Topological studies on IRC paths of X+H2→XH+H reactions

Topological properties of potential energy and electronic density distribution on five reaction paths X+H₂→XH+H (X=H, N, HN, H₂C, NC) are investigated at the level of UMP2/6–311G(d,p). It has been found that in the region of the reaction paths studied, where B(r_c)|_s>0 [B(r_c)|_s is the product of ρ(r_c) and ∇²ρ(r_c) at the point of reaction process, i.e., B(r_c)|_s=ρ(r_c)∇² ρ(r_c)] is basically the same as the region of V′(s)<0[V′(s) is the second derivative of potential energy with respect to the reaction coordinate, i.e., V′(s)=d²V/ds²], and the point with maximum B(r_c)|_s is almost coincident with the point of minimum V′(s). It can be concluded from the calculated results that there is a good correlation between the topological properties of potential energy and electronic density distribution along the reaction path. The structure transition state of such collinear reactions may be determined by topological analysis of electronic density. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1167–1174     

Chemical bond breaking/forming as a Franck–Condon electronic process

We describe chemical bond changes as Franck–Condon electronic processes within a new theoretical ansatz that we call ‘rigged’ Born–Oppenheimer (R-BO) approach. The notion of the separability of nuclear and electron states implied in the standard Born–Oppenheimer (BO) scheme is retained. However, in the present scheme the electronic wave functions do not depend upon the nuclear coordinate (R-space). The new functions are obtained from an auxiliary Hamiltonian corresponding to the electronic system (r-coordinates) submitted to a Coulomb potential generated by external sources of charges in real space (α-coordinates) instead of massive nuclear objects. A stationary arrangement characterized by the coordinates α_0A, is determined by a particular electronic wave function, ψ(r;α_0A); it is only at this stationary point, where an electronic Schrödinger equation: H_e(r,α_0A)|Ψ(r;α_0A)=E(α_0A)|Ψ(r;α_0A) must hold. This equation permits us to use modern electronic methods based upon analytic first and second derivatives to construct model electronic wave functions and stationary geometry for external sources. If the set of wave functions {Ψ(r;α_0A)} is made orthogonal, the energy functional in α-space, E(α;α_0A)=Ψ(r;α_0A)|H_e(r,α_0A)|Ψ(r;α_0A) is isomorphic to a potential energy function in R-space: E(R;α_0A)=Ψ(r;α_0A)|H_e(r,R)|Ψ(r;α_0A). This functional defines, by hypothesis, a trapping convex potential in R-space and the nuclear quantum states are determined by a particular Schrödinger equation. The total wave function for the chemical species A reads as a product of our electronic wave function with the nuclear wave function (Ξ_ik(R;α_0A)): Φ_ik(r,R)=Ψ_i(r,α_0A)Ξ_ik(R;α_0A). This approach facilitates the introduction of molecular frame without restrictions in the R-space. Two molecules (characterized with different electronic spectra) that are decomposable into the same number of particles (isomers) have the same Coulomb Hamiltonian and they are then characterized by different electronic wave functions for which no R-coordinate ‘deformation’ can possibly change its electronic structure. A bond breaking/forming process must be formally described as a spectroscopic-like electronic process. The theory provides an alternative to the adiabatic as well as the diabatic scheme for understanding molecular processes. As an illustration of the present ideas, the reaction of H₂+CO leading to formaldehyde is examined in some detail.     

Reinvestigation of intramolecular hydrogen bond in malonaldehyde derivatives: An ab initio,AIM and NBO study

The RAHB systems in malonaldehyde and its derivatives at MP2/ 6‐311++G(d,p) level of theory were studied and their intramolecular hydrogen bond energies by using the related rotamers method was obtained. The topological properties of electron density distribution in O? H···O intramolecular hydrogen bond have been analyzed in term of quantum theory of atoms in molecules (QTAIM). Correlations between the H‐bond strength and topological parameters are probed. The results of QTAIM clearly showed that the linear correlation between the electron density distribution at HB critical point and RAHB ring critical point with the corresponding hydrogen bond energies was obtained. Moreover, it was found a linear correlation between the electronic potential energy density, V(r_cp), and hydrogen bond energy which can be used as a simple equation for evaluation of HB energy in complex RAHB systems. Finally, the similar linear treatment between the geometrical parameters, such as O···O or O? H distance, and Lp(O)→σ*_OH charge transfer energy with the intramolecular hydrogen bond energy is observed. © 2010 Wiley Periodicals, Inc., Int J Quantum Chem, 2011     

