Frontier lowest unoccupied molecular orbital

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

Frontier orbitals (Section 10 14) Orbitals involved in a chem ical reaction usually the highest occupied molecular orbital of one reactant and the lowest unoccupied molecular orbital of the other... 

According to Frontier Molecular Orbital (FMO) theory, Diels-Alder reaction between an electron-rich diene and an electron-poor dienophile involves interaction between the highest-occupied molecular orbital (HOMO) on the diene and the lowest-unoccupied molecular orbital (LUMO) on the dienophile. The better the HOMO/LUMO overlap and the smaller their energy difference, the more favorable the interaction and the faster the reaction. 

The type of conjugation is also reflected in the frontier orbital profile, the charge distribution, and the permanent dipole moments. The results of semiempirical calculations on l-methylpyridinium-3-olate (16), Malloapeltine (17), Trigollenine (18), and Homarine (19) are presented in Scheme 7. Characteristically for the class of conjugated mesomeric betaines, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are distributed over the entire molecule as examplifled for l-methylpyridinium-3-olate. It was shown that 90% of the... 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

According to frontier molecular orbital theory (FMO), the reactivity, regio-chemistry and stereochemistry of the Diels-Alder reaction are controlled by the suprafacial in phase interaction of the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other. [17e, 41-43, 64] These orbitals are the closest in energy Scheme 1.14 illustrates the two dominant orbital interactions of a symmetry-allowed Diels-Alder cycloaddition. 

Chemical bonds are defined by their frontier orbitals. That is, by the highest molecular orbital that is occupied by electrons (HOMO), and the lowest unoccupied molecular orbital (LUMO). These are analogous with the top of the valence band and the bottom of the conduction band in electron band theory. However, since kinks are localized and non-periodic, band theory is not appropriate for this discussion. 

H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account, the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied anti-bonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden because of the rather weak interaction with the free electron cloud of the metal. 

Each reaction species must have molecular orbitals available and with the correct symmetry to allow bonding. These will be called frontier orbitals composed of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition to their involvement in bonding between species, these orbitals are of considerable interest in that they are largely responsible for many of the chemical and spectroscopic characteristics of molecules and species and are thus important in analytical procedures and spectroscopic methods of analysis [5-7],... 

In order to simplify mathematical treatment, less important contributions from interactions between orbitals with large energy differences are neglected. The procedure is limited to the interaction of the frontier orbitals, viz. the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs), as illustrated in Figure 2. 

The frontier molecular orbital, including the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital), plays a key... 

We may redraw 6 as 7a and 7b, in terms of frontier MOs. Here we emphasize the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) interactions that operate in the transition state 7a depicts the LUMO(carbene)/HOMO(alkene) or p-n interaction 7b shows the HOMO (carbene)/LUMO(alkene) or a-71 interaction. These formulations are especially... 

Further examination of the results indicated that by invocation of Pearson s Hard-Soft Acid-Base (HSAB) theory (57), the results are consistent with experimental observation. According to Pearson s theory, which has been generalized to include nucleophiles (bases) and electrophiles (acids), interactions between hard reactants are proposed to be dependent on coulombic attraction. The combination of soft reactants, however, is thought to be due to overlap of the lowest unoccupied molecular orbital (LUMO) of the electrophile and the highest occupied molecular orbital (HOMO) of the nucleophile, the so-called frontier molecular orbitals. It was found that, compared to all other positions in the quinone methide, the alpha carbon had the greatest LUMO electron density. It appears, therefore, that the frontier molecular orbital interactions are overriding the unfavorable coulombic conditions. This interpretation also supports the preferential reaction of the sulfhydryl ion over the hydroxide ion in kraft pulping. In comparison to the hydroxide ion, the sulfhydryl is relatively soft, and in Pearson s theory, soft reactants will bond preferentially to soft reactants, while hard acids will favorably combine with hard bases. Since the alpha position is the softest in the entire molecule, as evidenced by the LUMO density, the softer sulfhydryl ion would be more likely to attack this position than the hydroxide. 

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

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