Approximative "one particle" bridge function B(1)(r) for the theory of simple fluids

New properties for the one particle bridge function B(1)(r), which are necessary to the calculation of the excess chemical potential betamue), are derived for the hard sphere fluid. The method, which only requires the knowledge of the bridge function B(2)(r), is based on an investigation of the correlation function dependence on the Kirkwood charging parameter. In this framework, the unavoidable question of topological homotopy is addressed. As far as B(2)(r) is considered as exact, this work provides useful information on B(1)(r) in the well identified dynamical regimes of the hard sphere fluid. Signatures of the transitions between these regimes are identified on the trends of B(1)(r). This approach provides self-consistent results for betamue) that agree very well with simulation data.     

Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation

We report coefficients of the h-bond expansion of the bridge function of the hard-sphere system up to order rho(4) (where rho is the density in units of the hard-sphere diameter), which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r). Calculations are performed using the recently introduced Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein-Zernike equation with a closure given by the calculated clusters. Calculations are performed for reduced densities from 0.1 to 0.9 in increments of 0.1. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated this way.     

Simulating asymmetric colloidal mixture with adhesive hard sphere model

Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g(11)(r), g(22)(r), and g(12)(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum nsigma(1)+msigma(2) (sigma(1) and sigma(2) being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of g(ij)(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries.     

Rapid, accurate calculation of the s-wave scattering length

Transformation of the conventional radial Schro?dinger equation defined on the interval r ∈ [0, ∞) into an equivalent form defined on the finite domain y(r) ∈ [a, b] allows the s-wave scattering length a(s) to be exactly expressed in terms of a logarithmic derivative of the transformed wave function φ(y) at the outer boundary point y = b, which corresponds to r = ∞. In particular, for an arbitrary interaction potential that dies off as fast as 1/r(n) for n ≥ 4, the modified wave function φ(y) obtained by using the two-parameter mapping function r(y; ?r,β) = ?r[1 + 1/β tan(πy/2)] has no singularities, and a(s) = ?r[1 + 2/πβ 1/φ(1) dφ(1)/dy]. For a well bound potential with equilibrium distance r(e), the optimal mapping parameters are ?r ≈ r(e) and β ≈ n/2 - 1. An outward integration procedure based on Johnson's log-derivative algorithm [J. Comp. Phys. 13, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision a(s)-values both for model Lennard-Jones (2n, n) potentials and for realistic published potentials for the Xe-e(-), Cs(2)(aΣ(u)(+)(3)), and (3, 4)He(2)(XΣ(g)(+)(1)) systems. Use of this same transformed Schro?dinger equation was previously shown [V. V. Meshkov et al., Phys. Rev. A 78, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.     

Heuristic molecular lipophilicity potential (HMLP): lipophilicity and hydrophilicity of amino acid side chains

Heuristic molecular lipophilicity potential (HMLP) is applied in the study of lipophilicity and hydrophilicity of 20 natural amino acids side chains. The HMLP parameters, surface area S(i), lipophilic indices L(i), and hydrophilic indices H(i) of amino acid side chains are derived from lipophilicity potential L(r). The parameters are correlated with the experimental data of phase-transferring free energies of vapor-to-water, vapor-to-cyclohexane, vapor-to-octanol, cyclohexane-to-water, octanol-to-water, and cyclohexane-to-octanol through a linear free energy equation DeltaG(0)(tr,i) = b(0) + b(1)S(i) (+) + b(2)S(i) (-) + b(3)L(i) + b(4)H(i). For all above six phase-transfer free energies, the HMLP parameters of 20 amino acid side chains give good calculation results using linear free energy equation. HMLP is an ab initio quantum chemical approach and a structure-based technique. Except for atomic van der Waals radii, there are no other empirical parameters used. The HMLP has clear physical and chemical meaning and provides useful lipophilic and hydrophilic parameters for the studies of proteins and peptides.     

