## Moe Forcefield FacilitiesP. LabuteChemical Computing Group Inc.
1010 Sherbrooke Street W, Suite 910; Montreal, Quebec; Canada H3A 2R7
## INTRODUCTIONA potential energy model, equivalently, a The MOE forcefield facilities implement Cartesian coordinate,
empirical energy models that with support for 4D position
coordinates. The term In this article, we present the functional forms supported as well as an overview of the parameter file format and the atom typing system. ## FUNCTIONAL FORMSThe energy modeling services have been designed so that each of which models a particular interaction. In this section, the nature of the terms will be described. In some cases, there are alternatives for the functional forms that a particular set of parameters may employ. Each of the terms requires parameters that depend on the particular atoms involved in the interaction. Such parameter constants are located in the forcefield parameter file. The potential energy is a sum of individual interaction energies E = w +
_{b} E_{b}w + _{a} E_{a}w + _{n}
E_{n}w +
_{t} E_{t}w + _{o} E_{o}w + _{e}
E_{e}w +
_{v} E_{v}E_{c}where the ith atom,
and r = _{ij}r -
_{j}r._{i}
k ( |_{ij}r| -
_{ij}R )_{ij}^{2} + k' (
|_{ij}r| - _{ij}R )_{ij}^{3} +
k'' ( |_{ij}r| -
_{ij}R )_{ij}^{4}where the sum extends over all bonds k' and
_{ij}k'' are the force constants and
_{ij}R is the equilibrium bond length. Bond angle
energy, _{ij}E (the energy parameterized by the angle
between two bonds sharing an atom) is modeled as a quartic:_{a}k _{ijk}A +
^{2}_{ijk}k' _{ijk}A +
^{3}_{ijk}k''
_{ijk}A^{4}_{ijk}where the sum extends over all bond angles k' and
_{ijk}k'' are the force constants,
_{ijk}T is the equilibrium bond angle (in radians),
_{ijk}A is either _{ijk}t -
_{ijk}T or cos _{ijk}t - cos
_{ijk}T depending on the functional form chosen, and
_{ijk}t = _{ijk}r
^{T}_{ji}r / |_{jk}r|
|_{ji}r|. For linear molecules (e.g., _{jk}sp
hybridization), the form k (1 + cos
_{ijk}t) is used in place of the quartic
expression._{ijk}Stretch-bend cross terms, k (|_{ijk}r| -
_{ij}R) + _{ij}k
(|_{kji}r| - _{jk}R) ]
_{jk}A_{ijk}where the sum extends over all bond angles k are force
constants and the other terms are as above. Stretch-bend terms are
not used for linear or near-linear angles._{kji}The torsion energy, k [1 +/- cos n
_{n;ijkl}D ]_{ijkl}where the sum extends over all values of D is the dihedral angle
(radians) about the bond _{ijkl}j-k.Out of plane forces, i with three neighbors
j, k, and l. The second form uses
k _{i;jkl}X where
^{2}_{i;jkl}k is the force constant and
_{i;jkl}X is the Wilson angle (the angle between the
bond _{i;jkl}il and the plane ijk.
Electrostatics, c q _{i}q
s(|_{j}r|) (_{ij}r +
^{n}_{ij}d)^{-1}where i and
d is a buffering constant used to prevent division by 0.
Both forms can be scaled by a programmable factor when the two
atoms involved are related by a 1-4 interaction (i.e., a torsion).
Electrostatic forces are ignored for 1-3 (angle) and 1-2 (bond)
interactions. The function s is a smoothing function
and will be described below.Van der Waals forces, where the R,
_{ij}m and _{ij}n are empirically
determined constants. The _{ij}a and b constants prevent
division by 0 and are called buffering constants. Although
complicated, this form can reproduce the usual 12-6, 12-10 and 9-6
potentials by careful selection of the parameters. Like
electrostatic forces, van der Waals forces are scaled when the two
atoms are related by a 1-4 interaction (but ignored for 1-3 and 1-2
interactions).The function cutoff off distance r. The function
_{b}s(r) has the value 1 for r less than
r, 0 for _{a}r greater than
r and, for _{b}r in
[r,_{a}r],_{b}s(r) =
p((r-r) /
(_{r}r-_{b}r)),
_{a}p(x) = 1 + x ( -6
_{2}x + 15 _{2}x - 10 )To simulate larger systems of atoms, the
E = _{c}E +
_{cd}E + _{ca}E +
_{ct}E_{cx}where E is the angle constraint violation
energy, _{ca}E is the torsion constraint violation
energy, and _{ct}E is the chiral constraint
violation energy._{cx}Distance restraints, C ( |_{ij}r|_{ij}^{2}
- R_{ij}^{2} )^{2}where the sum extends over all distance restraints,
R is the desired value for the distance. Angle
restraints, _{ij}E, are modeled with_{ca}C ( cos _{ijk}t - cos
_{ijk}T)_{ijk}^{2}where the sum extends over all angle restraints,
T is the desired value for the angle. Torsion
restraints are modeled with a single term from the Fourier
expansion used to model proper torsion energy. Chiral constraints
are imposed on those chiral atoms that have four neighbors and a
specified R or S designation. MOE will assign a very large energy
value to violations of chirality._{ijk}MOE can prevent the modification of the positions of fixed (position constrained) atoms. The potential energy model will return a gradient of zero for fixed atoms, and furthermore, the positions of fixed atoms will be treated as constants for the purposes of the energy calculation. ## PARAMETERSThe parameters for the potential energy model are defined in a single ASCII parameter file which contains definitions for atom types, assignment rules, and individual parameters for the supported functional forms. By altering the parameters, different energy models can be used. The parameter file consists of a number of definition blocks beginning with a block that defines the atom types and basic properties. The remaining blocks contain forcefield term-specific parameters and definitions. Central to any empirical potential energy model is the notion of
Atom types are listed at the top of the parameter file. Each atom type declaration must be unique, and refers to a context-specific instantiation of an atom of a given element. Two or more atom types may refer to the same element. Each atom type definition consists of a single line containing the type symbol, the underlying element and a textual description of the type. Other lines contain information about the forcefield itself (e.g., the title) with possible references. MOE uses an automatic method of assigning atom types to atoms
during calculations. This automatic method is based on substructure
searching and pattern matching to detect the context in which an
atom type is to be assigned to a particular atom. This substructure
search is controlled by the The rules section is signalled by a line with type-name
expressionThe
The The following is an example rules section for the types defined above: [rules] # patterns that the atom
type contextC match '[CX4]' Csp2 match '[CX3]=*' or match 'c' HC match '[#1][#6]' ## SUMMARYThe MOE forcefield system is capable of describing a large family of potential energy models (e.g., Kollman's AMBER '89, '94 and the Merck MMFF94). The automatic atom typing system and flexible nonbonded parameter features allow efficient specification of novel or special atom types. Although the built-in functional forms are suitable for Class I and some Class II forcefields additional energy terms can be added through the use of the SVL programming language. |