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.     

Investigations into conformational transitions and solvation structure of a 7-piperidino-5,9-methanobenzo[8] annulene in water

Solvation shell structure of a 7-piperidino-5,9-methanobenzo[8] annulene (PMA) in water has been investigated in ambient conditions using both molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) calculations. From the MD calculations, we find that this molecule exists in three major conformational states out of which two are in twist-boat forms and one in chair form. Due to the limited time scale accessible in CPMD simulations, we have studied all the three conformational states separately using CPMD. The molecular geometry, electronic charge distribution and solvation structure for all three forms are investigated. The stability order of the chair and twist-boat conformations in water solvent has been reversed when compared to the gaseous phase results and in the case of polar aprotic solvents (J. Org. Chem., 1999, 61, 5979). From the radial distribution function, we find that the solvent density around the chair form is significantly lower, which has to be directly related to the smaller solvent accessible area for this conformation and this is in complete agreement with earlier reports. Among the findings are that the solvation shell structure around the nitrogen atom in the chair form of PMA is considerably different from the open conformational forms or the twist-boat forms. The dipole moment for the closed form is found to be significantly larger when compared to the twist-boat forms.     

Theoretical and photophysical investigation of biologically active fluorophore: 2-amino-6-chlorofluoren-9-one

The optimized geometric parameters of the 2-Amino-6-chlorofluoren-9-one (2A6CF9O) compound were estimated by employing density functional theory. The electronic characteristics of the molecule were explored using molecular frontier orbital energies and the MEP surface. Kamlet's and Catalan's multiple linear regression techniques along with different polarity functions were used to investigate the influence of pure solvents on spectral properties. In the system, both general solute-solvent and hydrogen bonding interactions are active. However, as compared to normal solute-solvent interactions, hydrogen bonding interactions have a smaller role. In addition, using computed ground state dipole moment, solvatochromic correlations were employed to infer excited state dipole moment.     

Ab initio molecular dynamics study of liquid methanol

We present a density-functional theory based molecular-dynamics study of the structural, dynamical, and electronic properties of liquid methanol under ambient conditions. The calculated radial distribution functions involving the oxygen and hydroxyl hydrogen show a pronounced hydrogen bonding and compare well with recent neutron diffraction data, except for an underestimate of the oxygen–oxygen correlation. We observe that, in line with infrared spectroscopic data, the hydroxyl stretching mode is significantly red-shifted in the liquid. A substantial enhancement of the dipole moment is accompanied by significant fluctuations due to thermal motion. Our results provide valuable data for improvement of empirical potentials.     

Cooperativity in ionic liquids

Cooperativity in ionic liquids is investigated by means of static quantum chemical calculations. Larger clusters of the dimethylimidazolium cation paired with a chloride anion are calculated within density functional theory combined with gradient corrected functionals. Tests of the monomer unit show that density functional theory performs reasonably well. Linear chain and ring aggregates have been considered and geometries are found to be comparable with liquid phase structures. Cooperative effects occur when the total energy of the oligomer differs from a simple sum of monomer energies. Cooperative effects have been found in the structural motifs examined. A systematic study of linear chains of increasing length (up to nine monomer units) has shown that cooperativity plays a more important role than expected and is stronger than in water. The Cl...H distance of the chloride to the most acidic proton increases with an increasing number of monomer units. The average bond distance approaches 218.9 pm asymptotically. The dipole moment grows almost linearly and the dipole moment per monomer unit reaches the asymptotic value of 16.3 D. The charge on the chloride atoms decreases with an increasing chain length. In order to detect local hydrogen bonding in the clusters a new parametrization of the shared-electron number method is introduced. We find decreasing hydrogen bond energies with an increasing cluster size for both the first hydrogen bond to the most acidic proton and the average hydrogen bond.     

The unexpected and large enhancement of the dipole moment in the 3,4-bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) molecule upon crystallization: a new role of the intermolecular CH...O interactions.

