Theoretical Electron Density Research Articles

Partial Hydrogen Bonds: Structural Studies on Thioureidoalkylphosphonates

X-ray crystal and molecular structures of the following compounds are investigated: diphenyl 1-(3-phenylthioureido)propylphosphonate (I), diphenyl 1-(3-phenylthioureido)methylthio-propylphosphonate (II), and diphenyl [2-methyl-1-(3-methylthioureido)propyl]phosphonate (III). Additionally single point density functional theory calculations at the B3LYP/6-311+G(d) level of theory are performed on dimers whose geometries are taken from the crystal structures. The additional diffuse and polarization components are included on H-atoms which participate in H-bonds. The obtained wave functions are applied later to study theoretical electron densities for these species. Bond critical points are determined for dimers investigated to characterize the nature of interactions, especially bifurcated acceptor hydrogen bonds. The characteristics of bond critical points are investigated in terms of the electron densities and their Laplacians.

MALDI-Fourier transform mass spectrometric and theoretical studies of donor–acceptor and donor–bridge–acceptor fullerenes

Fourier-transform ion cyclotron resonance (FTICR) mass spectrometric studies have been performed on donor-acceptor and donor-bridge acceptor fullerene-based systems. Matrix-assisted laser desorption/ionization (MALDI) was used for ion production; both the positive and negative ion modes were utilized. In addition, collision-induced dissociation (CID) experiments were carried out to study the movement of the charge (electron or hole) upon fragmentation. The experiments are complemented by ab initio theoretical calculations yielding both molecular orbital energies and electron density distributions. It was found that the theoretical electron density map predicted the experimentally observed fragmentation correctly in every case. Both the calculations and the MS experiments may be useful in studying these and related donor-acceptor systems in view of their use for charge separation and eventually, solar energy production.

Electron density profiles in the equatorial E region ionosphere derived from a bistatic coherent scatter radar experiment in Perú

A new bistatic radar system has been developed at the Jicamarca Radio Observatory. The system is a permanent addition to the facility designed to monitor electron density profiles in the equatorial electrojet region using a coherent scatter radar technique that utilizes the Faraday rotation of the scattered signal. A series of radar experiments has been conducted at Jicamarca since March, 2004. In this report, representative E region electron density profiles of the equatorial ionosphere are presented. We compare our electron density estimates with: theoretical electron densities derived from the Chapman production function, electron densities measured by rocket experiments, the International Reference Ionosphere (IRI‐2001) model, and peak electron density estimates from the Jicamarca Digisonde. Overall, the radar measured density profiles have magnitudes and shapes comparable to the electron density estimators mentioned above. However, the measured and IRI‐2001 model density profiles disagree significantly below the E region peak.

Experimental and theoretical electron density and electrostatic properties as a tool for understanding activity of HIV-1 integrase inhibitor precursors

1. High resolution X-ray diffraction data Collecte at 100K on a Smart CCD diffractometer 2. Data refinement by the Hansen-Coppens (2) multipole model 3. Characterization of the chemical bonds and the electrophilic/nucleophilic characters of the two precursors: electron density topological properties and the electrostatic potential 4. Comparaison between the experimental results and the ab initio quantum mechanic calculations for (2) and (3) isolated molecules 5. Theorical calculations for (1) molecule Styrylquinoline derivatives are potent inhibitors of the HIV-1 virus integrase activity (1). The biologically tested molecules contain one aromatic part connected to the quinoline group through different chemical spacers. The most promising molecule in the inhibition of the HIV-1 integrase is the (E)-8-hydroxy-2[2-(4,5-dihydroxy-3-methoxyphenyl)-ethenyl]-7-quinolinecarboxylic acid (1) where the spacer is a C=C double bond. The crystallization of this molecule is particularly difficult giving rise to very small needle-shape crystals which are instable in time. In order to recover the molecular property, we have synthesized and crystallized the two precursors of this molecule: the 3', 4', 5'-methoxy-dihydroxy benzaldehyde aromatic part (2) and the 8-hydroxy-7-quinolinic acid (3).

An experimental (120 K) and theoretical electron-density study of KMnO4 and KClO4.

