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.     

Experimental electron density overlapping in hydrogen bonds: topology vs. energetics

We have investigated the relationship between the energetic properties of the hydrogen bond (HB) interaction and the topological overlapping of the electronic clouds at the HO critical point r_CP. This study involves a total of 83 X–HO (X=C, N, O) HBs, which have been described in terms of the topological properties of the electron density ρ(r) at r_CP for a large set of compounds. Kinetic G(r_CP) and potential V(r_CP) contributions to the local energy density of electrons exhibit linear functionalities against, respectively, the positive and negative curvatures of ρ(r) at the critical point, showing an effective deconvolution in the local form of the Virial theorem. The topological variation of the curvatures at r_CP, and therefore changes in the HO overlapping, are related to the onset of the repulsion between the electronic clouds of the basic and acid atoms.     

3D supramolecular architectures of copper(II) complexes with 6-methylpicolinic and 6-bromopicolinic acid: Synthesis, spectroscopic, thermal and magnetic properties

Copper(II) complexes of 6-methylpicolinic (6-MepicH) and 6-bromopicolinic acid (6-BrpicH), namely [Cu(6-Mepic)₂(H₂O)] (1), [Cu(6-Mepic)₂(py)] (2) and [Cu(6-Brpic)₂(H₂O)] (3) were prepared and characterized by spectroscopic methods (IR, EPR). Their molecular and crystal structures were determined by X-ray crystal structure analysis, their thermal stability by TGA/DTA methods, while their magnetic properties were elucidated by the measurement of the magnetic susceptibility. X-ray structural analysis revealed an intermediate between square-pyramidal and trigonal-bipyramidal coordination polyhedron in 1 and 3 and a trigonal-bipyramidal one in 2 with the same N,O-chelated coordination mode for both 6-MepicH and 6-BrpicH in 1–3. EPR spectra showed three different types of copper(II) S = ½ symmetry signals. Most probably they could be assigned to the elongated axial in 1, the isotropic in 2 and the rhombic in 3. Both 1 and 2 showed the paramagnetic behaviour, while 3 exhibited an antiferromagnetic interaction, ascribed to the formation of pseudobinuclear units by the π···π stacking between pyridine rings.     

Five new dicarboxylate organotin complexes under hydrothermal condition: Syntheses, characterization and crystal structures of 1D, 2D and 3D polymers constructed from dimeric tetraorganodistannoxane units

Five new diorganotin(IV) complexes of the types {(Me₂Sn)₂[μ₄-(C₈H₃NO₆)](μ₃-O)}_n (1), {(Me₂Sn)₂[μ₃-(C₈H₈O₄)](μ₃-O)}_n (2), {(Me₂Sn)₂[μ₄-(C₈H₁₀O₄)](μ₃-O)}_n (3) {(Me₂Sn)₂[μ₄-(C₈H₁₀O₄)](μ₃-O)}_n (4) and {(Me₂Sn)₂[μ₄-(C₁₀H₁₄O₄)](μ₃-O)}_n (5) have been synthesized by reactions of 5-nitroisophthalic acid, meso-cis-4-cyclohexene-1,2-dicarboxylic, meso-cis-1,4-cyclohexanedicarboxylic acid, meso-cis-1,3-cyclohexanedicarboxylic acid and chiral cis-(1R,3S)-(+)-camphoric acid with trimethyltin chloride under hydrothermal condition. All complexes were characterized by elemental analysis, IR, ¹H NMR, ¹³C NMR, ¹¹⁹Sn NMR and X-ray crystallography. The structural analyses show that complex 1 has a 1D infinite polymeric chain in which 5-nitroisophthalic acid acts as a tetradentate ligand coordinating to dimethyltin(IV) ions, complexes 2, 3 and 4 possess 2D polymeric structures in which dicarboxylate acid act as tridentate or tetradentate ligands coordinating to dimethyltin(IV) ions, complex 5 possesses a irregular 3D framework in which chiral cis-(1R,3S)-(+)-camphoric acid acts as a tetradentate ligand coordinating to dimethyltin(IV) ions.     

