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A theoretical framework for the generation of natural orbitals, natural spin orbitals, as well as orbital- and spin-magnetizations, from multi-configurational ab initio wavefunction calculations including spin-orbit coupling is presented. Selected case studies show how these computational orbital and magnetization tools can be used to interpret and rationalize the magnetic properties of complexes containing transition metals, lanthanides, and actinides. [ABSTRACT FROM AUTHOR]

By using complementary experimental techniques and first-principles theoretical calculations, magnetic anisotropy in a series of five hexacoordinated nickel(II) complexes possessing a symmetry close to C2 v, has been investigated. Four complexes have the general formula [Ni(bpy)X2] n+ (bpy=2,2′-bipyridine; X2=bpy ( 1), (NCS−)2 ( 2), C2O42− ( 3), NO3− ( 4)). In the fifth complex, [Ni(HIM2-py)2(NO3)]+ ( 5; HIM2-py=2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1 H-imidazolyl-1-hydroxy), which was reported previously, the two bpy bidentate ligands were replaced by HIM2-py. Analysis of the high-field, high-frequency electronic paramagnetic resonance (HF-HFEPR) spectra and magnetization data leads to the determination of the spin Hamiltonian parameters. The D parameter, corresponding to the axial magnetic anisotropy, was negative (Ising type) for the five compounds and ranged from −1 to −10 cm−1. First-principles SO-CASPT2 calculations have been performed to estimate these parameters and rationalize the experimental values. From calculations, the easy axis of magnetization is in two different directions for complexes 2 and 3, on one hand, and 4 and 5, on the other hand. A new method is proposed to calculate the g tensor for systems with S=1. The spin Hamiltonian parameters ( D (axial), E (rhombic), and gi) are rationalized in terms of ordering of the 3 d orbitals. According to this orbital model, it can be shown that 1) the large magnetic anisotropy of 4 and 5 arises from splitting of the eg-like orbitals and is due to the difference in the σ-donor strength of NO3− and bpy or HIM2-py, whereas the difference in anisotropy between the two compounds is due to splitting of the t2g-like orbitals; and 2) the anisotropy of complexes 1- 3 arises from the small splitting of the t2g-like orbitals. The direction of the anisotropy axis can be rationalized by the proposed orbital model. [ABSTRACT FROM AUTHOR]

The electron densities associated with the Ln 4f shell, and spin and orbital magnetizations (‘magnetic moment densities’), are investigated for the Ln(COT)2− series. The densities are obtained from ab-initio calculations including spin–orbit coupling. For Ln = Ce, Pr the magnetizations are also derived from crystal field models and shown to agree with the ab-initio results. Analysis of magnetizations from ab-initio calculations may be useful in assisting research on single molecule magnets. [ABSTRACT FROM AUTHOR]

We investigate and compare the magnetic properties of two isostructural DyIII-containing complexes. The DyIII ions are chelated by hexadentate ligands and possess two apical bidendate nitrate anions. In dysprosium(III) N,N'-bis(imine-2-yl)methylene-1,8-diamino-3,6-dioxaoctane (1), the ligand's donor atoms are two alkoxo, two pyridine, and two imine nitrogen atoms. Dysprosium(III) N,N'-bis(amine-2-yl)methylene-1,8-diamino-3,6-dioxaoctane (2) is identical with 1 except for one modification: the two imine groups have been replaced by amine groups. This change has a minute effect on the structure and a larger effect the magnetic behavior. The two complexes possess slow relaxation of the magnetization in the presence of an applied field of 1000 Oe but with a larger barrier for reorientation of the magnetization for 1 (Ueff/kB = 50 K) than for 2 (Ueff/kB = 34 K). First-principles calculations using the spin-orbit complete active-space self-consistent-field method were performed and allowed to fit the experimental magnetization data. The calculations gave the energy spectrum of the 2J + 1 sublevels issued from the J = 15/2 free-ion ground state. The lowest-lying sublevels were found to have a large contribution of MJ = ±15/2 for 1, while for 2, MJ = ±13/2 was dominant. The observed differences were attributed to a synergistic effect between the electron density of the ligand and the small structural changes provoked by a slight alteration of the coordination environment. It was observed that the stronger ligand field (imine) resulted in complex 1 with a larger energy barrier for reorientation of the magnetization than 2. [ABSTRACT FROM AUTHOR]

The electron densities associated with the Ln 4f shell, and spin and orbital magnetizations (‘magnetic moment densities’), are investigated for the Ln(COT)2− series. The densities are obtained from ab-initio calculations including spin–orbit coupling. For Ln = Ce, Pr the magnetizations are also derived from crystal field models and shown to agree with the ab-initio results. Analysis of magnetizations from ab-initio calculations may be useful in assisting research on single molecule magnets. [ABSTRACT FROM AUTHOR]