Orbital energies description

I he Koothaan equations just described are strictly the equations fora closed-shell Restricted Hartrce-Fock fRHK) description only, as illustrated by the orbital energy level diagram shown earlier. To be more specific ... 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

Elements beyond the second row of the periodic table can form bonds to more than four ligands and can be associated with more than an octet of electrons. These features are possible for two reasons. First, elements with > 2 have atomic radii that are large enough to bond to 5, 6, or even more ligands. Second, elements with > 2 have d orbitals whose energies are close to the energies of the valence p orbitals. An orbital overlap description of the bonding in these species relies on the participation of d orbitals of the inner atom. 

We have checked, using as a test case, that the description of the optimum orbital of the molecular system is then complete in the sense that it allows (assuming that the orbital energy is known) to construct by a fit process an optimum orbital which is very close to the one obtained by a diagonalisation process in a gaussian basis. 

Table 3.4 compares the CMO and NBO descriptions of these molecules in terms of the orbital energies... 

This also ascribes a meaning to the other KS orbital energies. Without a reasonable description of the other ionization potentials, many excited state descriptions will fail because most excited states for molecules are of Rydberg character, or require some mixture of Rydberg character in their accurate description. 

Fig. 7 (a) Molecular orbital (MO) description for the charge-transfer state formation in organic donor/ acceptor systems, (b) Description for CT state emission energy using exciplex MOs in (a)... 

If experimental data is used to parameterize a semi-empirical model, then the model should not be extended beyond the level at which it has been parameterized. For example, experimental bond energies, excitation energies, and ionization energies may be used to determine molecular orbital energies which, in turn, are summed to compute total energies. In such a parameterization it would be incorrect to subsequently use these mos to form a wavefunction, as in Sections 3 and 6, that goes beyond the simple product of orbitals description. To do so would be inconsistent because the more sophisticated wavefunction would duplicate what using the experimental data (which already contains mother nature s electronic correlations) to determine the parameters had accomplished. 

Most of the stereochemical arrangements found in these complexes are based oil the octahedron or on the tetrahedron, and may be derived from these configurations by a suitable distortion. Both basic systems have cubic symmetry and d-orbital energies are split into a triplet and a doublet. The group-theoretical notation will be used for their description. ... 

This construction provides a more physically realistic description of the M-L bond which ultimately enables LFMM to mimic far more expensive quantum chemical methods. The AOM is superior to CFT since it retains all the appropriate symmetry behavior but allows us to focus on individual ligands. The d-orbital energies are thus, in general, a function of all the ligands although in high-symmetry cases such as Oh, there may be a convenient separation into a and n interactions. 

The He2A 2 state has nearly the same dissociation energy as the He (22J ion. This supports the idea that the excited He2 configurations can be described at small interatomic distances as an inner He core with an outer Rydberg orbital. This description is less quantitative for the heavier rare-gas pairs. The unusual maxima result either from curve crossing (e.g., C S ) or as for the state by a changeover in the... 

Another possibility concerns the resonance integrals /Sab which appear in the Klopman-Salera equation. In a Hiickel picture, these are independent of the orbital energy, but in a double-zeta or better description we would expect the more tightly-bound electrons to have more contracted orbitals, and the higher virtual orbitals to be more diffuse.131 It may be that the HOMO and LUMO have the optimum spatial distribution for strong interaction, and that interactions involving more contracted and more diffuse orbitals are weaker.122... 

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