Continua of interactions between pairs of atoms in molecular crystals

The electron density distributions in crystals of five previously studied DMAN complexes and five Schiff bases (two new ones) have been analysed in terms of various properties of bond critical points (BCPs) found in the pair-wise interactions in their lattices. We analysed the continua of interactions including covalent/ionic bonds as well as hydrogen bonds and all other types of weak interactions for all pairs of interacting atoms. The charge density at BCPs and local kinetic and potential energy densities vary exponentially with internuclear distance (or other measures of separation). The parameters of the dependences appear to be characteristics of particular pairs of atom types. The Laplacian and the total (sum of kinetic and potential) energy density at BCPs show similar behaviour with the dependence being of the Morse type. The components lambda1, lambda2, lambda3 of the Laplacian at BCPs vary systematically with internuclear distance according to the type of atom pair. For lambda1 and lambda2 the distribution is of the exponential type, whereas lambda3 does not seem to follow any simple functional form, consistent with previous theoretical findings. Analytical nonlinear dependences of Laplacian on charge density have been found. They agree reasonably well with those obtained by least square fit of the Laplacian to charge density data. There are four distinct regions of the [symbol: see text]2rho(BCP)/rho(BCP) space, generated by E(BCP) = 0 and G(BCP)/rho(BCP) = 1 conditions. Two regions clearly correspond to the shared-shell and closed-shell interactions and the other two to some intermediate situation.     

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).     

Hydrogen bonding in substituted formic acid dimers

The hydrogen-bonded dimers of formic acid derivatives XCOOH (X = H, F, Cl, and CH3) have been investigated using density functional theory (B3LYP) and second-order M?ller-Plesset perturbation (MP2) methods, with the geometry optimization carried out using 6-311++G(2d,2p) basis set. The dimerization energies calculated using aug-cc-pVXZ (with X = D and T) basis have been extrapolated to infinite basis set limit using the standard methodology. The results indicate that the fluorine-substituted formic acid dimer is the most stable one in comparison to the others. Topological analysis carried out using Bader's atoms in molecules (AIM) theory shows good correlation of the values of electron density and its Laplacian at the bond critical points (BCP) with the hydrogen bond length in the dimers. Natural bond orbital (NBO) analysis carried out to study the charge transfer from the proton acceptor to the antibonding orbital of the X-H bond in the complexes reveals that most of the dimers are associated with conventional H-bonding except a few, where improper blue-shifting hydrogen bonds are found to be present.     

Oxidative properties of FeO2+: electronic structure and solvation effects

An electronic structure analysis is provided of the action of solvated FeO(2+), [FeO(H(2)O)(5)](2+), as a hydroxylation catalyst. It is emphasized that the oxo end of FeO(2+) does not form hydrogen bonds (as electron donor and H-bond acceptor) with H-bond donors nor with aliphatic C-H bonds, but it activates C-H bonds as an electron acceptor. It is extremely electrophilic, to the extent that it can activate even such poor electron donors as aliphatic C-H bonds, the C-H bond orbital acting as electron donor in a charge transfer type of interaction. Lower lying O-H bonding orbitals are less easily activated. The primary electron accepting orbital in a water environment is the 3sigma*alpha orbital, an antibonding combination of Fe-3d(z(2)) and O-2p(z), which is very low-lying relative to the pi*alpha compared with, for example, the sigma* orbital in O(2) relative to its pi*. This is ascribed to relatively small Fe-3d(z(2)) with O-2p(z) overlap, due to the nodal structure of the 3d(z(2)).The H-abstraction barrier is very low in the gas phase, but it is considerably enhanced in water solvent. This is shown to be due to strong screening effects of the dielectric medium, leading to relative destabilization of the levels of the charged [FeO(H(2)O)(5)](2+) species compared to those of the neutral substrate molecules, making it a less effective electron acceptor. The solvent directly affects the orbital interactions responsible for the catalytic reaction.     

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.     

