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

The molecular structures of n-hexane were determined by RHF/4-21G ab initio geometry optimization at 30° grid points in its three-dimensional τ₁(C11–C8–C5–C1), τ₂(C14–C11–C8–C5), τ₃(C17–C14–C11–C8) conformational space. Of the resulting 12×12×12=1728 grid structures, 468 are symmetrically non-equivalent and were optimized constraining the torsions τ₁, τ₂, and τ₃ 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, |P|=[(∂P/∂τ_i)²+(∂P/∂τ_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 τ₁, τ₂ and τ₃ torsional angles in the crystal structures show conformational steering in the sense that, if τ₁ is trans peri-planar (170°≤τ₁≤180°; −180°≤τ₁≤−170°), the values of τ₂ and τ₃ are clustered closely around the ideal gauche (±60°) and trans (±180°) positions. In contrast, when τ₁ is in the region (50°≤τ₁≤70°), there is a definite increase in the populations of τ₂ and τ₃ at −90 and −150°.