Orbital calculations, extended Huckel

HOMO = highest occupied molecular orbital. 6LUMO = lowest unoccupied molecular orbital. CEH = extended Huckel (calculations). dCNDO = complete neglect of differential overlap. efcc = face-centered cubic. 

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... 

An extended Huckel calculation is a simple means for modeling the valence orbitals based on the orbital overlaps and experimental electron affinities and ionization potentials. In some of the physics literature, this is referred to as a tight binding calculation. Orbital overlaps can be obtained from a simplified single STO representation based on the atomic radius. The advantage of extended Huckel calculations over Huckel calculations is that they model all the valence orbitals. 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

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... 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

The dipolar parts of the analyzed hfs tensors have been compared with calculated values obtained from first order expressions of the electron-nuclear dipole interaction (5.3)57. The coefficients of the atomic orbitals used in this computation, which considers all two- and three-center contributions, are obtained from an extended Huckel calculation (ethyl groups replaced by protons). It has been found that almost 100% of the unpaired electron is located on the CuS4 fragment so that the replacement of the ethyl groups by protons is of minor importance for the calculation of the atomic orbital coefficients. The experimental and theoretical hfs data, summarized in Table 8, are found to... 

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. 

In this section we mention the paramagnetic monocationic complexes [Mo(CO)2(dppe)2]+ and [Mo(CO)2(bipy)2]+, both of which are produced by oxidation of the parent Mo° complexes. In the former case, the oxidants used include [MeCftKUNJfBFj,46 NO[PF6], I2 and AgIla-47 and a variety of analogues [Mo(CO)2L2]+ has been obtained (L2 - dppm, dmpe, diars, etc.).1 47 Electrochemical oxidation has also been used, with other measurements, to show that a rapid cis — trans isomerization follows oxidation and an explanation for this phenomenon has been proposed on the basis of extended Huckel molecular orbital calculations, the stereochemical change being dependent on the number of valence electrons and the nature of the coligand jr-donor or -acceptor capacity. Similar studies have been made upon the compounds [Mo(CO)2L2]+ (L = bipy or phen).47... 

Table 7.1 Atomic orbital parameters used in extended Huckel calculations. Single zeta STO functions are used for B and C and double zeta STO functions are used for the transition metals...

The tight-binding band structure calculations were based upon the effective one-electron Hamiltonian of the extended Huckel method. [5] The off-diagonal matrix elements of the Hamiltonian were calculated acording to the modified Wolfsberg-Helmholtz formula. All valence electrons were explicitly taken into account in the calculations and the basis set consisted of double- Slater-type orbitals for C, O and S and a single- Slater-type orbitals for H. The exponents, contraction coefficients and atomic parameters were taken from previous work [6],... 

A straightforward orbital correlation, made in Fig. 12, indicates that the thermal process is favored over any excited state process. This has been supported by an extended Huckel calculation (Hoffmann and Woodward, 1965a). An orbital correlation and energy level diagram have also been given for 1,3-dipolar cycloadditions (Eckell et al., 1967), e.g. (26). 

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/) ... 

Octahedral olefin-alkyne d4 complexes are characterized by a one-to-one match of each of the three metal dir orbitals with a ligand tt function as mentioned above. Three constructive two-center-two-electron metal-ligand tt bonds result. Extended Huckel calculations on W(H2C=CH2)-(HC=CH)(S2CNH2)2 produce the dv level ordering shown in Fig. 16... 

Both combinations of alkyne n orbitals find filled dir orbital symmetry matches in these d4 complexes. Extended Huckel calculations on Mo(HC=CH)2(S2CNH2)2 indicate a large HOMO-LUMO gap of 1.62 eV. These octahedral complexes have proved to be quite robust and resist exchange and substitution reactions in accord with a substantial frontier orbital energy gap (153). 

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