Full rate constant matrix contraction method for obtaining branching ratio of unimolecular decomposition

The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations. Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations. However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps. This problem is especially serious when elementary steps that occur in highly different timescales coexist. In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations. It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐RCMC (f‐RCMC). The f‐RCMC gives the branching ratio without solving the rate equations. Its performance was tested numerically for unimolecular decomposition of C₃H₅ and C₄H₅. Branching ratios obtained by the f‐RCMC precisely reproduced the values obtained by numerically solving the rate equations. It took about 95 h to solve the rate equations of C₄H₅ consisting of 234 elementary steps. In contrast, the f‐RCMC gave the branching ratio in less than 1 s. The f‐RCMC would thus be an efficient alternative of the conventional kinetic simulation approach. © 2016 Wiley Periodicals, Inc.     

Synthesis of new 3,3′‐(1,4‐phenylene)bis(1,5‐diones) derivatives

Several 3,3′‐(1,4‐phenylene)bis(1,5‐diones) and their chalcone precursors have been prepared in good to excellent yield via aldol addition and Michael addition starting from 3‐acetyl‐2,5‐dimethylfuran or 3‐acetyl‐2,5‐dimethyl‐thiophene with terephthalaldehyde in the presence of appropriate base NaOH or lithium diisopropylamide. The kind and amount of alkali played a critical role in improving the reaction rates and yields of the products. J. Heterocyclic Chem., (2011).     

1‐Phenyl‐1,2‐cyclohexadiene: Astoundingly High Enantioselectivities on Generation in a Doering–Moore–Skattebøl Reaction and Interception by Activated Olefins

The resolution of (1α,5α,6α)‐6‐bromo‐6‐fluoro‐1‐phenylbicyclo[3.1.0]hexane (rac‐ 5) provided the enantiomerically pure precursors (?)‐ 5 and (+)‐ 5 of 1‐phenyl‐1,2‐cyclohexadiene. On treatment of (?)‐ 5 with methyllithium in the presence of 2,5‐dimethylfuran, the pure (?)‐enantiomer of the [4+2] cycloadduct of 2,5‐dimethylfuran onto 1‐phenyl‐1,2‐cyclohexadiene was obtained exclusively. From this result, it is concluded that pure (M)‐1‐phenyl‐1,2‐cyclohexadiene ((M)‐ 7 ) emerged from (?)‐ 5 and was enantiospecifically intercepted to give the product. In the case of indene as trap for (M)‐ 7 , the (?)‐ and the (+)‐enantiomer of the [2+2] cycloadduct were formed in the ratio of 95:5. Highly surprising, remarkable enantioselectivities were also observed, when (M)‐ 7 was trapped with styrene to furnish two diastereomeric [2+2] cycloadducts. Hence, the achiral conformation of the diradical conceivable as intermediate cannot play a decisive part. The enantioselective generation of (M)‐ and (P)‐ 7 by the β‐elimination route was tested as well. Accordingly, 1‐bromo‐2‐phenylcyclohexene was exposed to the potassium salt of (?)‐menthol in the presence of 2,5‐dimethylfuran, and the enantiomeric [4+2] cycloadducts of the latter onto (M)‐ and (P)‐ 7 were produced in the ratio of 55:45.     

Energy transfer in master equation simulations: A new approach

Collisional energy transfer plays a key role in recombination, unimolecular, and chemical activation reactions. For master equation simulations of such reaction systems, it is conventionally assumed that the rate constant for inelastic energy transfer collisions is independent of the excitation energy. However, numerical instabilities and nonphysical results are encountered when normalizing the collision step‐size distribution in the sparse density of states regime at low energies. It is argued here that the conventional assumption is not correct, and it is shown that the numerical problems and nonphysical results are eliminated by making a plausible assumption about the energy dependence of the rate coefficient for inelastic collisions. The new assumption produces a model that is more physically realistic for any reasonable choice of collision step‐size distribution, but more work remains to be done. The resulting numerical algorithm is stable and noniterative. Testing shows that overall accuracy in master equation simulations is better with this new approach than with the conventional one. This new approach is appropriate for all energy‐grained master equation formulations. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 748–763, 2009     

Microwave‐Assisted Synthesis and Spectral Characterization of Biological Activity Heterocyclic Thiosemicarbazone and Its Organometallic Derivatives

The thiosemicarbazone coordinates to metal through the thionic sulfur and the azomethine nitrogen. The thiosemicarbazone was obtained by the thiosemicarbazide with 3‐acetyl‐2,5‐dimethylfuran by microwave irradiation. Metal complexes were prepared by the reaction of thiosemicarbazone with metal salts. IR, ¹H, ¹³C NMR, FAB‐mass spectroscopic methods, and elemental analysis elucidated the structure of these compounds. The antibacterial activity of these compounds were first tested in vitro by the disk diffusion assay against two Gram‐positive and two Gram‐negative bacteria, and then minimum inhibitory concentration was determined, chloramphenicol as reference drug. The results showed that copper ( II ) metal complex of the thiosemicarbazone ( 1.1 ) is a better inhibitor as compared with chloramphenicol.     

