Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Abstract

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid-1980s it was shown that the pseudoatom model commonly used in experimental X-ray charge density studies can be easily combined with the Buckingham-type approach for calculation of electrostatic interactions, plus atom-atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom-atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical singlemolecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of ␣-glycine, N-acetylglycine and L-(ϩ)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the MorokumaZiegler energy decomposition scheme. For ␣-glycine a comparison with direct "pixel-by-pixel" integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma-Ziegler partitioning, Gavezzotti's method, and the Buckingham approach with atoms-in-molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.

Molecular Recognition in Organic Crystals: Directed Intermolecular Bonds or Nonlocalized Bonding?

“…This reliability has been shown in detailed comparisons with the results of elaborate quantum mechanical calculations or of experimental electron-density measurements for glycine. [39] The repulsion energy is taken to be proportional to the overlap integral of the electron densities (calculated by numerical integration over the original uncondensed pixel grid), elevated to a power slightly smaller than one. This procedure requires at least two empirical parameters, the proportionality constant and the exponent, which are not always easy to determine.…”

Hierarchies of Intermolecular Potentials and Forces: Progress Towards a Quantitative Evaluation

“…The crystalline edifice takes that small amount of strain without apparent difficulty. In fact, the crystal structure of a fully charged species like the glycine zwitterion shows largely destabilizing near-neighbor partners [21,29]. In crystals, this fact is more and more unavoidable as the net charge of the constituting molecules increase (think of sodium chloride).…”

Dependence of the Intermolecular Electrostatic Interaction Energy on the Level of Theory and the Basis Set

“…4 We have recently embarked on a quest for an accurate yet efficient evaluation of electrostatic interaction energies in molecular complexes. 5 In widely used force field approaches, E es is commonly calculated with a multipole or Buckingham-type approximation: 2,6 where q, µ, Θ, etc. are the permanent atomic moments (monopole, dipole, quadrupole, etc.)…”