Consistent Valence Forcefield (CVFF)

Introduction
Functional Form
CVFF Atom Types

Introduction

The consistent-valence forcefield (CVFF), the original forcefield provided with the Discover program, is a generalized valence forcefield (Dauber-Osguthorpe 1988). Parameters are provided for amino acids, water, and a variety of other functional groups.

The new version of the Discover program (95.0/300) has undergone extensive validation tests comparing it with the previous version of Discover (2.x.x). These tests have indicated that the two programs provide exactly the same results for all components of the energy expression with one exception: the out-of-plane energy for the CVFF forcefield.

The out-of-plane energy for the CVFF forcefield is calculated as an improper torsion. Recall that an improper torsion views three connected atoms and a central atom as a torsion (e.g., if A2 is the central atom, construct a torsion as A1-A2-A3-A4--this last connection does not represent a real bond, hence the name improper torsion). There are three possible improper torsions that can be generated for a particular out-of-plane based on permutations of the connected atoms.

For CVFF, only one of these improper torsions is used. The rules that Discover 2.x.x employs to select the particular improper torsion are somewhat arbitrary, and it is not possible to replicate them in the Discover 95.0/300 program. However, the changes in energy are very small (on the order 0.01 kcal mol^-1). A more rigorously defined out-of-plane, the Wilson out-of-plane, is used in the CFF forcefield. This energy term provides exact agreement between the two programs.

Functional Form

The analytic form of the energy expression used in CVFF is given in Eq. 3-1. Most other forcefields in the literature use a subset of the terms included in CVFF, often only the diagonal terms.

Eq. 3-1:

Eq. 3-1 is illustrated schematically in Figure 3-2. Terms 1-4 in Figure 3-2 and Eq. 3-1 are commonly referred to as the diagonal terms of the valence forcefield and represent the energy of deformation of bond lengths, bond angles, torsion angles, and out-of-plane interactions, respectively. Note that a Morse potential (Term 1) is used for the bond-stretching term. The Discover program also supports a simple harmonic potential for this term. The Morse form is computationally more expensive than the harmonic form. Since the number of bond interactions is usually negligible relative to the number of nonbond interactions, the additional cost of using the more accurate Morse potential is insignificant, so this is the default option.

One exception to this rule is when the molecule being simulated is high in energy (caused, for example, by overlapping atoms or a high target temperature), which might force a Morse-style function to allow the bonded atoms to drift unrealistically far apart (see Figure 3-3).

Terms 5-9 in Figure 3-2 and Eq. 3-1 are off-diagonal (or cross) terms and represent couplings between deformations of internal coordinates. For example, Term 5 describes the coupling between stretching of adjacent bonds. These terms are required to accurately reproduce experimental vibrational frequencies and, therefore, the dynamic properties of molecules. In some cases, research has also shown them to be important in accounting for structural deformations. However, cross terms can become unstable when the structure is far from a minimum. Therefore, although the Discover program includes cross terms by default, input files created by the Insight program by default explicitly turn off the cross terms.

Terms 10-11 describe the nonbond interactions. Term 10 represents the van der Waals interactions with a Lennard-Jones function. Term 11 is the Coulombic representation of electrostatic interactions. The dielectric constant can be made distance dependent (i.e., a function of r_ij ). In the CVFF forcefield, hydrogen bonds are a natural consequence of the standard van der Waals and electrostatic parameters, and special hydrogen bond functions do not improve the fit of CVFF to experimental data (Hagler 1979a, 1979b).

Additional information on the forcefields and how they can be augmented is contained in the printed Files book, where the .frc file is described.

CVFF Atom Types

The CVFF forcefield supplied by Biosym/MSI defines atom types for the 20 commonly occurring amino acids, most hydrocarbons, and many other organic molecules (Table 3-1).

The bond increment sections of the .frc files for both CFF91 and CVFF have been expanded so that partial charges can be determined whenever the Discover program is able to assign automatic atom types.

Table 3-1. Atom Types--CVFF

The format is:

atom type: description

and you may quickly jump to the classes of atom types by clicking:

hydrogen
carbon
nitrogen
oxygen
sulfur
phosphorus
halogens
ions
argon
silicon

hydrogen types

d: general deuterium (equiv. to h)
dw: deuterium in heavy water (equiv. to h*)
h: generic hydrogen bonded to C, Si, or H
hc: hydrogen bonded to C (equiv. to h)
hi: hydrogen in charged imidazole ring (equiv. to hn)
hn: hydrogen bonded to N
ho: hydrogen bonded to O
hp: hydrogen bonded to P (equiv. to h)
hs: hydrogen bonded to S
hw: hydrogen in water (equiv. to h*)
h*: hydrogen in water
h+: charged hydrogen in cation (equiv. to hn)

