Molecular orbitals highest-occupied

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).

Gauge-including (or -independent) atomic orbitals Independent gauge for localized orbitals Atomic orbital, molecular orbital Highest occupied, lowest unoccupied MO Tetramethyl-silane... 

In the ground state of a covalent bond, the molecular orbital is occupied by at least one, usually two electrons with anti-parallel spins. This is said to be the HOMO level that is, the highest occupied molecular orbital. If the bond is slightly sheared, the kinetic energies of its electrons is not affected, but the... 

Quantities which can be derived from the energies of frontier orbitals are discussed in Sections III,B, III,C, and III,D. Here we mean by frontier orbitals the two highest occupied and the two lowest free molecular orbitals. The occupied orbitals are usually bonding and the unoccupied ones anti-bonding. The correlation of experimental with calculated (HMO) data reported thus far are compiled in Table II. Linear relations of the type... 

It is also worthwhile to compare the ferrocenyl ethylene (vinylferrocene) anion radicals and cation radicals. For the cyano vinylferrocene anion radical, the strong delocalization of an unpaired electron was observed see Section 1.2.2. This is accompanied by effective cis —> trans conversion (the barrier of rotation around the —C=C— bond is lowered). As for the cation radicals of the vinylferrocene series, a single electron remains in the highest molecular orbital formerly occupied by two electrons. According to photoelectron spectroscopy and quantum mechanical calculations, the highest occupied molecular orbital is mostly or even exclusively the orbital of iron (Todres et al. 1992). This orbital is formed without participation of the ethylenic fragment. The situation is quite different from the arylethylene radical cations, in which all ir-orbitals overlap. 

For a given value of k, the solution of eq. (3.79) provides Mbasis orbitals. In molecular systems, the molecular orbitals are filled with electrons according to the aufbau principle, i.e. according to energy. The same principle is used for periodic systems, and the equivalent of the molecular HOMO (highest occupied molecular orbital) is the Fermi energy level. Depending on the system, two situations can occur. 

Fig. 11 Energy-level scheme of device in Fig. 10, consisting of electrode work functions and molecular HOMOs (highest occupied molecular orbitals) and LUMOs (lowest unoccupied molecular orbitals)...

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. 

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. 

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). 

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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