Characters from orbits

the character table for the Ih group has been reduced in size so that more information can be displayed in the window. Secondly, the worksheet is protected [the general condition of all the worksheets] except for the cells used to input data, which, in all cases, are bordered in red. Thirdly, there is a series of command buttons on the right of the display, with actions described by the button labels. These observations are general for all the worksheet displays of the GT Calculator. 

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The Characters from Orbits command button leads to the worksheet displayed in Figure 1.7 and there are several features to note about the display in the figure. 

Figure 1.7 The worksheet for the calculation of the permutation character and its direct sum components, listed as Mulliken symbols from orbit lists. This display is accessed from the Characters from Orbits command button of the window shown in Figure 1.5.

In Figure 1.7, the input cell for the number of Oi orbits is greyed out. This is because the a, TV and 5 classification, which is used to describe radial and tangential properties on the surface of the sphere does not apply to the centre. In groups where the Oi orbit, if present, must lie at the centre, this input is locked in the Characters from Orbits and Isomers [Figure 1.18] displays. 

Figure 1.11 Demonstration of the error trapping routines in the code controlling worksheet calculations activated through the Character from Orbits command button. Note that the second screen dump has been enhanced to emphasise that a non-integer entry was made, because the default format for the of orbits input cells is integer.

This picture can qualitatively account for the g tensor anisotropy of nitrosyl complexes in which g = 2.08, gy = 2.01, and g == 2.00. However, gy is often less than 2 and is as small as 1.95 in proteins such as horseradish peroxidase. To explain the reduction in g from the free electron value along the y axis, it is necessary to postulate delocalization of the electron over the molecule. This can best be done by a complete molecular orbital description, but it is instructive to consider the formation of bonding and antibonding orbitals with dy character from the metal orbital and a p orbital from the nitrogen. The filled orbital would then contribute positively to the g value while admixture of the empty orbital would decrease the g value. Thus, the value of gy could be quite variable. The delocalization of the electron into ligand orbitals reduces the occupancy of the metal d/ orbital. This effectively reduces the coefficients of the wavefunction components which account for the g tensor anisotropy hence, the anisotropy is an order of magnitude less than might be expected for a pure ionic d complex in which the unpaired electron resides in the orbital. 

Resonance is possible, of course, between an ionic FeX structure, with ionic bonds between the Fe+ hf ion and surrounding anions, and a covalent structure in which only the outer orbitals 4s, 4p, 4d, and so on are used in bond formation. This covalent structure writh five unpaired electrons would be different in character from that using two 3d orbitals, however, and continuous transition to the latter could not occur. 

In the case of ET, the reaction path starts with the electron in LUMO of the donor. Along the reaction path, the orbital shifts character, from donor to acceptor orbital. At the transition state LUMO and LUMO+1 for the full system are symmetric and antisymmetric combinations of the two local LUMO s (fig.2). Since for any of the two orbitals, the negative of the orbital energy approximates the electron affinity according to Koopmans theorem, the following implication holds ... 

Alkanes, alkenes, and alkynes also have characteristic C — H stretching frequencies. Carbon-hydrogen bonds involving sp3 hybrid carbon atoms generally absorb at frequencies just below (to the right of) 3000 cm-1. Those involving sp2 hybrid carbons absorb just above (to the left of) 3000 cm-1. We explain this difference by the amount of 5 character in the carbon orbital used to form the bond. The s orbital is closer to the nucleus than the p orbitals, and stronger, stiffer bonds result from orbitals with more s character. Even if an alkene s C=C absorption is weak or absent, the unsaturated C—H stretch above 3000 cm-1 reveals the presence of the double bond. 

The hybridization of the orbital from which the proton is removed also affects the pKa. Since s orbitals are held closer to the nucleus than are p orbitals, the electrons in them are lower in energy, that is, more stable. Consequently, the more s character an orbital has, the more tightly held are the... 

In fact, there is little reason to believe that s, p, and d orbitals really do exist in the outer shells of many bonded atoms. Remember that these different orbitals arise in the first place from the interaction of the electron with the central electrostatic force field associated with the positive nucleus. An outer-shell electron in a bonded atom will be under the influence of a force field, emanating from two positive nuclei rather than one, so we would expect the orbitals in the bonded atoms to have a somewhat different character from those in free atoms. We can, in fact, throw out the concept of atomic orbital altogether and reassign the electrons to a new set of molecular orbitals that are characteristic of each molecular configuration. This approach is indeed valid, but we will defer a discussion of it until later. For now, we will look at a less-radical model that... 

Something like this must happen in the solid. In addition, there are Mn-Mn bonding contacts in the layer, and these will lead to dispersion in those bands that are built up from orbitals containing substantial metal character. The combined construction is shown in Fig. 26. 

In contrast to the nice, neat two-center-two-electron bond model, it is not so easy to determine the overall bonding character from MO orbital drawings alone. We need another measure. This comes from the Mulliken overlap population which is a numerical indicator of bonding (positive) and antibonding (negative) character between a pair of atoms within a molecule. For N2 in an approximate calculation the overall overlap populations are +0.68 for the three a filled MOs and +0.54 each for the it MOs. If one considers each it interaction of bond order one then the overall bond order is clearly three. 

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