Crystal molecular orbitals

Ti02, there is much more than a guess at a DOS. There is a chemical characterization of the localization in real space of the states (are they on Pt on H on Ti on O ) and a specification of their bonding properties (Pt-H bonding, antibonding, nonbonding, etc.). The chemist asks right away, where in space are the electrons Where are the bonds There must be a way that these inherently chemical, local questions can be answered, even if the crystal molecular orbitals, the Bloch functions, delocalize the electrons over the entire crystal. 

In a more accurate picture of ionic crystals, the ions are held together in a three-dimensional lattice by a combination of electrostatic attraction and covalent bonding. Although there is a small amount of covalent character in even the most ionic compounds, there are no directional bonds, and each Li ion is surrounded by six F ions, each of which in turn is surrounded by six Li ions. The crystal molecular orbitals form energy bands, described in Chapter 7. 

Another question which still remains is whether Loweinstein s aluminium avoidance rule [52] is obeyed in glasses, as it is in crystals. Molecular orbital calculations of de Jong and Brown[53] implied that Si-O-Al bonds should be more stable than Si-O-Si or Al-O-Al bonds in glass. How-... 

If a crystal molecular orbital had Just one nodal plane it could be represented as shown in Fig. 17.3(b). Extending this pattern, two nodal planes could occur in the way shown in Fig. 17.3(c). Equally, however, a... 

So far we have restricted our discussion to the A atoms and considered those things that can modify the pattern originally derived, one in which the occupancy of a band is determined solely by the occupancy of the orbital from which it is derived. Of course, everything that has been said about the band structure derived from the orbitals of A hold for the orbitals of B also. Next it has to be recognized that there can be interaction between the bands derived from the orbitals of A and B—this is the equivalent of bonding in an isolated AB molecule. In molecules, interaction only occurs between orbitals of the same symmetry. So, too, in solids. Interaction between crystal orbitals can only occur when the crystal molecular orbitals (which are... 

Consider again the one-dimensional lattice of Fig. 6.1, in which each lattice point is occupied by a non-bonding atom (for example, this could be a string of argon atoms). Finding the crystal vibrational normal coordinates is the equivalent of finding the crystal molecular orbitals. The vibrational Bloch functions have the same form as equation 6.15, with atomic displacements instead of atomic orbitals, and for this onedimensional lattice the Bloch function itself is a normal coordinate. The vibrational... 

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, ... 

YAcHMOP stands for yet another extended Hiickel molecular orbital package. The package has two main executables and a number of associated utilities. The bind program does molecular and crystal band structure extended Hiickel calculations. The viewkel program is used for displaying results. We tested Version 3.0 of bind and Version 2.0 of viewkel. 

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. 

Molecular orbital theory indicates that there is little difference between the stability of the two tautomers of purine, 42 and 43. Molecular orbital calculations indicate that purine forms a monocation by protonation at N-3 or at A precise X-ray crystal-... 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

For purposes of illustration, consider a lithium crystal weighing one gram, which contains roughly 1023 atoms. Each Li atom has a half-filled 2s atomic orbital (elect conf. Li = ls22s1). When these atomic orbitals combine, they form an equal number, 1023, of molecular orbitals. These orbitals are spread over an energy band covering about 100 kJ/moL It follows that the spacing between adjacent MOs is of the order of... 

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. 

The situation in beryllium metal is more complex. We might expect all of the 2s molecular orbitals to be filled because beryllium has the electron configuration ls22s2. However, in a crystal of beryllium, the 2p MO band overlaps the 2s (Figure 5). This means that, once again, there are vacant MOs that differ only infinitesimally in energy from filled MOs below them. This is indeed the basic requirement for electron conductivity it is characteristic of all metals, including lithium and beryllium. 

The lowest excited states in molecular crystals are singlet and triplet excitons [3]. Since it costs coulombic energy to transfer an electron that has been excited optically from the HOMO (highest occupied molecular orbital) to the LUMC)... 

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. 

The form of the functions may be closely similar to that of the molecular orbitals used in the simple theory of metals. If there are M interatomic positions in the crystal which might be occupied by any one of the N electron-pair bonds, then the M functions linear aggregates that approximate the solutions of the wave equation with inclusion of the interaction terms representing resonance. This combination can be effected with use of Bloch factors ... 

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