$\textit{Ab initio}$ correlated calculations without finite basis-set error: Numerically precise all-electron RPA correlation energies for diatomic molecules

TL;DR

This paper introduces a method to compute basis-error-free RPA correlation energies for diatomic molecules with high precision, providing reliable reference data for quantum chemistry calculations and basis set development.

Contribution

The authors develop a numerically precise all-electron RPA correlation energy calculation method that eliminates basis set errors for diatomic molecules.

Findings

Achieves meV-level accuracy in RPA energies

Provides benchmark data for assessing computational procedures

Guides development of correlation-consistent basis sets

Abstract

In wavefunction-based $\textit{ab-initio}$ quantum mechanical calculations, achieving absolute convergence with respect to the one-electron basis set is a long-standing challenge. In this work, using the random phase approximation (RPA) electron correlation energy as an example, we show how to compute the basis-error-free RPA correlation energy for diatomic molecules by iteratively solving the Sternheimer equations for first-order wave functions in the prolate spheroidal coordinate system. Our approach provides RPA correlation energies across the periodic table to any desired precision; in practice, the convergence of the absolute RPA energies to the meV-level accuracy can be readily attained. Our method thus provides unprecedented reference numbers that can be used to assess the reliability of the commonly used computational procedures in quantum chemistry, such as the counterpoise correction to the basis set superposition errors, the frozen-core approximation, and the complete-basis-set extrapolation scheme. Such reference results can also be used to guide the development of more efficient correlation-consistent basis sets. The numerical techniques developed in the present work also have direct implications for the development of basis error-free schemes for the GW method or the \textit{ab initio} quantum chemistry methods such as MP2.