Automated establishment and plotting of multivariate functions

The earlier package for univariate functions is extended to multivariate functions in the QQN series software, which contains millions of models. The models are characterized by numbered basic and compound functions which are selected by the user. Plots for a selected model are displayed in rotatablethree-dimensional coordinates. The package can be run on an IBM-PC or compatible computer.     

Scoring protein–protein docked structures based on the balance and tightness of binding

One main issue in protein-protein docking is to filter or score the putative docked structures. Unlike many popular scoring functions that are based on geometric and energetic complementarity, we present a set of scoring functions that are based on the consideration of local balance and tightness of binding of the docked structures. These scoring functions include the force and moment acting on one component (ligand) imposed by the other (receptor) and the second order spatial derivatives of protein-protein interaction potential. The scoring functions were applied to the docked structures of 19 test targets including enzyme/inhibitor, antibody/antigen and other classes of protein complexes. The results indicate that these scoring functions are also discriminative for the near-native conformation. For some cases, such as antibody/antigen, they show more discriminative efficiency than some other scoring functions, such as desolvation free energy (deltaG(des)) based on pairwise atom-atom contact energy (ACE). The correlation analyses between present scoring functions and the energetic functions also show that there is no clear correlation between them; therefore, the present scoring functions are not essentially the same as energy functions.     

Use of characteristic functions derived from proficiency testing data to evaluate measurement uncertainties

Interlaboratory comparisons show that reproducibility standard deviations are dependent on the concentration of the analyte. Many attempts have been made to model this. In this paper, ??characteristic?? functions are used for modelling the concentration dependence of the reproducibility standard deviations based on data from proficiency tests for water analysis. The characteristics of the resulting functions can be used for the estimation of measurement uncertainties at different concentration levels. These functions are especially useful to determine the concentration levels below which absolute uncertainties tend to be constant and above which the relative uncertainties are more constant. By comparing the characteristic functions of different analytical procedures for the determination of the same analyte, the performance of these procedures under routine application can be compared. Finally, these functions may be used to get an indication on the average quality of analytical result in a specific field to be used by regulators in order to formulate requirements in the legislation that are in accordance with current measurement quality.     

A Mathematical Discussion on Density and Shape Functions, Vector Semispaces and Related Questions

Density and shape functions are studied from the point of view of vector semispace structure and properties. Useful characteristics based on the shell structure of vector semispaces are used to analyze some properties of both functions. Fukui functions and quantum similarity indices are also studied when basic applications of the theory are discussed. Construction of approximate density functions and pseudo wave functions is also outlined. Finally, the original DFT variational theorem is reformulated within the frame of the shape function.     

Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions

High dimensional model representation is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The HDMR component functions are optimally constructed from zeroth order to higher orders step-by-step. This paper extends the definitions of HDMR component functions to systems whose input variables may not be independent. The orthogonality of the higher order terms with respect to the lower order ones guarantees the best improvement in accuracy for the higher order approximations. Therefore, the HDMR component functions are constructed to be mutually orthogonal. The RS-HDMR component functions are efficiently constructed from randomly sampled input-output data. The previous introduction of polynomial approximations for the component functions violates the strictly desirable orthogonality properties. In this paper, new orthonormal polynomial approximation formulas for the RS-HDMR component functions are presented that preserve the orthogonality property. An integrated exposure and dose model as well as ionospheric electron density determined from measured ionosonde data are used as test cases, which show that the new method has better accuracy than the prior one.     

A method to estimate the Leslie coefficients of liquid crystals based on MBBA data

A new effective approach for estimating the Leslie coefficients of liquid crystals based on MBBA data is presented. Literature values of the temperature-dependent Leslie viscosity coefficients of MBBA are used to fit with the analytical functions of Leslie coefficients based on the Imura and Okano theory, and a set of constants in these functions are determined. The same functions are then applied to two high birefringence liquid crystal mixtures, E7 and UCF-2, to extract their Leslie coefficients based on their order parameters. Using the extracted Leslie coefficients, the simulation results agree very well with the experimental data.     

Dynamical pruning of static localized basis sets in time-dependent quantum dynamics

We investigate the viability of dynamical pruning of localized basis sets in time-dependent quantum wave packet methods. Basis functions that have a very small population at any given time are removed from the active set. The basis functions themselves are time independent, but the set of active functions changes in time. Two different types of localized basis functions are tested: discrete variable representation (DVR) functions, which are localized in position space, and phase-space localized (PSL) functions, which are localized in both position and momentum. The number of functions active at each point in time can be as much as an order of magnitude less for dynamical pruning than for static pruning, in reactive scattering calculations of H2 on the Pt(211) stepped surface. Scaling of the dynamically pruned PSL (DP-PSL) bases with dimension is considerably more favorable than for either the primitive (direct product) or DVR bases, and the DP-PSL basis set is predicted to be three orders of magnitude smaller than the primitive basis set in the current state-of-the-art six-dimensional reactive scattering calculations.     

