Chemical Data Processing Library C++ API - Version 1.1.1
Namespaces | Classes | Typedefs | Functions
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< ElasticPotentialElasticPotentialList
 
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< MMFF94AngleBendingInteractionMMFF94AngleBendingInteractionList
 
typedef Util::Array< MMFF94BondStretchingInteractionMMFF94BondStretchingInteractionList
 
typedef Util::Array< MMFF94ElectrostaticInteractionMMFF94ElectrostaticInteractionList
 
typedef Util::Array< MMFF94OutOfPlaneBendingInteractionMMFF94OutOfPlaneBendingInteractionList
 
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< MMFF94StretchBendInteractionMMFF94StretchBendInteractionList
 
typedef Util::Array< MMFF94TorsionInteractionMMFF94TorsionInteractionList
 
typedef Util::Array< MMFF94VanDerWaalsInteractionMMFF94VanDerWaalsInteractionList
 
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::SharedPointergetMMFF94AromaticRings (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

◆ 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

◆ MMFF94BondStretchingInteractionList

◆ MMFF94ElectrostaticInteractionList

◆ 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

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

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

◆ MMFF94StretchBendInteractionList

◆ MMFF94TorsionInteractionList

◆ 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_posThe position of atom i.
atom2_posThe position of atom j.
force_constThe force constant \( k_{ij} \).
ref_lengthThe 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe position \( \vec{p_j} \) of atom j.
atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
atom2_gradThe output variable storing the accumulated energy gradient contributions for atom j.
force_constThe force constant \( k_{ij} \).
ref_lengthThe 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_posThe position of atom i.
atom2_posThe position of atom j.
force_constThe bond stretching force constant \( kb_{IJ} \).
ref_lengthThe 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_ijThe length of the bond between atom i and j.
force_constThe bond stretching force constant \( kb_{IJ} \).
ref_lengthThe 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
linearIf true, the bond angle is linear.
force_constThe angle bending force constant \( ka_{IJK} \).
ref_angleThe 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
r_ijThe length of the bond between atom i and j.
r_jkThe length of the bond between atom j and k.
linearIf true, the bond angle is linear.
force_constThe angle bending force constant \( ka_{IJK} \).
ref_angleThe 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
ijk_force_constThe stretch-bend force constant \( kba_{IJK} \).
kji_force_constThe stretch-bend force constant \( kba_{KJI} \).
ref_angleThe reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1The reference bond length \( r_{IJ}^0 \).
ref_length2The 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
r_ijThe length of the bond between atom i and j.
r_jkThe length of the bond between atom j and k.
ijk_force_constThe stretch-bend force constant \( kba_{IJK} \).
kji_force_constThe stretch-bend force constant \( kba_{KJI} \).
ref_angleThe reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1The reference bond length \( r_{IJ}^0 \).
ref_length2The 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
oop_atom_posThe position of the out-of-plane atom l.
force_constThe 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_posThe position of atom i.
ctr_atom_posThe position of the central atom j.
term_atom2_posThe position of atom k.
oop_atom_posThe position of the out-of-plane atom l.
r_jlThe length of the bond between atom j and atom l.
force_constThe 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_posThe position of the terminal atom i.
ctr_atom1_posThe position of the central atom j.
ctr_atom2_posThe position of the central atom k.
term_atom2_posThe position of the terminal atom l.
tor_param1The torsion parameter \( V_1 \).
tor_param2The torsion parameter \( V_2 \).
tor_param3The 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 (Ã…) (see calcDistance()).
\( \delta \) = Electrostatic buffering constant (0.05 Ã…).
\( n \) = 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_posThe position of atom i.
atom2_posThe position of atom j.
atom1_chgThe partial atom charge \( q_i \) of atom i.
atom2_chgThe partial atom charge \( q_j \) of atom j.
scale_factThe scaling factor for \( S \) depending on the topological i-j distance.
de_constThe dielectric constant \( D \).
dist_expoThe 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 (Ã…) (see calcDistance()).
\( \delta \) = Electrostatic buffering constant (0.05 Ã…).
\( n \) = 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_ijThe interatomic distance \( R_{ij} \) of atom i and atom j.
atom1_chgThe partial atom charge \( q_i \) of atom i.
atom2_chgThe partial atom charge \( q_j \) of atom j.
scale_factThe scaling factor for \( S \) depending on the topological i-j distance.
de_constThe dielectric constant \( D \).
dist_expoThe 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_posThe position of atom i.
atom2_posThe position of atom j.
e_IJThe precalculated value \( \varepsilon_{IJ} \).
r_IJThe precalculated value \( R_{IJ}^* \).
r_IJ_7The 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_ijThe interatomic distance \( R_{ij} \) of atom i and atom j.
e_IJThe precalculated value \( \varepsilon_{IJ} \).
r_IJThe precalculated value \( R_{IJ}^* \).
r_IJ_7The 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe position \( \vec{p_j} \) of atom j.
atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
atom2_gradThe output variable storing the accumulated energy gradient contributions for atom j.
force_constThe bond stretching force constant \( kb_{IJ} \).
