CDPL.ForceField Package Reference

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

Classes
class	AtomProperty
	Provides keys for built-in Chem.Atom properties. More...
class	BondProperty
	Provides keys for built-in Chem.Bond properties. More...
class	ElasticPotential
class	ElasticPotentialList
class	Error
class	InteractionFilterFunction2
class	InteractionFilterFunction3
class	InteractionFilterFunction4
class	InteractionType
	Provides flags for the specification of a set of force field interaction types. More...
class	MMFF94AngleBendingInteraction
class	MMFF94AngleBendingInteractionList
class	MMFF94AngleBendingInteractionParameterizer
class	MMFF94AngleBendingParameterTable
class	MMFF94AromaticAtomTypeDefinitionTable
class	MMFF94AromaticSSSRSubset
	Implements the extraction of all rings in the SSSR of a molecular graph that are aromatic according to MMFF94 conventions. More...
class	MMFF94AtomChargeFunction
	A generic wrapper class used to store a user-defined MMFF94 partial atom charge function. More...
class	MMFF94AtomTypePropertyTable
class	MMFF94AtomTyper
class	MMFF94BondChargeIncrementTable
class	MMFF94BondStretchingInteraction
class	MMFF94BondStretchingInteractionList
class	MMFF94BondStretchingInteractionParameterizer
class	MMFF94BondStretchingParameterTable
class	MMFF94BondStretchingRuleParameterTable
class	MMFF94BondTypeIndexFunction
	A generic wrapper class used to store a user-defined MMFF94 bond type index function. More...
class	MMFF94BondTyper
class	MMFF94ChargeCalculator
class	MMFF94DefaultStretchBendParameterTable
class	MMFF94ElectrostaticInteraction
class	MMFF94ElectrostaticInteractionList
class	MMFF94ElectrostaticInteractionParameterizer
class	MMFF94EnergyCalculator
class	MMFF94FormalAtomChargeDefinitionTable
class	MMFF94GradientCalculator
class	MMFF94HeavyToHydrogenAtomTypeMap
class	MMFF94InteractionData
class	MMFF94InteractionParameterizer
class	MMFF94NumericAtomTypeFunction
	A generic wrapper class used to store a user-defined numeric MMFF94 atom type function. More...
class	MMFF94OutOfPlaneBendingInteraction
class	MMFF94OutOfPlaneBendingInteractionList
class	MMFF94OutOfPlaneBendingInteractionParameterizer
class	MMFF94OutOfPlaneBendingParameterTable
class	MMFF94ParameterSet
	Provides flags for the specification of the MMFF94 parameter set to use. More...
class	MMFF94PartialBondChargeIncrementTable
class	MMFF94PrimaryToParameterAtomTypeMap
class	MMFF94RingSetFunction
	A generic wrapper class used to store a user-defined MMFF94 ring set function. More...
class	MMFF94StretchBendInteraction
class	MMFF94StretchBendInteractionList
class	MMFF94StretchBendInteractionParameterizer
class	MMFF94StretchBendParameterTable
class	MMFF94SymbolicAtomTypeFunction
	A generic wrapper class used to store a user-defined symbolic MMFF94 atom type function. More...
class	MMFF94SymbolicAtomTypePatternTable
class	MMFF94SymbolicToNumericAtomTypeMap
class	MMFF94TorsionInteraction
class	MMFF94TorsionInteractionList
class	MMFF94TorsionInteractionParameterizer
class	MMFF94TorsionParameterTable
class	MMFF94VanDerWaalsAtomParameters
class	MMFF94VanDerWaalsInteraction
class	MMFF94VanDerWaalsInteractionList
class	MMFF94VanDerWaalsInteractionParameterizer
class	MMFF94VanDerWaalsParameterTable
class	MolecularGraphProperty
	Provides keys for built-in Chem.MolecularGraph properties. More...
class	ParameterizationFailed
class	TopologicalAtomDistanceFunction
	A generic wrapper class used to store a user-defined topological atom-pair distance function. More...
class	UFFAtomType
	Provides constants for the specification of Universal Force Field (UFF) atom types. More...
class	UFFAtomTypePropertyTable

