Counterpoise-corrected potential energy surfaces of simple H-bonded systems

Geometries and stabilization energies of various simple H-bonded complexes (water dimer, hydrogen fluoride dimer, formamide dimer, formic acid dimer) have been determined by a gradient optimization that eliminates the basis set superposition error (BSSE) by the counterpoise (CP) method in each gradient cycle as well as by the standard gradient optimization. Both optimization methods lead to different potential energy surfaces (PES). The difference depends on the theoretical level used and is larger if correlation energy is considered. Intermolecular distances from the CP-corrected PES are consistently longer, and this difference might be significant (∼0.1 ?); also angular characteristics determined from both surfaces differ significantly. Different geometries were obtained even when passing to larger basis sets (aug-cc-pVDZ). The standard optimization procedure can result in a completely wrong structure. For example, the “quasi-linear” structure of the (HF)₂ (global minimum) does not exist at the standard MP2/ 6-31G** PES (where only cyclic structure was detected) and is found only at the CP-corrected PES. Stabilization energies obtained from the CP-corrected PES are always larger than these from the standard PES where the BSSE is added only a posteriori for the final optimized structure; both energies converge only when passing to a larger basis set (aug-cc-pVDZ). Received: 11 March 1998 / Accepted: 19 June 1998 / Published online: 4 September 1998 RID=" ID=" <E6>Acknowledgements.</E6> The project was supported by the Grant Agency of the Czech Republic (Grant No. 203/98/1166). RID=" ID=" <E5>Correspondence to</E5>: P. Hobza     

基于简化的应变梯度理论下Kirchhoff板模型边值问题的提法及其应用北大核心CSCD

考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据.     

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses北大核心CSCD

研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题.假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化.考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场.对具体梯度变化情况仅需代入相应梯度变化进行求解即可.数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度.其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响.提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

High-performance liquid chromatography with continuous gradient elution in screening for unknown metabolites of butoprozine directly in dog bile

This paper describes the screening for metabolites of butoprozine, a new anti-anginal drug, in dog bile by means of reverse-phase HPLC. Although it does involve a simple clean-up step to remove a substantial amount of endogenous bile compounds, this screening method nevertheless avoids extraction of metabolites and thus allows all metabolites to be introduced into the chromatographic system. A single run of 100 minutes from 100% water to 100% methanol in a linear gradient effects adequate separation of the great majority of metabolites without interference from remaining endogenous compounds. Two methods of differentiating between metabolite peaks and endogenous peaks have been worked out. The first one makes use of ¹⁴C-labeled butoprozine by measuring the amount of radioactivity in the column effluent while simultaneously recording the UV absorbance. The second method compares continuous gradient chromatograms of bile recorded before and after butoprozine administration under very similar conditions. The latter method can be applied to both radioactive and non-radioactive materials.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.     

Optimization of upper semidifferentiable functions

In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in ^m . The method generalizes Wolfe's algorithm for convex functions and Mifflin's algorithm for semismooth functions to a broader class of functions, so-called upper semidifferentiable. With this objective, we define a new enlargement of Clarke's generalized gradient that recovers, in special cases, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.The author would like to thank J. B. Hiriart-Urruty (Toulouse) for having provided him with Definition 2.1 and the referees for their constructive remarks about a first version of the paper.     

A quantitative method for dual‐pass electrostatic force microscopy phase measurements

Electrostatic force microscopy (EFM) has become a powerful tool for investigating charges on surfaces. The use of phase measurement in EFM is a direct and fast way to detect electrostatic force gradients, but only qualitatively. With the dual‐pass scheme, the phase signal at lifted height is often assumed to exclude any influences from the topography, but it does not. We report the collection of both topography and phase data by EFM on charged, micron‐sized metal wires. In order to quantify the electrostatic force, a cone model and finite element analysis are provided to integrate the force gradient from the phase signal. Copyright © 2007 John Wiley & Sons, Ltd.