Theoretical Calculation of a Solution Phase Torsional Free Energy Profile. π-Ethylimidazole in Water

Abstract

Ab initio molecular orbital calculations, in conjunction with Monte Carlo statistical mechanics simulations, have been used to calculate the torsional free energy profile for π-ethylimidazole in aqueous solution. Geometry optimisations were carried out with 3–21G and 6–31G* basis sets on various conformational forms of π-ethylimidazole. Electron correlation energies were calculated from the 6–31G* optimised geometries using Møller-Plesset second order perturbation theory and single point calculations with the STO-3G basis set were used to obtain an estimate of atomic polarisation effects. Gas phase torsional energy barriers were found to be small; ∼7–8kJmol⁻¹ for the principal barrier and ∼4.5–5.5 kJmol⁻¹ for the subsidiary barrier. Free energy perturbation theory was then applied in Monte Carlo simulations to examine the effect of solvation on the calculated gas phase torsional energy profile. The variable torsion angle of a single π-ethylimidazole molecule in a periodic box of 505 TIP4P water molecules was changed in discrete steps from 0° to 180° and the incremental free energy changes calculated. The calculated solution phase free energy results were of high precision and showed that solvation raised the principal torsional barrier (τ = 180°) by 1.8kJmol⁻¹ and moved the subsidiary barrier from τ= 45° to τ= 0°. The small free energy changes calculated were found to be the result of small differences between much larger enthalpy and entropy changes. Enthalpic and entropic effects were partly rationalised in terms of solute-solvent radial distribution functions although solvation effects were considerably more complex than expected.