TwoParticleCoulombInteractionFFTMethod

class TwoParticleCoulombInteractionFFTMethod(grid_sampling=None)

Calculate two-particle integrals by projecting single-particle orbitals on the real space grid and then evaluating the integral via Fast Fourier Transform as:

\(\langle \psi_a\psi_b | V | \psi_c\psi_d \rangle = \frac{\Omega}{N^2} \sum_{\mathbf{G}} V(\mathbf{G}) \mathrm{FFT}[\rho_{da}(\mathbf{r})]^*(\mathbf{G}) \mathrm{FFT}[\rho_{bc}(\mathbf{r})](\mathbf{G})\)

where \(\Omega\) is the supercell volume.

Parameters:

grid_sampling (PhysicalQuantity of type energy | GridSampling | OptimizedFFTGridSampling) – The grid sampling used to perform the FFT. For the best performance, use OptimizedFFTGridSampling. Note that the Coulomb integrals are sensitive to the grid sampling and might require a finer grid than the default values.
Default: The grid sampling set on the calculator. If the

static eigenstatesRequireNormalization(calculator)

Check if the eigenstates require a normalization before calculating the two particle integrals.