A non local density functional calculation of the diamagnetic susceptibilities and other electronic properties of noble gases and closed-shell ions

The non local weighted-density approximation (WDA) to the exchange-correlation potentialV _xc (r) is used to compute electron densities, ionization potentials and electron affinities of several atoms and ions. Especial care is taken in calculating and discussing 〈r ²〉 in noble gas atoms. Good results are obtained for all those quantities, but it is critical that the WDA is applied in such a way that it preserves the correct larger behaviour ofV _xc (r). A comparison of the calculated electron density with that of the Hartree-Fock method shows the effects of coulomb correlation. The density rearrangements upon the introduction of correlation agree qualitatively with the results of Configuration-Interaction calculations     

Theory of non-local (pair site) reactivity from model static-density response functions

Activation is a fundamental and well-known concept in chemistry. It may be qualitatively defined as an increase in the chemical reactivity pattern of a molecule at a given site k when the system is locally perturbed at a different site l, say. This external perturbation arise from a localized molecular rearrangement, a substitution, a selective solvation or simply by the approach of a reagent of variable hardness. This work presents a theoretical approach intending to quantify this activation concept in the density functional framework. This is done here by first calculating the fluctuation of the electron density at a given site k for the ground state of the isolated substrate (static reactivity model) and then incorporating the substrate and model electrophile reagents in a spatial disposition related to a virtual transition structure for the parent system. This perturbation is assumed representable by local changes in the external potential. It is shown that a local approximation to the softness kernel s(r, r′) yields a simple expression for the fluctuation of the electron density δρ(r _k ), which shows that this change becomes proportional to the variation of an effective potential δu(r _k ), containing the information on the variation in the chemical potential and the external perturbing potential at site k; the proportionality constant being the local softness s ⁰(r k) at that site. The strong local approximation made to the kernel s(r, r′) causes the second reactivity site (l) to implicitly appear in the formulation through the changes in the electronic chemical potential term. It is shown that the introduction of a less restrictive approach to the linear response function, obtained from a model Kohn-Sham one-electron density matrix, leads to the same result. Non-locality is therefore self-contained in the electronic chemical potential contribution to the modified potential, and may be associated with an intramolecular charge transfer between the active sites of the ambident nucleophilic/electrophilic substrate, promoted by the presence of the reagents. The resulting formulation of pair-site reactivity is illustrated for the electrophilic attack on the CN⁻ ion by different model electrophile agents of variable hardness. It is shown that correct reactivity indexes are obtained only when the topology of the transition structure is used as a vantage point to perturb the CN⁻ ion. The calculations were performed at both density functional theory and ab-initio Hartree-Fock levels. The results show that the proposed model is independent of the method used to obtain ρ(r). Received: 30 September 1997 / Accepted: 30 December 1997     

Topology of density difference and force analysis

The density difference (r) of a molecule A-B is defined as the difference of the density (r) of the molecule A-B and the density _A(r) + _B(r) put at the position of the atoms A and B. We investigate here the topological features of the density difference and define electron density flow (EDF) as representing the direction and the amount of the electron density flow in the course of the nuclear displacement processes. As such examples, we study H₂ molecule formation reaction and the interaction of two He atoms. By the topological analysis of (r), and by using the Hellmann-Feynman force and its partition into the AD, EC, and EGC forces, the characteristic behaviors of the (r) map are clarified. In particular, the electron cloud preceding and incomplete following are represented by using the concept of the EDF. The natures of the covalent bond are clarified based on the topological properties of the difference density (r) rather than that of the total density (r).On leave from the Department of Chemistry, Hebei Teachers' College, Shijiazhuang, Hebei, 050091, China     

Syntheses, structures, spectroscopic, electrochemical properties and DFT calculation of Ru(II)–thioarylazoimidazole complexes

The reaction of 1-alkyl-2-{(o-thioalkyl)phenylazo}imidazoles (SRaaiNR) (2a/2b) with Ru(II) has synthesized [Ru(SRaaiNR)₂](ClO₄)₂ (3a/3b) in 2-methoxyethanol. The reaction in methanol, however, has synthesized [Ru(SRaaiNR)(SRaaiNR)Cl](ClO₄) (4a/4b). The solid phase reaction of SRaaiNR and RuCl₃ on silica gel surface upon microwave irradiation has synthesized [Ru(SRaaiNR)(SaaiNR)](PF₆) (5a/5b) [SRaaiNR represents tridentate N,N′,S-chelator; SRaaiNR is N,N′-bidentate chelator where S does not coordinate and SaaiNR refers N,N′,S-chelator where S refers to thiolato binding]. The structural characterization of [Ru(SEtaaiNEt)(SEtaaiNEt)Cl](ClO₄) (4b) and [Ru(SEtaaiNEt)(SaaiNEt)](PF₆) (5b) has been confirmed by single crystal X-ray diffraction study. The IR, UV–Vis, and ¹H NMR spectral data also support the stereochemistry of the complexes. The complexes show metal oxidation, Ru(III)/Ru(II), and ligand reductions (azo/azo⁻, azo⁻/azo). The molecular orbital diagram has been drawn by density functional theory (DFT) calculation. Normal mode of analysis has been performed to correlate calculated and experimental frequencies of representative complexes. The electronic movement and assignment of electronic spectra have been carried out by TDDFT calculation both in gas and acetonitrile phase.     

