Excitons in Solids from Periodic Equation-of-Motion Coupled-Cluster Theory

Abstract

We present an ab initio study of electronically excited states of three-dimensional solids using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The explicit use of translational symmetry, as implemented via Brillouin zone sampling and momentum conservation, is responsible for a large reduction in cost. Our largest system studied, which samples the Brillouin zone using 64 k-points (a 4 × 4 × 4 mesh) corresponds to a canonical EOM-CCSD calculation of 768 electrons in 640 orbitals. We study eight simple semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean absolute error of 0.27 eV when compared to experiment. We furthermore calculate the energy of excitons with nonzero momentum and compare the exciton dispersion of LiF with experimental data from inelastic X-ray scattering. By calculating excitation energies under strain, we extract hydrostatic deformation potentials in order to quantify the strength of interactions between excitons and acoustic phonons. Our results indicate that coupled-cluster theory is a promising method for the accurate study of a variety of exciton phenomena in solids.

Ab initio modeling of excitons: from perfect crystals to biomaterials

“…CC has been successfully used for excited state calculations [28][29][30]. Wang and Berkelback [31] have recently shown that Equation-of-Motion Coupled-Cluster Theory can yield promising results for optical excitation energies, exciton binding energies, exciton dispersion relations, and exciton-phonon interaction energies of simple crystalline solids like Si, C, SiC, MgO, or LiF. Other attempts are made in this direction for ground-state and excited-state methods that combine CC and perturbation theory based on a partitioning of excitations that are internal or external to an active space [32][33][34][35].…”

Correlation-consistent Gaussian basis sets for solids made simple

“…In a similar spirit, one could perform a HF calculation in a large Gaussian basis and then perform an MP2 calculation with some number of frozen virtual orbitals. 10,84 Similar corrections are impossible with the original GTH basis set series due to the high linear dependencies at the QZ (or even TZ) level [Fig. 1(a)].…”

“…Recent years have witnessed a rapid growth of interest in understanding condensed-phase materials using quantum chemistry methods, [1][2][3][4][5][6][7][8][9][10][11][12][13] especially those beyond density functional theory 14,15 (DFT) with local and semi-local exchange-correlation functionals. 16,17 The non-local exchange and the many-body electron correlation in the quantum chemistry methods promise many advantages, such as systematic improvability 7 and the ability to describe dispersion interactions [18][19][20] and strong electron correlations, 21,22 but are also computationally demanding, especially when using a plane-wave (PW) basis set due to the slow convergence with the number of virtual bands.…”

A coupled cluster framework for electrons and phonons

“…The equation-of-motion (EOM) formalism is one way to obtain excited state properties from a coupled cluster ground state [50][51][52] . Though most commonly used for molecular electronic excited states, EOM-CC methods have been applied to excitations in periodic solids 36,[53][54][55] as well as to vibrational excited states in molecules 40,44,47,56 . In this work we describe a coupled cluster theory and corresponding EOM extension for interacting electrons and phonons.…”