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Inclusion of Three-body Correction to Relativistic Equation-of-Motion Coupled Cluster Method: The Application to Electron Detachment Problem

Mrinal Thapa, Achinyta Kumar Dutta

Abstract

We present the formulation and implementation of triples correction scheme to the relativistic equation-of-motion coupled-cluster method for ionization potential. Both full and partial triples correction schemes are implemented using the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with Cholesky-Decomposition (CD) of two-electron integrals and a frozen natural spinor (FNS) truncation scheme to reduce computational cost. Benchmark calculations on halide anions, noble gas atoms, hydrogen halides, and dihalogen molecules demonstrate that triple excitations are essential for achieving quantitative ionization potentials, reducing mean absolute errors to approximately 0.01--0.08~eV relative to reference and experimental values. The X2CAMF approximation reproduces four-component Dirac-Coulomb results with negligible deviations, while the CD-FNS strategy yields substantial reductions in wall time. The resulting partial triples correction scheme scales as non-iterative $\mathcal{O}(n^7)$ with storage comparable to CCSD, offering an accurate and practical route for relativistic ionization energy calculations in heavy-element systems.

Inclusion of Three-body Correction to Relativistic Equation-of-Motion Coupled Cluster Method: The Application to Electron Detachment Problem

Abstract

We present the formulation and implementation of triples correction scheme to the relativistic equation-of-motion coupled-cluster method for ionization potential. Both full and partial triples correction schemes are implemented using the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with Cholesky-Decomposition (CD) of two-electron integrals and a frozen natural spinor (FNS) truncation scheme to reduce computational cost. Benchmark calculations on halide anions, noble gas atoms, hydrogen halides, and dihalogen molecules demonstrate that triple excitations are essential for achieving quantitative ionization potentials, reducing mean absolute errors to approximately 0.01--0.08~eV relative to reference and experimental values. The X2CAMF approximation reproduces four-component Dirac-Coulomb results with negligible deviations, while the CD-FNS strategy yields substantial reductions in wall time. The resulting partial triples correction scheme scales as non-iterative with storage comparable to CCSD, offering an accurate and practical route for relativistic ionization energy calculations in heavy-element systems.
Paper Structure (22 sections, 50 equations, 5 figures, 2 tables)

This paper contains 22 sections, 50 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction:
  2. Theory and Computational Details
  3. Relativistic EOM-Coupled-Cluster for Ionised States
  4. Approximate Triples
  5. X2CAMF Approximation
  6. Cholesky Decomposition
  7. Natural Spinors
  8. Implementation and Computational Details
  9. Results and Discussion
  10. The choice of truncation threshold
  11. The comparison of accuracy in different partial triples correction schemes
  12. Comparision with experimental ionization potentials
  13. Comparison with 4-component results
  14. Ionization of Di-Halogen Molecules
  15. Time Calculations
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Schematic representation for different CD-based X2CAMF-FNS methods.
  • Figure 2: Convergence of the ionization energy calculated using different EOM-CC methods with respect to the FNS truncation threshold ($10^{−n}$) for the HCl molecule.
  • Figure 3: The deviations in ionization energies of atoms and anions obtained from different IP-EOM-CC methods relative to the reference IP-EOM-CCSDT values. The dyall.v3z basis set was employed for all atoms.
  • Figure 4: Deviations in ionization energies computed using X2CAMF and spin-free X2C Hamiltonians relative to the 4-c reference for FNS-IP-EOM-CCSD(T)(a)*. The basis set dyall.v4z was used for all atoms.
  • Figure 5: (A) Comparison of computation times for the evaluation of the correlation energy using the 4c-canonical, 4c-FNS, and CD-X2CAMF-FNS implementations of CCSD(T)(a)* for the HI molecule. (B) Breakdown of the individual timing components for the 4c-FNS and CD-X2CAMF-FNS implementations. The dyall.v4z basis set was used for both hydrogen and iodine atoms.