Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals

Experimental and theoretical studies of electron densities and the corresponding derived entities such as electrostatic potentials have been the primary means of understanding the chemical nature and electronic properties of crystalline substances. Conventional crystal calculation methods such as the embedded cluster models are capable of performing calculations on small and medium-sized molecules, while periodic ab initio methods can treat crystals with up to 200 atoms per unit cell. A linear scaling method, viz. the molecular tailoring approach, has recently been developed for obtaining ab initio quality one-electron properties. In the present study, the molecular tailoring approach is employed to generate electron density, electrostatic potential and interaction density maps with the ibuprofen crystal as a test case. The interaction density and electrostatic potential maps produced in the present work succinctly bring out the actual crystalline environment around a given reference molecule by including the interactions with atoms in its neighborhood. The results obtained from the molecular tailoring approach may thus be expected to enhance our understanding of the environment in the crystalline material with reasonably small computational effort.Contribution to the Jacopo Tomasi Honorary Issue     

Critical analysis and extension of the Hirshfeld atoms in molecules

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges.     

Dipole and quadrupole moments of molecules in crystals: a novel approach based on integration over Hirshfeld surfaces

Elegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic Hartree-Fock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%-40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zero-flux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zero-flux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement.     

Wave functions derived from experiment. V. Investigation of electron densities,electrostatic potentials,and electron localization functions for noncentrosymmetric crystals

The constrained Hartree-Fock method using experimental X-ray diffraction data is extended and applied to the case of noncentrosymmetric molecular crystals. A new way to estimate the errors in derived properties as a derivative with respect to added Gaussian noise is also described. Three molecular crystals are examined: ammonia [NH(3)], urea [CO(NH(2))(2)], and alloxan [(CO)(4)(NH)(2)]. The energetic and electrical properties of these molecules in the crystalline state are presented. In all cases, an enhancement of the dipole moment is observed upon application of the experimental constraint. It is found that the phases of the structure factors are robustly determined by the constrained Hartree-Fock model, even in the presence of simulated noise. Plots of the electron density, electrostatic potential, and the electron localization function for the molecules in the crystal are displayed. In general, relative to the Hartree-Fock model, there is a depletion of charge around hydrogen atoms and lone pair regions, and a build-up of charge within the molecular framework near nuclei, directed along the bonds. The electron localization function plots reveal an increase in the pair density between vicinal hydrogen atoms.     

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.     

Effect of SDBS solution on the surface potential properties of the Zhaozhuang coal

It is of great significance to study the effect of surfactants on the coal surface potential for effective dust suppression in mining faces. The effect of different concentrations of sodium dodecyl benzene sulfonate (SDBS) solution on the surface potential of the Zhaozhuang coal was measured by atomic force microscopy (AFM). The experimental results show that the SDBS solution has significant influence on the surface potential of the Zhaozhuang coal. The electrical characteristics of the coal surface at the nanometer scale are different from those of macroscopic or the mesoscopic level. The surface potential of coal is basically a normal distribution, showing certain electrical characteristics. The mean value of the surface potential of the Zhaozhuang coal is increased with the increase in concentration of the SDBS solution; when the concentration of the SDBS solution is 0.3%, the mean value of surface potential is 5.59 mv, which is about two times of the mean value of the surface potential without SDBS solution added. With the increase of the concentration of the SDBS solution, the maximum value of the surface potential of the Zhaozhuang coal increases, and the minimum value decreases. It shows that the SDBS solution has a significant effect on the potential distribution law and the magnitude of the coal surface. Subsequently, on the basis of the constructed Zhaozhuang coal macromolecule model, xtb and Multiwfn simulation software were used to calculate the molecular surface electrostatic potential value and electron density value of the Zhaozhuang coal molecules after adding water molecules. The variation law for the electrostatic potential surface of the molecule was obtained after adding numbers of water molecules to the surface of the coal molecule. The simulation results show that the area proportion of absolute molecular surface electrostatic potential greater than 10 kcal/mol is increased with the growth in the number of water molecules, while the area proportion of absolute molecular surface electrostatic potential less than 10 kcal/mol is decreased. Because of the free state O─H bond polarity of water molecules, the charges on the molecular surface are rearranged in order to change the electron density on the surface of coal molecules, which affects the overall electrostatic potential of the configuration.     

