Bonding MO calculations

The alkyl-bridged structures can also be described as comer-protonated cyclopropanes, since if the bridging C—C bonds are considered to be fully formed, there is an extra proton on the bridging carbon. In another possible type of structure, called edge-protonated cyclopropanes, the carbon-carbon bonds are depicted as fully formed, with the extra proton associated with one of the bent bonds. MO calculations, structural studies under stable-ion conditions, and product and mechanistic studies of reactions in solution have all been applied to understanding the nature of the intermediates involved in carbocation rearrangements. 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

In the case of covalent compounds, crystal-field theory is a poor model for estimating electric field gradients because of the extensive participation of ligand atomic orbitals in the chemical bonds. MO calculations are a much better choice, since the corresponding interactions are considered, and realistic (noninteger) population numbers are obtained for the central metal as well as the ligand atomic orbitals. 

Similarly x-ray crystallography of (MejC)jC H2N=PP(CMej)2 shows no N=P, P-P conjugation. The dimerization reactions of R2P(X)-NY species have been discussed with special emphasis on the role of the electrophilicity of the PX a bond. MO calculations on matrix isolated PN allow for an estimate of... 

Figure 7-18. Schematic representation of the LCAO scheme in a, T-only calculation for ethylene, The AOs

Th e ability to perform m oleciilar orbital (MO ) calculation s on m et-als is extremely useliil because molecular mechanics methods are gen erally unable to treat m etals. This is becau se m etals h ave a wide range of valences, oxidation states, spin multiplicities, and have 1111 usual bonding situations (e.g.. d%-p% back bonding). In addition. the 11 on direction al n at are o ( m etallic hon din g is less am en a-ble to a ball and spring interpretation. 

In the [3,2-c ] series the spectra of the parent compound and some closely related analogues have been compared with those predicted from MO calculations of electron densities. The results confirm the predicted occiurence of a considerable degree of bond localization in these compounds <80KGS54l), as was previously found in their deaza (cinnoline) analogues <67JCS(B)1243). Other comparisons of NMR values with those expected from MO calculations for a series of azanaphthalenes have included some results with pyridopyridazines <75MI21500). 

Figure 2 LCAO MO calculations of tt-electron densities and bond orders...

Typical coupling constants for isothiazoles are given in Table 5. The electronegative nitrogen atom reduces 3,4 and V3.5 from the values of 3.50 Hz and 0.27 Hz, respectively, in thiophene. The V values correlate quite well with rr-bond orders calculated by MO methods (74CJC833). 

Later there was an attempt by ab initio calculation to fit the electron structure of diazirine into the Walsh model of cyclopropane (69MI50800). According to these SCF-LCAO-MO calculations three MOs add to the description of the lone electron pairs, all of which also contribute to some extent to ring bonding. As to strain, 7r-character and conjugative effect, the term pseudo-rr-character was used. 

Furazano[3,4-/]quinoxaline, 7,8-diphenyl-synthesis, 6, 412 Furazanothiophene synthesis, 6, 417 Furazans, 6, 393-426 biological activity, 6, 425 bond angles, 6, 396 bond lengths, 6, 396 coordination compounds, 6, 403 diamagnetic susceptibilities, 6, 395 dipole moments, 6, 395, 400 heats of combustion, 6, 400 heterocyclic ring reactions, 6, 400-403 IR spectra, 6, 398 isoxazoles from, 6, 81 mass spectra, 6, 399 microwave spectroscopy, 6, 395, 396 MO calculations, 6, 395 monosubstituted... 

MO calculations can provide the minimum-energy structure, total energy, and overall electron density of a given molecule. However, this information is in the form of the sum of the individual MOs and cannot be easily dissected into contributions by specific atoms or groups. How can the properties described by the MOs be related to our concept of molecules as a colleetion of atoms or functional groups held together by chemical bonds ... 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

The barrier for conversion of the skew conformation to the s-trans conformation is 3.9kcal/mol. This energy maximum presiunably refers to the conformation (transition state) in which the two n bonds are mutually perpendicular. Various MO calculations find the s-trans conformation to be 2-5 kcal/mol lower in energy than either the planar or skew cisoid conformations. Most high-level calculations favor the skew conformation over the planar s-cis, but the energy differences found are quite small. ... 

The anomeric effect is also present in acyclic systems and stabilizes conformations that allow antiperiplanar (ap) alignment of the C—X bond with a lone-pair orbital of the heteroatom. Anomeric effects are prominent in determining the conformation of acetals and a-alkoxyamines, as well as a-haloethers. MO calculations (4-3IG) have found 4kcal/mol as the difference between the two conformations shown below for methoxy-methyl chloride. ... 

Whether AH for a projected reaction is based on bond-energy data, tabulated thermochemical data, or MO computations, there remain some fundamental problems which prevent reaching a final conclusion about a reaction s feasibility. In the first place, most reactions of interest occur in solution, and the enthalpy, entropy, and fiee energy associated with any reaction depend strongly on the solvent medium. There is only a limited amount of tabulated thermochemical data that are directly suitable for treatment of reactions in organic solvents. Thermodynamic data usually pertain to the pure compound. MO calculations usually refer to the isolated (gas phase) molecule. Estimates of solvation effects must be made in order to apply either experimental or computational data to reactions occurring in solution. 

Simple Hiickel calculations on benzene, in contrast, place all the n electrons in bonding MOs. The 7t-electron energy of benzene is calculated by summing the energies of the six 71 electrons, which is 6a -F 8/S, lower by 2/S than the value of 6a -F 6/S for three isolated double bonds. Thus, the HMO method predicts a special stabilization for benzene. 

Azulene does have an appreciable dipole moment (0.8 The essentially single-bond nature of the shared bond indicates, however, that the conjugation is principally around the periphery of the molecule. Several MO calculations have been applied to azulene. At the MNDO and STO-3G levels, structures with considerable bond alternation are found as the minimum-energy structures. Calculations which include electron correlation effects give a delocalized n system as the minimum-energy structure. ... 

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