New quantum number for the many-electron Dirac-Coulomb Hamiltonian

Abstract

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator ${\mathcal{K}}_{+}$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the ${\mathcal{K}}_{+}^2$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that ${\mathcal{K}}_{+}$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call ${\mathcal{K}}_{+}$ the generator of the many-electron TR symmetry. By diagonalizing the operator ${\mathcal{K}}_{+}^2$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with ${\mathcal{K}}_{+}^2$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

15 pages, published in Phys. Rev. A, one FORTRAN program; Changes: minor text formatting, add supplemental material as Appendix I, add comparison with three open-shell electrons to Sec. VII last paragraph

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