Chemical Data Processing Library C++ API - Version 1.1.1
|
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. | |
Typedefs | |
typedef Util::Array< ElasticPotential > | ElasticPotentialList |
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &)> | InteractionFilterFunction2 |
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)> | InteractionFilterFunction3 |
typedef std::function< bool(const Chem::Atom &, const Chem::Atom &, const Chem::Atom &, const Chem::Atom &)> | InteractionFilterFunction4 |
typedef Util::Array< MMFF94AngleBendingInteraction > | MMFF94AngleBendingInteractionList |
typedef Util::Array< MMFF94BondStretchingInteraction > | MMFF94BondStretchingInteractionList |
typedef Util::Array< MMFF94ElectrostaticInteraction > | MMFF94ElectrostaticInteractionList |
typedef Util::Array< MMFF94OutOfPlaneBendingInteraction > | MMFF94OutOfPlaneBendingInteractionList |
typedef std::function< unsigned int(const Chem::Atom &)> | MMFF94NumericAtomTypeFunction |
A generic wrapper class used to store a user-defined numeric MMFF94 atom type function. More... | |
typedef std::function< const std::string &(const Chem::Atom &)> | MMFF94SymbolicAtomTypeFunction |
A generic wrapper class used to store a user-defined symbolic MMFF94 atom type function. More... | |
typedef std::function< double(const Chem::Atom &)> | MMFF94AtomChargeFunction |
A generic wrapper class used to store a user-defined MMFF94 partial atom charge function. More... | |
typedef std::function< unsigned int(const Chem::Bond &)> | MMFF94BondTypeIndexFunction |
A generic wrapper class used to store a user-defined MMFF94 bond type index function. More... | |
typedef std::function< const Chem::FragmentList::SharedPointer &(const Chem::MolecularGraph &)> | MMFF94RingSetFunction |
A generic wrapper class used to store a user-defined MMFF94 ring set function. More... | |
typedef Util::Array< MMFF94StretchBendInteraction > | MMFF94StretchBendInteractionList |
typedef Util::Array< MMFF94TorsionInteraction > | MMFF94TorsionInteractionList |
typedef Util::Array< MMFF94VanDerWaalsInteraction > | MMFF94VanDerWaalsInteractionList |
typedef std::function< std::size_t(const Chem::Atom &, const Chem::Atom &, const Chem::MolecularGraph &)> | TopologicalAtomDistanceFunction |
A generic wrapper class used to store a user-defined topological atom-pair distance function. More... | |
Functions | |
CDPL_FORCEFIELD_API const std::string & | getMMFF94SymbolicType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API void | setMMFF94SymbolicType (Chem::Atom &atom, const std::string &type) |
CDPL_FORCEFIELD_API void | clearMMFF94SymbolicType (Chem::Atom &atom) |
CDPL_FORCEFIELD_API bool | hasMMFF94SymbolicType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API unsigned int | getMMFF94NumericType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API void | setMMFF94NumericType (Chem::Atom &atom, unsigned int type) |
CDPL_FORCEFIELD_API void | clearMMFF94NumericType (Chem::Atom &atom) |
CDPL_FORCEFIELD_API bool | hasMMFF94NumericType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API double | getMMFF94Charge (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API void | setMMFF94Charge (Chem::Atom &atom, double charge) |
CDPL_FORCEFIELD_API void | clearMMFF94Charge (Chem::Atom &atom) |
CDPL_FORCEFIELD_API bool | hasMMFF94Charge (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API unsigned int | getUFFType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API void | setUFFType (Chem::Atom &atom, unsigned int type) |
CDPL_FORCEFIELD_API void | clearUFFType (Chem::Atom &atom) |
CDPL_FORCEFIELD_API bool | hasUFFType (const Chem::Atom &atom) |
CDPL_FORCEFIELD_API unsigned int | perceiveUFFType (const Chem::Atom &atom, const Chem::MolecularGraph &molgraph) |
CDPL_FORCEFIELD_API unsigned int | getMMFF94TypeIndex (const Chem::Bond &bond) |
CDPL_FORCEFIELD_API void | setMMFF94TypeIndex (Chem::Bond &bond, unsigned int type_idx) |
CDPL_FORCEFIELD_API void | clearMMFF94TypeIndex (Chem::Bond &bond) |
CDPL_FORCEFIELD_API bool | hasMMFF94TypeIndex (const Chem::Bond &bond) |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcElasticPotentialEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcElasticPotentialEnergy (const ElasticPotential &pot, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcElasticPotentialEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &force_const, const ValueType &ref_length) |
Calculates the energy \( E_{ij} \) of an elastic potential applied on a pair of atoms i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcElasticPotentialGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcElasticPotentialGradient (const ElasticPotential &pot, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcElasticPotentialGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &force_const, const ValueType &ref_length) |
