Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD)

TL;DR

This study demonstrates the feasibility of self-energy functional theory (SFT) for electronic structure calculations of transition metal atoms and compares its Green's functions with those from the coupled-cluster singles and doubles (CCSD) method, highlighting their reliability.

Contribution

It introduces a self-consistent SFT approach for realistic systems and compares its results with CCSD, revealing their consistency and limitations beyond DFT.

Findings

SFT can produce degenerate spin-polarized ground states from unpolarized initial states.

Both SFT and CCSD reliably predict spectral functions for transition metals.

DFT may fail to accurately predict orbital energy spectra in these systems.

Abstract

We demonstrate in the present study that self-consistent calculations based on the self-energy functional theory (SFT) are possible for the electronic structure of realistic systems in the context of quantum chemistry. We describe the procedure of a self-consistent SFT calculation in detail and perform the calculations for isolated $3 d$ transition metal atoms from V to Cu as a preliminary study. We compare the one-particle Green's functions (GFs) obtained in this way and those obtained from the coupled-cluster singles and doubles (CCSD) method. Although the SFT calculation starts from the spin-unpolarized Hartree--Fock (HF) state for each of the target systems, the self-consistency loop correctly leads to degenerate spin-polarized ground states. We examine the spectral functions in detail to find their commonalities and differences among the atoms by paying attention to the characteristics of the two approaches. It is demonstrated via the two approaches that calculations based on the density functional theory (DFT) can fail in predicting the orbital energy spectra for spherically symmetric systems. It is found that the two methods are quite reliable and useful beyond DFT.