Analysis of the pyramidalization of the peptide group nitrogen: Implications for molecular mechanics energy functions

Pyramidalization at the peptide group nitrogen atom is analyzed using N-methylacetamide (NMA) as a model molecule. Mutually orthogonal peptide CN torsion and NH out-of-plane bend coordinates are necessary for a correct description of the energetics of nonplanar deformations of the peptide group. Using such coordinates, ab initio calculations at the MP2/6-31++G(d,p) level of theory show that the energy minimum of the NH out-of-plane bend angle shifts significantly away from zero for nonzero CN torsion angles. Not being due to nonbonded interactions alone, this energy behavior needs to be taken explicitly into account in molecular mechanics force fields. By use of different schemes for calculating potential-derived atomic charges, the charge distribution of NMA was also investigated in connection with the pyramidalization. Large variations in the charges were found as a function of the NH out-of-plane angle. These could not be reproduced only by polarization through the (molecular mechanics) electric field. An enhanced electrostatic model, using geometry-dependent charges (charge fluxes) is shown to provide a satisfactory physical description of this effect.