Hiickel molecular orbital calculations

A Hiickel molecular orbital calculation for the cyclopentadiene system can be carried out as illustrated in Chapter 5. As is shown in Figure 5.20, the Frost-Musulin diagram places the five molecular orbitals at energies of a + 2/3, a + 0.618/3 (2), and a — 1.618/3 (2). Because the cyclopentadienyl anion has six electrons, only the three lowest energy levels are populated and are the orbitals interacting with those on the iron. Figure 21.15 shows the orbitals of the cyclopentadienyl anion. 

Hiickel molecular-orbital calculation, 34 227 Hiickel theory, extended, 25 2, 3 approximations, 25 6... 

Were the isoelectronic anion (i.e., C2B3Hg ) to be prepared, the most stable configuration should have adjacent basal carbons to accommodate the basal bridge hydrogen as well as the carbon. Either cis or trans basal carbons should be anticipated in the isoelectronic dianion (C2B3H5 ) which would have no bridge hydrogens. Rudolphs s Extended Hiickel Molecular Orbital calculations would favor cis basal carbons in the latter case. 

The mass spectra of various pyridazino[l,2-a]pyridazines have been reported (74JOC47). Hiickel molecular orbital calculations have been reported for this ring system (66JSP(19)25). 

Extended Hiickel molecular orbital calculations have been made for the icosahedral platinaboranes and carbaboranes [Bn Pt(PH3)2 Hu]2-, [Bi0C Pt(PH3)2 Hu]2, and... 

It has been found that whereas Cu11 porphyrins luminesce, the Ag" complexes do not. By an examination of electronic absorption spectra, emission spectra, redox potentials and near-IR absorption data, it was proposed that this could be rationalized on the basis of the energy of the big (dx2 yi) orbital. Extended Hiickel molecular orbital calculations predicted that the d-n transition would be above the lowest (n, jt ) levels for Cu11 but below them in the Agn complexes. The near-IR absorptions found for Ag11 were attributed to CT transitions.554... 

Studies of the tautomeric state of 1,2,4-thiadiazines have been more or less confined to the biologically active 1,2,4-benzothiadiazines. Ultraviolet spectroscopic studies suggest that the 4//-tautomer of 1,2,4-benzothiadiazines, e.g. 152, is preferred in ethanol (60JOC970) in alkali, the anion dominates. Extended Hiickel molecular orbital calculations (70MI2) and 13C-NMR studies (79T2151) confirm this view (Scheme 6). 

It is noteworthy that about the same time as our book was published, two Russian chemists performed Hiickel molecular orbital calculation on C60 (Bochvar Galpern 1973). They named it carbo-s-icosahedrene. Their calculations gave the correct picture of the jt-orbital system. 

Hiickel molecular orbital calculation clearly shows the difference in the rc-electronic energy of anthracene (la) and phenanthrene (Ila) in accordance with their thermodynamic stability. 

Chapter 1 of Volume 15 deals with density functional theory (DFT). As with many quantum mechanical calculations, it is easy to become wrapped up in the theory and lose sight of the chemical phenomena we are trying to explain with the calculations. Equally important to how the numerical calculations are done is how the results can be interpreted to gain chemical insight. Dr. F. Matthias Bickelhaupt and Professor Evert Jan Baerends show how the results of DFT calculations can be analyzed to open up chemical understanding. This chapter illustrates that the plain numbers from a quantum mechanical calculation can be interpreted to be conceptually useful to chemists. In many ways, this chapter evokes memories of the famous way Professor Roald Hoffmann has extracted information from extended Hiickel molecular orbital calculations. 

Before concluding this section, it is noted that a fairly user-friendly SHMO (simple Hiickel molecular orbital) calculator is now available on the Internet, http //www.chem.ucalgary.ca/shmo/. With this calculator, the Hiickel energies and wavefunctions of planar conjugated molecules can be obtained on the fly. ... 

The program is reported to carry out simple Hiickel molecular orbital calculations to determine the relative sensitivity of aromatic carbon atoms to oxidation and the relative stability of keto and enol tautomers. Klopman et al. (1999) have reported that for polycyclic aromatic hydrocarbons, adequate reactivity is an essential but not sufficient condition for enzyme catalyzed reaction. The accessibility of the reactive site (i.e., the absence of steric hindrance) was also found to be important. Genetic algorithms have been used to optimize the performance of the biotransformation dictionary by treating the initial priority scores set by expert assessment as adjustable parameters (Klopman et al., 1997). 

As a measure of the activity of antioxidants and antiozonants, oxidation potential has been used (3, 15, 16, 19). Compounds having an oxidation potential lower than 0.44 volt seem to be effective as antiozonants (20), whereas good antioxidants are known to have the potentials between 0.7 and 0.9 volt (16). The Hiickel molecular orbital calculations... 

Oxidation potentials are recognized to be correlated with the highest occupied levels of electrons, which may be evaluated according to the Hiickel molecular orbital calculation. In this paper the calculations were carried out with the following values (18) as the Coulomb parameters. 

Silvestre and Hoffmann have considered the conversion of ruthenium acetylide complexes to the corresponding vinylidene species using extended Hiickel molecular orbital calculations (69). Although the rearrangement of free acetylene to its vinylidene isomer is thermodynamically disfavored, their results indicate that the transformation becomes thermodynamically... 

Dienamines differ from simple enamines in that (i) there is an additional nucleophilic site at the -position and (ii) an equilibrium mixture of three isomeric dienamines is frequently formed, consisting of the linear s-trans isomer 1, the linear s-cis isomer 2 and the cross-conjugated isomer 31 (Scheme 1). A variety of factors influence the outcome of electrophilic attack on such an equilibrium system. Hiickel molecular orbital calculations indicate a significantly higher electron density at the -positions compared to the -positions of the dienamine system2 (Figure 1). 

Graphics-based Hiickel molecular orbital calculator. 

This is, in principle, in agreement with extended Hiickel molecular-orbital calculations. The calculated binding energy and difference between the energies of the LUMO and HOMO for the four possible isomers indicate the experimentally isolated structure to be the most stable one, although the extended Hiickel calculation does not show a substantial relative stability (Table I). 

If the above generalization is correct, then simple extended Hiickel molecular orbital calculations for the surface chemisorption states of simple hydrocarbons or hydrocarbon fragments should sense this tendency for multicenter C-H-metal bonds to form (these... 

The generalized free electron molecular orbital method (G-FEMO) gives a good description of the ground state properties of imidazole and yields equivalent results299 to Hiickel molecular orbital calculations. 

Three-dimensional Hiickel molecular orbital calculations have been performed on a series of molecules made from the atoms H, C, N, O, F, and CL It has been found that the sum of the Mulliken overlap populations is closely related to the energy of atomization. For 40 compounds not containing carbon, the observed energies of atomization can be reproduced with a mean deviation of 11.1 kcal./mole by a simple empirical equation which includes a term to account for the extra stability of polar molecules. A slightly more complicated expression is needed for compounds of carbon, and the fit to the observed data is not as good. 

As an example of a symbolic calculation. Fig. 5 displays a Mathcad solution of one 4X4 block of the secular determinant of a Hiickel molecular orbital calculation done in Exp. 41 for orf/ro-benzosemiquinone (compare with Table 41-2). Mathcad is a software package for numerical analysis but also makes use of a subset of the symbohc routines of Maple. The algebraic expansion of the determinant is generated and solved with two... 

TABLE 1 Hiickel molecular-orbital calculations for para-benzosemiquinone... 

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