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An adaptation of the full configuration interaction quantum Monte Carlo(FCIQMC) method is presented, for correlated electron problems containing heavyelements and the presence of significant relativistic effects. The modifiedalgorithm allows for the sampling of the four-component spinors of theDirac--Coulomb(--Breit) Hamiltonian within the relativistic no-pairapproximation. The loss of spin symmetry and the general requirement forcomplex-valued Hamiltonian matrix elements are the most immediateconsiderations in expanding the scope of FCIQMC into the relativistic domain,and the alternatives for their efficient implementation are motivated anddemonstrated. For the canonical correlated four-component chemical benchmarkapplication of Thallium Hydride, we show that the necessary modifications donot particularly adversely affect the convergence of the systematic (initiator)error to the exact correlation energy for FCIQMC calculations, which isprimarily dictated by the sparsity of the wave function, allowing thecomputational effort to somewhat bypass the formal increases in Hilbert spacedimension for these problems. We apply the method to the larger problem of thespectroscopic constants of Tin Oxide, correlating 28 electrons in 122Kramers-paired spinors, finding good agreement with experimental and priortheoretical relativistic studies.

Four-component Full Configuration Interaction Quantum Monte Carlo for Relativistic Correlated Electron Problems