The molecular dipole moment of the 3,4-bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) molecule and its enhancement in the crystal was evaluated by periodic RHF ab initio computations. A discrete boundary partitioning of the electronic density that allows an unambiguous partitioning of the molecular space in the condensed phase was adopted. The resulting molecular dipole in the crystal compares favorably with the experimental value obtained by a multipolar analysis of single-crystal X-ray diffraction data recorded at 20 K, using a fuzzy boundary partitioning of the derived pseudoatom densities. We show that a large and highly significant molecular dipole enhancement may occur upon crystallization, despite the lack of a strongly hydrogen bonded environment in the crystal. The 23 unique C-H...O interactions which are formed upon packing of the DMACB molecule induce an increase in the molecular dipole (over 75%) that is comparable to or greater than that found in systems which are characterized by the stronger O-H...O and N-H...O hydrogen bonds. The DMACB molecule constitutes an excellent system for the study of C-H...O interactions in the condensed phase, since no other kind of competing hydrogen bonds is present in its crystal. A simple and qualitative model for the matrix contribution to the DMACB molecular dipole enhancement in the crystal is proposed. The formation of several weak C-H...O bonds is found to yield a small (about 0.2 e) net flux of electronic charge flowing from the hydrogens of the methyl groups to the carbonyl oxygen atoms. Despite the limited increase of the intramolecular charge transfer upon crystallization, a large molecular dipole enhancement occurs because the centroids of the positive and negative induced charges are quite far apart. This work highlights a new and important role of the C-H...O bond, besides those already known in the literature.     

Pressure and temperature dependence of the hydrogen bonding in supercritical ethanol: a computer simulation study

As a step toward deeper insight on the "hydrogen bonding" in supercritical ethanol (scEtOH), we carried out NVT molecular dynamics simulations of the fluid over a wide range of temperatures and pressures. The fluid was studied at SC conditions for which thermodynamic and spectroscopic (NMR, infrared, Raman, dielectric) data are available. The various site-site pair distribution functions (pdf's) were calculated, and their temperature and pressure dependence was obtained. It was found that over the thermodynamic conditions investigated here, scEtOH remains highly structured. Moreover, the characteristic behavior of the first peaks in H-H, O-O, and H-O pdf's reveals that hydrogen bonds still exist in scEtOH. The analysis focuses also on the reorientational dynamics of the bond unit vectors O-H, C-O, and of the permanent dipole moment of the molecules as well as the total dipole moment of the sample. The corresponding Legendre time correlation functions were discussed in connection to the "hydrogen bonding" in the fluid and in the context of experimental results. Specifically, the behavior of the O-H dynamics exhibits the well-known associative nature of the molecules in the system. A further analysis of the hydrogen bonds was carried out, and the degree of aggregation (average number of H-bonds per molecule) was obtained and compared with results from NMR chemical shift studies. Also the estimated monomer and free O-H groups in the fluid were compared with results from IR and Raman vibrational spectroscopy. The percentage analysis fi of the liquid and scEtOH molecules, with i = 0, 1, 2, 3, ... hydrogen bonds per molecule, has been obtained. The results show the existence of small, linear-chain oligomers formed mainly by two molecules, whereas the number of the three body oligomers, and specifically that of four body oligomers in the sample, is relatively small.     

Probing the configurational space of a metalloprotein core: an ab initio molecular dynamics study of Duo Ferro 1 binuclear Zn cofactor