Constraints for hierarchies of many electron distribution functions

Some inequalities that constrain the reconstruction of k-electron distribution functions from lower-order distribution functions are presented. These inequalities are related to the N-representability conditions on electron distributions functions and they have two basic types: (1) general N-representability inequalities, which are very powerful but difficult to apply and (2) generalized “Davidson” inequalities, which are less powerful but which may be more facile in computational implementations. A constraint on the exchange-correlation hole is also presented.     

An X-ray diffraction study of aqueous solutions of lutetium trichloride

The X-ray diffraction analysis is used to study aqueous solutions of lutetium chloride in a wide concentration range under standard conditions. Small angle peaks on the functions of the X-ray scattering intensity and the maxima of radial distribution functions of the atomic-electron density are interpreted. It is found that highly concentrated solutions are characterized by a unique quasi-crystalline structure distinguished by short- and long-range ordering. Dilution of solutions results in that the own structure of the solvent starts to play the major role in the structure of the systems. It is established for the first time that small angle peaks on the scattering intensity functions are also manifested for diluted solutions, which indicates that long-range ordering is preserved in them.     

An extensive test of 14 scoring functions using the PDBbind refined set of 800 protein-ligand complexes

Fourteen popular scoring functions, i.e., X-Score, DrugScore, five scoring functions in the Sybyl software (D-Score, PMF-Score, G-Score, ChemScore, and F-Score), four scoring functions in the Cerius2 software (LigScore, PLP, PMF, and LUDI), two scoring functions in the GOLD program (GoldScore and ChemScore), and HINT, were tested on the refined set of the PDBbind database, a set of 800 diverse protein-ligand complexes with high-resolution crystal structures and experimentally determined Ki or Kd values. The focus of our study was to assess the ability of these scoring functions to predict binding affinities based on the experimentally determined high-resolution crystal structures of proteins in complex with their ligands. The quantitative correlation between the binding scores produced by each scoring function and the known binding constants of the 800 complexes was computed. X-Score, DrugScore, Sybyl::ChemScore, and Cerius2::PLP provided better correlations than the other scoring functions with standard deviations of 1.8-2.0 log units. These four scoring functions were also found to be robust enough to carry out computation directly on unaltered crystal structures. To examine how well scoring functions predict the binding affinities for ligands bound to the same target protein, the performance of these 14 scoring functions were evaluated on three subsets of protein-ligand complexes from the test set: HIV-1 protease complexes (82 entries), trypsin complexes (45 entries), and carbonic anhydrase II complexes (40 entries). Although the results for the HIV-1 protease subset are less than desirable, several scoring functions are able to satisfactorily predict the binding affinities for the trypsin and the carbonic anhydrase II subsets with standard deviation as low as 1.0 log unit (corresponding to 1.3-1.4 kcal/mol at room temperature). Our results demonstrate the strengths as well as the weaknesses of current scoring functions for binding affinity prediction.     

处理量子反应散射的负虚数势方法

处理量子反应散射的负虚数势方法蔡宇民，胡旭光，李前树（西安石油学院化学工程系．西安，７１００６１）（吉林大学理论化学研究所，长春，１３００２３）关键词反应散射，反应几率，光学势近年来，处理反应散射问题的各种严格的和近似的量子力学方法发展迅速［１～５］...     

A simplified representation of the potential produced by Gaussian charge distributions

A procedure is presented which allows a more economical representation of the potential produced by orbital charge distributions in which the orbitals are expanded in terms of a finite set of polynomial Gaussian functions. The basic idea is that the products of pairs of Gaussian basis functions, on which the charge distributions are expanded, are expressed in terms of a new basis set of optimally chosen single Gaussian functions. Such a procedure has been tested in a particular case and a few possible applications have been suggested.     

Quantum Monte Carlo study of first-row atoms using transcorrelated variational Monte Carlo trial functions

The effect of using the transcorrelated variational Monte Carlo (TC-VMC) approach to construct a trial function for fixed node diffusion Monte Carlo (DMC) energy calculations has been investigated for the first-row atoms, Li to Ne. The computed energies are compared with fixed node DMC energies obtained using trial functions constructed from Hartree-Fock and density functional levels of theory. Despite major VMC energy improvement with TC-VMC trial functions, no improvement in DMC energy was observed using these trial functions for the first-row atoms studied. The implications of these results on the nodes of the trial wave functions are discussed.     

Evaluation of Seven Chromatographic Response Functions on Simulated and Experimentally Obtained Chromatograms in Hydrophilic Interaction Liquid Chromatography System

This paper investigates the ability of seven chromatographic response functions to measure the quality of chromatograms obtained in hydrophilic interaction liquid chromatography (HILIC). First, the functions were tested on a set of simulated chromatograms and differences in their mathematical design were discussed. Second, the functions were evaluated on the experimentally obtained chromatograms in HILIC analysis of model mixture consisted of beta agonists and antagonists. The ranking of chromatograms obtained by different functions was significantly different, implying that the accuracy of the optimization procedure is strongly dependent on the function that was selected as an output. Investigation of potential drawbacks of each function was conducted and general recommendations concerning the use of chromatographic response functions in optimization strategies are proposed.     

