Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches

TL;DR

This paper introduces a downfolding approach to improve the convergence of coupled-cluster calculations for metals, showing it outperforms traditional composite methods in basis set convergence and accurately estimates correlation energies.

Contribution

The study develops a downfolding technique for high-energy excitations in CCSD, enhancing basis set convergence for metallic systems compared to existing composite methods.

Findings

Downfolding approach converges faster with basis set size.

CCSD recovers over 90% of correlation energy at r_s=4.

Downfolding outperforms composite methods in accuracy and convergence.

Abstract

Coupled-cluster theory with single and double excitations (CCSD) is a promising ab initio method for the electronic structure of three-dimensional metals, for which second-order perturbation theory (MP2) diverges in the thermodynamic limit. However, due to the high cost and poor convergence of CCSD with respect to basis size, applying CCSD to periodic systems often leads to large basis set errors. In a common "composite" method, MP2 is used to recover the missing dynamical correlation energy through a focal-point correction, but the inadequacy of MP2 for metals raises questions about this approach. Here we describe how high-energy excitations treated by MP2 can be "downfolded" into a low-energy active space to be treated by CCSD. Comparing how the composite and downfolding approaches perform for the uniform electron gas, we find that the latter converges more quickly with respect to the basis set size. Nonetheless, the composite approach is surprisingly accurate because it removes the problematic MP2 treatment of double excitations near the Fermi surface. Using the method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find CCSD recovers over 90% of the exact correlation energy at $r_s=4$. We also test the composite and downfolding approaches with the random-phase approximation used in place of MP2, yielding a method that is more effective but more expensive.