Four-component full configuration interaction quantum Monte Carlo for relativistic correlated electron problems

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.