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

10.26434/chemrxiv.14103740.v1 ◽

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.

Download Full-text

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

10.26434/chemrxiv.14103740 ◽

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.

Download Full-text

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

Magnetochemistry ◽

10.3390/magnetochemistry5010017 ◽

2019 ◽

Vol 5 (1) ◽

pp. 17 ◽

Cited By ~ 1

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.

Download Full-text

Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

10.26434/chemrxiv.11858370 ◽

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 g tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.

Download Full-text

Ligand Field Model and d-d Spectra of dN Metallocene Complexes

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20010228 ◽

2001 ◽

Vol 66 (2) ◽

pp. 228-254 ◽

Cited By ~ 4

Author(s):

Ivan Pavlík ◽

Josef Fiedler ◽

Jaromír Vinklárek ◽

Martin Pavlišta

Keyword(s):

Field Model ◽

Strong Field ◽

Point Of View ◽

Orbit Coupling ◽

Orbital Energy ◽

Ligand Field ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

Field Splitting ◽

Metallocene Complexes

Complete ligand field calculations, including spin-orbit coupling, have been carried out for bent d1 metallocene complexes, [M(Cp)2Ln] (Cp = η5-cyclopentadienyl, n = 1 or 2), in C2v symmetry. Using the strong-field coupling formalism (with exclusion of spin-orbit coupling) the full energy matrices for d2, d3, and d4 bent metallocenes were constructed in terms of four ligand field splitting parameters and two Racah interelectronic repulsion parameters (only d2 energy matrices are presented here). The bonding in the bent d1 C2v M(Cp)2 fragment was analyzed from the point of view of the ligand field model. The experimental d-d transition energies of two d1 metallocene dichlorides, vanadocene and niobocene dichlorides, have been assigned, the values of four one-electron ligand field splitting parameters determined and the effect of spin-orbit coupling estimated. The ground state of both d1 metallocene dichlorides has shown to be 2A(111), the d-orbital energy order being 1a1 < b1 < b2 < 2a1 < a2. Finally, the prediction of d-d spectra for d2, d3, and d4 bent metallocene complexes is presented.

Download Full-text

Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

10.26434/chemrxiv.11858370.v1 ◽

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 g tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.

Download Full-text

Ground configuration splitting in UCl5

Canadian Journal of Physics ◽

10.1139/p77-125 ◽

1977 ◽

Vol 55 (10) ◽

pp. 937-942 ◽

Cited By ~ 12

Author(s):

A. F. Leung ◽

Ying-Ming Poon

Keyword(s):

Crystal Field ◽

Energy Levels ◽

Orbit Coupling ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

Coupling Constant ◽

Point Charge Model ◽

X Ray Crystallography ◽

Charge Model ◽

Crystal Field Parameters

The absorption spectra of UCl5 single crystal were observed in the region between 0.6 and 2.4 μm at room, 77, and 4.2 K temperatures. Five pure electronic transitions were assigned at 11 665, 9772, 8950, 6643, and 4300 cm−1. The energy levels associated with these transitions were identified as the splittings of the 5f1 ground configuration under the influence of the spin–orbit coupling and a crystal field of C2v symmetry. The number of crystal field parameters was reduced by assuming the point-charge model where the positions of the ions were determined by X-ray crystallography. Then, the crystal field parameters and the spin–orbit coupling constant were calculated to be [Formula: see text],[Formula: see text], [Formula: see text], and ξ = 1760 cm−1. The vibronic analysis showed that the 90, 200, and 320 cm−1 modes were similar to the T2u(v6), T1u(v4), and T1u(v3) of an UCl6− octahedron, respectively.

Download Full-text