Systematic Study of Selected Diagonalization Methods for Configuration Interaction Matrices

Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two‐vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large‐scale CI matrices by eliminating the need to ever store more than three expansion vectors ( b _i) and associated matrix‐vector products ( σ _i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal‐storage, single‐vector method of Olsen is found to be a reasonable alternative for obtaining energies of well‐behaved systems to within μE_h accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10^?10 E_h) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on‐the‐fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant‐based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574–1589, 2001     

Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation

The solution of the one-dimensional time-independent Schr?dinger equation is considered by exponentially fitted symplectic integrators. The Schr?dinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the doubly anharmonic oscillator.     

Two-dimensional model of intramolecular hydrogen bond

One- and two-dimensional vibrational problems were solved to determine the states of H and D in the intramolecular hydrogen bond of malonic dialdehyde. Within the one-dimensional approach the model potential (barrier height 51 kJ/mol) satisfied with the IR and microwave spectroscopy data. For the two-dimensional problem an approach to evaluation of eigenvalues with high accuracy based on the Ritz method was developed. Within the two-dimensional approximation the barrier height was taken to be 57 kJ/mol. An introduction of the second dimension was found to give rise to the vibrational non-adiabatic effects.     

Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique

Summary A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.Also affiliated with the Department of Chemistry, and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo Campus, University of Waterloo, Waterloo, Ontario, Canada. Killam Research Fellow 1987–89     

Exponentially - Fitted Multiderivative Methods for the Numerical Solution of the Schrödinger Equation

In this paper exponentially fitted multiderivative methods are developed for the numerical solution of the one-dimensional Schrödinger equation. The methods are called multiderivative since uses derivatives of order two and four. An application to the the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient than other similar well known methods of the literature.     

木质素结构及分析方法的研究进展

木质素广泛存在于高等植物中,是仅次于纤维素的地球上第二丰富的生物聚合体,有效地利用自然界中含量丰富的木质素具有重大的意义。然而,由于木质素结构的复杂性,对其具体结构的认识和寻找合适的木质素结构分析方法成为人们长期探索的课题。本文主要阐述了目前对木质素单体的生物合成途径和木质素的化学组成、官能团、单体间的连接方式、木质素模型化合物等木质素结构方面的研究进展,并从降解法和非降解法两个角度介绍了常用的木质素结构分析方法。     

Progress in the analytical research methods of polycyclic aromatic hydrocarbons (PAHs)

Abstract

Polycyclic aromatic hydrocarbons (PAHs) are one species of persistent organic pollutants (POPs) with strong carcinogenicity and teratogenicity. They can be widely found in the environment, which cause great harm to the ecological environment. In addition, they endanger human health by polluting food from the natural environment and food processing. Therefore, it is necessary to accurately detect PAHs in various sample matrices, which requires the accurate, practical and rapid detection methods. This review aims to investigate the progress of research methods for PAHs, including pretreatment methods and detection methods. A summary analysis of different methods is performed by searching the literature on numerous methods for detecting PAHs published in various journals. There are many pretreatment methods for PAHs, such as solid phase extraction (SPE), cloud point extraction (CPE) and so on. The most commonly used methods for detecting PAHs are high-performance liquid chromatography (HPLC) and gas chromatography-mass spectrometry (GC-MS). Spectrophotometry, chromatography and chromatography-mass spectrometry have been used more frequently owing to their accuracy and convenience. At the same time, some immunological methods, such as immunosensormethods, enzyme-linked immunosorbent assays (ELISA), immunofluorescence, etc. are also widely used.     

Avoiding the van der Waals endpoint problem using serial atomic insertion

In the past analyses of the so-called van der Waals end point problem focused on thermodynamic integration. Here we investigate which of the recommendations, such as the need for soft-core potentials, are still valid when Bennett's acceptance ratio method is used. We show that in combination with Bennett's acceptance ratio method intermediate states characterized by the coupling parameter λ can be replaced by intermediate states in which Lennard-Jones interactions are turned on or off on an "atom by atom" basis. By doing so, there is no necessity to use soft-core potentials. In fact, one can compute free energy differences without dedicated code, making it possible to use any molecular dynamics program to compute alchemical free energy differences. Such an approach, which we illustrate by several examples, makes it possible to exploit the tremendous computational power of the graphics processing unit.     

