title: One-electron contributions to the g-tensor for second-order Douglas-Kroll-Hess theory.
abstract: The electric g-tensor is a central quantity for the interpretation of electron paramagnetic resonance spectra. In this paper, a detailed derivation of the 1-electron contributions to the g-tensor is presented in the framework of linear response theory and the second-order Douglas-Kroll-Hess (DKH) transformation. Importantly, the DKH transformation in the presence of a magnetic field is not unique. Whether or not the magnetic field is included in the required Foldy-Wouthuysen transformation, different transformation matrices and, consequently, Hamiltonians result. In this paper, a detailed comparison of both approaches is presented, paying particular attention to the mathematical properties of the resulting Hamiltonians. In contrast to previous studies that address the g-tensor in the framework of DKH theory, the resulting terms are compared to those of the conventional Pauli theory and are given a physical interpretation. Based on these mathematical and physical arguments, we establish that the proper DKH transformation for systems with constant magnetic fields is based on a gauge-invariant Foldy-Wouthuysen transformation, i.e., a Foldy-Wouthuysen transformation including the magnetic field. Calculations using density functional theory (DFT) are carried out on a set of heavy, diatomic molecules, and a set of transition-metal complexes. Based on these calculations, the performance of the relativistic calculation with and without inclusion of picture-change effects is compared. Additionally, the g-tensor is calculated for the Lanthanide dihydrides. Together with the results from the other two molecular test sets, these calculations serve to quantify the magnitude of picture-change effects and elucidate trends across the periodic table.
authors.affiliation: Max Planck Institute for Bioinorganic Chemistry, Stiftstrasse 34-36, 45470 Mülheim an der Ruhr, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Sandhoefer
authors.forename: F
authors.initials: F
authors.lastname: Neese
mesh_terms: D004583:Electrons; D009682:Magnetic Resonance Spectroscopy; D009942:Organometallic Compounds / Q000737:chemistry; D011789:Quantum Theory; D015203:Reproducibility of Results
chemical_list: D009942:Organometallic Compounds