bond

)

Tells whether bond carries an explicit ForceField::BondProperty::MMFF94_TYPE_INDEX property.

Parameters

bond

The bond.

Returns

true if the MMFF94 bond type index is set, and false otherwise.

calcElasticPotentialEnergy() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcElasticPotentialEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Accumulates the energies calculated for the elastic potentials specified by the iterators in the given range.

Template Parameters

ValueType	The energy/atom coordinate value type.
Iter	The iterator type yielding ForceField::ElasticPotential instances.
CoordsArray	The array type storing the atom 3D coordinates.

Parameters

beg	Iterator pointing to the first elastic potential parameter set.
end	Iterator pointing past the last elastic potential parameter set.
coords	The atom 3D coordinates for which the energies shall be accumulated.

Returns

The accumulated elastic potential energies.

Since

1.1

calcElasticPotentialEnergy() [2/3]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcElasticPotentialEnergy	(	const ElasticPotential &	pot,
		const CoordsArray &	coords
	)

Calculates the energy of a single elastic potential pot for the supplied atom coordinates coords.

Template Parameters

ValueType	The energy/atom coordinate value type.
CoordsArray	The array type storing the atom 3D coordinates.

Parameters

pot	The parameters of the elastic potential to evaluate.
coords	The atom 3D coordinates for which the energy shall be calculated.

Returns

The calculated elastic potential energy.

Since

1.1

calcElasticPotentialEnergy() [3/3]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcElasticPotentialEnergy	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		const ValueType &	force_const,
		const ValueType &	ref_length
	)

Calculates the energy \( E_{ij} \) of an elastic potential applied on a pair of atoms i-j.

\( E_{ij} = k_{ij} \: \Delta r_{ij}^2 \)

where
\( k_{ij} \) = the force constant of the elastic potential.
\( \Delta r_{ij} \) = \( r_{ij} - r_{ij}^0 \), the difference between actual and reference distance of the atoms i and j.

Parameters

atom1_pos	The position of atom i.
atom2_pos	The position of atom j.
force_const	The force constant \( k_{ij} \).
ref_length	The reference distance \( r_{ij}^0 \).

Returns

The calculated elastic potential energy \( E_{ij} \).

Since

1.1

calcElasticPotentialGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcElasticPotentialGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Accumulates the energies and gradient contributions calculated for the elastic potentials specified by the iterators in the given range.

Template Parameters

ValueType	The energy/atom coordinate value type.
Iter	The iterator type yielding ForceField::ElasticPotential instances.
CoordsArray	The array type storing the atom 3D coordinates.
GradVector	The array type storing the atom gradient vectors.

Parameters

beg	Iterator pointing to the first elastic potential parameter set.
end	Iterator pointing past the last elastic potential parameter set.
coords	The atom 3D coordinates for which the energies/gradients shall be accumulated.
grad	The atom gradient vector array receiving the accumulated contributions.

Returns

The accumulated elastic potential energies.

Note

Gradient contributions for an atom are added to the corresponding entry of grad.

Since

1.1

calcElasticPotentialGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcElasticPotentialGradient	(	const ElasticPotential &	pot,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the energy and gradient contribution of a single elastic potential pot for the supplied atom coordinates coords.

Template Parameters

ValueType	The energy/atom coordinate value type.
CoordsArray	The array type storing the atom 3D coordinates.
GradVector	The array type storing the atom gradient vectors.

Parameters

pot	The parameters of the elastic potential to evaluate.
coords	The atom 3D coordinates for which the energies/gradients shall be calculated.
grad	The atom gradient vector array receiving the accumulated contributions.

Returns

The calculated elastic potential energy.

Note

Gradient contributions for the two atoms are added to the corresponding entries of grad.

Since

1.1

calcElasticPotentialGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcElasticPotentialGradient	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		GradVec &	atom1_grad,
		GradVec &	atom2_grad,
		const ValueType &	force_const,
		const ValueType &	ref_length
	)

Calculates the elastic potential energy gradient \( \nabla E_{ij} \) for a pair of atoms i-j.

Energy function:

\( E_{ij} = k_{ij} \: \Delta r_{ij}^2 \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial E_{ij}}{\partial \vec{p_x}} = \frac{\partial E_{ij}}{\partial \Delta r_{ij}} \: \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} \)

\( \frac{\partial E_{ij}}{\partial \Delta r_{ij}} = 2 \: \Delta r_{ij} \: k_{ij} \)

for the calculation of the partial derivatives \( \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} \) see calcDistanceDerivatives().

where
\( k_{ij} \) = the force constant of the elastic potential.
\( \Delta r_{ij} \) = \( r_{ij} - r_{ij}^0 \), the difference between actual and reference distance of the atoms i and j.
\( \vec{p_x} \) = coordinates of the atoms i and j.

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.
atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
atom2_grad	The output variable storing the accumulated energy gradient contributions for atom j.
force_const	The force constant \( k_{ij} \).
ref_length	The reference distance \( r_{ij}^0 \).

Returns

The calculated elastic potential energy \( E_{ij} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

Since

1.1

calcMMFF94BondStretchingEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the bond-stretching interaction energies of all MMFF94 bond-stretching interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94BondStretchingInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed bond-stretching interaction energy.

calcMMFF94BondStretchingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy	(	const MMFF94BondStretchingInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the bond-stretching interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 bond-stretching interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The bond-stretching interaction energy of iaction.

calcMMFF94BondStretchingEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		const ValueType &	force_const,
		const ValueType &	ref_length
	)

Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j.

\( EB_{ij} = 143.9325 \: \frac{kb_{IJ}}{2} \: \Delta r_{ij}^2 \: (1 + cs \: \Delta r_{ij} + \frac{7}{12} \: cs^2 \: \Delta r_{ij}^2) \)

where
\( kb_{IJ} \) = the bond stretching force constant in \( \frac{md}{Ang} \) for bonded atoms i and j of types I and J.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J (see calcDistance()).
\( cs \) = \( -2 \: Ang^{-1} \), the "cubic stretch" constant.

Note: throughout this description, the indices i, j, k, ... represent atoms; I, J, K, ... denote the corresponding numerical MMFF atom types (or, occasionally, the atomic species).

Parameters

atom1_pos	The position of atom i.
atom2_pos	The position of atom j.
force_const	The bond stretching force constant \( kb_{IJ} \).
ref_length	The reference bond length \( r_{IJ}^0 \).

Returns

The calculated bond stretching interaction energy \( EB_{ij} \).

calcMMFF94BondStretchingEnergy() [4/4]

template<typename ValueType >

ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy	(	const ValueType &	r_ij,
		const ValueType &	force_const,
		const ValueType &	ref_length
	)

Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j.

\( EB_{ij} = 143.9325 \: \frac{kb_{IJ}}{2} \: \Delta r_{ij}^2 \: (1 + cs \: \Delta r_{ij} + \frac{7}{12} \: cs^2 \: \Delta r_{ij}^2) \)

where
\( kb_{IJ} \) = the bond stretching force constant in \( \frac{md}{Ang} \) for bonded atoms i and j of types I and J.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J (see calcDistance()).
\( cs \) = \( -2 \: Ang^{-1} \), the "cubic stretch" constant.

Note: throughout this description, the indices i, j, k, ... represent atoms; I, J, K, ... denote the corresponding numerical MMFF atom types (or, occasionally, the atomic species).

Parameters

r_ij	The length of the bond between atom i and j.
force_const	The bond stretching force constant \( kb_{IJ} \).
ref_length	The reference bond length \( r_{IJ}^0 \).

Returns

The calculated bond stretching interaction energy \( EB_{ij} \).

calcMMFF94AngleBendingEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the angle-bending interaction energies of all MMFF94 angle-bending interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94AngleBendingInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed angle-bending interaction energy.

calcMMFF94AngleBendingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy	(	const MMFF94AngleBendingInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the angle-bending interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 angle-bending interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The angle-bending interaction energy of iaction.

calcMMFF94AngleBendingEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		bool	linear,
		const ValueType &	force_const,
		const ValueType &	ref_angle
	)

Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k.

\( EA_{ijk} = 0.043844 \: \frac{ka_{IJK}}{2} \: \Delta \vartheta_{ijk}^2 \: (1 + cb \: \Delta \vartheta_{ijk}) \)

where
\( ka_{IJK} \) = angle bending force constant in \( \frac{md Ang}{rad^2} \) for the angle between atoms i, j and k of atom types I, J and K.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees (see calcBondAngle()).
\( cb \) = \( -0.007 \: deg^{-1} \), the "cubic-bend" constant.

For linear or near-linear bond angles such as those which occur in alkynes, nitriles, isonitriles, azides, and diazo compounds, the form used in DREIDING and UFF is employed:

\( EA_{ijk} = 143.9325 \: ka_{IJK} \:(1 + \cos(\vartheta_{ijk})) \)

where \( ka_{IJK} \) and \( \vartheta_{ijk} \) are defined as above.

