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This study redefines relativistic correlation energy by optimizing projection operators in Multiconfigurational Self-Consistent Field (MCSCF) calculations. This approach yields a more accurate correlation energy compared to standard methods, improving relativistic quantum chemistry.

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Area of Science:

  • Quantum Chemistry
  • Relativistic Atomic and Molecular Calculations

Background:

  • The definition of correlation energy in nonrelativistic quantum chemistry is the difference between the exact electronic energy and the Hartree-Fock energy.
  • Extending this definition to relativistic calculations is challenging due to the Dirac-Coulomb Hamiltonian lacking bound solutions and the use of the no-pair approximation.
  • Current relativistic methods often freeze projection operators at the correlated level, potentially leading to inaccuracies.

Purpose of the Study:

  • To redefine and accurately calculate correlation energy within 4-component relativistic atomic and molecular calculations.
  • To investigate the optimization of projection operators in relativistic correlated calculations.
  • To compare the proposed method with existing approaches and analyze the scaling of relativistic correlation energy.

Main Methods:

  • Proposed optimizing projection operators in correlated calculations using full Multiconfigurational Self-Consistent Field (MCSCF) with a no-pair full Configuration Interaction (CI) expansion, including orbital relaxation from negative-energy orbitals.
  • Employed variational perturbation theory to analyze the nature of the correlation energy expressions.
  • Performed numerical calculations on two-electron rare gas atoms using tailored basis sets.

Main Results:

  • The proposed MCSCF correlation energy is shown to be a pure MP2-like expression, while the CI correlation energy includes an additional relaxation term.
  • The MCSCF-derived correlation energy is smaller than the no-pair full CI correlation energy, consistent with the minmax principle.
  • Relativistic correlation energy from no-pair full MCSCF calculations exhibits a scaling of at worst X(-2) with basis set size, an improvement over previous X(-1) findings.

Conclusions:

  • Optimizing projection operators in correlated relativistic calculations is crucial for an accurate definition of correlation energy.
  • The proposed MCSCF approach provides a more rigorous treatment of relativistic correlation energy.
  • Relativistic correlation energy scaling is dependent on nuclear charge, unlike its nonrelativistic counterpart, due to the need for explicit speed of light scaling.