Calculates the elastic potential energy gradient \( \nabla E_{ij} \) for a pair of atoms i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94BondStretchingEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94BondStretchingEnergy (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94BondStretchingEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &force_const, const ValueType &ref_length) |
Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More... | |
template<typename ValueType > | |
ValueType | calcMMFF94BondStretchingEnergy (const ValueType &r_ij, const ValueType &force_const, const ValueType &ref_length) |
Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94AngleBendingEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94AngleBendingEnergy (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94AngleBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, bool linear, const ValueType &force_const, const ValueType &ref_angle) |
Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94AngleBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk, bool linear, const ValueType &force_const, const ValueType &ref_angle) |
Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94StretchBendEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94StretchBendEnergy (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94StretchBendEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2) |
Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94StretchBendEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2) |
Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94OutOfPlaneBendingEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94OutOfPlaneBendingEnergy (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94OutOfPlaneBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &force_const) |
Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94OutOfPlaneBendingEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &r_jl, const ValueType &force_const) |
Calculates the out-of-plane bending interaction energy \( EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94TorsionEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94TorsionEnergy (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94TorsionEnergy (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, const ValueType &tor_param1, const ValueType &tor_param2, const ValueType &tor_param3) |
Calculates the torsion interaction energy \( ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94ElectrostaticEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94ElectrostaticEnergy (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94ElectrostaticEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo) |
Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More... | |
template<typename ValueType > | |
ValueType | calcMMFF94ElectrostaticEnergy (const ValueType &r_ij, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo) |
Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray > | |
ValueType | calcMMFF94VanDerWaalsEnergy (Iter beg, const Iter &end, const CoordsArray &coords) |
template<typename ValueType , typename CoordsArray > | |
ValueType | calcMMFF94VanDerWaalsEnergy (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcMMFF94VanDerWaalsEnergy (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7) |
Calculates the van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More... | |
template<typename ValueType > | |
ValueType | calcMMFF94VanDerWaalsEnergy (const ValueType &r_ij, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7) |
Calculates the van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94BondStretchingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94BondStretchingGradient (const MMFF94BondStretchingInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94BondStretchingGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &force_const, const ValueType &ref_length) |
Calculates the bond stretching interaction energy gradient \( \nabla EB_{ij} \) for the bond i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94AngleBendingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94AngleBendingGradient (const MMFF94AngleBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94AngleBendingGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, bool linear, const ValueType &force_const, const ValueType &ref_angle) |
