Si-O bonded interactions in silicate crystals and molecules: a comparison

Bond critical point, local kinetic energy density, G(rc), and local potential energy density, V(rc), properties of the electron density distributions, rho(r), calculated for silicates such as quartz and gas-phase molecules such as disiloxane are similar, indicating that the forces that govern the Si-O bonded interactions in silica are short-ranged and molecular-like. Using the G(rc)/rho(rc) ratio as a measure of bond character, the ratio increases as the Si-O bond length, the local electronic energy density, H(rc)= G(rc) + V(rc), and the coordination number of the Si atom decrease and as the accumulation of the electron density at the bond critical point, rho(rc), and the Laplacian, inverted Delta2 rho(rc), increase. The G(rc)/rho(rc) and H(rc)/rho(rc) ratios categorize the bonded interaction as observed for other second row atom M-O bonds into discrete categories with the covalent character of each of the M-O bonds increasing with the H(rc)/rho(rc) ratio. The character of the bond is examined in terms of the large net atomic charges conferred on the Si atoms comprising disiloxane, stishovite, quartz, and forsterite and the domains of localized electron density along the Si-O bond vectors and on the reflex side of the Si-O-Si angle together with the close similarity of the Si-O bonded interactions observed for a variety of hydroxyacid silicate molecules and a large number of silicate crystals. The bond critical point and local energy density properties of the electron density distribution indicate that the bond is an intermediate interaction between Al-O and P-O bonded interactions rather than being a closed-shell or a shared interaction.     

The possible covalent nature of N-H...O hydrogen bonds in formamide dimer and related systems: an ab initio study

The N-H...O hydrogen bonds are analyzed for formamide dimer and its simple fluorine derivatives representing a wide spectrum of more or less covalent interactions. The calculations were performed at the MP2/6-311++G(d,p) level of approximation. To explain the nature of such interactions, the Bader theory was also applied, and the characteristics of the bond critical points (BCPs) were analyzed: the electron density at BCP and its Laplacian, the electron energy density at BCP and its components, the potential electron energy density, and the kinetic electron energy density. These parameters are used to justify the statement that some of the interactions analyzed are partly covalent in nature. An analysis of the interaction energy components for the systems considered indicates that the covalent character of the hydrogen bond is manifested by a markedly increased contribution of the delocalization term relative to the electrostatic interaction energy. Moreover, the ratio of stabilizing the delocalization/electrostatic contributions grows linearly with the decreasing lengths of the hydrogen bond.     

Single‐electron halogen bond: Ab initio study

Ab initio calculations have been performed on single‐electron halogen bonds between methyl radical and bromine‐containing molecules to gain a deeper insight into the nature of such noncovalent interactions. Bader's atoms in molecules (AIM) theory have also been applied to the analysis of the linking of the single‐electron halogen bond. Various characteristics of the R? Br…CH₃ interaction, i.e., binding energies, geometrical parameters and topological properties of the electron density have been determined. The presence of the bond critical points (BCPs) between the bromine atom and methyl radical and the values of electron density and Laplacian of electron density at these BCPs indicate the closed‐shell interactions in the complexes. The single‐electron halogen bonds, which are significantly weaker than the normal halogen bonds, exhibit equally bond strength as compared to the single‐electron hydrogen bond. It has been also found that plotting of the binding energies versus topological properties of the electron density at the BCPs gives two straight lines. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Experimental and theoretical charge density distribution of the colossal magnetoresistive transition metal sulfide FeCr2S4

The total charge density distribution rho(r) of the colossal magnetoresistive transition metal sulfide FeCr(2)S(4) was evaluated through a multipole formalism from a set of structure factors obtained both experimentally, by means of single crystal high-quality x-ray diffraction data collected at T=23 K, and theoretically, with an extended-basis unrestricted Hartree-Fock periodic calculation on the experimental geometry. A full topological analysis, followed by the calculation of local energy density values and net atomic charges, was performed using the quantum theory of atoms in molecules. The experimental and theoretical results were compared. Good agreement was found for the topological properties of the system, as well as for the atomic net charges and the nature of the chemical bonds. An analysis of the electron density rho(r), its Laplacian nabla(2)[rho(r)], and the total energy density H(r) at the bond critical points was employed to classify all the interactions that resulted as predominantly closed shell (ionic) in nature. The topological indicators of the bonded interactions for Fe are distinct from those for Cr. The Fe-S bond distances were found to be 0.145 A shorter than the ideal values computed on the basis of Shannon's crystal radii, much shorter than the Cr-S distances with respect to their ideal Shannon lengths. Concomitantly, rho(r) and |H(r)| at the bond critical points are greater for Fe-S interactions, indicating that the local concentration of charge density in the internuclear region is larger for the tetrahedrally coordinated iron than for the octahedrally coordinated chromium. The isosurface in the real space for nabla(2)[rho(r)]=0 was plotted for both iron and chromium, pointing out the local zones of valence shell charge concentration and relating them to the partial d-orbital occupancy of the two transition metal atoms.     

