An empirical potential for hydrogen bond energies determination of the orientation of anthracene molecules in the unit cell by means of a refractivity method: some ab initio calculations involving acetonitrile exchange reaction
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Topic I An empirical potential for calculating hydrogen bonding energies is developed for systems of the type A-H--B, where A and/or B is oxygen or nitrogen. Point charge and van der Waals interaction are included in the potential. The parameters of the potential were optimized by means of a simplex algorithm within a range of A-B distances from 2.8 A through 5.0 A. The root mean square deviation between the empirical potential and the ab initio results of 216 configurations of (H₂O)₂, (NH₃)₂ and NH₃•H₂O is 0.9 kcal/mol and 0.5 kcal/mol for 61 configurations of methanol dimers. Applications of the potential to water dimers, ammonia dimers, their mixed dimers, water oligomers and ice-h as well as the β form of the methanol crystal show that the potential yields reasonable results compared to those computed by "ab initio" methods using 6-31G* basis sets. The potential is compatible with MM2 program. It is simpler than earlier potentials in that neither dipoles nor Morse potentials are involved. It should be superior to the empirical potentials developed by Jorgensen that used STO-3G ab initio calculated results as the standards. The potential might be useful for estimation of hydrogen bond energies in a local part of a large molecule to avoid the prohibitive expense of ab initio calculation. Topic II The monoclinic anthracene crystal is used as an example to demonstrate the feasibility of optimizing the orientation of molecules in the unit cell by matching calculated and experimental refractivity ellipsoids using a simplex algorithm. The calculated refractivity ellipsoid is determined by use of an empirical formula using bond directional polarizabilities. Optimization of the molecular orientations to provide the best fit to the experimental ellipsoid starting from several assumed orientations results in fits for which the maximum deviation from the experimental molecular orientation was no more than 10 degrees. The method can be applied to other monoclinic molecular crystals directly and could be extended to other crystal systems with anisotropic optical properties. Topic III Three mechanisms (Walden inversion, addition-rearrangement-elimination and proton 1,3 shift mechanisms) of the following reaction were suggested by Jay et al. and Andrade et al. respectively. CH₃CN + C⃰N- = CH₃C⃰N + CN-. The mechanism of Walden inversion was determined to be the least likely one based on Andrade's MNDO results. Our calculations, based on 3-21G and 4-31G results, show the contrary result that the Walden inversion is the most likely mechanism among the three considered. However, solvation effects were neglected in the calculations and these effects could play a major role in the choice of mechanisms. Simple calculations based on Boltzmann distribution of precursor concentrations and the Arrhenius law show that Walden inversion predominates over Jay's addition-elimination-rearrangement mechanism even when MNDO energy levels were used. Estimated orders of magnitude for the rate ratios were determined.
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