The experimental electron density rho(r) of the two isomorphic salts KMnO(4) and KClO(4) was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules was applied to rho(r) and to its Laplacian nabla(2)rho(r). The bonds were characterized using the topological parameters at the bond critical points of the density rho(r), nabla(2)rho(r), G(r) (kinetic energy density), V(r) (potential energy density) and H(r) (total energy density). According to the classification recently proposed by Espinosa, Alkorta, Elguero & Molins [J. Chem. Phys. (2002), 117, 5529-5542], the K-O and Cl-O bonds have a pure ionic and covalent character, respectively, while the Mn-O bonds show an intermediate behaviour. The results of the topological analysis of the experimental and theoretical (fully periodic Hartree-Fock and density functional calculations) electron density are in good agreement, even on a quantitative level. The atomic charges, determined by performing an integration over the topological basins, are about +2 e for Mn and Cl atoms. The ionic radius, estimated with the distance of the bond critical point from the nucleus, is in agreement with a charge of +2 e for the Mn atom.

Can topological analysis of intermolecular interactions explain differences in the physico-chemical properties of related chiral compounds?

Interactions between chiral molecules play a fundamental role for the most biological and many chemical processes. Due to the complexity of the interactions that range from normal hydrogen bonds to weaker interactions like C-H—O hydrogen bonds and stacking, it can be difficult to relate overall thermodynamic properties to the nature of the intermolecular interactions. The topological analysis developed by R.W. Bader for theoretical electron densities has proven to be a powerful tool to analyse intermolecular interactions in crystals based on an analysis of experimental electron densities obtained from accurate high resolution X-ray diffraction data. Our recent investigations of the molecular crystal naphthalene revealed that the topological analysis could reveal and characterize unexpected interatomic interactions [1]. The two pentose epimers xylitol and ribitol differ in the physico-chemical properties, the acentric xylitol being the higher melting and the less dense than ribitol. All possible hydrogen bond donors participate in the hydrogen bond interactions in both compounds, and the topological analysis confirms the energetic similarity of these interactions. The investigations suggest that the origin of the differences in physico-chemical properties is related to differences in the weaker intermolecular interactions and in the entropy. Crystallization of a racemate may lead to racemic compound composed of equal amounts of the two enantiomers or to a spontaneous resolution of crystals that are formed by the pure enantiomers, and the outcome of the process depends on differences in enthalpy and entropy. We have investigated the intermolecular interactions in closely related crystal structures, e.g. a racemic para-fluoromandelic acid and its corresponding enantiomer. The racemic para-fluoromandelic acid showing the unusual behaviour of being the higher melting. An earlier investigation showed that the two forms have an identical hydrogen bond pattern. This was confirmed by the topological analyses based on accurate X-ray diffraction data. Though additional features were revealed from the topological analysis it also showed the significance of supplementing the investigations with theoretical calculations.

A modeling of the structure and favorable H-docking sites and defects for the high-pressure silica polymorph stishovite

Employing first-principles methods, the docking sites for H were determined and H, Al, and vacancy defects were modeled with an infinite periodic array of super unit cells each consisting of 27 contiguous symmetry nonequivalent unit cells of the crystal structure of stishovite. A geometry optimization of the super-cell structure reproduces the observed bulk structure within the experimental error when P1 translational symmetry was assumed and an array of infinite extent was generated. A mapping of the valence electrons for the structure displays mushroom-shaped isosurfaces on the O atom, one on each side of the plane of the OSi3 triangle in the nonbonded region. An H atom, placed in a cell near the center of the super cell, was found to dock upon geometry optimization at a distance of 1.69 A from the O atom with the OH vector oriented nearly perpendicular to the plane of the triangle such that the OH vector makes a angle of 91° with respect to [001]. However, an optimization of a super cell with an Al atom replacing Si and an H atom placed nearby in a centrally located cell resulted in an OH distance of 1.02 A with the OH vector oriented perpendicular to [001] as observed in infrared studies. The geometry-optimized position of the H atom was found to be in close agreement with that (0.44, 0.12, 0.0) determined in an earlier study of the theoretical electron density distribution. The docking of the H atom at this site was found to be ∼330 kJ mol−1 more stable than a docking of the atom just off the shared OO edge of the octahedra as determined for rutile. A geometry optimization of a super cell with a missing Si generated a vacant octahedra that is 20% larger than that of the SiO6 octahedra. The valence electron density distribution displayed by the two-coordinate O atoms that coordinate the vacant octahedral site is very similar to those displayed by the bent SiOSi angles in coesite. The internal distortions induced by the defect were found to diminish rather rapidly with distance, with the structure annealing to that observed in the bulk crystal to within about three coordination spheres.