Organotin(IV) 4-nitrophenylethanoates: Synthesis, structural characteristics and intercalative mode of interaction with DNA

Four new organotin(IV) carboxylates, [Bu₂SnL₂] (1), [Et₂SnL₂] (2), [Bu₃SnL]_n (3), [Me₃SnL]_n (4), where L = 4-nitrophenylethanoates, were synthesized and characterized by elemental analysis, FT-IR and multinuclear NMR (¹H and ¹³C). Spectroscopic results authenticated the coordination of ligand to the organotin moiety via COO group while X-ray single crystal analysis revealed bidentate chelating mode of coordination of ligand in complex 2 and a bridging behavior in complexes 3 and 4. Cyclic voltammetric (CV) technique was used to evaluate the electrochemical, kinetic and thermodynamic parameters of complexes 1-4, interacting with DNA. The linearity of the plots between the peak current (I) and the square root of the scan rate (ν^1/2) indicated the electrochemical processes to be diffusion controlled. The diffusion coefficients of the free (D_f) and DNA bound forms (D_b), standard rate constants (ks) and charge transfer coefficients (α) were determined by the application of Randle–Sevcik, Nicholson and Kochi equations. Furthermore, the binding constants evaluated from voltammetric data revealed the following increasing order of binding strength: 2 < 1 < 4 < 3. For 1 and 2, the activity against prostate cancer cell lines (PC-3) was found consistent with the order obtained from voltammetric behavior.     

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.     

Fe–Hg Interactions and P Chemical Shifts in [Fe(CO)3 (PPh2R)2(HgCl2)] (R=pym, fur, py, thi)

In order to study the effects of R group on Fe–Hg interactions and 31P chemical shifts, the structures of mononuclear complexes Fe(CO)₃(PPh₂R)₂ (R=pym:1, fur: 2, py: 3,thi: 4; pym=pyrimidine, fur=furyl, py=pyridine, thi=thiazole) and binuclear complexes [Fe(CO)₃(PPh₂R)₂(HgCl₂)] (R=pym: 5, fur: 6, py: 7, thi: 8) were studied using the density functional theory (DFT) PBE0 method. The 31P chemical shifts were calculated by PBE0-GIAO method. Nature bond orbital (NBO) analyses were also performed to explain the nature of the Fe–Hg interactions. The conclusions can be drawn as follows: (1) The complexes with nitrogen donor atoms are more stable than those with O or S atoms. The more N atoms there are, the higher is the stabilility of the complex. (2) The Fe–Hg interactions play a dominant role in the stabilities of the complexes. In 5 or 6, thereisa σ-bond between Fe and Hg atoms. However, in 7 and 8, the Fe–Hg interactions act as σ_P–Fe→n_Hg and σ_C–Fe→n_Hg delocalization. (3) Through Fe→Hg interactions, there is charge transfer from R groups towards the P, Fe, and Hg atoms, which increases the electron density on P nucleus in binuclear complexes. As a result, compared with their mononuclear complexes, the 31P chemical shifts in binuclear complexes show some reduction.     

Photochemical reactions of aromatic compounds XLV: controlling factors for reactivities and mechanisms in photoelectron transfer reactions of some selected diarylcyclobutanes with electron acceptors

