Frontier orbital energies

Figure 1.3. Frontier orbital energies (eV) and confidents for acrolein and protonated acrolein. In the latter case the upper numbers refer to the situation where bond lengths and angles correspond to those of acrolein. The lower numbers are more suitable for a hydroxyallyl cation. The actual situation is assumed to be intermediate. The data are taken from ref. 104.

Figure 2. Frontier orbital energy levels for the reaction of hydrogen and naphthalene...

Ab initio Hartree-Fock and density functional theory (DFT) calculations were performed to study transition geometries in the intramolecular hetero-Diels-Alder cycloaddition reactions of azoalkenes 20 (LJ = CH2, NFI, O) (Equation 1). The order of the reactivities was predicted from frontier orbital energies. DFT calculations of the activation energies at the B3LYP level were in full agreement with the experimental results described in the literature <2001JST(535)165>. 

AMI Calculated Charge Distribution (e) and Frontier Orbital Energies ( ) and Coefficients for 4- and 5-Aminoimidazoles (179) and (180)... 

Frontier orbital energies and coefficients for sydnone, calculated by the MINDO/3 method, and the predicted dominant frontier orbital interaction with an electron-deficient alkene. 

This effect cannot be explained by simply considering differences in frontier orbital energies. A useful monofluorinated dienophile has been prepared [364] using metallated difluoroenol carbamate chemistry (Eq. 143) cycloaddition occurred smoothly with a range of dienes, and desulfination could be achieved under mild conditions without loss of the fluorine atom. Wakselman and co-workers [365] synthesised a rare competent difluorinated dienophile. Lewis acid catalysed Diels-Alder reaction with furan afforded an acceptable yield of (unfortunately) unstable cycloadduct which decomposed to a phenolic product via a dehydrofluorination reaction, circumscribing its utility (Eq. 144). 

Interrelations of Experimental (y) and HMO Theoretical Quantities (x) Based on Frontier Orbital Energies (y = ax + b)a... 

The molecular geometries and the frontier orbital energies of heterophospholes 28-31 were obtained from density functional theory (DFT) calculations at the B3LYP/6-311- -G, level. The 1,3-dipolar cycloaddition reactivity of these heterophospholes in reactions with diazo compounds was evaluated from frontier molecular orbital (FMO) theory. Among the different types of heterophospholes considered, the 2-acyl-l,2,3-diazaphosphole 28, 377-1,2,3,4-triazaphosphole 30, and 1,3,4-thiazaphosphole 31 were predicted to have the highest dipolarophilic reactivities. These conclusions are in qualitative agreement with available experimental results <2003JP0504>. 

As shown in the following exercise, a donor substituent raises the frontier orbital energies whereas acceptor lowers them. Consequently, introducing a substituent on the dipolarophile causes two of the frontier orbitals to become closer in energy and two to separate (see the scheme above). These frontier orbital changes mirror those discussed in relation to the Alder rule. Again, the presence of the substituent induces a faster reaction.29... 

Example. We will look at the reaction between 2-methoxybutadiene and methyl acrylate. The frontier orbital energies and coefficients at the reactive sites are... 

Photoelectron studies of (CH3)3P=CH2 have provided data on the energy of the highest occupied molecular orbital and some of the lower-lying states (4-9). The frontier orbital energy of 6.81 eV is very low and seems to illustrate the carbanionic nature of the carbon, where this orbital is largely localized. This is borne out by semiquantitative CNDO/2 calculations on this molecule. The orbital sequence obtained is satisfactory according to ab initio results. 

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