TwoParticleCoulombInteractionPointChargeMethod

class TwoParticleCoulombInteractionPointChargeMethod

Calculate the two-particle integrals in orbital space as:

\(\langle \psi_a\psi_b | V | \psi_c\psi_d \rangle = \sum_{\mathbf{R}_1,\mathbf{R}_2} V(\mathbf{R}_1 - \mathbf{R}_2) \sum_{\alpha \in U(\mathbf{R}_1)} c_{a,\alpha}^* c_{d,\alpha} \sum_{\beta \in U(\mathbf{R}_2)} c_{b,\beta}^* c_{c,\beta}\)

where \(c\) are the wavefunction coefficients in orbital space and \(U(\mathbf{R})\) the orbitals centered on \(\mathbf{R}\).

The divergent term \(\mathbf{R}_1 = \mathbf{R}_2\) is approximated by averaging on a sphere. This method is computationally very efficient, but it is a somewhat crude approximation only suitable for large systems (several thousands of atoms).