Crystal field method

The simple crystal field analysis of the effect of ligands on transition metal d-electron energies accords well with the deeper molecular orbital analysis (see e.g. [99]). In what way(s), however, is the crystal field method unrealistic ... 

Quantum mechanical methods have also been applied to crystal structure prediction. A recent example involved the use of ab initio crystal field methods with the SM (supermolecule) model and the PC (point charge) model applied to the three known polymorphs of glycine [77]. Comparison of the optimised structures with published X-ray structures for these forms indicated that the quantum-mechanically based SM model employing a 15-molecule cluster produced results in better agreement with experiment than the PC model which describes the crystal environment purely electrostatically. 

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

As was the case with lanthanide crystal spectra (25), we found that a systematic analysis could be developed by examining differences, AP, between experimentally-established actinide parameter values and those computed using Hartree-Fock methods with the inclusion of relativistic corrections (24), as illustrated in Table IV for An3+. Crystal-field effects were approximated based on selected published results. By forming tabulations similar to Table IV for 2+, 4+, 5+ and 6+ spectra, to the extent that any experimental data were available to test the predictions, we found that the AP-values for Pu3+ provided a good starting point for approximating the structure of plutonium spectra in other valence states. However,... 

A complete description of the effects of a crystal field upon a d" ion would include similar analysis of the behavours of all terms arising for that d" configuration. Box 3-7 summarizes the case for d, and in Box 3-8, we illustrate a method of using Fig. 3-19 to determine Dq and B values from real spectra. 

The method mentioned has been appUed to ClFe(Et2dfc)2 first, because for this compound, and some related ones, an abnormally large QS has been observed, while the crystal field theory predicts QS = 0 for this intermediate spin (S = 3/2) compound. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Brodersen S, Wilke S, Leusen FJJ, Engel GE (2005) Comparison of static and fluctuating charge models for force-field methods applied to organic crystals. Cryst Growth Des 5(3) 925—933... 

ABSTRACT The aim of this study was to test portable infrared spectroscopy for non-destructive analysis of ancient construction mortar. Mortar samples from the House of the Vestals, in Pompeii, Italy, were initially examined with traditional analytical techniques, including X-ray fluorescence, X-ray diffraction and thin section analysis. These techniques were used to establish mineralogical and chemical profiles of the samples and to verify the results of experimental field methods. Results showed the lime-based binder was composed of calcite, and the volcanic sand aggregate contained clinopyroxene, plagioclase, sanidine and olivine crystals. 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

Depending upon the size of the crystal field term //cf in comparison to these three free ion terms, different approaches can be considered to the solution of Equation (5.1) by perturbation methods ... 

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