Superlinearly converging dimer method for transition state search

Algorithmic improvements of the dimer method [G. Henkelman and H. Jonsson, J. Chem. Phys. 111, 7010 (1999)] are described in this paper. Using the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer for the dimer translation greatly improves the convergence compared to the previously used conjugate gradient algorithm. It also saves one energy and gradient calculation per dimer iteration. Extrapolation of the gradient during repeated dimer rotations reduces the computational cost to one gradient calculation per dimer rotation. The L-BFGS algorithm also improves convergence of the rotation. Thus, three to four energy and gradient evaluations are needed per iteration at the beginning of a transition state search, while only two are required close to convergence. Moreover, we apply the dimer method in internal coordinates to reduce coupling between the degrees of freedom. Weighting the coordinates can be used to apply chemical knowledge about the system and restrict the transition state search to only part of the system while minimizing the remainder. These improvements led to an efficient method for the location of transition states without the need to calculate the Hessian. Thus, it is especially useful in large systems with expensive gradient evaluations.     

The subspace iteration method in protein normal mode analysis

Normal mode analysis plays an important role in relating the conformational dynamics of proteins to their biological function. The subspace iteration method is a numerical procedure for normal mode analysis that has enjoyed widespread success in the structural mechanics community due to its numerical stability and computational efficiency in calculating the lowest normal modes of large systems. Here, we apply the subspace iteration method to proteins to demonstrate its advantageous properties in this area of computational protein science. An effective algorithm for choosing the number of iteration vectors in the method is established, offering a considerable improvement over the original implementation. In the present application, computational time scales linearly with the number of normal modes computed. Additionally, the method lends itself naturally to normal mode analyses of multiple neighboring macromolecular conformations, as demonstrated in a conformational change pathway analysis of adenylate kinase. These properties, together with its computational robustness and intrinsic scalability to multiple processors, render the subspace iteration method an effective and reliable computational approach to protein normal mode analysis. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Calculating particle pair potentials from fluid‐state pair correlations: Iterative ornstein–zernike inversion

An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this article. The new method, which is best referred to as Iterative Ornstein–Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique (Reith, Pütz and Müller‐Plathe, J. Comput. Chem. 2003, 24, 1624). Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant that is based on a trial bridge function in the Ornstein–Zernike integral equation formalism. As an input, the new method requires the particle pair correlations both in real space and in the Fourier conjugate wavenumber space. An accelerated iteration method is included in the discussion, by which the required number of iterations can be greatly reduced below that of the simple Picard iteration that underlies most common implementations of Iterative Boltzmann Inversion. Comprehensive tests with various pair potentials show that the new method generally surpasses the Iterative Boltzmann Inversion method in terms of reliability of the numerical solution for the particle pair potential. © 2018 Wiley Periodicals, Inc.     

Bayesian Error Propagation for a Kinetic Model of n‐Propylbenzene Oxidation in a Shock Tube

We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism for n‐propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi‐random global search using a Sobol low‐discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient‐descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second‐order response surfaces and assuming normal distributions for propagated errors is largely adequate, but not always.     

On the electronic structure and conduction properties of aperiodic DNA and proteins. I. Strategy and methods of investigations

The possibilites for applying the ab initio matrix block negative factor counting technique (NFC) for non-periodic nucleotide base stacks and for 4- and 5-component aperiodic model proteins are described. It is outlined how also correlation effects could be taken into account in an approximate way. After a brief summary of the basic equations of the NFC method the inverse iteration technique to study the Anderson localization of the wavefunctions belonging to the different energy levels is shortly reviewed. Also the calculation of hopping probabilities between different localization sites is sketched. Finally, the possibilites are outlined for the experiment verification of hopping conduction in proteins and (in a minor extent) in DNA, assuming the generation of free charge carriers in them through charge transfer.     

Linear combination of Lanczos vectors: A storage-efficient algorithm for sparse matrix eigenvector computations

We present a storage-efficient and robust algorithm for the computation of eigenvectors of large sparse symmetrical matrices using a Lanczos scheme. The algorithm is based upon a linear combination of Lanczos vectors (LCLV) with a variable iteration depth. A simple method is given to determine the iteration depth before the eigenvector computation is performed. Test calculations are reported for tight-binding models of ordered and disordered 2-D systems. The algorithm turns out to be reliable if an eigenvector residual less than 10^?4 is required. We report benchmarks for various computers. Possible fields of application are discussed. © 1993 John Wiley & Sons, Inc.     

A variational approach for a class of nonlocal elliptic boundary value problems

The aim of this paper is to apply the variational iteration method to a class of nonlinear, nonlocal, elliptic boundary value problems. The uniform convergence of the scheme is presented and the work is illustrated by considering a number of test examples that confirm the accuracy and efficacy of the iterative process. The computational results show that the scheme is reliable, converges fast and compares very well with the existing analytic solutions.     

Multigrid solver for the reference interaction site model of molecular liquids theory

In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid-based method with the one-grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one-grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method.     

Second-order post-Hartree-Fock perturbation theory for the electron current

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties.     

A minimal multiconfigurational technique

A direct minimization method previously presented by the authors is applied here to biconfigurational wave functions. A very moderate increasing in the time by iteration with respect to the one-determinant calculation and good convergence properties have been found. So qualitatively correct studies on singlet systems with strong biradical character can be performed with a cost similar to that required by Hartree-Fock calculations.     

Calculation of localized molecular orbitals

Two techniques are presented for reducing the effort required to determine localized orbitals based on the energy or density criteria. The first, population weighted editing of the electronic repulsion integrals, reduces the effort required for each iteration of the localization procedure. The second, damping/extrapolation of the transformation matrix, reduces the number of iterations required to reach convergence. Numerical results are provided for methane and formaldehyde (for the editing method) and for carbon monoxide and boron fluoride (for the damping/extrapolation technique).     

