ESF SPLINES

ESF_SPLINES = .FALSE. | .TRUE.
Default: ESF_SPLINES = .FALSE.

Description: ESF_SPLINES selects k-point interpolation in ACFDT(R) calculations using tri-cubic splines.

Interpolates the electronic structure factor in ACFDT/RPA calculations using tri-cubic splines to accelerate k-point convergence of the RPA correlation energy. This feature follows the same idea as in coupled cluster calculations.^[1]

To this end, the electronic structure factor in the RPA

${\displaystyle S({\bf q}+{\bf G}) =\int {\rm d}\omega \left\{(\mathrm{ln}[1-\tilde\chi^0({\mathbf{q}},\mathrm{i}\omega)V({\mathbf{q}})])_{{\mathbf{G,G}}} +V_{{\mathbf{G,G}}}({\mathbf{q}})\tilde\chi^0({\mathbf{q}},{\mathrm{i}}\omega) \right\} }$

is evaluated on the k-point grid defined in KPOINTS and the correlation energy (as its trace) is stored.^[2] To obtain the correlation energy on a finer k-point grid, more q-points are added using tri-cubic spline interpolation and the resulting energy is compared to the previous correlation energy. This procedure is repeated ESF_NINTER times until the difference in energy between the interpolation steps is less than ESF_CONV. The default settings of ESF_NINTER and ESF_CONV typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit ${\displaystyle \lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},{\rm i}\omega) \cdot {\bf V}_{\bf G G'}({\bf q}) }$ is stored to WAVECAR in a preceding DFT calculation using LOPTICS=T.

Tip: This method works for metals and insulators.

Warning: Remove WAVEDER before running the job and avoid setting LOPTICS.

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