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

Abstract

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger 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.

8 pages, 4 figures, 1 table

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• Periodic Local Coupled-Cluster Theory for Insulators and Metals
• Integral-direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal
• Interacting-bath dynamical embedding for capturing non-local electron correlation in solids
• The role of electron correlations in the electronic structure of putative Chern magnet TbMn${}_6$Sn${}_6$
• Machine learning for a finite size correction in periodic coupled cluster theory calculations
• Converging High-Level Coupled-Cluster Energetics via Adaptive Selection of Excitation Manifolds Driven by Moment Expansions
• Sampling the reciprocal Coulomb potential in finite and anisotropic cells
• Deep learning quantum Monte Carlo for solids
• Ground-States for Metals from Converged Coupled Cluster Calculations
• Resolving Finite-Size Errors in EOM-CCSD Band Gaps of Solids with Interacting-Bath Dynamical Embedding Theory