Functions
None	clearMMFF94Charge (Chem.Atom atom)
bool	hasMMFF94Charge (Chem.Atom atom)
float	getMMFF94Charge (Chem.Atom atom)
None	setMMFF94Charge (Chem.Atom atom, float charge)
int	perceiveUFFType (Chem.Atom atom, Chem.MolecularGraph molgraph)
None	clearUFFType (Chem.Atom atom)
bool	hasUFFType (Chem.Atom atom)
int	getUFFType (Chem.Atom atom)
None	setUFFType (Chem.Atom atom, int type)
None	clearMMFF94SymbolicType (Chem.Atom atom)
bool	hasMMFF94SymbolicType (Chem.Atom atom)
str	getMMFF94SymbolicType (Chem.Atom atom)
None	setMMFF94SymbolicType (Chem.Atom atom, str type)
None	clearMMFF94NumericType (Chem.Atom atom)
bool	hasMMFF94NumericType (Chem.Atom atom)
int	getMMFF94NumericType (Chem.Atom atom)
None	setMMFF94NumericType (Chem.Atom atom, int type)
None	clearMMFF94TypeIndex (Chem.Bond bond)
bool	hasMMFF94TypeIndex (Chem.Bond bond)
int	getMMFF94TypeIndex (Chem.Bond bond)
None	setMMFF94TypeIndex (Chem.Bond bond, int type_idx)
float	calcElasticPotentialGradient (ElasticPotentialList list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcElasticPotentialEnergy (ElasticPotentialList list, Math.Vector3DArray coords)
float	calcElasticPotentialGradient (ElasticPotential pot, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcElasticPotentialEnergy (ElasticPotential pot, Math.Vector3DArray coords)
float	calcMMFF94AngleBendingGradient (MMFF94AngleBendingInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94AngleBendingEnergy (MMFF94AngleBendingInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94AngleBendingGradient (MMFF94AngleBendingInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94AngleBendingEnergy (MMFF94AngleBendingInteraction iaction, Math.Vector3DArray coords)
float	calcMMFF94BondStretchingGradient (MMFF94BondStretchingInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94BondStretchingEnergy (MMFF94BondStretchingInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94BondStretchingGradient (MMFF94BondStretchingInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94BondStretchingEnergy (MMFF94BondStretchingInteraction iaction, Math.Vector3DArray coords)
float	calcMMFF94ElectrostaticGradient (MMFF94ElectrostaticInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94ElectrostaticEnergy (MMFF94ElectrostaticInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94ElectrostaticGradient (MMFF94ElectrostaticInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94ElectrostaticEnergy (MMFF94ElectrostaticInteraction iaction, Math.Vector3DArray coords)
None	filterInteractions (MMFF94InteractionData ia_data, MMFF94InteractionData filtered_ia_data, Util.BitSet inc_atom_mask)
float	calcMMFF94OutOfPlaneBendingGradient (MMFF94OutOfPlaneBendingInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94OutOfPlaneBendingEnergy (MMFF94OutOfPlaneBendingInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94OutOfPlaneBendingGradient (MMFF94OutOfPlaneBendingInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94OutOfPlaneBendingEnergy (MMFF94OutOfPlaneBendingInteraction iaction, Math.Vector3DArray coords)
float	calcMMFF94StretchBendGradient (MMFF94StretchBendInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94StretchBendEnergy (MMFF94StretchBendInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94StretchBendGradient (MMFF94StretchBendInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94StretchBendEnergy (MMFF94StretchBendInteraction iaction, Math.Vector3DArray coords)
float	calcMMFF94TorsionGradient (MMFF94TorsionInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94TorsionEnergy (MMFF94TorsionInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94TorsionGradient (MMFF94TorsionInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94TorsionEnergy (MMFF94TorsionInteraction iaction, Math.Vector3DArray coords)
float	calcMMFF94VanDerWaalsGradient (MMFF94VanDerWaalsInteractionList ia_list, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94VanDerWaalsEnergy (MMFF94VanDerWaalsInteractionList ia_list, Math.Vector3DArray coords)
float	calcMMFF94VanDerWaalsGradient (MMFF94VanDerWaalsInteraction iaction, Math.Vector3DArray coords, Math.Vector3DArray grad)
float	calcMMFF94VanDerWaalsEnergy (MMFF94VanDerWaalsInteraction iaction, Math.Vector3DArray coords)
None	assignMMFF94BondTypeIndices (Chem.MolecularGraph molgraph, bool strict, bool overwrite)
None	calcMMFF94AtomCharges (Chem.MolecularGraph molgraph, bool strict, bool overwrite)
None	assignMMFF94AtomTypes (Chem.MolecularGraph molgraph, bool strict, bool overwrite)
None	assignUFFAtomTypes (Chem.MolecularGraph molgraph, bool overwrite)
Chem.FragmentList	perceiveMMFF94AromaticRings (Chem.MolecularGraph molgraph)
Chem.FragmentList	perceiveMMFF94AromaticRings (Chem.MolecularGraph molgraph, bool overwrite)
None	clearMMFF94AromaticRings (Chem.MolecularGraph molgraph)
bool	hasMMFF94AromaticRings (Chem.MolecularGraph molgraph)
Chem.FragmentList	getMMFF94AromaticRings (Chem.MolecularGraph molgraph)
None	setMMFF94AromaticRings (Chem.MolecularGraph molgraph, Chem.FragmentList rings)
float	calcDistance (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos)
	Calculates the distance \( r_{ij} \) between two atoms i and j. More...
float	calcSquaredDistance (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos)
	Calculates the squared distance \( r_{ij}^2 \) between two atoms i and j. More...
tuple	calcBondLengthsAndAngle (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos)
float	calcBondAngle (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, float r_ij, float r_jk)
	Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
float	calcBondAngle (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos)
	Calculates the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
float	calcOutOfPlaneAngle (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D oop_atom_pos, float 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...
float	calcDistanceDerivatives (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, Math.Vector3D atom1_deriv, Math.Vector3D 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...
float	calcBondAngleCosDerivatives (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D term_atom1_deriv, Math.Vector3D ctr_atom_deriv, Math.Vector3D 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...
float	calcOutOfPlaneAngleCosDerivatives (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D oop_atom_pos, Math.Vector3D term_atom1_deriv, Math.Vector3D ctr_atom_deriv, Math.Vector3D term_atom2_deriv, Math.Vector3D 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...
