Theoretical studies of thermal decomposition of anhydrous cadmium and silver oxalates

The results of first principles calculations of band structure, density of states and electron density topology of CdC₂O₄ and Ag₂C₂O₄ crystals are presented. The calculations have been performed with WIEN2k ab initio program, using highly precise full potential linearized augmented plane wave (FP LAPW) method within Density Functional Theory formalism. The obtained SCF electron density has been used in calculations of Bader’s AIM (atoms in molecules) topological properties of the electron density in crystal. The obtained results show important similarities in electronic structure and electron density topology of both compounds and allow supposing, that during the thermal decomposition process these compounds should behave similarly, which is in agreement with the experiment.     

Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride

Chemical binding in crystalline ammonium chloride, a simple inorganic salt with an unexpectedly complex bonding pattern, was studied by using a topological analysis of electron density function derived from high‐resolution X‐ray diffraction. Supported by periodic quantum chemical calculations, it provided experimental evidence for weak σ‐hole bonds (1.5 kcal mol^?1) that involve ammonium cations in a crystal. Our results show this type of supramolecular interaction to be more numerous than has been found to date by using gas‐phase calculations or statistical analysis of CSD.     

The Electron Distribution in the Nonlinear Optical Material 2-Amino-5-Nitropyridinium Dihydrogen Phosphate

The topological analysis of the 2-amino-5-nitropyridinium dihydrogen phosphate, 2A5NPDP, and the experimental electron density distribution determined from X-ray diffraction data interpreted in terms of the Hansen & Coppens pseudoatom formalism [1] is presented. The bond critical point properties of the total experimental electron density agree fairly well with ab initio Hartree-Fock calculations for the isolated ions. The analysis of the hydrogen-bond critical points shows the crystal H-bond framework to involve four anions and one cation. All the H-bond critical points show small positive ²(r) values, consistent with ionic closed-shell interactions between the participant atoms.     

Determination of the electron density in methyl (±)‐(1S,2S,3R)‐2‐methyl‐1,3‐diphenylcyclopropanecarboxylate using refinements with X‐ray scattering factors from wavefunction calculations of the whole molecule

The molecule of the title compound, C₁₈H₁₈O₂, is a substituted cyclopropane ring. The electron density in this molecule has been determined by refining single‐crystal X‐ray data using scattering factors derived from quantum mechanical calculations. Topological analysis of the electron densities in the three cyclopropane C—C bonds was carried out. The results show the effects of this substitution on these C—C bonds.     

The experimental electron density distribution in the complex of (E)-1,2-bis(4-pyridyl)ethylene with 1,4-diiodotetrafluorobenzene at 90 K

The experimental electron density of the donor-acceptor complex of (E)-1,2-bis(4-pyridyl)ethylene (bpe) with 1,4-diiodotetrafluorobenzene (F(4)DIB) at 90 K has been determined with the aspherical atom formalism and analyzed by means of the topological theory of molecular structure. The bpe and F(4)DIB molecules are connected by intermolecular I.N bonds into infinite 1D chains. F.H bonds link these chains together to form the crystal assembly. The topological analysis reveals that the Cbond;I bond is of the "closed shell" type. Its bond-critical properties run parallel to those found in metal-metal and metal-ligand bonds of organometallic compounds. The integrated net charges show that the I.N halogen bond has an essentially electrostatic nature. F.F, F.C, and C.C intermolecular interactions, for which a bond path was found, contribute to reinforce the crystal structure.     

Testing theory beyond molecular structure: Electron density distributions of complex molecules

The electron density distribution (EDD) of a molecular system can be determined experimentally from elaborate X‐ray diffraction measurements or calculated with quantum mechanical methods: This provides a unique opportunity for mutual validation of the experimental and theoretical methods—a validation that goes far beyond comparison of molecular structures. Two examples of complex molecular systems of biologic relevance are presented. The first is the cocrystallized complex of betaine, imidazole, and picric acid, 1, which is a 75‐atom molecular complex serving as a model for the active site in the serine proteases class of enzymes, the so‐called catalytic triad. For 1 the experimental charge density was determined by combined modeling of single crystal synchrotron X‐ray and neutron diffraction data measured at 28(1) K, and it is compared with ab initio theoretical calculations at the B3LYP/6‐311G(d,p) level of theory. Overall, the agreement is good, but in one strong N? H? O hydrogen bond clear differences are observed. The second example concerns the EDD of the mixed valence trinuclear oxo‐centered iron carboxylate, [Fe₃O(OOCC(CH₃)₃)₆(NC₅H₅)₃], 2. This molecule contains 133 atoms (542 electrons) including three open‐shell iron atoms, and the experimental investigation is based on synchrotron X‐ray diffraction data. Calculations in the experimental geometry at the commonly used UB3LYP/LanL2DZ level of theory are not able to reproduce a number of experimentally observed electron density features. In particular, the sp³‐like distribution on the central oxygen atom and the electron deformations on the iron centers are at variance with experiment. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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.     