The structure and chemical bonding in the N(2)-CuX and N(2)...XCu (X = F, Cl, Br) systems studied by means of the molecular orbital and Quantum Chemical Topology methods

Ab initio studies carried out at the MP2(full)/6-311+G(2df) and MP2(full)/aug-cc-pVTZ-PP computational levels reveals that dinitrogen (N(2)) and cuprous halides (CuX, X = F, Cl, Br) form three types of systems with the side-on and end-on coordination of N(2): N[triple bond]N-CuX (C(infinity v)), N(2)-CuX (C(2v)) stabilized by the donor-acceptor bonds and weak van der Waals complexes N(2)...XCu (C(2v)) with dominant dispersive forces. An electron density transfer between the N(2) and CuX depends on type of the N(2) coordination and a comparison of the NPA charges yields the [N[triple bond]N](delta+)-[CuX](delta-) and [N(2)](delta-)-[CuX](delta+) formula. According to the NBO analysis, the Cu-N coordinate bonds are governed by predominant LP(N2)-->sigma*(Cu-X) "2e-delocalization" in the most stable N[triple bond]N-CuX systems, meanwhile back donation LP(Cu)-->pi*(N-N) prevails in less stable N(2)-CuX molecules. A topological analysis of the electron density (AIM) presents single BCP between the Cu and N nuclei in the N[triple bond]N-CuX, two BCPs corresponding to two donor-acceptor Cu-N bonds in the N(2)-CuX and single BCP between electron density maximum of the N[triple bond]N bond and halogen nucleus in the van der Waals complexes N(2)...XCu. In all systems values of the Laplacian nabla(2)rho(r)(r(BCP)) are positive and they decrease following a trend of the complex stability i.e. N[triple bond]N-CuX (C(infinity v)) > N(2)-CuX (C(2v)) > N(2)...XCu (C(2v)). A topological analysis of the electron localization function (ELF) reveals strongly ionic bond in isolated CuF and a contribution of covalent character in the Cu-Cl and Cu-Br bonds. The donor-acceptor bonds Cu-N are characterized by bonding disynaptic basins V(Cu,N) with attractors localized at positions corresponding to slightly distorted lone pairs V(N) in isolated N(2). In the N[triple bond]N-CuX systems, there were no creation of any new bonding attractors in regions where classically the donor-acceptor bonds are expected and there is no sign of typical covalent bond Cu-N with the bonding pair. Calculations carried out for the N[triple bond]N-CuX reveal small polarization of the electron density in the N[triple bond]N bond, which is reflected by the bond polarity index being in range of 0.14 (F) to 0.11 (Cl).     

Progress in the understanding of drug-receptor interactions, Part 1: experimental charge-density study of an angiotensin II receptor antagonist (C30H30N6O3S) at T = 17 K

