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A Third-Order Relativistic Algebraic Diagrammatic Construction Method for Double Ionization Potentials: Theory, Implementation, and Benchmark

Sujan Mandal, Achintya Kumar Dutta

TL;DR

This work introduces a third-order relativistic DIP-ADC method ($ADC(3)$) for computing double ionization potentials, implemented with the $X2CAMF$ two-component Hamiltonian, Cholesky-decomposed ERIs, and Frozen Natural Spinor truncation to drastically reduce memory and compute costs. The approach preserves accuracy relative to four-component Dirac–Coulomb results and experimental data across inert gases and diatomic species, while enabling large basis sets and heavy-element systems. Benchmarking shows near-perfect agreement with 4c results (differences around $10^{-3}$ eV) and excellent alignment with experimental DIP data when using a relativistic Hamiltonian, with ADC(3) outperforming ADC(2) due to proper treatment of $4h2p$-related relaxation effects. The method yields substantial computational savings (e.g., HI DIP-ADC(3) dropping from ~9 h to ~2 minutes) and offers a scalable route to accurate DIP predictions; the authors also discuss the need for ADC(4) to capture higher-order correlation effects fully and outline future extensions.

Abstract

We present a relativistic third-order algebraic diagrammatic construction (ADC(3)) approach for calculating double ionization potentials (DIPs). By employing the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with a Cholesky decomposition (CD) representation of two-electron integrals and the frozen natural spinor (FNS) framework for virtual space truncation, we achieve a significant reduction in both memory requirements and computational cost. The DIPs obtained using the X2CAMF Hamiltonian show excellent agreement with results from fully relativistic four-component calculations. We have validated the accuracy of our implementation through comparisons with available experimental and theoretical data for inert gas atoms and diatomic species. The effect of higher-order relativistic corrections is also explored.

A Third-Order Relativistic Algebraic Diagrammatic Construction Method for Double Ionization Potentials: Theory, Implementation, and Benchmark

TL;DR

This work introduces a third-order relativistic DIP-ADC method () for computing double ionization potentials, implemented with the two-component Hamiltonian, Cholesky-decomposed ERIs, and Frozen Natural Spinor truncation to drastically reduce memory and compute costs. The approach preserves accuracy relative to four-component Dirac–Coulomb results and experimental data across inert gases and diatomic species, while enabling large basis sets and heavy-element systems. Benchmarking shows near-perfect agreement with 4c results (differences around eV) and excellent alignment with experimental DIP data when using a relativistic Hamiltonian, with ADC(3) outperforming ADC(2) due to proper treatment of -related relaxation effects. The method yields substantial computational savings (e.g., HI DIP-ADC(3) dropping from ~9 h to ~2 minutes) and offers a scalable route to accurate DIP predictions; the authors also discuss the need for ADC(4) to capture higher-order correlation effects fully and outline future extensions.

Abstract

We present a relativistic third-order algebraic diagrammatic construction (ADC(3)) approach for calculating double ionization potentials (DIPs). By employing the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with a Cholesky decomposition (CD) representation of two-electron integrals and the frozen natural spinor (FNS) framework for virtual space truncation, we achieve a significant reduction in both memory requirements and computational cost. The DIPs obtained using the X2CAMF Hamiltonian show excellent agreement with results from fully relativistic four-component calculations. We have validated the accuracy of our implementation through comparisons with available experimental and theoretical data for inert gas atoms and diatomic species. The effect of higher-order relativistic corrections is also explored.

Paper Structure

This paper contains 15 sections, 24 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Relativistic DIP-ADC method
  4. The X2CAMF scheme
  5. Cholesky Decomposition
  6. Frozen Natural Spinor technique
  7. Computational details
  8. Results and discussions
  9. Choice of FNS threshold
  10. Benchmarking FNS-CD-X2CAMF results against 4c-DIP-ADC(3) method
  11. Choice of basis set
  12. Comparison of DIP-ADC results with available theoretical and experimental data
  13. Different levels of relativistic hamiltonian treatment
  14. Computational efficiency
  15. Conclusion

Figures (4)

  • Figure 1: Schematic representation of the FNS-CD-X2CAMF-DIP-ADC(3) algorithm.
  • Figure 2: Convergence of the absolute error (in eV) in the lowest DIP value with respect to the size of the virtual space in the canonical and FNS versions of CD-X2CAMF-DIP-ADC(3) method for the Cl$_2$ molecule. The full basis canonical CD-X2CAMF-DIP-ADC(3) result is used as reference, and the dyall.av4z basis set has been used for the calculations.
  • Figure 3: Convergence of the absolute error in the DIP value (in eV) computed using FNS-CD-X2CAMF-DIP-ADC(3) method, with respect to the FNS threshold for Cl$_2$ molecule. The dyall.av4z basis set has been used for the calculations, and the untruncated canonical value is taken as the reference.
  • Figure 4: Comparison of computational timings for different steps in the DIP calculation of HI using canonical 4c, FNS-4c, and FNS-CD-X2CAMF based DIP-ADC(3) methods.