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.     

Reassessment of large dipole moment enhancements in crystals: a detailed experimental and theoretical charge density analysis of 2-methyl-4-nitroaniline

The molecular dipole moment of MNA in the crystal has been critically reexamined, to test the conclusion from an earlier experimental charge density analysis that it was substantially enhanced due to a combination of strong intermolecular interactions and crystal field effects. X-ray and neutron diffraction data have been carefully measured at 100 K and supplemented with ab initio crystal Hartree-Fock calculations. Considerable care taken in the measurement and reduction of the experimental data excluded most systematic errors, and sources of error and their effects on the experimental electron density have been carefully investigated. The electron density derived from a fit to theoretical structure factors assisted in the determination of the scale and thermal motion model. The dipole moment enhancement for MNA in the crystal is much less than that reported previously and only on the order of 30-40% (approximately 2.5 D). In addition to the dipole moment, experimental deformation electron density maps, bond critical point data, electric field gradients at hydrogen nuclei, and atomic and group charges all agree well with theoretical results and trends. Anisotropic modeling of the motion of hydrogen atoms, integral use of periodic ab initio calculations, and improved data quality are all aspects of this study that represent a considerable advance over previous work.     

Computational Investigation on the Surface Electronic Density, Morphology and Detonation Property of 1,1-Diamino-2,2-dinitroethylene （FOX-7） Crystal

The present study constructed and optimized FOX-7 crystal using a novel technique including grand canonical monte carlo (GCMC), density functional theory (DFT) and molecular dynamics (MD) methods. Therein, the crystal density, atomic and electronic actions were considered. The results showed that the 1.96 g?cm-3 FOX-7 crystal has the highest stability and detonation properties, such as the total crystal energy, surface electronic density, friction sensitivity, detonation pressure, and so on. These results are close to the experimental data.     

Theoretical insights into the 1D‐charge transport properties in a series of hexaazatrinaphthylene‐based discotic molecules

Discotic liquid crystal (DLC) materials have attracted considerable attention mainly due to their high charge carrier mobilities in quasi‐one‐dimensional columns. In this article, five hexaazatrinaphthylene‐based DLC molecules were investigated theoretically, and their frontier molecular orbital energy levels, crystal structures, and electron/hole drift mobilities were calculated by combination of density functional theory (DFT) and semiclassical Marcus charge transfer theory. The systems studied in this work include three experimentally reported molecules ( 1 , 2 , and 3 ) and two theoretically designed molecules ( 4 and 5 ). Compared with the 1 – 3 compounds, 4 and 5 have three more extended benzene rings in the π‐conjugated core. The present results show that the orders of the frontier molecular orbital energy levels and electron drift mobilities agree very well with the experiment. For 4 and 5 , the electron/hole reorganization energies are lower than those of compounds 1 – 3 . Furthermore, the calculated electron/hole transfer integral of 5 is the largest among all the five systems, leading to the highest electron and hole mobilities. In addition, the hydrophobicity and solubility were also evaluated by DFT, indicating that compound 5 has good hydrophobicity and good solubility in trichloromethane. As a result, it is expected that compound 5 can be a potential charge transport material in electronic and optoelectronic devices. © 2017 Wiley Periodicals, Inc.     

The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several “sigma-hole” interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14–17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.     

Nature of weak inter- and intramolecular contacts in crystals 2. Character of electron delocalization and the nature of X—H...H—X (X = C,B) contacts in the crystal of 1-phenyl-<Emphasis Type="Italic">o</Emphasis>-carborane

High-resolution single crystal X-ray study of 1-phenyl-o-carborane was carried out and the experimental and theoretical (B3LYP/6-311G** calculated) electron density distributions in the title compound were investigated. Character of electron delocalization in 1-phenyl-o-carborane was examined by analyzing the deformation electron density maps, maps of the Laplacian of the electron density, and maps of the electron localization function. Crystal-structure-forming X—H...H—X (X = C, B) intermolecular contacts were revealed and analyzed. The energies and geometric parameters of these contacts were compared with the results of quantum chemical calculations of the crystal structure and with characteristics of the same type of intramolecular contacts.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 541–552, March, 2005.     

