HOMO and LUMO orbitals, energy

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

Figure 7. HOMO and LUMO orbital energies for C0 2Hg, plotted vs 1/N.

The HOMO and LUMO orbital energies seem to converge towards a value of about 4 eV, which would be an estimate of the work function for single sheet graphite. This is in reasonable agreement with the work function of 4.9 eV experimentally found for bulk graphite(58). 

Figure 10. Indicated are the HOMO and LUMO orbital energies obtained form EHT calculations for a variety of reactants. In the center are estimated orbital energies for a canonical metal cluster.

Yokoyama and coworkers investigated the discolouration of titanylphthalocyanine 60, and related porphyrins by silyl radicals derived from methylphenylpolysilane by molecular orbital methods60. Calculated values of AN, the index derived from the hard and soft acids and bases concept was determined from HF/3-21G calculated ionization potentials, electron affinities, and HOMO and LUMO orbital energies of the systems of interest. These studies predict that PhMe2Si should donate an electron readily to 60 to form 60 (equation 18). This prediction is of direct relevance to observations that irradiation of titanylphthalocyanine-coated methylphenylpolysilane films leads to discolouration of the film60. 

Some the results of calculations (total energy, heat of formation, HOMO and LUMO orbitals energies and so on) are collected in Table 2. 

HOMO and LUMO orbital energies lumo homo 20, 77... 

Table 6-2. HOMO and LUMO orbital energies (T2, T3) of diazomethane and its hetero-analogous compounds (after Caramella et al., 1977a Houk and Yamaguchi, 1984), in kJ mol ...

Figure 9. Gap between HOMO and LUMO orbital energy for various conjugated systems oligoynes, oligoenes, and fullerenes. The upper scale is for the oligoynes and oligoenes and the lower scale for fullerenes.

We often assume the double oeeupaney of orbitals within what is called the closed shell. The latter term has an approximate eharacter (Figs. 8.4 and 8.5). It means that for the studied system, there is a large energy difference between HOMO and LUMO orbital energies. 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

Figure 11-13. HOMO and LUMO orbitals are shown for several 2P derivatives, where X means electron-donating group (here it is amino), and Z means electron-withdrawing group (here it is nitrosyl). Orbital levels are relative and qualitative. MRCI Sj (it it ) energies are shown at bottom, in eV. (From Ref. [144])...

Pelletier and Reber315 present new luminescence and low-energy excitation spectra of Pd(SCN)42 in three different crystalline environments, K2Pd(SCN)4, [K(18-crown-6)]2Pd(SCN)4, and (2-diethylammonium A -(2,6-dimethylphcnyl)acetamide)2Pd(SCN)4, and analyze the vibronic structure of the luminescence spectra, their intensities, and lifetimes as a function of temperature. The spectroscopic results are compared to the HOMO and LUMO orbitals obtained from density functional calculations to qualitatively illustrate the importance of the bending modes in the vibronic structure of the luminescence spectra. 

The same equations are used to determine both the HOMO and LUMO values. This is consistent with the fact that the HOMO and LUMO orbitals are calculated from the same parent system, and that the difference between the orbital energies can be adequately covered by the two parameters 7(P) which represents the sensitivity of the parent to substitution and r(Y) which represents the electronic effect exerted by the functional group acting as a substituent. 

An additional point of interest concerns the behaviour of homo and lumo orbitals of reactants in allowed reactions. Fukui (1970, 1975) has pointed out that the frontier-orbital gap actually narrows as the reaction proceeds. This has been confirmed computationally for the cycloaddition of ethylene and butadiene (Townshend et al., 1976), and contrasts with what one might expect based on a static homo-lumo interaction. Such an interaction causes the energy gap between resultant orbitals to widen, as indicated in Fig. 29. 

This leads to a decrease in the energy difference between the HOMO and LUMO orbitals and an associated red or bathochromic... 

A condition for such a reaction to take place is a certain similarity of the interacting HOMO and LUMO orbitals, depending on the relative orbital energies of both the dipolarophile and the dipole. Electron-withdrawing groups on the dipolarophile normally favour an interaction of the LUMO of the dipolarophile with the HOMO of the dipole that leads to the formation of the new bonds, whereas electron donating groups on the dipolarophile normally... 

Figure 9.49 represents the HOMO/LUMO orbital-energy distribution in 18a,b and the hypothetical trimer with three oligofluorene units as linker. Again, we clearly distinguish the HOMO and LUMO orbitals localized on the donor and acceptor, respectively, demonstrating the charge-transfer features in these triads. 

Figure 2. Dependence of relative energy (AE), valence shell hardness (ri) and hardness computed taking into account the HOMO and LUMO orbitals (T HL) of HCN isomerization.

Abstract. Equilibrium configurations, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) of open and semi open carbon nanotubes of variable diameter such types as (6,6)+(6,0), (5,5)+(5,0) and (6,0)+(5,0) are determined in frames of semi-empirical quantum chemistry PM3-method. 

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