NONPLANAR SYSTEMS

FREQUENTLY one is interested in nonplanar unsaturated systems such that the orbitals are not nicely parallel to one another. No progress is possible without some way cf estimating the resonance integrals. The usual way of doing this is to calculate the overlap integral S between the orbitals cf interest and use it to estimate the resonance integral 3 by the relation 

The procedure is quite servieeable but suffers somewhat from the aesthetic dissatisfaction of assuming S— 0 to calculate P and then turning around and taking Sjj = 0 to get the energy levels. This dissatisfaction, of course, can be allayed by using Sy 0, but the assumption of =0 is no worse here than in the other calculations we have discussed. Our problem is reduced to determination cf S-j (orS). 

The customary procedure for estimating for p orbitals that are not parallel to one another is probably best 

Calculate the energy levels and DE, of butadiene in a configuration at the 2,3 bond such that the planes of the double bonds lie at 60 to one another. 

Values of S for 2 orbitals as a function of r and Z (the effective nuclear charge) have been tabulated by Kopineck. A selection of these are given in Table 7—1. The effective nuclear charge for carbon 2 orbitals is usually taken as 3.09, and to make the data of Table 7—1 more useful for calculations involving carbon—carbon bonds, the values of are listed which 

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RDF descriptors provide further valuable information, such as about bond distances, ring types, planar and nonplanar systems, and atom types. This is a valuable consideration for computer-assisted descriptor elucidation. 

Moreover, the RDF vectorial descriptor is interpretable by using simple rules and, thus, it provides a possibility of —> reversible decoding. Besides information about distribution of interatomic distances in the entire molecule, the RDF vector provides further valuable information for example, about bond distances, ring types, planar and nonplanar systems, and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

A generalization of the Hiickel method to nonplanar systems comprised of carbon and heteroatoms is the Extended Hiickel Theory (EHT) [27 30]. It takes explicitly into account all valence electrons, i.e., Is for H and 2s,2p for C, N, O, and F. Similar to the HMO method, the Fock matrix in EHT FEHT does not contain two-electron integrals. The diagonal elements F T are obtained from experimental ionization potentials (IPs) where the Koopmans theorem [31] has been used. 

The first application of quantitative qnantnm theory to chemical species significantly more complex than the hydrogen atom was the work of HiickeP on unsaturated organic componnds, in 1930-1937 [19], This approach, in its simplest form, focuses on the p electrons of double bonds, aromatic rings and heteroatoms. Althongh Hiickel did not initially explicitly consider orbital hybridization (the concept is nsnally credited to Panling, 1931 [20]), the method as it became widely applied [21] confines itself to planar arrays of -hybridized atoms, nsnally carbon atoms, and evaluates the consequences of the interactions among the p electrons (Fig. 4.4). Actually, the simple Hiickel method has been occasionally applied to nonplanar systems [22]. Because of the importance of the concept of hybridization in the simple Hiickel method a brief discussion of this concept is warranted. 

It is interesting to point out that the lowest proton affinity in polyfluorinated naphthalenes is found for ipso protonation (viz. systems 33, 35 and 36). It is a consequence of the out-of-plane shift of fluorine and the accompanying ring puckering. However, this is at the same time a manifestation of the rr-electron fluoro effect put forward by Liebman et al. [45]. It is very well known that multiply fluorinated compounds possess considerably stabilized a-MOs if the systems are planar, the 7r-manifold being almost unaffected [46]. However, in nonplanar systems all MOs at the carbon skeleton are significantly stabilized [45,46] which is exactly the ceise for the ipso protonation. Now, it can be easily shown... 

The inversion potential function is applied to aU atoms i connected to exactly three other atoms, j, k and /. For nonplanar systems it is given by ... 

Nonplanar systems require, of course, an all-valence description, and here explicit accounting for spin polarization is needed. For a long time, the modeling of ESR spectra of large organic molecules was the exclusive domain of semiempirical UHF methods such as Pople s INDO ° or Nelsen s modified AMI method.Calculations of Ps(X) by ab initio methods used to be restricted to very small radicals. ° As with most aspects of computational chemistry, however, this situation has changed dramatically in recent years. 

The special stability and reactivity associated with cyclic delocalization is not unique to benzene and polycyclic benzenoids. Thus, we shall see that other cyclic conjugated polyenes can be aromatic, but only if they contain (An + 2) tt electrons (n = 0, 1, 2, 3,. . . ). In contrast, An tt circuits may be destabilized by conjugation, or are antiaromatic. This pattern is known as Hiickel s rule. Nonplanar systems in which cyclic overlap is disrupted sufficiently to impart alkene-like properties are classified as nonaromatic. Let us look at some members of this series, starting with 1,3-cyclobutadiene. 

The discovery of a novel form of elemental carbon - the fullerenes - in the mid-1980s initiated unprecedented research activity in the field of physics, chemistry, and material science related to these carbon cages [1]. While expectations for the immediate widespread applications of fullerenes in technology have yet to be fully realized, progress in the basic understanding of carbon-rich systems, insight into the nature of the aromaticity of nonplanar systems, and the development of novel synthetic protocols are undisputed results of this research. 

A second weakness relates to errors resulting from assumptions and approximations made in the n system calculations. Strictly speaking, the PPP calculation applies only to planar n systems, where all the p orbitals are perpendicular to the plane determined by the atoms In the conjugated system thus the a-n separation assumption is valid. For nonplanar systems, this assumption, however, may still be made in the MM scheme. Its use Is justified by establishing the n bond order dependent parameters using the wavefunctions from the planarized molecule (the procedure will be described later.) In addition to the o-n separation assumption, it is assumed that the a and rr orbitals do not undergo rehybridization when bonds are distorted from planarity, so all n orbitals are assumed to be pure p, and overlap integrals and ionization potentials used in the calculations are those of p orbitals. 

To extend the notions of r-electron delocalization to nonplanar systems, concepts of the 71 orbital and 0—71 separability had to be defined for the three-dimensional case. Such a scheme, the so-called r-orbital axis vector (POAV), was introduced by Haddon. " The POAV analysis extends 0—71 separability into three dimensions with the use of the... 

A calculation using the semiempirical SIND01 method yields ring current indices of 1.14 for C-N3H3 and 1.01 for c-NaHa" which indicate the antiaromatic character of these nonplanar systems. The nonplanar c-NaHa" was found to be unstable [39]. The stabilization of C-N3H3 caused by arranging the H substituents out of the N3 plane was used to qualify the nonaromatic character of the molecule [40]. 

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