Molecular configurations, classifying

Atoms have complete spherical synnnetry, and the angidar momentum states can be considered as different synnnetry classes of that spherical symmetry. The nuclear framework of a molecule has a much lower synnnetry. Synnnetry operations for the molecule are transfonnations such as rotations about an axis, reflection in a plane, or inversion tlnough a point at the centre of the molecule, which leave the molecule in an equivalent configuration. Every molecule has one such operation, the identity operation, which just leaves the molecule alone. Many molecules have one or more additional operations. The set of operations for a molecule fonn a mathematical group, and the methods of group theory provide a way to classify electronic and vibrational states according to whatever symmetry does exist. That classification leads to selection rules for transitions between those states. A complete discussion of the methods is beyond the scope of this chapter, but we will consider a few illustrative examples. Additional details will also be found in section A 1.4 on molecular symmetry. 

We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. 

Valence and oxidation state are directly related to the valence-shell electron configuration of a group. Binary hydrides are classified as saline, metallic, or molecular. Oxides of metals tend to be ionic and to form basic solutions in water. Oxides of nonmetals are molecular and many are the anhydrides of acids. 

A representative molecular orbital diagram for an octahedral d-block metal complex ML6 is shown in Figure 1.8. The MOs are classified as bonding (oL and ttL), nonbonding (jtM) and antibonding (o, nl and ). The ground-state electronic configuration of an octahedral complex... 

Antibodies can be classified according to the GADME system based on their configuration and function. The five different classes (also referred to as isotypes) are presented, along with their function, in Table 3.2. Also integrated into this overview are the molecular mass, half-life and the proportion of each class. In the following section, emphasis will be placed on the kinetic aspects of the isotypes. 

The (R,S) stereoisomer of a model complex of 8 possesses C symmetry and allows us to classify the molecular orbitals in terms of the irreducible representations ag and a. It turned out that HOMO and LUMO belong to different irreducible representations. Exchange of occupation of these orbitals thus leads to different electronic configurations. While only one of the two electronic configurations corresponds to the ground state and then has a valid description in the framework of DFT, both electronic configurations can be subjected to a geometry optimization in C, symmetry and yield two different structures the results of the optimizations are depicted in Fig. 15. We took the... 

To obtain a qualitative picture of the complex structure of SO3 adsorbed on the Pt (111) surface, the density of states (DOS) was calculated from the DV-Xa molecular orbital method. The level width was broadened by a Gaussian function (1.0 eV FWHM) to mimic the solid state. The results of the studies are summarized in the following paragraphs. In each DOS, Fermi energy is set at 0. In configuration A, the adsorbed O atoms are classified as of two types. One is two O atoms bound to Pt surface atom (0(1)) and the other is one O atom unbound to Pt surface (0(2)). 

In order to illustrate the Molecular symmetry Group Theory, let us consider the methyl boron difluoride molecule CH3 — BF2), which contains a nearly free rotating methyl group. We shall see next that the torsional levels of this molecule can be classified according to the irreducible representations of the symmetry point group Csv, although this molecule does not possess, in a random configuration, any symmetry at all. 

Stereoisomers have the same molecular formula, but their atoms have a different spatial arrangement — a different configuration. Stereoisomers are classified as -Enantiomers when the isomers are mirror images of each other and cannot be superimposed... 

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