Charge Density  & Intermolecular Interactions

Christian Jelsch

Laboratoire Cristallographie Résonance Magnétique et Modélisations

CNRS & Université de Lorraine, CRM2.   54500,  Nancy, France.

E-mail:  christian.jelsch@univ-lorraine.fr

 Charge-density studies from single-crystal X-ray diffraction at ultra-high-resolution have become a powerful tool in modern crystallography to understand solid state properties of chemical compounds. To overcome a time-consuming process or an impossible experiment due to insufficient quality of the crystal diffraction, the molecular electron density can be reconstructed by using databases of multipolar atoms such as ELMAM2 (Domalaga et al., 2012), Invariom (Dittrich et al. 2013) and UBDB/MATTS (Bojarowski et al., 2022). This applies notably to biological macromolecules such as proteins and nucleic acids. This transferability approximation assumes however that the atomic electron density is not influenced by the surrounding atoms.  Within the framework of our software MoPro (Jelsch et al., 2005), the polarization of the transferred electron density by its immediate environment can now be accomplished using a database of anisotropic polarizabilities (Leduc et al., 2019). 

The electrostatic properties of molecules can be accurately computed from the multipolar description of atoms using the Hansen & Coppens (1978) model. We have found that the specific charge density of alcohols, phenols and carboxyl group does influence the stereochemistry of hydrogen bonds to oxygen acceptors (Ahmed et al., 2013). Electrostatic energy between molecules or between groups of atoms can be computed as the molecular charge density is considered as a summation over its constituting atoms.  

The numerical exact potential and multipole moment (nEP/MM) method initially implemented in VMoPro program is time-consuming since it performs a 3D integration to obtain the electrostatic energy at short interaction distances. Nguyen et al. (2018) reported a fully analytical computation of the electrostatic interaction energy (aEP/MM). This method performs much faster than nEP/MM (up to two orders of magnitude) and remains highly accurate. A new program library, Charger, contains an implementation of the aEP/MM method and is incorporated in the MoProViewer software (Vukovic et al., 2021). The protein glutathione transferase (GST) in complex with benzophenone ligands was studied due to the availability of both structural and thermodynamic data. The resulting analysis highlights the residues that stabilize the ligand but also those that hinder ligand binding from an electrostatic point of view.

The second part of the talk will be focused on the decomposition of the crystal contacts on the Hirshfeld surface between pairs of interacting chemical species which enables to derive a contact enrichment ratio (Jelsch et al., 2014, 2017). This descriptor yields information on the propensity of chemical species to interact with themselves and other species. The enrichment ratios are obtained by comparing the actual and equiprobable contacts and can be readily obtained with MoProViewer software, using the Hirshfeld surface analysis tool. Strong and weak hydrogen bonds appear generally enriched, depending on the context.

The electrostatic energy of contacts was also computed using a multipolar atom model and combined statistically to the contact enrichment ratios. The analyses suggest that hydrogen bonds are often the most enriched and attractive interactions and are a therefore a driving force in the crystal packing formation for organic molecules. The methodology also enables to compare different types of hydrogen bonds which are in competition within crystal packings. The behaviour of weaker interactions is less contrasted and will be discussed.

REFERENCES:

Ahmed, M., Jelsch, C., Guillot, B., Lecomte, C., & Domagała, S. (2013). Relationship between stereochemistry and charge density in hydrogen bonds with oxygen acceptors. Crystal growth & design, 13(1), 315-325.

Bojarowski, S. A., Gruza, B., Trzybiński, D., Kamiński, R., Hoser, A. A., Kumar, P., ... & Dominiak, P. M. (2022). New refinement strategies for pseudoatom databank-towards wider range of application.

Dittrich, B., Hübschle, C. B., Pröpper, K., Dietrich, F., Stolper, T., & Holstein, J. (2013). The generalized invariom database (GID). Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials, 69(2), 91-104.

Domagała, S., Fournier, B., Liebschner, D., Guillot, B., & Jelsch, C. (2012). An improved experimental databank of transferable multipolar atom models–ELMAM2. Construction details and applications. Acta Crystallographica Section A: Foundations of Crystallography, 68(3), 337-351.

Hansen, N. K., & Coppens, P. H. I. L. I. P. (1978). Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr. A34, 909-921.

Jelsch, C., Guillot, B., Lagoutte, A., & Lecomte, C. (2005). Advances in protein and small-molecule charge-density refinement methods using MoPro. Journal of applied crystallography, 38(1), 38-54.

Jelsch, C., Ejsmont, K., & Huder, L. (2014). The enrichment ratio of atomic contacts in crystals, an indicator derived from the Hirshfeld surface analysis. IUCrJ, 1(2), 119-128.

Jelsch, C., & Bibila Mayaya Bisseyou, Y. (2017). Atom interaction propensities of oxygenated chemical functions in crystal packings. IUCrJ, 4(2), 158-174.

Leduc, T., Aubert, E., Espinosa, E., Jelsch, C., Iordache, C., & Guillot, B. (2019). Polarization of Electron Density Databases of Transferable Multipolar Atoms. The Journal of Physical Chemistry A, 123, 7156-7170.

Nguyen, D., Kisiel, Z., & Volkov, A. (2018). Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. I. The Löwdin α-function method. Acta Crystallogr. A74, 524-536.

Vuković, V., Leduc, T., Jelić-Matošević, Z., Didierjean, C., Favier, F., Guillot, B., & Jelsch, C. (2021). A rush to explore protein–ligand electrostatic interaction energy with Charger. Acta Crystallogr D77. 1292-1304