Hiickel molecular orbital calculations, for

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. 

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... 

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

To synthesize a new electronic system, tri-heteroatom-substituted cyclopropenium, we thought it useful to examine beforehand the stability of the proposed trisubstituted cyclopropenium system by quantum mechanical methods (or, in other ways). A simple Hiickel molecular orbital calculation for the tri-heteroatom-substituted cyclopropenimn cation 3) gave the results shown in Table 1, where qc and -pc-c denote the n electron density on the ring carbon atom and the n bond order between ring carbon atoms, respectively. Ai it (additional resonance energy) as the measure of stability of 3) is a value obtained as a resonance energy difference between 3 a) and 3 b). 

Fig. 436. Hiickel molecular orbital calculations for C o- The orbital energy levels are given in units of beta. Reproduced with permission from Davinson RA (1981) Theor Chim Acta 58 193...

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

Molecular orbital calculations for the parent vinyl cation, Cj H3, were first reported by Hoffmann (161), who used the extended Hiickel method, and more recently by Yonezawa and co-workers (162), who used a semiempirical SCF procedure. Both treated the problem of classical, 172 (R = H), versus bridged structures, 173, but the methods suffered from their inability to account satisfactorily for bond-length changes, and neither discussed the question of linear, 172a, versus bent, 172b, structures. 

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... 

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). 

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). 

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... 

Whereas empirical force-field calculations predict a ring A boat conformation for lanost-8-en-3-one, combined empirical force-field-extended Hiickel molecular orbital calculations favour a ring A chair conformation. Europium-shift n.m.r. results indicate that the molecule adopts the latter conformation. Studies on the peracetic acid-boron trifluoride etherate Baeyer-Villiger oxidation of 4,4-dimethyl-3-keto-triterpenoids to 5-lactones (18) and their subsequent ring contraction to y-lactones have been reported. Dehydrogenation of lanost-8-en-3j8-ol with 2,3-dichloro-5,6-dicyanobenzoquinone afforded, in addition to the corresponding 7,9(1 l)-diene, the aromatic seco-lanostane derivatives (19)... 

Fig. 5.2. Bond overlap populations, n(Si-O), calculated using extended Hiickel molecular-orbital theory for the (SiOJ tetrahedron of forsterite and plotted against Si-O bond distance (A). Inset tetrahedron at left shows dimensions observed for SiO cluster and one at the right shows overlap populations with maximum range of (Si-0) in square brackets for the estimated standard deviations in the bond length (after Louisnathan and Gibbs, 1972b reproduced with the publisher s permission).

The experimental observations on the mechanism(s) of electroreduction of 2-thio-pyrimidines have been interpreted on the basis of their electronic structures as calculated with the aid of the CNDO/2 and Hiickel procedures The energies of LUMO (lowest unoccupied molecular orbitals), calculated for pyrimidine and its 2-oxo-and 2-thioderivatives, were compared with the reduction half-wave potentials (Table V). These show that the presence of a carbonyl or thione substituent at Cj enhances the electron acceptor properties of the molecule, which are correlated with formation of a dimer susceptible to photooxidation. 

Graphics-based Hiickel molecular orbital calculator of energies and orbitals of TT electrons. EnzymeKinetics for fitting Michaelis—Menten kinetics parameters. ESP (Experimental Section Processor) for organizing synthetic procedures in publication format. LabSystant for evaluating quantitative lab data. Diatomic Molecular Motion and Mechanics. PC-Mendeleev for studying periodic table. SynTree for creating database of reactions. TAPP (Thermodynamic and Physical Properties) database with physical and thermodynamic data on more than 10,000 compounds. PCs and Macintosh. 

A nonempirical molecular orbital calculation reported recently for COS by dementi" has indicated, however, that the first excited state is a 7T—IT type. Only s and p type atomic orbitals were used in these calculations. To examine the effect of the 3d orbitals of the sulfur atom on the molecular orbital energy values, an extended Hiickel molecular orbital calculation has also been carried out with and without the inclusion of the 3d orbitals. The resulting energy level diagram for the ground and excited molecular orbitals, in comparison with the atomic... 

The Hiickel molecular orbital theory for non-planar conjugated organic molecules has been applied to study the electronic structure and properties of the proposed icosahedral geometry of C ). The results support the suggestion that C o may be the first example of a spherical aromatic molecule. The molecule is calculated to have a stable closed shell singlet ground electronic state. 

We have examined the structure theoretically in several ways. First, we have performed Hiickel molecular orbital calculations at the naive level (a common )3 for all bonds), which reveal a small but significant HOMO-LUMO gap (0.344 or less than half of the 0.757 )3 found for Cgo (ref. 17)) and a large delocalization energy (0.5551 per atom, as compared with 0.5527 p for... 

The molecular and electronic structures of (CpM)4(//2-E)6 and (CpM)4(/x2-E)3(//3-E)3 (E = O, Se) for titanium as well as group 5 and 6 transition metals have been compared using extended Hiickel molecular orbital calculations. The conclusions indicate that the M4(/x2-0)3(/x3-0)3 structure cannot exist unless the M4-tetrahedron is severely distorted by lengthening of the M(apical)-M(basal) distance. The M4(/x2-Se)3(/x3-Se)3 structure can exist with a small distortion. The M4(/x2-E)6 structure is preferred over M4(//2-E)3(//3-E)3 when M-E multiple bonding is important, that is, when E = O. There is little M-M interaction in any of the cluster orbitals.830... 

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