HMO method

The PEOE method in conjunction with a modified Hiickel Molecular Orbital (HMO) method allows charge calculation in conjugated r-systems. 

HMO method. This is because electron repulsion is taken into account in the SCF calculation whereas it is not taken into account in the Huckel calculation. 

Fig. 1. Trends in effects of 4- and 5-substituenls (expressed as an a variation of R) on the proiomeric equilibrium calculated using the HMO method. When curves do not cross no inversion of protomeric equilibrium is expected to be induced by electronic substituent effects, 4-R-(----) 5-R-(-----). F,E formation energy (see Table 1).

As part of the same HMO method but with various approximations, appeared the calculations of Zahradnik and Koutecki (117). Vincent and Metzger (118), Vitry-Raymond and Metzger (119), Bonnier and Gelus (120), and Bonnier et al. (121). In 1966, Vincent et al. applied to thiazole the iterative methods restricted to the tt system in the following approximations w" (122), w (123). and P.P.P. (124, 123), This last method was later employed with different approximations and for various purposes by Chowdhury and Basu (125), J. Devanneaux and Labarre (126), Yoshida and Kobayashi (127). Witanowskiet et al. (128). and E. Corradi et al. (129). 

Until the end of the forties, when the HMO method was first applied to thiazole, most of the experimental results concerning its chemical reactivity remained of a qualitative nature. Papers devoted to the subject... 

At elevated temperatures (250-400°C) bromine reacts with thiazole in the vapor phase on pumice to afford 2-bromothiazole when equimolecu-lar quantities of reactants are mixed, and a low yield of a dibromothiazole (the 2,5-isomer) when 2 moles of bromine are used (388-390). This preferential orientation to the 2-position has been interpreted as an indication of the free-radical nature of the reaction (343), a conclusion that is in agreement with the free-valence distribution calculated in the early application of the HMO method to thiazole (Scheme 67) (6,117). 

Fig, H8. (a) Partial rale factors of free radical phenylation, relative to benzene (397). (b) Free valence calculated by HMO method (117). (c) Radical localization energy (in units) calculated by HMO method (117). 

Some results obtained by the HMO method (one of the more useful for reactivities comparisons) are summarized in Tables III-17 and III-18. 

Simple Hiickel calculations on benzene, in contrast, place all the n electrons in bonding MOs. The 7t-electron energy of benzene is calculated by summing the energies of the six 71 electrons, which is 6a -F 8/S, lower by 2/S than the value of 6a -F 6/S for three isolated double bonds. Thus, the HMO method predicts a special stabilization for benzene. 

In general conclusion, the HMO and SCF methods both appear able to make reasonably accurate predictions about the stabilization in conjugated moleeules. The stabilization is general for benzenoid compounds but quite restricted in nonbenzenoid systems. Because the HMO method of estimating stabiUty is based on the ideas of HMO theory, its general success vindicates the ability of this very simplified MO approach to provide insight into the structural nature of the aimulenes and other conjugated polyenes. More sophisticated MO methods, of course, are now accessible and should be applied for more detailed analysis of the structures of these molecules. 

Two independent molecular orbital calculations (HMO method) of delocalization energies for isoindole and isoindolenine tautomers agree that the isoindole form should possess the more resonance stabilization. The actual difference calculated for isoindole-isoindolenine is about 8 kcal/mole, but increases in favor of the isoindole with phenyl substitution at position 1 (Table VI).Since isoindole and isoindolenine tautomers have roughly comparable thermodynamic stabilities, the tautomeric proce.ss is readily obser-... 

The most important approximations of the HMO method are, the consideration of only the it-electrons, the neglect of the interaction between them and the neglect of all atom-atom-interactions, if the atoms are not neighbouring. Contrary to the other methods, the molecular geometry does not play a role in the HMO method because only the topologic connection of the atoms in the molecule is considered. In spite of these drastic approximations, the HMO method proved its worth as the first semiempirical procedure with a wide field of applications as well as in the theoretical interpretation of many chemical phenomenons. The method was broadly used in the field of cationic polymerizations in the 60-70 years too (see 2)). 

