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
class	Error
struct	GradientVectorTraits
struct	GradientVectorTraits< Math::VectorArray< V > >
struct	GradientVectorTraits< std::vector< V > >
class	MMFF94AngleBendingInteraction
class	MMFF94AngleBendingInteractionParameterizer
class	MMFF94AngleBendingParameterTable
class	MMFF94AromaticAtomTypeDefinitionTable
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
class	MMFF94AtomTyper
class	MMFF94BondChargeIncrementTable
class	MMFF94BondStretchingInteraction
class	MMFF94BondStretchingInteractionParameterizer
class	MMFF94BondStretchingParameterTable
class	MMFF94BondStretchingRuleParameterTable
class	MMFF94BondTyper
class	MMFF94ChargeCalculator
class	MMFF94DefaultStretchBendParameterTable
class	MMFF94ElectrostaticInteraction
class	MMFF94ElectrostaticInteractionParameterizer
class	MMFF94EnergyCalculator
class	MMFF94FormalAtomChargeDefinitionTable
class	MMFF94GradientCalculator
class	MMFF94HeavyToHydrogenAtomTypeMap
class	MMFF94InteractionData
class	MMFF94InteractionParameterizer
class	MMFF94OutOfPlaneBendingInteraction
class	MMFF94OutOfPlaneBendingInteractionParameterizer
class	MMFF94OutOfPlaneBendingParameterTable
class	MMFF94PartialBondChargeIncrementTable
class	MMFF94PrimaryToParameterAtomTypeMap
class	MMFF94StretchBendInteraction
class	MMFF94StretchBendInteractionParameterizer
class	MMFF94StretchBendParameterTable
class	MMFF94SymbolicAtomTypePatternTable
class	MMFF94SymbolicToNumericAtomTypeMap
class	MMFF94TorsionInteraction
class	MMFF94TorsionInteractionParameterizer
class	MMFF94TorsionParameterTable
class	MMFF94VanDerWaalsInteraction
class	MMFF94VanDerWaalsInteractionParameterizer
class	MMFF94VanDerWaalsParameterTable
class	ParameterizationFailed
class	UFFAtomTypePropertyTable