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
linear	If true, the bond angle is linear.
force_const	The angle bending force constant \( ka_{IJK} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).

Returns

The calculated angle bending interaction energy \( EA_{ijk} \).

calcMMFF94AngleBendingEnergy() [4/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	r_ij,
		const ValueType &	r_jk,
		bool	linear,
		const ValueType &	force_const,
		const ValueType &	ref_angle
	)

Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k.

\( EA_{ijk} = 0.043844 \: \frac{ka_{IJK}}{2} \: \Delta \vartheta_{ijk}^2 \: (1 + cb \: \Delta \vartheta_{ijk}) \)

where
\( ka_{IJK} \) = angle bending force constant in \( \frac{md Ang}{rad^2} \) for the angle between atoms i, j and k of atom types I, J and K.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees (see calcBondAngle()).
\( cb \) = \( -0.007 \: deg^{-1} \), the "cubic-bend" constant.

For linear or near-linear bond angles such as those which occur in alkynes, nitriles, isonitriles, azides, and diazo compounds, the form used in DREIDING and UFF is employed:

\( EA_{ijk} = 143.9325 \: ka_{IJK} \:(1 + \cos(\vartheta_{ijk})) \)

where \( ka_{IJK} \) and \( \vartheta_{ijk} \) are defined as above.

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
r_ij	The length of the bond between atom i and j.
r_jk	The length of the bond between atom j and k.
linear	If true, the bond angle is linear.
force_const	The angle bending force constant \( ka_{IJK} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).

Returns

The calculated angle bending interaction energy \( EA_{ijk} \).

calcMMFF94StretchBendEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the stretch-bend coupling interaction energies of all MMFF94 stretch-bend interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94StretchBendInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed stretch-bend interaction energy.

calcMMFF94StretchBendEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy	(	const MMFF94StretchBendInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the stretch-bend coupling interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 stretch-bend interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The stretch-bend interaction energy of iaction.

calcMMFF94StretchBendEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	ijk_force_const,
		const ValueType &	kji_force_const,
		const ValueType &	ref_angle,
		const ValueType &	ref_length1,
		const ValueType &	ref_length2
	)

Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k.

\( EBA_{ijk} = 2.51210 \: (kba_{IJK} \: \Delta r_{ij} + kba_{KJI} \: \Delta r_{kj}) \: \Delta \vartheta_{ijk} \)

where
\( kba_{IJK} \) = force constant in \( \frac{md}{rad} \) for i-j stretch coupled to i-j-k bend.
\( kba_{KJI} \) = force constant in \( \frac{md}{rad} \) for k-j stretch coupled to i-j-k bend.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J.
\( \Delta r_{kj} \) = \( r_{kj} - r_{KJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms k and j of types K and J.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees.

For the calculation of \( r_{ij} \), \( r_{kj} \), and \( \vartheta_{ijk} \) see calcBondLengthsAndAngle().

Currently, stretch-bend interactions are omitted when the i-j-k interaction corresponds to a linear bond angle.

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
ijk_force_const	The stretch-bend force constant \( kba_{IJK} \).
kji_force_const	The stretch-bend force constant \( kba_{KJI} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1	The reference bond length \( r_{IJ}^0 \).
ref_length2	The reference bond length \( r_{KJ}^0 \).

Returns

The calculated stretch-bend interaction energy \( EBA_{ijk} \).

calcMMFF94StretchBendEnergy() [4/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	r_ij,
		const ValueType &	r_jk,
		const ValueType &	ijk_force_const,
		const ValueType &	kji_force_const,
		const ValueType &	ref_angle,
		const ValueType &	ref_length1,
		const ValueType &	ref_length2
	)

Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k.

\( EBA_{ijk} = 2.51210 \: (kba_{IJK} \: \Delta r_{ij} + kba_{KJI} \: \Delta r_{kj}) \: \Delta \vartheta_{ijk} \)

where
\( kba_{IJK} \) = force constant in \( \frac{md}{rad} \) for i-j stretch coupled to i-j-k bend.
\( kba_{KJI} \) = force constant in \( \frac{md}{rad} \) for k-j stretch coupled to i-j-k bend.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J.
\( \Delta r_{kj} \) = \( r_{kj} - r_{KJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms k and j of types K and J.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees.

For the calculation of \( r_{ij} \), \( r_{kj} \), and \( \vartheta_{ijk} \) see calcBondLengthsAndAngle().

Currently, stretch-bend interactions are omitted when the i-j-k interaction corresponds to a linear bond angle.

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
r_ij	The length of the bond between atom i and j.
r_jk	The length of the bond between atom j and k.
ijk_force_const	The stretch-bend force constant \( kba_{IJK} \).
kji_force_const	The stretch-bend force constant \( kba_{KJI} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1	The reference bond length \( r_{IJ}^0 \).
ref_length2	The reference bond length \( r_{KJ}^0 \).

Returns

The calculated stretch-bend interaction energy \( EBA_{ijk} \).

calcMMFF94OutOfPlaneBendingEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the out-of-plane bending interaction energies of all MMFF94 out-of-plane bending interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94OutOfPlaneBendingInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed out-of-plane bending interaction energy.

calcMMFF94OutOfPlaneBendingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy	(	const MMFF94OutOfPlaneBendingInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the out-of-plane bending interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 out-of-plane bending interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The out-of-plane bending interaction energy of iaction.

calcMMFF94OutOfPlaneBendingEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos,
		const ValueType &	force_const
	)

Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k.

\( EOOP_{ijk;l} = 0.043844 \: \frac{koop_{IJK \colon L}}{2} \: \chi_{ijk;l}^2 \)

where
\( koop_{IJK \colon L} \) = out-of-plane bending force constant in \( \frac{md Ang}{rad^2} \).
\( \chi_{ijk;l} \) = angle in degrees between the bond j-l and the plane i-j-k, where j is the central atom (see calcOutOfPlaneAngle()).

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
oop_atom_pos	The position of the out-of-plane atom l.
force_const	The out-of-plane bending force constant \( koop_{IJK \colon L} \).

Returns

The calculated out-of-plane bending interaction energy \( EOOP_{ijk;l} \).

calcMMFF94OutOfPlaneBendingEnergy() [4/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos,
		const ValueType &	r_jl,
		const ValueType &	force_const
	)

Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k.

\( EOOP_{ijk;l} = 0.043844 \: \frac{koop_{IJK \colon L}}{2} \: \chi_{ijk;l}^2 \)

where
\( koop_{IJK \colon L} \) = out-of-plane bending force constant in \( \frac{md Ang}{rad^2} \).
\( \chi_{ijk;l} \) = angle in degrees between the bond j-l and the plane i-j-k, where j is the central atom (see calcOutOfPlaneAngle()).

Parameters

term_atom1_pos	The position of atom i.
ctr_atom_pos	The position of the central atom j.
term_atom2_pos	The position of atom k.
oop_atom_pos	The position of the out-of-plane atom l.
r_jl	The length of the bond between atom j and atom l.
force_const	The out-of-plane bending force constant \( koop_{IJK \colon L} \).

Returns

The calculated out-of-plane bending interaction energy \( EOOP_{ijk;l} \).

calcMMFF94TorsionEnergy() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94TorsionEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the torsion interaction energies of all MMFF94 torsion interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94TorsionInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed torsion interaction energy.

calcMMFF94TorsionEnergy() [2/3]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94TorsionEnergy	(	const MMFF94TorsionInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the torsion interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 torsion interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The torsion interaction energy of iaction.

calcMMFF94TorsionEnergy() [3/3]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94TorsionEnergy	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom1_pos,
		const CoordsVec &	ctr_atom2_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	tor_param1,
		const ValueType &	tor_param2,
		const ValueType &	tor_param3
	)

Calculates the torsion interaction energy \( ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l.

\( ET_{ijkl} = 0.5 \: (V_1 \: (1 + \cos(\Phi_{ijkl})) + V_2 \: (1 - \cos(2 \: \Phi_{ijkl})) + V_3 \: (1 + \cos(3 \: \Phi_{ijkl}))) \)

where \( \Phi_{ijkl} \) is the i-j-k-l dihedral angle. The constants \( V_1 \), \( V_2 \) and \( V_3 \) depend on the atom types I, J, K and L for atoms i, j, k and l, where i-j, j-k and k-l are bonded pairs and i is not equal to l.

For the calculation of \( \cos(\Phi_{ijkl}) \) see calcDihedralAngleCos().

Parameters

term_atom1_pos	The position of the terminal atom i.
ctr_atom1_pos	The position of the central atom j.
ctr_atom2_pos	The position of the central atom k.
term_atom2_pos	The position of the terminal atom l.
tor_param1	The torsion parameter \( V_1 \).
tor_param2	The torsion parameter \( V_2 \).
tor_param3	The torsion parameter \( V_3 \).

