HOMO-LUMO separation structure

This indicates that the deviations are due to systematic errors, for example deficiencies of the applied methods and basis sets. DFT-based methods, such as GIAO/DFT calculations are known to overestimate paramagnetic contributions to the chemical shielding. This results, for critical cases with small HOMO/LUMO separations, in overly deshielded competed chemical shifts. Notorious examples for these deficiencies are 29Si or 13C NMR chemical shift computations of silylenes, silylium ions or dienyl cation .(5/-54) Taking into account the deficiencies of the applied method, and bearing in mind very reasonable correlations shown in Figures 4 and 5, the computational results do support the structural characterization of the synthesized vinyl cations. 

Sinanoglu et al. used the HOMO and LUMO bonding types as indicators of aromaticity. Cioslowski and Polansky derived relationships between the Huckel ji electron energy, the number of Kekule structures, and the HOMO—LUMO separation. For benzenoid hydrocarbons, Cioslowski derived the following relationship between for the HOMO-LUMO gap Ahl... 

The effects of various structural factors of the molecular graph on the HOMO-LUMO separation, Ahl, of alternant conjugated hydrocarbons were investigated and some graph-theoretic formulas were obtained for Ahl- As can be derived from equation (77), when computed at the Hiickel level, the absolute hardness r] equals half the HOMO-LUMO separation Ahl as an important consequence of this fact, all theoretical relationships derived for Ahl are also valid for r). An approximation to Ahl for benzenoid hydrocarbons was derived by Cioslowski as a function of simple graph invariants, namely N, M, and KSC ... 

Some researchers use molecule computations to estimate the band gap from the HOMO-LUMO energy separation. This energy separation becomes smaller as the molecule grows larger. Thus, it is possible to perform quantum mechanical calculations on several molecules of increasing size and then extrapolate the energy gap to predict a band gap for the inhnite system. This can be useful for polymers, which are often not crystalline. One-dimensional band structures are... 

No ligand centered reduction has been observed in a cathodic region up to — 2.0 V (vs SCE) the HOMO-LUMO energy separation in corrole resulted then to be larger than 3.3 V, i.e. much greater than that present in porphyrins. This is consistent with the lower skeletal symmetry of the corrole structure with respect to porphyrin which is expected to increase the separation between HOMO and LUMO [46]. 

Now consider the solid. It is easy to understand why pure bulk C6o is semiconducting. The clusters are about 3.1 A apart and the interaction between clusters must be small. Therefore, the discrete levels in the HOMO-LUMO region of C6o give rise to narrow or flat occupied bands separated from flat unoccupied bands as shown by the band structure diagram in Figure 7.33 where the first Brillouin zone is shown at the right. Solid C6o is a molecular solid. 

Here two C fullerene structures are r ard l as distinct if they have different Huckel theory resonance enei es and/or HOMO-LUMO energy separations. This definition discounts the fact that identical resonance energies and HOMO-LUMO energy separations might conceivably be obtained for two different C fullerene molecular graphs. 

Cgo and the limiting value of 0.5743 for graphite). These values are in perfect agreement with those reported separately by Manolopoulos ". The HOMO-LUMO transition is allowed b, - a. A reasonably optimized structure has been found through molecular mechanics calculations, and used as the initial structure in semi-empirical molecular orbital calculations (AMl-Gaussian 90) within which the structure was further optimized. The important results are as follows. 

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