Local Potential Energy Density Research Articles

Study the Chemical Bonding of Heterometallic Trinuclear Cluster Containing Cobalt and Ruthenium: [(Cp*Co) (CpRu)2 (μ3-H) (μ-H)3] using QTAIM Approach

The topological parameters of the metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp*Co) (CpRu)2 (μ3-H) (μ-H)3]1 (Cp* = η5 -C5Me4Et), (Cp = η5 -C5Me5), was explored by using the Quantum Theory of Atoms-in-Molecules (QTAIM). The properties of bond critical points such as the bond delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density H(r), the local potential energy density V(r) and ellipticity ε(r) are compared with data from earlier organometallic system studies. A comparison of the topological processes of different atom-atom interactions has become possible thanks to these results. In the core of the heterometallic tetrahydrido cluster, the Ru2CoH4 part, the calculations show no existence of any bond critical points (BCP) or identical bond paths (BPs) between Ru-Ru and Ru-Co. Electron densities are determined by the position of bridging hydride atoms coordinated to Ru-Ru and Ru-Co, which significantly affects the bonds between these transition metal atoms. On the other hand, the results confirm that the cluster under study contains a 7c–11e bonding interaction delocalized over M3H4, as shown by the non-negligible delocalization index calculations. The small values for electron density ρ(b) above zero, together with the small values, again above zero, for Laplacian ∇2ρ(b) and the small positive values for total energy density H(b), are shown by the Ru-H and Co-H bonds in this cluster is typical for open-shell interactions. Also, the topological data for the bond interactions between Co and Ru metal atoms with the C atoms of the cyclopentadienyl Cp ring ligands are similar. They show properties very identical to open-shell interactions in the QTAIM classification.

A Theoretical Investigation of Chemical Bonding of a Heterometallic Trinuclear Cluster Containing Iridium and Ruthenium: [(Cp*Ir) (CpRu)2 (μ3-H) (μ-H)3] by QTAIM Approach

Numerous integral and local electron density’s topological parameters of significant metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp* Ir) (Cp Ru)2 (μ3-H) (μ-H)3]1 (Cp = η5 -C5Me5), (Cp* = η5 -C5Me4Et) were calculated and interpreted by using the quantum theory of atoms in molecules (QTAIM). The properties of bond critical points such as the delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density H(r), the local potential energy density V(r) and ellipticity ε(r) are compared with data from earlier organometallic system studies. A comparison of the topological processes of different atom-atom interactions has become possible thanks to these results. In the core of the heterometallic tetrahydrido cluster, the Ru2IrH4 part, the calculations showed that there are no bond critical points (BCPs) or identical bond paths (BPs) between Ru-Ru and Ru-Ir. The distribution of electron densities is determined by the position of bridging hydride atoms coordinated to Ru-Ru and Ru-Ir, which significantly affects the bonds between these transition metal atoms. On the other hand, the results confirm that the cluster under study contains a 7c–11e bonding interaction delocalized over M3H4, as shown by the non-negligible delocalization index calculations. The small values for ρ(b) above zero, together with the small values, again above zero, for Laplacian ∇2ρ(b) and the small positive values for total energy density H(b), are shown by the Ru-H and Ir-H bonds in this cluster is typical for open-shell interactions. Also, the topological data for the bond interactions between Ir and Ru metal atoms with the C atoms of the cyclopentadienyl Cp ring ligands are similar. They show properties very identical to open-shell interactions in the QTAIM classification.

Local potential energy density model (LPE): Applications and limitations to quantify intra/intermolecular interactions

In our previous work, we developed the local potential energy density model, LPE, based on the electrostatic force and QTAIM topological data with a high linearity with the supramolecular binding energy, SME, for the classical hydrogen bonds. In this work, we extended the investigation to other inter/intramolecular interactions. The LPE presented a high linearity with SME when excluding interactions of an ion with π-bonded groups or polar molecule. Due to this linearity, it is possible to obtain the SME of nearly all inter/intramolecular interaction from LPE values. The energy decomposition analysis from SAPT-DFT and LMOEDA showed that dispersion and electrostatic components are important to LPE, while polarization component impairs it. The LPE cannot be used for ions interacting with dipole or dipole or ion interacting with π-bonded systems). In addition, the absolute difference between the numerical values of LPE and SME is very small as in the case of our previous work.

