Molecular orbitals crystal field

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

Crystal field and ligand field molecular orbitals... 

Figure 7.41 Perturbation of crystal field molecular orbitals (MOs) by ligand MOs...

Color from Transition-Metal Compounds and Impurities. The energy levels of the excited states of the unpaked electrons of transition-metal ions in crystals are controlled by the field of the surrounding cations or cationic groups. Erom a purely ionic point of view, this is explained by the electrostatic interactions of crystal field theory ligand field theory is a more advanced approach also incorporating molecular orbital concepts. 

E. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd ed., John Wiley Sons, Inc., New York, 1967. An excellent volume that stresses the reactions of complexes ia solution a background and a detailed theory section is iacluded that is largely crystal field theory, but some advantages and disadvantages of molecular orbital theory are iacluded. 

Because each lithium atom has one valence electron and each molecular orbital can hold two electrons, it follows that the lower half of the valence band (shown in color in Figure 5) is filled with electrons. The upper half of the band is empty. Electrons near the top of the filled MOs can readily jump to empty MOs only an infinitesimal distance above them. This is what happens when an electrical field is applied to the crystal the movement of electrons through delocalized MOs accounts for the electrical conductivity of lithium metal. 

There are two major theories of bonding in d-metal complexes. Crystal field theory was first devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions, and then adapted to individual complexes. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory (Section 16.12), is based on molecular orbital theory. 

In the final section of this chapter, we shall attempt to give a brief rationalization of the regularities and peculiarities of the reactions of non-labile complexes which have been discussed in the previous sections. The theoretical framework in which the discussion will be conducted is that of molecular orbital theory (mot). The MOT is to be preferred to alternative approaches for it allows consideration of all of the semi-quantitative results of crystal field theory without sacrifice of interest in the bonding system in the complex. In this enterprise we note the apt remark d Kinetics is like medicine or linguistics, it is interesting, it js useful, but it is too early to expect to understand much of it . The electronic theory of reactivity remains in a fairly primitive state. However, theoretical considerations may not safely be ignored. They have proved a valuable stimulus to incisive experiment. 

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

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]. 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

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