HOMO/LUMO energy gap

The doubly charged polybenzenoid molecules are model compounds for antiaromaticity. It has been pointed out that there is a direct, unequivocal correlation, between the extent of paratropicity experienced by the 4njt-conjugated systems, and the corresponding LUMO-HOMO energy gap, as estimated by SCF-MO calculations35,... 

Table 8. H NMR Paratropic Shifts of Polybenzenoid Dianions vs. LUMO-HOMO Energy Gaps 36). 

Fig. 11. H NMRparatropic shifts of 4nrt polybenzenoid dianions vs. LUMO-HOMO energy gaps 361...

The dependence of NMR patterns upon states of solvation should not be overlooked. This aspect of polyanion chemistry has been discussed (Sect. 4). The influence of the counter cation upon the dianion though unaccounted for by simple calculations is supposed to vary from system to system. The different topologies of the anions and different modes of delocalization may be responsible for the deviations from a linear dependence of the correlation. From Table 9 one can arrive at conclusions on the relative antiaromaticity of the various anions. For example, benzanthracene dianion 49 ) is less antiaromatic than chrysene dianion (542 ), and dibenzo-anthracene dianion (J/2-) is more antiaromatic than the pentacene dianion (472 ). It is also proposed that H NMR paratropic shifts may be used to calibrate the LUMO-HOMO energy gap. 

Table 9. LUMO-HOMO Energy Gaps Estimated (to 3 Method) for Dianions Derived from Benzenoid Polycycles. ...

Table 10. Spectral Patterns and LUMO-HOMO Energy Gaps of the Three Subgroups of Doubly...

The influence of the position of fluorine substituent on the ionization energy, the frontier orbital energy gap, the site of protonation and the basicity of phospholes were studied using this technique. Remarkably, compound 211 has the lowest LUMO-HOMO energy gap, which is reduced by almost 1 eV. A similar decrease could be expected for electron affinities of these compounds. 

The observed red-shift is ascribed to the enhanced delocahzation of the excited Pt(Ill)-Pt(III) states in the coordination chain, which decreases the LUMO-HOMO energy gap of the one-dimensional complex. In the lipid complexes, densely packed sulfonate groups seem to direct the electrostatically bound Pt(en)2 and PtCl2(en)2 complexes to coordinate in higher density. This causes the increase in the overlap between dz2 and p orbitals, depending on the molecular packing and chemical structure of the lipid molecules. The shortened inter-platinum (Pt -Cl-Pt ) distance would pro-... 

Table 3.1 The energies of HOMO and LUMO, and energy gaps (AE) between HOMO and LUMO, the absorption (Eabs) and emission (Eemi) energies of SiQDs with different diameters (denoted by do in nanometers) in their ground and first singlet excited states [25]. Reprinted with permission from (Li QS, Zhang RQ, Lee ST, Niehaus TA, Frauenheim T (2008) Amine-capped silicon quantum dots, Appl Phys Lett 92 053107). Copyright (2008), American Institute of Physics...

Dipolar cycloaddition reactions are generally classified into three types, dipole HO controlled, dipole LU controlled or HO,LU controlled, depending upon the relative energies of the dipole and dipolarophile frontier molecular orbitals. If the energy gap separating the dipole HOMO from the dipolarophile LUMO is smaller than that between the dipole LUMO and the dipolarophile HOMO, then the reaction is said to be dipole HO controlled. If the dipole LUMO-dipolarophile HOMO energy gap is smaller, then dipole LU control prevails. If the energy difference between the dipole HOMO and the dipolarophile LUMO is about the same as that between the dipole LUMO and the dipolarophile HOMO, dien neither interaction dominates and HO,LU control is operable. 

The value of x falls on the midpoint between the HOMO and LUMO. The energy gap between the HOMO and the LUMO is equal to lr, Thus hard molecules have a large HOMO-LUMO gap, and soft molecules have a small gap. (6)... 

Quantum mechanical descriptors (e.g. HOMO-LUMO energy gap) 3D structure See Section 2.7.4... 

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... 

Many organic compounds such as lycopene are colored because their HOMO-LUMO energy gap is small enough that appears m the visible range of the spec trum All that is required for a compound to be colored however is that it possess some absorption m the visible range It often happens that a compound will have its k m the UV region but that the peak is broad and extends into the visible Absorption of the blue to violet components of visible light occurs and the compound appears yellow... 

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