The Buckingham-Coulomb potential

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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
[math]A_{ij}[/math] eV
[math]b_{ij}[/math] A-1
[math]C_{ij}[/math] A6
[math]q_{i}[/math] e
[math]\alpha[/math] A-1
[math]R_c[/math] A
  • [math]\alpha[/math] is the electrostatic damping factor and [math]R_c[/math] is the cutoff radius for the Coulomb potential.
  • In GPUMD, we have fixed [math]\alpha[/math] 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