# The Buckingham-Coulomb potential

## Potential form

• This is also called the rigid-ion (RI) potential. It consists of the Buckingham potential

$$U_{ij} = A_{ij} \exp\left( - b_{ij} r_{ij} \right) - \frac{C_{ij} }{ r_{ij}^{6} }$$ and a Coulomb potential.

• The Coulomb potential is evaluated using the damped-shifted-force (DSF) method by Fennell and Gezelter. The DSF version of the pairwise Coulomb potential can be written as:

$$U_{ij} = \frac{q_iq_j}{4\pi\epsilon_0} \left[ \frac{\text{erfc}(\alpha r_{ij})}{r_{ij}} - \frac{\text{erfc}(\alpha R_{c})}{R_{c}} + \left( \frac{\text{erfc}(\alpha R_{c})}{R_{c}^2} + \frac{2\alpha}{\sqrt{\pi}} \frac{\exp(-\alpha^2R_c^2)}{R_{c}} \right) (r_{ij} - R_c) \right],$$ where erfc is the complementary error function.

## Parameters

 Parameter Units $A_{ij}$ eV $b_{ij}$ A-1 $C_{ij}$ A6 $q_{i}$ e $\alpha$ A-1 $R_c$ A
• $\alpha$ is the electrostatic damping factor and $R_c$ is the cutoff radius for the Coulomb potential.
• In GPUMD, we have fixed $\alpha$ to 0.2 A-1, which is a good choice according to the results by Fennell and Gezelter.

## Potential file

Currently, this potential only applies to systems with two atom types in GPUMD. The potential file for this potential model reads

   ri
q_0   q_1  cutoff
A_00, b_00 C_00
A_11, b_11 C_11
A_01, b_01 C_01