Hiickel calculations heteroatoms

Method Donor substituents usually contain heteroatoms whose lone pairs can be modeled in Hiickel calculations by doubly occupied orbitals. To a first approximation, acceptor substituents (polar conjugating groups such as C=0, C=N, NOz) can be represented by a low-lying vacant orbital (jtco for C=0,7tCN for C=N, etc.). In cases where a more realistic model is required, the occupied (nco, 7tCN, etc.) orbitals are added to the calculation. 

There is no set of fundamentally sound values for a and ft to use in Hiickel calculations with heteroatoms. Everything is relative and approximate. The values for energies and coefficients that come from simple calculations on molecules with heteroatoms must be taken only as a guide and not as gospel. In simple Hiickel theory, the value of a to use in a calculation is adjusted for the element in question X from the reference value for carbon a0 by Equation 1.15. Likewise, the ft value for the C=C bond in ethylene ft0 is adjusted for C=X by Equation 1.16. 

Table 1.2 Parameters for simple Hiickel calculations for n bonds with heteroatoms...

Hiickel calculations of the electron affinities of these substituted compounds have been carried out. The heteroatom inductive and resonance parameters, ht and ku have been established for the previously mentioned substituents, and were determined by a procedure different from normal. The Hiickel calculations were made on the difference in electron affinity from the parent compound, and the parameters were adjusted to agree with the experimental change in electron affinity. In general, Hiickel calculations have severe limitations however, when the calculations are made only on the AEA, the inaccuracy of the Hiickel estimate of the aromatic framework is minimized. As a result good agreement was obtained between the Hiickel estimates and the experimental A EA. 

The electronic structures of furan, thiophene, and selenophene, their protonated complexes, and their anions have been calculated by the extended Hiickel method.6 The results of these calculations have been used to determine the influence of the heteroatom on the degree of aromaticity and electron density. 

The most extensive correlation of ESR results for trimethylsilyl-substituted aromatic radical anions with Hiickel MO calculations to date is the work of Sipe and West (118, 119). The optimum heteroatom parameters for both the simple Hiickel treatment and the Hiickel-McLachlan treatment, using a Qm = 28 G, for Me3Si were as follows Hiickel, hsi = -2.00, kcS1 = 0.70 Hiickel-McLachlan, hsi = -1.80, kcsi = 0.70, X = 0.30 The values for Me3Ge were as follows Hiickel, hoe = -1.45, kCGe = 0.40 Hiickel-Me Lachlan, = -1.40, kCGe = 0.40 X =... 

The first calculations of the frontier orbitals for acrolein gave the HOMO coefficients on the C=C double bond of acrolein, with the a carbon having the larger coefficient. This failed to explain the regiochemistry, but only because the simple Hiickel theory that was used is notoriously weak in dealing with electron distribution in heteroatom-containing systems. Later calculations gave a better set of coefficients, as shown in Fig. 6.29. 

To synthesize a new electronic system, tri-heteroatom-substituted cyclopropenium, we thought it useful to examine beforehand the stability of the proposed trisubstituted cyclopropenium system by quantum mechanical methods (or, in other ways). A simple Hiickel molecular orbital calculation for the tri-heteroatom-substituted cyclopropenimn cation 3) gave the results shown in Table 1, where qc and -pc-c denote the n electron density on the ring carbon atom and the n bond order between ring carbon atoms, respectively. Ai it (additional resonance energy) as the measure of stability of 3) is a value obtained as a resonance energy difference between 3 a) and 3 b). 

Huckel theory was extended to cover various other systems, including those with heteroatoms, but it was not particularly successful and has largely been superseded by other semi-empirical methods. Nevertheless, for appropriate problems Huckel theory can be very useful. One example is the calculations of P W Fowler and colleagues, who studied the relationship between geometry and electronic structure for a range of buckminster-fullerenes (the parent molecule of which, C50, was discovered in 1985) [Fowler 1993] The fullerenes (or buckyballs ) are excellent candidates for Hiickel theory as they are composed of carbon and have extensive tt systems three examples are shown in Figure 2.22. 

While Hiickel s 4n + 2 rule applies only to monocyclic systems, HMO theory is applicable to many other systems. HMO calculations of fiised-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the c and n systems of electrons, HMO theory is restricted to planar molecules. 

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