On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions

Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation.     

水、甲醇和乙醇液体微结构性质的Car-Parrinello 分子动力学模拟

采用Car-Parrinello 分子动力学(CPMD)方法分别研究了水、甲醇和乙醇的液体微结构性质.研究结果显示:在水、甲醇和乙醇三个体系中O…O径向分布函数曲线的第一个峰位置分别为0.278、0.276 和0.275nm; O…H径向分布函数曲线的第一个峰位置分别为0.178、0.176和0.177 nm.表明基团(氢原子、甲基、乙基)的差异对O…O第一个峰的位置影响很小.但基团的差异对径向分布函数峰高的影响却很显著,由水到乙醇第一个峰的高度逐渐变高.空间分布函数表明氧原子和氢原子在溶剂分子周围有取向地分布,这与径向分布函数所表现出尖锐的第一个峰相一致.氢键分布分析显示,水、甲醇和乙醇的平均氢键数分别为3.62、1.99 和1.87,表明水形成了网状氢键结构,而甲醇、乙醇形成链状氢键结构.     

蛋白质半胱氨酸上的翻译后修饰组分析方法进展

半胱氨酸的巯基具有很高的反应活性,作为亲核、氧化还原催化反应、金属结合及变构调节位点等在蛋白质的结构和功能中发挥着非常重要的作用,且容易发生多种翻译后修饰,调控亦或损伤蛋白功能,与人类许多重要疾病关系密切,因此,定性与定量分析蛋白质半胱氨酸上的翻译后修饰组对理解其生物学功能具有重要意义。本文综述了近年来蛋白质半胱氨酸上常见的翻译后修饰组的质谱和蛋白质组学分析方法进展。     

Statistical thermodynamics of bond torsional modes: tests of separable, almost-separable, and improved Pitzer-Gwinn approximations

Practical approximation schemes for calculating partition functions of torsional modes are tested against accurate quantum mechanical results for H(2)O(2) and six isotopically substituted hydrogen peroxides. The schemes are classified on the basis of the type and amount of information that is required. First, approximate one-dimensional hindered-rotator partition functions are benchmarked against exact one-dimensional torsion results obtained by eigenvalue summation. The approximate one-dimensional methods tested in this stage include schemes that only require the equilibrium geometries and frequencies, schemes that also require the barrier heights of internal rotation, and schemes that require the whole one-dimensional torsional potential. Then, three classes of approximate full-dimensional vibrational-rotational partition functions are calculated and are compared with the accurate full-dimensional path integral partition functions. These three classes are (1) separable approximations combining harmonic oscillator-rigid rotator models with the one-dimensional torsion schemes, (2) almost-separable approximations in which the nonseparable zero-point energy is used to correct the separable approximations, and (3) improved nonseparable Pitzer-Gwinn-type methods in which approaches of type 1 are used as reference methods in the Pitzer-Gwinn approach. The effectiveness of these methods for the calculation of isotope effects is also studied. Based on the results of these studies, the best schemes of each type are recommended for further use on systems where a corresponding amount of information is available.     

Nuclear attraction and electron interaction integrals of exponentially decaying functions and the Poisson equation

Summary The technique proposed by O-Ohata and Ruedenberg (J Math Phys 7:547 (1966)) and by Silver and Ruedenberg (J Chem Phys 49:4306 (1968)) of computing nuclear attraction and electron interaction integrals by solving an inhomogeneous Laplace equation can also be applied ifB functions (Filter E, Steinborn EO (1978) Phys Rev A 18:1) are used as basis functions in atomic and molecular calculations. It is shown that because of the remarkable mathematical properties ofB functions the derivation of compact explicit expressions for the multicenter integrals mentioned above is particularly simple. These results are also of interest in the context of other exponentially decaying functions, since all the other commonly occurring exponentially decaying functions as, for instance, Slater functions or bound state hydrogen eigenfunctions can be expressed as simple linear combinations ofB functions. Consequently, their multicenter integrals can also be expressed in terms of multicenter integrals ofB functions.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

Biological effects of polychromatic light

Predicting the effects of polychromatic light on biological systems is a central goal of environmental photobiology. If the dose-response function for a process is a linear function of the light incident on a system at each wavelength within the spectrum, the effect of a polychromatic spectrum is obtained by integrating the product of the cross section for the reaction at each wavelength and the spectral irradiance at that wavelength over both wavelength and time. This procedure cannot be used, however, if the dose-response functions for an effect are not linear functions of photon dose. Although many photochemical reactions are linear within the biologically relevant range of doses, many biological end points are not. I describe procedures for calculating the effects of polychromatic irradiations on systems that exhibit certain classes of dose-response functions, including power law responses typical of mutation induction and exponential dose-responses typical of cell survival. I also present an approach to predict the effects of polychromatic spectra on systems in which the ultraviolet components form pyrimidine dimers, and the longer-wavelength ultraviolet and visible components remove them by photoreactivation, thus generating complex dose-response functions for these coupled light-driven reactions.