# Valence Potentials¶

## Bond Stretching¶

BONDTYPE [HARMONIC / MORSE]

Chooses the functional form of the bond stretching potential. The HARMONIC option selects a Taylor series expansion containing terms from harmonic through quartic. The MORSE option selects a Morse potential fit to the ideal bond length and stretching force constant parameter values. The default is to use the HARMONIC potential.

BONDTERM [NONE / ONLY]

Controls use of the bond stretching potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

BONDUNIT [real]

Sets the scale factor needed to convert the energy value computed by the bond stretching potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the BONDUNIT keyword is not given in the force field parameter file or the keyfile.

BOND [2 integers & 2 reals]

Provides the values for a single bond stretching parameter. The integer modifiers give the atom class numbers for the two kinds of atoms involved in the bond which is to be defined. The real number modifiers give the force constant value in kcal/mol/Å2 for the bond and the ideal bond length in Angstroms. An example is as follows:

• BOND   A   B   Force   Ideal

BOND-CUBIC [real]

Sets the value (in 1/Å) of the cubic term in the Taylor series expansion form of the bond stretching potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the bond stretching energy unit conversion factor, the force constant, and the cube of the deviation of the bond length from its ideal value gives the cubic contribution to the bond stretching energy. The default value in the absence of the BOND-CUBIC keyword is zero; i.e., the cubic bond stretching term is omitted.

BOND-QUARTIC [real]

Sets the value (in 1/Å2) of the quartic term in the Taylor series expansion form of the bond stretching potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the bond stretching energy unit conversion factor, the force constant, and the forth power of the deviation of the bond length from its ideal value gives the quartic contribution to the bond stretching energy. The default value in the absence of the BOND-QUARTIC keyword is zero; i.e., the quartic bond stretching term is omitted.

Bond Stretching

## Angle Bending¶

ANGLETERM [NONE / ONLY]

Controls use of the bond angle bending potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

ANGLEUNIT [real]

Sets the scale factor needed to convert the energy value computed by the bond angle bending potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of $$(\pi/180)^2$$ is used, if the ANGLEUNIT keyword is not given in the force field parameter file or the keyfile.

ANGLE [3 integers & 4 reals]

Provides the values for a single bond angle bending parameter. The integer modifiers give the atom class numbers for the three kinds of atoms involved in the angle which is to be defined. The real number modifiers give the force constant value for the angle and up to three ideal bond angles in degrees. In most cases only one ideal bond angle is given, and that value is used for all occurrences of the specified bond angle. If all three ideal angles are given, the values apply when the central atom of the angle is attached to 0, 1 or 2 additional hydrogen atoms, respectively. This “hydrogen environment” option is provided to implement the corresponding feature of Allinger’s MM force fields. The default units for the force constant are kcal/mol/rad2, but this can be controlled via the ANGLEUNIT keyword. An example is as follows:

• ANGLE   A1   C   A2   Force   Ideal

ANGLEF [3 integers & 3 reals]

Provides the values for a single bond angle bending parameter for a SHAPES-style Fourier potential function. The integer modifiers give the atom class numbers for the three kinds of atoms involved in the angle which is to be defined. The real number modifiers give the force constant value for the angle, the angle shift in degrees, and the periodicity value. Note that the force constant should be given as the “harmonic” value and not the native Fourier value. The default units for the force constant are kcal/mol/rad2, but this can be controlled via the ANGLEUNIT keyword. An example is as follows:

• ANGLEF   A1   C   A2   Force   Ideal   Periodicity

ANGLEP [3 integers & 2 reals]

Provides the values for a single projected in-plane bond angle bending parameter. The integer modifiers give the atom class numbers for the three kinds of atoms involved in the angle which is to be defined. The real number modifiers give the force constant value for the angle and up to two ideal bond angles in degrees. In most cases only one ideal bond angle is given, and that value is used for all occurrences of the specified bond angle. If all two ideal angles are given, the values apply when the central atom of the angle is attached to 0 or 1 additional hydrogen atoms, respectively. This “hydrogen environment” option is provided to implement the corresponding feature of Allinger’s MM force fields. The default units for the force constant are kcal/mol/rad2, but this can be controlled via the ANGLEUNIT keyword. An example is as follows:

• ANGLEP   A1   C   A2   Force   Ideal

ANGLE-CUBIC [real]

Sets the value (in 1/deg) of the cubic term in the Taylor series expansion form of the bond angle bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the angle bending energy unit conversion factor, the force constant, and the cube of the deviation of the bond angle from its ideal value gives the cubic contribution to the angle bending energy. The default value in the absence of the ANGLE-CUBIC keyword is zero; i.e., the cubic angle bending term is omitted.

