# The Vashishita potential

## Potential form

• The Vashishta potential is essentially a pairwise potential plus a modified form of the three-body part of the Stillinger-Weber potential. Therefore, the site potential can be written in the same form as the Stillinger-Weber potential:

$$U_i = \frac{1}{2} V_2(r_{ij}) + \frac{1}{2}\sum_{j\neq i}\sum_{k\neq i,j} h_{ijk}.$$

$$V_2(r_{ij}) = \frac{H}{r_{ij}^{\eta}} + \frac{1}{4\pi\epsilon_0} \frac{q_{i}q_{j}}{r_{ij}} e^{-r_{ij}/\lambda} - \frac{1}{4\pi\epsilon_0} \frac{D}{2r_{ij}^4} e^{-r_{ij}/\xi} - \frac{W}{r_{ij}^6}.$$ The four terms on the right hand side of the above equation correspond to steric size effects, charge-charge interactions, charge-dipole interactions, and dipole-dipole interactions, respectively. The original paper has used Gauss units for the middle two terms and we have used the SI units.

• The two-body part is shifted in terms of both potential and force:

$$V_2^{\rm shifted}(r_{ij}) = V_2(r_{ij}) - V_2(r_{c}) -(r-r_c) \frac{dV_2(r_{ij})}{dr_{ij}}\Big|_{r=r_c}.$$ Therefore, both the potential and the force for the two-body part are continuous at the cutoff distance $r_c$.

• The three-body part is

$$h_{ijk}=B \exp \left[ \frac{\gamma}{r_{ij}-r_0} + \frac{\gamma}{r_{ik}-r_0} \right] \frac{\left(\cos \theta_{ijk} - h \right)^2}{1 + C \left(\cos \theta_{ijk} - h \right)^2}.$$ The parameter $\gamma$ is always 1 A and is thus redundant.

## Parameters

 Parameter Units $B$ eV $h$ dimensionless $C$ dimensionless $r_0$ A $r_c$ A $H$ eV A$^{\eta}$ $\eta$ dimensionless $q$ e $\lambda$ A $D$ e2 A3 $\xi$ A $W$ eV A6

## Potential file format

• The potential file for this potential model reads
   vashishta 2
B_0   B_1     h_0     h_1        C     r0     rc
H_00  eta_00  q0*q0   lambda_00  D_00  xi_00  W_00
H_01  eta_01  q0*q1   lambda_01  D_01  xi_01  W_01
H_11  eta_11  q1*q1   lambda_11  D_11  xi_11  W_11


## Tips

• The parameter $\eta$ should be entered as an integer in the potential file.