Returns

The calculated torsion interaction energy \( ET_{ijkl} \).

calcMMFF94ElectrostaticEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the electrostatic interaction energies of all MMFF94 electrostatic interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94ElectrostaticInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed electrostatic interaction energy.

calcMMFF94ElectrostaticEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy	(	const MMFF94ElectrostaticInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the electrostatic interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 electrostatic interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The electrostatic interaction energy of iaction.

calcMMFF94ElectrostaticEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		const ValueType &	atom1_chg,
		const ValueType &	atom2_chg,
		const ValueType &	scale_fact,
		const ValueType &	de_const,
		const ValueType &	dist_expo
	)

Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j.

\( EQ_{ij} = S \: 332.0716 \: \frac{q_i \: q_j}{D \: (R_{ij} + \delta)^n} \)

where
\( S \) = a scaling factor depending on the topological distance of i-j.
\( q_i \) and \( q_j \) = Partial atomic charges.
\( D \) = Dielectric constant.
\( R_{ij} \) = Interatomic distance (Å) (see calcDistance()).
\( \delta \) = Electrostatic buffering constant (0.05 Å).
\( n \) = Exponent (normally 1, but can be 2 for distance-dependent dielectric constant).

Note: 1-4 electrostatic interactions are scaled by 0.75 (thus, the electrostatic energy term becomes \( EQ_{14} \: 0.75 \)).

Parameters

atom1_pos	The position of atom i.
atom2_pos	The position of atom j.
atom1_chg	The partial atom charge \( q_i \) of atom i.
atom2_chg	The partial atom charge \( q_j \) of atom j.
scale_fact	The scaling factor for \( S \) depending on the topological i-j distance.
de_const	The dielectric constant \( D \).
dist_expo	The exponent \( n \).

Returns

The calculated electrostatic interaction energy \( EQ_{ij} \).

calcMMFF94ElectrostaticEnergy() [4/4]

template<typename ValueType >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy	(	const ValueType &	r_ij,
		const ValueType &	atom1_chg,
		const ValueType &	atom2_chg,
		const ValueType &	scale_fact,
		const ValueType &	de_const,
		const ValueType &	dist_expo
	)

Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j.

\( EQ_{ij} = S \: 332.0716 \: \frac{q_i \: q_j}{D \: (R_{ij} + \delta)^n} \)

where
\( S \) = a scaling factor depending on the topological distance of i-j.
\( q_i \) and \( q_j \) = Partial atomic charges.
\( D \) = Dielectric constant.
\( R_{ij} \) = Interatomic distance (Å) (see calcDistance()).
\( \delta \) = Electrostatic buffering constant (0.05 Å).
\( n \) = Exponent (normally 1, but can be 2 for distance-dependent dielectric constant).

Note: 1-4 electrostatic interactions are scaled by 0.75 (thus, the electrostatic energy term becomes \( EQ_{14} \: 0.75 \)).

Parameters

r_ij	The interatomic distance \( R_{ij} \) of atom i and atom j.
atom1_chg	The partial atom charge \( q_i \) of atom i.
atom2_chg	The partial atom charge \( q_j \) of atom j.
scale_fact	The scaling factor for \( S \) depending on the topological i-j distance.
de_const	The dielectric constant \( D \).
dist_expo	The exponent \( n \).

Returns

The calculated electrostatic interaction energy \( EQ_{ij} \).

calcMMFF94VanDerWaalsEnergy() [1/4]

template<typename ValueType , typename Iter , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords
	)

Sums the Van der Waals interaction energies of all MMFF94 Van der Waals interactions in the iterator range [beg, end).

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94VanDerWaalsInteraction records.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.

Returns

The summed Van der Waals interaction energy.

calcMMFF94VanDerWaalsEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy	(	const MMFF94VanDerWaalsInteraction &	iaction,
		const CoordsArray &	coords
	)

Calculates the Van der Waals interaction energy of iaction using the geometry from coords.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type (indexable via atom index).

Parameters

iaction	The MMFF94 Van der Waals interaction record.
coords	The atom-coordinates array providing the geometry.

Returns

The Van der Waals interaction energy of iaction.

calcMMFF94VanDerWaalsEnergy() [3/4]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		const ValueType &	e_IJ,
		const ValueType &	r_IJ,
		const ValueType &	r_IJ_7
	)

Calculates the Van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j.

\( E_{vdW_{ij}} = \varepsilon_{IJ} \: (\frac{1.07 \: R_{IJ}^*}{(R_{ij} + 0.07 \: R_{IJ}^*)})^7 \: (\frac{1.12 \: R_{IJ}^{*^7}}{(R_{ij}^7 + 0.12 \: R_{IJ}^{*^7})} - 2) \;\;\;\; (1) \)

where
\( R_{ij} \) = the interatomic distance (see calcDistance()).
\( R_{II}^* = A_I \: \alpha_I^{PEXP} \;\;\;\; (2) \)
\( R_{IJ}^* = 0.5 \: (R_{II}^* + R_{JJ}^*) \: (1 + AFACT(1 - \exp(-BFACT \: \gamma_{IJ}^2))) \;\;\;\; (3) \)
\( \gamma_{IJ} = \frac{(R_{II}^* - R_{JJ}^*)}{(R_{II}^* + R_{JJ}^*)} \;\;\;\; (4) \)
\( \varepsilon_{IJ} = \frac{181.16 \: G_I \: GJ \: \alpha_I \: \alpha_J}{((\alpha_I / N_I)^{1/2} + (\alpha_J / N_J)^{1/2})} \: \frac{1}{R_{IJ}^{*^6}} \;\;\;\; (5) \)

MMFF employs a "Buffered 14-7" form (eq 1) together with an expression which relates the minimum-energy separation \( R_{II}^* \) to the atomic polarizability \( \alpha_I \) (eq 2), a specially formulated combination rule (eqs 3, 4), and a Slater-Kirkwood expression for the well depth \( \varepsilon_{IJ} \) (eq 5): The first non-comment line in the parameter file "MMFFVDW.PAR" contains five floating point numbers which define the variables PEXP, AFACT, BFACT, DARAD, and DAEPS, respectively. PEXP (currently 0.25), AFACT (currently 0.2) and BFACT (currently 12.0) are used in the equations shown above; DARAD and DAEPS are used as follows:

When either i or j is a hydrogen-bond donor, MMFF uses the simple arithmetic mean \( 0.5 \: (R_{II}^* + R_{JJ}^*) \) instead of eq 3 to obtain \( R_{IJ}^* \). If the i-j interaction is a donor-acceptor interaction, MMFF also scales \( R_{IJ}^* \) as given by eq 3 by DARAD (currently 0.8) and \( \varepsilon_{IJ} \) as given by eq 5 by DAEPS (currently 0.5).

Parameters

atom1_pos	The position of atom i.
atom2_pos	The position of atom j.
e_IJ	The precalculated value \( \varepsilon_{IJ} \).
r_IJ	The precalculated value \( R_{IJ}^* \).
r_IJ_7	The precalculated value \( R_{IJ}^{*^7} \).

Returns

The calculated Van der Waals interaction energy \( E_{vdW_{ij}} \).

calcMMFF94VanDerWaalsEnergy() [4/4]

template<typename ValueType >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy	(	const ValueType &	r_ij,
		const ValueType &	e_IJ,
		const ValueType &	r_IJ,
		const ValueType &	r_IJ_7
	)

Calculates the Van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j.

\( E_{vdW_{ij}} = \varepsilon_{IJ} \: (\frac{1.07 \: R_{IJ}^*}{(R_{ij} + 0.07 \: R_{IJ}^*)})^7 \: (\frac{1.12 \: R_{IJ}^{*^7}}{(R_{ij}^7 + 0.12 \: R_{IJ}^{*^7})} - 2) \;\;\;\; (1) \)

where
\( R_{ij} \) = the interatomic distance (see calcDistance()).
\( R_{II}^* = A_I \: \alpha_I^{PEXP} \;\;\;\; (2) \)
\( R_{IJ}^* = 0.5 \: (R_{II}^* + R_{JJ}^*) \: (1 + AFACT(1 - \exp(-BFACT \: \gamma_{IJ}^2))) \;\;\;\; (3) \)
\( \gamma_{IJ} = \frac{(R_{II}^* - R_{JJ}^*)}{(R_{II}^* + R_{JJ}^*)} \;\;\;\; (4) \)
\( \varepsilon_{IJ} = \frac{181.16 \: G_I \: GJ \: \alpha_I \: \alpha_J}{((\alpha_I / N_I)^{1/2} + (\alpha_J / N_J)^{1/2})} \: \frac{1}{R_{IJ}^{*^6}} \;\;\;\; (5) \)

MMFF employs a "Buffered 14-7" form (eq 1) together with an expression which relates the minimum-energy separation \( R_{II}^* \) to the atomic polarizability \( \alpha_I \) (eq 2), a specially formulated combination rule (eqs 3, 4), and a Slater-Kirkwood expression for the well depth \( \varepsilon_{IJ} \) (eq 5): The first non-comment line in the parameter file "MMFFVDW.PAR" contains five floating point numbers which define the variables PEXP, AFACT, BFACT, DARAD, and DAEPS, respectively. PEXP (currently 0.25), AFACT (currently 0.2) and BFACT (currently 12.0) are used in the equations shown above; DARAD and DAEPS are used as follows:

When either i or j is a hydrogen-bond donor, MMFF uses the simple arithmetic mean \( 0.5 \: (R_{II}^* + R_{JJ}^*) \) instead of eq 3 to obtain \( R_{IJ}^* \). If the i-j interaction is a donor-acceptor interaction, MMFF also scales \( R_{IJ}^* \) as given by eq 3 by DARAD (currently 0.8) and \( \varepsilon_{IJ} \) as given by eq 5 by DAEPS (currently 0.5).