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.

Charge Density Study of Naphthalene Based on X-ray Diffraction Data at Four Different Temperatures and Theoretical Calculations

The crystal electron density of naphthalene has been investigated on the basis of highly redundant X-ray diffraction data collected to high resolution at 100, 135, 170, and 205 K and from quantum chemical calculations. An analysis of the X-ray diffraction data showed that for the data collected below 200 K thermal motion can be successfully deconvoluted from the diffraction data. A topological analysis of the resulting static crystal electron-density map revealed that the intramolecular bond critical points have characteristics that are very similar to those of the isolated molecule. There is excellent agreement between the bond critical points corresponding to the intermolecular interactions in the experimental and theoretical crystal electron densities. The strongest intermolecular interaction is a C−H···π interaction that causes a change in the electron distribution of the C−H bond.

Extreme ultraviolet emission lines of Ar XIV in solar active region and flare spectra

New R-matrix calculations of electron impact excitation rates for transitions among the 2s 2 2p, 2s2p 2 and 2p 3 levels of Ar XIV are presented. These data are subsequently used to derive the theoretical electron density diagnostic emission-line intensity ratios R 1 = I(187.95 A)/I(194.41 A) and R 2 = I(257.40 A)/I(243.78 A) for a range of densities (N e = 10 9 -10 1 3 cm - 3 ) and electron temperatures (T e = 10 6 . 3 -10 6 . 7 K) appropriate to solar transition region and coronal plasmas. A comparison of these diagnostics with observational data for solar active regions and flares, obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab, reveals that the electron densities determined from R 1 are in good agreement with those estimated from line ratios in Fe XIV or Fe xv, which are formed at similar electron temperatures to Ar XIV. However, there are large discrepancies between densities inferred from the R 2 ratio and those from Fe xiv or Fe xv, confirming that the Ar XIV 243.78- and 257.40-A lines are badly blended with Fe xv 243.79 A and Fe XIV 257.38 A, respectively. Hence, R 2 cannot be employed as a density diagnostic, in contrast to R 1 , which does provide reliable N e estimates.

An Exploration of Theoretical and Experimental Electron Density Distributions and SiO Bonded Interactions for the Silica Polymorph Coesite

A multipole representation of the experimental electron density distribution for the high-pressure silica polymorph coesite, using Hirshfeld-type radial functions, has been generated with single-crystal X-ray diffraction data recorded to a sin θmax/λ value of 1.21 Å-1 at 100 K. Unlike an earlier modeling of the distribution, where a more limited data set was analyzed, deformation electron density maps display banana-shaped isosurfaces in the lone-pair regions of each of the oxide anions involved in the bent SiOSi angles as well as teardrop-shaped ones along each of the SiO bond vectors. They also display a ring torus isosurface about O1, the oxide anion involved in the straight angle. Laplacian −∇2ρ maps display belt-shaped isosurfaces, centered near the apexes of the bent angles, that wrap about halfway around the oxide anions, with a ring torus-shaped isosurface surrounding O1. An analysis of −∇2ρ revealed that the (3,−3) critical point associated with the anions involved in the bent angles are associated in general with larger maxima than that associated with the straight angle, evidence that the electron density is more locally concentrated on the oxide anions involved in the bent angles. As such, these anions are asserted to be more susceptible to electrophilic attack by hydrogen, a feature that provides an experimental basis for why hydrogen in H- and Al-bearing coesite avoids O1 and is observed to dock in the vicinity of the oxide anions involved in the bent angles. The bond critical point properties of the experimental multipole representation of the electron density distribution for coesite together with those for the very high-pressure silica polymorph, stishovite, conform with those calculated for the SiO bonded interactions for a relatively large number of silicate crystals. Not only are they similar in value with the theoretical properties, but together they correlate with the observed SiO bond lengths as predicted by the calculations. The observed SiO bonds display a relatively wide range of ∇2ρ(rc) values between ∼10 e Å-5 for stishovite and ∼20 e Å-5 for coesite. The larger ∇2ρ(rc) values recorded for coesite, considered typical of first row closed-shell ionically bonded atoms, may not be typical for a closed-shell bonded interaction involving second row atoms such as the four-coordinate Si in coesite. The maxima along the bond vectors and in the lone-pair regions displayed by the experimental Δρ and −∇2ρ maps are indicative of shared covalent bonded interactions. The evidence suggests that the value of the electron density at the bond critical point for a given bonded interaction is a reliable measure of bond type: the larger the value ρ(rc), the greater the shared covalent interaction.

