Analysis of supramolecular architectures: beyond molecular packing diagrams

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

Long-range supramolecular synthon polymorphism: a case study of two new polymorphic cocrystals of Ph2Te2–1,4-C6F4I2

Two new polymorphic forms of Ph2Te2–1,4-C6F4I2 cocrystals feature an unusual packing of Ph2Te2 molecules, which is typical for native Ph2Se2 but not Ph2Te2. This suggests the existence the yet unknown, Ph2Se2-like polymorph of Ph2Te2.

Crystal Structure of 9-Dibenzylsulfide-7,8-dicarba-nido-undecaborane 9-Bn2S-7,8-C2B9H11

The crystal structure of 9-dibenzylsulfide-7,8-dicarba-nido-undecaborane 9-Bn2S-7,8-C2B9H11 was determined by a single-crystal X-ray diffraction. One of the benzyl groups is located above the open face of the carborane cage with a short H···H distance (2.29 and 2.71 Å for two symmetrically independent molecules) between the BHB-bridging hydrogen atom of the carborane fragment and the ortho-CH group of the aromatic ring. Topological analysis has revealed the existence of a critical bond point with a calculated energy of −0.8 kcal/mol in accordance with an X-ray diffraction molecular geometry. The crystal packing analysis revealed that this benzyl group is also involved in π-stacking interactions, while another benzyl group participates in numerous weak H···π, H···H and van der Waals interactions.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π⋅⋅⋅π and Reverse Electron Lone Pair⋅⋅⋅π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the crystal of a uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Partitioning of crystal space into atomic basins and atomic-like potential basins led us to the definite description of interatomic interaction and charge transfer. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of π-stacking and intricate C=O⋅⋅⋅π interactions and nonclassical hydrogen bonds present in the crystal. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with well-known functions, e. g., deformation electron density and electron localization function. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

1,12-Diiodo-Ortho-Carborane: A Classic Textbook Example of the Dihalogen Bond

The crystal structure of 1,12-diiodo-ortho-carborane 1,12-I2-1,2-C2B10H10 was determined by single crystal X-ray diffraction. In contrary to earlier studied 1,12-dibromo analogue 1,12-Br2-1,2- C2B10H10, its crystal packing is governed by the presence of the intermolecular I⋯I dihalogen bonds between the iodine atom attached to the carbon atom (acceptor) and the iodine atom attached to the antipodal boron atom (donor) of the carborane cage. The observed dihalogen bonds belong to the II type and are characterized by classical parameters: shortened I⋯I distance of 3.5687(9) Å, C–I⋯I angle of 172.61(11)° and B–I⋯I angle of 92.98(12)°.

Strength of the [Z-I···Hal]- and [Z-Hal···I]- Halogen Bonds: Electron Density Properties and Halogen Bond Length as Estimators of Interaction Energy

Bond energy is the main characteristic of chemical bonds in general and of non-covalent interactions in particular. Simple methods of express estimates of the interaction energy, Eint, using relationships between Eint and a property which is easily accessible from experiment is of great importance for the characterization of non-covalent interactions. In this work, practically important relationships between Eint and electron density, its Laplacian, curvature, potential, kinetic, and total energy densities at the bond critical point as well as bond length were derived for the structures of the [Z-I···Hal]- and [Z-Hal···I]- types bearing halogen bonds and involving iodine as interacting atom(s) (totally 412 structures). The mean absolute deviations for the correlations found were 2.06-4.76 kcal/mol.