The gadolinium(III)-water hydrogen distance in MRI contrast agents

The ion-nuclear distance of Gd(III) to a coordinated water proton, r(Gd)(-)(H), is central to the understanding of the efficacy of gadolinium-based MRI contrast agents. The dipolar relaxation mechanism operative for contrast agents has a 1/r(6) dependence. Estimates in the literature for this distance span 0.8 A (2.5-3.3 A). This study describes a direct determination of r(Gd)(-)(H) using the anisotropic hyperfine constant T( perpendicular ) determined from pulsed ENDOR spectra. Five Gd(III) complexes were examined: [Gd(H(2)O)(8)](3+), [Gd(DTPA)(H(2)O)](2)(-), [Gd(BOPTA)(H(2)O)](2)(-), MS-325, and [Gd(HP-DO3A)(H(2)O)]. The distance, r(Gd)(-)(H), was the same within error for all five complexes: 3.1 +/- 0.1 A. These distance estimates should aid in the design of new contrast agents, and in the interpretation of other molecular factors influencing relaxivity.     

一个新的桥泛函及其在非均一流体密度泛函理论中的应用

基于对OZ 方程的渐近行为与Taylor级数展开的分析，提出了一个新的桥泛函，桥泛函被表达为间接相关函数的函数，Taylor级数展开的重整化导致了一个可调参数，通过将所提出的桥泛函与一个最近提出的密度泛函理论方法学，以及单个硬墙的sum 规则结合，可以确定可调参数.所提出的桥泛函能预言如下非均一流体的密度分布：硬球流体接近一个硬墙与在球形空隙内，Lennard-Jones 流体与缔合硬球流体在两个硬墙之内.理论预言与文献所报导的模拟数据符合很好.     

A consistent calculation of the chemical potential for dense simple fluids

A general method to calculate the excess chemical potential betamuex, that is based on the Kirkwood coupling parameter's dependence of the correlation functions, is presented. The expression for the one particle bridge function B(1)r is derived for simple fluids with spherical interactions. Only the knowledge of the bridge function B(2)r is required. The accuracy of our approach is illustrated for a dense hard sphere fluid. As far as B(2)r is considered as exact, B(1)r is found to be, at high densities, the normalized bridge function -B(2)rB(2)(r=0). This expression ensures a consistent calculation of the excess chemical potential by satisfying implicitly the Gibbs-Duhem constraint. Only the pressure-consistency condition is necessary to calculate the structural and thermodynamic properties of the fluid.     

Solution structure investigation of Ru(II) complex ion pairs: quantitative NOE measurements and determination of average interionic distances.

The structure of the Ru(II) ion pairs trans-[Ru(COMe)[(pz(2))CH(2)](CO)(PMe(3))(2)]X (X(-) = BPh(4)(-), 1a; BPh(3)Me(-), 1b; BPh(3)(n-Bu)(-), 1c; BPh(3)(n-Hex)(-), 1d; B(3, 5-(CF(3))(2)(C(6)H(3)))(4)(-), 1e; PF(6)(-), 1f; and BF(4)(-), 1g; pz = pyrazol-1-yl-ring) was investigated in solution from both a qualitative (chloroform-d, methylene chloride-d(2), nithromethane-d(3)) and quantitative (methylene chloride-d(2)) point of view by performing 1D- and 2D-NOE NMR experiments. In particular, the relative anion-cation localization (interionic structure) was qualitatively determined by (1)H-NOESY and (19)F, (1)H-HOESY (heteronuclear Overhauser effect spectroscopy) NMR experiments. The counteranion locates close to the peripheral protons of the bispyrazolyl ligand independent of its nature and that of the solvent. In complexes 1c and 1d bearing unsymmetrical counteranions, the aliphatic chain points away from the metal center as indicated by the absence of NOE between the terminal Me group and any cationic protons. An estimation of the average interionic distances in solution was obtained by the quantification of the NOE build-up versus the mixing time under the assumption that the interionic and intramolecular correlation times (tau(c)) are the same. Such an assumption was checked by the experimental measurements of tau(c) from both the dipolar contribution to the carbon-13 longitudinal relaxation time T(DD-1)and the comparison of the intramolecular and interionic cross relaxation rate constant (sigma) dependence on the temperature. Both the methodologies indicate that anion and cation have comparable tau(c) values. The determined correlation time values were compared with those obtained for the neutral trans-[Ru(COMe)[(pz(2))BH(2)](CO)(PMe(3))(2)] complex (2), isosteric with the cation of 1. They were significantly shorter (approximately 3.8 times), indicating that the main contribution to dipolar relaxation processes comes from the overall ion pair rotation. As a consequence, the determined average interionic distances appear to be accurate. By using such interionic distances, it was possible to verify that the counteranion in complex 1b also orients the BMe group far away from the metal center.     