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     

Linear scaling local correlation approach for solving the coupled cluster equations of large systems

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.     

Analysis of exhaled breath from smokers,passive smokers and non‐smokers by solid‐phase microextraction gas chromatography/mass spectrometry

In this study, 38 samples of expired air were collected and analyzed from 20 non‐smoking volunteers, four passive smokers and 14 smokers (21 women and 17 men). Measurements were carried out using solid‐phase microextraction (SPME) as an isolation and preconcentration technique. The determination and identification were accomplished by gas chromatography coupled with mass spectrometry (GC/MS). Our data showed that ca 32% of all identified compounds in the breath of healthy non‐smokers were saturated hydrocarbons. In the breath of smoking and passive smoking volunteers hydrocarbons were predominant, but also present were more exogenous analytes such as furan, acetonitrile and benzene than in the breath of non‐smokers. Acetonitrile, furan, 3‐methylfuran, 2,5‐dimethylfuran, 2‐butanone, octane and decane were identified in breath of smoking and passive smoking persons. Copyright © 2008 John Wiley & Sons, Ltd.     

Kinetics of elimination reactions of 1,2‐diphenyl ethyl substrates in acetonitrile: A mechanistic change in the presence of a strong base

Kinetics of elimination of methanesulfonic acid from 1,2‐diphenylethylmethane sulfonate and its 1‐p‐methylphenyl‐ and 1‐p‐chlorophenyl‐substituted derivatives is studied. The results show that the elimination reaction is unimolecular (E1) as reported in the case of 1‐chloro‐1‐(4‐methoxyphenyl)‐2‐phenylethane. The rate of the elimination reaction in the presence of added weak base pyridine is independent of the concentration of the base, but in the presence of a strong base piperidine the rate shows a linear upward drift and this is due to the appearance of a bimolecular component along with the unimolecular pathway. The shift from the unimolecular to bimolecular process takes place independently of the nature of the leaving group and the parasubstituent in the 1,2‐diphenylethyl substrate. © 2008 Wiley Periodicals, Inc. 40: 481–487, 2008     

A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation

The Poisson‐Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson‐Boltzmann equation. We expose the flux directly through a first‐order system form of the equation. Using this formulation, we propose a system that yields a tractable least‐squares finite element formulation and establish theory to support this approach. The least‐squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Approximate Analytical Expressions for the Steady‐State Concentration of Substrate and Cosubstrate over Amperometric Biosensors for Different Enzyme Kinetics

Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first‐order and nonlinear term related to the Michaelis–Menten and ping–pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed‐form analytical solutions for the nonlinear equations under steady‐state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.     

An efficient approach for self-consistent-field energy and energy second derivatives in the atomic-orbital basis

Based on self-consistent-field (SCF) perturbation theory, we recast the SCF and the coupled-perturbed SCF (CPSCF) equations for time-independent molecular properties into the atomic-orbital basis. The density matrix and the perturbed density matrix are obtained iteratively by solving linear equations. Only matrix multiplications and additions are required, and this approach can exploit sparse matrix multiplications and thereby offer the possibility of evaluating second-order properties in computational effort that scales linearly with system size. Convergence properties are similar to conventional molecular-orbital-based CPSCF procedures, in terms of the number of derivative Fock matrices that must be constructed. We also carefully address the issue of the numerical accuracy of the calculated second derivatives of the energy, in order to specify the minimum precision necessary in the CPSCF procedure. It is found that much looser tolerances for the perturbed density matrices are adequate when using an expression for the second derivatives that is correct through second order in the CPSCF error.     

Comparison of Hyperbranched and Linear Polyglycidol Unimolecular Reverse Micelles as Nanoreactors and Nanocapsules

Summary: Amphiphilic‐hyperbranched polyglycidols and a linear analogue were tested for their ability to act as nanoreactors for the unimolecular elimination (E1) reactions of tert‐alkyl iodides. Their encapsulation properties were also compared. The linear polymer was found to have very good “unimolecular reverse micellar” characteristics as well, even though the results showed the advantages of a hyperbranched nature over a linear one. Our results stress the need for a direct comparison of branched and linear polymers for any application.

Amphiphilic polyglycidol unimolecular reverse micelles.     

