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# Electronic Structure and Optical Spectra of Transition Metal Complexes via the Effective Hamiltonian Method

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A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF 64− (M=Mn, Fe, Co, Ni) anions, Mn(FH) 62+ cation, CoCl 64− anion, and a tetrahedral CoCl 42− anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.
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... This expression can be considered as an extension of the EHCF d-shell Hamiltonian [18] on account of the spin-orbit interaction operator H so and the operator describing the interaction with the applied magnetic field H mag . Fig. 4 shows the experimental magnetization (µ eff , SI units; µ eff = 797.74 ...
... This data set was fitted to the above-stated Hamiltonian using the ligand-field effect, spin-orbit coupling, and exchange coupling. The values for the spin-orbit coupling parameter and Racah parameters were chosen on the basis of the optical spectra and are consistent with our EHCF calculations [18]. The exchange interactions between the metal ions are taken into account in the molecular field approximation ...
... where C k q (i) are the Racah tensor components describing the angular dependence of the ligand field. The B k q ligand-field parameters can be determined by the EHCF procedure [18]. At room temperature, the effective Bohr magneton number of 2 is roughly 5.9 per Mn(NCNH 2 ) 4 Cl 2 unit or per high-spin Mn 2+ ion, a value that corresponds to the spin-only value of 5.92 (see Fig. 4). ...
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The two isotypic compounds Cr(NCNH 2) 4Cl2 and Mn(NCNH 2) 4Cl 2 have been synthesized and characterized by X-ray diffraction. They crystallize in the cubic space group Im3̄m (Z = 6) with a = 12.643(2) Å for Cr(NCNH 2)4Cl 2 and a = 12.821(1) Å for Mn(NCNH 2) 4Cl 2. The divalent transition metal ions are octahedrally coordinated by four H 2NCN molecules in equatorial and two chloride ions in axial positions. The magnetic susceptibility data of the four Curie-paramagnetic compounds Cr(NCNH 2) 4Cl 2, Mn(NCNH 2) 4Cl 2, Co(NCNH 2) 4Cl 2, and Ni(NCNH 2) 4Cl 2 have been analyzed in greater detail, including many-body quantum theory.
... or further notation ). It ultimately comes from the mixing of the states in the model configuration subspace—that with the fixed number of electrons in the d-shell—with those in the outer subspace— one spanned by the MLCT and LMCT states as depicted inFig- ure 1. This comprises original form of the effective Hamiltonian crystal field (EHCF) theory. [12] It inherits the form of the WF describing the ground and low-lying excited states of a TMC which the CFT uses implicitly. This move turned out to be very much successful numerically as we described previously many times. It was the first example of using explicitly the group product in quantum chemistry at least in the semi-empirical co ...
... This has been reached by taking into account the energies of the respective d-shells calculated by the EHCF method. Since the intrashell static correlations were of crucial importance here, the hybrid QM/MM-like incarnation of the EHCF contained its local version which can be briefly characterized as a method of sequential derivation and independent esti- mation [12] of parameters of the Angular Overlap Model (AOM) [5,17] —the successful empirical systematics of the spectrochemical data combined with the correlated calculation of the d-shell energy. It represents the crystal filed felt by the d-shells as a superposition of ligand-specific increments e l known as AOM parameters determined from experiment. ...
... where D 16 ð Þ LL j ð Þ are elements of the Green's functions in the local basis. More details can be found elsewhere. [12] There are Implications for extending this approach to the solid state. [18] Nephelauxetic effect ...
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We review the basics of the Effective Hamiltonian Crystal Field (EHCF) method originally targeted for calculations of the intra-shell excitations in the d-shells of coordination compounds of the first row transition metal. The formalism employs in the concerted way the McWeeny's group-function approximation and the Lowdin partition technique. It is needed for description of the transition metal complexes with partially filled d-shells where the (static) electronic correlations are manifested. These features are particularly important for electron fillings close to " half shell " ones occurring, for example, in the Fe 21 and Fe 31 ions. Recently we extended this methodology to polynuclear coordination compounds to describe magnetic interactions of the effective spins residing in several open d-shells. This improves the accuracy from about 1000 cm 21 to that of about 100 cm 21 , that is, eventually by an order of magnitude. This approach implemented in the MagAixTic package is applied here to a series of binuclear Fe(III) complexes featuring l-oxygen super-exchange pathways. The results of calculations are in a reasonable agreement with available experimental data and other theoretical studies of protonated bridges. Further we discuss the application of the EHCF to analysis of Mosbauer experiments performed on two organometallic solids: FeNCN and Fe(HNCN) 2 and conjecture a new thermal effect in the latter material. V
... The Fe 2+ ion in the trigonally distorted octahedral environment formed by the NCN 2À groups, as depicted in Fig. 1, has been employed as input for the Effective Hamiltonian Crystal Field (EHCF) method. 33,34 This calculation reveals the ground state of the Fe 2+ ion to be high-spin, in agreement with previous calculations 11 and the observed isomer shift. The octahedral environment leads to the 5 T 2g ground state. ...
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Three-dimensional non-oxidic extended frameworks offer the possibility to design novel materials with unique properties, which can be different from their oxide analogues. Here, we present first experimental results concerning unusual magnetic properties of FeNCN, investigated using Mossbauer spectroscopy and magnetometry between 5 and 380 K. This study reveals an unconventional behaviour of the magnetic parameters below the Neel temperature of 350 K, i.e., the hyperfine field on iron decreases with decreasing temperature. At room temperature, quadrupole and hyperfine magnetic field interaction energies are comparable in magnitude, which leads to a rare five-line absorption spectrum. We suggest that these features in the hyperfine field are caused by the combination of a small Fermi contact term and a temperature-dependent contribution from the orbital momentum and the dipole term. One additional spectral component is observed, which exhibits a magnetic relaxation behaviour and slows down at low temperatures to yield a sextet. The magnetometry data suggest that the antiferromagnetic FeNCN is rich in structural distortions, which results in a splitting of the field-cooled and zero-field-cooled curves. The lattice dynamics of FeNCN were investigated using nuclear inelastic scattering. The comparison of the obtained data with literature data of iron monoxide reveals very similar iron phonon modes with a small softening and a slightly reduced sound velocity.
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Modeling of structure and properties of molecules and materials (crystals/solids) on the basis of their electronic structure is one of the most important consumers of computer resources (processor time, memory and storage). The known attempts to improve its efficiency reduce to massive parallelization. This approach ignores enormous diversity of types of structures and behaviors of molecules and materials. Moreover, this diversity is by no means reflected in the paradigm currently dominating the field of molecular/material modeling.
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Chapter
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Chapter
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