We present three theoretical models of various degree of completeness to explore the chemical phase space available to the Glu4His2Zn2 cofactor found in the four-helix bundle of de novo designed metalloprotein Duo Ferro 1. We have found that the planewave DFT geometry optimization of 94-atom Model I, which contains both the protein scaffold constraints as well as the second shell hydrogen bonding network, reproduces the crystal structure bonding with remarkable accuracy (0.34 A). Surprisingly, the geometry optimization of 66-atom Model II (lacking the second shell hydrogen bonding) and 48-atom Model III (being also free of the protein scaffold constraints) still result in the fidelity with the crystallographic structure (RMSDs 0.29 and 0.34 A, respectively). To examine whether these structures are close to the global minimum as well as to investigate various conformational transitions to which the di-Zn cofactor may be susceptible to, we have carried out a 10 ps Car-Parrinello Molecular Dynamics (CPMD) simulation of Model III. We suggest that weak hydrogen bonds between imidazole hydrogens and carboxylate oxygens modulate the dynamical behavior of the system. One part of the molecule was found to be rigid due to the particular H(imidazole)-O(carboxylate) interaction restricting both the motion of the imidazole ring as well as the terminal carboxylate conformational mobility. The second half of the system was very flexible demonstrating a coupling of a transient formation of H(imidazole)-O(carboxylate) bonds with the spinning of the imidazole ring and syn-anti isomerization of the terminal carboxylate group. In addition, two low-energy snapshots from the 10 ps CPMD run were quenched, and their geometries were optimized, leading to two new isomers 48 kJ/mol lower in energy than the one associated with the crystal structure. We suggest that periodic quenching of the CPMD simulation snapshots of a minimalist model may be used as an efficient method to generate a large number of competitive local minima, which may be consequently pruned by imposing the protein scaffold constraints as well as further tuned by the second shell hydrogen bonding network.     

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.     

Density-functional theory-based molecular simulation study of liquid methanol

We present a density-functional theory based molecular dynamics study of the structural, dynamical, and electronic properties of liquid methanol under ambient conditions. The calculated radial distribution functions involving the oxygen and hydroxyl hydrogen show a pronounced hydrogen bonding and compare well with recent neutron diffraction data. We observe that, in line with infrared spectroscopic data, the hydroxyl-stretching mode is significantly redshifted in the liquid, whereas the hydroxyl bending mode shows a blueshift. A substantial enhancement of the molecular dipole moment is accompanied by significant fluctuations due to thermal motion. We compute a value of 32 for the relative permittivity, almost identical to the experimental value of 33. Our results provide valuable data for improvement of empirical potentials.     

Solvent Effects on Spectral Property and Dipole Moment of the Lowest Excited State of Coumarin 343 Dye

Steady-state absorption and fluorescence spectra, and time-resolved fluorescence spectra of coumarin 343 (C343) were measured in different solvents. The effect of the solvent on the spectral properties and dipole moment of the lowest excited state of C343 were investigated. It was found that the absorption and fluorescence spectra red-shifted slightly and strongly with increasing solvent polarity, respectively, because the charge distribution of the excited state leaded to the increasing difference between the absorption and fluorescence spectra with increasing solvent polarity. The dipole moment of the lowest excited state of C343was determined from solvatochromic measurements and the quantum chemical calculation, and the results obtained from these two methods were fully consistent. Investigations of the time-resolved fluorescence of C343 in different solvents indicated that the fluorescence lifetimes increased nearly linearly with increasing solvent polarity from 3.09 ns in toluene to 4.45 ns in water. This can be ascribed to the intermolecular hydrogen bonding interactions between C343 and hydrogen donating solvents.     

A Combined Experimental and Theoretical Electron Density Study of Intra‐ and Intermolecular Interactions in Thiourea S,S‐Dioxide

The thiourea S,S‐dioxide molecule is recognized as a zwitterion with a high dipole moment and an unusually long C? S bond. The molecule has a most interesting set of intermolecular interactions in the crystalline state—a relatively strong O???H? N hydrogen bond and very weak intermolecular C???S and N???O interactions. The molecule has C_s symmetry, and each oxygen atom is hydrogen‐bonded to two hydrogen atoms with O???H? N distances of 2.837 and 2.826 Å and angles of 176.61 and 158.38°. The electron density distribution is obtained both from Xray diffraction data at 110 K and from a periodic density functional theory (DFT) calculation. Bond characterization is made in terms of the analysis of topological properties. The covalent characters of the C? N, N? H, C? S, and S? O bonds are apparent, and the agreement on the topological properties between experiment and theory is adequate. The features of the Laplacian distributions, bond paths, and atomic domains are comparable. In a systematic approach, DFT calculations are performed based on a monomer, a dimer, a heptamer, and a crystal to see the effect on the electron density distribution due to the intermolecular interactions. The dipole moment of the molecule is enhanced in the solid state. The typical values of ρ_b and H_b of the hydrogen bonds and weak intermolecular C???S and N???O interactions are given. All the interactions are verified by the location of the bond critical point and its associated topological properties. The isovalue surface of Laplacian charge density and the detailed atomic graph around each atomic site reveal the shape of the valence‐shell charge concentration and provide a reasonable interpretation of the bonding of each atom.     

