HOMO highest occupied molecular energy

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

Alkenes absorb ultraviolet (UV) light and use the absorbed energy to excite an electron from the HOMO (highest-occupied molecular orbital) to the LUMO (lowest-unoccupied molecular orbital). 

In more detail, the interaction energy between donor and acceptor is determined by the ionisation potential of the donor and the electron affinity of the acceptor. The interaction energy increases with lowering of the former and raising of the latter. In the Mulliken picture (Scheme 2) it refers to a raising of the HOMO (highest occupied molecular orbital) and lowering of the LUMO (lowest unoccupied molecular orbital). Alternatively to this picture donor-acceptor formation can be viewed in a Born-Haber cycle, within two different steps (Scheme 3). 

HOMO = highest occupied molecular orbital) is the Fermi limit. Whenever the Fermi limit is inside a band, metallic electric conduction is observed. Only a very minor energy supply is needed to promote an electron from an occupied state under the Fermi limit to an unoccupied state above it the easy switchover from one state to another is equivalent to a high electron mobility. Because of excitation by thermal energy a certain fraction of the electrons is always found above the Fermi limit. 

Figure 1 shows the electron attachment energies (AE) and ionization potentials (IP) of silyl substituted 7t-systems and related compounds [4], AE can be correlated with the energy level of the LUMO (lowest unoccupied molecular orbital) and IP can be correlated with the energy level of the HOMO (highest occupied molecular orbital). For a-substituted 7t-systems, the introduction of a silyl group produces a decrease in the tc -(LUMO) level. This effect is attributed to the interaction between a low-lying silicon-based unoccupied orbital such as the empty d orbital of silicon and the it orbital (d -p interaction) as shown in Fig. 2. Recent investigations on these systems, however, indicate that d orbitals on silicon are not necessarily required for interpreting this effect a-effects of SiR3 can also be explained by the interaction between Si-R a orbitals and the 7r-system.

Fig. 2.1. Energy levels of molecular orbitals in formaldehyde (HOMO Highest Occupied Molecular Orbitals LUMO Lowest Unoccupied Molecular Orbitals) and possible electronic transitions.

Fig. 5-3. Electron energy levels in an isolated adsorbate particle and an adsorbent solid metal M = metal R = isolated particle LUMO = lowest unoccupied molecular orbital (lowest vacant electron level) HOMO = highest occupied molecular orbital (highest occupied electron level).

The Sc -promoted photoinduced electron transfer can be generally applied for formation of the radical cations of a variety of fullerene derivatives, which would otherwise be difficult to oxidize [135]. It has been shown that the electron-transfer oxidation reactivities of the triplet excited states of fullerenes are largely determined by the HOMO (highest occupied molecular orbital) energies of the fullerenes, whereas the triplet energies remain virtually the same among the fullerenes [135]. 

QSAR methods can be divided into several categories dependent on the nature of descriptors chosen. In classical one-dimensional (ID) and two-dimensional (2D) QSAR analyses, scalar, indicator, or topological variables are examples of descriptors used to explain differences in the dependent variables. 3D-QSAR involves the usage of descriptors dependent on the configuration, conformation, and shape of the molecules under consideration. These descriptors can range from volume or surface descriptors to HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy values obtained from quantum mechanics (QM) calculations. 

AMI calculations were performed using SPARTAN software, and these FMO predictions are consistent with the fact that the observed cycloaddition regiochemistry is generally /t -FMO . The HOMO/LUMO energies are listed in Table 9, and Figure 10 depicts the coefficients for the favored HOMO(miinchnone) - - LUMO(nitroindole) interaction (HOMO = highest, occupied molecular orbital LUMO = lowest unoccupied molecular orbital). 

FIG. 7. Dependence of energy bands of three-dimensional Ag clusters on size. LUMO-lowest unoccupied molecular orbital HOMO-highest occupied molecular orbital. 

FIG. 17. Energy levels of carbon model with and without adsorbed Ag2. HOMO-highest occupied molecular orbital. 

ADE = adiabatic detachment energies ESC A = electron spectroscopy for chemical analysis HOMO = highest occupied molecular orbitals MAES = metastable atom electron spectroscopy MIES = metastable ionization electron spectroscopy OAT = oxygen atom transfer PES = photoelectron spectra PEI = pulsed field ionization PIES = Penning ionization electron spectroscopy QM = quantum-mechanical REMPI = resonantly enhanced multiphoton ionization SC = semiclassical VDE = vertical detachment energies XPS = x-ray photoelectron spectroscopy ZEKE = zero electron kinetic energy Cp = cyclopentadienyl, Ph = phenyl, CeHs Tp =... 

Table I shows that the band gap, the energy difference between HOMO (highest occupied molecular orbitals) and LUMO (lowest unoccupied molecular orbitals) levels, decreases monotonically with the increase in network dimension. This decrease is caused by the delocalization of skeleton a electrons, which form both band edges. As is well known, eigenvalues of delocalized wave functions confined to a potential well are determined by the well size and potential-barrier heights. When delocalized wave functions are confined to a smaller area, the HOMO level moves downward and the LUMO level moves upwards, which results in the increase in band gap energy. This quantum size effect is given by...

HOMO (highest occupied molecular orbital) with symmetry label b and 1-4 bonding character declines from -9.83 to -10.18 eV. Accentuation of the 1-4 interaction in the gauche-gauche conformer, in which nonadjacent Si-Si bonds come into closer proximity, controls the energies of these MOs. 

Density functional theory (DFT) calculations at the B3LYP/6-31H-G"" level were carried out on the 1,3-dipolar cycloadditions of various heterophospholes, including 1,3-azaphosphole, with diazo compounds across the P=N bond <2003JP0504>. In most cases, the dominant frontier orbital interaction is between HOMO(diazo) with LUMO(heterophosphole) however, 1,3-azaphosphole has a HOMO of high energy and for it, HOMO(heterophosphole)-LUMO(diazo) is also important (HOMO = highest occupied molecular orbital LUMO = lowest unoccupied molecular orbital). 

---