Parameters

r_ij	The interatomic distance \( R_{ij} \) of atom i and atom j.
e_IJ	The precalculated value \( \varepsilon_{IJ} \).
r_IJ	The precalculated value \( R_{IJ}^* \).
r_IJ_7	The precalculated value \( R_{IJ}^{*^7} \).

Returns

The calculated Van der Waals interaction energy \( E_{vdW_{ij}} \).

calcMMFF94BondStretchingGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94BondStretchingGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 bond-stretching interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94BondStretchingInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed bond-stretching interaction energy.

calcMMFF94BondStretchingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94BondStretchingGradient	(	const MMFF94BondStretchingInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the bond-stretching interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 bond-stretching interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The bond-stretching interaction energy of iaction.

calcMMFF94BondStretchingGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94BondStretchingGradient	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		GradVec &	atom1_grad,
		GradVec &	atom2_grad,
		const ValueType &	force_const,
		const ValueType &	ref_length
	)

Calculates the bond stretching interaction energy gradient \( \nabla EB_{ij} \) for the bond i-j.

Energy function:

\( EB_{ij} = 143.9325 \: \frac{kb_{IJ}}{2} \: \Delta r_{ij}^2 \: (1 + cs \: \Delta r_{ij} + \frac{7}{12} \: cs^2 \: \Delta r_{ij}^2) \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EB_{ij}}{\partial \vec{p_x}} = \frac{\partial EB_{ij}}{\partial \Delta r_{ij}} \: \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} \)

\( \frac{\partial EB_{ij}}{\partial \Delta r_{ij}} = (167.92125 \: \Delta r_{ij}^3 \: cs^2 + 215.89875 \: \Delta r_{ij}^2 \: cs + 143.9325 \: \Delta r_{ij}) \: kb_{IJ} \)

for the calculation of the partial derivatives \( \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} \) see calcDistanceDerivatives().

where
\( kb_{IJ} \) = the bond stretching force constant in \( \frac{md}{Ang} \) for bonded atoms i and j of types I and J.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J.
\( cs \) = \( -2 \: Ang^{-1} \), the "cubic stretch" constant.
\( \vec{p_x} \) = coordinates of the involved atoms i and j.

Note: throughout this description, the indices i, j, k, ... represent atoms; I, J, K, ... denote the corresponding numerical MMFF atom types (or, occasionally, the atomic species).

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.
atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
atom2_grad	The output variable storing the accumulated energy gradient contributions for atom j.
force_const	The bond stretching force constant \( kb_{IJ} \).
ref_length	The reference bond length \( r_{IJ}^0 \).

Returns

The calculated bond stretching interaction energy \( EB_{ij} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94AngleBendingGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94AngleBendingGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 angle-bending interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94AngleBendingInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed angle-bending interaction energy.

calcMMFF94AngleBendingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94AngleBendingGradient	(	const MMFF94AngleBendingInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the angle-bending interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 angle-bending interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The angle-bending interaction energy of iaction.

calcMMFF94AngleBendingGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94AngleBendingGradient	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		GradVec &	term_atom1_grad,
		GradVec &	ctr_atom_grad,
		GradVec &	term_atom2_grad,
		bool	linear,
		const ValueType &	force_const,
		const ValueType &	ref_angle
	)

Calculates the angle bending interaction energy gradient \( \nabla EA_{ijk} \) for two bonds i-j and j-k.

Energy function employed for the non-linear case:

\( EA_{ijk} = 0.043844 \: \frac{ka_{IJK}}{2} \: \Delta \vartheta_{ijk}^2 \: (1 + cb \: \Delta \vartheta_{ijk}) \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EA_{ijk}}{\partial \vec{p_x}} = \frac{\partial EA_{ijk}}{\partial \vartheta_{ijk}} \: \frac{\partial \vartheta_{ijk}}{\partial \cos(\vartheta_{ijk})} \: \frac{\partial \cos(\vartheta_{ijk})}{\vec{p_x}} \)

\( \frac{\partial EA_{ijk}}{\partial \vartheta_{ijk}} = -ka_{IJK} \: (86.58992538 \: \vartheta_{ijk}^2 - 3.022558594 \: \vartheta_{ijk} \: \vartheta_{IJK}^0 - 143.9313616 \: \vartheta_{ijk} + 0.02637679965 \: \vartheta_{IJK}^{0^2} + 2.512076157 \: \vartheta_{IJK}^0) \)

\( \frac{\partial \vartheta_{ijk}}{\partial \cos(\vartheta_{ijk})} = \frac{-1}{\sqrt{1 - \cos(\vartheta_{ijk})^2}} \)

for the calculation of the partial derivatives \( \frac{\partial \cos(\vartheta_{ijk})}{\vec{p_x}} \) see calcBondAngleCosDerivatives().

For linear or near-linear bond angles such as those which occur in alkynes, nitriles, isonitriles, azides, and diazo compounds, the energy function form used in DREIDING and UFF is employed:

\( EA_{ijk} = 143.9325 \: ka_{IJK} \:(1 + \cos(\vartheta_{ijk})) \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EA_{ijk}}{\partial \vec{p_x}} = 143.9325 \: ka_{IJK} \: \frac{\partial \cos(\vartheta_{ijk})}{\vec{p_x}} \)

where
\( ka_{IJK} \) = angle bending force constant in \( \frac{md Ang}{rad^2} \) for the angle between atoms i, j and k of atom types I, J and K.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees.
\( cb \) = \( -0.007 \: deg^{-1} \), the "cubic-bend" constant.
\( \vec{p_x} \) = coordinates of the involved atoms i, j and k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of atom k.
term_atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_grad	The output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_grad	The output variable storing the accumulated energy gradient contributions for atom k.
linear	If true, the bond angle is linear.
force_const	The angle bending force constant \( ka_{IJK} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).

Returns

The calculated angle bending interaction energy \( EA_{ijk} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94StretchBendGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94StretchBendGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 stretch-bend coupling interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94StretchBendInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed stretch-bend interaction energy.

calcMMFF94StretchBendGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94StretchBendGradient	(	const MMFF94StretchBendInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the stretch-bend coupling interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 stretch-bend interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The stretch-bend interaction energy of iaction.

calcMMFF94StretchBendGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94StretchBendGradient	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		GradVec &	term_atom1_grad,
		GradVec &	ctr_atom_grad,
		GradVec &	term_atom2_grad,
		const ValueType &	ijk_force_const,
		const ValueType &	kji_force_const,
		const ValueType &	ref_angle,
		const ValueType &	ref_length1,
		const ValueType &	ref_length2
	)

Calculates the stretch-bend interaction energy gradient \( \nabla EBA_{ijk} \) for two bonds i-j and j-k.

Energy function:

\( EBA_{ijk} = 2.51210 \: (kba_{IJK} \: \Delta r_{ij} + kba_{KJI} \: \Delta r_{kj}) \: \Delta \vartheta_{ijk} \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EBA_{ijk}}{\partial \vec{p_x}} = 2.5121 \: \Delta \vartheta_{ijk} \: (kba_{IJK} \: \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} + kba_{KJI} \: \frac{\partial \Delta r_{kj}}{\partial \vec{p_x}}) + 2.5121 \: \frac{\partial \Delta \vartheta_{ijk}}{\partial \vec{p_x}} \: (kba_{IJK} \: \Delta r_{ij} + kba_{KJI} \: \Delta r_{kj}) \)

\( \frac{\partial \Delta \vartheta_{ijk}}{\partial \vec{p_x}} = \frac{\partial \Delta \vartheta_{ijk}}{\partial \vartheta_{ijk}} \: \frac{\partial \vartheta_{ijk}}{\partial \cos(\vartheta_{ijk})} \: \frac{\partial \cos(\vartheta_{ijk})}{\vec{p_x}} \)
\( \frac{\partial \Delta \vartheta_{ijk}}{\partial \vartheta_{ijk}} = \frac{180}{\pi} \)
\( \frac{\partial \vartheta_{ijk}}{\partial \cos(\vartheta_{ijk})} = \frac{-1}{\sqrt{1 - \cos(\vartheta_{ijk})^2}} \)

for the calculation of the partial derivatives \( \frac{\partial \cos(\vartheta_{ijk})}{\vec{p_x}} \) see calcBondAngleCosDerivatives() and for the calculation of \( \frac{\partial \Delta r_{ij}}{\partial \vec{p_x}} \) see calcDistanceDerivatives().

where
\( kba_{IJK} \) = force constant in \( \frac{md}{rad} \) for i-j stretch coupled to i-j-k bend.
\( kba_{KJI} \) = force constant in \( \frac{md}{rad} \) for k-j stretch coupled to i-j-k bend.
\( \Delta r_{ij} \) = \( r_{ij} - r_{IJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms i and j of types I and J.
\( \Delta r_{kj} \) = \( r_{kj} - r_{KJ}^0 \), the difference in angstroms between actual and reference bond lengths between bonded atoms k and j of types K and J.
\( \Delta \vartheta_{ijk} \) = \( \vartheta_{ijk} \: \frac{180}{\pi} - \vartheta_{IJK}^0 \), the difference between actual and reference i-j-k bond angles in degrees.
\( \vec{p_x} \) = coordinates of the involved atoms i, j and k.