Cooperative effects, strengths of hydrogen bonds, and intermolecular interactions in circular cis, trans-cyclotriazane clusters (n = 3-8)

Based on Becke's three parameter functional [J. Chem. Phys. 98, 5648 (1993)] of density functional theory (DFT) with the correlation of Lee-Yang-Parr [Phys. Rev. B 37, 785 (1988)] (DFT/B3LYP), the natural bond orbital (NBO) analysis, the Bader's theory of atoms in molecule (AIM), our calculations indicate that as cluster size (n) increases, the n-dependent cooperative changes in the lengths of the N...H H bonds (HBs) and N-H bonds, the N-H stretching frequencies and intensities, and the n(N)-->sigma*(N-H) charge transfers are observed to be pervasive in the circular cis, trans-cyclotriazane clusters (n = 3-8), which is very different from the linear cis, trans-cyclotriazane clusters reported in previous work. According to the NBO and AIM theories, the cooperativity of the intermolecular n(N)-->sigma*(N-H) interaction leads to the n-dependent N...H contractions. In this way, the stronger N...H bond is formed, as reflected in the increase in their rho(r(cp)) values. This increased electron density is translated into the improved capacity to concentrate electrons at the HB bond critical point (BCP), i.e., a higher potential energy V(r(cp)). On the other hand, stronger repulsion is also activated to counteract the contraction, which is reflected in the increased G(r(cp)) value that gives the tendency of the system to dilute electrons at the HB BCP. In terms of the three-body symmetry-adapted perturbation theory (three-body SAPT), the induction nonadditivity accounts for up to 97% of the nonadditive energy in the circular trimer. It can believed that the marked cooperativity of the n(N)-->sigma*(N-H) interactions is of nonadditive induction in nature. The N...H formation and nature of cooperativity in the circular clusters differ from those in the linear clusters that have been reported previously. According to the SAPT(DFT) method which is a combination of SAPT with the asymptotically corrected DFT, the cis, trans-cyclotriazane systems should contain remarkable dispersion interactions. However, the short-range dispersion cannot be reproduced thoroughly by DFT/B3LYP. A quantum cluster equilibrium model illustrates the neglected dispersion energies and the nonadditive energies can affect markedly the properties of the liquid consisting of the circular clusters.     

Protonation of gas-phase aromatic molecules: IR spectrum of the fluoronium isomer of protonated fluorobenzene

The IR spectrum of the fluoronium isomer of protonated fluorobenzene (F-C(6)H(6)F(+), phenylfluoronium) is recorded in the vicinity of the C-H and F-H stretch fundamentals to obtain the first structured spectrum of an isolated protonated aromatic molecule in the gas phase. Stable F-C(6)H(6)F(+) ions are produced via proton transfer from CH(5)(+) to fluorobenzene (C(6)H(5)F) in a supersonic plasma expansion. The F-C(6)H(6)F(+) spectrum recorded between 2,540 and 4,050 cm(-1) is consistent with a weakly bound ion-dipole complex composed of HF and the phenyl cation, HF-C(6)H(5)(+). The strongest transition occurs at 3,645 cm(-1) and is assigned to the F-H stretch (sigma(FH)). The antisymmetric C-H stretch of the two ortho hydrogen atoms, sigma(CH) = 3,125 cm(-1), is nearly unshifted from bare C(6)H(5)(+), indicating that HF complexation has little influence on the C-H bond strength of C(6)H(5)(+). Despite the simultaneous production of the more stable ring protonated carbenium isomers of C(6)H(6)F(+) (fluorobenzenium) in the electron ionization source, F-C(6)H(6)F(+) can selectively be photodissociated into C(6)H(5)(+) and HF under the present experimental conditions, because it has a much lower dissociation energy than all carbenium isomers. Quantum chemical calculations at the B3LYP and MP2 levels of theory using the 6-311G(2df,2pd) basis support the interpretation of the experimental data and provide further details on structural, energetic, and vibrational properties of F-C(6)H(6)F(+), the carbenium isomers of C(6)H(6)F(+), and other weakly bound HF-C(6)H(5)(+) ion-dipole complexes. The dissociation energy of F-C(6)H(6)F(+) with respect to dehydrofluorination is calculated as D(0) = 4521 cm(-1) (approximately 54 kJ/mol). Analysis of the charge distribution in F-C(6)H(6)F(+) supports the notation of a HF-C(6)H(5)(+) ion-dipole complex, with nearly the whole positive charge of the added proton distributed over the C(6)H(5)(+) ring. As a result, protonation at the F atom strongly destabilizes the C-F bond in C(6)H(5)F.     

