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State Interaction for Relativistic Four-Component Methods: Choose the Right Zeroth-Order Hamiltonian for Late-Row

Chad E Hoyer1, Can Liao1, Kirill D Shumilov1

  • 1Department of Chemistry, University of Washington, Seattle, Washington 98195, United States.

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|September 11, 2024
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Summary
This summary is machine-generated.

We developed new methods for calculating relativistic effects in atoms and molecules. Augmenting the standard approach improves accuracy for heavy elements, paving the way for efficient, high-precision calculations.

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Area of Science:

  • Quantum Chemistry
  • Relativistic Quantum Mechanics
  • Computational Chemistry

Background:

  • Relativistic effects are crucial for accurately describing heavy elements.
  • State interaction methods traditionally use simplified scalar-relativistic Hamiltonians.
  • Accurate treatment of electron correlation and relativistic effects is computationally demanding.

Purpose of the Study:

  • To develop and investigate novel perturbative schemes for relativistic four-component Hamiltonians.
  • To improve the accuracy of state interaction methods by augmenting the zeroth-order Hamiltonian.
  • To establish a theoretical foundation for low-scaling, high-accuracy relativistic calculations.

Main Methods:

  • Spin-separation of the Dirac-Coulomb-Breit Hamiltonian.
  • Development of augmented zeroth-order Hamiltonians with increasing accuracy.
  • Benchmarking against ground-state fine-structure splitting in late-row atoms and diatomic hydrides.

Main Results:

  • Augmenting the zeroth-order Hamiltonian with vector-relativistic operators significantly improves accuracy.
  • Scalar-relativistic approximations lead to substantial errors in fine-structure splitting.
  • The proposed schemes show convergence towards the variational limit.

Conclusions:

  • Augmented zeroth-order Hamiltonians offer a pathway to high-accuracy relativistic calculations.
  • The developed methods are suitable for describing late-row elements where relativistic effects dominate.
  • This work provides a theoretical basis for future efficient relativistic quantum chemistry methods.