Hiickel-type theories

All carbon-carbon bonds in the skeleton have 50% double bond character. This fact was later confirmed by X-ray diffraction studies. A simple free-electron model calculation shows that there is no energy gap between the valence and conduction bands and that the limit of the first UV-visible transition for an infinite chain is zero. Thus a simple free-electron model correctly reproduces the first UV transition with a metallic extrapolation for the infinite system. Conversely, in the polyene series, CH2=CH-(CH=CH) -CH=CH2, he had to disturb the constant potential using a sinusoidal potential in order to cover the experimental trends. The role of the sinusoidal potential is to take into account the structural bond alternation between bond lengths of single- and double-bond character. When applied to the infinite system, in this type of disturbed free-electron model or Hiickel-type theory, a non-zero energy gap is obtained (about 1.90 eV in Kuhn s calculation), as illustrated in Fig. 36.9. 

The iterative extended Hiickel type of calculation has been widely used, especially by Gray and his co-workers (13) to interpret the visible and ultraviolet spectra of transition metal complexes, but from a quantitative point of view it has not proved to be very reliable. This difficulty arises primarily because the theory is based on a 1-electron Hamiltonian and, therefore, neglects important electron repulsion effects. 

For bonded atoms, the off-diagonal terms (where i j) are taken to depend on the type and length of the bond joining the atoms on which the basis functions Xi and Xj arc centred. The entire integral is written as a constant, j8y, which is not the same as the Pxy in Hiickel -electron theory. The are taken to be parameters, fixed by calibration against experiment. It is usual to set /, to zero when the pair of atoms are not formally bonded. 

However, QMe (or B) may vary with type of radical, especially charge type, and also with the nature of the a-atom. Thus, methyl hyperfine splittings in alternant hydrocarbon anion- and cation-radicals, for which Hiickel MO theory predicts identical spin populations at the methylated positions, typically differ by a factor of at least two.15... 

Tihis study was initiated to determine to what extent empirical molecu-lar orbital (MO) theories of the Hiickel type can provide information on the thermodynamic stability of a hypothetical unknown compound. The test, of course, has to be made on known compounds. Our interests have centered on compounds involving atoms such as N, O, F, and Cl, but compounds with C and H have also been included. The results thus far have been encouraging. 

In semiempirical Hiickel-type model, the energy of one electron in A is taken to be the same as that of two electrons in A and it results in zero energy change for disproportionation reaction of the type (Eq. (26)). However, in other semiempirical models such as PPP theory, which is related to Hubbard model in solid state physics, repulsion between two electrons in A has been approximated as (I—A) and, hence, in these type of models (PPP, CNDO, INDO, and MINDO), hardness may be thought of as electronic repulsion [36,53,54]. 

In this review, the basics of common semiempirical theories, especially models of the ZDO types or extended Hiickel types, have been examined with reasonable completeness. Various parameterization schemes have been examined that are in most common use today. The results that one might expect from these models have been focused on. Some important models, and several come to mind, have been neglected. In general, these methods have had only a limited evaluation in the literature as practical tools, or they are closely related to those described here. Others are theoretically interesting and have great potential, but have as yet not been fully exploited or shown to be of practical utility. 

There are, of course, certain circumstances in which the SCF equations can easily be shown to reduce to Hiickel-type equations. Thus in the standard excited-state equations of Hall for 7r-electron aromatic hydrocarbons, it can be shown that the LCAO coefficients are often precisely the same as in the Hiickel scheme. However, this particular state is not of direct value for our purposes. Further, Pople has shown that if the Pariser-Parr approximation of zero differential overlap is accepted, then, apart from some (usually) small terms in inverse internuclear distances, the total w-electron energy is given by an expression identical in form to that of Hiickel theory. Both writers adopt the approximation of neglecting all overlap integrals. This is particularly serious with overlap integral may be as large as... 

Nucleus-independent chemical shifts, introduced by Schleyer et al. as a measure for aromaticity [20], can also be computed at the GIAO-MNDO level of theory, making this useful tool also available to much larger aromatic structures such as graphenes and fullerenes [21]. The ab initio reference data are generally reproduced well, but four-membered rings are still problematic. The aromatic properties of Hiickel-type hydrocarbons, Mobius aromatics, and three-dimensional cage com-... 

Brief mention may be made of earlier bonding indices (often originating from Hiickel MO theory) whose usefulness can be enhanced in the modem ab initio context by using NAOs or NHOs. These allow a closer connection to be drawn between the qualitative Huckel-type concepts of elementary valence theory and the quantitative results of rigorous quantum chemical methods. 

Rabbit-ears depictions are sometimes argued to be mathematically equivalent to the no forms, but such (Hiickel-type) arguments cannot be justified at any level of theory that is relevant to the contemporary scale of chemical accuracy.]... 

One of molecular- orbital theories early successes came in 1931 when Erich Hiickel discovered an interesting pattern in the tt orbital energy levels of benzene, cyclobutadiene, and cyclooctatetraene. By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar- geometries, Hiickel found that whether a hydrocar bon of this type was aromatic depended on its number of tt electrons. He set forth what we now call Hiickel s rule ... 

The hole correction of the electrostatic energy is a nonlocal mechanism just like the excluded volume effect in the GvdW theory of simple fluids. We shall now consider the charge density around a hard sphere ion in an electrolyte solution still represented in the symmetrical primitive model. In order to account for this fact in the simplest way we shall assume that the charge density p,(r) around an ion of type i maintains its simple exponential form as obtained in the usual Debye-Hiickel theory, i.e.,... 

Type A photorearrangement, 323, 329, 331 Type I cleavage of carbonyls, 135-171 application of extended Hiickel theory to, 179-181... 

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