The Vashishta potential

From GPUMD
Jump to navigation Jump to search

Brief descriptions

  • This is the Vashishta potential corresponding to [Vashishta 2007].
  • It only applies to systems with two atom types.

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:

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

  • The two-body part reads

\begin{equation} 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}. \end{equation} 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:

\begin{equation} 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}. \end{equation} Therefore, both the potential and the force for the two-body part are continuous at the cutoff distance [math]r_c[/math].

  • The three-body part is

\begin{equation} 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}. \end{equation} The parameter [math]\gamma[/math] is always 1 A and is thus redundant.

Parameters

Parameter Units
[math]B[/math] eV
[math]h[/math] dimensionless
[math]C[/math] dimensionless
[math]r_0[/math] A
[math]r_c[/math] A
[math]H[/math] eV A[math]^{\eta}[/math]
[math]\eta[/math] dimensionless
[math]q[/math] e
[math]\lambda[/math] A
[math]D[/math] e2 A3
[math]\xi[/math] A
[math]W[/math] 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
  • The parameter [math]\eta[/math] should be entered as an integer in the potential file.

References