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Direct Atomic-Orbital-Based Relativistic Two-Component Linear Response Method for Calculating Excited-State Fine

Franco Egidi1, Joshua J Goings1, Michael J Frisch2

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Summary

This study introduces a new computational method for calculating relativistic effects in molecules, accurately predicting excited-state zero-field splittings for various systems. The approach shows good agreement with experimental data, particularly for lighter elements.

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Area of Science:

  • Quantum Chemistry
  • Relativistic Effects in Molecules
  • Computational Spectroscopy

Background:

  • Relativistic effects are crucial for accurately describing electronic structures of heavy elements.
  • Existing methods often struggle to incorporate these effects efficiently, especially for excited states.
  • Accurate computation of excited-state properties like zero-field splittings is vital for understanding molecular behavior.

Purpose of the Study:

  • To develop and present a linear-response formalism for the complex two-component Hartree-Fock Hamiltonian.
  • To include scalar and spin relativistic effects within Douglas-Kroll-Hess and Exact-Two-Component frameworks.
  • To enable the computation of excited-state zero-field splittings, particularly when one-electron relativistic effects dominate.

Main Methods:

  • Developed a linear-response formalism for a complex two-component Hartree-Fock Hamiltonian.
  • Incorporated scalar and spin relativistic effects using Douglas-Kroll-Hess and Exact-Two-Component methods.
  • Implemented an efficient direct formalism for solving the complex two-component response function.

Main Results:

  • The developed method accurately computes excited-state zero-field splittings, showing good agreement with experimental values.
  • All approximations within the method performed similarly for the studied systems.
  • The accuracy decreased for heavy elements and states with high orbital angular momentum, indicating the importance of two-electron relativistic effects.

Conclusions:

  • Relativistic two-component linear response methods effectively capture excited-state zero-field splittings.
  • The method provides a reliable tool for studying relativistic effects in molecular excited states.
  • Further development is needed to fully account for two-electron relativistic effects in heavy elements.