Highest occupied molecular orbital wave function

Hartree-Fock wave functions, 269 High resolution electron energy loss spectroscopy, HREELS, 43, 69 Highest occupied molecular orbital, HOMO, 269... 

According to a modified intermediate neglect of differential overlap (MINDO)/3 calculation, the highest occupied molecular orbital (HOMO) of a dicyanoDHI 7 shows a wave function similar to the lowest unoccupied molecular orbital (LUMO). Thus a locally excited (LE) transition (n-Jt ) is most probably hidden under this band. The assignment of a second band of 7 is less clear. 

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...

The mechanisms of chemical reactions and the reactivity properties of the molecules involved started to be elucidated through the analysis of the wave functions defining the quantum state of molecular systems,5-7 for instance the Fukui s frontier molecular orbital (FMO) theory8,9 has been very successful in rationalizing organic reactions basically through the analysis of the in- and out-of-phase overlap between the highest occupied molecular orbital (HOMO) of the nucleophile and the lowest unoccupied molecular... 

We are only interested in the localized wave function of the electron, for example, the highest occupied molecular orbital (HOMO), of the transition state complex with the electron transferred. Hence, we may use the HOMO wave function of the transition state complex after the electron transfer, including only the nearby surface metal atoms that contribute significantly to this HOMO [40]. This wave function at the cluster is calculated using the EHMO method together with the parameters of VSIP and double-zeta orbitals given in [31] ... 

If the wave function for the highest occupied molecular orbital (HOMO) of the complex is expressed in the form homo = (carbanion) + metai-Hgand, (carbanion) would not necessarily have the same symmetry as the HOMO of the isolated carbanion in the absence of the metal atom perturbations. However in all the systems we have examined, this is... 

The VEH band structure computed for PTV is presented in Fig. 4, where all the crossings among k bands and among a bands are avoided due to the low symmetry of the unit cell. The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands are, as expected, n bands, and show the same atomic orbital composition patterns as those reported for PT. The HOMO band of PTV corresponds to wave functions delocalized over the carbon backbone,with essentially no contribution from... 

Although it is more fruitfiil to constmct a correlation diagram for the detailed analysis of an electrocyclic reaction, there is, nevertheless, an alternative method that also enables us to reach similar conclusions. In this approach, which is extremely simple, our only guide is the symmetry of the highest occupied molecular orbital (HOMO) of the open-chain partner in an electrocyclic reaction. If this orbital has a C2 symmetry, then the reaction follows a conrotatory path, and if it has a mirror plane symmetry, a disrotatory mode is observed. The explanation for this alternative approach is based on the fact that overlapping of wave functions of the same sign is essential for bond formation. 

The intermolecular resonance can also be accounted for by simple molecular orbital theory [17, 18, 19] the linear combination of donor-acceptor molecular orbitals (LCDA-MO) theory. It is supposed that the wave function of the complex is the linear combination of the molecular orbitals implied, in first approximation, in the charge-transfer the highest occupied molecular orbital of the donor and the lowest vacant orbital of the acceptor ( a)-... 

Figures 2 and 3 show the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the carbon monoxide molecule. In the figures, white colour is for the positive sign of the wave function, while black colour indicates the negative sign of the wave function.

The first term is the screened electrostatic interaction between the donor and acceptor charges Qi and Q2 - assumed to be point charges - at the equilibrium distance Rn in the adduct. The second term accounts for covalent effects. The factor of 2 indicates that two electrons are shared. The c coefficients are the molecular wave-function weights on atoms 1 and 2. The energies Em and E are equal, to a first approximation, to the frontier orbital energies the base HOMO (HOMO = highest occupied molecular orbital) and the acid LUMO (LUMO = lowest unoccupied molecular orbital), i.e. to the base first ionization potential and to the acid electron aflSnity. A typical frontier orbital diagram is shown in Fig. 6.1. 

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