On evaluation of electrostatic interaction energies in molecular crystals within the pseudoatom electron density formalism

Abstract

X-ray crystallography is considered to be one of the most accurate and reliable techniques for determination of the atomic and molecular structure of crystals. Whenever high-resolution low-temperature data are available, it is also possible to model the molecular aspherical electron density distribution, ρ(r). In the field of experimental X-ray charge density determination, the electron density at each point in space ρ(r) is modelled as a superposition of atomic-like densities ρ_a (r), called pseudoatoms [Hirshfeld, F. L. (1971). Acta Cryst. B27, 769-781; Stewart, R. F. (1976). Acta Cryst. A32, 565-574; Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909–921]: ρ(r)=∑_a▒〖ρ_a (r-R_a)〗, where R_a denotes the location of the nucleus of pseudoatom a. This thesis consists of three studies that describe newly-developed techniques for fast and accurate evaluation of the electrostatic interaction energies in molecular dimers and infinite crystal structures in which the charge distributions are modelled using the Hansen-Coppens pseudoatom formalism [Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909–921]. For example, using a 2015 2.8 GHz Intel Xeon E3-1505M v5 computer processor, our Fortran-based implementation evaluates the electrostatic interaction energy between two monomers of a benchmark 181-atom decapeptide molecule in under 3 seconds with a precision of at least 10-5 kJ/mol. Using the enhanced Ewald-summation technique which includes interactions up to the hexadecapolar level, the electrostatic intermolecular interaction energy in a crystal of the same 181-atom decapeptide molecule with a total of 724 atoms in the unit cell (Z=4, space group P212121) is calculated with the same precision in under 50 seconds. In addition to being fast, the described methods correctly account for the electron density penetration effects arising from overlap of the neighbouring charge distributions (a common feature of molecular crystals) which contribute 30-60% to the total electrostatic energy in the examined molecular systems, and thus cannot be neglected. While electron densities of the benchmark compounds used in our studies were generated using the University at Buffalo theoretical databank of transferable pseudoatoms [Dominiak, P. M., Volkov, A., Li, X., Messerschmidt, M. & Coppens, P. (2007). J. Chem. Theory Comput. 3, 232-247], the described implementations are directly applicable to electron densities determined from experimental X-ray diffraction experiments.