径向Hartree-Fock-Slater方程的新的数值解法

本文提出径向Hartree-Fock-Slater(HFS)方程的一种新的数值解法。使用二阶或四阶有限差分法,把HFS方程离散化,构成一组拟线性代数本征值问题。其系数矩阵与解有关,需用迭代方法求近似解。本工作对数值方法做了改进,使得数值处理比较完整和统一。已编成计算机程序,对Cu⁺和Mn²⁺进行了计算。所得结果与文献[1,2]的结果一致,表明此法的稳定性和精确性良好。还对一系列原子和离子问题进行过计算,证明此法能成功地用于中性原子和正离子的计算。     

Use of molecular symmetry in two-electron integral transformation An MP2 program compatible with HONDO 5

A computer program is described which evaluates the second-order Møller-Plesset energy using the integral list formed by HONDO 5. In this program use may be made of full molecular symmetry for most common point groups, even if they contain two-dimensional representations. The algorithm for the integral transformation may also be applied to other methods beyond Hartree-Fock. Some numerical results and timings are presented.     

New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation

This paper investigates a family of modified Runge-Kutta-Nyström (RKN) methods for the integration of second-order ordinary differential equations with oscillatory solutions. The order conditions for up to order five are presented. Two new optimized explicit four-stage modified RKN methods are derived by nullifying their dispersions and the dissipations in two different ways, respectively. These methods are checked to be of algebraic order five and both are dispersive of order six and dissipative of order five. The stability is examined and the error formulas are analyzed to show that advantages of the new methods compared with some highly efficient integrators from the recent literature. The high accuracy of the second new method is explained by its comparatively small dispersion and dissipation constants. In the integration of the resonance problem and the bound-states problem of the radial Schrödinger equation with the Woods-Saxon potential, the numerical results show the effectiveness and robustness of the new methods.     

High-resolution modeling of isotachophoresis and zone electrophoresis

The space-time conservation element and solution element (CESE) method is applied to simulate the ITP and zone electrophoresis (ZE) separation phenomena. The CESE method expresses the governing equation in the integral form of the conservation law, and has a second-order accuracy in both space and time. The current results show that the CESE solutions for the ITP and ZE phenomena are more accurate than those obtained using conventional numerical schemes, which are characterized by serious numerical diffusion and oscillation. Furthermore, the CESE method suppresses the numerical oscillations or peaks observed in the results obtained using traditional second-order finite difference schemes. Finally, the results reveal that the CESE method accurately models the sharp boundaries between adjacent ITP samples under steady-state conditions. Overall, the results presented in this study demonstrate the numerical accuracy of the CESE method and confirm its applicability to the modeling of a range of electrophoretic phenomena.     

A new efficient technique for solving two-point boundary value problems for integro-differential equations

In this paper, we propose a new efficient method based on a combination of Adomian decomposition method (ADM) and Green’s function for solving second-order boundary value problems (BVPs) for integro-differential equations (IDEs). The proposed method depends on constructing Green’s function before establishing the recursive scheme for the solution components. Unlike the ADM or modified ADM , the proposed method avoids solving a sequence of difficult nonlinear equations (transcendental equations) for the unknown parameters. The proposed method provides a direct recursive scheme for obtaining the series solution with easily calculable components. We also provide a sufficient condition that guarantees a unique solution to the second-order BVPs for IDEs. Convergence and error analysis of the proposed method are also discussed. Convergence analysis is reliable enough to estimate the error bound of the series solution. Some numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed approach. The numerical results reveal that the proposed method is very effective and simple.     

Theoretical studies on magnetic circular dichroism by the finite perturbation method with relativistic corrections

A theoretical method for calculating magnetic circular dichroism (MCD) of molecules is presented. We examined the numerical accuracy and the stability of the finite perturbation (FP) method and the sum-over-state (SOS) perturbation method. The relativistic effects are shown to be important for the MCD spectra of molecules containing heavy elements. Calculations using the FP and the SOS methods were carried out for ethylene, para- and ortho-benzoquinone, showing that the FP method is superior to the SOS method, as expected. The relativistic effect was examined using the second-order Douglas-Kroll Hamiltonians for the halogen molecules F2, Cl2, Br2, and I2. The Faraday terms of I2 and Br2 were strongly affected by the relativistic effects, while the effect was negligible for Cl2 and F2.     

