Extended Hiickel molecular orbital method

The method was first used by Roald Hoffmann, who developed, with R. B. Woodward, the rnles for elucidating reaction mechanisms (the Woodward-Hoffmann rnles). These rnles explain the stereospecifity of electrocyclic reactions under thermal and photochemical conditions. The rules illustrated elegantly and simply the power of molecnlar orbital theory to experimental chemists. 

The Woodward-Hoffmann rules [32,34-37] have been widely used ever since their introdnction, bnt they have not been often explicitly stated, so we felt that, due to their inherent simplicity, elegance, and importance, they deserve better publicity. Below we have reproduced them as published in [29]  

In an open-chain system containing 4n-electrons, the orbital symmetry of the highest occupied molecule orbital is such that a bonding interaction between the termini must involve overlap between orbital envelopes on opposite faces of the system and this can only be achieved in a conrotatory process. 

In open systems containing 4 + 2 electrons, tenninal bonding interaction within ground-state molecules requires overlap of orbital envelopes on the same face of the system, attainable only by disrotatory displacements. 

In a photochemical reaction an electron in the HOMO of the reactant is promoted to an excited state leading to a reversal of terminal symmetry relationships and reversal of stereospecificity. 

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Professors Kenichi Fukui (Kyoto University) and Roald Hoffmann (Cornell University) received the 1981 Nobel Prize in Chemistry for their quantum mechanical studies of chemical reactivity. Their applied theoretical chemistry research is certainly at the core of computational chemistry by today s yardstick. Professor Fukui s name is associated with frontier electrons, which govern the transition states in reactions, while that of Hoffmann is often hyphenated to R. B. Woodward s name in regard to their orbital symmetry rules. In addition, Professor Hoffmann s name is strongly identified with the extended Hiickel molecular orbital method. Not only was he a pioneer in the development of the method, he has continued to use it in almost all of his over 300 papers. 

Early work on the quantum mechanical analysis of chemisorption and chemisorbed states is admirably covered in Clark s monograph. Application of the extended Hiickel molecular orbital method in the hands of A. B. 

In Sect. 5.3 that follows, we report on the electronic structural characteristics of the C-based hexagonite structure from the point of view of the extended Hiickel molecular orbital method (EHMO), which is an approximate solid state electronic structure algorithm based upon the tight binding methodology (Hoffmann 1963 ... 

The band structure of a three-dimensional solid, such as a semiconductor crystal, can be obtained in a similar fashion to that of a polyene. Localized molecular orbitals are constructed based on an appropriate set of valence atomic orbitals, and the effects of delocalization are then incorporated into the molecnlar orbital as the number of repeat units in the crystal lattice is increased to infinity. This process is widely known to the chemical conununity as extended Hiickel theory (see Extended Hiickel Molecular Orbital Theory). It is also called tight binding theory by physicists who apply these methods to calcnlate the band structures of semiconducting and metallic solids. 

Qualitative MO theory (extended Hiickel molecular orbital ((EHMO) method) was employed for a rationalization of the electron density distributed over the three centers S-I-I in diiodine adducts of 4,5-ethylenedithio-l,3-dithiole-2-thione <1999IC4626>. 

Historically, there have been two major efforts in the development of semiempiri-cal calculations under the direction of John Pople (Nobel Laureate 1998) and M.J.S. Dewar. The earliest calculations of this nature are, however, the Hiickel (HMO) and extended Hiickel molecular orbital calculations (EHMO). While not mathematically rigorous, or used extensively at the present time, these calculations can provide considerable insight into the methods and in specific applications can be quite accurate. 

The mathematical formalism employed in the theory of orbital interactions has been elaborated both in general terms [8-12] and at different levels of the MO theory approximation, including the Hiickel [13] and extended Hiickel molecular orbital [14] as well as the SCF MO [15] and configuration interaction [16, 17] methods. In what follows, only the principal general relationships and conclusions will be dealt with. 

The molecular orbital methods which have been employed for such studies include extended Hiickel theory (EHT), CNDO, and ab initio LCAO-SCF. 

Over the past 20 years and, in particular since 1955, many theoretical studies of the electronic structure of pyrrole using the molecular orbital approach with varying degrees of refinement have been reported. The 7r-electronic structure of pyrrole has been extensively discussed in terms of both the simple Hiickel molecular orbital (LCAO) theory37- 41-55-65 and the more sophisticated self-consistent field molecular orbital method (SCFMO method).18- 66-77 Extended... 

The extended Hiickel method (EHM) 74> is the simplest empirical all valence electron molecular-orbital method available at present. 

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