float	calcDihedralAngleCosDerivatives (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom1_pos, Math.Vector3D ctr_atom2_pos, Math.Vector3D term_atom2_pos, Math.Vector3D term_atom1_deriv, Math.Vector3D ctr_atom1_deriv, Math.Vector3D ctr_atom2_deriv, Math.Vector3D 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...
tuple	calcBondLengthsAndAngleCos (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos)
float	calcBondAngleCos (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, float r_ij, float r_jk)
	Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
float	calcBondAngleCos (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos)
	Calculates the cosine of the bond angle \( \vartheta_{ijk} \) between the two bonds i-j and j-k. More...
float	calcDihedralAngleCos (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom1_pos, Math.Vector3D ctr_atom2_pos, Math.Vector3D 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...
float	calcMMFF94ElectrostaticGradient (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, Math.Vector3D atom1_grad, Math.Vector3D atom2_grad, float atom1_chg, float atom2_chg, float scale_fact, float de_const, float dist_expo)
	Calculates the electrostatic interaction energy gradient \( \nabla EQ_{ij} \) for the atom pair i-j. More...
float	calcMMFF94StretchBendGradient (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D term_atom1_grad, Math.Vector3D ctr_atom_grad, Math.Vector3D term_atom2_grad, float ijk_force_const, float kji_force_const, float ref_angle, float ref_length1, float ref_length2)
	Calculates the stretch-bend interaction energy gradient \( \nabla EBA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94AngleBendingGradient (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D term_atom1_grad, Math.Vector3D ctr_atom_grad, Math.Vector3D term_atom2_grad, bool linear, float force_const, float ref_angle)
	Calculates the angle bending interaction energy gradient \( \nabla EA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94OutOfPlaneBendingGradient (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D oop_atom_pos, Math.Vector3D term_atom1_grad, Math.Vector3D ctr_atom_grad, Math.Vector3D term_atom2_grad, Math.Vector3D oop_atom_grad, float 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...
float	calcMMFF94BondStretchingGradient (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, Math.Vector3D atom1_grad, Math.Vector3D atom2_grad, float force_const, float ref_length)
	Calculates the bond stretching interaction energy gradient \( \nabla EB_{ij} \) for the bond i-j. More...
float	calcElasticPotentialGradient (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, Math.Vector3D atom1_grad, Math.Vector3D atom2_grad, float force_const, float ref_length)
	Calculates the elastic potential energy gradient \( \nabla E_{ij} \) for a pair of atoms i-j. More...
float	calcMMFF94TorsionGradient (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom1_pos, Math.Vector3D ctr_atom2_pos, Math.Vector3D term_atom2_pos, Math.Vector3D term_atom1_grad, Math.Vector3D ctr_atom1_grad, Math.Vector3D ctr_atom2_grad, Math.Vector3D term_atom2_grad, float tor_param1, float tor_param2, float 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...
float	calcMMFF94VanDerWaalsGradient (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, Math.Vector3D atom1_grad, Math.Vector3D atom2_grad, float e_IJ, float r_IJ, float r_IJ_7)
	Calculates the van der Waals interaction energy gradient \( \nabla E_{vdW_{ij}} \) for the atom pair i-j. More...
float	calcMMFF94ElectrostaticEnergy (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, float atom1_chg, float atom2_chg, float scale_fact, float de_const, float dist_expo)
	Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More...
float	calcMMFF94StretchBendEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, float ijk_force_const, float kji_force_const, float ref_angle, float ref_length1, float ref_length2)
	Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94StretchBendEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, float r_ij, float r_jk, float ijk_force_const, float kji_force_const, float ref_angle, float ref_length1, float ref_length2)
	Calculates the stretch-bend interaction energy \( EBA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94AngleBendingEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, bool linear, float force_const, float ref_angle)
	Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94AngleBendingEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, float r_ij, float r_jk, bool linear, float force_const, float ref_angle)
	Calculates the angle bending interaction energy \( EA_{ijk} \) for two bonds i-j and j-k. More...
float	calcMMFF94OutOfPlaneBendingEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D oop_atom_pos, float 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...
float	calcMMFF94OutOfPlaneBendingEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom_pos, Math.Vector3D term_atom2_pos, Math.Vector3D oop_atom_pos, float r_jl, float 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...
float	calcMMFF94BondStretchingEnergy (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, float force_const, float ref_length)
	Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More...
float	calcElasticPotentialEnergy (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, float force_const, float ref_length)
	Calculates the energy \( E_{ij} \) of an elastic potential applied on a pair of atoms i-j. More...
float	calcMMFF94TorsionEnergy (Math.Vector3D term_atom1_pos, Math.Vector3D ctr_atom1_pos, Math.Vector3D ctr_atom2_pos, Math.Vector3D term_atom2_pos, float tor_param1, float tor_param2, float 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...
float	calcMMFF94VanDerWaalsEnergy (Math.Vector3D atom1_pos, Math.Vector3D atom2_pos, float e_IJ, float r_IJ, float r_IJ_7)
	Calculates the van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More...
float	calcMMFF94ElectrostaticEnergy (float r_ij, float atom1_chg, float atom2_chg, float scale_fact, float de_const, float dist_expo)
	Calculates the electrostatic interaction energy \( EQ_{ij} \) for the atom pair i-j. More...
float	calcMMFF94BondStretchingEnergy (float r_ij, float force_const, float ref_length)
	Calculates the bond stretching interaction energy \( EB_{ij} \) for the bond i-j. More...
float	calcMMFF94VanDerWaalsEnergy (float r_ij, float e_IJ, float r_IJ, float r_IJ_7)
	Calculates the van der Waals interaction energy \( E_{vdW_{ij}} \) for the atom pair i-j. More...