A family of numerical multistep methods with three distinct schemes: explicit advanced step-point (EAS) methods and the EAS1 approach

In this work, for the first time in an article, we present in a comprehensive way the explicit advanced step-point (EAS) methods. The EAS methods is a family of methods designed for the numerical solution of non-stiff and mildly stiff initial value problems (IVPs) and comprises three distinct schemes: EAS1, EAS2 and EAS3. A thorough theoretical analysis of the EAS family of predictor–corrector methods is presented in terms of their accuracy and stability characteristics and requirements, as well as the rationale for creating the three distinct schemes mentioned above. In this paper we also examine in detail one of the three schemes, the EAS1 methods. EAS1 are assessed for the very first time, are meticulously studied and their superior regions of absolute stability are presented. Furthermore the computational efficiency of EAS1 is examined and comparative numerical results are presented with the use of a variable step, variable order EAS1 code. The numerical results provide good evidence that EAS1 could be seen as superior to the well established Adams methods for the numerical solution of mildly stiff initial value problems.     

Gas-phase stability of tetrahedral multiply charged anions: a conceptual and computational DFT study

Multiply charged anions (MCA's) are unstable relative to electron autoejection; however, the repulsive Coulomb barrier (RCB) provides electronic stability. In view of their interest in biological systems, the behavior of isolated AsO(4)(3-), PO(4)(3-), SO(4)(2-), and SeO(4)(2-) in the gas phase and in solution has been studied. To calculate the RCB values, the electrostatic and point charge model-two methods currently used in the literature-are applied, together with a recently introduced Conceptual Density Functional Theory (DFT) based approach. The relative stability of the above-mentioned MCA's is compared. The trends of the RCB are analyzed by including analogous compounds from the second and third row and by passing from dianionic to trianionic systems. Considering the effect of solvent, using the SCI-PCM solvent model, the evolution of the RCB when passing to higher dielectric constants is evaluated. The RCB is related to the properties of the system as polarizability/softness. Both a numerical and a conceptual correlation between the RCB and the global softness is found.     

The maintenance of the second-order advantage: second-order calibration of excitation-emission matrix fluorescence for quantitative analysis of herbicide napropamide in various environmental samples

A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L⁻¹ sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL⁻¹, respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices.     

New two stages high order symmetric six-step method with vanished phase–lag and its first,second and third derivatives for the numerical solution of the Schrödinger equation

In the present paper, we obtain and analyze, for the first time in the literature, a new two-stages high order symmetric six-step method. The specific characteristics of the new proposed method are the highest possible algebraic order, the elimination of the phase–lag and its first, second and third derivatives. Additionally, for the new method we give the analysis of the method (both error and stability and interval of periodicity analysis) and the comparison of the effectiveness of the new developed method with the effectiveness of well known methods and very recently produced methods in the literature. The comparison is based on the numerical solution of the Schrödinger equation. The theoretical achievements and the numerical results show the effectiveness of the new developed method in comparison with other well known or recently developed numerical methods.     

Non-iterative and exact method for constraining particles in a linear geometry

We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations and is limited in accuracy only by the numerical methods for solving small systems of linear equations. As a result of the non-iterative and exact (within numerical accuracy) nature of the procedure, there is no drift in the constrained geometry, and the method is therefore readily applied to molecular dynamics simulations of, for example, rigid linear molecules or materials of non-spherical grains. We illustrate the approach through implementation in the commonly used second-order velocity-explicit Verlet method. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 911-916, 2005     

Elliptic solution to the Young-Laplace differential equation

The Young-Laplace equation differential form can be solved under the elliptic representation for a fluid-fluid interface in the range 0 相似文献   

A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schr?dinger equation

A family of tenth algebraic order eight-step methods is constructed in this paper. For this family of methods, we require the phase-lag and its first, second and third derivatives to be vanished. Three alternative methods are proposed which satisfy the above requirements. An error analysis and a stability analysis is also investigated in this paper and a comparison with other methods is also studied. The new proposed methods are applied for the numerical solution of the one dimensional Schrödinger equation. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.     

Rapid separation and laser-induced fluorescence detection of mutated DNA by capillary electrophoresis in a self-coating, low-viscosity polymer matrix

