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A finite-element Delta-Sternheimer approach for accurate all-electron RPA correlation energies of arbitrary molecules

Hao Peng, Haochen Liu, Chuhao Li, Hehu Xie, Xinguo Ren

TL;DR

This work introduces a finite-element Delta-Sternheimer framework to compute all-electron RPA correlation energies for general molecules, addressing single-particle basis-set incompleteness by marrying real-space FEM with a localized atomic-orbital basis. The approach removes basis-set errors in the first-order KS response and leverages adaptive mesh refinement to achieve meV-level convergence with a manageable number of FE degrees of freedom, while RI errors are carefully analyzed and controlled. Benchmark results on water dimers and 50 small molecules demonstrate near CBS-quality accuracy, with CBS extrapolation significantly reducing basis-set errors and RI errors being the dominant residual source. Overall, the method provides high-accuracy RPA energies for general molecules and offers a scalable, benchmark-quality framework that can impact correlated electronic-structure calculations beyond small systems.

Abstract

The incompleteness of single-particle basis sets has long cast a shadow over correlated electronic-structure methods, making it highly challenging to obtain numerically converged results. In this work, we compute the RPA correlation energies of general molecules using the finite element method, while ingeniously combining atomic orbital basis sets to accelerate the convergence of total energies. We report atomization energies for 50 molecules within the RPA framework, achieving accuracies on the order of meV per atom. The computational strategy that integrates real-space discretization techniques with atomic orbitals is expected to inspire the entire correlated electronic-structure community.

A finite-element Delta-Sternheimer approach for accurate all-electron RPA correlation energies of arbitrary molecules

TL;DR

This work introduces a finite-element Delta-Sternheimer framework to compute all-electron RPA correlation energies for general molecules, addressing single-particle basis-set incompleteness by marrying real-space FEM with a localized atomic-orbital basis. The approach removes basis-set errors in the first-order KS response and leverages adaptive mesh refinement to achieve meV-level convergence with a manageable number of FE degrees of freedom, while RI errors are carefully analyzed and controlled. Benchmark results on water dimers and 50 small molecules demonstrate near CBS-quality accuracy, with CBS extrapolation significantly reducing basis-set errors and RI errors being the dominant residual source. Overall, the method provides high-accuracy RPA energies for general molecules and offers a scalable, benchmark-quality framework that can impact correlated electronic-structure calculations beyond small systems.

Abstract

The incompleteness of single-particle basis sets has long cast a shadow over correlated electronic-structure methods, making it highly challenging to obtain numerically converged results. In this work, we compute the RPA correlation energies of general molecules using the finite element method, while ingeniously combining atomic orbital basis sets to accelerate the convergence of total energies. We report atomization energies for 50 molecules within the RPA framework, achieving accuracies on the order of meV per atom. The computational strategy that integrates real-space discretization techniques with atomic orbitals is expected to inspire the entire correlated electronic-structure community.
Paper Structure (22 sections, 38 equations, 5 figures, 13 tables)

This paper contains 22 sections, 38 equations, 5 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Results and Discussions
  3. Basis-set-issue check for water dimer
  4. Atomization energies
  5. Summary
  6. Method
  7. Acknowledgment.
  8. Numerical methods
  9. Finite element method
  10. Mesh adaptive refinement
  11. Delta-Sternheimer Framework
  12. Implementation details
  13. Obtaining adaptive mesh
  14. Convergence test
  15. Converge behavior with respect to the mesh density for the standard Sternheimer method and the Delta-Sternheimer method.
  16. ...and 7 more sections

Figures (5)

  • Figure 1: The RPA total energy differences of 20 different configurations of the water dimer.
  • Figure 2: Workflow.
  • Figure 3: Workflow.
  • Figure 4: Converge behavior with respect to the mesh density of CH$_4$.
  • Figure 5: The RPA total energy differences of 20 different configurations of the water dimer.