We have attempted to explore mechanistic aspects of the photosensitized ring-cleavage reactions of cis-1,2-diphenylcyclobutane (1), cis-transoid-cis-cyclobutal[1,2-a:4,3-a′] diindene (2) and r-1,c-2-dimethyl-t-3,t-4-di(4-methoxyphenyl)cyclobutane (3) by electron acceptors (A) in acetonitrile. The experimental results demonstrate that the ring cleavage of 1 and 2 occurs as a consequence of the rapid geminate recombination of ion-radical pairs occurring at a rate of well over 10⁹ s⁻¹ without ionic dissociation. In the case of 3, however, the photoreactions proceed by way of a chain-reaction mechanism involving the free cation radical of 3 which undergoes ring cleavage at much less than 10⁷ s⁻¹. The rapid ring cleavage of 1⁺ and 2⁺ is attributed to significant perturbations of the cyclobutane ring by the population of positive charge on the orbital array of the two π-electron systems and the cyclobutane-ring σ framework because of strong through-bond couplings. It is presumed that the cyclobutane ring of 3⁺ is much less distorted since the positive charge is mostly localized on the aryl group. The rapid geminate recombination of the A⁻⁻−1⁺ and A⁻⁻−2⁺ pairs is discussed in terms of a very efficient transition from the “distorted” and “ring-opened” minima of the A⁻⁻−D⁺ surface to the A–D surface. In the case of 3, this mechanism cannot be expected to operate in the geminate recombination.     

Coordination formulation of tetrahedrally close packed structures: An addendum to the observations of Yarmolyuk and Kripyakevich

Ya. P. Yarmolyuk and P. I. Kripyakevich (Kristallographiya 19, 539 (1974)) showed that all tetrahedrally close packed (t.c.p.) structures have coordination formulae P_pQ_qR_rX_x → (PX₂)_i(Q₂R₂X₃)_j (R₃X)_k, where P, Q, R, and X represent coordination numbers (CN) 16, 15, 14, and 12 polyhedra respectively: p, q, r, and x indicate the numbers of such polyhedra in the unit cells of t.c.p. structures and i, j, and k are positive integers. We propose and demonstrate a limitation to the above formulation: if i ≥ 1 and k ≥ 1, then j ≥ 1 (or if both p> 0 and r> 0, then q> 0). We give reasons for this and discuss the Aufbauprinzip of t.c.p. structures and the results of C. B. Shoemaker and D. P. Shoemaker (Acta Crystallogr. B 42, 3 (1986)).     

The preparation of dimolybdenum(V,V) complexes from molybdenum quadruply bonded metal-metal dimers

Oxidation of quadruply bonded metal-metal dimers in the presence of good π-accepting ligands results in the formation of Mo^V---Mo^V compounds of the type [MO₂(μ-X)₂(Y)(Y′)]²⁺ (X = O or S; Y,Y′ = O,O; S,S; O,S). Reaction of MO₂(O₂CCH₃)₄ with oxygen in the presence of Na₂mnt (mnt = 1,2-dicyanoethylene-2,2-dithiolate) gives [MO₂(μ-S)₂(O)(S)(mnt)₂]²⁻ (1). The compound crystallizes in the monoclinic space group P2₁/c, with cell dimensions a = 19.547(4), b = 15.210(4), c = 18.754(6) Å, β = 101.69(2)°, V= 5460(2) ų, and Z = 4. Similarly, oxidation of o-dichlorobenzene solutions of Mo₂Cl₄(CH₃CN)₄ and 4,4′-dimethyl-2,2′-dipyridyl (dmpby) or, more directly, the reaction of Mo₂Cl₄(dmbpy)₂ with oxygen leads to the formation of a red solid, which was characterized by X-ray crystallography to be Mo₂(μ-O)₂(O)₂(Cl)₂(dmbpy)₂ (2). Red diamond crystals, prepared by slow evaporation of CH₃CN solutions of 2, are trigonal and in the space group P3₁21 with cell dimensions a = 16.135(4), b = 16.135(4), c = 10.709(3) Å, V = 2414.4(13) ų and Z = 3. In both structures, the geometry about each of the molybdenum atoms is a distorted square pyramid with terminal oxygen or sulphur atoms at the apices and in a syn conformation. The molybdenum-molybdenum bond distances of 2.858(1) Å and 2.562(2) Å in structures of 1 and 2, respectively, are typical of other Mo^V---Mo^V dimers and indicative of a single Mo---Mo bond.     

