Direct correlation functions and bridge functions in additive hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the generalized mean spherical approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boublik-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzman and del Rio (1998, 98, Molec. Phys., 95, 645), stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions, is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.     

Exploring the MRCI method for calculating interaction energies: application to the HeNe potential curve

A multi-reference configuration interaction (MRCI) method is described, which is devised for the calculation of interaction energies of van der Waals complexes and applied to calculating the HeNe potential energy curve. The MRCI calculations make use of a generalized Pople-correction in order to account for the lack of size consistency. The orbital space is partitioned into three subspaces: the first active space (AS1), which contains the strongly occupied orbitals; the second active space (AS2), which contains the main intra-correlating orbitals; and the external space (ES). It is shown that, to keep the error below ± 0.2 K in the excitation scheme and the active orbital space it is sufficient to include only σ-orbitals in AS2 and to use an excitation scheme (labelled Qq-MRCI) that encompasses only up to quadruply excited configurations. The final active orbital space (AS2) turned out to be 2s(He), 2pσ(He), 3s(Ne), 3σ(Ne) and 3dσ(Ne). Other MRCI variants, in which most or all quadruply excited configurations were deleted from the CI expansion (Qt- and Tt-MRCI), were found to be inadequate. Using the Qq-MRCI scheme together with a 197-orbital ‘interaction optimized’ basis set (IO197), the MRCI interaction energy at R = 5.7 _a0 was calculated to be -21.12K. The corresponding values at the MP4 and CCSD(T) levels of theory are -20.06 K and -20.99 K, respectively, indicating that the MP4 method is inappropriate for highly accurate calculations on this system. Fitting the calculated data using a generalized Morse function, including an additional C₆/R⁶ term to account for a correct long-range behaviour of the potential, the MRCI well depth was calculated to be -21.16K at R_eq = 5.73a ₀. The MRCI and CCSD(T) potentials have the same quality and are found to be in good agreement with the Hartree-Fock dispersion (HFD-B) potential of Keil, M., Danielson, L. J., and Dunlop, P. J., 1991, J. Chem. Phys., 94, 296. It is concluded that, for basis IO197, the CCSD(T) method is sufficiently accurate for calculating the HeNe interaction. To recover the small, missing contributions (a few tenths of a Kelvin), MRCI should be used.     

Dynamics on reactive potential energy surfaces: hyperspherical view and signatures of ‘quantum chaos’

Adiabatic energy levels for two prototypical reactions, F + H₂ → HF + H and He + H⁺ ₂ → HeH⁺ + H, are analysed by means of statistical tests. These levels result from quantum mechanical calculations of dynamics based on the hyperspherical approach, and are given as a function of the total inertia of the system measured by the hyperradius ρ The nearest neighbour level spacing distributions of Brody and of Berry and Robnik, the spectral rigidity δ₃ of Dyson and Mehta and the correlation coefficient are reported, together with other properties, such as variance, skewness and kurtosis of the distributions. Trends are studied as a function of ρ, proposed as a natural control variable. For low ρ, which correspond to the transition state, evidence is found of Wigner-like behaviour, which is interpreted as the signature of quantum chaos. On the passage of the systems through intermediate ρ a mixture of Wigner- and Poisson-like behaviour emerges. The situation for high ρ where reactants and products of the reactions are well separated, is characterized by a tendency towards regular Poisson-like behaviour. A comparison between the two investigated systems shows that the chaotic regime in the transition state region is more pronounced for the He reaction, which proceeds through a deep well and whose dynamics are characterized by a rich resonance pattern.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

金属卟啉催化条件下有机化合物与二氧化碳的电羧化反应Ⅰ. 金属卟啉对苄基氯电羧化催化活性的研究

本文研究了系列金属卟啉对苯基氯(phCH~2Cl)和CO~2电羧化反应的催化活性.用熔点,MS,IR,UV鉴别产物为苯乙酸卟脂,利用高效液相色谱(HPLC)定量分析了羧化产物,选出最佳电羧化电解电位为-1.6v(相对于饱和甘汞电极,vs.SCE,下同). 并对催化活性较高的钴卟啉系列配合物进行了深入研究. 探讨了金属卟啉具有催化活性的原因,认为能形成M(Ⅰ)中间体的金属卟啉配合物.具有较高的催化活性.     

AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS

An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.     

THE PROTONATION OF A RETINYL SCHIFF BASE

The hydrogen bonding-protonation equilibrium for retinyl Schiff base/propionic acid or 3-chloropropionic acid systems was examined by Fourier transform infrared spectroscopy in non polar solutions at temperatures ranging from 25 degrees C to about -150 degrees C. The spectra give evidence for the gradual increase in the degree of protonation as temperature is lowered. The bearing of this on applying low temperature spectroscopic results to physiological conditions in rhodopsin research is discussed.     

Linear dynamical systems with integer constraints

We study properties of dynamic discrete-time linear systemswith the input or the state constrained to have integer components.The reachability of input-constrained systems is investigated,and consistency conditions for state-constrained systems aregiven.     

The numerical solution of Stokes flow in a domain with re-entrant boundaries by the boundary element method

Numerical solutions are presented for two-dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re-entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.     

钾蒸气中的偶极禁戒双光子共振四波混频和混合激发能量转移受激辐射

本文首次报道了由钾分子-原子系统的混合激发和碰撞能量转移过程产生4F→3D受激辐射以及由钾原子的4S→4F偶极禁戒双光子共振产生4F→3D受激辐射和四波混频的研究结果。