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Analytic second derivatives for the spin-free exact two-component theory.

Lan Cheng1, Jürgen Gauss

  • 1Institut für Physikalische Chemie, Universität Mainz, Mainz, Germany. chengl@uni-mainz.de

The Journal of Chemical Physics
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This study extends spin-free exact two-component theory to calculate second energy derivatives. This advancement enables accurate predictions of molecular properties like geometry and vibrational frequencies for relativistic systems.

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Area of Science:

  • Quantum Chemistry
  • Relativistic Quantum Mechanics

Background:

  • The exact two-component (X2C) theory simplifies relativistic quantum chemistry calculations.
  • Spin-free (SF) approximations reduce computational cost while retaining accuracy.
  • Analytic calculation of energy derivatives is crucial for predicting molecular properties.

Purpose of the Study:

  • To extend the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) to the analytic evaluation of second energy derivatives.
  • To enable efficient and accurate calculation of molecular properties for relativistic systems.
  • To assess scalar-relativistic, electron-correlation, and basis-set effects on molecular properties.

Main Methods:

  • Formulation and implementation of SFX2c-1e theory for analytic second energy derivatives.
  • Block diagonalization of the four-component Dirac Hamiltonian to obtain the "electrons-only" two-component Hamiltonian.
  • Utilizing untransformed two-electron interactions and derivative integrals from the four-component Hamiltonian.
  • Application to the copper hydroxide (CuOH) molecule.

Main Results:

  • Successful analytic evaluation of second energy derivatives within the SFX2c-1e framework.
  • Systematic study of equilibrium geometry and vibrational frequencies for CuOH.
  • Assessment of scalar-relativistic, electron-correlation, and basis-set effects on CuOH properties.

Conclusions:

  • The developed analytic SFX2c-1e second derivative method is a valuable tool for relativistic quantum chemistry.
  • The approach allows for straightforward integration with existing nonrelativistic quantum chemical codes.
  • Accurate predictions of molecular properties for relativistic systems are achievable with this method.