Highest occupied

One can detennine the total number of electrons in the system by integrating the density of states up to the highest occupied energy level. The energy of the highest occupied state is called the Eermi level or Eermi energy, E ... 

The occupied bands are called valence bands the empty bands are called conduction bands. The top of tire valence band is usually taken as energy zero. The lowest conduction band has a minimum along the A direction the highest occupied valence band has a maximum at F. Semiconductors which have the highest occupied k -state and lowest empty state at different points are called indirect gap semiconductors. If k = k, the semiconductor is call direct gap semiconductor. Gennanium is also an indirect gap semiconductor whereas GaAs has a direct gap. It is not easy to predict whether a given semiconductor will have a direct gap or not. 

Most electronic valence transitions shift to longer wavelengths at higher pressures drat is, the gap between the highest occupied orbital and lowest unoccupied orbital tends to decrease upon compression. The rates of shift usually are larger (1) for pure materials than for solutes in a solvent and (2) for stronger (more allowed) transitions. However, these correlations are not quantitative, and many transitions shift in the opposite... 

Kleinman L 1997 Significance of the highest occupied Kohn-Sham eigenvalue Phys. Rev. B 56 12 042-5... 

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

Knowledge of molecular orbitals, particularly of the HOMO Highest Occupied Molecular Orbital) and the LUMO Lowest Unoccupied Molecular Orbital), imparts a better understanding of reactions Figure 2-125b). Different colors e.g., red and blue) are used to distinguish between the parts of the orbital that have opposite signs of the wavefunction. 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

In the spirit of Koopmans theorem, the local ionization potential, IPi, at a point in space near a molecule is defined [46] as in Eq. (54), where HOMO is the highest occupied MO, p( is the electron density due to MO i at the point being considered, and ej is the eigenvalue of MO i. 

MR Molecular ReFraciivity llOMO Fnergy of Highest Occupied MO... 

Not all Iterative semi-empirical or ah iniiio calculations converge for all cases. For SCF calculation s of electronic stnictiire. system s with a small energy gap between the highest occupied orbital and the lowest unoccupied orbital may not converge or may converge slowly. (They are generally poorly described by the Ilartree-Foch method.)... 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

The. more tightly held an electron is. the more difficult it is to remove, hence the higher the electrode potential necessary to remove it. Make the reasonable hypothesis that the electron removed in a one-electron oxidation comes from the highest occupied orbital. HOMO. Using SHMO. determine the HOMO for ben7 ene, biphenyl, and naphthalene. 

Considering Highest Occupied Molecular Orbital and Lowest Unoccupied Molecular Orbital (providing that solvation energies are equal) 44 might be.a better reducer than 43 (Schemes 65-68). 

The thermal stability can be correlated with the energy of the highest occupied molecular orbital of the molecule (HMO approximation) (300). 

FIGURE 13 38 The ir ir transition in as trans 1 3 cyclooctadiene involves exci tation of an electron from the highest occupied molec ular orbital (HOMO) to the lowest unoccupied molecu lar orbital (LUMO)... 

Frontier orbitals (Section 10 14) Orbitals involved in a chem ical reaction usually the highest occupied molecular orbital of one reactant and the lowest unoccupied molecular orbital of the other... 

HOMO (Section 10 13) Highest occupied molecular orbital (the orbital of highest energy that contains at least one of a molecule s electrons)... 

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