Accurate spin–orbit and spin–other-orbit contributions to the g-tensor for transition metal containing systems

Abstract

In this paper an overview is presented of several approximations within Density Functional Theory (DFT) to calculate g-tensors in transition metal containing systems and a new accurate description of the spin-other-orbit contribution for high spin systems is suggested. Various implementations in a broad variety of software packages (ORCA, ADF, Gaussian, CP2K, GIPAW and BAND) are critically assessed on various aspects including (i) non-relativistic versus relativistic Hamiltonians, (ii) spin-orbit coupling contributions and (iii) the gauge. Particular attention is given to the level of accuracy that can be achieved for codes that allow g-tensor calculations under periodic boundary conditions, as these are ideally suited to efficiently describe extended condensed-phase systems containing transition metals. In periodic codes like CP2K and GIPAW, the g-tensor calculation schemes currently suffer from an incorrect treatment of the exchange spin-orbit interaction and a deficient description of the spin-other-orbit term. In this paper a protocol is proposed, making the predictions of the exchange part to the g-tensor shift more plausible. Focus is also put on the influence of the spin-other-orbit interaction which becomes of higher importance for high-spin systems. In a revisited derivation of the various terms arising from the two-electron spin-orbit and spin-other-orbit interaction (SOO), new insight has been obtained revealing amongst other issues new terms for the SOO contribution. The periodic CP2K code has been adapted in view of this new development. One of the objectives of this study is indeed a serious enhancement of the performance of periodic codes in predicting g-tensors in transition metal containing systems at the same level of accuracy as the most advanced but time consuming spin-orbit mean-field approach. The methods are first applied on rhodium carbide but afterwards extended to a broad test set of molecules containing transition metals from the fourth, fifth and sixth row of the periodic table. The set contains doublets as well as high-spin molecules.

On the identity of the last known stable radical in X-irradiated sucrose

“…27 using the same level of theory as for the final geometry refinement -all-electron approach with 350 Ry cutoff and 6-311G** basis sets. To account for the spin-orbit and spin-other-orbit contributions erroneously described by effective potential methods [28], the g tensors were calculated by employing a scaling approximation proposed by Van Yperen-De Deyne et al [29].…”

Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

“…However, the Breit-Pauli operator is quite complex, and different approximations are often used in the literature 20 . While many studies have been published on the performances of the different SOC approximations in the accurate modeling of spectroscopic transitions in organic molecules and inorganic complexes, including inter-multiplet transitions in lanthanide systems [20][21][22][23][24] , to our knowledge we present here the first extensive comparison of the performance of different approximations to the full Breit-Pauli Hamiltonian in the calculation of the crystal field splitting of the ground multiplets of lanthanide complexes, i.e. of their magnetic excitations.…”

An animated visualization of orbital angular momentum and spin‐orbit coupling

“…In this event, the simplest option is to plot the density of the orbital, and forget the phase information. However, this information may be of interest to researchers in fields where orbital angular momentum or spin‐orbit coupling are relevant (e.g., the field of magnetic resonance parameters, where SOC in the singly‐occupied molecular orbitals (SOMO) is a major consideration in calculating the EPR g‐tensor …”

“…However, this information may be of interest to researchers in fields where orbital angular momentum or spin-orbit coupling are relevant (e.g., the field of magnetic resonance parameters, where SOC in the singly-occupied molecular orbitals (SOMO) is a major consideration in calculating the EPR g-tensor. [8,9] ) An obvious option is to decompose the wavefunction into real and imaginary parts and plot the isosurfaces of both; the presence of orbital angular momentum (including SOC) is not intuitively visible but may be deduced quite simply. More usefully, the complex phase of the orbital may be color-coded, as in Ref.…”