Mathematical optimization in the determination of the dissociation constants of a tribasic organic acid by 13C NMR spectroscopy

The calculation of dissociation constants from the chemical shifts of (13)C NMR spectra leads to a complicated non-linear equation. Two different mathematical methods for solution of this equation have been chosen--an iterative step method and a matrix pseudo-inversion method. When the iteration method is used the initial guesses for the parameters, the initial value of the step size and the escalation of the iteration must be optimized. For comparison the matrix pseudo-inversion method was used because it gives a unique result. With the optimized step method the results were as accurate or even better than those obtained with the matrix method. Although it takes time to optimize the system, the step method is the more suitable method of solving the problem. The matrix inversion can be done only with a computer with 13 significant digits and exponent capacity larger than +/- 38.     

Analytic perturbation theory and localization phenomena

This paper attempts to apply the results of analytic perturbation theory to systems exhibiting some degree of randomness in their state variables. In particular, we focus on the localization problem in the Anderson model. It is shown that this approach proves the existence of bound states as a result of the statistical treatment of the Weinberg–van Winter–Hunziker irreducible N-particle kernel. The analysis is extended beyond the one-particle cluster approach and the occurrence of higher-order clusters is discussed in relation to the diluteness criterion and the conditions set on the interaction potential V.     

Water sorption and permeation in chitosan films: Relation between gas permeability and relative humidity

The water sorption of chitosan has been studied at 20 °C. Water transport is governed by a Fickian process for relative humidities lower than 0.4, and in that range of partial pressures, the diffusion coefficient is concentration‐dependent. At a higher activity, anomalous diffusion is observed. The sorption isotherm is well described by the Guggenheim‐Anderson‐de Boer (GAB) model, and the clustering phenomenon observed at high relative pressures can be studied with the parameters of this model. The water permeability coefficient greatly increases with the relative pressure, and the water plasticization effect leads to a loss of the gas barrier properties under wet conditions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3114–3127, 2001     

An approach to reduce the computational effort in accurate DFT calculations

An approach is proposed to reduce the computational effort required for solving Kohn–Sham equation through rejecting some unoccupied orbitals with negligible influence on the total energy in the process of iteration. A formula has been derived to estimate the error of the total energy resulted from rejecting some unoccupied orbitals and it is used to set up the threshold for rejection of orbitals. The method has been tested with several representative molecules as samples and the obtained result is satisfactory.     

Voltammetry using a dental amalgam electrode for heavy metal monitoring of wines and spirits

We have introduced a non-toxic electrode material similar to dental amalgam for use in voltammetry. Its electrochemical properties are like a silver electrode. However, it possesses a higher overvoltage towards hydrogen than silver, and therefore enables detection of metals like zinc, nickel and cobalt. As such solid electrodes are found to give stable results over several weeks, without any maintenance, and because this method greatly facilitates monitoring of heavy metals, attempts to apply such methods to various samples have been are carried out. The present paper deals with the determination of zinc and lead at nanogram per milliliter levels in wines and spirits with only minor treatment of the samples. The procedure may easily be adapted to continuous monitoring.We have previously found that audible sound may greatly increase the voltammetric signal using liquid mercury as well as silver as electrode material. This is also applied to the actual systems.Finally, model determinations of thallium in brandy with the dental amalgam electrode are compared with atomic absorption spectrometric (AAS) measurements. It was found that the electrode could be used repeatedly, without fouling, and with results close to those found by the AAS method.     

Direct determination of pair natural orbitals

A method is proposed to solve the two-electron Schrödinger equation by a rapidly converging iterative procedure. The wavefunction is obtained in terms of its NO's. The special features of the present method are:

1. Each iteration requires only the computational equivalent of a conventional Hartree-Fock iteration.
2. Within each iteration we improve simultaneously the NO's, the CI expansion coefficients and the total energy.
3. The construction of a CI matrix is never required.

We further propose simplified NO-equations the solution of which requires a small fraction of computertime only. As examples of the efficiency of these methods we report applications to the 1¹ Sstate of He, the 1¹∑ _g ⁺ , 1³∑ _u ⁺ states of H₂, and IEPA,PNO-CI, and CEPA type computations on CH₄.     

Designed Assembly of Heterometallic Cluster Organic Frameworks Based on Anderson‐Type Polyoxometalate Clusters

A new approach to prepare heterometallic cluster organic frameworks has been developed. The method was employed to link Anderson‐type polyoxometalate (POM) clusters and transition‐metal clusters by using a designed rigid tris(alkoxo) ligand containing a pyridyl group to form a three‐fold interpenetrated anionic diamondoid structure and a 2D anionic layer, respectively. This technique facilitates the integration of the unique inherent properties of Anderson‐type POM clusters and cuprous iodide clusters into one cluster organic framework.     

Direct correlation analysis improves fold recognition

The extraction of correlated mutations through the method of direct information (DI) provides predicted contact residue pairs that can be used to constrain the three dimensional structures of proteins. We apply this method to a large set of decoy protein folds consisting of many thousand well-constructed models, only tens of which have the correct fold. We find that DI is able to greatly improve the ranking of the true (native) fold but others still remain high scoring that would be difficult to discard due to small shifts in the core beta sheets.     

Numerical solution of eigenvalue problems by means of a wavelet‐based Lanczos decomposition

The simple Lanczos process is very efficient for finding a few extreme eigenvalues of a large symmetric matrix. The main task in each iteration step consists in evaluating a matrix‐vector product. It is shown how to apply a fast wavelet‐based product in order to speed up computations. Some numerical results are given for three different monodimensional cases: the harmonic oscillator case, the hydrogenlike atoms, and a problem with a pseudo‐double‐well potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 552–562, 2000