Computational investigation of the CH3XC=S...S (X = H, HO, HS, PH2, CH3) bonding type

The CH₃XC=S...S (X = H, HO, HS, PH₂, CH₃) bonding types are investigated using the second order Møller-Plesset perturbation approximation with the cc-pVDZ basis set. Electrostatic density potential maps of CH₃XC=S (X = H, HO, HS, PH₂, CH₃) are generated at the MP2/cc-pVDZ level of theory. The interaction energy and topological property are theoretically encompassed for the five complexes. Electrostatic density potential maps of five monomers are generated for the determination of attractive interaction sites. There are different misshaped electron clouds. The red-shifting character is obtained for the CH₃XC=S...S (X = H, HO, HS, PH₂) interaction. For all complexes the S...S bonds are typical closedshell interactions, and the topological properties of the S...S bond fall short of three criteria for the existence of the hydrogen bond. Theoretical values are in very good agreement with the experimental results.     

Molecular structure of the unusual complex of 1-piperidineacetic acid with 2,4,6-trinitrophenol studied by X-ray, FTIR and H, C and C CP MAS NMR

Crystals containing three kinds of molecules 1-piperidiniumacetate (II), 1-piperidiniumacetic acid (III) and 2,4,6-trinitrophenolate (picrate, TNP⁻), belong to the monoclinic system, space group P2₁/c and Z=4, a=12.831(3), b=26.093(5), c=7.157(1) Å, β=101.18(3)°, R=0.0758. The zwitterion molecule (II) is a double acceptor of protons from two molecules of 1-piperidiniumacetic acid (III) (N–HO, 2.735(5) Å and O–HO, 2.472(5) Å), and a donor of proton to the picrate molecule (N–HO, 2.747(5) Å). These three molecules, which have three donor centers and several acceptor groups, form hydrogen-bonded chains parallel to the z axis. The oxygen atoms inactive in these hydrogen bonds, are engaged in the C–HO short contacts, which can be treated as weak hydrogen bonds, and join the chains into a three-dimensional network. The presence of protonated 1-piperidineacetic acid (III) and its zwitterion (II) in the crystal has been confirmed by ¹³C CP MAS NMR and solid state FTIR spectra.     

Interpenetrating metal-organic frameworks formed by self-assembly of tetrahedral and octahedral building blocks

To investigate the relationship between topological types and molecular building blocks (MBBs), we have designed and synthesized a series of three-dimensional (3D) interpenetrating metal-organic frameworks based on different polygons or polyhedra under hydrothermal conditions, namely [Cd(bpib)_0.5(L¹)] (1), [Cd(bpib)_0.5(L²)]·H₂O (2), [Cd(bpib)_0.5(L³)] (3) and [Cd(bib)_0.5(L¹)] (4), where bpib=1,4-bis(2-(pyridin-2-yl)-1H-imidazol-1-yl)butane, bib=1,4-bis(1H-imidazol-1-yl)butane, H₂L¹=4-(4-carboxybenzyloxy)benzoic acid, H₂L²=4,4′-(ethane-1,2-diylbis(oxy))dibenzoic acid and H₂L³=4,4′-(1,4-phenylenebis(methylene))bis(oxy)dibenzoic acid, respectively. Their structures have been determined by single crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectra, and thermogravimetric (TG) analyses. Compounds 1–3 display α-Po topological nets with different degrees of interpenetration based on the similar octahedral [Cd₂(–COO)₄] building blocks. Compound 4 is a six-fold interpenetrating diamondoid net based on tetrahedral MBBs. By careful inspection of these structures, we find that various carboxylic ligands and N-donor ligands with different coordination modes and conformations, and metal centers with different geometries are important for the formation of the different MBBs. It is believed that different topological types lie on different MBBs with various polygons or polyhedra. Such as four- and six-connected topologies are formed by tetrahedral and octahedral building blocks. In addition, with the increase of carboxylic ligands’ length, the degrees of interpenetration have been changed in the α-Po topological nets. And the luminescent properties of these compounds have been investigated in detail.     