Extreme Ultraviolet Emission Lines of ca xv in Solar and Laboratory Spectra

New R-matrix calculations of electron impact excitation rates in Ca xv are used to derive theoretical electron density diagnostic emission line intensity ratios involving 2s22p2–2s2p3 transitions, specifically R1=I(208.70 A)/I(200.98 A), R2=I(181.91 A)/I(200.98 A), and R3=I(215.38 A)/I(200.98 A), for a range of electron temperatures (Te=106.4–106.8 K) and densities (Ne=109–1013 cm−3) appropriate to solar coronal plasmas. Electron densities deduced from the observed values of R1, R2, and R3 for several solar flares, measured from spectra obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab, are found to be consistent. In addition, the derived electron densities are in excellent agreement with those determined from line ratios in Ca xvi, which is formed at a similar electron temperature to Ca xv. These results provide some experimental verification for the accuracy of the line ratio calculations, and hence the atomic data on which they are based. A set of eight theoretical Ca xv line ratios involving 2s22p2–2s2p3 transitions in the wavelength range ∼ 140–216 A are also found to be in good agreement with those measured from spectra of the TEXT tokamak plasma, for which the electron temperature and density have been independently determined. This provides additional support for the accuracy of the theoretical line ratios and atomic data.

Bonding in Polycyclic Aromatic Hydrocarbons in Terms of the Electron Density and of Electron Delocalization

We show that the delocalization indices calculated within the framework of the quantum theory of atoms in molecules provide an excellent basis for the definition of a bond order in polycyclic aromatic hydrocarbons. We show that the two-electron information contained within the delocalization index can be estimated from the electron density at the bond critical point, a mapping that has no a priori reason to exist. The mapping between the bond order and the electron density at the bond critical point can be exploited to provide a fast estimate of bond orders from theoretical or experimental electron densities. Bond orders in these molecules are shown to be associated to other one-electron properties. We provide evidence to the strong coupling of the σ and π contributions to the electron density at the bond critical point, a nonseparability by virtue of which the electron density at the bond critical point reflects both contributions. Another remarkable finding is that the delocalization indices between bonded carbon atoms are also strongly negatively correlated to the electronic energy density at the bond critical point, the latter being another example of a two electron property. In this manner, bond order is associated to a stabilizing effect quantified by the electronic energy density at the bond critical point. Because aromaticity is rooted in electron delocalization within a ring system, the delocalization index is used to define an aromaticity index that measures alternation in the delocalization of electrons within a ring of a polycyclic aromatic hydrocarbon. The proposed aromaticity index represents a “local aromaticity measure”. We have analyzed in detail the effects of ring annealation on bond orders and on the aromatic character of a ring and explored its correlation with independent measures of aromaticity such as NICS and HOMA.

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

AbstractThe thioureaS,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 hasCssymmetry, 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 ofρbandHbof 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.

A Classification of Covalent, Ionic, and Metallic Solids Based on the Electron Density.

The electron density of crystals contains all of the information required to complete a classification of their bonding types. We propose here a set of three different indexes, flatness, charge transfer, and molecularity, easily obtained from the experimental or theoretical electron density, which give rise to a classification in close resemblance to the classical van Arkel−Ketelaar diagrams.