Detailed Description

Contains classes and functions related to molecular force fields.

Function Documentation

clearMMFF94Charge()

None CDPL.ForceField.clearMMFF94Charge

(

Chem.Atom

atom

)

Parameters

atom

hasMMFF94Charge()

bool CDPL.ForceField.hasMMFF94Charge

(

Chem.Atom

atom

)

Parameters

atom

Returns

getMMFF94Charge()

float CDPL.ForceField.getMMFF94Charge

(

Chem.Atom

atom

)

Parameters

atom

Returns

setMMFF94Charge()

None CDPL.ForceField.setMMFF94Charge	(	Chem.Atom	atom,
		float	charge
	)

Parameters

atom
charge

perceiveUFFType()

int CDPL.ForceField.perceiveUFFType	(	Chem.Atom	atom,
		Chem.MolecularGraph	molgraph
	)

Parameters

atom
molgraph

Returns

clearUFFType()

None CDPL.ForceField.clearUFFType

(

Chem.Atom

atom

)

Parameters

atom

hasUFFType()

bool CDPL.ForceField.hasUFFType

(

Chem.Atom

atom

)

Parameters

atom

Returns

getUFFType()

int CDPL.ForceField.getUFFType

(

Chem.Atom

atom

)

Parameters

atom

Returns

setUFFType()

None CDPL.ForceField.setUFFType	(	Chem.Atom	atom,
		int	type
	)

Parameters

atom
type

clearMMFF94SymbolicType()

None CDPL.ForceField.clearMMFF94SymbolicType

(

Chem.Atom

atom

)

Parameters

atom

hasMMFF94SymbolicType()

bool CDPL.ForceField.hasMMFF94SymbolicType

(

Chem.Atom

atom

)

Parameters

atom

Returns

getMMFF94SymbolicType()

str CDPL.ForceField.getMMFF94SymbolicType

(

Chem.Atom

atom

)

Parameters

atom

Returns

setMMFF94SymbolicType()

None CDPL.ForceField.setMMFF94SymbolicType	(	Chem.Atom	atom,
		str	type
	)

Parameters

atom
type

clearMMFF94NumericType()

None CDPL.ForceField.clearMMFF94NumericType

(

Chem.Atom

atom

)

Parameters

atom

hasMMFF94NumericType()

bool CDPL.ForceField.hasMMFF94NumericType

(

Chem.Atom

atom

)

Parameters

atom

Returns

getMMFF94NumericType()

int CDPL.ForceField.getMMFF94NumericType

(

Chem.Atom

atom

)

Parameters

atom

Returns

setMMFF94NumericType()

None CDPL.ForceField.setMMFF94NumericType	(	Chem.Atom	atom,
		int	type
	)

Parameters

atom
type

clearMMFF94TypeIndex()

None CDPL.ForceField.clearMMFF94TypeIndex

(

Chem.Bond

bond

)

Parameters

bond

hasMMFF94TypeIndex()

bool CDPL.ForceField.hasMMFF94TypeIndex

(

Chem.Bond

bond

)

