Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

Abstract

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.

Perspective: Explicitly correlated electronic structure theory for complex systems

“…90 In the case of the uniform electron gas, such a correlation factor strongly depends on the average density of the valence electron gas. 120 The optimum γ increases with the gas density when modeling a strongly confined electron correlation hole. This observation suggests that the correlation factor can be parametrized as a function of the average valence electron gas density.…”

“…Numerical characterization is, therefore, valuable for an exhaustive list of correlation factors, and such a study is easily possible and well underway for MC-MP2-F12. Other approaches that have the same flexibility include the QMC methods, 96,98 GTG expansions, 65 and plane-wavebased methods, 120,121 with which excellent accuracy of the socalled Yukawa-Coulomb geminal was observed for a homogeneous electron gas (HEG). 120 To a lesser extent, the mixed Gaussian-basis-set and multicenter-grid method 68 also lifts TABLE I.…”

“…Other approaches that have the same flexibility include the QMC methods, 96,98 GTG expansions, 65 and plane-wavebased methods, 120,121 with which excellent accuracy of the socalled Yukawa-Coulomb geminal was observed for a homogeneous electron gas (HEG). 120 To a lesser extent, the mixed Gaussian-basis-set and multicenter-grid method 68 also lifts TABLE I. The average error (in mE h ) in the MC-MP2-F12(VBX) correlation energies from the MP2 correlation energies in the CBS limits for 17 small molecules.…”

“…This is one reason why there have been relatively few studies on explicitly correlated methods including TC implementations for solids. 42,44,45,120,121,158 Alternatively, it is possible to employ Gaussian basis sets in explicitly correlated theory for solids. 129,159 The main advantage of this approach is that one can exploit the framework developed in F12 theory for many-electron integrals in conjunction with the local correlation techniques described in Sec.…”

Range-separated double-hybrid density-functional theory applied to periodic systems

“…14 Concerning the study of solids, we note that the introduction of wave-function-based correlation treatment for periodic systems is relatively recent. [18][19][20][21][22][23][24][25][26] Martinez-Casado and a) lorenzo.maschio@unito.it coworkers proposed to estimate the correlation energy as a MP2 contribution using a B3LYP reference state and applied this scheme to the study of the adsorption of helium atoms on a MgO surface. 27 Del Ben and coworkers 24 benchmarked the performance of some global double hybrids on a set of molecular crystals.…”