Lowest unoccupied MO

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... 

According to one classification (15,16), symmetrical dinuclear PMDs can be divided into two classes, A and B, with respect to the symmetry of the frontier molecular orbital (MO). Thus, the lowest unoccupied MO (LUMO) of class-A dyes is antisymmetrical and the highest occupied MO (HOMO) is symmetrical, and the TT-system contains an odd number of TT-electron pairs. On the other hand, the frontier MO symmetry of class-B dyes is the opposite, and the molecule has an even number of TT-electron pairs. 

We will perform an AMI calculation on tetraphenylporphin (TPP), pictured at right, in order to examine the four important molecular orbitals for this molecule the second-highest and highest occupied MO s and the lowest and second-lowest unoccupied MO s (which we denote HOMO-1, HOMO, LUMO and LUMO-ll, respectively). 

The energies of the highest occupied MO (HOMO) and of the lowest unoccupied MO... 

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 ... 

MO) with the protons in the nodal plane. The mechanism of coupling (discussed below) requires contact between the unpaired electron and the proton, an apparent impossibility for n electrons that have a nodal plane at the position of an attached proton. A third, pleasant, surprise was the ratio of the magnitudes of the two couplings, 5.01 G/1.79 G = 2.80. This ratio is remarkably close to the ratio of spin densities at the a and (3 positions, 2.62, predicted by simple Hiickel MO theory for an electron placed in the lowest unoccupied MO (LUMO) of naphthalene (see Table 2.1). This result led to Hiickel MO theory being used extensively in the semi-quantitative interpretation of ESR spectra of aromatic hydrocarbon anion and cation radicals. 

For polyenes in their ground state, the highest occupied MO (HOMO) will be symmetric with respect to m2 for 2, 6, 10. .. n electron systems and antisymmetric for 4, 8, 12. .. n electron systems. The lowest unoccupied MO (LUMO) has the symmetry opposite to that of HOMO. In the first excited state, the LUMO of the ground state will become singly occupied because of the promotion of an electron and it will thus become the new highest occupied orbital. Therefore in the circumstances the symmetry of the highest occupied orbital is opposite to that of the ground state. 

We now turn to the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne. The concerted, almost synchronous nature of this reaction might create the impression that the electronic mechanism of this process should be very similar to that of the Diels-Alder reaction. Such an expectation is reinforced by frontier orbital theory, which treats both reactions in very much the same way (see Ref. 32). The only significant differences are related to the fact that the lowest unoccupied MO (LUMO) for a linear 1,3-dipole... 

The same inertness holds for many inoperative cyclization paths that would have given highly quinoid systems such as 104 (cf 44 and 45), 105 (cf 86). 106(cf 87) and 107 c 88). Under certain circumstances such topological factors can not only modify the AO coefficients at the reacting atoms but can also result in an interchange of the usual topmost occupied MO and lowest unoccupied MO with other orbitals which prevent the photocyclization altogether. This situation has been deduced for the pentahelicenes series (Table In this series, (Table 20) benzo... 

Fig. 5 a and b. Schematic representation of a highest occupied MO, b lowest unoccupied MO in hexa-triene... 

Fig. 25 Energy crossing between the lowest unoccupied MOs of the P2Wig062 heteropolyanion upon substitution by three molybdenum centers in a cap (02 positions) (EH calculations) (taken from Ref 78).

In these relationships, IP and EA refer to free atoms or ions, whole molecules or radicals, rather than atoms within molecules, and so — p bears little relationship to Pauling s x- I 1 terms of molecular orbital (MO) theory, IP is the negative of the energy of the highest occupied MO (-chomo), and EA is the energy of the lowest unoccupied MO (clumo)- Thus, hard molecules... 

Thus the ionization potential corresponding to removal of the electron from occupied is just the negative of that MO s energy. This observation is known as Koopmans theorem. One can similarly show that the energy of the lowest unoccupied MO is an estimate of the electron affinity of the molecule. In fact, ionization potentials estimated by Koopmans theorem are fairly accurate, but the electron affinities calculated this way are much less so. 

HOMO = highest occupied MO LUMO = lowest unoccupied MO. 

For the naphthalene negative ion, Hiickel MO theory puts the unpaired electron in the lowest unoccupied MO of the neutral naphthalene molecule this MO is (Levine, Section 15.8)... 

A ligand field model has been used for the interpretation of the magnetic behavior of the Mo(R2Dtc)4 complexes (485). Extended Hiickel calculations compare the electron-donating characteristics of the dithiocarbamate ligand to other 1,1-dithio chelates. This calculation concluded that (1) there is more metal character in the lowest unoccupied MO in the dithiocarbamate complexes, and (2) there is more ligand character in the lowest unoccupied MO in the dithioacid complexes (485). This seems to be in agreement with the electronic spectra. 

Each of the two bands in diamond can accommodate four electrons per C atom. Because carbon has just four valence electrons (2s2 2p2), the valence band is completely filled and the conduction band is completely empty. Diamond is therefore an insulator because there are no vacant MOs in the valence band to which electrons can be excited by an electrical potential, and because population of the vacant MOs of the conduction band is prevented by the large band gap. By contrast, metallic conductors have no energy gap between the highest occupied and lowest unoccupied MOs. This fundamental difference between the energy levels of metals and insulators is illustrated in Figure 21.10. 

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