Parameters

bond

Returns

getMMFF94TypeIndex()

int CDPL.ForceField.getMMFF94TypeIndex

(

Chem.Bond

bond

)

Parameters

bond

Returns

setMMFF94TypeIndex()

None CDPL.ForceField.setMMFF94TypeIndex	(	Chem.Bond	bond,
		int	type_idx
	)

Parameters

bond
type_idx

calcElasticPotentialGradient() [1/3]

float CDPL.ForceField.calcElasticPotentialGradient	(	ElasticPotentialList	list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

list
coords
grad

Returns

calcElasticPotentialEnergy() [1/3]

float CDPL.ForceField.calcElasticPotentialEnergy	(	ElasticPotentialList	list,
		Math.Vector3DArray	coords
	)

Parameters

list
coords

Returns

calcElasticPotentialGradient() [2/3]

float CDPL.ForceField.calcElasticPotentialGradient	(	ElasticPotential	pot,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

pot
coords
grad

Returns

calcElasticPotentialEnergy() [2/3]

float CDPL.ForceField.calcElasticPotentialEnergy	(	ElasticPotential	pot,
		Math.Vector3DArray	coords
	)

Parameters

pot
coords

Returns

calcMMFF94AngleBendingGradient() [1/3]

float CDPL.ForceField.calcMMFF94AngleBendingGradient	(	MMFF94AngleBendingInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94AngleBendingEnergy() [1/4]

float CDPL.ForceField.calcMMFF94AngleBendingEnergy	(	MMFF94AngleBendingInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94AngleBendingGradient() [2/3]

float CDPL.ForceField.calcMMFF94AngleBendingGradient	(	MMFF94AngleBendingInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94AngleBendingEnergy() [2/4]

float CDPL.ForceField.calcMMFF94AngleBendingEnergy	(	MMFF94AngleBendingInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

calcMMFF94BondStretchingGradient() [1/3]

float CDPL.ForceField.calcMMFF94BondStretchingGradient	(	MMFF94BondStretchingInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94BondStretchingEnergy() [1/4]

float CDPL.ForceField.calcMMFF94BondStretchingEnergy	(	MMFF94BondStretchingInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94BondStretchingGradient() [2/3]

float CDPL.ForceField.calcMMFF94BondStretchingGradient	(	MMFF94BondStretchingInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94BondStretchingEnergy() [2/4]

float CDPL.ForceField.calcMMFF94BondStretchingEnergy	(	MMFF94BondStretchingInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

calcMMFF94ElectrostaticGradient() [1/3]

float CDPL.ForceField.calcMMFF94ElectrostaticGradient	(	MMFF94ElectrostaticInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94ElectrostaticEnergy() [1/4]

float CDPL.ForceField.calcMMFF94ElectrostaticEnergy	(	MMFF94ElectrostaticInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94ElectrostaticGradient() [2/3]

float CDPL.ForceField.calcMMFF94ElectrostaticGradient	(	MMFF94ElectrostaticInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94ElectrostaticEnergy() [2/4]

float CDPL.ForceField.calcMMFF94ElectrostaticEnergy	(	MMFF94ElectrostaticInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

filterInteractions()

None CDPL.ForceField.filterInteractions	(	MMFF94InteractionData	ia_data,
		MMFF94InteractionData	filtered_ia_data,
		Util.BitSet	inc_atom_mask
	)

Parameters

ia_data
filtered_ia_data
inc_atom_mask

calcMMFF94OutOfPlaneBendingGradient() [1/3]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingGradient	(	MMFF94OutOfPlaneBendingInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94OutOfPlaneBendingEnergy() [1/4]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingEnergy	(	MMFF94OutOfPlaneBendingInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94OutOfPlaneBendingGradient() [2/3]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingGradient	(	MMFF94OutOfPlaneBendingInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94OutOfPlaneBendingEnergy() [2/4]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingEnergy	(	MMFF94OutOfPlaneBendingInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

calcMMFF94StretchBendGradient() [1/3]

float CDPL.ForceField.calcMMFF94StretchBendGradient	(	MMFF94StretchBendInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94StretchBendEnergy() [1/4]

float CDPL.ForceField.calcMMFF94StretchBendEnergy	(	MMFF94StretchBendInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94StretchBendGradient() [2/3]

float CDPL.ForceField.calcMMFF94StretchBendGradient	(	MMFF94StretchBendInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94StretchBendEnergy() [2/4]

float CDPL.ForceField.calcMMFF94StretchBendEnergy	(	MMFF94StretchBendInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

calcMMFF94TorsionGradient() [1/3]

float CDPL.ForceField.calcMMFF94TorsionGradient	(	MMFF94TorsionInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94TorsionEnergy() [1/3]