An experimental study of the electron-density distribution rho(r) in an angiotensin II receptor antagonist 1 has been made on the basis of single-crystal X-ray diffraction data collected at a low temperature. The crystal structure of 1 consists of infinite ribbons in which molecules are connected by an N-H...N hydrogen bond and several interactions of the C-H...O, C-H...N, and C-H...S type. The molecular conformation, characterized by the syn orientation of a tetrazole and a pyrimidinone ring with respect to a phenyl spacer group, is stabilized by two short SO and SN intramolecular contacts between a substituted thiophene fragment and the other two heterocycles of 1. The electrostatic nature of these interactions is documented. Furthermore, the Laplacian of rho(r) in the plane defined by the sulfur, oxygen, and nitrogen atoms involved in these interactions shows their strongly directional character as the regions of charge concentration on the valence shell of the nitrogen and oxygen atoms directly face the regions of charge depletion on the valence shell of the sulfur atom. All the chemical bonds and the relevant intra- and intermolecular interactions of 1 have been quantitatively described by the topological analysis of rho(r). Simple relationships between the bond path lengths (R(b)) and the values of rho at the bond critical points (rho(bcp)) have been obtained for the 28 C-C bonds, the seven N-C bonds, and the four O-C bonds. For the first two classes of bonds the relationship is in the form of a straight line, whose parameters, for the C-C bonds, agree, within experimental uncertainty, with those previously derived in our laboratory from a 19 K X-ray diffraction study of crystals of a different compound. Maps of the molecular electrostatic potential phi(r) derived from the experimental charge density display features that are important for the drug-receptor recognition of 1.     

Strength and nature of hydrogen bonding interactions in mono- and di-hydrated formamide complexes

In this work, mono- and di-hydrated complexes of the formamide were studied. The calculations were performed at the MP2/6-311++G(d,p) level of approximation. The atoms in molecules theory (AIM), based on the topological properties of the electronic density distribution, was used to characterize the different types of bonds. The analysis of the hydrogen bonds (H-bonds) in the most stable mono- and di-hydrated formamide complexes shows a mutual reinforcement of the interactions, and some of these complexes can be considered as "bifunctional hydrogen bonding hydration complexes". In addition, we analyzed how the strength and the nature of the interactions, in mono-hydrated complexes, are modified by the presence of a second water molecule in di-hydrated formamide complexes. Structural changes, cooperativity, and electron density redistributions demonstrate that the H-bonds are stronger in the di-hydrated complexes than in the corresponding mono-hydrated complexes, wherein the σ- and π-electron delocalization were found. To explain the nature of such interactions, we carried out the atoms in molecules theory in conjunction with reduced variational space self-consistent field (RVS) decomposition analysis. On the basis of the local Virial theorem, the characteristics of the local electron energy density components at the bond critical points (BCPs) (the 1/4? (2)ρ(b) component of electron energy density and the kinetic energy density) were analyzed. These parameters were used in conjunction with the electron density and the Laplacian of the electron density to analyze the characteristics of the interactions. The analysis of the interaction energy components for the systems considered indicates that the strengthening of the hydrogen bonds is manifested by an increased contribution of the electrostatic energy component represented by the kinetic energy density at the BCP.     

Experimental electron density analysis of Mn2(CO)10: metal-metal and metal-ligand bond characterization

The experimental electron density rho(r) of Mn2(CO)10 was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules (QTAM) was applied to rho(r) and its Laplacian [symbol: see text] 2 rho(r). The QTAM analysis of rho(r) showed the presence of a bond critical point (rc); its associated bond path connects the two Mn atoms, but no cross interaction line was found between one manganese and the equatorial carbonyls of the other. The distribution of [symbol: see text] 2 rho(r) indicated "closed-shell" interactions for the metallic Mn-Mn bond and the dative Mn-CO bonds. The values of the topological parameters of the density at rc, rho(rc), [symbol: see text] 2 rho(rc), G(rc) (kinetic energy density), and V(rc) (potential energy density), characterize the bonds and are intermediate to those corresponding to typical ionic and covalent bonds.     

Topological analysis of the electron density distribution in perturbed systems. I. Effect of charge on the bond properties of hydrogen fluoride

Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4sigma antibonding orbital of the neutral (F...H) system or the removal of one electron from its pi nonbonding orbitals, leading to (F...H)- and to (F...H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of rho(r). For (F...H), (F...H)-, and (F...H)+, the topological and energetic properties calculated at the F...H bond critical point (BCP) have been related to the 3sigma bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to rho(r) at the interatomic surface. The analysis has been carried out at several F...H internuclear distances, ranging from 0.8 to 3.0 A. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the pi and 4sigma electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F...H), (F...H)-, and (F...H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F-H bond but soften it, giving rise to the stable species (F-H)- and (F-H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F...H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F...H)+ and of the BMO expansion toward both nuclei in (F...H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F...H) (d(eq)0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system rho(d(eq)0), inverted triangle2 rho(d(eq)0), and H(d(eq)0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution.     