Typedefs
typedef Util::Array< ElasticPotential >	ElasticPotentialList
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction2
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction3
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)>	InteractionFilterFunction4
typedef Util::Array< MMFF94AngleBendingInteraction >	MMFF94AngleBendingInteractionList
typedef Util::Array< MMFF94BondStretchingInteraction >	MMFF94BondStretchingInteractionList
typedef Util::Array< MMFF94ElectrostaticInteraction >	MMFF94ElectrostaticInteractionList
typedef Util::Array< MMFF94OutOfPlaneBendingInteraction >	MMFF94OutOfPlaneBendingInteractionList
typedef std::function< unsigned int(const Chem::Atom &)>	MMFF94NumericAtomTypeFunction
	A 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
	A generic wrapper class used to store a user-defined symbolic MMFF94 atom type function. More...
typedef std::function< double(const Chem::Atom &)>	MMFF94AtomChargeFunction
	A generic wrapper class used to store a user-defined MMFF94 partial atom charge function. More...
typedef std::function< unsigned int(const Chem::Bond &)>	MMFF94BondTypeIndexFunction
	A 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
	A generic wrapper class used to store a user-defined MMFF94 ring set function. More...
typedef Util::Array< MMFF94StretchBendInteraction >	MMFF94StretchBendInteractionList
typedef Util::Array< MMFF94TorsionInteraction >	MMFF94TorsionInteractionList
typedef Util::Array< MMFF94VanDerWaalsInteraction >	MMFF94VanDerWaalsInteractionList
typedef std::function< std::size_t(const Chem::Atom &, const Chem::Atom &, const Chem::MolecularGraph &)>	TopologicalAtomDistanceFunction
	A 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)
CDPL_FORCEFIELD_API void	setMMFF94SymbolicType (Chem::Atom &atom, const std::string &type)
CDPL_FORCEFIELD_API void	clearMMFF94SymbolicType (Chem::Atom &atom)
CDPL_FORCEFIELD_API bool	hasMMFF94SymbolicType (const Chem::Atom &atom)
CDPL_FORCEFIELD_API unsigned int	getMMFF94NumericType (const Chem::Atom &atom)
CDPL_FORCEFIELD_API void	setMMFF94NumericType (Chem::Atom &atom, unsigned int type)
CDPL_FORCEFIELD_API void	clearMMFF94NumericType (Chem::Atom &atom)
CDPL_FORCEFIELD_API bool	hasMMFF94NumericType (const Chem::Atom &atom)
CDPL_FORCEFIELD_API double	getMMFF94Charge (const Chem::Atom &atom)
CDPL_FORCEFIELD_API void	setMMFF94Charge (Chem::Atom &atom, double charge)
CDPL_FORCEFIELD_API void	clearMMFF94Charge (Chem::Atom &atom)
CDPL_FORCEFIELD_API bool	hasMMFF94Charge (const Chem::Atom &atom)
CDPL_FORCEFIELD_API unsigned int	getUFFType (const Chem::Atom &atom)
CDPL_FORCEFIELD_API void	setUFFType (Chem::Atom &atom, unsigned int type)
CDPL_FORCEFIELD_API void	clearUFFType (Chem::Atom &atom)
CDPL_FORCEFIELD_API bool	hasUFFType (const Chem::Atom &atom)
CDPL_FORCEFIELD_API unsigned int	perceiveUFFType (const Chem::Atom &atom, const Chem::MolecularGraph &molgraph)
CDPL_FORCEFIELD_API unsigned int	getMMFF94TypeIndex (const Chem::Bond &bond)
CDPL_FORCEFIELD_API void	setMMFF94TypeIndex (Chem::Bond &bond, unsigned int type_idx)
CDPL_FORCEFIELD_API void	clearMMFF94TypeIndex (Chem::Bond &bond)
CDPL_FORCEFIELD_API bool	hasMMFF94TypeIndex (const Chem::Bond &bond)
template<typename ValueType , typename Iter , typename CoordsArray >
ValueType	calcElasticPotentialEnergy (Iter beg, const Iter &end, const CoordsArray &coords)
template<typename ValueType , typename CoordsArray >
ValueType	calcElasticPotentialEnergy (const ElasticPotential &pot, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcElasticPotentialGradient (const ElasticPotential &pot, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94BondStretchingEnergy (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94AngleBendingEnergy (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94StretchBendEnergy (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94OutOfPlaneBendingEnergy (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94TorsionEnergy (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94ElectrostaticEnergy (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray >
ValueType	calcMMFF94VanDerWaalsEnergy (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94BondStretchingGradient (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94AngleBendingGradient (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94StretchBendGradient (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94OutOfPlaneBendingGradient (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94TorsionGradient (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94ElectrostaticGradient (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
template<typename ValueType , typename CoordsArray , typename GradVector >
ValueType	calcMMFF94VanDerWaalsGradient (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords, GradVector &grad)
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)
CDPL_FORCEFIELD_API void	setMMFF94AromaticRings (Chem::MolecularGraph &molgraph, const Chem::FragmentList::SharedPointer &rings)
CDPL_FORCEFIELD_API void	clearMMFF94AromaticRings (Chem::MolecularGraph &molgraph)
CDPL_FORCEFIELD_API bool	hasMMFF94AromaticRings (const Chem::MolecularGraph &molgraph)
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer	perceiveMMFF94AromaticRings (const Chem::MolecularGraph &molgraph)
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer	perceiveMMFF94AromaticRings (Chem::MolecularGraph &molgraph, bool overwrite)
CDPL_FORCEFIELD_API void	assignMMFF94AtomTypes (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
CDPL_FORCEFIELD_API void	assignMMFF94BondTypeIndices (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
CDPL_FORCEFIELD_API void	calcMMFF94AtomCharges (Chem::MolecularGraph &molgraph, bool strict, bool overwrite)
CDPL_FORCEFIELD_API void	assignUFFAtomTypes (Chem::MolecularGraph &molgraph, bool overwrite)
CDPL_FORCEFIELD_API void	filterInteractions (const MMFF94InteractionData &ia_data, MMFF94InteractionData &filtered_ia_data, const Util::BitSet &inc_atom_mask)
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