Charge penetration and the origin of large O-H vibrational red-shifts in hydrated-electron clusters, (H2O)n-

The origin of O-H vibrational red-shifts observed experimentally in (H2O)n(-) clusters is analyzed using electronic structure calculations, including natural bond orbital analysis. The red-shifts are shown to arise from significant charge transfer and strong donor-acceptor stabilization between the unpaired electron and O-H sigma* orbitals on a nearby water molecule in a double hydrogen-bond-acceptor ("AA") configuration. The extent of e(-) --> sigma* charge transfer is comparable to the n --> sigma* charge transfer in the most strongly hydrogen-bonded X(-)(H2O) complexes (e.g., X = F, O, OH), even though the latter systems exhibit much larger vibrational red-shifts. In X(-)(H2O), the proton affinity of X(-) induces a low-energy XH...(-)OH diabatic state that becomes accessible in v = 1 of the shared-proton stretch, leading to substantial anharmonicity in this mode. In contrast, the H + (-)OH(H2O)(n-1) diabat of (H2O)n(-) is not energetically accessible; thus, the O-H stretching modes of the AA water are reasonably harmonic, and their red-shifts are less dramatic. Only a small amount of charge penetrates beyond the AA water molecule, even upon vibrational excitation of these AA modes. Implications for modeling of the aqueous electron are discussed.     

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.     

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.     

Cooperative effects and strengths of hydrogen bonds in open-chain cis-triaziridine clusters (n = 2-8): a DFT investigation

We employ DFT/B3LYP method to investigate linear open-chain clusters (n = 2-8) of the cis-triaziridine molecule that is a candidate molecule for high energy density materials (HEDM). Our calculations indicate that the pervasive phenomena of cooperative effects are observed in the clusters of n = 3-8, which are reflected in changes in lengths of N...H hydrogen bonds, stretching frequencies, and intensities of N-H bonds, dipole moments, and charge transfers as cluster size increases. The n(N) --> sigma*(N-H) interactions, i.e., the charge transfers from lone pairs (n(N)) of the N atoms into antibonds (sigma*) of the N-H bonds acting as H-donors, can be used to explain the observed cooperative phenomena. The approaches based upon natural bond orbital (NBO) method and theory of atoms in molecule (AIM) to evaluating N...H strengths are found to be equivalent. In the process of N...H bonding, cooperative nature of n(N) --> sigma*(N-H) interactions promotes formation of stronger N...H bonds as reflected in increases in the capacities of cis-triaziridine clusters to concentrate electrons at the bond critical points of N...H bonds. The calculated nonadditive energies also show that the cooperative effects due to n(N) --> sigma*(N-H) interactions indeed provide additional stabilities for the clusters.     

DFT-UX3LYP studies on the coordination chemistry of Ni2+. Part 1: Six coordinate [Ni(NH3)n(H2O)(6-n)]2+ complexes

DFT calculations with the UX3LYP hybrid functional and a medium-sized 6-311++G(d,p) basis set were performed to examine the gas-phase structure of paramagnetic (S = 1) six-coordinate complexes [Ni(NH3)n(H2O)(6-n)](2+), 0 < or = n < or = 6. Significant interligand hydrogen bonding was found in [Ni(H2O)6](2+), but this becomes much less significant as NH3 replaces H2O in the coordination sphere of the metal. Bond angles and bond lengths obtained from these calculations compare reasonably well with available crystallographic data. The mean calculated Ni-O bond length in [Ni(H2O)6](2+) is 2.093 A, which is 0.038 A longer than the mean of the crystallographically observed values (2.056(22) A, 108 structures) but within 2sigma of the experimental values. The mean calculated Ni-N bond length in [Ni(NH3)6](2+) is 2.205(3) A, also longer (by 0.070 A) than the crystallographically observed mean (2.135(18) A, 7 structures). Valence bond angles are reproduced within 1 degree. The successive replacement of H2O by NH3 as ligands results in an increase in the stabilization energy by 7 +/- 2 kcal mol(-1) per additional NH3 ligand. The experimentally observed increase in the lability of H2O in Ni(II) as NH3 replaces H2O in the coordination sphere is explained by an increase in the Ni-OH2 bond length. It was found from a natural population analysis that complexes with the highest stabilization energies are associated with the greatest extent of ligand-to-metal charge transfer, and the transferred electron density is largely accommodated in the metal 4s and 3d orbitals. An examination of the charge density rho bcp and the Laplacian of the charge density nabla(2)rho(bcp) at the metal-ligand bond critical points (bcp) in the series show a linear correlation with the charge transferred to the metal. Values of nabla(2)rho(bcp) are positive, indicative of a predominantly closed-shell interaction. The charge transferred to the metal increases as n, the number of NH3 ligands in the complex, increases. This lowers the polarizing ability of the metal on the ligand donors and the average metal-ligand bond length increases, resulting in a direct correlation between the dissociation energy of the complexes and the reciprocal of the average metal-ligand bond length. There is a strong correlation between the charge transferred to the metal and experimental DeltaH values for successive replacement of H2O by NH3, but a correlation with stability constants (log beta values) breaks when n = 5 and 6, probably because of entropic effects in solution. Nevertheless, DFT calculations may be a useful way of estimating the stability constants of metal-ligand systems.     

Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.     

Transition-state variation in the nucleophilic substitution reactions of aryl bis(4-methoxyphenyl) phosphates with pyridines in acetonitrile

The kinetics and mechanism of the reactions of Z-aryl bis(4-methoxyphenyl) phosphates, (4-MeOC(6)H(4)O)(2)P(=O)OC(6)H(4)Z, with pyridines (XC(5)H(4)N) are investigated in acetonitrile at 55.0 degrees C. In the case of more basic phenolate leaving groups (Z = 4-Cl, 3-CN), the magnitudes of beta(X) (beta(nuc)) and beta(Z) (beta(lg)) indicate that mechanism changes from a concerted process (beta(X) = 0.22-0.36, beta(Z) = -0.42 to -0.56) for the weakly basic pyridines (X = 3-Cl, 4-CN) to a stepwise process with rate-limiting formation of a trigonal bipyramidal pentacoordinate (TBP-5C) intermediate (beta(X) = 0.09-0.14, beta(Z) = -0.08 to -0.28) for the more basic pyridines (X = 4-NH(2), 3-CH(3)). This proposal is supported by a large negative cross-interaction constant (rho(XZ) = -1.98) for the former and a positive rho(XZ) (+0.97) for the latter processes. In the case of less basic phenolate leaving groups (Z = 3-CN, 4-NO(2)), the unusually small magnitude of beta(Z) values is indicative of a direct backside attack TBP-5C TS in which the two apical sites are occupied by the nucleophile and leaving group, ap(NX)-ap(LZ). The instability of the putative TBP-5C intermediate leading to a concerted displacement is considered to result from relatively strong proximate charge transfer interactions between the pi-lone pairs on the directly bonded equatorial oxygen atoms and the apical bond (n(O)(eq) - sigma(ap)). These are supported by the results of natural bond orbital (NBO) analyses at the NBO-HF/6-311+G//B3LYP/6-311+G level of theory.     

Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.     

Computational study of the process of hydrogen bond breaking: the case of the formamide-formic acid complex

MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) quantum calculations are used to study the formamide-formic acid complex (FFAC), a system bound by two hydrogen bonds, N--H...O and O--H...O, that forms a bond ring at equilibrium. When the intermolecular separation between monomers R increases, this ring opens at a distance for which the weaker N--H...O bond breaks remaining the stronger O--H...O bond. The computational study characterizes that process addressing changes of interaction energy DeltaE, structure and properties of the electron density rho(r) as well as spatial distributions of rho(r), the electrostatic potential U(r), and the electron localization function eta(r). It is shown that the spatial derivatives of DeltaE, the topology of rho(r), and qualitative changes noticed in U(r) = 0 isocontours allow to identify a precise distance R for which one can say the N--H...O hydrogen bond has broken. Both levels of theory predict essentially the same changes of structure and electron properties associated to the process of breaking and virtually identical distances at which it takes place.     

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).     

The nature of the chemical bond revisited: an energy-partitioning analysis of nonpolar bonds

