Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Many-body post-processing of density functional calculations using the variational quantum eigensolver for Bader charge analysis

Erik Schultheis, Alexander Rehn, Gabriel Breuil

TL;DR

This work introduces Dopyqo, a many-body post-processing workflow that builds a KS-derived, plane-wave-based Hamiltonian and solves it with a variational quantum eigensolver to obtain Bader charges in periodic systems. By computing real-space densities from VQE-optimized wavefunctions within a frozen-core active space, the method yields Bader charges $Q_I= int_{B_I} ho(m{r})d^3m{r}$ that more accurately reflect strong electronic correlations, especially in transition-metal oxides, compared to standard DFT. Across MgH$_2$ and TMOs, Dopyqo brings Bader-excess charges closer to DFT+U references, while MgH$_2$ remains well-described by DFT, illustrating selective improvement where correlation effects are critical. The approach avoids Hubbard parameter tuning, offers a scalable path to include correlation in charge analyses, and is made available as open-source software for integration with quantum resources and broader material studies.

Abstract

Quantum chemistry and condensed matter physics are among the most promising applications of quantum computers. Further, estimating properties of a material is crucial to evaluate its industrial applications. To investigate charge distributions of weakly and strongly correlated systems we calculate Bader charges for various periodic systems by solving many-body Hamiltonians using the variational quantum eigensolver. The Hamiltonians are computed from Kohn-Sham orbitals obtained from a prior DFT calculation. We first demonstrate the accuracy of our method on various doped MgH2 supercells. Further, we show that our approach, compared to standard DFT, significantly improves the Bader charge values for strongly correlated transition metal oxides, where we take DFT+U results as a reference. The computational framework behind our many-body calculations, called Dopyqo, is made openly available as a software package.

Many-body post-processing of density functional calculations using the variational quantum eigensolver for Bader charge analysis

TL;DR

This work introduces Dopyqo, a many-body post-processing workflow that builds a KS-derived, plane-wave-based Hamiltonian and solves it with a variational quantum eigensolver to obtain Bader charges in periodic systems. By computing real-space densities from VQE-optimized wavefunctions within a frozen-core active space, the method yields Bader charges that more accurately reflect strong electronic correlations, especially in transition-metal oxides, compared to standard DFT. Across MgH and TMOs, Dopyqo brings Bader-excess charges closer to DFT+U references, while MgH remains well-described by DFT, illustrating selective improvement where correlation effects are critical. The approach avoids Hubbard parameter tuning, offers a scalable path to include correlation in charge analyses, and is made available as open-source software for integration with quantum resources and broader material studies.

Abstract

Quantum chemistry and condensed matter physics are among the most promising applications of quantum computers. Further, estimating properties of a material is crucial to evaluate its industrial applications. To investigate charge distributions of weakly and strongly correlated systems we calculate Bader charges for various periodic systems by solving many-body Hamiltonians using the variational quantum eigensolver. The Hamiltonians are computed from Kohn-Sham orbitals obtained from a prior DFT calculation. We first demonstrate the accuracy of our method on various doped MgH2 supercells. Further, we show that our approach, compared to standard DFT, significantly improves the Bader charge values for strongly correlated transition metal oxides, where we take DFT+U results as a reference. The computational framework behind our many-body calculations, called Dopyqo, is made openly available as a software package.
Paper Structure (23 sections, 67 equations, 3 figures)

This paper contains 23 sections, 67 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Density functional theory
  4. Many-body Hamiltonian and matrix elements
  5. Periodicity of the matrix elements
  6. Single-electron matrix elements
  7. Nuclear interaction
  8. Two-electron matrix elements and electron self-energy
  9. Frozen core approximation
  10. Variational quantum eigensolver
  11. Bader charges
  12. Results
  13. Computational methods
  14. Bader Excess Charges in Magnesium Systems and Transition Metal Oxides
  15. MgH$_2$ systems
  16. ...and 8 more sections

Figures (3)

  • Figure 1: The computational cell used for crystal structures taken from PaskasMamula2014Electronic representing a $2\times 2\times 2$ supercell of MgH$_2$. The orange spheres represent an Mg atom, the white spheres are hydrogen atoms and the central light blue sphere is either a Mg atom or a TM atom (Ti, Cr, Fe, Ni, Zn).
  • Figure 2: BECs on the central atom of the $2\times 2\times 2$ supercell of MgH$_2$. The orange circles are the reference data points PaskasMamula2014Electronic, the green triangles are DFT-NC results and the black crosses are Dopyqo results.
  • Figure 3: BECs on the different atom types in transition metal oxides (TMOs) and transition metal disulfide (TMS) for a given active space for two electronic structure calculations: DFT-NC and Dopyqo. The BEC are compared to Refs. Lu2018UnravelingChoudhuri2020Calculating.