Ab initio structural trends and torsional sensitivity in n-hexane and comparisons with crystallographic structural results

by Yu, C. H.; Paulus, E. F.; Ramek, M.; Schafer, L.

The molecular structures of rr-hexane were determined by RHF/4-21G ab initio geometry optimization at 30 degrees grid points in its three-dimensional tau(1)(C11-C8-C5-C1), tau(2)(C14-C11-C8-C5), tau(3)(C17-C14-C11 -C8) conformational space. Of the resulting 12 x 12 x 12 = 1728 grid structures, 468 are symmetrically non-equivalent and were optimized constraining the torsions tau(1), tau(2), and tau(3) to the respective grid points, while all other structural parameters were relaxed without any constraints. From the results, complete parameter surfaces were constructed using natural cubic spline functions, which make it possible to calculate parameter gradients, \ VP \ = [(P/partial derivative tau(i))(2) + (partial derivative P/partial derivative tau(j))(2)](1/2), where P is a C-C bond length or C-C-C angle. The parameter gradients provide an effective measure of the torsional sensitivity of the system and indicate that dynamic activities in one part of the molecule can significantly affect the density of states, and thus the contributions to vibrational entropy, in another part. This opens the possibility of dynamic entropic conformational steering in complex molecules; i.e. the generation of free energy contributions from dynamic effects of one part of a molecule on another. When the conformational trends in the calculated C-C bond lengths and C-C-C angles are compared with average parameters taken from some 900 crystallographic structures containing n-hexyl fragments or longer C-C bond sequences, some correlation between calculated and experimental trends in angles is found, in contrast to the bond lengths for which the two sets of data are in complete disagreement. The results confirm experiences often made in crystallography. That is, effects of temperature, crystal structure and packing, and molecular volume effects are manifested more clearly in bond lengths than bond angles which depend mainly on intramolecular properties. Frequency analyses of the tau(1), tau(2) and tau(3) torsional angles in the crystal structures show conformational steering in the sense that, if tau(1) is rrans peri-planar (170 degrees less than or equal to tau(1) less than or equal to 180 degrees less than or equal to 180 degrees less than or equal to tau(1) less than or equal to -170 degrees), the values of tau(2) and tau(3) are clustered closely around the ideal gauche (+/-60 degrees) and trans (+/-180 degrees) positions. In contrast, when tau(1) is in the region (50 degrees less than or equal to tau(1) less than or equal to 70 degrees), there is a definite increase in the populations of tau(2) and tau(3) at -90 and -150 degrees.

Journal of Molecular Structure-Theochem
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