Atomistic simulation of discotic liquid crystals: transition from isotropic to columnar phase example

Molecular dynamics simulations at atomistic level have been performed on a metal-porphyrazine complex. Starting from an isotropic state, the system was cooled until transition from isotropic to columnar phase was observed; no nematic phase was encountered. Many tools were utilized to follow the system evolution: order parameter, g(r), g(||)(r(||)), g(c)(r(||)), g(perpendicular)(r(perpendicular)), g(2)(r), also density and energy changes. Very long runs were required to get reliable results, times greater than 40 ns of simulation. The structure of columnar phase was analyzed and the organization of molecules in the columns was investigated, along with the role of conformation of side chains. We found that in columnar phase the molecules are tilted versus the column axis and the conformation of side chains changes during the phase transition to allow this kind of organization; moreover the direction of columns axes is different from that of the director.     

Theoretical analysis of reaction kinetics with singlet oxygen molecules

A comparative analysis of predictive ability of three approaches to estimate the rate constants of reactions of H(2), H, H(2)O and CH(4) with electronically excited O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) molecules is conducted. The first approach is based on a detailed ab initio study of potential energy surfaces. The second one is known as the "bond energy-bond order" method, and the third approach is a modification of the updated method of vibronic terms that makes it possible to evaluate the activation energy of reactions involving electronically excited species. The comparison showed that the estimates of the energy barrier by the updated method of vibronic terms for some reactions can be in good agreement with ab initio calculations and available experimental data. It was revealed that reactions of O(2)(b(1)Σ(g)(+)) molecules with H(2), H(2)O and CH(4) molecules and with the H atom result in the formation of electronically excited species. The reactivity of O(2)(b(1)Σ(g)(+)) molecules is smaller than that of O(2)(a(1)Δ(g)) ones, but much higher as compared to the reactivity of ground state O(2) molecules. For each reaction under study involving oxygen molecules in the excited electronic states O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) the recommended temperature-dependent rate constants are presented.     

Positron annihilation and relaxation dynamics from dielectric spectroscopy and nuclear magnetic resonance: cis-trans-1,4-poly(butadiene)

We report a joint analysis of positron annihilation lifetime spectroscopy (PALS), dielectric spectroscopy (BDS), and nuclear magnetic resonance (NMR) on cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD). Phenomenological analysis of the orthopositronium lifetime τ(3)-T dependence by linear fitting reveals four characteristic PALS temperatures: T(b1)(G)=0.63T(g)(PALS), T(g)(PALS), T(b1)(L)=1.22T(g)(PALS), and T(b2)(L)=1.52T(g)(PALS). Slight bend effects in the glassy and supercooled liquid states are related to the fast or slow secondary β process, from neutron scattering, respectively, the latter being connected with the trans-isomers. In addition, the first bend effect in the supercooled liquid coincides with a deviation of the slow effective secondary β(eff) relaxation related to the cis-isomers from low-T Arrhenius behavior to non-Arrhenius one and correlates with the onset of the primary α process from BDS. The second plateau effect in the liquid state occurs when τ(3) becomes commensurable with the structural relaxation time τ(α)(T(b2)). It is also approximately related to its crossover from non-Arrhenius to Arrhenius regime in the combined BDS and NMR data. Finally, the combined BDS and NMR structural relaxation data, when analyzed in terms of the two-order parameter (TOP) model, suggest the influence of solidlike domains on both the annihilation behavior and the local and segmental chain mobility in the supercooled liquid. All these findings indicate the influence of the dynamic heterogeneity in both the primary and secondary relaxations due to the cis-trans isomerism in c-t-1,4-PBD and their impact into the PALS response.     

Synthesis and Crystal Structure of a Three-dimensional Mn(Ⅱ) Coordination Polymer with 3-(Pyrazin-2-yloxy)-pyridine and Azide Anion as Mixed Bridge Ligand

A three-dimensional coordination polymer [Mn2(μ1,3-N3)4(μ-PP)2]n(PP = 3-(pyra-zin-2-yloxy)-pyridine) has been synthesized with 3-(pyrazin-2-yloxy)-pyridine and azide anion as mixed bridge ligand,and its crystal structure was determined by X-ray crystallography.The crystal data:triclinic system,space group P,with a = 6.794(4),b = 9.885(6),c = 9.947(6) ,α = 64.170(6),β = 84.190(8),γ = 85.319(8)°,V = 597.7(6) 3,Z = 1,C18H14Mn2N18O2,Mr = 624.35,Dc = 1.735 g/cm3,F(000) = 314 and μ = 1.117 mm-1.In the crystal,the azide anion acts as a bridge ligand and makes adjacent Mn(II) ions connect into a two-dimensional sheet on the ab plane,then 3-(pyrazin-2-yloxy)-pyridine serves as a bidentate bridge ligand to connect neighboring sheets along the c axis,and finally a three-dimensional structure is formed.     

