Resonance integral parameters

Additional problems in theoretical calculations are (1) selection of the coulomb and resonance integral parameters (2) whether an auxiliary inductive parameter be used for the a-carbons (3) whether d orbitals, etc., be taken into account for S, Se, and Te and (4) what type of calculations to use. 

Empirical resonance-integral parameters have been derived for C—S TT-bonds in tetracyano-l,4-dithiin (47) and thianthrene. Dithiin (47) undergoes ready aminolysis with secondary amines giving salts (48) which. 

The Hrst low-level theory is an NDDO-SRP calculation in which the functional form of the PM3 version of NDDO theory was generalized to allow a larger number of resonance integral parameters. In the original AMI and PM3 parameterizations, there are five resonance parameters for a system composed of H, C, and N, namely Phs. Pcs Pcp. Pns> and PNp. Resonance parameters Px/X7 - ° interaction of an -type orbital on atom X with an / -type orbital on atom X are then approximated by... 

The developers of ZINDO found that the parameters required to reproduce orbital energy orderings and UV spectra are different from those required to reproduce accurate structures by geometry optimization. They introduced anew pair of parameters, called the overlap weighting factors, to account for this. These parameters are provided in HyperChem in the Semi-empirical Options dialog box. Their effect is to modify the resonance integrals for the off-diagonal elements of the Fock matrix. 

The resonance integral of the 7r-bond between the heteroatom and carbon is another possible parameter in the treatment of heteroatomic molecules. However, for nitrogen compounds more detailed calculations have suggested that this resonance integral is similar to that for a C—C bond and moreover the relative values of the reactivity Indices at different positions are not very sensitive to change in this parameter. 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

The parameter ais the ionization energy of an electron from the p,th atomic orbital located on the Ath atom and ft is the so-called resonance integral (represented here by a simple exponential). The QB and P terms of represent corrections to the effective ionization potential due to the residual charges on the different atoms. The charges are determined by... 

It is possible that the explanation of these discrepancies is to be found in the fact that the resonance integral, may vary with the row and group of the periodic table. Such a variation must almost certainly exist, but it can be taken into account only with difficulty. Furthermore, the introduction of the large number of additional arbitrary parameters would deprive the whole procedure of much of its significance. A second possible explanation is that, with phenol for ex-... 

Here Zg is the number of tt electrons provided by atom is essentially an ionization potential for an electron extracted from in the presence of the part of the framework associated with atom r alone (a somewhat hypothetical quantity), is a framework resonance integral, and is the coulomb interaction between electrons in orbitals < >, and <(>,. The essential parameters, in the semi-empirical form of the theory, are cug, and and from their definition these quantities are expected to be characteristic of atom r or bond r—s, not of the particular molecule in which they occur (for a discussion see McWeeny, 1964). In the SCF calculation, solution of (95) leads to MO s from which charges and bond orders are calculated using (97) these are used in setting up a revised Hamiltonian according to (98) and (99) and this is put back into (95) which is solved again to get new MO s, the process being continued until self-consistency is achieved. It is now clear that prediction of the variation of the self-consistent E with respect to the parameters is a matter of considerable difficulty. 

The valence state ionization potential —the resonance integrals and the one-center electron repulsion integrals can be considered as basic parameters of the semiempirical method and can be adjusted to give optimal agreement. The core charges Z, indicate the number of 71 electrons the center M contributes to the n system, and the two-center electron repulsion integrals are obtained from an empirical relationship such as the Mataga-Nishimoto formula ... 

The interaction parameters z, z, and Ji are defined in the usual way, and t) = /S"//8, where /3" is the resonance integral between nearest neighbors in the adsorbed layer. If rj = 1, the eigenvalue condition. Equation (19), is the same as for the one-dimensional model. The only change is that the discrete localized states (CP and 91) of the one-dimensional model now appear as bands of surface states (CP or 91 bands) associated with the adsorbed layer and the crystal surface. At most, two such bands may be formed, and each band contains levels. This is the number of atoms in the adsorbed layer. Depending on the values of the interaction parameters z and z, these bands may or may not overlap the normal band of crystal states. All this was to be expected, and Fig. 2 gives the occurrence of (P and 91 surface bands when = 1. It is when tj 7 1 (and this will be the usual situation) that a new feature arises. In this case, the second term in the second bracket in Equation (19) does not vanish, and the eigenvalue condition is not the same as in the one-dimensional model. In fact we have z - - 2(1 — jj )(cos 02 - - cos 03) in place of z, and this varies between z - - 4(1 — ij ) and z — 4(1 — tj ). We can still use Fig. 2 if we remember that z varies between these two limits. Then if, for example, this variation... 

To summarize, the HSAB principle is a very good first approximation but is usually inadequate for detailed analysis of reaction mechanisms. This is not really surprising. After all, this principle is nothing else than a two parameters relationship each reactant is characterized by its acidic or basic strength and by its hardness (softness). And obviously, we cannot expect to describe the complexity of chemistry with only two parameters. On the other hand, one should not underestimate its utility. Simple Hiickel calculations are also a two parameters treatment where the initial choice of the coulombic and resonance integrals a and )3 is critical. There is no doubt however that, handled with care, these calculations may give valuable insights. The same may be said for the HSAB principle. 

For unsubstituted aromatic hydrocarbons all the carbon atoms are assigned the same Coulomb integral (a°) and all C—C bonds are assigned the same resonance integral 0°). In heteroaromatic molecules the approximate Coulomb integral for heteroatom ax is expressed as in Eq. (1) in terms of a0 and (3° and the electronegativity parameter h. 

Resonance integrals of bonds between atoms X and Y, XY, are expressed as defined in Eq. (2), where kXY depends on the bond length. There has been considerable variation in the values taken for the Coulomb and resonance integrals for heterocyclic molecules. One of the best available set of parameters is still that originally suggested by A. Streitwieser (Molecular orbital theory. J. Wiley Sons, Inc., N.Y.-L., 1961) ... 

The parameters Aab and Bab are estimated by fitting the observed heats of formation of suitable reference compounds. In their most recent (MINDO/2) method, Dewar et al. have expressed the resonance integral in the form... 

Discussions of heteroatoms in the SHM written in the heyday of that method present the heteroatom parameters in a slightly more complicated way, in terms of the coulomb and resonance integrals a and p, rather than as simple numbers. 

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