Structure-directing sulfur...metal noncovalent semicoordination bonding

The abundance and geometric features of nonbonding contacts between metal centers and `soft' sulfur atoms bound to a non-metal substituent R were analyzed by processing data from the Cambridge Structural Database. The angular arrangement of M, S and R atoms with ∠(R-S...M) down to 150° was a common feature of the late transition metal complexes exhibiting shortened R-S...M contacts. Several model nickel(II), palladium(II), platinum(II) and gold(I) complexes were chosen for a theoretical analysis of R-S...M interactions using the DFT method applied to (equilibrium) isolated systems. A combination of the real-space approaches, such as Quantum Theory of Atoms in Molecules (QTAIM), noncovalent interaction index (NCI), electron localization function (ELF) and Interacting Quantum Atoms (IQA), and orbital (Natural Bond Orbitals, NBO) methods was used to provide insights into the nature and energetics of R-S...M interactions with respect to the metal atom identity and its coordination environment. The explored features of the R-S...M interactions support the trends observed by inspecting the CSD statistics, and indicate a predominant contribution of semicoordination bonds between nucleophilic sites of the sulfur atom and electrophilic sites of the metal. A contribution of chalcogen bonding (that is formally opposite to semicoordination) was also recognized, although it was significantly smaller in magnitude. The analysis of R-S...M interaction strengths was performed and the structure-directing role of the intramolecular R-S...M interactions in stabilizing certain conformations of metal complexes was revealed.

Relationships between Interaction Energy and Electron Density Properties for Homo Halogen Bonds of the [(A)nY-X···X-Z(B)m] Type (X = Cl, Br, I)

Relationships between interaction energy (Eint) and electron density properties at the X···X bond critical point or the d(X···X) distance were established for the large set of structures [(A)nY-X···X-Z(B)m] bearing the halogen bonds Cl···Cl, Br···Br, and I···I (640 structures in total). The best estimator of Eint is the kinetic energy density (Gb), which reasonably approximates the whole set of the structures as -Eint = 0.128Gb2 - 0.82Gb + 1.66 (R2 = 0.91, mean absolute deviation 0.39 kcal/mol) and demonstrates low dispersion. The potential and kinetic energy densities, electron density, and the d(X···X) distance behave similarly as estimators of Eint for the individual series Cl···Cl, Br···Br, and I···I. A number of the Eint(property) correlations are recommended for the practical application in the express estimates of the strength of the homo-halogen bonds.

Interplay of noncovalent interactions in antiseptic quaternary ammonium surfactant Miramistin

The molecular and crystal structure of the widely used antiseptic benzyldimethyl{3-[(1-oxotetradecyl)amino]propyl}ammonium chloride monohydrate (Miramistin, MR), C26H47N2O+·Cl−·H2O, was determined by a single-crystal X-ray diffraction study and analyzed in the framework of the QTAIM (quantum theory of atoms in molecules) approach using both periodic and molecular DFT (density functional theory) calculations. The various noncovalent intermolecular interactions of different strengths were found to be realized in the hydrophilic parts of the crystal packing (i.e. O—H...Cl, N—H...Cl, C—H...Cl, C—H...O and C—H...π). The hydrophobic parts are built up exclusively by van der Waals H...H contacts. Quantification of the interaction energies using calculated electron-density distribution revealed that the total energy of the contacts within the hydrophilic and hydrophobic regions are comparable in value. The organic MR cation adopts the bent conformation with the head group tilted back to the long-chain alkyl tail in both the crystalline and the isolated state due to stabilization of this geometry by several intramolecular C—H...π, C—H...N and H...H interactions. This conformation preference is hypothesized to play an important role in the interaction of MR with biomembranes.

Estimations of energy of noncovalent bonding from integrals over interatomic zero-flux surfaces: Correlation trends and beyond

Bonding energies of 50 associates composed by neutral molecules (atoms) and bounded by various weak noncovalent interactions are calculated within the DFT framework using the PBE0/aug-cc-pVTZ combination. The electronic virial and electron density values at bond critical points together with their integrals over interatomic surfaces are tested to check their ability to estimate bonding energies. Two correlations schemes dealing with integrals over interatomic surface are suggested to estimate bonding energy of any noncovalent interaction. The physical meaning of explored and several known correlations is discussed. Methods to estimate interatomic surface integrals of electronic virial and electron density are proposed. © 2018 Wiley Periodicals, Inc.

Conformational analysis of a supramolecular synthon: a case study of 8-hydroxyquinoline

Conformational analysis of a supramolecular synthon in polymorphic modifications of 8-hydroxyquinoline.

