Zhiber-Shabat方程的多辛几何和多辛隐式格式研究

Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

Rate and Product Studies in the Solvolyses of Two Cyclic Phosphorochloridate Esters

Kinetic and product studies of the solvolyses of acyclic phosphorochloridates are extended to two cyclic diesters, 2-chloro-1,3,2-dioxaphospholane-2-oxide (1) and 2-chloro-5,5-dimethyl-1,3,2-dioxaphosphorinane-2-oxide (2). Slightly faster solvolyses are observed for 1 than for the acyclic dimethyl phosphorochloridate (3), and 2 solvolyzes somewhat slower than 3. An extended Grunwald–Winstein equation treatment shows similar sensitivities to changes in solvent nucleophilicity and solvent ionizing power for 1, 2, and 3, and a concerted S_N2 attack is proposed in each case. Product studies for the solvolyses of 2 in aqueous alcohols are presented.

     

Simultaneously Probing Two Ultrafast Condensed‐Phase Molecular Symmetry Breaking Events by Two‐Dimensional Infrared Spectroscopy

In condensed phases, a highly symmetric gas‐phase molecule lowers its symmetry under perturbation of the solvent, which is vital to a variety of structural chemistry related processes. However, the dynamical aspects of solvent‐mediated symmetry‐breaking events remain largely unknown. Herein, direct evidence for two types of solvent‐mediated symmetry‐breaking events that coexist on the picosecond timescale in a highly symmetric anion, namely, hexacyanocobaltate, is presented: 1) an equilibrium symmetry‐breaking event in which a solvent‐bound species having lowered symmetry undergoes a population exchange reaction with the symmetry‐retaining species; 2) a dynamic symmetry‐breaking event that is composed of many dynamic population‐exchange reactions under fluctuating solvent interactions. Ultrafast two‐dimensional infrared spectroscopy is used to simultaneously observe and dynamically characterize these two events. This work opens a new window into molecular symmetry and structural dynamics under equilibrium and non‐equilibrium conditions.     

The temperature-dependent domains, SHG effect and piezoelectric coefficient of TGS

The temperature-dependent,second-order,nonlinear,optical coefficient(x^（2）).piezoelectric coefficient (d₃₃),pyroelectric coefficient（Ps） and domains on triglycine sulfate（TGS） reported herein provide a clue for us to investigate these as a typical second-order phase transition.The symmetry breaking occurrence is definitely confirmed by the temperature-dependent x^（2） in which x^（2） displays a limited value at the ferroelectric phase,indicating the space group（P2₁） chosen is correct,and when x^（2） basically maintains a zero value at the paraelectric phase,indicating the space group should be centric.Interestingly,after normalization of x^（2）,d₃₃ or Ps,the change trend with temperature is basically overlapped,probably abiding by Landau theory.Moreover,temperature-dependent domains directly show the symmetry breaking occurrence.     

Volumetric behaviour of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system and its binary sub-systems within the temperature range (298.15–328.15) K

Densities and speeds of sound of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system as well as all its binary sub-systems were measured at four temperatures, namely 298.15 K, 308.15 K, 318.15 K, and 328.15 K at atmospheric pressure by a vibrating-tube densimeter DSA 5000. The binary (isooctane + toluene) system was studied previously. Excess quantities (molar volume, adiabatic compressibility, and isobaric thermal expansivity) of the mixtures studied were calculated from the experimental densities and speed of sounds. The excess molar volume data were correlated using the Redlich–Kister equation. Both the positive and S-shaped excess molar volume curves were found for the systems studied. The excess molar volumes versus concentration of binary systems differed in the shape and temperature dependence. The experimental binary data were compared with literature data. The experimental excess molar volumes were analyzed by means of the Extended Real Associated Solution (ERAS) model. The experimental data and the ERAS model can help to estimate real behaviour of the systems studied.     

Continuous development of schemes for parallel computing of the electrostatics in biological systems: Implementation in DelPhi

Due to the enormous importance of electrostatics in molecular biology, calculating the electrostatic potential and corresponding energies has become a standard computational approach for the study of biomolecules and nano‐objects immersed in water and salt phase or other media. However, the electrostatics of large macromolecules and macromolecular complexes, including nano‐objects, may not be obtainable via explicit methods and even the standard continuum electrostatics methods may not be applicable due to high computational time and memory requirements. Here, we report further development of the parallelization scheme reported in our previous work (Li, et al., J. Comput. Chem. 2012, 33, 1960) to include parallelization of the molecular surface and energy calculations components of the algorithm. The parallelization scheme utilizes different approaches such as space domain parallelization, algorithmic parallelization, multithreading, and task scheduling, depending on the quantity being calculated. This allows for efficient use of the computing resources of the corresponding computer cluster. The parallelization scheme is implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential, and electric field distributions are calculated for the bovine mitochondrial supercomplex illustrating their complex topology, which cannot be obtained by modeling the supercomplex components alone. © 2013 Wiley Periodicals, Inc.     

FEW: A workflow tool for free energy calculations of ligand binding

In the later stages of drug design projects, accurately predicting relative binding affinities of chemically similar compounds to a biomolecular target is of utmost importance for making decisions based on the ranking of such compounds. So far, the extensive application of binding free energy approaches has been hampered by the complex and time‐consuming setup of such calculations. We introduce the free energy workflow (FEW) tool that facilitates setup and execution of binding free energy calculations with the AMBER suite for multiple ligands. FEW allows performing free energy calculations according to the implicit solvent molecular mechanics (MM‐PB(GB)SA), the linear interaction energy, and the thermodynamic integration approaches. We describe the tool's architecture and functionality and demonstrate in a show case study on Factor Xa inhibitors that the time needed for the preparation and analysis of free energy calculations is considerably reduced with FEW compared to a fully manual procedure. © 2013 Wiley Periodicals, Inc.     

Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson–Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane‐alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM‐based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane‐alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane‐alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug‐binding in computer‐aided drug design. © 2013 Wiley Periodicals, Inc.