Highest occupied molecular orbital separation

Frontier Orbital theory supplies an additional assumption to this calculation. It considers only the interactions between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These orbitals have the smallest energy separation, leading to a small denominator in the Klopman-Salem equation. The Frontier orbitals are generally diffuse, so the numerator in the equation has large terms. 

In the simplest frozen orbital approach, both IE and EA values can be approximated as the negative of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, respectively, following the Koopmans theorem. A better way is to calculate the energies of the system and its cationic and anionic counterparts separately and then estimate fx and 17 from Equations 12.4 and 12.5, respectively. 

Now the molecule M = AB at large separation has an ionization energy /jf equal to the lowest ionization energy of one of the atomic fragments, in our case /m = I A- This means that the highest occupied molecular orbital <1) satisfies... 

The mechanism of the reaction has generally been discussed in terms of a thermally allowed concerted 1,3-dipoIar cycloaddition process, in which control is realized by interaction between the highest occupied molecular orbital (HOMO) of the dipole (diazoalkane) and the lowest unoccupied molecular orbital (LUMO) of the dipolarophile (alkyne).76 In some cases unequal bond formation has been indicated in the transition state, giving a degree of charge separation. Compelling evidence has also been presented for a two-step diradical mechanism for the cycloaddition77 but this issue has yet to be resolved. 

The valence electron orbitals and energies of CO and C are sketched in Fig. 4.2. In a molecule, atomic orbitals form bonding and antibonding orbitals, separated by an energy gap. In CO the highest occupied molecular orbital, the 5a orbital is a symmetric with respect to the molecule s axis. It is separated by approximately 7 eV from the lowest two unoccupied degenerate 2re orbitals, of re symmetry with respect to the molecule s axis. The unoccupied 2k orbitals are antibonding and result from the interaction between the CPt and 0Px and CPy and 0Pj( orbitals. In the atom, atomic p orbitals are partially occupied, separated by approximately 20 eV from the doubly occupied 2s atomic orbital. CO adsorbs perpendicular to the transition metal surface, attached via its carbon atom. When adsorbed atop the surface valence s-electrons will interact with the 5a orbital, but their interaction is symmetry forbidden with the p-symmetric 2re orbitals. 

Photoelectron (PE) spectra have been measured for several (s-cis-diene)zirconocenes (5g, 51, 5s), for one example of the hafnium analogue (5n), and for (s-t/-ans-i7 -butadiene)Zr(C5Me5)2 (3c) (54). For both Cp and Cp series the highest occupied molecular orbital (HOMO) is separated from subsequent molecular orbitals (MO s) by a substantial energy difference. The observed PE spectra of 5 each exhibit a band around 6-6.5 eV (oi), well separated from several overlapping bands at 8-9 eV (6], f>2, fl2> bi). The PE spectrum of 3c shows a similar pattern [5.9 eV (aj) 7.1, 7.5, 7.5, 8.3 eV (fl2, i)]- The PE bands are in good accord with the... 

The square of the molecular orbital coefficient for the K L" state is summarized in Table I. Also shown, in parentheses, is the energy (eV) relative to the energy of the highest occupied molecular orbital (HOMO). Here the orbital components are expressed as the sum of the squares of the partial expansion coefficients and of the overlap populations for the orbitals. From Table 1 it is easily seen that the K L X-ray line is mainly composed of three components each separated by leV. The observed X-ray satellite spectra for MgF and NiFj are shown in the solid lines in Figs. 8 and 9. Fig. 8 shows spectra induced by 2 MeV He impact, and Fig. 9 by 84 MeV impact. These excitation conditions produce mostly direct Coulomb ionization, not shake ionization. The observed spectra are now deconvoluted into K L" components. The rather broad K L line is further deconvoluted into three molecular orbital components each separated by... 

Figure 1.6 Exciton formation and charge separation in a bulk heterojunction, for the case that the donor phase absorbs the incident light. The energies of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of the donor (D) and acceptor (A) phases are shown. The exciton binding energy Af b is (AEg + AEn).

Some dispute persists as to the size of the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap in the closed-shell 24-electron species. This aspect of the molecular orbital diagram is of particular interest for its implications on the photophysical properties of the clusters. Electrochemical measurements are consistent with a large, 2- to 3-eV, separation however, the exact nature of the excited state remains uncertain. 

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