Toward a Rigorous Definition of a Strength of Any Interaction Between Bader's Atomic Basins

Strength of interaction between Bader's atomic basins, enclosed by zero-flux surfaces of electron distribution, was proposed to be a measure of elastic deformation of an interaction. The set containing 53 atomic aggregate and covering all range of interaction strength (from van der Waals interactions to triple covalent bonds) was calculated by DFT and perturbation theory methods. Further analysis was performed to seek correlations between various local quantities based on electron density and effective force constants of stretching diatomic vibrations. The linear trend between effective force constants and the potential energy density at the (3, -1) critical point of electron distribution was found. This correlation was improved by the integration of the potential energy density over an interbasin zero-flux surface of electron density. Simple mechanical explanation of established trends is presented. The correlations can be further used to at least semiquantitatively compare any pair of interactions between Bader's atomic basins.

Transferable Aspherical Atom Modeling of Electron Density in Highly Symmetric Crystals: A Case Study of Alkali-Metal Nitrates

A comparative electron density study (from X-ray diffraction and periodic quantum chemistry) of sodium and potassium nitrates is performed to test the performance of a transferrable aspherical atom model, which is based on the invarioms, to describe chemical bonding features of ions occurring in sites of different symmetry typical of inorganic salts and in different crystal environments. Relying on tabulated entries for the isolated ions (although tailor-made to account for different site symmetries), it takes the same time to employ as the spherical atom model routinely used in X-ray diffraction studies but provides an electron density distribution that faithfully reveals all the interionic interactions-even the weakest ones (such as between the nitrate anions or a K···N interaction found in the metastable form of KNO₃) yet important for properties of inorganic materials-as if obtained from high-resolution X-ray diffraction data.

Invariom approach to electron density studies of open-shell compounds: the case of an organic nitroxide radical

The study reports the successful modeling of electron density with invarioms for an open-shell compound, an organic nitroxide radical.

Stabilization of 1T-MoS₂ Sheets by Imidazolium Molecules in Self-Assembling Hetero-layered Nanocrystals

We report a facile, room-temperature assembly of MoS2-based hetero-layered nanocrystals (NCs) containing embedded monolayers of imidazolium (Im), 1-butyl-3-methylimidazolium (BuMeIm), 2-phenylimidazolium, and 2-methylbenzimidazolium molecules. The NCs are readily formed in water solutions by self-organization of the negatively charged, chemically exfoliated 0.6 nm thick MoS2 sheets and corresponding cationic imidazole moieties. As evidenced by transmission electron microscopy, the obtained NCs are anisotropic in shape, with thickness varying in the range 5-20 nm and lateral dimensions of hundreds of nanometers. The NCs exhibit almost turbostratic stacking of the MoS2 sheets, though the local order is preserved in the orientation of the imidazolium molecules with respect to the sulfide sheets. The atomic structure of NCs with BuMeIm molecules was solved from powder X-ray diffraction data assisted by density functional theory calculations. The performed studies evidenced that the MoS2 sheets of the NCs are of the nonconventional 1T-MoS2 (metallically conducting) structure. The sheets' puckered outer surface is formed by the S atoms and the positioning of the BuMeIm molecules follows the sheet nanorelief. According to thermal analysis data, the presence of the BuMeIm cations significantly increases the stability of the 1T-MoS2 modification and raises the temperature for its transition to the conventional 2H-MoS2 (semiconductive) counterpart by ∼70 °C as compared to pure 1T-MoS2 (∼100 °C). The stabilizing interaction energy between inorganic and organic layers was estimated as 21.7 kcal/mol from the calculated electron density distribution. The results suggest a potential for the design of few-layer electronic devices exploiting the charge transport properties of monolayer thin MoS2.

Probing Ionic Crystals by the Invariom Approach: An Electron Density Study of Guanidinium Chloride and Carbonate

A comparative study of two guanidinium salts, chloride and carbonate, is carried out to test the performance of the invariom approach for ionic crystals. Although treating them as formed by isolated ions with no charge transfer between them, the invariom approach provides features of interionic contacts that are amazingly similar to those obtained from conventional charge density analysis of high-resolution X-ray diffraction data, thus emerging as an easy way towards reliable description of chemical bonding peculiarities in ionic crystals.