Calculates the angle bending interaction energy gradient \( \nabla EA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94StretchBendGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94StretchBendGradient (const MMFF94StretchBendInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94StretchBendGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, const ValueType &ijk_force_const, const ValueType &kji_force_const, const ValueType &ref_angle, const ValueType &ref_length1, const ValueType &ref_length2) |
Calculates the stretch-bend interaction energy gradient \( \nabla EBA_{ijk} \) for two bonds i-j and j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94OutOfPlaneBendingGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94OutOfPlaneBendingGradient (const MMFF94OutOfPlaneBendingInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94OutOfPlaneBendingGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, GradVec &term_atom1_grad, GradVec &ctr_atom_grad, GradVec &term_atom2_grad, GradVec &oop_atom_grad, const ValueType &force_const) |
Calculates the out-of-plane bending interaction energy gradient \( \nabla EOOP_{ijk;l} \) for the bond j-l and the plane i-j-k. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94TorsionGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94TorsionGradient (const MMFF94TorsionInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94TorsionGradient (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_grad, GradVec &ctr_atom1_grad, GradVec &ctr_atom2_grad, GradVec &term_atom2_grad, const ValueType &tor_param1, const ValueType &tor_param2, const ValueType &tor_param3) |
Calculates the torsion interaction energy gradient \( \nabla ET_{ijkl} \) for the central bond j-k and the connected bonds i-j and k-l. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94ElectrostaticGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94ElectrostaticGradient (const MMFF94ElectrostaticInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94ElectrostaticGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &atom1_chg, const ValueType &atom2_chg, const ValueType &scale_fact, const ValueType &de_const, const ValueType &dist_expo) |
Calculates the electrostatic interaction energy gradient \( \nabla EQ_{ij} \) for the atom pair i-j. More... | |
template<typename ValueType , typename Iter , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94VanDerWaalsGradient (Iter beg, const Iter &end, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsArray , typename GradVector > | |
ValueType | calcMMFF94VanDerWaalsGradient (const MMFF94VanDerWaalsInteraction &iaction, const CoordsArray &coords, GradVector &grad) |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcMMFF94VanDerWaalsGradient (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_grad, GradVec &atom2_grad, const ValueType &e_IJ, const ValueType &r_IJ, const ValueType &r_IJ_7) |
Calculates the van der Waals interaction energy gradient \( \nabla E_{vdW_{ij}} \) for the atom pair i-j. More... | |
CDPL_FORCEFIELD_API const Chem::FragmentList::SharedPointer & | getMMFF94AromaticRings (const Chem::MolecularGraph &molgraph) |
CDPL_FORCEFIELD_API void | setMMFF94AromaticRings (Chem::MolecularGraph &molgraph, const Chem::FragmentList::SharedPointer &rings) |
CDPL_FORCEFIELD_API void | clearMMFF94AromaticRings (Chem::MolecularGraph &molgraph) |
CDPL_FORCEFIELD_API bool | hasMMFF94AromaticRings (const Chem::MolecularGraph &molgraph) |
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer | perceiveMMFF94AromaticRings (const Chem::MolecularGraph &molgraph) |
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer | perceiveMMFF94AromaticRings (Chem::MolecularGraph &molgraph, bool overwrite) |
CDPL_FORCEFIELD_API void | assignMMFF94AtomTypes (Chem::MolecularGraph &molgraph, bool strict, bool overwrite) |
CDPL_FORCEFIELD_API void | assignMMFF94BondTypeIndices (Chem::MolecularGraph &molgraph, bool strict, bool overwrite) |
CDPL_FORCEFIELD_API void | calcMMFF94AtomCharges (Chem::MolecularGraph &molgraph, bool strict, bool overwrite) |
CDPL_FORCEFIELD_API void | assignUFFAtomTypes (Chem::MolecularGraph &molgraph, bool overwrite) |
CDPL_FORCEFIELD_API void | filterInteractions (const MMFF94InteractionData &ia_data, MMFF94InteractionData &filtered_ia_data, const Util::BitSet &inc_atom_mask) |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcSquaredDistance (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos) |
Calculates the squared distance \( r_{ij}^2 \) between two atoms i and j. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcDistance (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos) |
Calculates the distance \( r_{ij} \) between two atoms i and j. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondLengthsAndAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, ValueType &bond_length1, ValueType &bond_length2) |
Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondLengthsAndAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, ValueType &bond_length1, ValueType &bond_length2) |
Calculates bond lengths \( r_{ij} \) and \( r_{jk} \) and the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos) |
Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk) |
Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos) |
Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcBondAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const ValueType &r_ij, const ValueType &r_jk) |
Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcOutOfPlaneAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos) |
Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcOutOfPlaneAngle (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, const ValueType &r_jl) |
Calculates the out-of-plane angle \( \chi_{ijk;l} \) between the bond j-l and the plane defined by the atoms i-j-k. More... | |
template<typename ValueType , typename CoordsVec > | |
ValueType | calcDihedralAngleCos (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos) |
Calculates the cosine of the dihedral angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l. More... | |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcDistanceDerivatives (const CoordsVec &atom1_pos, const CoordsVec &atom2_pos, GradVec &atom1_deriv, GradVec &atom2_deriv) |
Calculates the partial derivatives \( \frac{\partial r_{ij}}{\partial \vec{p_x}} \) of the distance \( r_{ij} \) between two atoms i and j. More... | |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcBondAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom_deriv, GradVec &term_atom2_deriv) |
Calculates the partial derivatives \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_x}} \) of the of the cosine of the angle \( \vartheta_{ijk} \) between the bonds i-j and j-k. More... | |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcDihedralAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom1_pos, const CoordsVec &ctr_atom2_pos, const CoordsVec &term_atom2_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom1_deriv, GradVec &ctr_atom2_deriv, GradVec &term_atom2_deriv) |
Calculates the partial derivatives \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_x}} \) of the cosine of the angle \( \Phi_{ijkl} \) between the planes defined by the atom triplets i-j-k and j-k-l. More... | |
template<typename ValueType , typename CoordsVec , typename GradVec > | |
ValueType | calcOutOfPlaneAngleCosDerivatives (const CoordsVec &term_atom1_pos, const CoordsVec &ctr_atom_pos, const CoordsVec &term_atom2_pos, const CoordsVec &oop_atom_pos, GradVec &term_atom1_deriv, GradVec &ctr_atom_deriv, GradVec &term_atom2_deriv, GradVec &oop_atom_deriv) |
Calculates the partial derivatives \( \frac{\partial \cos(\omega_{ijk;l})}{\partial \vec{p_x}} \) of the cosine of the angle \( \omega_{ijk;l} \) between the bond j-l and the normal of the plane defined by the atoms i-j-k. More... | |
Contains classes and functions related to molecular force fields.
typedef std::function<bool(const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction2 |
typedef std::function<bool(const Chem::Atom&, const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction3 |
typedef std::function<bool(const Chem::Atom&, const Chem::Atom&, const Chem::Atom&, const Chem::Atom&)> CDPL::ForceField::InteractionFilterFunction4 |
typedef Util::Array<MMFF94AngleBendingInteraction> CDPL::ForceField::MMFF94AngleBendingInteractionList |
typedef Util::Array<MMFF94BondStretchingInteraction> CDPL::ForceField::MMFF94BondStretchingInteractionList |
typedef Util::Array<MMFF94ElectrostaticInteraction> CDPL::ForceField::MMFF94ElectrostaticInteractionList |
typedef Util::Array<MMFF94OutOfPlaneBendingInteraction> CDPL::ForceField::MMFF94OutOfPlaneBendingInteractionList |
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.
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.
typedef std::function<double(const Chem::Atom&)> CDPL::ForceField::MMFF94AtomChargeFunction |
A generic wrapper class used to store a user-defined MMFF94 partial atom charge function.
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.
typedef std::function<const Chem::FragmentList::SharedPointer&(const Chem::MolecularGraph&)> CDPL::ForceField::MMFF94RingSetFunction |
A generic wrapper class used to store a user-defined MMFF94 ring set function.
typedef Util::Array<MMFF94StretchBendInteraction> CDPL::ForceField::MMFF94StretchBendInteractionList |
typedef Util::Array<MMFF94VanDerWaalsInteraction> CDPL::ForceField::MMFF94VanDerWaalsInteractionList |
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.
