Molecular orbital theory Hiickel model

The VSEPR model works at its best in rationalizing ground state stereochemistry but does not attempt to indicate a more precise electron distribution. The molecular orbital theory based on 3s and 3p orbitals only is also compatible with a relative weakening of the axial bonds. Use of a simple Hiickel MO model, which considers only CT orbitals in the valence shell and totally neglects explicit electron repulsions can be invoked to interpret the same experimental results. It was demonstrated that the electron-rich three-center bonding model could explain the trends observed in five-coordinate speciesVarious MO models of electronic structure have been proposed to predict the shapes and other properties of non-transition element... 

So here, the term theory will be used in a way that embraces the typical named theories of chemistry such things as molecular orbital theory, valence shell electron pair repulsion theory, transition state theory of reactions, and Debye Hiickel theory of electrolyte solutions. No decisive distinction will be made between theory, model, and other similar terms. But there is one distinction that we do make. The term theory is considered in an epistemological sense—as an expression of oin best knowledge and belief about the way chemical systems work. 

The bent bond picture, later restated in terms of localized molecular orbitals, extends the model presented by Pauling and Slater for ethylene to a stem with three centers. Walsh s model parallels that of Mulliken for the a, w model of the double bond widely used in Hiickel theory. Since the canonical orbitals are good models for the interpretation of photoelectron spectra (see Introduction) we will discuss the Walsh model briefly. 

A chemist learns to associate energetic quantities to orbitals at an early stage in his education. Aufbau principles for atomic structure are encountered typically in the first few weeks of an introductory course in chemistry. Hiickel molecular orbital theory enables organic chemists to discern patterns in structure, spectra and reactivity without the need for complicated calculations. Model one-electron systems such as the particle in a box and are treated at length in typical physical chemistry courses. 

The Kronig-Penney model, although rather crude, has been used extensively to generate a substantial amount of useful solid-state theory [73]. Simple free-electron models have likewise been used to provide logical descriptions of a variety of molecular systems, by a method known in modified form as the Hiickel Molecular Orbital (HMO) procedure [74]. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

Orbital interaction theory forms a comprehensive model for examining the structures and kinetic and thermodynamic stabilities of molecules. It is not intended to be, nor can it be, a quantitative model. However, it can function effectively in aiding understanding of the fundamental processes in chemistry, and it can be applied in most instances without the use of a computer. The variation known as perturbative molecular orbital (PMO) theory was originally developed from the point of view of weak interactions [4, 5]. However, the interaction of orbitals is more transparently developed, and the relationship to quantitative MO theories is more easily seen by straightforward solution of the Hiickel (independent electron) equations. From this point of view, the theoretical foundations lie in Hartree-Fock theory, described verbally and pictorially in Chapter 2 [57] and more rigorously in Appendix A. 

Hiickel molecular orbitals in porphin were investigated by Longuet-Higgins et al. (68), and the extended Hiickel molecular orbital model was applied to metalloporphyrins in attempts by Pullman et al. (93), Ohno et al. (86), and Zerner et al. (120) to explain various experimental observations. Let us briefly consider a description of cyanoferriporphin. According to the Hiickel theory all but the -orbitals of each carbon and nitrogen atom of porphin are used up to form the relatively inert skeleton of single bonds. To describe the -bonding twenty-four molecular orbitals of porphin can then be formed as linear combinations of... 

---