Welch

This keyword specifies a Welch potential[70,71] of the form

$$\sum_{{i<j}}^{} \Bigg[ {\frac{{\displaystyle q_i q_j}}{{\displaystyle r_{ij}}}} {\frac{{\displaystyle q_i({\bf\mu}_j\cdot{\bf r}_{ij})}}{{\displaystyle r_{ij}^3}}} {\frac{{\displaystyle q_j({\bf\mu}_i\cdot{\bf r}_{ji})}}{{\displaystyle r_{ij}^3}}}$$ E =

$${\frac{{\displaystyle ({\bf\mu}_i\cdot{\bf r}_{ij}) ({\bf\mu}_j\cdot{\bf r}_{ij})}}{{\displaystyle r_{ij}^5}}} {\frac{{\displaystyle {\bf\mu}_i\cdot{\bf\mu}_j}}{{\displaystyle r_{ij}^3}}} \Bigg] \sum_{i}^{} {\frac{{\displaystyle \mu_i^2}}{{\displaystyle 2\alpha_i}}}$$

where

$$\bf r_{{ij}}^{{\rm eff}}$$ = $$\bf r_{{ij}}^{}$$ + $${\frac{{{\bf\mu}_i}}{{Q_i}}}$$ - $${\frac{{{\bf\mu}_j}}{{Q_j}}}$$,        r_ij^eff = $$\left\vert\vphantom{{\bf r}_{ij}^{\rm eff}}\right.$$$$\bf r_{{ij}}^{{\rm eff}}$$$$\left.\vphantom{{\bf r}_{ij}^{\rm eff}}\right\vert$$.

Welch parameters in atomic units should be entered after the Welch keyword in the order A₊₊, A_–, A_+-, ρ, Q₊, Q_-, α₊, α_-. The ions are then specified using atom types PL and MI for plus and minus, respectively, and can be in any order. There need not be equal numbers of positive and negative ions.