Three copper(II) complexes of thiophene-2,5-dicarboxylic acid with dissimilar ligands: Synthesis, IR and UV–Vis spectra, thermal properties and structural characterizations

Three thiophene-2,5-dicarboxylic acid (H₂tdc) complexes of copper(II) with 2-aminomethylpyridine (ampy), {[Cu₂(μ-tdc)₂(ampy)₂]·2DMF}_n (1), ethylenediamine (en), trans-[Cu(H₂O)₂(en)₂](tdc) (2) and 4-methylimidazole (4-meim), trans-[Cu(H₂O)₂(4-meim)₄](tdc)·4H₂O (3) have been synthesized and characterized by spectral (IR, UV–Vis), thermal analyses and X-ray diffraction techniques. In 1, thiophene-2,5-dicarboxylate acts as a bridging bis(bidentate) ligand through four carboxylate oxygen atoms forming a 1-D zigzag polymeric chain, whereas in 2 and 3 the tdc dianion behaves as a counter ion. In all cases, the Cu(II) centers have an octahedral coordination geometry. Three-dimensional frameworks are constructed though hydrogen bonding and/or C–H···π interactions in the three complexes.     

Platinum(IV) complexes with α,ω-bis(pyrazol-1-yl) alkanediyl and diethyl ether/thioether ligands. Crystal structures of dibromodimethyl[1,2-bis(pyrazol-1-yl)ethane]platinum(IV) and trimethyl-bis[2-(pyrazol-1-yl)ethyl]etherplatinum(IV) tetrafluoroborate

Reactions of the flexible α,ω-bis(pyrazol-1-yl) compounds 1,2-bis(pyrazol-1-yl)ethane (L1), 1,8-bis(pyrazol-1-yl)-n-octane (L2), bis[2-(pyrazol-1-yl)ethyl]ether (L3) and bis[2-(pyrazol-1-yl)ethyl]thioether (L4) with precursor organometallic platinum complexes ([(PtBr₂Me₂)_n], [(PtIMe₃)₄] and [(PtMe₂(cod)]/I₂) are described herein. The spectroscopic characterization of the platinum(IV) products of these reactions [PtBr₂Me₂{pz(CH₂)_mpz}], m = 2 (1) or 8 (2), [PtI₂Me₂{pz(CH₂)₂pz}] (3), [PtMe₃(pzCH₂CH₂OCH₂CH₂pz)][BF₄] (4) and [PtMe₃(pzCH₂CH₂SCH₂CH₂pz)][CF₃SO₃] (5), where ‘pz’ is pyrazol-1-yl, is discussed. Furthermore, solid state structures of 1, a complex with a seven-membered chelate ring, and 4, a complex bearing the neutral κ²N,N′,κO ligand bis[2-(pyrazol-1-yl)ethyl]ether (L3) are reported.     

