Hiickel MO method

The Hiickel MO method is based on the LCAO method for diatomic molecules discussed in Section 7.2.1. Extension of the LCAO method to polyatomic molecules gives a secular determinant of the general type... 

To examine the effect of covalency on the QS, the values of the QS of some compounds have been calculated with the aid of the Extended Hiickel MO method (i 82, 61). In these calculations the values for the empirical parameters used were obtained from comparison with EPR experiments (see EPR studies). This method is suitable only for molecules with low symmetry, because effectsoof spin-orbit coupling and thermal mixing have been neglected. 

These indices were initially used in the frame of Hiickel MO method. But the theory has been shown to be valid also in more elaborate methods... 

Earlier definition of resonance energies comes down to an evaluation of the QMRE within the framework of the Hiickel MO method (HMO) (61MI1 75MI1 86MI1). Hiickel resonance energy (HRE) is defined as... 

Several approaches have been made to calculate 13C chemical shifts of coumarins by MO methods. Good correlations were found between the 13C chemical shift values of coumarin (also protonated) and the n charge densities calculated by the CNDO/2 method [962], and of coumarins with it charge densities calculated by the Hiickel MO method (which, however, fails for methoxylated coumarins) [965]. Chemical shifts of mono- and dimethoxycoumarins have been correlated with parameters determined by refined INDO MO calculations, in which n bond orders, atom-atom polarizabilities, excitation energies and electron-nucleus distances were taken into consideration [966], In 3-substituted 4-hydroxy and 4-hydroxy-7-methoxycoumarins chemical shifts were found to be related to Swain and Lupton s parameters iF and M [388], according to equation 5.4 (SE = Substitution Effect) ... 

Platinum (n)—Group VII and Hydride Donors. SCF—Xa calculations have been made for the ions [MC14]2 (M = Pd or Pt) (see p. 384).13 In addition the extended Hiickel MO method has been employed to calculate activation energies of the halide-... 

Historically, the first proposal was the single bond-no bond resonance concept,5 later used for calculations by Giacometti and Rigatti93 carried out according to the Hiickel MO method. In this 93 G. Giacometti and G. Rigatti, J. Chem. Phya. 30, 1633 (1959). 

Reactivity indexes and 7r-electron densities of 4-aryl-l,3-dithiolylium ions have also been calculated by the Hiickel MO method (70CPB865, 65ZC23). 

Calculation of electron densities of some 8-azapurines by a Hiickel MO method successfully predicted NMR proton chemical shifts and the reactivity with nucleophiles but failed to predict the experimentally determined ionization constants. Solid-state binding energies of 8-azaguanine and 8-... 

Furthermore, Gunther et al (14) found a result similar to Sojka s (15) when correlating coumarin shifts with n charge densities calculated by the Hiickel MO method (63). This, however, fails for methoxylated coumarins (14) demonstrating that simple charge density - shift relationships are not generally applicable reliably. Ernst (20) reported a linear relationship between fi-methyl substituent effects in unhindered methylated coumarins and the it bond order, P , of the C-a—C-f) bond calculated by the INDO MO method (64) ... 

This will be called the bond order approximation. It might be noted that this approximation is at the heart of the Hiickel MO method. Using this approximation ... 

The chemical shifts of the sp -hybridized carbons for methylbenzenium ions were compared with the jt-electron (q,) and the total (q = q, + q ) electron defkioM calculated by the Htickel LCAO MO and CNDO/2 methods. To judge by the values of root-mean-square deviations (s) and of correlation coefficients (r) the chemical shifts of the sp -hybridized carbons of the ions under consideration correlate better with the Tc-electron deficiency calculated by the simple Hiickel MO method... 

The estimation of the partial positive charge of the Cjq atom obtained from 8(C, ) yields 0.56 units this agrees well with the value 0.52 units predicted by the Hiickel MO method for the o-phenylbenzylic cation. 

The Hiickel MO method assumes that the a and n systems can be treated independently and then considers only the n system. The extended Hiickel theory (EHT), developed by Hoffmann, considers all of the valence electrons in the system, but it does not deal with the core electrons (those in orbitals below the valence shell). ° The EHT wave function is then written as a linear combination of functions describing each type of valence orbital on each atom in the structure. For hydrocarbons, the EHT wave fimctions include the 2s and all three 2p atomic orbitals of carbon as well as the Is orbitals of hydrogen atoms. The overlap integrals (S,y) are computed, whereas they were ignored in HMO theory. The elements of the secular determinant are assigned a value... 

A prototype reaction for preparing benzocyclobutenes is the addition of benzyne to ethylene, and the extended Hiickel MO method has been used to calculate an energy surface for this reaction. The results, whilst not entirely consistent with some experimental evidence, indicate that the reaction is not simple. The preparation of benzocyclobutenyl acetate from benzyne and vinyl acetate is a known reaction but the reduction of this benzylic ester by lithium and ammonia is a newly reported convenient preparation of benzocyclobutene itself. The stereochemistry of the formation of benzocyclobutene by thermolysis of (178) implicates the o-quinodimethane (179) as an intermediate. The stereospecifically labelled ds-compound (178) gave trans-product (180) contaminated by amounts of the ds-compound (181) which varied with experimental conditions. The direct product under the mildest conditions and with low conversion is (180), which presumably isomerizes to (181) under the more... 

In Table 47 we have collected RE and REPE values obtained by the ambitious VB calculations of Wu and Jiang,and those of Alexander and Schmalz, to be compared to the RE values calculated by the simple Hiickel MO method. Both VB calculations used the graphical unitary group technique that have produced highly efficient methods for ab initio calculations, the so-called graphical unitary group approach (GUGA), in which only the non-zero matrix elements are computed.One should recall that the... 

The differences in internal energy between several triarylcarbonium ions and the related triarylchloromethanes have been calculated by Streitwieser (83) by simple Hiickel MO method and have been compared, inappropriately, with values of AFexp. The correlation is qualitatively successful but the calculated increments in bonding energy coefficient differences, AMt, arising from successive introduction of m-phenyl groups are very small and would require that d be approximately 100 kcal./mole to correspond to the observed increments in AFexp. Comparison of increments in AMi with values of the more relevant AFi does not improve the situation ance AFi values are more widely spaced than are AFexp values and would require that j3 be of the order of 200 kcal./mole. In contrast, comparison of AM and AF] for p-phenyl substituted trityl chlorides indicates that is 38 kcal./mole. A more thorough theoretical treatment is apparently needed. 

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