Electron crystallization in two dimensions

The ground state of the 2D electron crystal is investigated using a localized representation for the electrons. Assuming a neutralizing background, calculation for a nonmagnetic electron crystal is performed. The areal electron densities corresponding to the crystallization for different r_s values are computed and these are compared with the available experimental areal densities. An upper limit for the obtainable areal density has been predicted from our results. © 1994 John Wiley & Sons, Inc.     

Structural and Electron Density Studies on a Chromium(IV)-Oxo Complex [CrIV(O)(TMP)]

The electron density distribution of a chromium(IV)-oxo complex, [Cr^IV(O)(TMP)] (TMP = 5,10,15,20-tetrakis-p-methoxyphenyl porphyrin), is investigated by molecular orbital calculation. The molecular and crystal structure of the compound is studied by x-ray diffraction. It belongs to the space group 1 2, Z = 2, a = 14.979(4) Å, b = 9.752(3), c = 15.605(3) Å, β = 100.97(2)°, V = 2238(1) ų, Mo Kα radiation λ = 0.7107 Å, R = 4.9%, Rw = 3.5% for 3575 observed reflections. Cr is five-coordinated in a square pyramidal fashion with the Cr atom located 0.42 Å toward the oxo-ligand. Deformation density maps are derived from the single point molecular orbital calculation on the basis of HF and DFT(density functional theory) calculations. The accumulation of deformation density along the C-H, C-C, C-N and C-O bonds in the porphyrin ligand is well represented. The asphericity in electron density around the Cr ion is clearly demonstrated. Natural bond orbital analysis (NBO) reveals that the Cr-O_oxo is actually a triple-bond character (σ²π⁴) and the four N of pyrrole serves as a σ-donor to Cr. The Cr-N_pyrrole bond is essentially a dative bond d-Orbital populations of Cr derived from both calculations are in good agreement with each other. Planar d_π-orbital is the most populated, which is in accord with the prediction from crystal field theory. Detail bond characterization of the Cr-L, multiple bond is discussed.     

Experimental and theoretical electron density study of estrone

The electron density and the electrostatic potential (ESP) distributions of estrone have been determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer at 20 K. The electron density in the estrone crystal has been described with the multipole model, which allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution was obtained via a single-point calculation with a large basis set at the experimental geometry and subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be well correlated to the experimental electron density at the bond critical points through an exponential relationship. The aromaticity of ring A, chemical bonding, the O(1)...O(2) distance necessary for estrogenic activity, and the electrostatic potential features are also discussed.     

The Transannular Interaction in [2.2]Paracyclophane: Repulsive or Attractive?

The molecular structure and charge density distribution in the crystal of [2.2]paracyclophane derived from the high‐resolution single crystal X‐ray diffraction data at 100 K is reported together with ab initio calculations of this molecule. Analysis of the atomic, anisotropic displacement parameters in a “rigid‐body” model approximation has revealed that the molecule is ordered in the crystal. Topological analysis of the electron density and potential‐energy density‐distribution functions has demonstrated that there is no “through‐space” interaction between the rings in the molecule. The role of the ethylene bridges and distortion of the aromatic desks on the inter‐ring interaction are discussed.     

First Experimental Quantitative Charge Density Studies of Advanced Intermediate of Vitamin D Analogues

Vitamins D are a group of fat-soluble secosteroids which play a regulatory role in the functioning of most cells. Rational design of new vitamin D analogs, of increased therapeutic potency and lowered calcemic side effects, requires high-resolution initial structures and a deep understanding of interactions with the molecular targets. In this paper, using quantum crystallography, we present the first determination of the experimental quantitative charge density of an advanced intermediate of vitamin D analogues as well as a reconstruction of the theoretical electron density of final vitamin D analogues. Application of these methods allows for topological and electrostatic interaction energy analysis. We showed that the A-ring chair conformation has a significant influence on the topological properties of vitamin D compounds. Moreover, the interactions between the CD-ring and side-chain additionally stabilize the crystal structure. These results are supported by our theoretical calculations and previous biological studies.     

Theoretically Calculated Deformation Density of Small Molecules

Analysis of the theoretical electron deformation density based on EHMO and ab initio calculations has been applied to the simple molecules F₂, H₂O and SO₂ The effects from varied basis sets for such deformation density were sought. The accumulation of electron density between the bonded atoms calculated from EHMO and ab initio methods with STO-3G is generally under-estimated. Such phenomena are significantly improved by using split-valence basis sets e.g. 3–21G and 4–31G. The addition of d polarization functions is apparently important for the sulfur atom in sulfur-related bonding. 3–21G or 3–21G^* basis sets were found to provide not only valuable deformation density distributions of molecules but also comparable orbital energy states with respect to the experimental values.     

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.