Energies of frontier orbitals

Table 6a EHT energy and energy of frontier orbitals (eV) of (001), (010) and (100) surface clusters.

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... 

Table 2 HMO Energies of Frontier Orbitals of Some Six-membered Heterocycles...

Mayr has also commented on the need for compensation for Marcus curvature in an extended free energy relationship. In the context of a discussion of the reactions of carbocations with alkenes, he suggests the alternative possibility that this compensation might arise from a log A-dependent change in the relative energies of frontier orbitals on the carbocation and the nucleophile.30... 

Figure 2.11. (A) Relative energies of frontier orbitals of dioxygen and substituted Co ph-thalocyanines. For simplicity, only one electron is shown on the SOMO of the CoPcs. (B) Plot of log k (at constant potential) vs. the donor-acceptor intermolecular hardness for the different O2-C0PC pairs. From ref. [33], reproduced with permission of Elsevier.

Clearly, the above-mentioned values of the philicity relate each time to a particular alkene, and the orders of philicity may be different with different alkenes [45]. Figure 8.3 visualizes this behavior the stabilization or destabilization of the 7r7i -levels of alkene, induced by substituents, may alter relative values of the contributions from the n — p and a — n interactions. In practice, their values are often estimated without calculating AE confining oneself to finding the difference between the energies of frontier orbitals. Thus, the relative rate constants of addition of dichlorocarbene with substituted styrenes correlate well with the difference between the energies of the HOMO of styrene and the LUMO of carbene [47]. 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

A complete mechanistic description of these reactions must explain not only their high degree of stereospecificity, but also why four-ir-electron systems undergo conrotatory reactions whereas six-Ji-electron systems undergo disrotatory reactions. Woodward and Hoifinann proposed that the stereochemistry of the reactions is controlled by the symmetry properties of the HOMO of the reacting system. The idea that the HOMO should control the course of the reaction is an example of frontier orbital theory, which holds that it is the electrons of highest energy, i.e., those in the HOMO, that are of prime importance. The symmetry characteristics of the occupied orbitals of 1,3-butadiene are shown in Fig. 11.1. 

Both the reactivity data in Tables 11.3 and 11.4 and the regiochemical relationships in Scheme 11.3 ean be understood on the basis of frontier orbital theory. In reactions of types A and B illustrated in Seheme 11.3, the frontier orbitals will be the diene HOMO and the dienophile LUMO. This is illustrated in Fig. 11.12. This will be the strongest interaction because the donor substituent on the diene will raise the diene orbitals in energy whereas the acceptor substituent will lower the dienophile orbitals. The strongest interaction will be between j/2 and jc. In reactions of types C and D, the pairing of diene LUMO and dienophile HOMO will be expected to be the strongest interaction because of the substituent effects, as illustrated in Fig. 11.12. 

Fig. 11.15. Estimated energies of frontier n orbitals for some common 1,3-dipoles. [From K. N. Houk, J. Sims, R. E. Duke, Jr., R. W. Strozier, and J. K. George, J. Am. Chem. Soc. 95 7287 (1973).]...

Apeloig and Kami (13) have also studied the effects of substituents on the reactivity of silenes by the frontier molecular orbital (FMO) approach. They have concluded that, concerning electronic factors, the polarity of the carbon-silicon double bond, and thus the coefficients of the frontier orbitals, play a more important role than the energies of these orbitals in controlling the reactivity of silenes. 

Based on the number of n electrons in polyenes, we can predict which type of intermolecular cycloadditions will be symmetry allowed. The close in energy the frontier orbitals are, the stronger will be the interaction between them and therefore the more easily the reaction will occur. The orbital coefficients at the interacting centres can also influence the rate and the direction of addition. 

The analytic activity of Lewis acids in this reaction can also be interpreted on the basis of frontier orbital theory. A Lewis acid coordinates with the electron-withdrawing group on the dienophile (in this case LtAlCL with the carbonyl group), thereby further lowering the energy of the LUMO This in turn leads to an energy ad vantage and thus acceleration of the reaction... 

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