Application of charge density methods to a protein model compound: calculation of Coulombic intermolecular interaction energies from the experimental charge density

Towards the use of experimental electron densities to estimate reliable lattice energies

Lattice energies derived from experimental charge densities are critically assessed, with a view to encouraging further research of this nature.

Topological characterization of electron density, electrostatic potential and intermolecular interactions of 2-nitroimidazole: an experimental and theoretical study

An experimental charge density distribution of 2-nitroimidazole was determined from high-resolution X-ray diffraction and the Hansen-Coppens multipole model. The 2-nitroimidazole compound was crystallized and a high-angle X-ray diffraction intensity data set has been collected at low temperature (110 K). The structure was solved and further, an aspherical multipole model refinement was performed up to octapole level; the results were used to determine the structure, bond topological and electrostatic properties of the molecule. In the crystal, the molecule exhibits a planar structure and forms weak and strong intermolecular hydrogen-bonding interactions with the neighbouring molecules. The Hirshfeld surface of the molecule was plotted, which explores different types of intermolecular interactions and their strength. The topological analysis of electron density at the bond critical points (b.c.p.) of the molecule was performed, from that the electron density ρ_bcp(r) and the Laplacian of electron density ∇²ρ_bcp(r) at the b.c.p.s of the molecule have been determined; these parameters show the charge concentration/depletion of the nitroimidazole bonds in the crystal. The electrostatic parameters like atomic charges and the dipole moment of the molecule were calculated. The electrostatic potential surface of the molecule has been plotted, and it displays a large electronegative region around the nitro group. All the experimental results were compared with the corresponding theoretical calculations performed using CRYSTAL09.

Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges

Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.

Contributions of charge-density research to medicinal chemistry

This article reviews efforts in accurate experimental charge-density studies with relevance to medicinal chemistry. Initially, classical charge-density studies that measure electron density distribution via least-squares refinement of aspherical-atom population parameters are summarized. Next, interaction density is discussed as an idealized situation resembling drug-receptor interactions. Scattering-factor databases play an increasing role in charge-density research, and they can be applied both to small-molecule and macromolecular structures in refinement and analysis; software development facilitates their use. Therefore combining both of these complementary branches of X-ray crystallography is recommended, and examples are given where such a combination already proved useful. On the side of the experiment, new pixel detectors are allowing rapid measurements, thereby enabling both high-throughput small-molecule studies and macromolecular structure determination to higher resolutions. Currently, the most ambitious studies compute intermolecular interaction energies of drug-receptor complexes, and it is recommended that future studies benefit from recent method developments. Selected new developments in theoretical charge-density studies are discussed with emphasis on its symbiotic relation to crystallography.

Progress in the understanding of drug-receptor interactions, part 2: experimental and theoretical electrostatic moments and interaction energies of an angiotensin II receptor antagonist (C30H30N6(O)3S)

A combined experimental and theoretical charge density study of an angiotensin II receptor antagonist (1) is presented focusing on electrostatic properties such as atomic charges, molecular electric moments up to the fourth rank and energies of the intermolecular interactions, to gain an insight into the physical nature of the drug-receptor interaction. Electrostatic properties were derived from both the experimental electron density (multipole refinement of X-ray data collected at T=17 K) and the ab initio wavefunction (single molecule and fully periodic calculations at the DFT level). The relevance of SO and SN intramolecular interactions on the activity of 1 is highlighted by using both the crystal and gas-phase geometries and their electrostatic nature is documented by means of QTAIM atomic charges. The derived electrostatic properties are consistent with a nearly spherical electron density distribution, characterised by an intermingling of electropositive and -negative zones rather than by a unique electrophilic region opposed to a nucleophilic area. This makes the first molecular moment scarcely significant and ill-determined, whereas the second moment is large, significant and highly reliable. A comparison between experimental and theoretical components of the third electric moment shows a few discrepancies, whereas the agreement for the fourth electric moment is excellent. The most favourable intermolecular bond is show to be an NHN hydrogen bond with an energy of about 50 kJ mol(-1). Key pharmacophoric features responsible for attractive electrostatic interactions include CHX hydrogen bonds. It is shown that methyl and methylene groups, known to be essential for the biological activity of the drug, provide a significant energetic contribution to the total binding energy. Dispersive interactions are important at the thiophene and at both the phenyl fragments. The experimental estimates of the electrostatic contribution to the intermolecular interaction energies of six molecular pairs, obtained by a new model proposed by Spackman, predict the correct relative electrostatic energies with no exceptions.

Dipole Moment Enhancement in Molecular Crystals from X-ray Diffraction Data

Although reliable determination of the molecular dipole moment from experimental charge density analyses on molecular crystals is a challenging undertaking, these values are becoming increasingly common experimental results. We collate all known experimental determinations and use this database to identify broad trends in the dipole moment enhancements implied by these measurements as well as outliers for which enhancements are pronounced. Compelling evidence emerges that molecular dipole moments from X-ray diffraction data can provide a wealth of information on the change in the molecular charge distribution that results from crystal formation. Most importantly, these experiments are unrivalled in their potential to provide this information in such detail and deserve to be exploited to a much greater extent. The considerable number of experimental determinations now available has enabled us to pinpoint those studies that merit further attention, either because they point unequivocally to a considerable enhancement in the crystal (of 50 % or more), or because the experimental determinations suggest enhancements of 100 % or more--much larger than independent theoretical estimates. In both cases further detailed experimental and theoretical studies are indicated.

Quantum chemical studies of protein structure

Quantum chemical methods now permit the prediction of many spectroscopic observables in proteins and related model systems, in addition to electrostatic properties, which are found to be in excellent accord with those determined from experiment. I discuss the developments over the past decade in these areas, including predictions of nuclear magnetic resonance chemical shifts, chemical shielding tensors, scalar couplings and hyperfine (contact) shifts, the isomer shifts and quadrupole splittings in Mössbauer spectroscopy, molecular energies and conformations, as well as a range of electrostatic properties, such as charge densities, the curvatures, Laplacians and Hessians of the charge density, electrostatic potentials, electric field gradients and electrostatic field effects. The availability of structure/spectroscopic correlations from quantum chemistry provides a basis for using numerous spectroscopic observables in determining aspects of protein structure, in determining electrostatic properties which are not readily accessible from experiment, as well as giving additional confidence in the use of these techniques to investigate questions about chemical bonding and chemical reactions.

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

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 single-molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of alpha-glycine, N-acetylglycine and L-(+)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the Morokuma-Ziegler energy decomposition scheme. For alpha-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.