Topology of charge density of flucytosine and related molecules and characteristics of their bond charge distributions

The molecular charge distribution of flucytosine (4-amino-5-fluoro-2-pyrimidone), uracil, 5-fluorouracil, and thymine was studied by means of density functional theory calculations (DFT). The resulting distributions were analyzed by means of the atoms in molecules (AIM) theory. Bonds were characterized through vectors formed with the charge density value, its Laplacian, and the bond ellipticity calculated at the bond critical point (BCP). Within each set of C=O, C-H, and N-H bonds, these vectors showed little dispersion. C-C bonds formed three different subsets, one with a significant degree of double bonding, a second corresponding to single bonds with a finite ellipticity produced by hyperconjugation, and a third one formed by a pure single bond. In N-C bonds, a decrease in bond length (an increase in double bond character) was not reflected as an increase in their ellipticity, as in all C-C bonds studied. It was also found that substitution influenced the N-C, C-O, and C-C bond ellipticity much more than density and its Laplacian at the BCP. The Laplacian of charge density pointed to the existence of both bonding and nonbonding maxima in the valence shell charge concentration of N, O, and F, while only bonding ones were found for the C atoms. The nonbonding maxima related to the sites for electrophilic attack and H bonding in O and N, while sites of nucleophilic attack were suggested by the holes in the valence shell of the C atoms of the carbonyl groups.     

The kinetic energy of molecular charge distributions and molecular stability

This paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.     

Theoretical electron density distributions for Fe- and Cu-sulfide earth materials: a connection between bond length, bond critical point properties, local energy densities, and bonded interactions

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, rho(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, rho(rc), the Laplacian, triangle down2rho(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of rho(rc) and triangle down2rho(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of rho(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the high-spin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the rho(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.     

Bond length and local energy density property connections for non-transition-metal oxide-bonded interactions

For a variety of molecules and earth materials, the theoretical local kinetic energy density, G(r(c)), increases and the local potential energy density, V(r(c)), decreases as the M-O bond lengths (M = first- and second-row metal atoms bonded to O) decrease and the electron density, rho(r(c)), accumulates at the bond critical points, r(c). Despite the claim that the local kinetic energy density per electronic charge, G(r(c))/rho(r(c)), classifies bonded interactions as shared interactions when less than unity and closed-shell when greater, the ratio was found to increase from 0.5 to 2.5 au as the local electronic energy density, H(r(c)) = G(r(c)) + V(r(c)), decreases and becomes progressively more negative. The ratio appears to be a measure of the character of a given M-O bonded interaction, the greater the ratio, the larger the value of rho(r(c)), the smaller the coordination number of the M atom and the more shared the bonded interaction. H(r(c))/rho(r(c)) versus G(r(c))/rho(r(c)) scatter diagrams categorize the M-O bonded interactions into domains with the local electronic energy density per electron charge, H(r(c))/rho(r(c)), tending to decrease as the electronegativity differences for the bonded pairs of atoms decrease. The values of G(r(c)) and V(r(c)), estimated with a gradient-corrected electron gas theory expression and the local virial theorem, are in good agreement with theoretical values, particularly for the bonded interactions involving second-row M atoms. The agreement is poorer for shared C-O and N-O bonded interactions.     

Electron density and energy decomposition analysis in hydrogen-bonded complexes of azabenzenes with water, acetamide, and thioacetamide

Ab initio and density functional theoretical studies on hydrogen-bonded complexes of azabenzenes with water, acetamide, and thioacetamide have been carried out to explore the controversy involved in the relative order of their stability in a systematic way. The interaction energies of these complexes have been analyzed using the Morokuma energy decomposition method, and the nature of the various hydrogen bonds formed has been investigated through topological aspects using Bader's atom in a molecule (AIM) theory. Morokuma energy decomposition analysis reveals that the major contributions to the energetics are from the polarization (PL) and charge transfer (CT) energies. From the calculated topological results, excellent linear correlation is shown to exist between the hydrogen-bond length, electron density [rho(r)], and its Laplacian [nabla(2)rho(r)] at the bond critical points for all the complexes considered.     