CDPL_FORCEFIELD_API const std::string& CDPL::ForceField::getMMFF94SymbolicType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94SymbolicType | ( | Chem::Atom & | atom, |
const std::string & | type | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94SymbolicType | ( | Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94SymbolicType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94NumericType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94NumericType | ( | Chem::Atom & | atom, |
unsigned int | type | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94NumericType | ( | Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94NumericType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API double CDPL::ForceField::getMMFF94Charge | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94Charge | ( | Chem::Atom & | atom, |
double | charge | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94Charge | ( | Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94Charge | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getUFFType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setUFFType | ( | Chem::Atom & | atom, |
unsigned int | type | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearUFFType | ( | Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasUFFType | ( | const Chem::Atom & | atom | ) |
CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::perceiveUFFType | ( | const Chem::Atom & | atom, |
const Chem::MolecularGraph & | molgraph | ||
) |
CDPL_FORCEFIELD_API unsigned int CDPL::ForceField::getMMFF94TypeIndex | ( | const Chem::Bond & | bond | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94TypeIndex | ( | Chem::Bond & | bond, |
unsigned int | type_idx | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94TypeIndex | ( | Chem::Bond & | bond | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94TypeIndex | ( | const Chem::Bond & | bond | ) |
ValueType CDPL::ForceField::calcElasticPotentialEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcElasticPotentialEnergy | ( | const ElasticPotential & | pot, |
const CoordsArray & | coords | ||
) |
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.
atom1_pos | The position of atom i. |
atom2_pos | The position of atom j. |
force_const | The force constant \( k_{ij} \). |
ref_length | The reference distance \( r_{ij}^0 \). |
ValueType CDPL::ForceField::calcElasticPotentialGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcElasticPotentialGradient | ( | const ElasticPotential & | pot, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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.
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
atom2_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
force_const | The force constant \( k_{ij} \). |
ref_length | The reference distance \( r_{ij}^0 \). |
ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94BondStretchingEnergy | ( | const MMFF94BondStretchingInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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).
atom1_pos | The position of atom i. |
atom2_pos | The position of atom j. |
force_const | The bond stretching force constant \( kb_{IJ} \). |
ref_length | The reference bond length \( r_{IJ}^0 \). |
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).
r_ij | The length of the bond between atom i and j. |
force_const | The bond stretching force constant \( kb_{IJ} \). |
ref_length | The reference bond length \( r_{IJ}^0 \). |
ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94AngleBendingEnergy | ( | const MMFF94AngleBendingInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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.
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
linear | If true , the bond angle is linear. |
force_const | The angle bending force constant \( ka_{IJK} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
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.
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
r_ij | The length of the bond between atom i and j. |
r_jk | The length of the bond between atom j and k. |
linear | If true , the bond angle is linear. |
force_const | The angle bending force constant \( ka_{IJK} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94StretchBendEnergy | ( | const MMFF94StretchBendInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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.
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
ijk_force_const | The stretch-bend force constant \( kba_{IJK} \). |
kji_force_const | The stretch-bend force constant \( kba_{KJI} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
ref_length1 | The reference bond length \( r_{IJ}^0 \). |
ref_length2 | The reference bond length \( r_{KJ}^0 \). |
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.
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
r_ij | The length of the bond between atom i and j. |
r_jk | The length of the bond between atom j and k. |
ijk_force_const | The stretch-bend force constant \( kba_{IJK} \). |
kji_force_const | The stretch-bend force constant \( kba_{KJI} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
ref_length1 | The reference bond length \( r_{IJ}^0 \). |
ref_length2 | The reference bond length \( r_{KJ}^0 \). |
ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingEnergy | ( | const MMFF94OutOfPlaneBendingInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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()).