高中学生化学概念掌握和问题表征程度关系的实证研究

本研究结合国内外有关化学概念教学的研究情况,对高中学生化学概念掌握和问题表征程度的关系进行了实证性的探索和研究。设计并在江苏省7所不同类型的学校进行了有关化学概念掌握的研究测试,同时选取优差学生进行有关化学问题的口语报告作业。研究结果表明：学生化学概念理解水平显著地影响着其解题时的表征程度。     

A Family of Trigonometrically-Fitted Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related Problems

In this paper a family of trigonometrically-fitted symmetric ten-step methods for the efficient solution of the Schrödinger equation and related problems is presented. Construction and stability analysis of the new methods is described. Numerical results obtained for the resonance problem of the one-dimensional Schrödinger equation show the efficiency of the new methods when they are compared with known methods in the literature.     

Reducing I/O costs for the eigenvalue procedure in large-scale configuration interaction calculations

Several aspects of the matrix diagonalization method used for CI calculations in the COLUMBUS Program System are discussed, including a linear basis-contraction algorithm and the use of a nonorthogonal expansion basis. Both of these features significantly reduce the I/O requirements during the iterations.     

Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation

Summary The problem of spin-adaptation of the multi-reference (MR) coupled-cluster (CC) formalism, employing Jeziorski-Monkhorst ansatz, is addressed. The diagrammatic technique based on graphical methods of spin algebras is generalized to the MR case, so that both direct and coupling terms can be determined. Usefulness of this fully diagrammatic spin-adaptation approach is illustrated on a derivation of explicit expressions for the linear and bilinear coupling terms that are required in the special two-reference MR-CC theory involving singly and doubly excited states (MR-CCSD formalism). Results obtained with the diagrammatic approach are compared with those derived earlier using the algebraic technique and relative advantages of both procedures are compared.To Prof. Klaus Ruedenberg at the occasion of his 70th anniversary     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. I. Theoretical background

It is demonstrated that, if the activation energy depends on the degree of conversion, its values obtained by isoconversional differential and integral methods are different. This revised version was published online in August 2006 with corrections to the Cover Date.     

氮杂环丙烷衍生物的合成方法研究进展

氮杂环丙烷衍生物是重要的有机中间体,广泛应用于某些药物和具有生物活性化合物的合成,同时它还是许多天然产物的重要构件砌块。长期以来它的合成方法研究一直受到人们的广泛关注,文章对此进行了比较详细的综述。     

Remarks on the updated Hessian matrix methods

Optimizing a function with respect to a set of variables using the quasi‐Newton–Raphson method implies updating the Hessian matrix at each iteration. The Broyden–Fletcher–Goldfarb–Shanno update formula is used for minimization and the Murtagh–Sargent–Powell update formula for optimization of first‐order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first‐order saddle points. The second formula is a modification of the TS–Broyden–Fletcher–Goldfarb–Shanno update and could used for both minimum and first‐order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden–Fletcher–Goldfarb–Shanno and Murtagh–Sargent–Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324–332, 2003     

Computational study of the reaction of the methylsulfonyl radical,CH3S(O)2, with NO2

The mechanism of the reaction between the methylsulfonyl radical, CH₃S(O)₂, and NO₂ is examined using density functional theory and ab initio calculations. Two stable association intermediates, CH₃SNO₂ and CH₃S(O)ONO, may be formed through the attack of the nitrogen or the oxygen atom of NO₂ radical to the S atom. Interisomerization and decomposition of these intermediates are investigated using high level energy methods and specifically, CCSD(T), CBS‐QB3, and G3//B3LYP. The computational investigation indicates that the lowest energy reaction pathway leads to the products CH₃S(O)₃ + NO, through the decomposition of the most stable association adduct CH₃S(O)ONO. This result fully supports the relevant assumption of Ray et al. (Ray et al., J. Phys. Chem. 1996, 100, 8895], on which the experimental evaluation of the rate constant was based, namely that CH₃S(O)₃ + NO are the most probable products of the reaction CH₃S(O)₂ + NO₂. © 2014 Wiley Periodicals, Inc.     

Family of Twelve Steps Exponential Fitting Symmetric Multistep Methods for the Numerical Solution of the Schrödinger Equation

In the present paper we present a family of twelve steps symmetric multistep methods. The explicit part of new family of methods is applied to the scattering problems of the radial Schrödinger equation. This application shows the efficiency of the new family of methods.     

Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding

The Shift‐and‐invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density‐functional based tight‐binding (DFTB) Hamiltonian and overlap matrices for single‐wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ～330,000 (～5600) eigenvalues and eigenfunctions are obtained in ～190 (～5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time‐to‐solution at the strong scaling limit. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated. © 2015 Wiley Periodicals, Inc.     

X-Ray Crystallography: The Past and Present of the Phase Problem

The story of the progress thus far made on the phase problem of X-ray crystallography is briefly reviewed.