On the structure and dynamics of secondary n-alkyl cations

Abstract

A variety of computational studies was undertaken to examine and establish the relative importance of open versus closed structures for unbranched secondary n-alkyl cations. First, the PW91 level of density functional theory was used to optimize over 20 minimum-energy structures of sec-pentyl, sec-hexyl, and sec-heptyl ions, demonstrating that closed structures are more stable than open ones on the potential energy surface (PES). Second, PW91 was used with a theoretical Andersen thermostat to perform a molecular dynamics simulation (150 ps) of C9H19+ at a typical catalytic temperature of 800 K, demonstrating that the structure preference is inverted on the free-energy surface. Third, both quantum (rigid-rotor/harmonic oscillator) and classical partition functions were used to demonstrate that the simulated structure-opening at catalytic temperatures is due to the floppiness of the open forms, which improves its free energy by both lowering its zero-point vibrational energy and increasing its molecular entropy. The particular conformer of the preferred open form (at 800 K) is dependent on length of alkyl ion, with pentyl ions preferring syn/anti structures but longer ions preferring open-clinal ones. These results, plus an additional set of PES optimized structures from an alternative level of theory (MP2/6-31G(d,p)), are used to discuss the likely nature of secondary n-alkyl ions.