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
oop_atom_pos | The position of the out-of-plane atom l. |
force_const | The out-of-plane bending force constant \( koop_{IJK \colon L} \). |
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()).
term_atom1_pos | The position of atom i. |
ctr_atom_pos | The position of the central atom j. |
term_atom2_pos | The position of atom k. |
oop_atom_pos | The position of the out-of-plane atom l. |
r_jl | The length of the bond between atom j and atom l. |
force_const | The out-of-plane bending force constant \( koop_{IJK \colon L} \). |
ValueType CDPL::ForceField::calcMMFF94TorsionEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94TorsionEnergy | ( | const MMFF94TorsionInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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().
term_atom1_pos | The position of the terminal atom i. |
ctr_atom1_pos | The position of the central atom j. |
ctr_atom2_pos | The position of the central atom k. |
term_atom2_pos | The position of the terminal atom l. |
tor_param1 | The torsion parameter \( V_1 \). |
tor_param2 | The torsion parameter \( V_2 \). |
tor_param3 | The torsion parameter \( V_3 \). |
ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94ElectrostaticEnergy | ( | const MMFF94ElectrostaticInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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 \( EQ_{14} \: 0.75 \)).
atom1_pos | The position of atom i. |
atom2_pos | The position of atom j. |
atom1_chg | The partial atom charge \( q_i \) of atom i. |
atom2_chg | The partial atom charge \( q_j \) of atom j. |
scale_fact | The scaling factor for \( S \) depending on the topological i-j distance. |
de_const | The dielectric constant \( D \). |
dist_expo | The exponent \( n \). |
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 \( EQ_{14} \: 0.75 \)).
r_ij | The interatomic distance \( R_{ij} \) of atom i and atom j. |
atom1_chg | The partial atom charge \( q_i \) of atom i. |
atom2_chg | The partial atom charge \( q_j \) of atom j. |
scale_fact | The scaling factor for \( S \) depending on the topological i-j distance. |
de_const | The dielectric constant \( D \). |
dist_expo | The exponent \( n \). |
ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords | ||
) |
ValueType CDPL::ForceField::calcMMFF94VanDerWaalsEnergy | ( | const MMFF94VanDerWaalsInteraction & | iaction, |
const CoordsArray & | coords | ||
) |
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).
atom1_pos | The position of atom i. |
atom2_pos | The position of atom j. |
e_IJ | The precalculated value \( \varepsilon_{IJ} \). |
r_IJ | The precalculated value \( R_{IJ}^* \). |
r_IJ_7 | The precalculated value \( R_{IJ}^{*^7} \). |
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).
r_ij | The interatomic distance \( R_{ij} \) of atom i and atom j. |
e_IJ | The precalculated value \( \varepsilon_{IJ} \). |
r_IJ | The precalculated value \( R_{IJ}^* \). |
r_IJ_7 | The precalculated value \( R_{IJ}^{*^7} \). |
ValueType CDPL::ForceField::calcMMFF94BondStretchingGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94BondStretchingGradient | ( | const MMFF94BondStretchingInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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).
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
atom2_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
force_const | The bond stretching force constant \( kb_{IJ} \). |
ref_length | The reference bond length \( r_{IJ}^0 \). |
ValueType CDPL::ForceField::calcMMFF94AngleBendingGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94AngleBendingGradient | ( | const MMFF94AngleBendingInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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.
term_atom1_pos | The position \( \vec{p_i} \) of atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of atom k. |
term_atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
ctr_atom_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
term_atom2_grad | The output variable storing the accumulated energy gradient contributions for atom k. |
linear | If true , the bond angle is linear. |
force_const | The angle bending force constant \( ka_{IJK} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
ValueType CDPL::ForceField::calcMMFF94StretchBendGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94StretchBendGradient | ( | const MMFF94StretchBendInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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.