Multiresolution non-covalent interaction analysis for ligand–protein promolecular electron density distributions

Nowadays, the topology of electron density (ED) distributions as well as the non-covalent interaction (NCI) analysis of reduced density gradient (RDG) distributions, are extensively used to characterize intermolecular contacts. Here, topological and NCI-based analyses are combined for the multiresolution study of the intermolecular interactions occurring in a drug-protein system (PDB access code: 3UNK). The method involves the search for the critical points (CP) of the well-known PASA model developed by Carbo-Dorca and co-workers, and the minima in the corresponding RDG grids. The CP-based representation of the intermolecular contacts enriches the geometry-based interactions found using a Web server. The stability of the intermolecular interactions is studied by following their corresponding CP trajectory in space at several degrees of the ED smoothing, and by the evaluation of the local potential energy density (LPDE). It is observed that several RDG minima are located at the meeting point of CP trajectories initiated in the unsmoothed ED distribution. At high smoothing levels, the accumulation of ED charges at the ligand–protein interface progressively emerges and is detected through the study of the Laplacian values at the CPs and RDG minima. In parallel, the distance-dependency of the LPED values is less and less clear while the density-dependency is favored. The CP networks and their descriptors are seen as a signature of the ligand–protein arrangement, which is proposed to be further used in the characterization of ligand–protein stackings obtained from, e.g., crystal structures, docking calculations, Molecular Dynamics simulations, and pharmacophore designs.

The QTAIM Approach to Chemical Bonding in Triruthenium Carbonyl Cluster: [Ru3 (μ-H)(μ3-κ2-Haminox-N,N)(CO)9

The bonding in the hydride triruthenium carbonyl cluster [Ru3 (μ-H)(μ3-κ2-Haminox-N,N)(CO)9 is investigated by using the Quantum Theory of Atoms-in-Molecules (QTAIM). Calculated metal–metal and metal–ligand bond critical points (bcp) properties, electron density ρ(b), Laplacian ∇2ρ(b), local energy density H(b), local kinetic (Lagrangian) energy density G(b), local potential energy density V(b) ellipticity ε(b), and bond delocalization indices δ(A, B) are consistent with the relevant transition metal clusters in the literature. The topological data recognizes bond paths (bp) and bond critical points for metal-metal interactions in the core of the hydride triruthenium cluster [Ru(1)-Ru(3) and Ru(2)-Ru(3)]. However, no direct bond path is found for the interaction between the hydride bridged Ru atoms, while a non-negligible delocalization index δ(Ru(1)…Ru(2)) is obtained for this non-bonding interaction. An interaction of 5-center 6-electron type is proposed for the core. The topological parameters of Ru-N oxazoline ring bond suggest a pure σ-bond.

Synthesis, structure, and photophysical properties of luminescent zinc and cadmium complexes containing 2-pyridyl-substituted pyrrolo[2,3-b]quinoxaline

New [N,N,N]-tridentate ligand containing 2-aminomethylpyridyl group at the enamino-pyrrolo[2,3-b]quinoxalin-2-one system (2) was synthesized and characterized. The reaction of ligand with zinc acetate and zinc acetylacetonate resulted in five-coordinated zinc complexes: coordination polymer (E)-2-Zn(µ2-η1:η1-OAc) and (E)-2-ZnPyacac. Cadmium acetate and also acetylacetonate with the ligand both formed six-coordinated complexes with binding mode 2:1. The new complexes were characterized by NMR, elemental analysis, UV–Vis, and fluorescence spectroscopy. X-ray structural analysis of the single crystals of [(E)-2]2Cd, (E)-2-Zn(µ2-η1:η1-OAc), and (E)-2-ZnPyacac showed the orientation of nitrogen and oxygen donor groups, the distortion of the fluorophore conformations, CH-π and π-π non-covalent interactions and formation of hydrogen bonds were responsible for the fluorescence enhancement in the solid state. The effect of an alkyl linker (CH2)n, n=0, 1 or 2 length, between the enamine-pyrrolo[2,3-b]quinoxaline fluorophore and an ionophore pyridyl group, on the coordination geometry of fluorescent zinc and cadmium complexes and on the fluorescence quantum yields was discussed. The increase of zinc coordination numbers from 4 to 6 is accompanied by a substantial decrease of the fluorescence quantum yield from 0.109 to 0.006 for the complexes in acetonitrile as well as the decrease of dipole moments in ground state from 9.87D to 6.04D. Comparing the local potential energy density to charge density ratio, G(r)/ρ(r), calculated using a density functional theory (DFT), indicated that the zinc complexes were more stable when the coordination number of the zinc ion is lower than 6.

