On the Accuracy of Mean-Field Spin–Orbit Operators for 3d Transition-Metal Systems

Abstract

We present an extensive study of the performance of mean-field approximations to the spin−orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically closelying open-shell configurations that can couple via the spin−orbit operator. We performed complete active space spin−orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin−orbit operator to different approximations: the one-center approximation, the spin−orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin−orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Simulating Spin–Orbit Coupling with Quasidegenerate N-Electron Valence Perturbation Theory

“…Alternatively, incorporating the spin–orbit coupling effects can be simplified by invoking the spin–orbit mean-field approximation (SOMF), , which describes the two-electron spin–orbit interactions in a way analogous to the mean-field treatment of electronic repulsion in Hartree–Fock theory. The SOMF approximation has been used to incorporate spin–orbit coupling in a variety of electronic structure theories with a wide range of applications. ,,,,− …”

Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac–Coulomb–Breit Hamiltonian

“…The mean-field spin–orbit approaches including molecular and atomic mean-field approaches have been demonstrated to provide accurate results and are being widely used in practical calculations. The one-center approximation has recently been shown to offer more accurate treatments than mean-field approximations for calculations of g tensors and zero-field splittings for molecules containing 3d transition metals . More approximate approaches include screened nuclear charge approaches − and relativistic effective-core potentials. − Although they rely on semiempirical parametrizations, these approaches provide efficient and fairly accurate treatments of spin–orbit effects on the valence properties.…”

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple

“…Although it has in the meantime been employed successfully in highly sophisticated electron correlation calculations of heavy-element complexes, 48 limitations of the underlying atomic approximation to account for 2eSO PCEs have recently been pointed out in the context of zero-field splittings of first-row transition metal complexes. 49 In this paper we introduce an atomic mean-field (amfX2C) as well as an extended atomic mean-field (eamfX2C) approach within the X2C Hamiltonian framework which not only takes into account the above mentioned four main ideas in relativistic quantum chemistry but also amends them such that the resulting amfX2C and eamfX2C approaches will bridge the gap between a full molecular 4c and mmfX2C framework in a computationally efficient, yet highly accurate way. In contrast to most existing correction schemes for 2ePCE, our amfX2C and eamfX2C approaches are laid out to comprise full 2ePCE corrections, that is treating the 2eSO and 2eSC ones on the same footing, whether they arise from the (relativistic) 2e Coulomb, Coulomb-Gaunt, or Coulomb-Breit interaction.…”