This shows that despite the extreme simplicity of the HMO method, it is thoroughly suited to providing first impressions concerning the question of cationic polymerizability of vinyl monomers. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

Values of MO energies for many aromatic systems, calculated by the HMO method, are given in Coulson, C.A. Streitwieser Jr., A., Ref. 26. Values calculated by a variation of the SCF method are given by Dewar, M.J.S. Trinajstic, N. Collect. Czech. Chem. Commun., 1970, 35, 3136, 3484. 

These methods can give us useful information on radicals in a manner similar to that for closed-shell systems, provided the exploitation is correct. Of course, in expressions for total energy, bond orders, etc., a singly occupied orbital must be taken into account. One should be aware of areas where the simple methods give qualitatively incorrect pictures. The HMO method, for example, cannot estimate negative spin densities or disproportionation equilibria. On the other hand, esr spectra of thousands of radicals and radical ions have been interpreted successfully with HMO. On the basis of HMO orbital energies and MO symmetry... 

In the following, the MO applications will be demonstrated with two selected equilibrium reactions, most important in radical chemistry disproportionation and dimerization. The examples presented will concern MO approaches of different levels of sophistication ab initio calculations with the evaluation of partition functions, semiempirical treatments, and simple procedures employing the HMO method or perturbation theory. 

Hence, the HMO method is inherently incapable of giving any picture for disproportionation equilibria, the reason being the neglect of electronic repulsion. In the SCF treatment, it is convenient to assume that all three systems in the redox equilibrium are built up from the same MO s, the only difference being the number of n electrons. Adopting this convention and denoting the oxidized form, radical, and reduced form as Ox, Sem (semiquinone), and Red, we can write... 

The PPP-MO method is suitable for the treatment of large molecules, does not present major computing demands and programs are now routinely used as a tool to calculate the colour properties of dyes. Unlike the HMO method, it handles heteroatomic species well. The method has been remarkably successful in calculating /lmax values for a wide range of dyes from virtually all of the chemical classes. For example, the method provides a reasonably accurate account of substituent effects in the range of aminoazobenzene dyes, including compounds 15a-f and 16a-f which have been discussed in terms of the valence-bond approach in the previous section of this chapter. 

Generated from diacetyl peroxide, methyl radicals attack 2-methylfuran at position 5 preferentially if both 2- and 5-positions are occupied as in 2,5-dimethylfuran there is still little or no attack at the 3(4)-position. If there is a choice of 2(5)-positions, as in 3-methylfuran, then that adjacent to the methyl substituent is selected.249 These orientation rules are very like those for electrophilic substitution, but are predicted for radical attack by calculations of superdelocalizability (Sr) by the simple HMO method. Radical bromination by IV-bromsuccinimide follows theory less closely, presumably because it does not occur through a pure radical-chain mechanism.249... 

To compensate for the drastic assumptions an effective Hamiltonian for the system is defined in such a way that it takes into account some of the factors ignored by the model and also factors only known experimentally. The HMO method is therefore referred to as semi-empirical. As an example, the Pauli principle is recognized by assigning no more than two electrons to a molecular orbital. 

The HMO method is demonstated well by a simple example, such as planar cis-butadiene ... 

Pople (1953, 1955). In these calculations the HMO method forms the first part of the procedure (cf. Daudel et al., 1959 Streitwieser, 1961). 

In contrast to the HMO method, the repulsion forces of the electrons are taken into account when carrying out the SCF method, so that it may be expected that the results of these calculations will give better results for the positive aromatic ions than do the HMO calculations. If the pif -values are plotted against the localization energies obtained by this method, one obtains excellent conformity with the requisite linearity, as shown in Fig. 27. The figures for peri-condensed aromatic... 

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