Synthesis and reactivity of new heterodinuclear iron/rhenium Cx complexes of the formula (η-C5Me5)Re(NO)(PPh3)(CC)n(η-dppe)Fe(η-C5Me5) (n = 3, 4): Redox properties and a dicobalt hexacarbonyl adduct

We report in this communication the synthesis and characterization of two Fe/Re heterodinuclear complexes 3_n of formula (η⁵-C₅Me₅)Re(NO)(PPh₃)(CC)_n(η²-dppe)Fe(η⁵-C₅Me₅) (n = 3, 4) as well as the hexacarbonyl dicobalt adduct (4) of the hexatriynediyl complex 3₃. We show by cyclic voltammetry that the “electronic communication” between the organometallic endgroups and thereby the thermodynamic stability of the corresponding mixed-valent (MV) parent 3_n⁺ is strongly influenced by bridge extension or by complexation of the [Co₂(CO)₆] fragment. In the case of the hexatriynediyl complex, the MV complex 3₃⁺ or 4 can be isolated by performing the chemical oxidation of 3₃ at low temperature. Spectroscopic studies of this compound and of other stable oxidized redox congeners should now help us to unravel how bridge extension modifies the electronic communication between the different redox-active endgroups in this family of unsymmetrically-substituted polyynediyl compounds.     

DFT studies and AIM analysis of AlN-polycycles

The structure and properties of AlN-polycycles were studied by DFT (density functional theory) method. The results of calculations were obtained at B3LYP/6-311G(d, p) level on model species. Topological parameters such as electron density, its Laplacian, kinetic electron energy density, potential electron energy density, and total electron energy density at the ring critical points (RCP) from Bader’s ‘Atoms in molecules’ (AIM) theory were analyzed in detail. These results indicate a good correlation between ρ(3, +1), G(r), H(r), and V(r) averaged values and hardness of AlN-polycycles. The aromaticity of all molecules has been studied by nucleus-independent chemical shift. There is a linear correlation between ΣNICS(0.0)_molecule values and polarizability.     

Correlation energy correction as a density functional. A model of the pair distribution function and its application to the first- and second-row atoms and hydrides

A scheme for correlation energy corrections E_c based on asymptotic properties of the effective pair distribution function g(r₁; r₂) and correlation energy densities ϵ_c{ϱ(r₁)} has been considered. To obtain ϵ_c{ϱ(r₁)} model functions g(r₁; r₂) are used in the local spin density approximation (LSDA). This model yields the correct high-density limit for the homogeneous electron gas ϵ_c{ϱ} and reproduces empirical E_c values with an average error amounting to 2.2% for the first- and second-row closed-shell atoms, 5.6% for the first-row hydrides XH and 3.4% for the second-row hydrides XH.     

Charge density studies on [(NO)Fe(S2C6H4)2][PPN] and [(NO)3Fe(S2C6H4)3] complexes

Charge density studies of chemical bonds for two iron complexes, [(NO)Fe(S,S-C₆H₄)₂] [PPN] (1), where PPN = N(Pph₃)₂ and Fe₃(NO)₃(S,S-C₆H₄)₃ (2) are investigated in terms of the topological properties at bond critical points based on the ‘atoms in molecule’ theory. The one electron reduction form (1R) of complex 1 and the one electron oxidation form (2O) of complex 2 are also included for comparison. The X-ray absorption spectroscopy of Fe K- and L_III,II-edges, as well as the N/S K-edge are applied to verify the illustration in the variation of the electronic structures. Based on the ρ_c, ?²ρ_c, and H_b values among the compound studied, Fe-S/N can be regarded as polarized covalent bond, and Fe-N bonds show stronger covalent character than that of the Fe–S bond, which is believed to be a highly polarized covalent bond.     

