Highest occupied molecular orbital levels

The Diels-Alder reaction is believed to proceed m a single step A deeper level of understanding of the bonding changes m the transition state can be obtained by examining the nodal properties of the highest occupied molecular orbital (HOMO) of the diene and the lowest unoccupied molecular orbital (LUMO) of the dienophile... 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

FuUerene compounds have receieved a lot of attention in recent years. In this exercise we predict the energy of Cgg and look at its highest occupied molecular orbital, predicted at the Hartree-Fock level with the 3-21G basi set. Include SCF=1ight in the route section of the job. 

Each energy level in the band is called a state. The important quantity to look at is the density of states (DOS), i.e. the number of states at a given energy. The DOS of transition metals are often depicted as smooth curves (Fig. 6.10), but in reality DOS curves show complicated structure, due to crystal structure and symmetry. The bands are filled with valence electrons of the atoms up to the Fermi level. In a molecule one would call this level the highest occupied molecular orbital or HOMO. 

The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied MO) levels for hydrogen donors used in coal liquefaction are not yet well known, but the principles involved can be illustrated with the group transfer reaction between molecular hydrogen, a (4n+2)e donor with n=0, and naphthalene, a (4m)e acceptor with m=l ... 

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... 

Molecular engineering of ruthenium complexes that can act as panchromatic CT sensitizers for Ti02-based solar cells presents a challenging task as several requirements have to be fulfilled by the dye, which are very difficult to be met simultaneously. The lowest unoccupied molecular orbitals (LUMOs) and the highest occupied molecular orbitals (HOMOs) have to be maintained at levels where photo-induced electron transfer into the Ti02 conduction band and regeneration... 

Fig. 9 OMT bands for NiOEP, associated with transient reduction (1.78 V) and transient oxidation (—1.18 V). Data obtained from a single molecule in a UHV STM. The ultraviolet photoelectron spectrum is also shown, with the energy origin shifted (by the work function of the sample, as discussed in [25]) in order to allow direct comparison. The highest occupied molecular orbital, n, and the lowest unoccupied molecular orbital, %, are shown at their correct energy, relative to the Fermi level of the substrate. As in previous diagrams,

The nature of the electronic states for fullerene molecules depends sensitively on the number of 7r-electrons in the fullerene. The number of 7r-electrons on the Cgo molecule is 60 (i.e., one w electron per carbon atom), which is exactly the correct number to fully occupy the highest occupied molecular orbital (HOMO) level with hu icosahedral symmetry. In relating the levels of an icosahedral molecule to those of a free electron on a thin spherical shell (full rotational symmetry), 50 electrons fully occupy the angular momentum states of the shell through l = 4, and the remaining 10 electrons are available... 

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.

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

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