Simple Hiickel theory

In analogy to extended Hiickel theory, there are also charge iterative methods for simple Hiickel theory. The equivalent of eq. (3.90) is 

The Hiickel method is essentially only used for educational purposes or for very qualitative orbital ronsirterntions It has the ability to produce qualitatively correct MOs, involving a computational effort which is within reach of doing by hand. 

The neglect of all three- and four-centre two-electron integrals reduces the construction of the Fock matrix from a formal order of M to M. However, the time required for 

The parameterization of MNDO/AM1/PM3 is performed by adjusting the constants involved in the different methods so that the results of HF calculations fit experimental 

Semi-empirical methods are zero-dimensional, just as force field methods are. There is no way of assessing the reliability of a given result within the method. This is due to the selection of a fixed (minimum) basis set. The only way of judging results is by comparing the ficenraey of other calculations on similar systems with experimental data. 

Atoms are assigned types , much as in force field methods, i.e. the parameters depend on the nuclear charge and the bonding situation. The a a and /3ab parameters for atom types A and B are related to the corresponding parameters for sp -hybridized carbon by means of dimensionless constants /ia and /cab- 

The carbon parameters ac and /3cc are normally just denoted a and (3, and are rarely assigned numerical values. Simple Hiickel theory thus only considers the connectivity of the TT-atoms, there is no information about the molecular geometry entering the calculation (e.g. whether some bonds are shorter or longer than others, or differences in bond angles). 

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In terms of simple Hiickel theory the change from polyenic to aromatic the system experiences on passing from (1) and (2) to (3) was attributed primarily to the lower LVMO energy of the latter (B-73MI52000). A more detailed Hiickel calculation (72T3657) utilizing properly selected models in conjunction with thermochemical data also correctly accounts for the differences in tt-electron makeup between 1/Z-azonine (3a) and oxonin (1), which... 

STOs have a number of features that make them attractive. The orbital has the correct exponential decay with increasing r, the angular component is hydrogenic, and the Is orbital has, as it should, a cusp at the nucleus (i.e., it is not smooth). More importantly, from a practical point of view, overlap integrals between two STOs as a function of interatomic distance are readily computed (Mulliken Rieke and Orloff 1949 Bishop 1966). Thus, in contrast to simple Hiickel theory, overlap matrix elements in EHT are not assumed to be equal to the Kronecker delta, but are directly computed in every instance. 

A recent Hflckel calculation based on the proper choice of models correctly accounts for the observed differences in w-electronic makeup between lff-azonine (26a) and oxonin (24a) which were calculated to possess resonance energies of 0.139 and 0.0010, respectively [B. A. Hess, L- J. Schaad, and C. W. Holyoke, Tetrahedron 28, 3657 (1972)]. In terms of simple Hiickel theory the differences between 26a and 24a were attributed chiefly to the lower LVMO energy of the latter (A. G. Anastassiou, in Topics in Nonbenzenoid Aromatic Chemistry (T. Nozoe, R. Breslow, K. Hafner, S. Ito, and I. Murata, eds.), Vol. I, pp. 1-27. Hirokawa Publ., Tokyo, 1973). 

It has recently become clear113 114 that simple Hiickel theory, as well as some more elaborate techniques such as MINDO/2, are unreliable for use in conjunction with frontier orbital theory. For example, Hiickel molecular orbital coefficients suggest97 that acrolein (30) will dimerize to (31), but in fact the product is (32). SCF orbitals... 

FIGURE 5.3 The VB structures for singlet and triplet states of C3H3 +, along with the graphical representation of their interaction matrix elements. The spread of the states is easily predicted from the circle mnemonic used in simple Hiickel theory. The expressions for the VB structures (dropping normalization) are deduced from each other by circular permutations 1 , = ab — ab, 1 <1>2 = bc — bc, 3 = ca — cI = ab, 34>2 = bc, 33 = ca. ... 

At the extreme of an infinite polyene, however, simple Hiickel theory reduces the HOMO—LUMO gap to zero, since the secants in diagrams like Fig. 1.33, would become infinitely small. Such a polyene would have equal bond lengths between each pair of carbon atoms, the gap between the HOMO and the LUMO would be zero. 

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. 

In order to calculate the energy, the simple Hiickel theory for tt systems is used. That is, only the tt interactions between adjacent p orbitals are considered the overlap integrals are neglected. Equation 5.21 then becomes equal to ... 

On the basis of the simple Hiickel theory, the two NMBOs of both 33 and 34 will be degenerate. Hund s rule therefore dictates a triplet state. However, Borden and Davidson argued that since the electrons in the two NBMOs of 33 are specially isolated and have reduced the electrostatic repulsion, the singlet state will not violate the Pauli s exclusion principle and will be energy competitive with the triplet... 

The only closed-shell fullerenes predicted by simple Hiickel theory fall into two types the leapfrog fullerenes Ceo+en (n 1), and the cylinders 70+30 and 34+36 (m > 0) formed by stretching Dsh-Cio and Da-C 4 along then-respective 5 and 5 axes. The simplicity of the theory unfortunately prevents these rules having any general utility. Neither of the two IPR-isomers of 75 is predicted to be stable but Z>2- 76 has been isolated, whereas the expected fiillerene Ded-Cji has not, although its apparent low stability may be... 

An interesting correlation is found between the kinetic stabilities of the fullerenes ] to C70. as determined by simple Hiickel theory HOMO-LUMO energy separations, and the intensities of photoionisation signals from carbon clusters produced by laser vaporisation of graphite. This correlation provides further circumstantial evidence that the observed C34 to C70 clusters are indeed fullerenes, closed carbon cages containing only five- and six-membered rings. 

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