Structure of star-burst dendrimers: a comparison between small angle x-ray scattering and computer simulation results

We investigated the generation dependent shape and internal structure of star-burst dendrimers under good solvent conditions using small angle x-ray scattering and molecular modeling. Measurements have been performed on poly(amidoamine) dendrimers with generations ranging from g=0 up to g=8 at low concentrations in methanol. We described the static form factor P(q) by a model taking into account the compact, globular shape as well as the loose, polymeric character of dendrimers. Monomer distributions within dendrimers are of special interest for potential applications and have been characterized by the pair correlation function gamma(r), as well as by the monomer and end-group density profile, rho(r) and rho(e)(r), respectively. Monomer density profiles and gamma(r) can be derived from P(q) by modeling and via a model independent approach using the inverse Fourier transformation algorithm first introduced by Glatter. Experimental results are compared with computer simulations performed for single dendrimers of various generations using the cooperative motion algorithm. The simulation gives direct access to gamma(r) and rho(r), allows an independent determination of P(q), and yields in addition to the scattering experiment information about the distribution of the end groups. Excellent qualitative agreement between experiment and simulation has been found.     

熔融CaF2的径向分布函数

熔融CaF_2是一种典型的离子液体,又是一种重要的冶金熔体.径向分布函数不仅是描述熔体结构的重要物理量,而且是计算熔体热力学性质的基础.实验上可以通过X 射线、中子衍射测得结构因子经Fourier 变换得到径向分布函数.已有使用X 射线衍射方法实验测定熔融CaF_2结构因子的报导.但由于实验上分解三种离子对Ca~(2+)-Ca~(2+),Ca~(2+)-F~-、F~--F~-偏结构因子的困难,未能给出相应的三种径向分布函数g++(r)、g+-(r)、g--(r),仅估计出三种径     

Kinetics of elementary steps in the reactions of atomic bromine with isoprene and 1,3-butadiene under atmospheric conditions

Laser flash photolysis of CF(2)Br(2) has been coupled with time-resolved detection of atomic bromine by resonance fluorescence spectroscopy to investigate the gas-phase kinetics of early elementary steps in the Br-initiated oxidations of isoprene (2-methyl-1,3-butadiene, Iso) and 1,3-butadiene (Bu) under atmospheric conditions. At T ≥ 526 K, measured rate coefficients for Br + isoprene are independent of pressure, suggesting that hydrogen transfer (1a) is the dominant reaction pathway. The following Arrhenius expression adequately describes all kinetic data at 526 K ≤ T ≤ 673 K: k(1a)(T) = (1.22 ± 0.57) × 10(-11) exp[(-2100 ± 280)/T] cm(3) molecule(-1) s(-1) (uncertainties are 2σ and represent precision of the Arrhenius parameters). At 271 K ≤ T ≤ 357 K, kinetic evidence for the reversible addition reactions Br + Iso ? Br-Iso (k(1b), k(-1b)) and Br + Bu ? Br-Bu (k(3b), k(-3b)) is observed. Analysis of the approach to equilibrium data allows the temperature- and pressure-dependent rate coefficients k(1b), k(-1b), k(3b), and k(-3b) to be evaluated. At atmospheric pressure, addition of Br to each conjugated diene occurs with a near-gas-kinetic rate coefficient. Equilibrium constants for the addition/dissociation reactions are obtained from k(1b)/k(-1b) and k(3b)/k(-3b), respectively. Combining the experimental equilibrium data with electronic structure calculations allows both second- and third-law analyses of thermochemistry to be carried out. The following thermochemical parameters for the addition reactions 1b and 3b at 0 and 298 K are obtained (units are kJ mol(-1) for Δ(r)H and J mol(-1) K(-1) for Δ(r)S; uncertainties are accuracy estimates at the 95% confidence level): Δ(r)H(0)(1b) = -66.6 ± 7.1, Δ(r)H(298)(1b) = -67.5 ± 6.6, and Δ(r)S(298)(3b) = -93 ± 16; Δ(r)H(0)(3b) = -62.4 ± 9.0, Δ(r)H(298)(3b) = -64.5 ± 8.5, and Δ(r)S(298)(3b) = -94 ± 20. Examination of the effect of added O(2) on Br kinetics under conditions where reversible adduct formation is observed allows the rate coefficients for the Br-Iso + O(2) (k(2)) and Br-Bu + O(2) (k(4)) reactions to be determined. At 298 K, we find that k(2) = (3.2 ± 1.0) × 10(-13) cm(3) molecule(-1) s(-1) independent of pressure (uncertainty is 2σ, precision only; pressure range is 25-700 Torr) whereas k(4) increases from 3.2 to 4.7 × 10(-13) cm(3) molecule(-1) s(-1) as the pressure increases from 25 to 700 Torr. Our results suggest that under atmospheric conditions, Br-Iso and Br-Bu react with O(2) to produce peroxy radicals considerably more rapidly than they undergo unimolecular decomposition. Hence, the very fast addition reactions appear to control the rates of Br-initiated formation of Br-Iso-OO and Br-Bu-OO radicals under atmospheric conditions. The peroxy radicals are relatively weakly bound, so conjugated diene regeneration via unimolecular decomposition reactions, though unimportant on the time scale of the reported experiments (milliseconds), is likely to compete effectively with bimolecular reactions of peroxy radicals under relatively warm atmospheric conditions as well as in 298 K competitive kinetics experiments carried out in large chambers.     