term_atom1_pos | The position \( \vec{p_i} \) of atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of atom k. |
term_atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
ctr_atom_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
term_atom2_grad | The output variable storing the accumulated energy gradient contributions for atom k. |
ijk_force_const | The stretch-bend force constant \( kba_{IJK} \). |
kji_force_const | The stretch-bend force constant \( kba_{KJI} \). |
ref_angle | The reference bond angle \( \vartheta_{IJK}^0 \). |
ref_length1 | The reference bond length \( r_{IJ}^0 \). |
ref_length2 | The reference bond length \( r_{KJ}^0 \). |
ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94OutOfPlaneBendingGradient | ( | const MMFF94OutOfPlaneBendingInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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.
term_atom1_pos | The position \( \vec{p_i} \) of atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of atom k. |
oop_atom_pos | The position \( \vec{p_l} \) of the out-of-plane atom l. |
term_atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
ctr_atom_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
term_atom2_grad | The output variable storing the accumulated energy gradient contributions for atom k. |
oop_atom_grad | The output variable storing the accumulated energy gradient contributions for atom l. |
force_const | The out-of-plane bending force constant \( koop_{IJK \colon L} \). |
ValueType CDPL::ForceField::calcMMFF94TorsionGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94TorsionGradient | ( | const MMFF94TorsionInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom1_pos | The position \( \vec{p_j} \) of the central atom j. |
ctr_atom2_pos | The position \( \vec{p_k} \) of the central atom k. |
term_atom2_pos | The position \( \vec{p_l} \) of the terminal atom l. |
term_atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
ctr_atom1_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
ctr_atom2_grad | The output variable storing the accumulated energy gradient contributions for atom k. |
term_atom2_grad | The output variable storing the accumulated energy gradient contributions for atom l. |
tor_param1 | The torsion parameter \( V_1 \). |
tor_param2 | The torsion parameter \( V_2 \). |
tor_param3 | The torsion parameter \( V_3 \). |
ValueType CDPL::ForceField::calcMMFF94ElectrostaticGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94ElectrostaticGradient | ( | const MMFF94ElectrostaticInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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 \( EQ_{14} \: 0.75 \)).
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
atom2_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
atom1_chg | The partial atom charge \( q_i \) of atom i. |
atom2_chg | The partial atom charge \( q_j \) of atom j. |
scale_fact | The scaling factor for \( S \) depending on the topological i-j distance. |
de_const | The dielectric constant \( D \). |
dist_expo | The exponent \( n \). |
ValueType CDPL::ForceField::calcMMFF94VanDerWaalsGradient | ( | Iter | beg, |
const Iter & | end, | ||
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
ValueType CDPL::ForceField::calcMMFF94VanDerWaalsGradient | ( | const MMFF94VanDerWaalsInteraction & | iaction, |
const CoordsArray & | coords, | ||
GradVector & | grad | ||
) |
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).
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
atom1_grad | The output variable storing the accumulated energy gradient contributions for atom i. |
atom2_grad | The output variable storing the accumulated energy gradient contributions for atom j. |
e_IJ | The precalculated value \( \varepsilon_{IJ} \). |
r_IJ | The precalculated value \( R_{IJ}^* \). |
r_IJ_7 | The precalculated value \( R_{IJ}^{*^7} \). |
CDPL_FORCEFIELD_API const Chem::FragmentList::SharedPointer& CDPL::ForceField::getMMFF94AromaticRings | ( | const Chem::MolecularGraph & | molgraph | ) |
CDPL_FORCEFIELD_API void CDPL::ForceField::setMMFF94AromaticRings | ( | Chem::MolecularGraph & | molgraph, |
const Chem::FragmentList::SharedPointer & | rings | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::clearMMFF94AromaticRings | ( | Chem::MolecularGraph & | molgraph | ) |
CDPL_FORCEFIELD_API bool CDPL::ForceField::hasMMFF94AromaticRings | ( | const Chem::MolecularGraph & | molgraph | ) |
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer CDPL::ForceField::perceiveMMFF94AromaticRings | ( | const Chem::MolecularGraph & | molgraph | ) |
CDPL_FORCEFIELD_API Chem::FragmentList::SharedPointer CDPL::ForceField::perceiveMMFF94AromaticRings | ( | Chem::MolecularGraph & | molgraph, |
bool | overwrite | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::assignMMFF94AtomTypes | ( | Chem::MolecularGraph & | molgraph, |
bool | strict, | ||
bool | overwrite | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::assignMMFF94BondTypeIndices | ( | Chem::MolecularGraph & | molgraph, |
bool | strict, | ||
bool | overwrite | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::calcMMFF94AtomCharges | ( | Chem::MolecularGraph & | molgraph, |
bool | strict, | ||
bool | overwrite | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::assignUFFAtomTypes | ( | Chem::MolecularGraph & | molgraph, |
bool | overwrite | ||
) |
CDPL_FORCEFIELD_API void CDPL::ForceField::filterInteractions | ( | const MMFF94InteractionData & | ia_data, |
MMFF94InteractionData & | filtered_ia_data, | ||
const Util::BitSet & | inc_atom_mask | ||
) |
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.