The detection of point and other simple mutations in DNA is important for cancer research and diagnosis and other biological studies. Capillary electrophoresis has been successfully used for separating DNA fragments. However, a low-viscosity polymer sieving buffer for DNA separation with on-line coating has never been reported. In this paper, a new method using capillary electrophoresis with on-line coating and laser-induced fluorescence detection (CE-LIF) for screening for point or simple DNA mutations has been demonstrated. The method uses an on-line dynamic coating technique that increases capillary lifetime and analysis reproducibility, and employs a low-viscosity polymer solution, which allows the user to rinse the capillary rapidly and refill with polymer solution easily. Experiments proved that the additives in the separation buffer for on-line capillary coating do not affect the separation efficiency of the running buffer, and do not interfere with the formation of hydrogen-bonded network between boric acid, mannitol and hydroxypropylmethylcellulose polymers. The stability of the dynamically coated capillary was quantitatively studied; the capillary lifetime was increased 6- to 7-fold compared with that of permanently coated CE columns. Standard DNA fragments containing mutations, with sizes of 209, 219, and 338 bps, were successfully separated and detected with this system, after the mutated DNA fragments were cleaved by CEL-I endonuclease. The technique is very sensitive for the size-separation of low-range, middle-range, and high-range DNA fragments. Results were compared with the HPLC methods developed by Transgenomic, Inc. and were in good agreement. The method should be applicable to mutation detection for all relevant biological and clinical studies. The factors influencing separations and the stability of dynamic capillary coatings are also discussed in the paper.     

Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods

We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. © 1995 by John Wiley & Sons, Inc.     

Optimization with a direct search for orbital localization

Two direct-search approaches to obtain the SCF solution for a true maximum of the self-repulsion energy with energy-localized orbitals are proposed: an approach based on the level-shifted second-order method and another approach based on scaling of the orbital transformation vector to obtain an approximate solution for a true maximum. The latter is more advantageous to obtain convergence for large systems. Both methods involve calculation of the exact self-repulsion energy hypersurface in the controlling parameter space via a set of unitary transformations and selection of the unitary transformation which increases the self-repulsion energy. These approaches are found to converge efficiently even when started from a point far from convergence.     

几种查耳酮的二阶非线性光学性质解析

合成了一系列的查耳酮衍生物,系统地测量了其ＳＨＧ（二次谐波产生）效率和截止吸以长,并用ＣＮＤＯ／Ｓ－ＣＩ方法计算了它们的二阶非线性光学系数β值。通过对这些化合物性质的分析发现：（１）取代基Ｂｒ不仅能有效地增强微观非线性能能有效地增强材料的宏观非线性效应。（２）取代基Ｂｒ有利于改善材料的透光性能的和热稳定性;（３）分子在晶体中的空间取向是影响材料宏观非线性的另一个重要因素。     

Effect of ion solvation on the diffuse layer structure in mixed electrolytes

A “solvionic” model of a multicomponent electrochemical system (mixed electrolyte) is considered. An ion in the solution is considered as a point charge rigidly fixed inside its solvation shell. The corresponding equations for the diffuse layer on an ideally polarizable electrode are derived, and an effective method of their numerical solution is formulated. The calculations are performed in order to follow the changes in the diffuse layer structure with variations in the electrode charge and electrolyte composition. Far from the zerocharge potential of solution, the dependences of distributions of solution components over the diffuse layer on the electrode charge radically differ from those within the classic Gouy-Chapman theory. Analytical equations (asymptotics at large electrode charges) for concentrations of solvated ions in the plane of their maximum approach and for their “surface excesses” (diffuse adsorption) are determined. Results of numerical calculations for a 0.2 M LiCl + 0.05 M BaCl₂ solution are plotted.     

Practical conversion from torsion space to Cartesian space for in silico protein synthesis

Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but computationally consuming task occurs ubiquitously in modeling proteins, DNA, and other polymers as well as in many other fields such as robotics. To find an optimal method, algorithms can be compared by a number of operations, speed, intrinsic numerical stability, and parallelization. We discuss five established methods for growing a protein backbone by serial chain extension from bond angles and bond lengths. We introduce the Natural Extension Reference Frame (NeRF) method developed for Rosetta's chain extension subroutine, as well as an improved implementation. In comparison to traditional two-step rotations, vector algebra, or Quaternion product algorithms, the NeRF algorithm is superior for this application: it requires 47% fewer floating point operations, demonstrates the best intrinsic numerical stability, and offers prospects for parallel processor acceleration. The NeRF formalism factors the mathematical operations of chain extension into two independent terms with orthogonal subsets of the dependent variables; the apparent irreducibility of these factors hint that the minimal operation set may have been identified. Benchmarks are made on Intel Pentium and Motorola PowerPC CPUs.     

Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation

A tenth algebraic order eight-step method is developed in this paper. For this method  we require the phase-lag and its first and second derivatives to be vanished. A comparative error analysis and a comparative stability analysis are also presented in this paper. The new proposed method is applied for the numerical solution of the one-dimensional Schrödinger equation. The efficiency of the new methodology is proved via the theoretical analysis and the numerical applications. General conclusions about the importance of several properties on the construction of numerical algorithms for the approximate solution of the radial Schrödinger equation are also presented.