A scheme of numerical solution for three‐dimensional isoelectronic series of hydrogen atom using one‐dimensional basis functions

The solution of three‐dimensional Schrödinger wave equations of the hydrogen atoms and their isoelectronic ions (Z = 1 − 4) are obtained from the linear combination of one‐dimensional hydrogen wave functions. The use of one‐dimensional basis functions facilitates easy numerical integrations. An iteration technique is used to obtain accurate wave functions and energy levels. The obtained ground state energy level for the hydrogen atom converges stably to −0.498 a.u. The result shows that the novel approach is efficient for the three‐dimensional solution of the wave equation, extendable to the numerical solution of general many‐body problems, as has been demonstrated in this work with hydrogen anion.     

A high dimensional model representation based numerical method for solving ordinary differential equations

A new numerical method for solving ordinary differential equations by using High Dimensional Model Representation (HDMR) has been developed in this work. Higher order ordinary differential equations can be reduced to a set of first order ODEs. Although HDMR is generally used for multivariate functions, univariate functions are taken into account throughout the work because of the ODEs’ natures. Not the numerical solution but its image under an appropriately chosen linear ordinary differential operator is expressed as a linear combination of the positive deviation powers of independent variable from its initial value. The linear combination of these image functions are expected to form a basis set under consideration. The unknown constants in the linear combination are found by maximizing the constancy measurer formed in terms of the HDMR components after they are evaluated. Results are compared with well-known step size based numerical methods. A semi qualitative error analysis of the proposed method is also established.     

A Novel Algorithm for the Numerical Integration of Systems of Ordinary Differential Equations Arising in Chemical Problems

Simulation of large networks of chemical reactions via the numerical integration of large systems of ordinary differential equations is of growing importance in real-world problems. We propose an attractive novel numerical integration method, that is largely independent from ill-conditioning and is suitable for any nonlinear problem; moreover, the method, being exact for linear problems, is especially precise for quasi-linear problems, the most frequent kind in the real world. The method is based on a new approach to the computation of a matrix exponential, includes an automatic correction of rounding errors, is not too expensive computationally, and lends itself to a short and robust software implementation that can be easily inserted in large simulation packages. A preliminary numerical verification has been performed, with encouraging results, on two sample problems. The full source listing (in standard C language) of an academic version of the algorithm is freely available on request (e-mail address: Valerio.Parisi@roma2.infn.it), together with a very simple but very stiff chemical problem.     

Co‐evolution of non‐linear PLS model components

The issue of outer model weight updating is important in extending partial least squares (PLS) regression to modelling data that shows significant non‐linearity. This paper presents a novel co‐evolutionary component approach to the weight updating problem. Specification of the non‐linear PLS model is achieved using an evolutionary computational (EC) method that can co‐evolve all non‐linear inner models and all input projection weights simultaneously. In this method, modular symbolic non‐linear equations are used to represent the inner models and binary sequences are used to represent the projection weights. The approach is flexible, and other representations could be employed within the same co‐evolutionary framework. The potential of these methods is illustrated using a simulated pH neutralisation process data set exhibiting significant non‐linearity. It is demonstrated that the co‐evolutionary component architecture can produce results which are competitive with non‐linear neural network‐based PLS algorithms that use iterative projection weight updating. In addition, a data sampling method for mitigating overfitting to the training data is described. Copyright © 2007 John Wiley & Sons, Ltd.     

On the classical simulation of unimolecular reaction processes

The numerical simulation of the internal motions of a molecule undergoing a unimolecular reaction on an assumed potential energy surface requires the step-by-step solution of a set of simultaneous differential equations. After several thousand time steps, due to differences in the handling of rounding errors in different computing systems, the situation often arises that no two computing machines will give the same result for a given trajectory, even when running the identical algorithm.     

Range of Validity of a Simplified Model for Diffuse Charge Dynamics

The modelling of electrochemical processes often requires the solution of the Poisson‐Nernst‐Planck (PNP) equations. In complex geometries, such as porous electrodes, that is challenging due to the presence of disparate length scales, ranging from the Debye screening length (～nm) to the device length scale (～cm). To overcome this difficulty, one often assumes that the electric double layer (EDL) is at quasi‐equilibrium to construct a simplified model that accounts for ion diffusion in the electro‐neutral bulk of the electrolyte while replacing the EDLs with appropriate boundary conditions. Various researchers have demonstrated that such an approach is valid in the asymptotic limit of a thin EDL and moderate electrode potentials. In this note, we explore the range of validity of this approximation by considering a one‐dimensional electrolytic cell with blocking electrodes subjected to a step change and time‐periodic alternations in the electrodes’ potentials by calculating the errors associated with the approximate approach as functions of the EDL thickness and electric field frequency and intensity. Additionally, we delineate numerical instabilities associated with the numerical solutions of the bulk equations with the nonlinear boundary condition peculiar to this problem.