Van der Waals

The van der Waals interactions describe the forces resulting from local interactions of atoms. The van der Waals energy between two atoms i and j is described by

$$E_{\text{vdw}} = \frac{A}{\vert\vec{r}_{ij}\vert^{12}} - \frac{B}{\vert\vec{r}_{ij}\vert^6}$$

where

• A = constant determined as described below
• B = constant determined as described below
• $\vert\vec{r}_{ij}\vert$ = calculated distance between atoms i and j

The constants A and B can be specified for a pair of atom types explicitly in the parameter file using the NBFix command. With this command, values of A and B for normal interactions and modified 1-4 interactions are specified explicitly.

If the NBFix command is not used, the constants A and B are calculated using the parameters $\sigma_{ij}$ and $\epsilon_{ij}$ using the equations
$$\begin{gather*}A = 4 \sigma_{ij}^{12} \epsilon_{ij} \\ B = 4 \sigma_{ij}^6 \epsilon_{ij} \end{gather*}$$
where $\sigma_{ij}$ and $\epsilon_{ij}$ are calcuated from the $\sigma$ and $\epsilon$ values specifed for the atom types of atoms i and j in the NBOnd commands in the parameter file using the equations
$$\begin{gather*}\sigma_{ij} = \frac{\sigma_{ii} + \sigma_{jj}}{2} \\ \epsilon_{ij} = \sqrt{\epsilon_{ii}\epsilon_{jj}} \end{gather*}$$
where

• $\sigma_{ii}$ = $\sigma$ value for atom i
• $\epsilon_{ii}$ = $\epsilon$ value for atom i

Also, $\sigma$ and $\epsilon$ for a pair can be related to the minimum energy, $E_{\text{min}}$, and minimum distance, $R_{\text{min}}$ by the equations
$$\begin{gather*}R_{\text{min}} = \sigma \sqrt[6]{2} \\ E_{\text{min}} = -\epsilon \end{gather*}$$
For modified 1-4 interactions, the $\sigma_{ij}$ and $\epsilon_{ij}$ values are calculated as above, except that the $\sigma_{ii}$, $\epsilon_{ii}$, $\sigma_{jj}$, and $\epsilon_{jj}$ are replaced by the $\sigma_{ii}^{14}$, $\epsilon_{ii}^{14}$, $\sigma_{jj}^{14}$, and $\epsilon_{jj}^{14}$ that are specified by the NBOnd lines of the parameter files. Section 5.1.3 describes when the modified parameters are used.