InteractionFilterFunction2

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

InteractionFilterFunction3

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

InteractionFilterFunction4

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

MMFF94AngleBendingInteractionList

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

MMFF94BondStretchingInteractionList

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

MMFF94ElectrostaticInteractionList

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

MMFF94OutOfPlaneBendingInteractionList

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

MMFF94NumericAtomTypeFunction

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

A 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

A 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

A 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

A 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

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

MMFF94StretchBendInteractionList

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

MMFF94TorsionInteractionList

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

MMFF94VanDerWaalsInteractionList

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

TopologicalAtomDistanceFunction

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

A 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

)

setMMFF94SymbolicType()

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

clearMMFF94SymbolicType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94SymbolicType

(

Chem::Atom &

atom

)

hasMMFF94SymbolicType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94SymbolicType

(

const Chem::Atom &

atom

)

getMMFF94NumericType()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94NumericType

(

const Chem::Atom &

atom

)

setMMFF94NumericType()

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

clearMMFF94NumericType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94NumericType

(

Chem::Atom &

atom

)

hasMMFF94NumericType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94NumericType

(

const Chem::Atom &

atom

)

getMMFF94Charge()

CDPL_FORCEFIELD_API double CDPL::ForceField::getMMFF94Charge

(

const Chem::Atom &

atom

)

setMMFF94Charge()

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

clearMMFF94Charge()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94Charge

(

Chem::Atom &

atom

)

hasMMFF94Charge()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94Charge

(

const Chem::Atom &

atom

)

getUFFType()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getUFFType

(

const Chem::Atom &

atom

)

setUFFType()

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

clearUFFType()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearUFFType

(

Chem::Atom &

atom

)

hasUFFType()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasUFFType

(

const Chem::Atom &

atom

)

perceiveUFFType()

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

getMMFF94TypeIndex()

CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94TypeIndex

(

const Chem::Bond &

bond

)

setMMFF94TypeIndex()

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

clearMMFF94TypeIndex()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94TypeIndex

(

Chem::Bond &

bond

)

hasMMFF94TypeIndex()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94TypeIndex

(

const Chem::Bond &

bond

)

calcElasticPotentialEnergy() [1/3]

template<typename ValueType , typename Iter , typename CoordsArray >

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

calcElasticPotentialEnergy() [2/3]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcElasticPotentialGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94BondStretchingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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.

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

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.

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

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
	)

calcMMFF94AngleBendingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94StretchBendEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94OutOfPlaneBendingEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94TorsionEnergy() [2/3]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94ElectrostaticEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94VanDerWaalsEnergy() [2/4]

template<typename ValueType , typename CoordsArray >

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

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
	)

calcMMFF94BondStretchingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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:

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

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
	)

calcMMFF94AngleBendingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94StretchBendGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94OutOfPlaneBendingGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94TorsionGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94ElectrostaticGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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
	)

calcMMFF94VanDerWaalsGradient() [2/3]

template<typename ValueType , typename CoordsArray , typename GradVector >

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

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

)

setMMFF94AromaticRings()

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

clearMMFF94AromaticRings()

CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94AromaticRings

(

Chem::MolecularGraph &

molgraph

)

hasMMFF94AromaticRings()

CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94AromaticRings

(

const Chem::MolecularGraph &

molgraph

)

perceiveMMFF94AromaticRings() [1/2]

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

(

const Chem::MolecularGraph &

molgraph

)

perceiveMMFF94AromaticRings() [2/2]

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

assignMMFF94AtomTypes()

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

assignMMFF94BondTypeIndices()

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

calcMMFF94AtomCharges()

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

assignUFFAtomTypes()

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

filterInteractions()

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

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

\( \vec{p_i} \) = 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 \( \omega_{ijk;l} \).