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
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.
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
bond_length1 | Output variable for the bond length \( r_{ij} \). |
bond_length2 | Output variable for the bond length \( r_{jk} \). |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
bond_length1 | Output variable for the bond length \( r_{ij} \). |
bond_length2 | Output variable for the bond length \( r_{jk} \). |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
r_ij | The length of the bond between atom i and j. |
r_jk | The length of the bond between atom j and k. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
r_ij | The length of the bond between atom i and j. |
r_jk | The length of the bond between atom j and k. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
oop_atom_pos | The position \( \vec{p_l} \) of the out-of-plane atom l. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
oop_atom_pos | The position \( \vec{p_l} \) of the out-of-plane atom l. |
r_jl | The length of the bond between atom j and atom l. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom1_pos | The position \( \vec{p_j} \) of the central atom j. |
ctr_atom2_pos | The position \( \vec{p_k} \) of the central atom k. |
term_atom2_pos | The position \( \vec{p_l} \) of the terminal atom l. |
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.
atom1_pos | The position \( \vec{p_i} \) of atom i. |
atom2_pos | The position \( \vec{p_j} \) of atom j. |
atom1_deriv | Output variable for the calculated partial derivative \( \frac{\partial r_{ij}}{\partial \vec{p_i}} \) at the given atom positions. |
atom2_deriv | Output variable for the calculated partial derivative \( \frac{\partial r_{ij}}{\partial \vec{p_j}} \) at the given atom positions. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of atom k. |
term_atom1_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_i}} \) at the given atom positions. |
ctr_atom_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_j}} \) at the given atom positions. |
term_atom2_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\vartheta_{ijk})}{\partial \vec{p_k}} \) at the given atom positions. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom1_pos | The position \( \vec{p_j} \) of the central atom j. |
ctr_atom2_pos | The position \( \vec{p_k} \) of the central atom k. |
term_atom2_pos | The position \( \vec{p_l} \) of the terminal atom l. |
term_atom1_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions. |
ctr_atom1_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions. |
ctr_atom2_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions. |
term_atom2_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\Phi_{ijkl})}{\partial \vec{p_l}} \) at the given atom positions. |
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.
term_atom1_pos | The position \( \vec{p_i} \) of the terminal atom i. |
ctr_atom_pos | The position \( \vec{p_j} \) of the central atom j. |
term_atom2_pos | The position \( \vec{p_k} \) of the terminal atom k. |
oop_atom_pos | The position \( \vec{p_l} \) of the out-of-plane atom l. |
term_atom1_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_i}} \) at the given atom positions. |
ctr_atom_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_j}} \) at the given atom positions. |
term_atom2_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_k}} \) at the given atom positions. |
oop_atom_deriv | Output variable for the calculated partial derivative \( \frac{\partial \cos(\omega_{ijkl})}{\partial \vec{p_l}} \) at the given atom positions. |