float CDPL.ForceField.calcMMFF94TorsionEnergy	(	MMFF94TorsionInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94TorsionGradient() [2/3]

float CDPL.ForceField.calcMMFF94TorsionGradient	(	MMFF94TorsionInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94TorsionEnergy() [2/3]

float CDPL.ForceField.calcMMFF94TorsionEnergy	(	MMFF94TorsionInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

calcMMFF94VanDerWaalsGradient() [1/3]

float CDPL.ForceField.calcMMFF94VanDerWaalsGradient	(	MMFF94VanDerWaalsInteractionList	ia_list,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

ia_list
coords
grad

Returns

calcMMFF94VanDerWaalsEnergy() [1/4]

float CDPL.ForceField.calcMMFF94VanDerWaalsEnergy	(	MMFF94VanDerWaalsInteractionList	ia_list,
		Math.Vector3DArray	coords
	)

Parameters

ia_list
coords

Returns

calcMMFF94VanDerWaalsGradient() [2/3]

float CDPL.ForceField.calcMMFF94VanDerWaalsGradient	(	MMFF94VanDerWaalsInteraction	iaction,
		Math.Vector3DArray	coords,
		Math.Vector3DArray	grad
	)

Parameters

iaction
coords
grad

Returns

calcMMFF94VanDerWaalsEnergy() [2/4]

float CDPL.ForceField.calcMMFF94VanDerWaalsEnergy	(	MMFF94VanDerWaalsInteraction	iaction,
		Math.Vector3DArray	coords
	)

Parameters

iaction
coords

Returns

assignMMFF94BondTypeIndices()

None CDPL.ForceField.assignMMFF94BondTypeIndices	(	Chem.MolecularGraph	molgraph,
		bool	strict,
		bool	overwrite
	)

Parameters

molgraph
strict
overwrite

calcMMFF94AtomCharges()

None CDPL.ForceField.calcMMFF94AtomCharges	(	Chem.MolecularGraph	molgraph,
		bool	strict,
		bool	overwrite
	)

Parameters

molgraph
strict
overwrite

assignMMFF94AtomTypes()

None CDPL.ForceField.assignMMFF94AtomTypes	(	Chem.MolecularGraph	molgraph,
		bool	strict,
		bool	overwrite
	)

Parameters

molgraph
strict
overwrite

assignUFFAtomTypes()

None CDPL.ForceField.assignUFFAtomTypes	(	Chem.MolecularGraph	molgraph,
		bool	overwrite
	)

Parameters

molgraph
overwrite

perceiveMMFF94AromaticRings() [1/2]

Chem.FragmentList CDPL.ForceField.perceiveMMFF94AromaticRings

(

Chem.MolecularGraph

molgraph

)

Parameters

molgraph

Returns

perceiveMMFF94AromaticRings() [2/2]

Chem.FragmentList CDPL.ForceField.perceiveMMFF94AromaticRings	(	Chem.MolecularGraph	molgraph,
		bool	overwrite
	)

Parameters

molgraph
overwrite

Returns

clearMMFF94AromaticRings()

None CDPL.ForceField.clearMMFF94AromaticRings

(

Chem.MolecularGraph

molgraph

)

Parameters

molgraph

hasMMFF94AromaticRings()

bool CDPL.ForceField.hasMMFF94AromaticRings

(

Chem.MolecularGraph

molgraph

)

Parameters

molgraph

Returns

getMMFF94AromaticRings()

Chem.FragmentList CDPL.ForceField.getMMFF94AromaticRings

(

Chem.MolecularGraph

molgraph

)

Parameters

molgraph

Returns

setMMFF94AromaticRings()

None CDPL.ForceField.setMMFF94AromaticRings	(	Chem.MolecularGraph	molgraph,
		Chem.FragmentList	rings
	)

Parameters

molgraph
rings

calcDistance()

float CDPL.ForceField.calcDistance	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos
	)

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

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

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

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

Parameters

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

Returns

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

calcSquaredDistance()

float CDPL.ForceField.calcSquaredDistance	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos
	)

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

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

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

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

Parameters

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

Returns

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

calcBondLengthsAndAngle()

tuple CDPL.ForceField.calcBondLengthsAndAngle	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos
	)

Parameters

term_atom1_pos
ctr_atom_pos
term_atom2_pos

Returns

calcBondAngle() [1/2]

float CDPL.ForceField.calcBondAngle	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		float	r_ij,
		float	r_jk
	)

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

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

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

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

Parameters

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

Returns

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

calcBondAngle() [2/2]

float CDPL.ForceField.calcBondAngle	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos
	)

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

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

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

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

Parameters

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

Returns

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

calcOutOfPlaneAngle()

float CDPL.ForceField.calcOutOfPlaneAngle	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	oop_atom_pos,
		float	r_jl
	)

