Cis-Trans Energy Difference for the Peptide Bond in the Gas Phase and in Aqueous Solution

Ab initio molecular orbital calculations and Monte Carlo statistical mechanics simulations have been used to study the cis-trans equilibrium for N-methylacetamide (NMA) in the gas phase and in dilute aqueous solution. Geometry optimizations were carried out with the 6-31G(d) basis set for the cis and trans forms of NMA. After calculation of the correlation energies with second-order M⊘ller-Plesset theory and the vibrational frequencies, the computed ΔH²⁹⁸ and ΔG²⁹⁸ favor the trans form by 2.1 and 2.5 kcal/mol in the gas phase. Then, in order to proceed to the simulations in water, the predictions of the OPLS potential functions were compared to results of 6-31G(d) ab initio calculations for complexes of cis- and trans-N-methylformamide (NMF) with a single water molecule. This revealed that the OPLS functions erroneously favor the hydrogen bond to the N-H group in the trans form by ca. 1.3 kcal/mol in comparison to the cis. Compensation requires the use of slightly different charge distributions for the cis and trans forms, which are consistent with the order of the ab initio dipole moments (μ_cis > μ_trans). Statistical perturbation theory was then applied in Monte Carlo simulations using 216 TIP4P water molecules to compute the difference in free energies of hydration as trans-NMA is converted to cis-NMA at 298 K. If the OPLS parameters are used for both the cis and trans conformers, the trans isomer is computed to be better hydrated by 2.2 ± 0.3 kcal/mol. However, utilization of the refined charge distributions yields no statistically significant difference in the free energies of hydration (0.1 ± 0.3 kcal/mol favoring trans). These findings emphasize the sensitivity of such results to the details of the intermolecular potential functions. For NMA, the predicted free energy difference of 2.6 ± 0.3 kcal/mol in water is in accord with NMR results (2.5 ± 0.4 kcal/mol), and the negligible solvent effect is consistent with the observed insensitivity of the cis-trans equilibria for NMA and NMF to changes in solvent.