Oligomerization and structural variation of alkali metal silyloxides

Lithium and potassium silyloxide complexes [Li(OSiPh₃)]_n (1), [K(thf)_0.2 (OSiPh₃)]_n (3) and [K(OSiMe₂^tBu)]_n (6) were prepared by deprotonation of HOSiPh₃ or HOSiMe₂^tBu with [Li(ⁿBu)] in hexane or KH in THF, respectively. Crystalline DME adducts [Li(μ-OSiPh₃)(η²-DME)]₂ (2) and [K₄(μ₃-OSiPh₃)₃(μ₃-OSiPh₂(η¹-Ph))(η²-DME)]₂ (μ-DME) (4) were prepared by dissolving 1 or 3, respectively, in dimethoxyethane followed by precipitation with alkane. The potassium-sequestered complexes [K(18-crown-6) (OSiPh₃)]₂ (5) and [K(18-crown-6)(OSiMe₂^tBu)]_n (7) were prepared from 3 or 5, respectively, and one equiv. of 18-crown-6 ether. The complexes were characterized by single-crystal X-ray diffraction: [Li(μ-OSiPh₃)(η²-DME)]₂ (2): a dimer featuring tetrahedral lithium centres linked by bridging —OSiPh₃ ligands. [Crystal data ( − 156°C): space group P , a = 14.238(6), b = 15.182(7), c = 11.796(5) Å, α = 110.57(2), β = 112.02(2), γ = 63.02(1) Å, V = 2055.33 ų, Z = 2.] [K₄(μ₃-OSiPh₃)₃{μ₃-OSiPh₂(η¹-Ph)}(η²-DME)]₂(μ-DME) (4): (1) two cubanes each having every potassium vertex chemically distinct; (2) one chelating DME ligand, one DME ligand bridging between two cubanes; and (3) a K-ipso-phenyl carbon contact. [Crystal data ( − 133°C): a = 14.246(4), b = 30.939(9), c = 17.981(5) Å, β = 112.33(1)° with Z = 2 in space group P2₁/c.] [K(18-crown-6)OSiPh₃]₂ (5): A dimer with slipped face-to-face stacking of the quasi-planar K(18-crown-6)⁺ part of the two Ph₃SiOK(18-crown-6) molecules; these are linked by a dative bond from one ether oxygen of a given crown to potassium contained in the other crown. [Crystal data ( − 155°C): a = 9.324(2), b = 17.640(5), c = 18.148(15) Å, β = 91.60(1)° with Z = 4 in space group P2₁/c.]     

On the inner and outer radial density functions

Starting from the two-electron radial density D ₂(r ₁,r ₂), a generalized partitioning of the one-electron radial density function D(r) into two component densities D _a (r) and D _b (r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D _<(r) and outer D _>(r) radial densities is shown to minimize the average variance of the two component density functions D _a (r) and D _b (r). It is also found that the average radial separation halved, , constitutes a lower bound to the standard deviation σ of D(r).     

Organometallic complexes for nonlinear optics: Part 21. Syntheses and quadratic hyperpolarizabilities of alkynyl complexes containing optically active 1,2-bis(methylphenylphosphino)benzene ligands

The preparation of the chloro complex trans-[FeCl₂{(R,R)-diph}₂] (1) and the alkynyl complexes trans-[M(4-CCC₆H₄R)Cl{(R,R)-diph}₂] [M=Fe, R=NO₂ (2); M=Ru, R=H (4), NO₂ (5), (E)-CH=CH-4-C₆H₄NO₂ (6); M=Os, R=NO₂ (7)], incorporating the optically active diphosphine 1,2-bis(methylphenylphosphino)benzene (diph), are described. Oxidation potentials, as determined by cyclic voltammetry, increase as 2<7<5. Molecular quadratic nonlinearities by hyper-Rayleigh scattering at 1064 nm increase upon introduction of an acceptor group (4<5), chain-lengthening of bridging group (5<6), and proceeding from 3d to 4d and 5d metal (2≤5≤7). Two-level-corrected nonlinearities reproduce the first two trends, but metal variation follows the sequence 2<7<5. The experimental and two-level-corrected nonlinearities for 6 (2795×10⁻³⁰ and 406×10⁻³⁰ esu, respectively), are amongst the largest observed thus far for organometallic complexes. Crystals of complexes 2 and 7 exhibit second-harmonic generation (assessed using the Kurtz powder technique), with an efficiency for the former of twice that of urea.     

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.     

Lanthanide-organic frameworks constructed from multi-functional ligands: Syntheses, structures, near-infrared and visible photoluminescence properties

A series of multi-functional ligands supported lanthanide-organic frameworks, formulated as [Ln(HL₁)(H₂L₂)_0.5(H₄L₂)_0.5(H₂O)]·(H₂O)_1.5·{Ln=La (1), Pr (2), Nd (3), Sm (4), Eu (5); H₃L₁=5-Sulfosaclicylic acid; H₄L₂=N,N′-piperazine (bis-methylene phosphonic acid)}, have been synthesized by hydrothermal reactions. Single crystal X-ray diffractions and powder XRD patterns confirm they are isostructural. They feature 3D framework structures based on extension of a “zigzag” inorganic chain by organic linkers. Moreover, the photoluminescence properties of 5 and 3 have been investigated, and they show strong solid-state emissions in the visible and near-infrared (IR) regions at room temperature.     