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

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

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

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

Parameters

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

Returns

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

calcDistanceDerivatives()

float CDPL.ForceField.calcDistanceDerivatives	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		Math.Vector3D	atom1_deriv,
		Math.Vector3D	atom2_deriv
	)

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

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

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

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

Parameters

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

Returns

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

calcBondAngleCosDerivatives()

float CDPL.ForceField.calcBondAngleCosDerivatives	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	term_atom1_deriv,
		Math.Vector3D	ctr_atom_deriv,
		Math.Vector3D	term_atom2_deriv
	)

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

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

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

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

Parameters

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

Returns

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

calcOutOfPlaneAngleCosDerivatives()

float CDPL.ForceField.calcOutOfPlaneAngleCosDerivatives	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	oop_atom_pos,
		Math.Vector3D	term_atom1_deriv,
		Math.Vector3D	ctr_atom_deriv,
		Math.Vector3D	term_atom2_deriv,
		Math.Vector3D	oop_atom_deriv
	)

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

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

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

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

Parameters

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

Returns

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

calcDihedralAngleCosDerivatives()

float CDPL.ForceField.calcDihedralAngleCosDerivatives	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom1_pos,
		Math.Vector3D	ctr_atom2_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	term_atom1_deriv,
		Math.Vector3D	ctr_atom1_deriv,
		Math.Vector3D	ctr_atom2_deriv,
		Math.Vector3D	term_atom2_deriv
	)

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

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

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

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

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

Parameters

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

Returns

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

calcBondLengthsAndAngleCos()

tuple CDPL.ForceField.calcBondLengthsAndAngleCos	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos
	)

Parameters

term_atom1_pos
ctr_atom_pos
term_atom2_pos

Returns

calcBondAngleCos() [1/2]

float CDPL.ForceField.calcBondAngleCos	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		float	r_ij,
		float	r_jk
	)

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

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

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

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

Parameters

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

Returns

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

calcBondAngleCos() [2/2]

float CDPL.ForceField.calcBondAngleCos	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos
	)

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

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

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

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

Parameters

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

Returns

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

calcDihedralAngleCos()

float CDPL.ForceField.calcDihedralAngleCos	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom1_pos,
		Math.Vector3D	ctr_atom2_pos,
		Math.Vector3D	term_atom2_pos
	)

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

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

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

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

Parameters

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

Returns

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

calcMMFF94ElectrostaticGradient() [3/3]

float CDPL.ForceField.calcMMFF94ElectrostaticGradient	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		Math.Vector3D	atom1_grad,
		Math.Vector3D	atom2_grad,
		float	atom1_chg,
		float	atom2_chg,
		float	scale_fact,
		float	de_const,
		float	dist_expo
	)

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

Energy function:

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94StretchBendGradient() [3/3]

float CDPL.ForceField.calcMMFF94StretchBendGradient	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	term_atom1_grad,
		Math.Vector3D	ctr_atom_grad,
		Math.Vector3D	term_atom2_grad,
		float	ijk_force_const,
		float	kji_force_const,
		float	ref_angle,
		float	ref_length1,
		float	ref_length2
	)

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

Energy function:

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94AngleBendingGradient() [3/3]

float CDPL.ForceField.calcMMFF94AngleBendingGradient	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	term_atom1_grad,
		Math.Vector3D	ctr_atom_grad,
		Math.Vector3D	term_atom2_grad,
		bool	linear,
		float	force_const,
		float	ref_angle
	)

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

Energy function employed for the non-linear case:

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

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

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

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

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94OutOfPlaneBendingGradient() [3/3]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingGradient	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	oop_atom_pos,
		Math.Vector3D	term_atom1_grad,
		Math.Vector3D	ctr_atom_grad,
		Math.Vector3D	term_atom2_grad,
		Math.Vector3D	oop_atom_grad,
		float	force_const
	)

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

Energy function:

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94BondStretchingGradient() [3/3]

float CDPL.ForceField.calcMMFF94BondStretchingGradient	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		Math.Vector3D	atom1_grad,
		Math.Vector3D	atom2_grad,
		float	force_const,
		float	ref_length
	)

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

Energy function:

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcElasticPotentialGradient() [3/3]

float CDPL.ForceField.calcElasticPotentialGradient	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		Math.Vector3D	atom1_grad,
		Math.Vector3D	atom2_grad,
		float	force_const,
		float	ref_length
	)

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

Energy function:

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

Since

1.1

calcMMFF94TorsionGradient() [3/3]

float CDPL.ForceField.calcMMFF94TorsionGradient	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom1_pos,
		Math.Vector3D	ctr_atom2_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	term_atom1_grad,
		Math.Vector3D	ctr_atom1_grad,
		Math.Vector3D	ctr_atom2_grad,
		Math.Vector3D	term_atom2_grad,
		float	tor_param1,
		float	tor_param2,
		float	tor_param3
	)

