Huckel model, free-electron

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

Little is also known about photoelectron spectra of pteridines. The unsubstituted nucleus and its 4-methyl- and 2,4,6,7-tetramethyl derivative have been recorded and analyzed in terms of both a simple Huckel-model and semiempirical calculations <86CB1275>. The assignment of the n- and n-type PE bands of pteridine indicates that the low energy band is associated with an ionization process involving the nitrogen n electrons and followed by rc-bands. Furthermore, the pKa of free pteridine, which is masked in aqueous solution by partial covalent hydration, is suggested from the PE data to be in the order of —2. 

The first calculations of the r-electron polarizabilities of long-chain molecules employed the free-electron model and simple Huckel theoryIn both cases the computed polarizability tensor elements were proportional to the cube of the length of the chain, a / P. In these calculations (and in the calculation of p by Zyss, who showed also a definite dependence of the elements of P on chain length), no electron-electron interaction was taken into account. In order to take Coulomb interaction at least partially into account one must perform Hartree-Fock calculations on the ab initio level. Such calculations would be expected to affect (most probably decrease somewhat) the dependence on /. 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

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