Analytical Hartree-Fock electron densities for singly charged cations and anions

The Hartree-Fock (HF) electron density has an important property that it is identical to the unknown exact density to the first order in the perturbation theory. We generate the spherically averaged HF electron density ρ(r) by using the numerical HF method for the singly charged 53 cations from Li⁺ to Cs⁺ and 43 anions from H⁻ to I⁻ in their ground state. The resultant density is then accurately fitted into an analytical function F(r), which is expressed by a linear combination of basis functions r ⁿⁱ exp(−ζ _i r). The present analytical approximation F(r) has the following properties: (1) F(r) is nonnegative, (2) F(r) is normalized, (3) F(r) reproduces the HF moments <r ^k > (k=−2 to +6), (4) F(0) is equal to ρ(0), (5) F ^′(0) satisfies the cusp condition and (6) F(r) has the correct exponential decay in the long-range asymptotic region. The present results together with our previous ones for neutral atoms provide a compilation of accurate analytical approximations of the HF electron densities for all the neutral and singly charged atoms with the number of electrons N≤54. Received: 11 July 1997 / Accepted: 27 August 1997     

A small methanoato ligand in the structural differentiation of copper(II) complexes

Several copper(II) methanoato complexes, namely mononuclear [Cu(O₂CH)₂(2-mpy)₂] (1) (2-mpy = 2-methylpyridine), binuclear [Cu₂(μ-O₂CH)₄(2-mpy)₂] (2), and the polynuclear {[Cu(μ-O₂CH)₂(2-mpy)₂][Cu₂(μ-O₂CH)₄]}_n (3) and {Na₂[Cu(μ-O₂CH)₂(O₂CH)₂][Cu₂(μ-O₂CH)₄]}_n (4), have been synthesized. The mononuclear complex 1 is formed by two asymmetric chelate methanoate anions and two 2-methylpyridine molecules, giving a highly distorted ‘elongated octahedral’ coordination sphere. Complex 1 decomposes outside the mother-liquid, transforming into a regular isolated binuclear paddle-wheel complex 2 with four intra-binuclear bridging methanoates and two axial 2-mpy ligands. The polynuclear complex 3 is formed of alternate mononuclear and binuclear building blocks resembling the central cores of 1 and 2, but with significant differences, especially for the methanoates of the mononuclear units. The oxygen atom of the mononuclear unit in the octahedral axial position in 3 is simultaneously coordinated to the axial position of the binuclear paddle-wheel central core, thus enabling a chain type of structure. A chain of alternate mononuclear and binuclear building blocks, as in the neutral compound 3, are found as well in the ionic polymeric compound 4, though two types of bridges are found in 4, while there is only one type in 3. Namely, the axial position of the octahedral mononuclear unit in 4 is occupied by the methanoate oxygen atom that is already a part of the binuclear paddle-wheel unit, while one equatorial methanoate from the mononuclear unit serves as a triatomic bridge to the axial position of the binuclear building block. A very strong antiferromagnetic interaction is found for all the complexes with the paddle-wheel building blocks [Cu₂(μ-O₂CH)₄] 2–4 (−2J = 444–482 cm⁻¹), attributed to the methanoate intra-binuclear bridges. On the other hand, this strong antiferromagnetism, found already at room temperature, reduces the intensity of the EPR S = 1 spin signals reported for the isolated paddle-wheel complex 2. For the polymeric 3, only the spin S = ½ signals are found in the EPR spectra, and they are assigned to the mononuclear building blocks. No signals with a clear origin are however seen in the room temperature EPR spectrum of the polymeric analogue 4, only the S = ½ signals in the low temperature spectra. This feature is suggested to be due to a specific influence between the adjacent S = 1 (binuclear) and S = ½ (mononuclear) species via their bridges.