Currently, stretch-bend interactions are omitted when the i-j-k interaction corresponds to a linear bond angle.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of atom k.
term_atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_grad	The output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_grad	The output variable storing the accumulated energy gradient contributions for atom k.
ijk_force_const	The stretch-bend force constant \( kba_{IJK} \).
kji_force_const	The stretch-bend force constant \( kba_{KJI} \).
ref_angle	The reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1	The reference bond length \( r_{IJ}^0 \).
ref_length2	The reference bond length \( r_{KJ}^0 \).

Returns

The calculated stretch-bend interaction energy \( EBA_{ijk} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94OutOfPlaneBendingGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 out-of-plane bending interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94OutOfPlaneBendingInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed out-of-plane bending interaction energy.

calcMMFF94OutOfPlaneBendingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingGradient	(	const MMFF94OutOfPlaneBendingInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the out-of-plane bending interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 out-of-plane bending interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The out-of-plane bending interaction energy of iaction.

calcMMFF94OutOfPlaneBendingGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingGradient	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos,
		GradVec &	term_atom1_grad,
		GradVec &	ctr_atom_grad,
		GradVec &	term_atom2_grad,
		GradVec &	oop_atom_grad,
		const ValueType &	force_const
	)

Calculates the out-of-plane bending interaction energy gradient \( \nabla EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k.

Energy function:

\( EOOP_{ijk;l} = 0.043844 \: \frac{koop_{IJK \colon L}}{2} \: (\chi_{ijk;l} \: \frac{180}{\pi})^2 \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EOOP_{ijk;l}}{\partial \vec{p_x}} = \frac{\partial EOOP_{ijk;l}}{\partial \chi_{ijk;l}} \: \frac{\partial \chi_{ijk;l}}{\partial \cos(\alpha_{ijk;l})} \: \frac{\partial \cos(\alpha_{ijk;l})}{\partial \vec{p_x}} \)

\( \frac{\partial EOOP_{ijk;l}}{\partial \chi_{ijk;l}} = 0.043844 \: (\frac{180}{\pi})^2 \: \chi_{ijk;l} \: koop_{IJK \colon L} \)
\( \chi_{ijk;l} = \frac{\pi}{2} - \alpha_{ijk;l} \)
\( \frac{\partial \chi_{ijk;l}}{\partial \cos(\alpha_{ijk;l})} = \frac{-1}{\sqrt{1 - \cos(\alpha_{ijk;l})^2}} \)

for the calculation of the partial derivatives \( \frac{\partial \cos(\alpha_{ijk;l})}{\partial \vec{p_x}} \) see calcOutOfPlaneAngleCosDerivatives().

where
\( koop_{IJK \colon L} \) = out-of-plane bending force constant in \( \frac{md Ang}{rad^2} \).
\( \chi_{ijk;l} \) = angle in radians between the bond j-l and the plane i-j-k, where j is the central atom.
\( \vec{p_x} \) = coordinates of the involved atoms i, j, k and l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of atom k.
oop_atom_pos	The position \( \vec{p_l} \) of the out-of-plane atom l.
term_atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_grad	The output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_grad	The output variable storing the accumulated energy gradient contributions for atom k.
oop_atom_grad	The output variable storing the accumulated energy gradient contributions for atom l.
force_const	The out-of-plane bending force constant \( koop_{IJK \colon L} \).

Returns

The calculated out-of-plane bending interaction energy \( EOOP_{ijk;l} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94TorsionGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94TorsionGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 torsion interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94TorsionInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed torsion interaction energy.

calcMMFF94TorsionGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94TorsionGradient	(	const MMFF94TorsionInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the torsion interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 torsion interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The torsion interaction energy of iaction.

calcMMFF94TorsionGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94TorsionGradient	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom1_pos,
		const CoordsVec &	ctr_atom2_pos,
		const CoordsVec &	term_atom2_pos,
		GradVec &	term_atom1_grad,
		GradVec &	ctr_atom1_grad,
		GradVec &	ctr_atom2_grad,
		GradVec &	term_atom2_grad,
		const ValueType &	tor_param1,
		const ValueType &	tor_param2,
		const ValueType &	tor_param3
	)

Calculates the torsion interaction energy gradient \( \nabla ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l.

Energy function:

\( ET_{ijkl} = 0.5 \: (V_1 \: (1 + \cos(\Phi_{ijkl})) + V_2 \: (1 - \cos(2 \: \Phi_{ijkl})) + V_3 \: (1 + \cos(3 \: \Phi_{ijkl}))) \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial ET_{ijkl}}{\partial \vec{p_x}} = \frac{\partial ET_{ijkl}}{\partial \Phi_{ijkl}} \: \frac{\partial \Phi_{ijkl}}{\partial \cos(\Phi_{ijkl})} \: \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_x}} \)

\( \frac{\partial ET_{ijkl}}{\partial \Phi_{ijkl}} = V_2 \: \sin(2 \: \Phi_{ijkl}) - 0.5 \: V_1 \: \sin(\Phi_{ijkl}) - 1.5 \: V_3 \: \sin(3 \: \Phi_{ijkl}) \)
\( \frac{\partial \Phi_{ijkl}}{\partial \cos(\Phi_{ijkl})} = \frac{-1}{\sqrt{1 - \cos(\Phi_{ijkl})^2}} \)

for the calculation of the partial derivatives \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_x}} \) see calcDihedralAngleCosDerivatives().

where
\( \Phi_{ijkl} \) is the i-j-k-l dihedral angle. The constants \( V_1 \), \( V_2 \) and \( V_3 \) depend on the atom types I, J, K and L for atoms i, j, k and l, where i-j, j-k and k-l are bonded pairs and i is not equal to l.

\( \vec{p_x} \) = coordinates of the involved atoms i, j, k and l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_pos	The position \( \vec{p_j} \) of the central atom j.
ctr_atom2_pos	The position \( \vec{p_k} \) of the central atom k.
term_atom2_pos	The position \( \vec{p_l} \) of the terminal atom l.
term_atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom1_grad	The output variable storing the accumulated energy gradient contributions for atom j.
ctr_atom2_grad	The output variable storing the accumulated energy gradient contributions for atom k.
term_atom2_grad	The output variable storing the accumulated energy gradient contributions for atom l.
tor_param1	The torsion parameter \( V_1 \).
tor_param2	The torsion parameter \( V_2 \).
tor_param3	The torsion parameter \( V_3 \).

Returns

The calculated torsion interaction energy \( ET_{ijkl} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94ElectrostaticGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 electrostatic interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94ElectrostaticInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed electrostatic interaction energy.

calcMMFF94ElectrostaticGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticGradient	(	const MMFF94ElectrostaticInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the electrostatic interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 electrostatic interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The electrostatic interaction energy of iaction.

calcMMFF94ElectrostaticGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94ElectrostaticGradient	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		GradVec &	atom1_grad,
		GradVec &	atom2_grad,
		const ValueType &	atom1_chg,
		const ValueType &	atom2_chg,
		const ValueType &	scale_fact,
		const ValueType &	de_const,
		const ValueType &	dist_expo
	)

Calculates the electrostatic interaction energy gradient \( \nabla EQ_{ij} \) for the atom pair i-j.

Energy function:

\( EQ_{ij} = S \: 332.0716 \: \frac{q_i \: q_j}{D \: (R_{ij} + \delta)^n} \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial EQ_{ij}}{\partial \vec{p_x}} = \frac{\partial EQ_{ij}}{\partial R_{ij}} \: \frac{\partial R_{ij}}{\partial \vec{p_x}} \)

\( \frac{\partial EQ_{ij}}{\partial R_{ij}} = -S \: 332.0716 \: n \: \frac{q_i \: q_j}{D \: (R_{ij} + \delta)^{n + 1}} \)

for the calculation of the partial derivatives \( \frac{\partial R_{ij}}{\partial \vec{p_x}} \) see calcDistanceDerivatives().

where
\( S \) = a scaling factor depending on the topological distance of i-j.
\( q_i \) and \( q_j \) = partial atomic charges.
\( D \) = dielectric constant.
\( R_{ij} \) = interatomic distance (Å).
\( \delta \) = electrostatic buffering constant (0.05 Å).
\( n \) = exponent (normally 1, but can be 2 for distance-dependent dielectric constant).
\( \vec{p_x} \) = coordinates of the involved atoms i and j.