Quantum chemistry aspects of the solvent effects on the ene reaction of 1‐Phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene

A density functional theory study was used to investigate the quantum aspects of the solvent effects on the kinetic and mechanism of the ene reaction of 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene. Using the B3LYP/6–311++ G(d,p) level of the theory, reaction rates have been calculated in the various solvents and good agreement with the experimental data has been obtained. Natural bond orbital analysis has been applied to calculate the stabilization energy of N18? H19 bond during the reaction. Topological analysis of quantum theory of atom in molecule (QTAIM) studies for the electron charge density in the bond critical point (BCP) of N18? H19 bond of the transition states (TSs) in different solvents shows a linear correlation with the interaction energy. It is also seen form the QTAIM analysis that increase in the electron density in the BCP of N18? H19, raises the corresponding vibrational frequency. Average calculated ratio of 0.37 for kinetic energy density to local potential energy density at the BCPs as functions of N18? H19 bond length in different media confirmed covalent nature of this bond. Using the concepts of the global electrophilicity index, chemical hardness and electronic chemical potentials, some correlations with the rate constants and interaction energy have been established. Mechanism and kinetic studies on 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene ene reaction suggests that the reaction rate will boost with interaction energy enhancement. Interaction energy of the TS depends on the solvent nature and is directly related to electron density of the bonds involved in the reaction proceeding, global electrophilicity index and electronic chemical potential. However, the chemical hardness relationship is reversed. Finally, an interesting and direct correlation between the imaginary vibrational frequency of the N18? H19 critical bond and its electron density at the TS has been obtained. © 2014 Wiley Periodicals, Inc.     

Infrared intensity analysis of hydroxyl stretching modes in carboxylic acid dimers by means of the charge–charge flux–dipole flux model

The Charge‑Charge Flux‑Dipole Flux (CCFDF) model in terms of multipoles from the quantum theory of atoms in molecules (QTAIM) was used to investigate the variations in infrared intensities of hydroxyl (O H) stretching modes during the dimerization of carboxylic acids. The hydrogen bond formation in these systems results into bathochromic shifts of vibrational frequencies for all the O H stretching modes along with huge infrared intensity increments for some of them. These bands become more intense on dimerization due mainly to changes in the cross-term contribution between charge and charge flux. In addition, interaction energies for the pair of atoms directly involved in individual hydrogen bonds (O…H) are linearly correlated to electron densities at their bond critical points (BCPs). Therefore, the hydrogen bonds between the carbonyl group (CO) of acetic acid and the hydroxyl group of halogenated monomers show the largest electron density values at their BCPs. The formation of these intermolecular interactions is also accompanied by ionic character enhancements of O H bonds and electron density decrements at their BCPs. We finally noticed that the hydrogen atom belonging to the hydroxyl group loses electronic charge, while the oxygen from the CO end becomes more negatively charged during dimerization. © 2019 Wiley Periodicals, Inc.     

Topological properties of the electrostatic potential in weak and moderate N...H hydrogen bonds

The topological analyses of the electrostatic potential phi(r) and the electron density distribution rho(r) have been performed for a set of 20 neutral complexes with weak and moderate N...H bonds. In all cases, a zero flux surface of the electrostatic potential containing a saddle point analogous to the bond critical point of the electron density distribution is observed. These surfaces define an equivalent of the atomic basin of rho(r) for the electrostatic potential, which exhibits zero net charge and can be regarded as an electrostatically isolated region if its volume is finite. The phi(r) and rho(r) zero flux surfaces divide the hydrogen-bonding region in three parts, being the central one related to the electrostatic interaction between donor and acceptor. This central region exhibits a relative size of approximately 13-14% of the N...H distance dNH, it belongs to the outermost shell of the nitrogen and is mainly associated with its lone pair. Topological properties of both rho(r) and phi(r), as well as the electron kinetic (G) and potential (V) energy densities, show similar dependences with dNH at both bond critical points (phi-BCP and rho-BCP). Phenomenological proportionalities between the rho(r) curvatures and G and V are also found at the electrostatic potential critical point. The curvatures of the electrostatic potential, which are interpreted in terms of the electrostatic forces in the bonding region, present the same exponential dependency as the electron density distribution, to which they are related by Poisson's equation.     

