Correlation Energy in Solids

Andrzej M. Oleś, K. A. Chao

Andreas Grüneis

We introduce a novel and efficient explicitly correlated implementation of second-order perturbation theory for solids. The required three-electron integrals are computed directly using a plane wave basis set. We parametrize the employed correlation factors using results previously obtained for a finite uniform electron gas simulation cell. We demonstrate for a range of solids that basis set converged correlation energies, equilibrium volumes, and bulk moduli can be obtained efficiently in this theory using a few ten orbitals per atom. To stretch the capabilities of this novel method we compute the Schottky defect formation energy in MgO, studying systems with 54 atoms in the supercell. We verify the accuracy of the calculated formation energies using the more accurate coupled cluster singles and doubles theory. Furthermore, we discuss other potential applications for the derived and implemented expressions such as an occupied orbital only correlation energy functional.

Soohaeng Yoo Willow, Kwang S. Kim, So Hirata

A quantum Monte Carlo method that combines the second-order many-body perturbation theory and Monte Carlo (MC) integration has been developed for correlation and correlation-corrected (quasiparticle) energy bands of one-dimensional solids. The sum-of-product expressions of correlation energy and self-energy are transformed, with the aid of a Laplace transform, into high-dimensional integrals, which are subject to a highly scalable MC integration with the Metropolis algorithm for importance sampling. The method can compute correlation energies of polyacetylene and polyethylene within a few $\text{m}{E}_{\text{h}}$ and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.

Peter Horsch, Peter Fulde

Sergei Iskakov, А. И. Русаков, Emanuel Gull +1 more

Jeffrey A. Cina, R. Silbey

We propose the use of optical Hartmann–Hahn resonance between guest molecules in a solid in order to study the extent of spatial correlation of site energies in the inhomogeneous distribution. The correlation length and the form of the interaction which mediates the resonance between guest molecules can be determined from the time development of fluorescence.