Bonding orbital calculation

In chemical shift calculations for acylium ions, it was not necessary to model the ionic lattice to obtain accurate values. These ions have tetravalent carbons with no formally empty orbitals, as verified by natural bond orbital calculations (89). Shift calculations for simple carbenium ions with formally empty orbitals may require treatment of the medium. We prepared the isopropyl cation by the adsorption of 2-bromopropane-2-13C onto frozen SbF5 at 223 K and obtained a 13C CP/MAS spectrum at 83 K (53). Analysis of the spinning sidebands yielded experimental values of = 497 ppm, 822 = 385 ppm, and (%3 = 77 ppm. The isotropic 13C shift, 320 ppm, is within 1 ppm of the value in magic acid solution (17). Other NMR evidence includes dipolar dephasing experiments and observation at higher temperature of a scalar doublet ( c-h = 165 Hz) for the cation center. 

Figure 6-22 Generalized valence-bond orbitals calculated for ethene by the ab initio method. The nuclei are located in the x,y plane of the coordinate system at the positions indicated by crosses. The long dashes correspond to locations of change of phase. The dotted lines are contour lines of electron amplitude of opposite phase to the solid lines. Top shows both m-bonding carbon orbitals (almost sp2), middle-left is the carbon orbital and middle-right the hydrogen orbital of one of the C-H bonds, and bottom represents a side view of the ir orbitals in perpendicular section to the x,y plane. (Drawings furnished by Dr. W, A. Goddard, III.)...

The crystal structures of allyl-,25 cyclopent-2-enyl-,26 cyclohex-2-enyl-, and cyclo-hept-2-enyl-triphenyl-tin27 show that the Sn-allyl bond is oriented orthogonally to the plane of the C=C group with a Sn-C-C=C dihedral angle of 100 10°, and this is ascribed to a-n conjugation (carbon-metal hyperconjugation) (9-1) between the cj-Sn-C bond and the rT -C=C orbitals. This is supported by the photoelectron spectra, and by linear combination of bond orbitals calculations (see Section 3.1.2.3).28... 

The lowest I.E. band in all cases is assigned to the 2Alg ion state. This is consistent with e.s.r. evidence on [Cr(r -C6H6)2]+ 3I 33) and other bis-Jj-arene complexes34). This band is extremely sharp for an organometallic compound indicating ionization from a non-bonding orbital calculations consistently predict the alg orbital of metal sandwich compounds to be practically pure metal dz2 in character as a consequence of... 

I iiis can be helpful because it may enable more meaningful sets of orbitals to be generated from the original solutions. Molecular orbital calculations may give solutions that are nioared out throughout the entire molecule, whereas we may find orbitals that are Im alised in specific regions (e.g. in the bonds between atoms) to be more useful. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

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... 

High level molecular orbital calculations of cyclobutadiene itself and experimen tally measured bond distances of a stable highly substituted derivative both reveal a pat tern of alternating short and long bonds characteristic of a rectangular rather than square geometry... 

The reaction between a trinuclear metal carbonyl cluster and trimetbyl amine borane has been investigated (41) and here the cluster anion functions as a Lewis base toward the boron atom, forming a B—O covalent bond (see Carbonyls). Molecular orbital calculations, supported by stmctural characterization, show that coordination of the amine borane causes small changes in the trinuclear framework. 

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 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... 

Unlike the stable molecule N2O, the sulfur analogue N2S decomposes above 160 K. In the vapour phase N2S has been detected by high-resolution mass spectrometry. The IR spectrum is dominated by a very strong band at 2040 cm [v(NN)]. The first ionization potential has been determined by photoelectron spectroscopy to be 10.6 eV. " These data indicate that N2S resembles diazomethane, CH2N2, rather than N2O. It decomposes to give N2 and diatomic sulfur, S2, and, hence, elemental sulfur, rather than monoatomic sulfur. Ab initio molecular orbital calculations of bond lengths and bond energies for linear N2S indicate that the resonance structure N =N -S is dominant. 

The tetramethylammonium salt [Me4N][NSO] is obtained by cation exchange between M[NSO] (M = Rb, Cs) and tetramethylammonium chloride in liquid ammonia. An X-ray structural determination reveals approximately equal bond lengths of 1.43 and 1.44 A for the S-N and S-O bonds, respectively, and a bond angle characteristic bands in the IR spectrum at ca. 1270-1280, 985-1000 and 505-530 cm , corresponding to o(S-N), o(S-O) and (5(NSO), respectively. Ab initio molecular orbital calculations, including a correlation energy correction, indicate that the [NSO] anion is more stable than the isomer [SNO] by at least 9.1 kcal mol . ... 

Hiickel s calculations on planar conjugated systems were extensively exploited, and I refer you once again to Streitwieser s classic book. Molecular Orbital Theory for Organic Chemists. What few calculations that had been done at that time on the (T framework had used the method of linear combination of bond orbitals. 

Hydroxypyridine 1-oxide is insoluble in chloroform and other suitable solvents, and, although the solid-state infrared spectrum indicates that strong intermolecular hydrogen bonding occurs, no additional structural conclusions could be reached. Jaffe has attempted to deduce the structure of 4-hydroxypyridine 1-oxide using the Hammett equation and molecular orbital calculations. This tautomeric compound reacts with diazomethane to give both the 1- and 4-methoxy derivatives, " and the relation of its structure to other chemical reactions has been discussed by Hayashi. ... 

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