Improving the efficiency of beyond-RPA methods within the dielectric matrix formulation: Algorithms and applications to the A24 and S22 test sets

Within a formalism based on dielectric matrices, the electron-hole time-dependent Hartree-Fock (eh-TDHF) and the adiabatic connection second-order screened exchange (AC-SOSEX) are promising approximations to improve ground-state correlation energies by including exchange effects beyond the random phase approximation (RPA)¹. We introduce here an algorithm based on a Gram-Schmidt orthogonalization (GSO) procedure that significantly reduces the number of matrix elements to be computed to evaluate the response functions that enter in the formulation of these two methods². This approach does not lead to a significant loss of accuracy and extends the applicability of the eh-TDHF and AC-SOSEX to much larger systems. The inclusion of exchange effects beyond the RPA significantly improves the accuracy, with mean absolute errors that decrease by almost 40% for the A24 test set and by almost 50% for the S22 test set. This approach might be used in the future to improve the correlation energy in solid state applications.

¹ A. Dixit, J. Angyan, and D. Rocca, JCP 145, 104105 (2016)
² A. Dixit, J. Claudot, S. Lebègue, and D. Rocca, JCTC (2017), DOI: 10.1021/acs.jctc.7b00837