ref_lengthThe 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_posThe position \( \vec{p_i} \) of atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of atom k.
term_atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_gradThe output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_gradThe output variable storing the accumulated energy gradient contributions for atom k.
linearIf true, the bond angle is linear.
force_constThe angle bending force constant \( ka_{IJK} \).
ref_angleThe 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_posThe position \( \vec{p_i} \) of atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of atom k.
term_atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_gradThe output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_gradThe output variable storing the accumulated energy gradient contributions for atom k.
ijk_force_constThe stretch-bend force constant \( kba_{IJK} \).
kji_force_constThe stretch-bend force constant \( kba_{KJI} \).
ref_angleThe reference bond angle \( \vartheta_{IJK}^0 \).
ref_length1The reference bond length \( r_{IJ}^0 \).
ref_length2The 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_posThe position \( \vec{p_i} \) of atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of atom k.
oop_atom_posThe position \( \vec{p_l} \) of the out-of-plane atom l.
term_atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom_gradThe output variable storing the accumulated energy gradient contributions for atom j.
term_atom2_gradThe output variable storing the accumulated energy gradient contributions for atom k.
oop_atom_gradThe output variable storing the accumulated energy gradient contributions for atom l.
force_constThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_posThe position \( \vec{p_j} \) of the central atom j.
ctr_atom2_posThe position \( \vec{p_k} \) of the central atom k.
term_atom2_posThe position \( \vec{p_l} \) of the terminal atom l.
term_atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
ctr_atom1_gradThe output variable storing the accumulated energy gradient contributions for atom j.
ctr_atom2_gradThe output variable storing the accumulated energy gradient contributions for atom k.
term_atom2_gradThe output variable storing the accumulated energy gradient contributions for atom l.
tor_param1The torsion parameter \( V_1 \).
tor_param2The torsion parameter \( V_2 \).
tor_param3The 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 (Ã…).
\( \delta \) = electrostatic buffering constant (0.05 Ã…).
\( n \) = 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe position \( \vec{p_j} \) of atom j.
atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
atom2_gradThe output variable storing the accumulated energy gradient contributions for atom j.
atom1_chgThe partial atom charge \( q_i \) of atom i.
atom2_chgThe partial atom charge \( q_j \) of atom j.
scale_factThe scaling factor for \( S \) depending on the topological i-j distance.
de_constThe dielectric constant \( D \).
dist_expoThe 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe position \( \vec{p_j} \) of atom j.
atom1_gradThe output variable storing the accumulated energy gradient contributions for atom i.
atom2_gradThe output variable storing the accumulated energy gradient contributions for atom j.
e_IJThe precalculated value \( \varepsilon_{IJ} \).
r_IJThe precalculated value \( R_{IJ}^* \).
r_IJ_7The 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
bond_length1Output variable for the bond length \( r_{ij} \).
bond_length2Output 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
bond_length1Output variable for the bond length \( r_{ij} \).
bond_length2Output 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
r_ijThe length of the bond between atom i and j.
r_jkThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
r_ijThe length of the bond between atom i and j.
r_jkThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
oop_atom_posThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
oop_atom_posThe position \( \vec{p_l} \) of the out-of-plane atom l.
r_jlThe 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_posThe position \( \vec{p_j} \) of the central atom j.
ctr_atom2_posThe position \( \vec{p_k} \) of the central atom k.
term_atom2_posThe 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_posThe position \( \vec{p_i} \) of atom i.
atom2_posThe position \( \vec{p_j} \) of atom j.
atom1_derivOutput variable for the calculated partial derivative \( \frac{\partial r_{ij}}{\partial \vec{p_i}} \) at the given atom positions.
atom2_derivOutput 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_posThe position \( \vec{p_i} \) of atom i.
ctr_atom_posThe position \( \vec{p_j} \) of atom j.
term_atom2_posThe position \( \vec{p_k} \) of atom k.
term_atom1_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_j}} \) at the given atom positions.
term_atom2_derivOutput 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom1_posThe position \( \vec{p_j} \) of the central atom j.
ctr_atom2_posThe position \( \vec{p_k} \) of the central atom k.
term_atom2_posThe position \( \vec{p_l} \) of the terminal atom l.
term_atom1_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom1_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions.
ctr_atom2_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions.
term_atom2_derivOutput 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_posThe position \( \vec{p_i} \) of the terminal atom i.
ctr_atom_posThe position \( \vec{p_j} \) of the central atom j.
term_atom2_posThe position \( \vec{p_k} \) of the terminal atom k.
oop_atom_posThe position \( \vec{p_l} \) of the out-of-plane atom l.
term_atom1_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions.
ctr_atom_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions.
term_atom2_derivOutput variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions.
oop_atom_derivOutput 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 \( \omega_{ijk;l} \).