Note: 1-4 electrostatic interactions are scaled by 0.75 (thus, the electrostatic gradient term becomes \( EQ_{14} \: 0.75 \)).

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.
atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
atom2_grad	The output variable storing the accumulated energy gradient contributions for atom j.
atom1_chg	The partial atom charge \( q_i \) of atom i.
atom2_chg	The partial atom charge \( q_j \) of atom j.
scale_fact	The scaling factor for \( S \) depending on the topological i-j distance.
de_const	The dielectric constant \( D \).
dist_expo	The exponent \( n \).

Returns

The calculated electrostatic interaction energy \( EQ_{ij} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

calcMMFF94VanDerWaalsGradient() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsGradient	(	Iter	beg,
		const Iter &	end,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Sums the MMFF94 Van der Waals interaction energies of the interactions in [beg, end) and accumulates the corresponding atom-position gradient contributions into grad.

Template Parameters

ValueType	The result value type.
Iter	The iterator type over MMFF94VanDerWaalsInteraction records.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

beg	An iterator pointing to the first interaction.
end	An iterator pointing one past the last interaction.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The summed Van der Waals interaction energy.

calcMMFF94VanDerWaalsGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsGradient	(	const MMFF94VanDerWaalsInteraction &	iaction,
		const CoordsArray &	coords,
		GradVector &	grad
	)

Calculates the Van der Waals interaction energy of iaction and accumulates the corresponding atom-position gradient contribution into grad.

Template Parameters

ValueType	The result value type.
CoordsArray	The atom-coordinates array type.
GradVector	The atom-position gradient vector type.

Parameters

iaction	The MMFF94 Van der Waals interaction record.
coords	The atom-coordinates array providing the geometry.
grad	The gradient vector to accumulate into.

Returns

The Van der Waals interaction energy of iaction.

calcMMFF94VanDerWaalsGradient() [3/3]

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcMMFF94VanDerWaalsGradient	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		GradVec &	atom1_grad,
		GradVec &	atom2_grad,
		const ValueType &	e_IJ,
		const ValueType &	r_IJ,
		const ValueType &	r_IJ_7
	)

Calculates the Van der Waals interaction energy gradient \( \nabla E_{vdW_{ij}} \) for the atom pair i-j.

Energy function:
\( E_{vdW_{ij}} = \varepsilon_{IJ} \: (\frac{1.07 \: R_{IJ}^*}{(R_{ij} + 0.07 \: R_{IJ}^*)})^7 \: (\frac{1.12 \: R_{IJ}^{*^7}}{(R_{ij}^7 + 0.12 \: R_{IJ}^{*^7})} - 2) \;\;\;\; (1) \)

The partial derivatives with respect to the atom coordinates \( \vec{p_x} \) are calculated by:

\( \frac{\partial E_{vdW_{ij}}}{\partial \vec{p_x}} = \frac{\partial E_{vdW_{ij}}}{\partial R_{ij}} \: \frac{\partial R_{ij}}{\partial \vec{p_x}} \)

\( \frac{\partial E_{vdW_{ij}}}{\partial R_{ij}} = \frac{-R_{IJ}^{*^7} \: \varepsilon_{IJ}}{(R_{ij} + 0.07 \: R_{IJ}^*)^8 \: (R_{ij}^7 + 0.12 \: R_{IJ}^{*^7})^2} \: (-22.48094067 \: R_{ij}^{14} + 19.78322779 \: R_{ij}^7 \: R_{IJ}^{*^7} + 0.8812528743 \: R_{ij}^6 \: R_{IJ}^{*^8} + 1.186993667 \: R_{IJ}^{*^{14}}) \)

for the calculation of the partial derivatives \( \frac{\partial R_{ij}}{\partial \vec{p_x}} \) see calcDistanceDerivatives().

where
\( R_{ij} \) = the interatomic distance.
\( R_{II}^* = A_I \: \alpha_I^{PEXP} \;\;\;\; (2) \)
\( R_{IJ}^* = 0.5 \: (R_{II}^* + R_{JJ}^*) \: (1 + AFACT(1 - \exp(-BFACT \: \gamma_{IJ}^2))) \;\;\;\; (3) \)
\( \gamma_{IJ} = \frac{(R_{II}^* - R_{JJ}^*)}{(R_{II}^* + R_{JJ}^*)} \;\;\;\; (4) \)
\( \varepsilon_{IJ} = \frac{181.16 \: G_I \: GJ \: \alpha_I \: \alpha_J}{((\alpha_I / N_I)^{1/2} + (\alpha_J / N_J)^{1/2})} \: \frac{1}{R_{IJ}^{*6}} \;\;\;\; (5) \)
\( \vec{p_x} \) = coordinates of the involved atoms i and j.

MMFF employs a "Buffered 14-7" form (eq 1) together with an expression which relates the minimum-gradient separation \( R_{II}^* \) to the atomic polarizability \( \alpha_I \) (eq 2), a specially formulated combination rule (eqs 3, 4), and a Slater-Kirkwood expression for the well depth \( \varepsilon_{IJ} \) (eq 5): The first non-comment line in the parameter file "MMFFVDW.PAR" contains five floating point numbers which define the variables PEXP, AFACT, BFACT, DARAD, and DAEPS, respectively. PEXP (currently 0.25), AFACT (currently 0.2) and BFACT (currently 12.0) are used in the equations shown above; DARAD and DAEPS are used as follows:

When either i or j is a hydrogen-bond donor, MMFF uses the simple arithmetic mean \( 0.5 \: (R_{II}^* + R_{JJ}^*) \) instead of eq 3 to obtain \( R_{IJ}^* \). If the i-j interaction is a donor-acceptor interaction, MMFF also scales \( R_{IJ}^* \) as given by eq 3 by DARAD (currently 0.8) and \( \varepsilon_{IJ} \) as given by eq 5 by DAEPS (currently 0.5).

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.
atom1_grad	The output variable storing the accumulated energy gradient contributions for atom i.
atom2_grad	The output variable storing the accumulated energy gradient contributions for atom j.
e_IJ	The precalculated value \( \varepsilon_{IJ} \).
r_IJ	The precalculated value \( R_{IJ}^* \).
r_IJ_7	The precalculated value \( R_{IJ}^{*^7} \).

Returns

The calculated Van der Waals interaction energy \( E_{vdW_{ij}} \).

Note

The calculated partial energy derivative (see above) for an atom gets added to the corresponding output variable!

getMMFF94AromaticRings()

CDPL_FORCEFIELD_API const Chem::FragmentList::SharedPointer& CDPL::ForceField::getMMFF94AromaticRings

(

const Chem::MolecularGraph &

molgraph

)

Returns the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property of molgraph.

Parameters

molgraph

The molecular graph.

Returns

A const reference to the list of MMFF94 aromatic rings.

setMMFF94AromaticRings()

CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94AromaticRings	(	Chem::MolecularGraph &	molgraph,
		const Chem::FragmentList::SharedPointer &	rings
	)

Sets the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property of molgraph to rings.

Parameters

molgraph	The molecular graph.
rings	The new list of MMFF94 aromatic rings.

clearMMFF94AromaticRings()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94AromaticRings

(

Chem::MolecularGraph &

molgraph

)

Removes the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property from molgraph.

Parameters

molgraph

The molecular graph.

hasMMFF94AromaticRings()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94AromaticRings

(

const Chem::MolecularGraph &

molgraph

)

Tells whether molgraph carries an explicit ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property.

Parameters

molgraph

The molecular graph.

Returns

true if the list of MMFF94 aromatic rings is set, and false otherwise.

perceiveMMFF94AromaticRings() [1/2]

CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer CDPL::ForceField::perceiveMMFF94AromaticRings

(

const Chem::MolecularGraph &

molgraph

)

Perceives the list of MMFF94 aromatic rings of the molecular graph molgraph without storing the result.

Parameters

molgraph

The molecular graph.

Returns

A shared pointer to the perceived list of MMFF94 aromatic rings.

perceiveMMFF94AromaticRings() [2/2]

CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer CDPL::ForceField::perceiveMMFF94AromaticRings	(	Chem::MolecularGraph &	molgraph,
		bool	overwrite
	)

Perceives the list of MMFF94 aromatic rings of molgraph and stores the result as the value of the ForceField::MolecularGraphProperty::MMFF94_AROMATIC_RINGS property.

Parameters

molgraph	The molecular graph.
overwrite	Specifies whether an already existing value of the property should be replaced.

