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

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 main-group semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean signed error of 0.24 eV and a mean absolute error of 0.27 eV when compared to experimental values. Although this error is similar to that found for EOM-CCSD applied to molecules, it may also reflect the role of vibrational effects, which are neglected in the calculations. Our results support recently proposed revisions of experimental optical gaps for AlP and cubic BN. 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 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.