Extended Hiickel MO theory

A theoretical study of the interaction of sulfur atoms with ethylene within the framework of the Extended Hiickel MO theory has been reported by HoflFmann and co-workers (19). Potential surface calculations revealed two minima for the 8( 02) + C2H4 system. The higher corresponds to vinyl mercaptan formation via C-H bond insertion, and the lower, lying about 20 kcal below the former, to the least-motion, symmetry-allowed addition of sulfur across the double bond. The two are viewed as competing concerted processes. Similar calculations for the... 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

These arguments go hand in hand with Extended Hiickel Theory (EHT), both being based on overlap (symmetry) considerations. In fact, an EHT calculation will provide almost exactly the same results as a skilful use of the qualitative MO building scheme we have provided in this section. 

Extended Hiickel theory (EHT) was applied to study the decomposition of the five-membered metallacycle intermediate proposed by Mimoun for the epoxidation by Mo bisperoxo complexes [44, 45]. Another EHT study [40] proposed the coordination of ethene to the metal center of an MoO(02)2 complex as the first step, followed by a slipping motion of ethene toward... 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Hiickel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be intuitive. One such model that continues to see extensive use today is the so-called extended Hiickel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

By far, the theoretical approaches that experimental inorganic chemists are most familiar with and in fact nse to solve questions qnickly and qnalitatively are the simple Huckel method and Hoffinann s extended Hiickel theory. These approaches are nsed in concert with the application of symmetry principles in the bnUding of syimnetry adapted linear combinations (SALCs) or gronp orbitals. The ab initio and other SCF procednres ontlined above prodnce MOs that are treated by gronp theory as well, bnt that type of rigor is not usually necessary to achieve good qnahtative pictures of the character aud relative orderiugs of the molecular orbitals. 

All valence electron (AVE) calculations (simultaneous treatment of tr- and ir-electrons) Three treatments (i) EHT (extended Hiickel theory) (ii) lEHT (iterative extended Huckel theory) (iii) CNDO treatment (an SCF MO type) 68MI40908 68MI40907 69MI40907... 

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>. 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended Hiickel Theory (EHT) or Intermediate Neglect aif Differential Overlap (TNDO) (Sections 3.12 and 3.9). The EHT method has the advantage that it is readfiy parameterized for allEIements, and irxau provide starF orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The EMDO... 

K. G. R. Pachler, Extended Hiickel theory MO calculations of proton-proton coupling constants-II. The effect of substituents on vicinal couplings in monosubstituted ethanes, Tetrahedron, 27 (1971) 187-199. 

Extended Hiickel Theory (EHT) uses the highest degree of approximation of any of the approaches we have already considered. The Hamiltonian operator is the least complex and the basis set of orbitals includes only pure outer atomic orbitals for each atom in the molecule. Many of the interactions that would be considered in semi-empirical MO theory are ignored in EHT. EHT calculations are the least computationally expensive of all, which means that the method is often used as a quick and dirty means of obtaining electronic information about a molecule. EHT is suitable for all elements in the periodic table, so it may be applied to organometallic chemistry. Although molecular orbital energy values and thermodynamic information about a molecule are not accessible from EHT calculations, the method does provide useful information about the shape and contour of molecular orbitals. 

Extended Hiickel Theory (EHT) Poor Determining shapes of MOs Good Low Upto 100 atoms or more... 

The most serious drawback to Stone s elementary TSH theory is that all of the (2 L -I- 1) cluster MO s of a given L value are taken to be degenerate. For a real cluster, with non-spherical symmetry, the orbital degeneracies are generally lower than (2 L + 1). Fowler and Porterfield have circumvented this problem by introducing the Extended Hiickel... 

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