Secondary Structure Effects on the Acidity of Histidine and Lysine-Based Peptides Model; A Theoretical Study

In this study, the effect of the secondary structure of the protein on the acid strength of three structures of random (R), alpha helix (α) and beta sheet () were investigated theoretically. These structures are related to the cationic amino acids of histidine and lysine in the polypeptide chain of eight-glycine residue. Computational methods at the HF, B3LYP, X3LYP and M05-2X levels in the gas and solution phases were applied. Implicit CPCM solvation model and explicit 2-layer ONIOM methods for the computations in solution were used with the 6-31G (d) basis set. Comparison of pKa values of histidine-based peptide shows that acid strength is accorded to: > α > R, while in the case of lysine, acid strength is accordance to: α >  > R. Based on the obtained data, ONIOM method is unable to predict the pKa values in the explicit solvation model. NBO analysis showed that one of the main reasons for the increase in the acidity of the solution phase is the increase in delocalization energy difference (ΔEdelocal) of the neutral acid and the corresponding cation. Topological analysis of quantum theory of atoms in molecules for the electron charge density at the bond critical points of the hydrogen bonds of the secondary structures in the presence of the solvent does not show a meaningful correlation with the interaction energy or acid strength. The absolute average ratio of 1.37 and 1.34 for the kinetic energy density to the local potential energy density of lysine and histidine-based peptides, respectively, reveals the non-covalent nature of the O … H bonds. Finally, based on the obtained results, pKa of the proteins can be predicted as a function of hydrogen bond characters and their delocalization energy differences between the cationic and neutral forms.

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 N18H19 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 N18H19 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 N18H19, 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 N18H19 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 N18H19 critical bond and its electron density at the TS has been obtained. © 2014 Wiley Periodicals, Inc.

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.

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.

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.

From weak interactions to covalent bonds: a continuum in the complexes of 1,8-bis(dimethylamino)naphthalene.

Experimental charge density distributions in a series of ionic complexes of 1,8-bis(dimethylamino)naphthalene (DMAN) with four different acids: 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid), 4,5-dichlorophthalic acid, dicyanoimidazole, and o-benzoic sulfimide dihydrate (saccharin) have been analyzed. Variation of charge density properties and derived local energy densities are investigated, over all inter- and intramolecular interactions present in altogether five complexes of DMAN. All the interactions studied [[O...H...O](-), C[bond]H...O, [N[bond]H...N](+), O[bond]H...O, C[bond]H...N, C pi...N pi, C pi...C pi, C[bond]H...Cl, N[bond]H(+)] follow exponential dependences of the electron density, local kinetic and potential energies at the bond critical points on the length of the interaction line. The local potential energy density at the bond critical points has a near-linear relationship to the electron density. There is also a Morse-like dependence of the laplacian of rho on the length of interaction line, which allows a differentiation of ionic and covalent bond characters. The strength of the interactions studied varies systematically with the relative penetration of the critical points into the van der Waals spheres of the donor and acceptor atoms, as well as on the interpenetration of the van der Waals spheres themselves. The strong, charge supported hydrogen bond in the DMANH(+) cation in each complex has a multicenter character involving a [[Me(2)N[bond]H....NMe(2)](+)....X(delta-)] assembly, where X is the nearest electronegative atom in the crystal lattice.