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Electronic Structure and Optical Spectra of Transition Metal Complexes via the Effective Hamiltonian Method
Abstract and Figures
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). ...
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 ...
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. ...
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.
Here we presented a pretreatment method for measurement of Fe-55 and Ni-63 in leaching solution of hardened cement. This work was divided into two parts, the first part describes the development of pretreatment method, the second part describes the pretreatment method validation. The results indicated that the chemical recovery of Fe(III) and Ni(II) were 92.25% ± 3.21% and 83.40% ± 4.52%, respectively. Impurity ion Co-60 and Sr-90 removal rate was more than 99%. It was proved that this ion exchange and extraction process could be used as a pretreatment method for leaching solution of cement solidification.
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.
A model electronic Hamiltonian to describe ligand exchange reactions of palladium(II) complexes with pyridine (Py) and tridentate (L) ligands was developed. It was shown that the model Hamiltonian can adequately reproduce the structures and potential energies of the reactant/product, intermediate, and transition state of the ligand exchange reaction of [PdPy4]²⁺ with free Py. The model Hamiltonian was extended to describe reactions of multi-metal complexes and was adequately applied to describe various clusters, [PdaLbPyc]2a+, in the self-assembly of an octahedron-shaped coordination capsule, [Pd6L8]¹²⁺. The heterogeneity in the energetics of intermediate species [PdaLbPyc]2a+ was strongly suggested by the calculations, and the underlying microscopic interactions were clarified with the geometrical motif. The present framework provides a way to examine the reaction mechanisms of complex metal ligand self-assembly, which can be complementary microscopic information to the recently investigated novel experimental results for the real time evolutions.
In the last chapter of this book, we employ the general methods developed in the previous chapters in the context of a specific class of molecular systems known as coordination compounds. The simplest statement about this class of systems is negative: it is poorly describable by transitional (classical) MM methods. The reasons are twofold and manifest themselves differently for different subclasses of coordination compounds. The first is the non-directional character of coordination bonds and their unsaturability. This feature is common to all types of coordination centers that manifest a wide variety of coordination numbers and coordination polyhedra. The second important source of problems relates to the coordination compounds of transition metal ions with open d-shells. In this case, the situation is that each of the multiple electronic states available for the open d-shell produces corresponding PES which all lie in a narrow energy interval and may intersect due to their sophisticated dependence on molecular geometry. This produces a picture in which a unique PES usually assumed in the classical MM models does not exist, but a bunch of them is present, all of which must be uniformly treated. As a result of these two sources of problems, the material of this chapter is divided into two parts. In the first we consider the factors responsible for the “unspecific” behavior – a group of electrons occupying three-dimensionally delocalized orbitals of the central atom (ion) of the complex and its close vicinity. This produces a mechanistic picture of PES of coordination compounds capable of reproducing the effects of ligand mutual influence. In the second we address the transition metal complexes with open d-shells. We apply the general hybrid methodology to develop a true QM/MM scheme of including sufficiently quantum subsystem (the d-shell) in the general classical (MM treated) environment.
In this chapter we provide a hybrid perspective of the methods of molecular modeling present in the literature. The widespread viewpoint is that hybrid modeling is a rather specific, restricted field in the otherwise universal modeling realm of quantum chemistry. From this perspective, classical models of molecular potential known as Molecular Mechanics seem a completely foreign subject that has to be artificially attached to the quantum description. This presupposes the problems of the process of developing quantum-classical junctions. We take a different view of this area, based on the general scheme of variable separation as presented in the previous chapter. On that basis we analyze, the entire realm of molecular modeling and arrive at a conclusion that basically all modeling methods employ – although largely implicitly – the electron variable separation. This forms the hybrid perspective of molecular modeling mentioned above. Based ou it, we present a short review of the methods of quantum chemistry, including a description of the unsolved problems of semi-empirical quantum chemistry and suggest solutions to these problems, on the basis of the patterns of variable separations which are alternative to those accepted in traditional semi-empirical quantum chemistry. Finally we use the general scheme of variable separation to classify the existing methods of hybrid molecular modeling (in the narrow sense) and clarify the origins of the problems these methods face. Some ways of solving or avoiding these problems are suggested.
