Investigation of Intramolecular Interactions in N-Alkanes - Cooperative Energy Increments Associated with Gg and Gtg' Sequences

by Tsuzuki, S.; Schafer, L.; Goto, H.; Jemmis, E. D.; Hosoya, H.; Siam, K.; Tanabe, K.; Osawa, E.

Energies of rotational isomers of n-alkanes are largely determined by the number of individual gauche bonds (G). However, according to molecular mechanics calculations (MM2), within a group of rotamers with equal number of G bonds, there are characteristic energy variations due to cooperative effects involving sequences of several bonds. For example, the energy is increased by inserting a trans bond (T) between two consecutive G bonds of the same sign (e.g., TGGG < GTGG in n-heptane), and special long-range repulsive interactions seem to exist between G and G', a gauche bond of opposite sign, in a GTG' sequence (e.g., GTG < GTG' in n-hexane). With use of ab initio MP4SDQ/6-31G*//6-31G* energies and geometries of ethane to n-hexane, including all rotamers, a 0.16 kcal/mol stabilizing energy increment is found to be characteristic for GG sequences. The potential source of this increment is found in nonbonded attractive interactions between 1,5-CH3/CH3, -CH3/CH2, and -CH2/CH2 groups, which are specific for GG but not for other combinations, such as GT, TT, or GG'. In addition, a 0.12 kcal/mol destabilizing energy increment is found to be associated with GTG' sequences relative to GTG. It is rationalized by unfavorable nonbonded interactions that can be relaxed in GTG but not in GTG' due to symmetry constraints. Whereas these cooperative energy increments are small for a single GG or GTG' sequence, their accumulation in polymers can be considerable. The GG' equilibrium structure of n-pentane belongs to the C1 point group due to unequal C-C-C-C dihedral angles (+/- 63 and +/- 95-degrees). A symmetric GG' conformer (C(s)) is 0.28 kcal/mol above the GG' energy minimum and is identified as a saddle point. In contrast to a generally accepted rule, the lack of local symmetry in GG' sequences implies the possible existence of more than 3n rotamers for alkanes with n rotatable bonds. Good agreement is found for the order of MM2 and ab initio conformational energies. The results of this study are also of general interest, because they demonstrate one of the factors that can contribute to errors in conformational energies at the SCF level: Different conformations of a molecule may differ in stabilizing van der Waals interactions whose neglect leads to errors in all energy calculations that do not include dispersion forces.

Journal of the American Chemical Society
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1520-5126; 0002-7863