ANGLE-QUARTIC [real]

Sets the value (in 1/deg2) of the quartic term in the Taylor series expansion form of the bond angle bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the angle bending energy unit conversion factor, the force constant, and the forth power of the deviation of the bond angle from its ideal value gives the quartic contribution to the angle bending energy. The default value in the absence of the ANGLE-QUARTIC keyword is zero; i.e., the quartic angle bending term is omitted.

ANGLE-PENTIC [real]

Sets the value (in 1/deg3) of the fifth power term in the Taylor series expansion form of the bond angle bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the angle bending energy unit conversion factor, the force constant, and the fifth power of the deviation of the bond angle from its ideal value gives the pentic contribution to the angle bending energy. The default value in the absence of the ANGLE-PENTIC keyword is zero; i.e., the pentic angle bending term is omitted.

ANGLE-SEXTIC [real]

Sets the value (in 1/deg4) of the sixth power term in the Taylor series expansion form of the bond angle bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the angle bending energy unit conversion factor, the force constant, and the sixth power of the deviation of the bond angle from its ideal value gives the sextic contribution to the angle bending energy. The default value in the absence of the ANGLE-SEXTIC keyword is zero; i.e., the sextic angle bending term is omitted.

Angle Bending

## Stretch-Bend Coupling¶

STRBNDTERM [NONE / ONLY]

Controls use of the bond stretching-angle bending cross term potential energy. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

STRBNDUNIT [real]

Sets the scale factor needed to convert the energy value computed by the bond stretching-angle bending cross term potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of $$\pi/180$$ is used, if the STRBNDUNIT keyword is not given in the force field parameter file or the keyfile.

STRBND [3 integers & 2 reals]

Provides the values for a single stretch-bend cross term potential parameter. The integer modifiers give the atom class numbers for the three kinds of atoms involved in the angle which is to be defined. The real number modifiers give the force constant values for the first bond (first two atom classes) with the angle, and the second bond with the angle, respectively. The default units for the stretch-bend force constant are kcal/mol/Å/rad, but this can be controlled via the STRBNDUNIT keyword. An example is as follows:

• STRBND   A1   C   A2   Force1   Force2

UREYTERM [NONE / ONLY]

Controls use of the Urey-Bradley potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

UREYUNIT [real]

Sets the scale factor needed to convert the energy value computed by the Urey-Bradley potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the UREYUNIT keyword is not given in the force field parameter file or the keyfile.

UREYBRAD [3 integers & 2 reals]

Provides the values for a single Urey-Bradley cross term potential parameter. The integer modifiers give the atom class numbers for the three kinds of atoms involved in the angle for which a Urey-Bradley term is to be defined. The real number modifiers give the force constant value for the term and the target value for the 1-3 distance in Angstroms. The default units for the force constant are kcal/mol/Å2, but this can be controlled via the UREYUNIT keyword. An example is as follows:

• UREYBRAD   A1   C   A3   Force   Ideal

UREY-CUBIC [real]

Sets the value (in 1/Å) of the cubic term in the Taylor series expansion form of the Urey-Bradley potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. The default value in the absence of the UREY-CUBIC keyword is zero; i.e., the cubic Urey-Bradley term is omitted.

UREY-QUARTIC [real]

Sets the value (in 1/Å2) of the quartic term in the Taylor series expansion form of the Urey-Bradley potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. The default value in the absence of the UREY-QUARTIC keyword is zero; i.e., the quartic Urey-Bradley term is omitted.

## Out-of-Plane Bending¶

OPBENDTYPE [W-D-C / ALLINGER]

Sets the type of angle to be used in the out-of-plane bending potential energy term. The choices are to use the Wilson-Decius-Cross (W-D-C) formulation from vibrational spectroscopy, or the Allinger angle from the MM2/MM3 force fields. The default value in the absence of the OPBENDTYPE keyword is to use the W-D-C angle.

OPBENDTERM [NONE / ONLY]

Controls use of the out-of-plane bending potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

OPBENDUNIT [real]

Sets the scale factor needed to convert the energy value computed by the out-of-plane bending potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default of $$(\pi/180)^2$$ is used, if the OPBENDUNIT keyword is not given in the force field parameter file or the keyfile.

