Effective Hamiltonians for the study of real metals using quantum chemical theories

TL;DR

This paper demonstrates that coupled cluster singles and doubles (CCSD) methods can be effectively applied to real metals by using an effective Hamiltonian approach, significantly reducing computational costs and overcoming size limitations.

Contribution

The authors introduce a novel effective Hamiltonian approach using the transition structure factor, enabling CCSD to be applied to metals with reduced finite size effects and computational cost.

Findings

Successful application of CCSD to lithium and silicon metals

Reduction of computational cost by two orders of magnitude

Achievement of the thermodynamic limit in simulations

Abstract

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a central role in molecular quantum chemistry because of its systematic improvability and computational efficiency. In this hierarchy, coupled cluster singles and doubles (CCSD) is one of the most important steps in moving towards chemical accuracy and, in recent years, its scope has successfully been expanded to the study of insulating surfaces and solids. Here, we show that CCSD theory can also be applied to real metals. In so doing, we overcome the limitation of needing extremely large supercells to capture long range electronic correlation effects. An effective Hamiltonian can be found using the transition structure factor--a map of electronic excitations from the Hartree--Fock wavefunction--which has fewer finite size effects than conventional periodic boundary conditions. This not only paves the way of applying coupled cluster methods to real metals but also reduces the computational cost by two orders of magnitude compared to previous methods. Our applications to phases of lithium and silicon show a resounding success in reaching the thermodynamic limit, taking the first step towards a truly universal quantum chemical treatment of solids.