On the interplay between CH...O and OH...O interactions in determining crystal packing and molecular conformation: an experimental and theoretical charge density study of the fungal secondary metabolite austdiol (C12H12O5)

The total experimental electron density rho(r), its Laplacian inverted delta(2)rho(r), the molecular dipole moment, the electrostatic potential phi(r), and the intermolecular interaction energies have been obtained from an extensive set of single-crystal X-ray diffracted intensities, collected at T = 70(1) K, for the fungal metabolite austdiol (1). The experimental results have been compared with theoretical densities from DFT calculations on the isolated molecule and with fully periodic calculations. The crystal structure of (1) consists of zigzag ribbons extended along one cell axis and formed by molecules connected by both OH...O and CH...O interactions, while in a perpendicular direction, adjacent molecules are linked by short CH...O intermolecular contacts. An extensive, quantitative study of all the intra- and intermolecular H...O interactions, based not only on geometrical criteria, but also on the topological analysis of rho(r), as well as on the evaluation of the pertinent energetics, allowed us (i) to assess the mutual role of OH...O and CH...O interactions in determining molecular conformation and crystal packing; (ii) to identify those CH...O contacts which are true hydrogen bonds (HBs); (iii) to determine the relative hydrogen bond strengths. An experimental, quantitative evidence is given that CH...O HBs are very similar to the conventional OH...O HBs, albeit generally weaker. The comparison between experimental and theoretical electric dipole moments indicates that a noticeable charge rearrangement occurs upon crystallization and shows the effects of the mutual cooperation of HBs in the crystal. The total intermolecular interaction energies and the electrostatic energy contribution obtained through different theoretical methods are reported and compared with the experimental results. It is found that the new approach proposed by Spackman, based on the use of the promolecular charge density to approximate the penetration contribution to intermolecular electrostatic energies, predicts the correct relative electrostatic interaction energies in most of the cases.     

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)_max = 1.143 Å⁻¹ are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ^–3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long–range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least–squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Electron density,electrostatic potential,and spatial organization of ammonium hydrooxalate oxalic acid dihydrate heteromolecular crystal from data of diffraction experiment at 15 K using synchrotron radiation and theoretical calculations

A high-precision diffraction study at 15 K using synchrotron radiation and theoretical calculation of a heteromolecular crystal ammonium hydrooxalate oxalic acid dihydrate NH₄ ⁺·C₂HO₄ ^?·C₂H₂O₄·2H₂O (1) were carried out. The calculation was performed with the Kohn-Sham method taking into account periodic boundary conditions. The joint experimental and theoretical study allowed one to locate positions of hydrogen atoms and to reliably establish peculiar features of the electron density and electrostatic potential distributions in 1. Interatomic and molecular interactions were characterized based on the electron density properties within the framework of a quantum topological theory. The bond order indices were calculated from the experimental electron density without using the orbital notions. A new approach based on visualization of the ellipsoids whose semiaxes depend on the principal values of the electron density curvature at the bond critical points was used. It was found that charge transfer between ammonium cation and hydrooxalate anion in 1 dominates other electrostatic interactions in the crystal. Based on analysis of peculiar features of the electron density and electrostatic potential distributions in the crystal of 1, it was found that spatial organization of the crystal in hand is also governed by one more, weaker, electrostatic factor that originated from the presence of well-localized regions behind protons on the extensions of the lines of covalent bonds at the periphery of the molecules. In those regions, the electrostatic potential is higher than in other directions due to anisotropy of the electron density distribution. This feature mainly ensures directed complementary electrostatic interaction between corresponding fragments with negatively charged regions of neighboring molecules, such as the lone electron pairs and p-electrons.     