Returns

A shared pointer to the perceived list of MMFF94 aromatic rings.

assignMMFF94AtomTypes()

CDPL_FORCEFIELD_API void CDPL::ForceField::assignMMFF94AtomTypes	(	Chem::MolecularGraph &	molgraph,
		bool	strict,
		bool	overwrite
	)

Assigns MMFF94 atom types to the atoms of molgraph.

Parameters

molgraph	The molecular graph whose atoms will be typed.
strict	If true, atom typing operates in strict MMFF94 mode (rejecting unsupported chemistries).
overwrite	Specifies whether already assigned atom-type properties should be replaced.

assignMMFF94BondTypeIndices()

CDPL_FORCEFIELD_API void CDPL::ForceField::assignMMFF94BondTypeIndices	(	Chem::MolecularGraph &	molgraph,
		bool	strict,
		bool	overwrite
	)

Assigns MMFF94 bond type indices to the bonds of molgraph.

Parameters

molgraph	The molecular graph whose bonds will be typed.
strict	If true, bond typing operates in strict MMFF94 mode (rejecting unsupported chemistries).
overwrite	Specifies whether already assigned bond-type-index properties should be replaced.

calcMMFF94AtomCharges()

CDPL_FORCEFIELD_API void CDPL::ForceField::calcMMFF94AtomCharges	(	Chem::MolecularGraph &	molgraph,
		bool	strict,
		bool	overwrite
	)

Calculates and assigns MMFF94 partial atomic charges to the atoms of molgraph.

Parameters

molgraph	The molecular graph whose atoms will be charged.
strict	If true, charge calculation operates in strict MMFF94 mode (rejecting unsupported chemistries).
overwrite	Specifies whether already assigned charge properties should be replaced.

assignUFFAtomTypes()

CDPL_FORCEFIELD_API void CDPL::ForceField::assignUFFAtomTypes	(	Chem::MolecularGraph &	molgraph,
		bool	overwrite
	)

Assigns UFF atom types to the atoms of molgraph.

Parameters

molgraph	The molecular graph whose atoms will be typed.
overwrite	Specifies whether already assigned atom-type properties should be replaced.

filterInteractions()

CDPL_FORCEFIELD_API void CDPL::ForceField::filterInteractions	(	const MMFF94InteractionData &	ia_data,
		MMFF94InteractionData &	filtered_ia_data,
		const Util::BitSet &	inc_atom_mask
	)

Filters an MMFF94 interaction-data set, retaining only those interactions that exclusively reference atoms in inc_atom_mask.

Parameters

ia_data	The input interaction-data set.
filtered_ia_data	The output interaction-data set receiving the retained interactions.
inc_atom_mask	A bit set whose set bits identify the atom indices that may appear in a retained interaction.

calcSquaredDistance()

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcSquaredDistance	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos
	)

Calculates the squared distance \( r_{ij}^2 \) between two atoms i and j.

\( r_{ij}^2 = |\vec{v_{ij}}|^2 \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.

Returns

The calculated squared distance \( r_{ij}^2 \).

calcDistance()

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcDistance	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos
	)

Calculates the distance \( r_{ij} \) between two atoms i and j.

\( r_{ij} = |\vec{v_{ij}}| \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.

Returns

The calculated distance \( r_{ij} \).

calcBondLengthsAndAngleCos()

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondLengthsAndAngleCos	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		ValueType &	bond_length1,
		ValueType &	bond_length2
	)

Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( r_{ij} = |\vec{v_{ij}}| \)
\( r_{jk} = |\vec{v_{jk}}| \)
\( \cos(\vartheta_{ijk}) = \frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{r_{ij} \: r_{jk}} \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
bond_length1	Output variable for the bond length \( r_{ij} \).
bond_length2	Output variable for the bond length \( r_{jk} \).

Returns

The calculated cosine of the bond angle \( \vartheta_{ijk} \).

calcBondLengthsAndAngle()

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondLengthsAndAngle	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		ValueType &	bond_length1,
		ValueType &	bond_length2
	)

Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( r_{ij} = |\vec{v_{ij}}| \)
\( r_{jk} = |\vec{v_{jk}}| \)
\( \vartheta_{ijk} = \arccos(\frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{r_{ij} \: r_{jk}}) \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
bond_length1	Output variable for the bond length \( r_{ij} \).
bond_length2	Output variable for the bond length \( r_{jk} \).

Returns

The calculated bond angle \( \vartheta_{ijk} \).

calcBondAngleCos() [1/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondAngleCos	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos
	)

Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( \cos(\vartheta_{ijk}) = \frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{|\vec{v_{ij}}| \: |\vec{v_{jk}}|} \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.

Returns

The calculated cosine of the bond angle \( \vartheta_{ijk} \).

calcBondAngleCos() [2/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondAngleCos	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	r_ij,
		const ValueType &	r_jk
	)

Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( \cos(\vartheta_{ijk}) = \frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{|\vec{v_{ij}}| \: |\vec{v_{jk}}|} \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
r_ij	The length of the bond between atom i and j.
r_jk	The length of the bond between atom j and k.

Returns

The calculated cosine of the bond angle \( \vartheta_{ijk} \).

calcBondAngle() [1/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondAngle	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos
	)

Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( \vartheta_{ijk} = \arccos(\frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{|\vec{v_{ij}}| \: |\vec{v_{jk}}|}) \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.

Returns

The calculated bond angle \( \vartheta_{ijk} \).

calcBondAngle() [2/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcBondAngle	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const ValueType &	r_ij,
		const ValueType &	r_jk
	)

Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k.

\( \vartheta_{ijk} = \arccos(\frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{|\vec{v_{ij}}| \: |\vec{v_{jk}}|}) \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
r_ij	The length of the bond between atom i and j.
r_jk	The length of the bond between atom j and k.

Returns

The calculated bond angle \( \vartheta_{ijk} \).

calcOutOfPlaneAngle() [1/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcOutOfPlaneAngle	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos
	)

Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k.

\( \chi_{ijk;l} = \frac{\pi}{2} - \arccos(\frac{\vec{n_{ijk}} \cdot \vec{v_{jl}}}{|\vec{n_{ijk}}| \: |\vec{v_{jl}}|}) \)

where
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( \vec{v_{jl}} = \vec{p_l} - \vec{p_j} \)
\( \vec{n_{ijk}} = \vec{v_{ji}} \times \vec{v_{jk}} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.
\( \vec{p_l} \) = coordinates of atom l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
oop_atom_pos	The position \( \vec{p_l} \) of the out-of-plane atom l.

Returns

The calculated out-of-plane angle \( \chi_{ijk;l} \).

calcOutOfPlaneAngle() [2/2]

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcOutOfPlaneAngle	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos,
		const ValueType &	r_jl
	)

Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k.

\( \chi_{ijk;l} = \frac{\pi}{2} - \arccos(\frac{\vec{n_{ijk}} \cdot \vec{v_{jl}}}{|\vec{n_{ijk}}| \: |\vec{v_{jl}}|}) \)

where
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( \vec{v_{jl}} = \vec{p_l} - \vec{p_j} \)
\( \vec{n_{ijk}} = \vec{v_{ji}} \times \vec{v_{jk}} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.
\( \vec{p_l} \) = coordinates of atom l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
oop_atom_pos	The position \( \vec{p_l} \) of the out-of-plane atom l.
r_jl	The length of the bond between atom j and atom l.

Returns

The calculated out-of-plane angle \( \chi_{ijk;l} \).

calcDihedralAngleCos()

template<typename ValueType , typename CoordsVec >

ValueType CDPL::ForceField::calcDihedralAngleCos	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom1_pos,
		const CoordsVec &	ctr_atom2_pos,
		const CoordsVec &	term_atom2_pos
	)

Calculates the cosine of the dihedral angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l.

\( \cos(\Phi_{ijkl}) = \frac{\vec{n_{ijk}} \cdot \vec{n_{jkl}}}{|\vec{n_{ijk}}| \: |\vec{n_{jkl}}|} \)

where
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( \vec{v_{lk}} = \vec{p_k} - \vec{p_l} \)
\( \vec{n_{ijk}} = \vec{v_{ji}} \times \vec{v_{jk}} \)
\( \vec{n_{jkl}} = \vec{v_{jk}} \times \vec{v_{lk}} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.
\( \vec{p_l} \) = coordinates of atom l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_pos	The position \( \vec{p_j} \) of the central atom j.
ctr_atom2_pos	The position \( \vec{p_k} \) of the central atom k.
term_atom2_pos	The position \( \vec{p_l} \) of the terminal atom l.

Returns

The calculated cosine of the dihedral angle \( \Phi_{ijkl} \).

calcDistanceDerivatives()

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcDistanceDerivatives	(	const CoordsVec &	atom1_pos,
		const CoordsVec &	atom2_pos,
		GradVec &	atom1_deriv,
		GradVec &	atom2_deriv
	)

Calculates the partial derivatives \( \frac{\partial r_{ij}}{\partial \vec{p_x}} \) of the distance \( r_{ij} \) between two atoms i and j.

