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). We introduce here an algorithm based on a Gram-Schmidt orthogonalization (GSO) procedure that significantly reduce the number of matrix elements to be computed to evaluate the response functions that enter in the formulation of these two methods. By considering the A24 test set, we show that this approach does not lead to a significant loss of accuracy and can be effectively applied to compute the small interaction energies involved in weakly bound dimers. Importantly, the GSO method significantly extends the applicability of the eh-TDHF and AC-SOSEX to large systems. This is shown by considering the S22 test set, which includes dimers with up to one hundred valence electrons requiring hundreds of thousands of plane-waves in the basis set. By comparing our results to coupled-cluster benchmark values, we show that 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 based on dielectric matrices is particularly suited for plane-wave implementations and might be used in the future to improve the description of the correlation energy in solid state applications.