OPBEND [4 integers & 1 real]

Provides the values for a single out-of-plane bending potential parameter. The first integer modifier is the atom class of the out-of-plane atom and the second integer is the atom class of the central trigonal atom. The third and fourth integers give the atom classes of the two remaining atoms attached to the trigonal atom. Values of zero for the third and fourth integers are treated as wildcards, and can represent any atom type. The real number modifier gives the force constant value for the out-of-plane angle. The default units for the force constant are kcal/mol/rad2, but this can be controlled via the OPBENDUNIT keyword. An example is as follows:

• OPBEND A   B   0   0   force

OPBEND-CUBIC [real]

Sets the value (in 1/deg) of the cubic term in the Taylor series expansion form of the out-of-plane bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the out-of-plane bending energy unit conversion factor, the force constant, and the cube of the deviation of the out-of-plane angle from zero gives the cubic contribution to the out-of-plane bending energy. The default value in the absence of the OPBEND-CUBIC keyword is zero; i.e., the cubic out-of-plane bending term is omitted.

OPBEND-QUARTIC [real]

Sets the value (in 1/deg2) of the quartic term in the Taylor series expansion form of the out-of-plane bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the out-of-plane bending energy unit conversion factor, the force constant, and the forth power of the deviation of the out-of-plane angle from zero gives the quartic contribution to the out-of-plane bending energy. The default value in the absence of the OPBEND-QUARTIC keyword is zero; i.e., the quartic out-of-plane bending term is omitted.

OPBEND-PENTIC [real]

Sets the value (in 1/deg3) of the fifth power term in the Taylor series expansion form of the out-of-plane bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the out-of-plane bending energy unit conversion factor, the force constant, and the fifth power of the deviation of the out-of-plane angle from zero gives the pentic contribution to the out-of-plane bending energy. The default value in the absence of the OPBEND-PENTIC keyword is zero; i.e., the pentic out-of-plane bending term is omitted.

OPBEND-SEXTIC [real]

Sets the value (in 1/deg4) of the sixth power term in the Taylor series expansion form of the out-of-plane bending potential energy. The real number modifier gives the value of the coefficient as a multiple of the quadratic coefficient. This term multiplied by the out-of-plane bending energy unit conversion factor, the force constant, and the sixth power of the deviation of the out-of-plane angle from zero gives the sextic contribution to the out-of-plane bending energy. The default value in the absence of the OPBEND-SEXTIC keyword is zero; i.e., the sextic out-of-plane bending term is omitted.

## Improper Dihedral¶

IMPROPTERM [NONE / ONLY]

Controls use of the CHARMM-style improper dihedral angle potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

IMPROPUNIT [real]

Sets the scale factor needed to convert the energy value computed by the CHARMM-style improper dihedral angle potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of $$(\pi/180)^2$$ is used, if the IMPROPUNIT keyword is not given in the force field parameter file or the keyfile.

IMPROPER [4 integers & 2 reals]

Provides the values for a single CHARMM-style improper dihedral angle parameter. The integer modifiers give the atom class numbers for the four kinds of atoms involved in the torsion which is to be defined. The real number modifiers give the force constant value for the deviation from the target improper torsional angle, and the target value for the torsional angle, respectively. The default units for the improper force constant are kcal/mol/rad2, but this can be controlled via the IMPROPUNIT keyword.

The real number modifiers give the force constant in kcal/mol/rad2 and ideal dihedral angle in degrees. An example is as follows:

• IMPROPER   D   A   B   C   Force   Ideal

## Improper Torsion¶

IMPTORTERM [NONE / ONLY]

Controls use of the AMBER-style improper torsional angle potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

IMPTORUNIT [real]

Sets the scale factor needed to convert the energy value computed by the AMBER-style improper torsional angle potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the IMPTORSUNIT keyword is not given in the force field parameter file or the keyfile.

IMPTORS [4 integers & up to 3 real/real/integer triples]

Provides the values for a single AMBER-style improper torsional angle parameter. The first four integer modifiers give the atom class numbers for the atoms involved in the improper torsional angle to be defined. By convention, the third atom class of the four is the trigonal atom on which the improper torsion is centered. The torsional angle computed is literally that defined by the four atom classes in the order specified by the keyword. Each of the remaining triples of real/real/integer modifiers give the half-amplitude in kcal/mol, phase offset in degrees and periodicity of a particular improper torsional term, respectively. Periodicities through 3-fold are allowed for improper torsional parameters. An example is as follows:

• IMPTORS   A   B   C   D   Amplitude   PhaseOffset   Periodicity

Improper Torsion

## Torsional Angle¶

TORSIONTERM [NONE / ONLY]

Controls use of the torsional angle potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

TORSIONUNIT [real]

Sets the scale factor needed to convert the energy value computed by the torsional angle potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the TORSIONUNIT keyword is not given in the force field parameter file or the keyfile.

