Orbital interactions frontier molecular orbitals

Interaction matrix for the 24 different types of chemical reactions involving Lewis acids and bases, organized according to the topology of their interacting frontier molecular orbitals. [ Mark R Leach, meta-synthesis (accessed October 22, 2013).]... 

The frontier molecular orbital approach provides a description of the bonding interactions that occur in the 8 2 process. The orbitals involved are depicted in Fig. 

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. 

Frontier Molecular Orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

Frontier-molecular-orbital Interactions for Carbo-Diels-Alder Reactions... 

To explain tlie stereodieniistiy of tlie allylic substitution reaction, a simple stereoelectronic model based on frontier molecular orbital considerations bas been proposed fl55. Fig. G.2). Organocopper reagents, unlike C-nudeopbiles, possess filled d-orbitals fd - configuration), wbidi can interact botli witli tlie 7t -fC=C) orbital at tlie y-carbon and to a minor extent witli tlie cr -fC X) orbital, as depicted... 

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. 

Atomic orbitals interact with each other to give bond orbitals (Sect. 1), which mutually interact to give molecular orbitals (Sect. 2). Here we will examine interactions of molecular orbitals, especially those of frontier orbitals important for chemical reactions. 

The reactivity and selectivity of the Diels-Alder reaction can be understood in terms of Frontier Molecular Orbital (FMO) theory which evolved during studies of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffmann58 and, independently, by Fukui59. FMO theory explains the driving force of a reaction between two compounds by the efficiency with which the molecular orbitals of the two partners overlap. This orbital interaction is maximized when their energy separation is small. FMO theory further states that the two most important interacting orbitals are the Highest Occupied... 

According to frontier molecular orbital theory, the strongest interactions are between those orbitals that have coefficients with similar magnitudes relative to the unperturbed molecules, t.e. the interaction is between the small coefficient on the dienophile and the small coefficient on the diene [16], [17]. 

Woodward-Hoffmann Rules. A set of rules based on the symmetry of Frontier Molecular Orbitals on interacting molecules which indicate whether a particular reaction will be favorable or unfavorable. 

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. 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

As with the chloropalladation reaction (vide supra)m the rearrangement of >/2-methyl-enecyclopropane to >/4-TMM was shown experimentally to proceed stereoselectively by disrotatory ring cleavage of the distal frontier molecular orbital considerations, which predict that the out-of-phase interaction between the metal orbital in the distal ring-opening of -methylenecyclopropane complexes can be minimized by bending the bond up away from the metal (equation 348)410 ... 

---