Elucidating the vibrational spectra of hydrogen-bonded aggregates in solution: electronic structure calculations with implicit solvent and first-principles molecular dynamics simulations with explicit solvent for 1-hexanol in n-hexane

Fourier transform infrared spectroscopy is a popular method for the experimental investigation of hydrogen-bonded aggregates, but linking spectral information to microscopic information on aggregate size distribution and aggregate architecture is an arduous task. Static electronic structure calculations with an implicit solvent model, Car-Parrinello molecular dynamics (CPMD) using the Becke-Lee-Yang-Parr (BLYP) exchange and correlation energy functionals and classical molecular dynamics simulations for the all-atom version of the optimized parameters for liquid simulations (OPLS-AA) force field were carried out for an ensemble of 1-hexanol aggregates solvated in n-hexane. The initial configurations for these calculations were size-selected from a distribution of aggregates obtained from a large-scale Monte Carlo simulation. The vibrational spectra computed from the static electronic structure calculations for monomers and dimers and from the CPMD simulations for aggregates up to pentamers demonstrate the extent of the contribution of dangling or nondonating hydroxyl groups found in linear and branched aggregates to the "monomeric" peak. Furthermore, the computed spectra show that there is no simple relationship between peak shift and aggregate size nor architecture, but the effect of hydrogen-bond cooperativity is shown to differentiate polymer-like (cooperative) and dimer-like (noncooperative) hydrogen bonds in the vibrational spectrum. In contrast to the static electronic structure calculations and the CPMD simulations, the classical molecular dynamics simulations greatly underestimate the vibrational peak shift due to hydrogen bonding.     

Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation

Pairwise interaction correction (PIC) is introduced to account for electron density polarization due to short-range interactions such as hydrogen bonding and close contact between molecular fragments in the molecular fractionation with conjugated caps density matrix (MFCC-DM) approach for energy calculation of protein and other polymers [Chen et al., J. Chem. Phys. 122, 184105 (2005)]. With this PIC, the accuracy of the calculated protein energy and other electronic properties are improved, and the MFCC approach can be applied to study real proteins with short-range structural complexity. In the present MFCC-DM-PIC approach, the short-range interresidual interactions are represented by a pair of small molecules (interacting units) which are made from the two residues that fall within a certain distance criterion. The density matrices of fragments, concaps, interacting units and pairs are calculated by conventional Hartree-Fock or density functional theory methods and are combined to construct the full density matrix which is finally employed to calculate the total energy, electron density, electrostatic potential, dipole moment, etc., of the protein. Numerical tests on seven conformationally varied peptides are presented to demonstrate the accuracy of the MFCC-DM-PIC method.     

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.     

Glycosidic linkage conformation of methyl-alpha-mannopyranoside

We study the preferred conformation of the glycosidic linkage of methyl-alpha-mannopyranoside in the gas phase and in aqueous solution. Results obtained utilizing Car-Parrinello molecular dynamics (CPMD) simulations are compared to those obtained from classical molecular dynamics (MD) simulations. We describe classical simulations performed with various water potential functions to study the impact of the chosen water potential on the predicted conformational preference of the glycosidic linkage of the carbohydrate in aqueous solution. In agreement with our recent studies, we find that results obtained with CPMD simulations differ from those obtained from classical simulations. In particular, this study shows that the trans (t) orientation of the glycosidic linkage of methyl-alpha-mannopyranoside is preferred over its gauche anticlockwise (g-) orientation in aqueous solution. CPMD simulations indicate that this preference is due to intermolecular hydrogen bonding with surrounding water molecules, whereas no such information could be demonstrated by classical MD simulations. This study emphasizes the importance of ab initio MD simulations for studying the structural properties of carbohydrates in aqueous solution.