Delocalization energy analysis

Interatomic distances calculated from the detailed analysis of rotational fine structure of the UV spectrum of pyrazine are in close agreement with those observed in (7) and (8), with the calculated bond lengths for C—C of 1.395, C—N 1.341 and C—H 1.085 A (60DIS(20)4291). Thermochemical data have provided a figure of 75 kJ moP for the delocalization energy of the pyrazine ring (B-67MI21400). 

Repeat your analysis fox phenoxy radical. Instead of charge, focus on the spin density. Calculate the delocalization energy using phenoxy radical at phenol geometry. Is it of the same order of magnitude as that for phenoxy anion Explain. 

A mathematical analysis of all four isomeric thiadiazoles by the simple molecular orbital method has provided molecular diagrams of the free base and conjugate acid of each thiadiazole, with electron densities, bond orders, and free valencies. On this basis, predictions have been made concerning the reactivities of the six non-equivalent carbon atoms, the basicities of the nitrogen atoms, and the delocalization energies in these molecules. The 5-position in free 1,2,4-thiadiazole should possess maximum reactivity in nucleophilic substitution reactions. The treatment also accounts for the order of the polarographic half-wave potentials and the position of the absorption maxima in the ultraviolet region of the spectra of 1,2,4- and 1,3,4-thiadiazoles.4... 

In order to estimate and compare the magnitude of the M-B interactions in these isoelectronic complexes, a whole set of structural and spectroscopic parameters determined experimentally and/or computed theoretically were considered. This includes the M - B distance the ratio r between the M -B distance and the sum of covalent radii (to take into account the different sizes of the metals involved), the pyramidaliza-tion of the boron environment XB, the rlB NMR chemical shift <5 11B, the difference AqB between the charge at boron in the metal boratrane and the free ligand TPB, the difference A M between the charge at the metal in the metal boratrane and that in the related borane-free complex [M(i-Pr2PPh)3], and the NBO delocalization energy A NBo associated with the main donor-acceptor M-B interaction found at the second order in the NBO analysis (Table 2). Only the conclusions of this detailed analysis will be recalled here ... 

Interatomic distances as calculated from the analysis of the rotational fine structure of the ultraviolet spectrum are C-C, 1.395 A C-N, 1.341A and C-H, 1.085 A.66 These are very similar to the bond lengths for pyridine which are C-2-C-3, 1.3945 A C-3-C-4, 1.3944 A and C-2-N, 1.3402 A. The C-N-C bond angle in pyrazine is 115° and the C-C-N bond angle 122.5°.56,67 A delocalization energy for pyrazine of ca. 18 kcal/mole is indicated from heats of combustion data.68 The C=N bond energy in 2,2,5,5-tetramethyl-2,5-dihydropyrazine has been calculated to be 130.3 kcal.58a... 

While considering bond separation energies A i in terms of NBO analysis Reed and Schleyer (143) presented a very informative breakdown of A ,s into the change of energy of the localized NBO Lewis structure A l and the change in net delocalization energy A d (Eq. [40]). Let us examine poly-fluoromethanes. The reactions shown in Table 13 correspond to the loss of... 

In polar media, the dipolar resonance structure la is favored and the spin density is shifted towards the N-atom. X-Ray analysis of several cyclic nitroxides revealed that the R R >NO moiety is planar for five-membered nitroxides but clearly pyramidal for six- and seven-membered ring nitroxides. The N-0 bond length is not much influenced by the ring size. Nitroxides do not form stable, isolable 0-0 dimers because the loss of the delocalization energy (l<->la 120kJmoN nitroxide) is greater than the peroxide bond... 

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. 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

TABLE 10. Vicinal oHX —Fock matrix by second-order perturbation theory (energies in kcal mol-1)... 

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