Chemical reactivity LUMO-HOMO interaction

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. 

According to the frontier molecular orbital theory (FMO) of chemical reactivity, the formation of a transition state is due to an interaction between the frontier orbitals, such as HOMO and LUMO of reacting species. In general, the important frontier orbitals for a nucleophile reacting with an electrophile are HOMO (nucleophile) and LUMO (electrophile). 

The existence of a charge density presupposes a concomitant set of MOs and Sect 2.3 describes how chemical reactivity can be based on the notion of Frontier Molecular Orbital (FMO) control i.e. the most important orbital interactions are between the HOMO on one species and the LUMO on the other or vice versa. FMO control, together with electrostatic charge control, provides a powerful qualitative basis for interpreting reactivity. The relative energies and compositions of MOs are vital and many computer programs now provide 3-dimensional representations of MOs to facilitate analysis. 

Hudson and Klopman proposed an equation to describe the effect of orbital perturbation of two molecules on chemical reactivity. Their hypothesis is that the initial perturbation determines the course of a reaction or an interaction. They applied quantum-mechanical method to treat the encounter of two interacting systems as reactivity. Their equation for interaction energy can be simplified by including only two terms [10.2.2] the Coulombic interaction and the frontier orbital interaction between HOMO and LUMO. 

The HOMO-LUMO energy gap of a material is one of the properties that will influence its chemical reactivity. Data from NMR and QENS measurements of the ring rotation dynamics of ferrocene will reflect only effects of any interaction of the ferrocene molecule with the zeolite cage up to the HOMO level of the ferrocene molecule. This is because the LUMO is empty of electrons and any interaction of this level with the zeolite cage orbitals, to a first approximation, will have no effect on the QENS measured dynamic parameters, unless electron density flows into this orbital from the zeolite host. Such a transfer of a small amount of electron density will explain the slightly higher activation energy measured by QENS for ferrocene when encapsulated in zeolite. However, the jlSR measurements are made of a molecule of ferrocene with an additional electron introduced into the LUMO. Thus any interaction of the LUMO with the... 

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