Germanium K edge in GeO2 polymorphs. Correlation between local coordination and electronic structure of germanium

The electronic properties of two room temperature persistent phases of germanium dioxide have been studied by means of experimental and theoretical techniques. We collected the Ge-K edge XANES spectra of these materials at the GILDA beamline of ESRF. The density of states of the two crystal phases, obtained from fully periodic Hartree–Fock and density functional calculations, is taken as the reference term to rationalise and assign the manifolds of the XANES spectra. Although this scheme requires a number of severe approximations, we obtained a good overall agreement between experiment and theory. The topological analysis of the theoretical electron density distribution in the crystals gave further information regarding the electronic properties of germanium dioxide.

Polarizabilities and excitation energies from the multiplicative Kohn-Sham (MKS) approach

The conventional Kohn-Sham expressions for the static isotropic polarizability and vertical excitation energy are evaluated using Kohn-Sham orbitals and eigenvalues determined directly from theoretical electron densities. For a series of small molecules, polarizabilities determined from wavefunction-based BD(T) electron densities differ, on average, by about 2% from conventional BD(T) polarizabilities when the LDA exchange-correlation integrand is used in the electric Hessian matrix. Also polarizabilities determined from Kohn-Sham densities, using the B97-2 hybrid functional, are close to the conventional B97-2 values. To quantify the dependence on the choice of exchange-correlation integrand, calculations are performed also using the HCTH integrand. Rydberg excitation energies determined from BD(T) and B97-2 densities exhibit errors due to inaccuracies in the asymptotic exchange-correlation potential. This category of excitation energy is relatively insensitive to the choice of exchange-correlation integrand; valence excitations can be more sensitive.

A classification of covalent, ionic, and metallic solids based on the electron density.

The electron density of crystals contains all of the information required to complete a classification of their bonding types. We propose here a set of three different indexes, flatness, charge transfer, and molecularity, easily obtained from the experimental or theoretical electron density, which give rise to a classification in close resemblance to the classical van Arkel-Ketelaar diagrams.

Prediction and interpretation of the 57Fe isomer shift in Mössbauer spectra by density functional theory

The calibration of two popular density functionals (B3LYP and BP86) for the prediction of isomer shifts (IS) in 57Fe Mössbauer (MB) spectra is reported. A linear correlation between non-relativistically calculated theoretical electron densities and experimentally measured ISs is established. Both functionals lead to accurate predictions of MB ISs with standard deviations on the order of approximately 0.1 mm s−1 over a range of approximately 2 mm s−1. The correlation holds for complexes of different total charge, total spin, valence state at the iron, coordination number and coordination geometry. A detailed analysis of the contributions to the IS is presented. It is shown that the important contributions are: (a) the variation of the 3s-contribution which is mainly caused by differing shielding according to the d-population of the metal; and (b) variations in the valence shell contribution. The latter contribution accounts for approximately 70% of the totally observed variation. The interpretation of the valence contribution is complex and involves contributions from changes in covalencies, orbital distortions due to bonding and shielding effects. The changes in metalligand distances are also an important factor, which influences the shape of the 4s-orbital and therefore modulates ISs.

Extreme‐Ultraviolet Emission Lines of Sxiiin Solar Active Region and Flare Spectra

New -matrix calculations of electron impact excitation rates for transitions among the 2s22p, 2s2p2 and 2p3 levels of S XII are presented. These data are subsequently used to derive the theoretical electron density diagnostic emission line intensity ratios R1 = I(215.16 A)/I(299.50 A), R2 = I(218.19 A)/I(299.50 A), R3 = I(288.40 A)/I(299.50 A), and R4 = I(221.41 A)/I(299.50 A). A comparison of these with observational data for solar active regions and flares, obtained with the Naval Research Laboratory's S082A spectrograph on board Skylab and the Solar EUV Rocket Telescope and Spectrograph (SERTS), reveals that the electron densities determined from R1, R3, and R4 are consistent with each other. In addition, the densities deduced from these ratios are in good agreement with those estimated from diagnostic lines in Fe XIV or Fe XV, which are formed at similar electron temperatures to S XII. However, the R2 ratios in the flare observations imply densities smaller than those from Fe XIV/Fe XV, although the active region measurements do not show such discrepancies, suggesting that the 218.19 A line may be blended with a transition from a high-temperature ion. An emission feature in the SERTS active region spectrum at 215.29 A, previously identified as the 2s2p 3P2-2s3s 3S1 transition in O V, may be due primarily to the S XII 215.16 A line.