\( \frac{\partial r_{ij}}{\partial \vec{p_i}} = \frac{-\vec{v_{ij}}}{r_{ij}} \)
\( \frac{\partial r_{ij}}{\partial \vec{p_j}} = \frac{\vec{v_{ij}}}{r_{ij}} \)
\( r_{ij} = |\vec{v_{ij}}| \)

where
\( \vec{v_{ij}} = \vec{p_j} - \vec{p_i} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.

Parameters

atom1_pos	The position \( \vec{p_i} \) of atom i.
atom2_pos	The position \( \vec{p_j} \) of atom j.
atom1_deriv	Output variable for the calculated partial derivative \( \frac{\partial r_{ij}}{\partial \vec{p_i}} \) at the given atom positions.
atom2_deriv	Output variable for the calculated partial derivative \( \frac{\partial r_{ij}}{\partial \vec{p_j}} \) at the given atom positions.

Returns

The calculated distance \( r_{ij} \).

calcBondAngleCosDerivatives()

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcBondAngleCosDerivatives	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		GradVec &	term_atom1_deriv,
		GradVec &	ctr_atom_deriv,
		GradVec &	term_atom2_deriv
	)

Calculates the partial derivatives \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_x}} \) of the of the cosine of the angle \( \vartheta_{ijk} \) between the bonds i-j and j-k.

\( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_i}} = \frac{\vec{v_{jk}}}{r_{ji} \: r_{jk}} - \frac{\vec{v_{ji}} \: (\vec{v_{ji}} \cdot \vec{v_{jk}})}{r_{ji}^3 \: r_{jk}} \)
\( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_k}} = \frac{\vec{v_{ji}}}{r_{ji} \: r_{jk}} - \frac{\vec{v_{jk}} \: (\vec{v_{ji}} \cdot \vec{v_{jk}})}{r_{ji} \: r_{jk}^3} \)
\( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_j}} = -(\frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_i}} + \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_k}}) \)
\( \cos(\vartheta_{ijk}) = \frac{\vec{v_{ij}} \cdot \vec{v_{jk}}}{r_{ij} \: r_{jk}} \)

where
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( r_{ji} = |\vec{v_{ji}}| \)
\( r_{jk} = |\vec{v_{jk}}| \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of atom j.
term_atom2_pos	The position \( \vec{p_k} \) of atom k.
term_atom1_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_j}} \) at the given atom positions.
term_atom2_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_k}} \) at the given atom positions.

Returns

The calculated cosine of the bond angle \( \vartheta_{ijk} \).

calcDihedralAngleCosDerivatives()

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcDihedralAngleCosDerivatives	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom1_pos,
		const CoordsVec &	ctr_atom2_pos,
		const CoordsVec &	term_atom2_pos,
		GradVec &	term_atom1_deriv,
		GradVec &	ctr_atom1_deriv,
		GradVec &	ctr_atom2_deriv,
		GradVec &	term_atom2_deriv
	)

Calculates the partial derivatives \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_x}} \) of the cosine of the angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l.

\( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_i}} = \vec{v_{jk}} \times \vec{a} \)

\( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_j}} = \vec{r_{ki}} \times \vec{a} - \vec{v_{lk}} \times \vec{b} \)
\( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_l}} = \vec{v_{jk}} \times \vec{b} \)
\( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_k}} = -(\frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_i}} + \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_j}} + \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_l}}) \)
\( \cos(\Phi_{ijkl}) = \frac{\vec{n_{ijk}} \cdot \vec{n_{jkl}}}{|\vec{n_{ijk}}| \: |\vec{n_{jkl}}|} \)

where
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( \vec{v_{lk}} = \vec{p_k} - \vec{p_l} \)
\( \vec{r_{ki}} = \vec{p_i} - \vec{p_k} \)
\( \vec{n_{ijk}} = \vec{v_{ji}} \times \vec{v_{jk}} \)
\( \vec{n_{jkl}} = \vec{v_{jk}} \times \vec{v_{lk}} \)
\( \vec{a} = \frac{\frac{\vec{n_{jkl}}}{|\vec{n_{jkl}}|} - \cos(\Phi_{ijkl}) \: \frac{\vec{n_{ijk}}}{|\vec{n_{ijk}}|}}{|\vec{n_{ijk}}|} \)
\( \vec{b} = \frac{\frac{\vec{n_{ijk}}}{|\vec{n_{ijk}}|} - \cos(\Phi_{ijkl}) \: \frac{\vec{n_{jkl}}}{|\vec{n_{jkl}}|}}{|\vec{n_{jkl}}|} \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.
\( \vec{p_l} \) = coordinates of atom l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_pos	The position \( \vec{p_j} \) of the central atom j.
ctr_atom2_pos	The position \( \vec{p_k} \) of the central atom k.
term_atom2_pos	The position \( \vec{p_l} \) of the terminal atom l.
term_atom1_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom1_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions.
ctr_atom2_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions.
term_atom2_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_l}} \) at the given atom positions.

Returns

The calculated cosine of the dihedral angle \( \Phi_{ijkl} \).

calcOutOfPlaneAngleCosDerivatives()

template<typename ValueType , typename CoordsVec , typename GradVec >

ValueType CDPL::ForceField::calcOutOfPlaneAngleCosDerivatives	(	const CoordsVec &	term_atom1_pos,
		const CoordsVec &	ctr_atom_pos,
		const CoordsVec &	term_atom2_pos,
		const CoordsVec &	oop_atom_pos,
		GradVec &	term_atom1_deriv,
		GradVec &	ctr_atom_deriv,
		GradVec &	term_atom2_deriv,
		GradVec &	oop_atom_deriv
	)

Calculates the partial derivatives \( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_x}} \) of the cosine of the angle \( \omega_{ijk;l} \) between the bond j-l and the normal of the plane defined by the atoms i-j-k.

\( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_i}} = \frac{\vec{v_{jk}} \times \vec{v_{jl}}}{|\vec{n_{ijk}}| \: r_{jl}} - \cos(\omega_{ijk;l}) \: \frac{M_1 \cdot \vec{n_{ijk}}}{|\vec{n_{ijk}}|^2} \)
\( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_k}} = \frac{\vec{v_{jl}} \times \vec{v_{ji}}}{|\vec{n_{ijk}}| \: r_{jl}} - \cos(\omega_{ijk;l}) \: \frac{M_2 \cdot \vec{n_{ijk}}}{|\vec{n_{ijk}}|^2} \)
\( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_l}} = \frac{-1}{|\vec{n_{ijk}}| \: r_{jl}} \: (\frac{\vec{v_{jl}} (\vec{n_{ijk}} \cdot \vec{v_{jl}})}{r_{jl}^2} + \vec{r_{kl}} \times \vec{v_{il}} + \vec{v_{jl}} \times \vec{v_{ji}} + \vec{v_{jk}} \times \vec{v_{jl}}) \)
\( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_j}} = -(\frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_i}} + \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_k}} + \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_l}}) \)
\( \cos(\omega_{ijk;l}) = \frac{\vec{n_{ijk}} \cdot \vec{v_{jl}}}{|\vec{n_{ijk}}| \: r_{jl}} \)

where
\( M_1 = \begin{vmatrix} 0 & -\vec{v_{jk}}.z & \vec{v_{jk}}.y \\ \vec{v_{jk}}.z & 0 & -\vec{v_{jk}}.x \\ -\vec{v_{jk}}.y & \vec{v_{jk}}.x & 0 \end{vmatrix} \)
\( M_2 = \begin{vmatrix} 0 & \vec{v_{ji}}.z & -\vec{v_{ji}}.y \\ -\vec{v_{ji}}.z & 0 & \vec{v_{ji}}.x \\ \vec{v_{ji}}.y & -\vec{v_{ji}}.x & 0 \end{vmatrix} \)
\( \vec{v_{ji}} = \vec{p_i} - \vec{p_j} \)
\( \vec{v_{jk}} = \vec{p_k} - \vec{p_j} \)
\( \vec{v_{jl}} = \vec{p_l} - \vec{p_j} \)
\( \vec{r_{kl}} = \vec{p_l} - \vec{p_k} \)
\( \vec{v_{il}} = \vec{p_l} - \vec{p_i} \)
\( \vec{n_{ijk}} = \vec{v_{ji}} \times \vec{v_{jk}} \)
\( r_{jl} = |\vec{v_{jl}}| \)

\( \vec{p_i} \) = coordinates of atom i.
\( \vec{p_j} \) = coordinates of atom j.
\( \vec{p_k} \) = coordinates of atom k.
\( \vec{p_l} \) = coordinates of atom l.

Parameters

term_atom1_pos	The position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_pos	The position \( \vec{p_j} \) of the central atom j.
term_atom2_pos	The position \( \vec{p_k} \) of the terminal atom k.
oop_atom_pos	The position \( \vec{p_l} \) of the out-of-plane atom l.
term_atom1_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions.
term_atom2_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions.
oop_atom_deriv	Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_l}} \) at the given atom positions.

Returns

The calculated cosine of the angle \( \omega_{ijk;l} \).