Extended Huckel Theories

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

Hoffman s extended Huckel theory, EHT (Hoffman, 1963), includes all bonding orbitals in the secular matrix rather than just all n bonding orbitals. This inclusion increases the complexity of the calculations so that they are not practical without a computer. The basis set is a linear combination that includes only valence orbitals... 

Molecular mechanics and semiempirical calculations are all relativistic to the extent that they are parameterized from experimental data, which of course include relativistic effects. There have been some relativistic versions of PM3, CNDO, INDO, and extended Huckel theory. These relativistic semiempirical calculations are usually parameterized from relativistic ah initio results. 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended HUckel Theory (EHT) or Intermediate Neglect of Differential Overlap (INDO) (Sections 3.12 and 3.9). The EHT method has the advantage that it is readily parameterized for all elements, and it can provide start orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The INDO... 

The Huckel methods perform the parameterization on the Fock matrix elements (eqs. (3.50) and (3.51)), and not at the integral level as do NDDO/INDO/CNDO. This means that Huckel methods are non-iterative, they only require a single diagonalization of the Fock (Huckel) matrix. The Extended Huckel Theory (EHT) or Method (EHM), developed primarily by Hoffmann again only considers the valence electrons. It makes use of Koopmans theorem (eq. (3.46)) and assigns the diagonal elements in the F... 

MD simulations have been used for water at Pt(100) and (111 ),880-882 as well as at Ag(l 11 ).883 The stmcture of water is predicted to conform to a hexagonal pattern and the metal-water interaction is probably stronger for the (111) than the (100) surface.882 On the basis of the extended Huckel theory, Estiu et a/.884,885 have reached different conclusions in favor of the... 

These arguments go hand in hand with Extended Huckel Theory (EHT), both being based on overlap (symmetry) considerations. In fact, an EHT calculation will provide almost exactly the same results as a skilful use of the qualitative MO building scheme we have provided in this section. 

Hoffmann, R. 1963. An extended Huckel theory I. Hydrocarbons. J. Chem. Phys. 39 1397. 

Several different molecular orbital methods have been used in SAR investigations. These include simple Huckel theory, HT,(38) extended Huckel theory, EHT,(39) CND0,( ) NDD0,(41) MINDO/3,(42) and PCILO,(43)... 

In an early investigation (66T539) the two highest occupied and the two lowest unoccupied orbitals were calculated on the basis of an extended Huckel theory to determine the electron transition responsible for the long wavelength UV absorption. An Ai >Bi, a -nr transition was discussed. 

Prior to considering semiempirical methods designed on the basis of HF theory, it is instructive to revisit one-electron effective Hamiltonian methods like the Huckel model described in Section 4.4. Such models tend to involve the most drastic approximations, but as a result their rationale is tied closely to experimental concepts and they tend to be inmitive. One such model that continues to see extensive use today is the so-called extended Huckel theory (EHT). Recall that the key step in finding the MOs for an effective Hamiltonian is the formation of the secular determinant for the secular equation... 

Slater-type orbitals were introduced in Section 5.2 (Eq. (5.2)) as the basis functions used in extended Huckel theory. As noted in that discussion, STOs have a number of attractive features primarily associated with the degree to which they closely resemble hydrogenic atomic orbitals. In ab initio HF theory, however, they suffer from a fairly significant limitation. There is no analytical solution available for the general four-index integral (Eq. 

Equation (3.43) resembles the formula [equation (3.44)] adopted by Wolfsberg and Helmholtz [59] for the interaction matrix elements. This form, with the empirical factor k — 1.75, was adopted by Hoffmann in his derivation of extended Huckel theory [60], namely... 

Alder reactions to give the endo adduct as in (18) ->(19) rather than the exo one as in (18) ->(20)] in terms of qualitative perturbation theory. Similar methods were used by Hoffmann and his co-workers in discussion of favourable and unfavourable conformations of conjugated systems,93 and of relative stabilities of isomers.94 All these treatments are based, implicitly or explicitly, on extended Huckel theory,... 

Extended Huckel theory is useful for calculating the properties of molecules containing a ox it bonds. The molecular orbitals (linear combination of the valence atomic orbitals (x/) ... 

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