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This study adapts the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method for heavy elements with relativistic effects. The new approach efficiently calculates correlated electron problems, showing accurate results for thallium hydride and tin oxide.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Relativistic Quantum Mechanics

Background:

  • Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a powerful method for electron correlation.
  • Heavy elements and relativistic effects pose significant challenges for standard quantum chemical methods.
  • Existing methods struggle to accurately incorporate relativistic effects in correlated calculations.

Purpose of the Study:

  • To adapt the FCIQMC method for systems with heavy elements and relativistic effects.
  • To develop an efficient algorithm for sampling four-component spinors within the Dirac-Coulomb(-Breit) Hamiltonian.
  • To address challenges like loss of spin symmetry and complex-valued matrix elements in relativistic FCIQMC.

Main Methods:

  • Modified FCIQMC algorithm for relativistic calculations.
  • Sampling of four-component spinors using the Dirac-Coulomb(-Breit) Hamiltonian.
  • Implementation strategies for complex-valued Hamiltonian matrix elements and broken spin symmetry.

Main Results:

  • The adapted FCIQMC method shows efficient convergence of initiator error to exact correlation energy for thallium hydride.
  • Computational effort is manageable despite increased Hilbert space dimensions.
  • Accurate spectroscopic constants for tin oxide were obtained, showing good agreement with experimental and prior theoretical data.

Conclusions:

  • The adapted FCIQMC method is effective for correlated electron problems involving heavy elements and relativistic effects.
  • The modifications do not hinder the convergence of FCIQMC calculations.
  • This approach provides a viable computational tool for studying relativistic quantum chemistry.