Highest-occupied molecular orbital energy eigenvalue

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 standard potentials f/R,oo, which hold for Oox = red in Eq. (21) or y = 1/2 in Eq. (22), depend directly on the chemical nature of the compound. Consequently, they are linked to the corresponding electronic energy levels derived from the molecular orbital (MO) theory. A linear dependency between [/r,oo and the corresponding eigenvalue coefficients for the lowest unoccupied molecular orbital (LUMO) or highest occupied molecular orbital (HOMO) energy levels was found... 

Highest eigenvalue of bond-bond polarizability matrix (d ). )) Free valence (unitless), m) Localization energy for electrophilic attack. ") Localization energy for radical attack. o) Localization energy for nucleophilic attack. P) Energy of highest occupied molecular orbital. 

HOMO Highest Occupied Molecular Orbital. A molecular orbital calculation yields a set of eigenvalues or energy levels in which all the available electrons are accommodated. The highest filled energy level is called the HOMO. The next higher energy level which is unoccupied because no more electrons are available is the LUMO or Lowest Unoccupied Molecular Orbital. On the basis of Koopman s theorem the HOMO and LUMO of a molecule can be approximated as its ionization and electron affinity, respectively. 

Total Energies, Interatomic Separations (A), Binding Energy per Atom (B.E.) Energy Eigenvalue of the Highest Occupied Molecular Orbitals (HOMO)... 

Figure 1. Schematic representation of some important Kohn-Sham eigenvalues relative to the vacuum level, denoted by 0, and their relation to observables. / is the ionization energy of the many-body system, which is equal to that of the Kohn-Sham system., 4 is the many-body electron affinity, is the electron affinity of the Kohn-Sham system, A is the fundamental gap, Aks the single-particle highest occupied molecular orbital-lowest unoccupied molecular orbital gap and Axe is the derivative discontinuity. (Reprinted from Ref. [23]. Copyright 2006 with permission from the Brazilian Journal of Physics.)...

Fig. 4.16 The n molecular orbitals and n energy levels for an acyclic three-p-orbital system in the simple Hiickel method. The MOs are composed of the basis functions (three p AOs) and the eigenvectors (the c s), while the energies of the MOs follow from the eigenvalues (Eq. 4.68). In the drawings of the MOs, the relative sizes of the AOs in each MO suggest the relative contribution of each AO to that MO. This diagram is for the propenyl radical. The paired arrows represent a pair of electrons of opposite spin, in the fully-occupied lowest MO, i/q, and the single arrow represents an unpaired electron in the nonbonding MO, 1j/2 the highest n MO, ij/3, is empty in the radical...

The most traditional way to address the stability of any finite molecular model (more on this in Sect. 2.3.3) is to extract and use the molecular orbitals (MOs) resulting from an electronic structure calculation - most often the highest occupied MOs (HOMOs) and the lowest unoccupied MOs (LUMOs) (Fig. 9.1) - and the corresponding eigenvalues. As an example the energy of the HOMO-LUMO gap for a species has often been invoked as a measure of its stability vs. oxidation - quite naturally as it will be a measure of the ease of the transfer of an electron from the... 

---