The nature of the chemical bond in nonpolar molecules has been investigated by energy-partitioning analysis (EPA) of the ADF program using DFT calculations. The EPA divides the bonding interactions into three major components, that is, the repulsive Pauli term, quasiclassical electrostatic interactions, and orbital interactions. The electrostatic and orbital terms are used to define the nature of the chemical bond. It is shown that nonpolar bonds between main-group elements of the first and higher octal rows of the periodic system, which are prototypical covalent bonds, have large attractive contributions from classical electrostatic interactions, which may even be stronger than the attractive orbital interactions. Fragments of molecules with totally symmetrical electron-density distributions, like the nitrogen atoms in N(2), may strongly attract each other through classical electrostatic forces, which constitute 30.0 % of the total attractive interactions. The electrostatic attraction can be enhanced by anisotropic charge distribution of the valence electrons of the atoms that have local areas of (negative) charge concentration. It is shown that the use of atomic partial charges in the analysis of the nature of the interatomic interactions may be misleading because they do not reveal the topography of the electronic charge distribution. Besides dinitrogen, four groups of molecules have been studied. The attractive binding interactions in H(n)E-EH(n) (E=Li to F; n=0-3) have between 20.7 (E=F) and 58.4 % (E=Be) electrostatic character. The substitution of hydrogen by fluorine does not lead to significant changes in the nature of the binding interactions in F(n)E-EF(n) (E=Be to O). The electrostatic contributions to the attractive interactions in F(n)E-EF(n) are between 29.8 (E=O) and 55.3 % (E=Be). The fluorine substituents have a significant effect on the Pauli repulsion in the nitrogen and oxygen compounds. This explains why F(2)N-NF(2) has a much weaker bond than H(2)N-NH(2), whereas the interaction energy in FO-OF is much stronger than in HO-OH. The orbital interactions make larger contributions to the double bonds in HB=BH, H(2)C=CH(2), and HN=NH (between 59.9 % in B(2)H(2) and 65.4 % in N(2)H(2)) than to the corresponding single bonds in H(n)E-EH(n). The orbital term Delta E(orb) (72.4 %) makes an even greater contribution to the HC triple bond CH triple bond. The contribution of Delta E(orb) to the H(n)E=EH(n) bond increases and the relative contribution of the pi bonding decreases as E becomes more electronegative. The pi-bonding interactions in HC triple bond CH amount to 44.4 % of the total orbital interactions. The interaction energy in H(3)E-EH(3) (E=C to Pb) decreases monotonically as the element E becomes heavier. The electrostatic contributions to the E-E bond increases from E=C (41.4 %) to E=Sn (55.1 %) but then decreases when E=Pb (51.7 %). A true understanding of the strength and trends of the chemical bonds can only be achieved when the Pauli repulsion is considered. In an absolute sense the repulsive Delta E(Pauli) term is in most cases the largest term in the EPA.     

Solvolysis of para-substituted cumyl chlorides. Brown and Okamoto's electrophilic substituent constants revisited using continuum solvent models

Brown and Okamoto (J. Am. Chem. Soc. 1958, 80, 4979) derived their electrophilic substitutent constants, sigma(p)+, from the relative rates of solvolysis of ring-substituted cumyl chlorides in an acetone/water solvent mixture. Application of the Hammett equation to the rates for the meta-substituted cumyl chlorides, where there could be no resonance interaction with the developing carbocation, gave a slope, rho(+) = -4.54 ( identical with 6.2 kcal/mol free energy). Rates for the para-substituted chlorides were then used to obtain sigma(p)+ values. We have calculated gas-phase C-Cl heterolytic bond dissociation enthalpy differences, Delta BDE(het) (= BDE(het)(4-YC(6)H(4)CMe(2)Cl) - BDE(het)(C(6)H(5)CMe(2)Cl)), for 16 of the 4-Y substituents employed by Brown and Okamoto. The plot of Delta BDE(het) vs sigma(p)+ gave rho(+) (SD) = 16.3 (2.3) kcal/mol, i.e., a rho(+) value roughly 2.5 times greater than experiment. Inclusion of solvation (water) energies, calculated using three continuum solvent models, reduced rho(+) and SD. The computationally least expensive model used, SM5.42R (Li et al. Theor. Chem. Acc. 1999, 103, 9) gave the best agreement with experiment. This model yielded rho(+) (SD) = 7.7 (0.9) kcal/mol, i.e., a rho(+) value that is only 24% larger than experiment.     

Extension of the experimental electron density analysis to metastable states: a case example of the spin crossover complex Fe(btr)2(NCS)2.H2O

An experimental electron density (ED) analysis of the spin crossover coordination complex Fe(btr)(2)(NCS)(2).H(2)O has been performed in the ground low-spin (LS) state and in the metastable thermally quenched high-spin (HS) state at 15 K by fitting a multipolar model to high-resolution X-ray diffraction measurements. The ED has been quantitatively analyzed using the quantum theory of atoms in molecules. This is the first time the ED distribution of a molecular metastable state has been experimentally investigated. The electron deformation densities and derived Fe 3d orbital populations are characteristic of LS (t(2g)(6) e(g)(0)) and HS (t(2g)(4) e(g)(2)) electron configurations and indicate significant sigma donation to the Fe d(x)2(-)(y)2 and d(z)2 atomic orbitals. The Fe-N(NCS) and Fe-N(btr) coordination interactions are characterized using the laplacian distribution of the ED, the molecular electrostatic potential, and the fragment charges obtained by integration over the topological atomic basins. A combination of electrostatic and covalent contributions to these interactions is pointed out. Interlayer interactions are evidenced by the presence of bond critical points in N...H hydrogen bonds involving the non-coordinated water molecule. Systematic differences in the atomic displacement parameters between the LS and HS states have been described and rationalized in terms of modifications of bond force constants.