carbon types

c: generic sp³ carbon
ca: general amino acid alpha carbon (sp³) (equiv. to cg)
cg: sp³ alpha carbon in glycine
ci: sp² aromatic carbon in charged imidazole ring (his⁺ )
cn: sp³ carbon bonded to N (equiv. to cg)
co: sp³ carbon in acetal (equiv. to c)
coh: sp³ carbon in acetal with hydrogen (equiv. to cg)
cp: sp² aromatic carbon (partial double bonds)
cr: carbon in guanidinium group (HN=C(NH₂)₂) (arg)
cs: sp² carbon in 5-membered ring next to S
ct: sp carbon involved in triple bond
c1: sp³ carbon bonded to 1 H, 3 heavy atoms (equiv. to cg)
c2: sp³ carbon bonded to 2 H's, 2 heavy atoms (equiv. to cg)
c3: sp³ carbon in methyl (CH₃) group (equiv. to cg)
c5: sp² aromatic carbon in 5-membered ring
c3h: sp³ carbon in 3-membered ring with hydrogens (equiv. to cg)
c3m: sp³ carbon in 3-membered ring (equiv. to c)
c4h: sp³ carbon in 4-membered ring with hydrogens (equiv. to cg)
c4m: sp³ carbon in 4-membered ring (equiv. to c)
c: sp² carbon in carbonyl (C=O) group of amide
c": carbon in carbonyl group, not amide (equiv. to c)
c*: carbon in carbonyl group, not amide (equiv. to c)
c-: carbon in charged carboxylate (COO^- ) group (equiv. to c)
c+: carbon in guanidinium group (equiv. to cr)
c=: nonaromatic end doubly bonded carbon
c=1: nonaromatic, next-to-end doubly bonded carbon
c=2: nonaromatic doubly bonded carbon

nitrogen types

n: generic sp² nitrogen in amide
na: sp³ nitrogen in amine (equiv. to n3)
nb: sp² nitrogen in aromatic amine (equiv. to n3)
nh: sp² nitrogen in 5- or 6-membered ring, with hydrogen attached (equiv. to np)
nho: sp² nitrogen in 6-membered ring, next to a carbonyl group and with a hydrogen (equiv. to np)
nh+: protonated nitrogen in 6-membered ring
ni: sp² nitrogen in charged imidazole ring (his⁺)
nn: sp² nitrogen in aromatic amine (equiv. to n3)
np: sp² nitrogen in 5- or 6-membered ring
npc: sp² nitrogen in 5- or 6-membered ring, bonded to a heavy atom (equiv. to np)
nr: sp² nitrogen in guanidinium group (HN=C(NH₂)₂)
nt: sp nitrogen involved in triple bond
nz: sp nitrogen in N₂
n1: sp² nitrogen in charged arginine
n2: sp² nitrogen in guanidinium group (HN=C(NH₂)₂)
n3: sp³ nitrogen with 3 substituents
n4: sp³ nitrogen in protonated amine
n3m: sp³ nitrogen in 3-membered ring (equiv. to n3)
n3n: sp² nitrogen in 3-membered ring (equiv. to n)
n4m: sp³ nitrogen in 4-membered ring (equiv. to n3)
n4n: sp² nitrogen in 4-membered ring (equiv. to n)
n+: sp³ nitrogen in protonated amine (equiv. to n4)
n=: nonaromatic end doubly bonded nitrogen
n=1: nonaromatic, next-to-end doubly bonded nitrogen
n=2: nonaromatic doubly bonded nitrogen

oxygen types

o: generic sp³ oxygen
oc: sp³ oxygen in ether or acetal (equiv. to o)
oe: sp³ oxygen in ester (equiv. to o)
oh: oxygen bonded to H
op: sp² aromatic oxygen in 5-membered ring
o3e: sp³ oxygen in 3-membered ring (equiv. to o)
o4e: sp³ oxygen in 4-membered ring (equiv. to o)
o: oxygen in carbonyl (C=O) group
o*: oxygen in water molecule
o-: oxygen in charged carboxylate (COO^- ) group

sulfur types

s: sp³ sulfur
sc: sp³ sulfur in methionine (C-S-C) group (equiv. to s)
sh: sulfur in sulfhydryl (SH) group
sp: sulfur in aromatic ring, e.g., thiophene
s1: sulfur involved in S-S disulfide bond (equiv. to s)
s3e: sulfur in 3-membered ring (equiv. to s)
s4e: sulfur in 4-membered ring (equiv. to s)
s: sulfur in thioketone (>C=S) group
s-: partial-double sulfur bonded to something that is bonded to another partial-double oxygen or sulfur