Application of Charge Density Methods to a Protein Model Compound: Calculation of Coulombic Intermolecular Interaction Energies from the Experimental Charge Density

A combined experimental and theoretical charge density study of the pentapeptide Boc-Gln-d-Iva-Hyp-Ala-Phol (Boc, butoxycarbonyl; Gln, glutamine; Iva, isovaline; Hyp, hydroxyproline; Ala, ethylalanine; Phol, phenylalaninol) is described. The experimental analysis, based on synchrotron x-ray data collected at 20 K, is combined with ab initio theoretical calculations. The topologies of the experimental and theoretical densities are analyzed in terms of the atoms in molecules quantum theory. Topological parameters, including atomic charges and higher moments integrated over the atomic basins, have been evaluated with the program topxd and are used to calculate the electrostatic interactions between the molecules in the crystal. The interaction energies obtained after adding dispersive and repulsive van der Waals contributions agree quite well with those based on M-B3LYP/6-31G** dimer calculations for two of the three dimers in the crystal, whereas for the third a larger stabilization is obtained than predicted by the calculation. The agreement with theory is significantly better than that obtained with multipole moments derived directly from the aspherical atom refinement. The convergence of the interaction as a function of addition of successively higher moments up to and including hexadecapoles (l = 4) is found to be within 2-3 kJ/mol. Although shortcomings of both the theoretical and experimental procedures are pointed out, the agreement obtained supports the potential of the experimental method for the evaluation of interactions in larger biologically relevant molecules.