Surface-integral QSPR models: local energy properties

Surface-integral models based on AM1 semiempirical molecular orbital calculations are presented for the free energies of solvation in water, n-octanol, and chloroform and for the enthalpy of solvation in water. A parametrized function of four local properties calculated at the isodensity surface (the molecular electrostatic potential, local ionization energy, electron affinity, and polarizability) is integrated over the triangulated surface area to obtain the target quantity. The resulting models give results only slightly less accurate than those reported for parametrized generalized Born/polar surface area models despite relying only on gas-phase calculations. The water and octanol free-energy models were validated by calculating the water-octanol partition coefficient for a test set of organic compounds with moderate success. The models lead to a local solvation energy, which can be projected onto the molecular isodensity surface and provides insight into "hot" areas for solvation in water or the other solvents.     

Experimental electron density study of a complex between copper(II) and the antibacterial quinolone family member ciprofloxacin

An experimental charge density study of a 1 : 1 complex of Cu-cfx (cfx = ciprofloxacin), 1 [Cu(cfx)(H(2)O)(3)]SO4.2H(2)O, has been performed using single-crystal X-ray diffraction data collected at 100 K using conventional Mo Kalpha radiation. Metal-ligand (ML) bonds and hydrogen bonds (HBs) have been analysed using topological analysis of the electron density with the atoms in molecules (AIM) approach. The copper atom binds to two oxygen atoms in one end of the zwitterionic form of the cfx molecule, in addition to forming bonds with three water molecules, forming a square pyramidal coordination geometry. AIM decomposition of the experimental electron density establishes that the copper atom binds more strongly to the cfx molecule than to the water molecules, suggesting that the latter can be detached leaving behind a reactive, water-free Cu-cfx complex available for interaction with e.g. a macromolecular site. AIM analysis of the extensive hydrogen bond pattern reveals that the positively charged N-end of the zwitterionic cfx forms a relatively strong N-H-O hydrogen bond implying that this region of cfx may play an important role in the docking process in the active site. Visualisation and statistics of selected density derived properties on the molecular surface of the isolated cfx molecule vs its metal complexed counterpart points out regions of potential reactivity. The effect of the fluorine atom is to expand the negative region of the electrostatic potential, while the nitrogen end is heavily electropositive and willingly donates to--for molecular docking purposes--relatively strong hydrogen bonding. The Cu atom is highlighted as a potentially highly reactive site which is likely to interact strongly with any given negative ligand.     

To What Extent are “Atoms in Molecules” Structures of Hydrocarbons Reproducible from the Promolecule Electron Densities?

The “atoms in molecules” structures of 225 unsubstituted hydrocarbons are derived from both the optimized and the promolecule electron densities. A comparative analysis demonstrates that the molecular graphs derived from these two types of electron densities at the same geometry are equivalent for almost 90 % of the hydrocarbons containing the same number and types of critical points. For the remaining 10 % of molecules, it is demonstrated that by inducing small perturbations, through the variation of the used basis set or slight changes in the used geometry, the emerging molecular graphs from both densities are also equivalent. Interestingly, the (3, ?1) critical point between two “non‐bonded” hydrogen atoms, which triggered “H?H bonding” controversy is also observed in the promolecule densities of certain hydrocarbons. Evidently, the topology of the electron density is not dictated by chemical bonds or strong interactions and deformations induced by the interactions of atoms in molecules have a quite marginal role, virtually null, in shaping the general traits of the topology of molecular electron densities of the studied hydrocarbons, whereas the key factor is the underlying atomic densities.     

Advances in electric field and atomic surface derived properties from experimental electron densities

The present study is devoted to a general use of the Gauss law. This is applied to the atomic surfaces derived from the topological analysis of the electron density. The method proposed here is entirely numerical, robust and does not necessitate any specific parametrization of the atomic surfaces. We focus on two fundamental properties: the atomic charges and the electrostatic forces acting on atoms in molecules. Application is made on experimental electron densities modelized by the Hansen-Coppens model from which the electric field is derived for a heterogenic set of compounds: water molecule, NO(3) anion, bis-triazine molecule and MgO cluster. Charges and electrostatic forces are estimated by the atomic surface flux of the electric field and the Maxwell stress tensor, respectively. The charges obtained from the present method are in good agreement with those issued from the conventional volume integration. Both Feynman and Ehrenfest forces as well as the electrostatic potential at the nuclei (EPN) are here estimated from the experimental electron densities. The values found for the molecular compounds are presented and discussed in the scope of the mechanics of atomic interactions.