Methods for converging correlation energies within the dielectric matrix formalism

Abstract

Within the dielectric matrix formalism, the random phase approximation (RPA) and analogous methods that include exchange effects are promising approaches to overcome some of the limitations of traditional density functional theory approximations. The RPA-type methods however have a significantly higher computational cost, and, similarly to correlated quantum chemical methods, are characterized by a slow basis set convergence. In this work we analyzed two different schemes to converge the correlation energy, one based on a more traditional complete basis set (CBS) extrapolation and one that converges energy differences by accounting for the size-consistency property. These two approaches have been systematically tested on the A24 test set, for six points on the potential energy surface of the methane-formaldehyde complex, and for reaction energies involving the breaking and formation of covalent bonds. While both methods converge to similar results at similar rates, the computation of size-consistent energy differences has the advantage of not relying on the choice of a specific extrapolation model. E CBS(11,30) RPA , E CBS(21,40) RPA , and E CBS(31,50) RPA, and obtained from energy differences for three

Computing RPA Adsorption Enthalpies by Machine Learning Thermodynamic Perturbation Theory

“…The RPA is a correlated method that can be derived in the framework of DFT, , Green’s functions, , and coupled-cluster theory . Successful (zero temperature) applications of this approach include description of properties of liquids, layered materials, , bulk solids, − and molecules adsorbed on surfaces. − The RPA is considered particularly accurate for the description of systems where weak van der Waals (vdW) interactions play a dominant role. , In order to improve the description of short-range interactions, a series of beyond-RPA approaches have been developed based on considerations on the homogeneous electron gas, , by using the adiabatic hybrid functional approximation, by including single excitations, or based on exact exchange kernels both in the local − and approximate nonlocal forms. − …”

Bridging molecular dynamics and correlated wave-function methods for accurate finite-temperature properties

“…Whether via RPA, MP or CC theories, correlated wave-function methods hold the promise of a significantly higher level of accuracy, which is of fundamental importance for design of truly predictive approaches to assist experimental and technological developments. However, they are characterized by an unfavorable scaling, slow basis set convergence [26,28,44], and slow cell size convergence [45], making them expensive.…”