The fundamentals of the Effective Hamiltonian Crystal Field (EHCF) method, used originally to calculate intra-shell excitations in the d-shells of coordination compounds of the first row transition metals, are reviewed. The formalism of effective operators is applied to derive an explicit form of the effective operator for a dipole moment in d-shell electronic subspace, allowing us to calculate the oscillator strengths of optical d-d transitions, which are otherwise forbidden when treated in the standard EHCF approach. EHCF methodology is also extended to describing magnetic interactions of the effective spin in several open d-shells of polynuclear coordination compounds. The challenging task of improving a precision of ∼1000 cm−1 (describing the excitation energies of single d-shells by EHCF) to one of ∼100 cm−1 for the energies required to reorient spins by an order of magnitude is considered within the same paradigm as EHCF: the targeted use of McWeeny’s group function approximation and the Löwdin partition technique. These are applied to develop an effective description of a d-system. This approach is tested on a series of binuclear complexes [{(NH3)5M}2O]4+ of trivalent cations featuring oxygen super-exchange paths in order to confirm the reproducibility of the trends in the series of exchange constants values for compounds that differ in the nature of their metal ions. The results from calculations are in reasonable agreement with the available experimental data and other theoretical methods.
A guided self-consistent field (SCF) method is presented in this paper. This method uses the eigenspace update-and-following idea to improve the SCF method for optimizing wave functions that are higher-energy solutions to the Roothaan–Hall equation. In this method, the eigenvectors of the previous SCF step are used to prediagonalize the current Fock/Kohn–Sham matrix, preserving the ordering of orbital occupations. When the subject of interest is an excited state of the same spin symmetry as the ground state, the initial guess of excited wave function is improved with a preconditioning step. The preconditioning step is an SCF iteration applied to the β spin manifold if the initial guess is generated by orbital permutation in the α spin manifold. This simple preconditioning step gives rise to more-stable SCF convergence using the algorithm presented herein. The guided SCF method is used to optimize ligand-field excited states in tetrahedral transition-metal complexes, and calculate ΔSCF excitation energies. The calculated ligand-field transition energies are compared with those obtained from orbital energy differences, linear response time-dependent density functional theory, and experiments. The excitation energies obtained using the method presented in this work show a significant improvement over orbital energy differences and linear response method.
A circular scale of time is proposed and applied to the calculation of the Rayleigh-Schrödinger perturbation energy for a non-degenerate state
The basic starting point for calculating ab initiowave functions of molecules is generally the Hartree—Fock (HF) wave function, which in the simplest case involves two electrons (one with each spin) in each orbital Φi with the total wave function antisymmetrized in order to satisfy the Pauli principle $$ a[({\phi _{1}}\alpha )({\phi _{1}}\beta )({\phi _{2}}\alpha )({\phi _{2}}\beta )...({\phi _{n}}\alpha )({\phi _{n}}\beta )] = a[({\phi _{1}}{\phi _{1}}{\phi _{2}}{\phi _{2}}...{\phi _{n}}{\phi _{n}}\alpha \beta \alpha \beta ...\alpha \beta )] $$ (1) Here a is the antisymmetrizer or determinant operator* and α and β are the usual spin functions. In Eq. (1) as elsewhere, we arrange products of spatial functions and spin functions in order of increasing electron numbers.
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Molecular-orbital calculations within the INDO framework are reported for the hexafluoro, hexachloro, and hexaaquo metallate (II) ions of the first transition series. The parameterization scheme and choice of orbital exponents have been detailed. The results indicate that the method in its present form gives fairly satisfactory predictions of molecular properties.
When the atomic-scale geometry of an interface or surface is known, its properties can be estimated and understood in terms of elementary theory of its electronic structure, or can be accurately calculated using full local-density theory. This is illustrated in terms of semiconductor heterojunctions and ideal semiconductor surfaces. The necessity for self-consistency is discussed in this connection. It is less certain that the atomic-scale geometries can be reliably predicted. This is discussed in terms of reconstruction of semiconductor surfaces, and the silicon surface in particular.
Some of the challenges facing scientists in the area of the electronic structure and properties of solids are reviewed. At a time when computational advances have made possible high-quality calculations, not even conceivable 10 years ago, the article stresses the importance of going beyond the raw output of the calculation and understanding where the result originates. The areas selected for study include the Fermi surface and charge density waves, the stability of solids and the structures of solids under pressure, metal-insulator transitions, the method of moments, superconductivity, and the use of a relatively new technique for the study of chemical bonding, the electron localization function (ELF). 77 refs., 16 figs., 1 tab.