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

Energy function:

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94VanDerWaalsGradient() [3/3]

float CDPL.ForceField.calcMMFF94VanDerWaalsGradient	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		Math.Vector3D	atom1_grad,
		Math.Vector3D	atom2_grad,
		float	e_IJ,
		float	r_IJ,
		float	r_IJ_7
	)

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

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

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

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

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

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

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

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

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

Parameters

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

Returns

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

Note

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

calcMMFF94ElectrostaticEnergy() [3/4]

float CDPL.ForceField.calcMMFF94ElectrostaticEnergy	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		float	atom1_chg,
		float	atom2_chg,
		float	scale_fact,
		float	de_const,
		float	dist_expo
	)

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

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

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

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

Parameters

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

Returns

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

calcMMFF94StretchBendEnergy() [3/4]

float CDPL.ForceField.calcMMFF94StretchBendEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		float	ijk_force_const,
		float	kji_force_const,
		float	ref_angle,
		float	ref_length1,
		float	ref_length2
	)

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

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

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

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

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

Parameters

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

Returns

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

calcMMFF94StretchBendEnergy() [4/4]

float CDPL.ForceField.calcMMFF94StretchBendEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		float	r_ij,
		float	r_jk,
		float	ijk_force_const,
		float	kji_force_const,
		float	ref_angle,
		float	ref_length1,
		float	ref_length2
	)

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

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

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

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

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

Parameters

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

Returns

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

calcMMFF94AngleBendingEnergy() [3/4]

float CDPL.ForceField.calcMMFF94AngleBendingEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		bool	linear,
		float	force_const,
		float	ref_angle
	)

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

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

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

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

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

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

Parameters

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

Returns

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

calcMMFF94AngleBendingEnergy() [4/4]

float CDPL.ForceField.calcMMFF94AngleBendingEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		float	r_ij,
		float	r_jk,
		bool	linear,
		float	force_const,
		float	ref_angle
	)

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

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

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

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

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

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

Parameters

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

Returns

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

calcMMFF94OutOfPlaneBendingEnergy() [3/4]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	oop_atom_pos,
		float	force_const
	)

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

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

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

Parameters

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

Returns

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

calcMMFF94OutOfPlaneBendingEnergy() [4/4]

float CDPL.ForceField.calcMMFF94OutOfPlaneBendingEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom_pos,
		Math.Vector3D	term_atom2_pos,
		Math.Vector3D	oop_atom_pos,
		float	r_jl,
		float	force_const
	)

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

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

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

Parameters

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

Returns

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

calcMMFF94BondStretchingEnergy() [3/4]

float CDPL.ForceField.calcMMFF94BondStretchingEnergy	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		float	force_const,
		float	ref_length
	)

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

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

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

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

Parameters

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

Returns

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

calcElasticPotentialEnergy() [3/3]

float CDPL.ForceField.calcElasticPotentialEnergy	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		float	force_const,
		float	ref_length
	)

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

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

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

Parameters

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

Returns

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

Since

1.1

calcMMFF94TorsionEnergy() [3/3]

float CDPL.ForceField.calcMMFF94TorsionEnergy	(	Math.Vector3D	term_atom1_pos,
		Math.Vector3D	ctr_atom1_pos,
		Math.Vector3D	ctr_atom2_pos,
		Math.Vector3D	term_atom2_pos,
		float	tor_param1,
		float	tor_param2,
		float	tor_param3
	)

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

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

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

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

Parameters

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

Returns

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

calcMMFF94VanDerWaalsEnergy() [3/4]

float CDPL.ForceField.calcMMFF94VanDerWaalsEnergy	(	Math.Vector3D	atom1_pos,
		Math.Vector3D	atom2_pos,
		float	e_IJ,
		float	r_IJ,
		float	r_IJ_7
	)

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

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

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

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

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

Parameters

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

Returns

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

calcMMFF94ElectrostaticEnergy() [4/4]

float CDPL.ForceField.calcMMFF94ElectrostaticEnergy	(	float	r_ij,
		float	atom1_chg,
		float	atom2_chg,
		float	scale_fact,
		float	de_const,
		float	dist_expo
	)

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

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

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

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

Parameters

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

Returns

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

calcMMFF94BondStretchingEnergy() [4/4]

float CDPL.ForceField.calcMMFF94BondStretchingEnergy	(	float	r_ij,
		float	force_const,
		float	ref_length
	)

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

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

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

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

Parameters

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

Returns

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

calcMMFF94VanDerWaalsEnergy() [4/4]

float CDPL.ForceField.calcMMFF94VanDerWaalsEnergy	(	float	r_ij,
		float	e_IJ,
		float	r_IJ,
		float	r_IJ_7
	)

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

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

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

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

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

Parameters

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

Returns

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