From plane waves to local Gaussians for the simulation of correlated periodic systems

Abstract

We present a simple, robust and black-box approach to the implementation and use of local, periodic, atomcentered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cut-off radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.

Low rank factorization of the Coulomb integrals for periodic coupled cluster theory

“…In this subsection, we only employ MP2 theory to investigate the behavior of the correlation energy calculated from the factorized Coulomb integrals. This study focuses on the decomposition of the Coulomb vertex, neither employing the optimized auxiliary field nor the pseudized Gaussian type virtual orbitals 45 technique. The resulting Coulomb vertices that need to be fit are large, such that only the particle/hole part Γ a iF is used for this study.…”

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions

“…Fully periodic localized orbitals can also be used to construct a Fock space in which to form a CPS, and here we consider an infinitely periodic graphene sheet with 4 × 4 k-point sampling [58]. From a double-zeta periodic Gaussian basis, we choose one localized, translationally invariant 2p z orbital centred on each carbon atom.…”

A many-electron perturbation theory study of the hexagonal boron nitride bilayer system*

“…These choices include a full canonical Hartree-Fock orbital basis, approximate natural orbitals and pseudized Gaussian type orbitals [23]. We note that the implementation of pseudized Gaussian type orbitals has recently been outlined in reference [28]. The use of canonical Hartree-Fock or DFT orbitals corresponds to the standard approach in post-HF or post-DFT calculations of extended systems using a plane wave basis set.…”

“…As such it is sufficient to describe the polarizability of their constituent subsystems on the same level of accuracy. We have recently proposed a method called pseudized Gaussian type orbitals (PGTOs), which allows for employing pseudized GTOs in a planewave basis set code such as VASP [28]. In this work we will explore its accuracy for the study of the interlayer binding energy.…”