Perturbation theory HOMO-LUMO interactions

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

Using perturbation theory. Hammer and Nprskov developed a model for predicting molecular adsorption trends on the surfaces of transition metals (HN model). They used density functional theory (DFT) to show that molecular chemisorption energies could be predicted solely by considering interactions of a molecule s HOMO and LUMO with the center of the total d-band density of states (DOS) of the metal.In particular. 

We have discussed in Section 10.3 the application of perturbation theory to processes in which two molecules come together. We saw there that the most important interactions will be between the HOMO of one molecule and the LUMO of the other. This method can serve as a useful guide in deciding whether there will be a stabilization as a pericyclic reaction begins to occur. The HOMO-LUMO approach was the first one that Woodward and Hoffmann used for ana-... 

Theoretical analysis of this [4% + 27r]-cycloaddition reaction by consideration of frontier-orbital interactions between the electron-rich olefin (highest occupied molecular orbital, HOMO) and the electron-poor 5-nitropyrimidine (LUMO) has shown that the FMO perturbation theory correctly predicts an exclusive regiospecific addition of the enamine to N-l and C-4 of the pyrimidine ring (86JOC4070). 

Here the term orbital may refer to a discrete molecular orbital or a band (or an atomic orbital in the case of atomic species). The donor orbital on the base is usually the highest occupied MO (or HOMO), and the acceptor orbital on the acid is usually the lowest unoccupied MO (or LUMO). Simple perturbational MO theory predicts that for two interacting orbitals of suitable symmetry and overlap, the smaller the difference in the orbital energies, the greater the mutual perturbation or interaction. The terms soft and hard relate to a range of properties, but essentially soft acids are... 

Fukui and Inagaki have proposed an orbital interaction role for catalysts in the valence isomerization of tricyclo[4,2,0,0 ]octa-3,7-diene and in the rearrangement of syn-tricyclo[4,2,0,0 ]octane to tetrahydrosemibulvalene. The importance of the interactions with the HOMO and LUMO is stressed, and perturbation theory is used to explain how the catalysis can assist an energetically- or symmetry-disfavoured process. 

Theoretical determinations are mainly based on the assumption that the initial perturbation of the orbital of interacting species determines the course of a reaction or an interaction. In terms of equation of state, the perturbation theory was developed first. In terms of energy gap between HOMO and LUMO, acids and bases were defined by their hardness and softness. The Hard-Soft Acid-Base principle (Pearson 1963) describes some basic rules about kinetics and equilibrium of the acid-base interactions. The HSAB principle will be described as it has evolved in recent years on the basis of the density-functional theory (Parr and Yang 1989). For organic interactions, the following statements were proposed ... 

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... 

Experimental log k2 values were correlated with Brown para-localization energies, Dewar reactivity numbers, Herndon structure count ratios, Hess-Schaad resonance energy differences, indices of free valence, and second-order perturbation stabilization energies. The latter are based on Fukui s frontier orbital theory [67] which classifies the Diels-Alder reaction of benzenoid hydrocarbons with maleic anhydride as mainly HOMO (aromatic hydrocarbon)-LUMO (maleic anhydride) controlled. However, the corresponding orbital interaction energy given by... 

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