Gyromagnetic Factors and Spin—Orbit Coupling in Ligand Field Theory

1964 ◽  
Vol 41 (8) ◽  
pp. 2524-2529 ◽  
Author(s):  
Antonio A. Misetich ◽  
Tomas Buch
Keyword(s):  
Field Theory ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Ligand Field Theory

Über die Spin-Bahn-Wechselwirkung in der Ligandenfeldtheorie

1963 ◽  
Vol 18 (3) ◽  
pp. 276-280
Author(s):  
H.-H. Schmidtke
Keyword(s):  
Field Theory ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Potentials ◽  
Coupling Energy ◽  
Ligand Field Theory ◽  
Transition Series ◽  
Low Symmetry ◽  
Made In

The spin-orbit coupling operators in ligand field theory for octahedral, tetragonal, trigonal and axial symmetry are derived from the corresponding crystal field potentials. An estimate of the coupling energy for the low symmetry part of this operator is made in the case of octahedrally symmetric complexes of the first transition series. The results are discussed and compared with other approaches to this problem.

Spin-Orbit Coupling in Tetragonal d3 Systems

1981 ◽  
Vol 36 (12) ◽  
pp. 1276-1288 ◽  
Author(s):  
Patrick E. Hoggard
Keyword(s):  
Metal Ions ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Angular Overlap Model ◽  
Forbidden Transitions ◽  
Complete Set ◽  
Overlap Model

Abstract The complete set of energy matrices for tetragonal d3 systems, including spin-orbit coupling, has been constructed within the framework of the Angular Overlap Model. Examples are presented of the variation in energy of the intraconfigurational (t32g) doublets as a function of spin-orbit coupling (appropriate to first row metal ions) and ligand field asymmetry. It is seen that asymmetry in Dq values is much less important than the relative partitioning of Dq into eσ and eπ. The use of spin-orbit matrix elements in the calculation of intensities of spin-forbidden transitions is also illustrated.

scholarly journals Electronic Structure of Ytterbium(III) Solvates – A Combined Spectro-scopic and Theoretical Study

2021 ◽  
Author(s):  
Nicolaj Kofod ◽  
Patrick Nawrocki ◽  
Carlos Platas-Iglesias ◽  
Thomas Just Sørensen
Keyword(s):  
Lanthanide Complexes ◽  
Energy Levels ◽  
Electronic Energy ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Coordination Geometry ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Splitting ◽  
Electronic Energy Levels

The wide range of optical and magnetic properties of the lanthanide(III) ions is associated to their intricate electronic structures, which in contrast to lighter elements is characterized by strong relativistic effects and spin-orbit coupling. Nevertheless, computational methods are now capable of describing the ladder of electronic energy levels of the simpler trivalent lanthanide ions, as well as the lowest energy term of most of the series. The electronic energy levels result from electron configurations that are first split by spin-orbit coupling into groups of energy levels denoted by the corresponding Russel-Saunders terms. Each of these groups are then split by the ligand field into the actual electronic energy levels known as microstates or sometimes mJ levels. The ligand field splitting directly informs on coordination geometry, and is a valuable tool for determining structure and thus correlating the structure and properties of metal complexes in solution. The issue with lanthanide complexes is that the determination of complex structures from ligand field splitting remains a very challenging task. In this manuscript, the optical spectra – absorption, luminescence excitation and luminescence emission – of ytterbium(III) solvates were rec-orded in water, methanol, dimethyl sulfoxide and N,N-dimethylformamide. The electronic energy levels, that is the microstates, were resolved experimentally. Subsequently, density functional theory (DFT) calculations were used to model the structures of the solvates and ab initio relativistic complete active space self-consistent field (CASSCF) calculations were employed to obtain the microstates of the possible structures of each solvate. By comparing experimental and theoretical data, it was possible to determine both the coordination number and solution structure of each solvate. In water, methanol and N,N-dimethylformamide the solvates were found to be eight-coordinated and to have a square anti-prismatic coordination geometry. In DMSO the speciation was found to be more complicated. The robust methodology developed for comparing experimental spectra and computational results allows the solution structures of lanthanide complexes to be determined, paving the way for the design of complexes with predetermined properties. <br>

scholarly journals Theoretical Equations of Zeeman Energy Levels for Distorted Metal Complexes with 3T1 Ground Terms

2019 ◽  
Vol 5 (1) ◽  
pp. 17 ◽  
Author(s):  
Hiroshi Sakiyama
Keyword(s):  
Coupling Parameter ◽  
Energy Levels ◽  
Axial Ligand ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Zeeman Energy ◽  
Field Splitting

The theoretical equations of Zeeman energy levels, including the zero-field energies and the first- and second-order Zeeman coefficients, have been obtained in closed form for nine states of the 3 T 1 ( g ) ground term, considering the axial ligand-field splitting and the spin-orbit coupling. The equations are expressed as the functions of three independent parameters, Δ , λ , and κ , where Δ is the axial ligand-field splitting parameter, λ is the spin-orbit coupling parameter, and κ is the effective orbital reduction factor, including the admixing. The equations are useful in simulating magnetic properties (magnetic susceptibility and magnetization) of the complexes with 3 T 1 ( g ) ground terms, e.g., octahedral vanadium(III), octahedral low-spin manganese(III), octahedral low-spin chromium(II), and tetrahedral nickel(II) complexes.

scholarly journals Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

2020 ◽  
Author(s):  
Shashank Vittal Rao ◽  
MATTEO PICCARDO ◽  
Alessandro Soncini
Keyword(s):  
Crystal Field ◽  
Electron Spin ◽  
Single Molecule ◽  
Lanthanide Complexes ◽  
Mean Field ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Magnetic Excitations

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and <sub>g</sub> tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.<br>

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