Van der Waals Function

The van der Waals function is given by

$$f_{VDW}(R) = \left\{ \begin{array}{lll} \frac{A}{R^{12}} - \... ...rexp} - R^{irexp}))^{rexp} & \mbox{repel} \end{array}\right.$$

where $H$ is the heavy-side function and $SW$ is a switching function. $SW$ has the form

$$SW(R,R_{on},R_{off}) = \left\{ \begin{array}{lll} 0 & \mbox{... ... > R_{on}$} \\ 1 & \mbox{if $R < R_{on}$} \end{array}\right.$$

For both the truncated and the switched option, the van der Waals function is described by a Lennard-Jones potential. In this potential, the attractive force is proportional to $R^{-6}$, while the repulsive force varies as $R^{-12}$. $A$,$B$ and $\varepsilon$,$\sigma$ are related to the well depth $E_{min}$ and the minimum distance $R_{min}$ (van der Waals radius) by

$$R_{min} = \sigma \sqrt[6]{2}$$ (4.10)

$$E_{min} = -\varepsilon$$ (4.11)

$$A=4\sigma^{12}\varepsilon$$ (4.12)

$$B=4 \sigma^{6}\varepsilon$$ (4.13)

The repel option uses a simple repulsive potential. It is used primarily for structure refinements with X-ray crystallographic and solution NMR spectroscopic data.

The NBON statement (Section 3.2.1) defines $\varepsilon,\sigma$ for the Lennard-Jones potential between identical atom types. Between different atom types, the following combination rule is used by default:

$$\sigma_{ij} = \frac{\sigma_{ii}+\sigma_{jj}}{2}$$ (4.14)

$$\varepsilon_{ij}= \sqrt{\varepsilon_{ii}\varepsilon_{jj}}$$ (4.15)

The NBFix statement allows one to deviate from this combination rule; i.e, one can explicitly specify the $A,B$ coefficients for an atom type pair (see Section 3.2.1).

Minimization of the empirical potential energy for initial coordinates with very close nonbonded contacts is often ill behaved because the Lennard-Jones potential produces a very large gradient reflecting the close contacts. To avoid this problem, the Lennard-Jones and electrostatic potential can be replaced with the repel potential, which is softer and purely repulsive.