Auxiliary basis sets for density‐fitting second‐order Møller–Plesset perturbation theory: Weighted core‐valence correlation consistent basis sets for the 4d elements Y–Pd

Auxiliary basis sets (ABS) specifically matched to the cc‐pwCVnZ‐PP and aug‐cc‐pwCVnZ‐PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y‐Pd at the second‐order Møller‐Plesset perturbation theory level. Calculation of the core‐valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution‐of‐the‐identity component of explicitly correlated calculations is also investigated, where it is shown that i‐type functions are important to produce well‐controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double‐ζ calculations produce results close to conventional quadruple‐ζ, and triple‐ζ is within chemical accuracy of the complete basis set limit. © 2013 Wiley Periodicals, Inc.     

A class of explicit forward time-difference square conservative schemes

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications. Partly supported by the State Major Key Project for Basic Researches of China Worked as a post doctor in Computing Center, Chinese Academy of Sciences, when this paper was submitted     

一类四项非常系数齐次差分方程的解公式

对于非常系数的差分方程，由于无法写出其相应的有限次的特征方程，经典方法或算符演算方法都是无能为力的．本文突破上述传统方法，根据代数方程的基本原理，直接将所述差分方程之解表示成其系数与初始值的显函数，从而避免了一般解法中可能出现的困难．     

Parking Cars with Spin but no Length

The car parking problem is a one-dimensional model of random packing. Cars arrive to park on a block of length x, sequentially. Each car has, independently, spin up or spin down, w.p. 0 < p 1, for spin up and q = 1 – p for spin down, respectively. Each car tries to park at a uniformly distributed random point t [0, x]. If t is within distance 1 of the location of a previously parked car of the same spin, or within distance a of the location of a previously parked car of the opposite spin, then the new car leaves without parking and the next car arrives, until saturation. We study the problem analytically as well as numerically. The expected number of up spins c(p, a) per unit length for sufficiently large x is neither monotonic in p for fixed a, nor is it monotone in a for fixed p, in general. An intuitive explanation is given for this nonmonotonicity.     

A Modified Phase-Fitted Runge–Kutta Method for the Numerical Solution of the Schrödinger Equation

A modified phase-fitted Runge–Kutta method (i.e., a method with phase-lag of order infinity) for the numerical solution of periodic initial-value problems is constructed in this paper. This new modified method is based on the Runge–Kutta fifth algebraic order method of Dormand and Prince [33]. The numerical results indicate that this new method is more efficient for the numerical solution of periodic initial-value problems than the well known Runge–Kutta method of Dormand and Prince [33] with algebraic order five.     

Comparison of various implicit solvent models in molecular dynamics simulations of immunoglobulin G light chain dimer

The present study tests performance of different solvation models applied to molecular dynamics simulation of a large, dimeric protein molecule. Analytical Continuum Electrostatics (ACE) with two different parameter sets, older V98 and new V01, and Effective Energy Function (EEF) are employed in molecular dynamics simulation of immunoglobulin G (IgG) light chain dimer and variable domain of IgG light chain. Results are compared with explicit solvent and distance dependent dielectric constant (DDE) calculations. The overall analysis shows that the EEF method yields results comparable to explicit solvent simulations; however, the stability of simulations is lower. On the other hand, the ACE_V98 model does not seem to achieve the accuracy or stability expected in nanosecond timescale MD simulation for the studied systems. The ACE_V01 model greatly improves stability of the calculation; nonetheless, changes in radius of gyration and solvent accessible surface of the studied systems may indicate that the parameter set still needs to be improved if the method is supposed to be used for simulations of large, polymeric proteins. Additionally, electrostatic contribution to the solvation free energy calculated in the ACE model is compared with a numerical treatment of the dielectric continuum model. Wall clock time of all simulations is compared. It shows that EEF calculation is six times faster than corresponding ACE and 50 times faster than explicit solvent simulations.     

Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations

We present an explicit Runge-Kutta scheme devised for the numerical solution ofdelay differential equations (DDEs) where a delayed argument lies in the current Runge-Kutta interval. This can occur when the lag is small relative to the stepsize, and the more obvious extensions of the explicit Runge-Kutta method produce implicit equations. It transpires that the scheme is suitable forparallel implementation for solving both ODEs and more general DDEs. We associate our method with a Runge-Kutta tableau, from which the order of the method can be determined. Stability will affect the usefulness of the scheme and we derive the stability equations of the scheme when applied to the constant-coefficient test DDEu(t)=u(t) +u(t –), where the lag and the Runge-Kutta stepsizeH _n H are both constant. (The case=0 is treated separately.) In the case that 0, we consider the two distinct possibilities: (i) H and (ii)<H.In memory of Professor Leslie Fox, Balliol College, OxfordWork performed in part at The University of Auckland, New Zealand.This paper is presented as an outcome of the LMS Durham Symposium convened by Professor C.T.H. Baker on 4th–14th July 1992 with support from the SERC under Grant reference number GR/H03964.     

Theoretical and Experimental Conformational Studies of Oligoglucosides Structurally Related to Fragments of Fungal Cell Wall β-(1→3)-D-Glucan

The conformational behavior of linear oligo-β-(1→3)-D-glucosides was studied using NMR experiments and molecular modeling. The explicit solvent model in calculations yielded the best coincidence between experimental and theoretical values of NOE and spin-spin coupling constants to evidence the strong influence of solvation upon the conformations of the oligoglucosides. Long-range coupling constants calculated for di- and trimeric clusters of the studied glucosides fit the experimental data much better than the single-molecule approach. It was shown that conformational properties of disaccharide fragments in studied oligoglucosides depended on neither their position in the chain nor the length of the chain.     

On the stability of alternating‐direction explicit methods for advection‐diffusion equations

Alternating‐Direction Explicit (A.D.E.) finite‐difference methods make use of two approximations that are implemented for computations proceeding in alternating directions, e.g., from left to right and from right to left, with each approximation being explicit in its respective direction of computation. Stable A.D.E. schemes for solving the linear parabolic partial differential equations that model heat diffusion are well‐known, as are stable A.D.E. schemes for solving the first‐order equations of fluid advection. Several of these are combined here to derive A.D.E. schemes for solving time‐dependent advection‐diffusion equations, and their stability characteristics are discussed. In each case, it is found that it is the advection term that limits the stability of the scheme. The most stable of the combinations presented comprises an unconditionally stable approximation for computations carried out in the direction of advection of the system, from left to right in this case, and a conditionally stable approximation for computations proceeding in the opposite direction. To illustrate the application of the methods and verify the stability conditions, they are applied to some quasi‐linear one‐dimensional advection‐diffusion problems. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

用explicit Euler 方法研究含时受迫谐振子的演化及对系统循环初态的讨论

利用Ioan Sturzu 提出的explicit Euler方法 (EEM) 计算了含时受迫谐振子的系统初态随时间的演化及概率分布规律，分析了EEM的可行性及适用性，并由相干态讨论了受迫谐振子系统循环初态的存在条件以及非绝热几何相. 关键词： explicit Euler 方法 含时受迫谐振子 循环初态 非绝热几何相