The Laplacian of the electronic density at the valence-shell charge concentration (VSCC): A comparative study of effective core potential and full-electron calculations in Mo compounds. II

The effective core potential (ECP), using a basis set of different qualities, and ab initio full-electron (FE) calculations were carried out for MoS⁻²₄, MoO⁻²₄, and MoOCl₄ molecules. The topology of − ▿²p(r_cp) (the negative Laplacian of the charge density at its critical points) in the atomic valence shell was studied. Results clearly indicate that semicore (ECP2) approaches are able to reproduce, in a qualitative way, the topology of the Laplacian distribution with respect to those obtained by the FE method. Modifications of basis sets, such as introduction of polarization functions on the ligands, affect the electronic charge distribution (number of critical points in MoOCl₄) for FE as well as for ECP2 approaches. The ECP2 scheme predicts correctly the order of − ▿²p_x(r_cp) (X = O, S, Cl, Mo) in the valence shell; nevertheless, it fails in the relative magnitudes of − ▿²p_Mo(r_cp) between Mo compounds in respect to FE calculations. A scaling factor consistently improves the values of − ▿²p(r_cp) and p(r_cp), which are larger than those obtained with FE, particularly the − ▿²p(r_c) values. © 1996 John Wiley & Sons, Inc.     

Exchange energy for two closed shells generated by a bare Coulomb potential energy −<Emphasis Type="Italic">Ze</Emphasis><Superscript>2</Superscript>/<Emphasis Type="Italic">r</Emphasis> in the limit of large <Emphasis Type="Italic">Z</Emphasis>, in two dimensions

Two-dimensional (2D) inhomogeneous electron assemblies are becoming increasingly important in Condensed Matter and associated technologies. Here, therefore, we contribute to the Density Functional Theory of such 2D electronic systems by calculating, analytically, (i) the idempotent Dirac density matrix γ(r, r′) generated by two closed shells for the bare Coulomb potential −Ze ²/r and (ii) the exchange energy density e_x(r){\varepsilon_x({\bf r})} . Some progress is also possible concerning the exchange potential V _x (r), one non-local approximation being the Slater potential 2e_x(r)/n(r){2\varepsilon_x(r)/n(r)} , with n(r) the ground state electron density. However, to complete the theory of V _x (r), the functional derivative of the single-particle kinetic energy per unit area δt(s)/δn(r) is still required.     

Hydrogen bond in 3-acetyl-4-hydroxycoumarin: X-ray diffraction study and quantum-chemical calculations

The proton transfer and the character of the strong intramolecular O--H...O hydrogen bond (O...O 2.442 ) in 3-acetyl-4-hydroxycoumarin were analyzed based on the results of X-ray diffraction study in the temperature range from 100 to 353 K and quantum-chemical B3LYP/6-31G(d,p) calculations. The barrier to proton transfer along the H-bond line is low (2 kcal mol^–1). However, no proton transfer was observed in the crystal at 100 K. Bader's topological analysis of the electron density distribution both in the crystal and in the isolated molecule demonstrated that the hydrogen bond corresponds to an intermediate type of interatomic interactions (E(r) < 0, ²(r) > 0 at the critical point (3, –1)).     

Influence of d-p π-conjugate interaction upon electronic spectra in some cluster compounds

The UV-vis electronic absorption spectra of the clusters Mo₂S₄(dtp)₂ and Mo₃S₄(dtp)₄·Py have been observed, and the electronic excitation energies have been calculated using the INDO/S-CI method. Comparing the calculated values with the observed results, the absorption bands have been assigned. The influence of d-p π-conjugate interaction strength upon the electronic absorption spectrum is discussed in the clusters Mo₂S₄(dtp)₂ (1), Mo₃S₄(dtp)₄·Py (2), Mo₃O₄(H₂O)₉⁴⁺ (3) and Mo₃S₄(H₂O)₉⁴⁺ (4) [dtp = S₂P(OC₂H₅), Py = pyridine]. It has been found that the absorption bands of clusters 2 and 4, with larger d-p π-conjugate interaction over rings, causes a red-shift compared with those of clusters 1 and 3, with a smaller d-p π-conjugate interaction.     

Electron-pair radial density functions

We introduce and discuss a generalized electron-pair radial density function G(q; a) that represents the probability density for the electron-pair radius |r ₁+ar ₂| to be q, where a is a real-valued parameter. The density function G(q; a) is a projection of the two-electron radial density D ₂(r ₁, r ₂) along lines r ₁ + ar ₂ ± q = 0 in the r ₁ r ₂ plane onto a point in the qa plane, and connects three densities S(s), D(r), and T(t), defined independently in the literature, as a smooth function of a: For an N-electron (N ≥ 2) system, S(s) = G(s; + 1), D(r) = 2G(r; 0)/(N − 1), and T(t) = G(|t|;−1)/2, where S(s) and T(t) are the electron-pair radial sum and difference densities, respectively, and D(r) is the single-electron radial density. Simple illustrations are given for the helium atom in the ground 1s² and the first excited 1s2s ³S states.