Bonding Htickel calculations

For C70 and higher fullerenes addition also occurs only at the [6,6] fusions. However, these sites are no longer all equivalent, and a variety of regioisomers can result. For C70, of the four possible products, as illustrated in Fig. 10, addition occurs exclusively at the polar fusion, A (,14). This is the sterically most accessible site, and energy calculations have shown there is the greatest release of steric strain on com-plexation (91). The equatorial [6,6] fusion, D, has lowest bond order, and correspondingly, no complexations to it have been observed. For C84, complexation with Vaska s compound occurs at the fusion with the highest bond order, as shown by Htickel calculations (28). 

Table 1.2 Parameters for simple Htickel calculations for bonds with heteroatoms...

Extended Htickel calculations have been used to analyze the electronic structure of platinum complexes and also to rationalize their reactivity with various nucleophiles. Their inability to form four coordinate species of the type [Pt(S2CNR2)(ri -S2CNR2)2] has been ascribed to the lower charge on platinum (when compared with xanthate complexes), strong platinum-sulfur bonds and a repulsive interaction between the platinum 2>d electrons and the incoming ligand (1601). 

The next example for this rule may be the heterolytic addition of chlorine to the C=C bond. Fig. 4.3b indicates the partial valence-inactive population 60> of the 2pz AO of the /9-carbon in LU, calculated by the extended Htickel method. It is seen that this quantity, (c )2, largely increases according to the approach of the chlorine cation to the carbon atom at which the addition is to take place, so that the reactivity of the /9-position towards the second chlorine atom (anionic species) grows. Also Fig. 4.3a shows the decrease of the LU energy in the direction of the reaction path which has already been mentioned above. 

Htickel molecular orbital calculations have been performed for anthranil the n electron densities and mobile bond orders of Del Re80 and Berthier and Del Re81 are given in Fig. 2. 

In this Appendix, Htickel theory calculations are used to demonstrate that the polynomials of Appendix 1 can be applied as basis functions for the irreducible subspaces of a Hamiltonian invariant under icosahedral point symmetry, while extended Htickel theory calculations on cubium cages of cubic point symmetry are used to demonstrate the same result for the kubic harmonics, since single bond-length regular orbits are not possible in all cases. 

Extended Htickel theory calculations are the maximum level of approximation that can be employed for the calculation of the eigenvalue spectra for the regular orbit cages of the cubic point groups, since different bond lengths have to be accommodated on the His orbital... 

The Htickel method predicts that in the case of a long polyene chain the longitudinal polarizability of n electrons varies as the cube of the molecular length, while the o polarizability should increase only linearly 18>. Refined molecular orbital calculations (taking into account bond alternation etc.) do not exhibit this abnormal asymptotic behaviour. 

Another fairly new method, using the electrostatic molecular potential, will not be discussed here since it is the subject of another contribution to this volume 50>. I will now consider methods that have had the widest application in the theoretical study of chemical reactivity, in order of increasing complexity a) molecular mechanics b) extended Htickel method c), d) empirical self-consistent field methods such as CNDO and MINDO e) the simplest ab initio approach f) the different S.C.F. methods, possibly including configuration interaction g) valence bond methods, and h) the dynamical approach, including the calculation of trajectories 61>. 

To produce more reliable predictions of aromaticity, Hess and Schaad (following a suggestion of Dewar) calculated delocalization (resonance) energies of cyclic hydrocarbons by comparing the compounds Htickel-theory with a value calculated for a hypothetical acyclic conjugated polyene with the same number and kinds of bonds as in a localized structure of the cyclic hydrocarbon. [B. A. Hess and L. J. Schaad, J. Am. Chem. Soc., 93, 305, 2413 (1971) 94, 3068 (1972) 95, 3907 (1973) B. A. Hess, L. J. Schaad, and C. W. Holyoke, Tetrahedron, 28, 3657, 5299 (1972) Schaad and Hess,... 

The carbon parameters cfc and Pec are normally just denoted aand P, and are rarely assigned numerical values. Simple Htickel theory thus only considers the connectivity of the ji-atoms there is no information about the molecular geometry entering the calculation (e.g. whether some bonds are shorter or longer than others, or differences in bond angles). 

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