TORSION [4 integers & up to 6 real/real/integer triples]

Provides the values for a single torsional angle parameter. The first four integer modifiers give the atom class numbers for the atoms involved in the torsional angle to be defined. Each of the remaining triples of real/real/integer modifiers give the amplitude in kcal/mol, phase offset in degrees and periodicity of a particular torsional function term, respectively. Periodicities through 6-fold are allowed for torsional parameters. An example is as follows:

• TORSION   A   B   C   D   Amplitude   PhaseOffset   Periodicity

Torsional Angle

## Pi-Orbital Torsional Angle¶

PITORSTERM [NONE / ONLY]

Controls use of the pi-orbital torsional angle potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

PITORSUNIT [real]

Sets the scale factor needed to convert the energy value computed by the pi-orbital torsional angle potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the PITORSUNIT keyword is not given in the force field parameter file or the keyfile.

PITORS [2 integers & 1 real]

Provides the values for a single pi-orbital torsional angle potential parameter. The two integer modifiers give the atom class numbers for the atoms involved in the central bond of the torsional angle to be parameterized. The real modifier gives the value of the 2-fold Fourier amplitude in kcal/mol for the torsional angle between p-orbitals centered on the defined bond atom classes. The default units for the stretch-torsion force constant can be controlled via the PITORSUNIT keyword. An example is as follows:

• PITORS   A   B   Amplitude

## Stretch-Torsion Coupling¶

STRTORTERM [NONE / ONLY]

Controls use of the bond stretching-torsional angle cross term potential energy. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

STRTORUNIT [real]

Sets the scale factor needed to convert the energy value computed by the bond stretching-torsional angle cross term potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the STRTORUNIT keyword is not given in the force field parameter file or the keyfile.

STRTORS

Provides the values for a single stretch-torsion cross term potential parameter. The two integer modifiers give the atom class numbers for the atoms involved in the central bond of the torsional angles to be parameterized. The real modifier gives the value of the stretch-torsion force constant for all torsional angles with the defined atom classes for the central bond. The default units for the stretch-torsion force constant can be controlled via the STRTORUNIT keyword.

## Angle-Torsion Coupling¶

ANGTORTERM [NONE / ONLY]

Controls use of the angle bending-torsional angle cross term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

ANGTORUNIT [real]

Sets the scale factor needed to convert the energy value computed by the angle bending-torsional angle cross term into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of $$\pi/180$$ is used, if the ANGTORUNIT keyword is not given in the force field parameter file or the keyfile.

ANGTORS [4 integers & 6 reals]

Provides the values for a single bond angle bending-torsional angle parameter. The integer modifiers give the atom class numbers for the four kinds of atoms involved in the torsion and its contained angles. The real number modifiers give the force constant values for both angles coupled with 1-, 2- and 3-fold torsional terms. The default units for the force constants are kcal/mol/rad, but this can be controlled via the ANGTORUNIT keyword.

## Torsion-Torsion Coupling¶

TORTORTERM [NONE / ONLY]

Controls use of the torsion-torsion potential energy term. In the absence of a modifying option, this keyword turns on use of the potential. The NONE option turns off use of this potential energy term. The ONLY option turns off all potential energy terms except for this one.

TORTORUNIT [real]

Sets the scale factor needed to convert the energy value computed by the torsion-torsion potential into units of kcal/mol. The correct value is force field dependent and typically provided in the header of the master force field parameter file. The default value of 1.0 is used, if the TORTORUNIT keyword is not given in the force field parameter file or the keyfile.

TORTORS [7 integers, then multiple lines of 2 integers and 1 real]

Provides the values for a single torsion-torsion parameter. The first five integer modifiers give the atom class numbers for the atoms involved in the two adjacent torsional angles to be defined. The last two integer modifiers contain the number of data grid points that lie along each axis of the torsion-torsion map. For example, this value will be 13 for a 30 degree torsional angle spacing, i.e., 360/30 = 12, but 13 values are required since data values for -180 and +180 degrees must both be supplied. The subsequent lines contain the torsion-torsion map data as the integer values in degrees of each torsional angle and the target energy value in kcal/mol.