Structural and magnetic studies of Schiff base complexes of nickel(II) nitrite: change in crystalline state, ligand rearrangement and a very rare μ-nitrito-1κO:2κN:3κO' bridging mode

Four new nickel(II) complexes, [Ni(2)L(2)(NO(2))(2)]·CH(2)Cl(2)·C(2)H(5)OH, 2H(2)O (1), [Ni(2)L(2)(DMF)(2)(μ-NO(2))]ClO(4)·DMF (2a), [Ni(2)L(2)(DMF)(2)(μ-NO(2))]ClO(4) (2b) and [Ni(3)L'(2)(μ(3)-NO(2))(2)(CH(2)Cl(2))](n)·1.5H(2)O (3) where HL = 2-[(3-amino-propylimino)-methyl]-phenol, H(2)L(') = 2-({3-[(2-hydroxy-benzylidene)-amino]-propylimino}-methyl)-phenol and DMF = N,N-dimethylformamide, have been synthesized starting with the precursor complex [NiL(2)]·2H(2)O, nickel(ii) perchlorate and sodium nitrite and characterized structurally and magnetically. The structural analyses reveal that in all the complexes, Ni(II) ions possess a distorted octahedral geometry. Complex 1 is a dinuclear di-μ(2)-phenoxo bridged species in which nitrite ion acts as chelating co-ligand. Complexes 2a and 2b also consist of dinuclear entities, but in these two compounds a cis-(μ-nitrito-1κO:2κN) bridge is present in addition to the di-μ(2)-phenoxo bridge. The molecular structures of 2a and 2b are equivalent; they differ only in that 2a contains an additional solvated DMF molecule. Complex 3 is formed by ligand rearrangement and is a one-dimensional polymer in which double phenoxo as well as μ-nitrito-1κO:2κN bridged trinuclear units are linked through a very rare μ(3)-nitrito-1κO:2κN:3κO' bridge. Analysis of variable-temperature magnetic susceptibility data indicates that there is a global weak antiferromagnetic interaction between the nickel(ii) ions in four complexes, with exchange parameters J of -5.26, -11.45, -10.66 and -5.99 cm(-1) for 1, 2a, 2b and 3, respectively.     

Hard-sphere radial distribution function again

A theoretically based closed-form analytical equation for the radial distribution function, g(r), of a fluid of hard spheres is presented and used to obtain an accurate analytic representation. The method makes use of an analytic expression for the short- and long-range behaviors of g(r), both obtained from the Percus-Yevick equation, in combination with the thermodynamic consistency constraint. Physical arguments then leave only three parameters in the equation of g(r) that are to be solved numerically, whereas all remaining ones are taken from the analytical solution of the Percus-Yevick equation.