HOMO-LUMO splitting

The interaction diagram for the cis and trans union of two FHC radical fragments is shown in Fig. 38. From Fig. 38 it is obvious that the pi HOMO-LUMO splitting is larger for the case of cis union than for trans union. The final conclusions is that the HOMO and LUMO energies in cis and trans 1,2-difluoroethylene vary in the following way ... 

Ease of dimerization (Scheme 3) is related to HOMO-LUMO splitting. Within the framework of the frontier molecular orbital (FMO) approximation, reducing the frontier orbital gap favors symmetry allowed cycloadditions (e.g., 99 - 97) by stabilizing the transition state. Since the... 

The effect of heteroatoms on the LUMO energy of mesomeric betaines can be treated similary, and this leads to an estimate of the HOMO-LUMO splitting. If E is the splitting in an AH anion, the change (A ) upon substitution of a heteroatom at position r is given by Eq. (2). 

Using Eq. (2) we can estimate the HOMO-LUMO splitting of the nitrogen... 

Fio. 1. Calculated change in HOMO-LUMO splitting of heterocycles isoconjugate with the benzyl anion vs frequency of their first n-> n absorption in ethanol solution. 

Fig. 3. Calculated change in HOMO LUMO splitting of heterocycles isoconjugate with the -naphthylmethyl anion vs frequency of their first n - n absorption band in (i) ethanol ( ), (ii) water (ffi), (iii) water at pH > 7 (O). or (iv) chloroform (C),...

Let us return to the results obtained in the CNDO/BW realization of the CTP scheme. The calculations for the Si(OA)4 cluster la give a quasi-band picture of electron levels with HOMO-LUMO splitting of 12eV that is somewhat (but quite reasonably) higher than the experimental estimate of the band gap in Si02. The HOMO is mainly composed of 2p AOs of O atoms, whereas the LUMO is constituted by 3s AOs of Si that are quite in agreement with the band structure of Si02. 

The calculated one-electron energy levels of clusters (a)-(c) are presented in Fig. 17. In all the clusters, LUMO is mainly represented by the sp hybrid AO. The picture obtained actually corresponds to centers accepting an electron pair. HOMO-LUMO splitting is about 12 eV. HOMO is composed mainly of AOs of oxygen atoms. Substitution of Si by Al results in... 

Using Eq. (2) we can estimate the HOMO-LUMO splitting of the nitrogen heterocycles 396-398 (Fig. 1). Assuming that perturbations due to exocyclic oxygen are constant, the separation of the frontier orbitals (Ehet) given by... 

The outstanding feature of replacing a carbon by a nitrogen atom is an increase in the stength of an a band. As stated previously, in the case of the alternant hydrocarbons, the degenerate pair of transitions (HOMO-next-LUMO and next-HOMO-LUMO) splits into two components by the Cl procedure. If , and u2 denote the transition moments of these two transitions, respectively, the transition moments of the two components (MH and ML) can be written as weighted sums of w, and u2 as follows ... 

An example is shown in Figure 2.15 where an even perturbation produces the orbitals of azulene and an odd perturbation (/ j) those of naphthalene from the perimeter orbitals of cyclodecapentaene. (Cf. Example 2.5.]) The energies of 0, and 0,. are not affected to the first order by the odd perturbation producing naphthalene, whereas 0s is stabilized and 0,- destabilized. Therefore, 0, becomes the HOMO and 0. the LUMO, and the HOMO-LUMO splitting AEhomo-lumo he same as for cyclodecapentaene. The HOMO- LUMO transition is referred to as L according to Platt. In azulene, on the other hand, 0, is destabilized and becomes the HOMO, whereas 0s- is stabilized and becomes the LUMO. The HOMO-LUMO splitting is markedly smaller than for cyclodecapentaene, and the HOMO-LUMO transition is of the Lb type. 

The second important periodic trend is a significant increase in the energy of the HOMO-LUMO splitting upon moving down a group (i.e., CrO ... 

FIGURE 1.5 Crystal field splitting patterns for the common four- and five-coordinate geometries tetrahedral, square pyramidal, and square planar. For the square pyramidal and square planar arrangements, the z axis is conventionally taken to be perpendicular to the L4 plane. Octahedral geometry is expected for d while square planar and square pyramidal are preferred in d the A HOMO-LUMO splittings shown apply to those d " configurations. 

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