The nature of bond critical points in dinuclear copper(I) complexes

Closed-shell contacts between two copper(I) ions are expected to be repulsive. However, such contacts are quite frequent and are well documented. Crystallographic characterization of such contacts in unsupported and bridged multinuclear copper(I) complexes has repeatedly invited debates on the existence of cuprophilicity. Recent developments in the application of Bader's theory of atoms-in-molecules (AIM) to systems in which weak hydrogen bonds are involved suggests that the copper(I)-copper(I) contacts would benefit from a similar analysis. Thus the nature of electron-density distributions in copper(I) dimers that are unsupported, and those that are bridged, have been examined. A comparison of complexes that are dimers of symmetrical monomers and those that are dimers of two copper(I) monomers with different coordination spheres has also been made. AIM analysis shows that a bond critical point (BCP) between two Cu atoms is present in most cases. The nature of the BCP in terms of the electron density, ρ, and its Laplacian is quite similar to the nature of critical points observed in hydrogen bonds in the same systems. The ρ is inversely correlated to Cu-Cu distance. It is higher in asymmetrical systems than what is observed in corresponding symmetrical systems. By examining the ratio of the local electron potential-energy density (V(c)) to the kinetic energy density (G(c)), |V(c)|/G(c) at the critical point suggests that these interactions are not perfectly ionic but have some shared nature. Thus an analysis of critical points by using AIM theory points to the presence of an attractive metallophilic interaction similar to other well-documented weak interactions like hydrogen bonding.     

Theoretical study of hydrogen bonding interaction in nitroxyl (HNO) dimer: interrelationship of the two N-H...O blue-shifting hydrogen bonds

The hydrogen bonding interactions of the HNO dimer have been investigated using ab initio molecular orbital and density functional theory (DFT) with the 6-311++G(2d,2p) basis set. The natural bond orbital (NBO) analysis and atom in molecules (AIM) theory were applied to understand the nature of the interactions. The interrelationship between one N-H...O hydrogen bond and the other N-H...O hydrogen bond has been established by performing partial optimizations. The dimer is stabilized by the N-H...O hydrogen bonding interactions, which lead to the contractions of N-H bonds as well as the characteristic blue-shifts of the stretching vibrational frequencies nu(N-H). The NBO analysis shows that both rehybridization and electron density redistribution contribute to the large blue-shifts of the N-H stretching frequencies. A quantitative correlations of the intermolecular distance H...O (r(H...O)) with the parameters: rho at bond critical points (BCPs), s-characters of N atoms in N-H bonds, electron densities in the sigma*(N-H), the blue-shift degrees of nu(N-H) are presented. The relationship between the difference of rho (|Deltarho|) for the one hydrogen bond compared with the other one and the difference of interaction energy (DeltaE) are also illustrated. It indicates that for r(H...O) ranging from 2.05 to 2.3528 A, with increasing r(H...O), there is the descending tendency for one rho(H...O) and the ascending tendency for the other rho(H...O). r(H...O) ranging from 2.3528 to 2.85 A, there are descending tendencies for the two rho(H...O) with increasing r(H...O). On the potential energy surface of the dimer, the smaller the difference between one rho(H...O) and the other rho(H...O) is, the more stable the structure is. As r(H...O) increases, the blue-shift degrees of nu(N-H) decrease. The cooperative descending tendencies in s-characters of two N atoms with increasing r(H...O) contribute to the decreases in blue-shift degrees of nu(N-H). Ranging from 2.05 to 2.55 A, the increase of the electron density in one sigma*(N-H) with elongating r(H...O) weakens the blue-shift degrees of nu(N-H), simultaneously, the decrease of the electron density in the other sigma*(N-H) with elongating r(H...O) strengthens the blue-shift degrees of nu(N-H). Ranging from 2.55 to 2.85 A, the cooperative ascending tendencies of the electron densities in two sigma*(N-H) with increasing r(H...O) contribute to the decreases in blue-shift degrees of nu(N-H).     

Electron density based characterization of π bonds in planar molecules

A new method has been developed to detect and analyze molecular π systems. The concept of bonding critical point is generalized to electronic π systems, and it is shown how a π bond can be characterized via the corresponding bond critical point (BCP) in planar molecules. In this context, charge density and its Laplacian at the BCP(π) of a strongly delocalized π system can be distinguished from that of a localized one. The presented formalism is applied to three types of nanoconductors as conjugated polyenes, which revealed the alternative pattern of the double bonds. Also, several cyclic conjugated molecules are considered to explore their π electronic structure and aromaticity.