A unified approach to kinetic processing of nonisothermal data

Basic problems of kinetic processing of nonisothermal data ascertained from thermal analysis measurements can be solved by isoconversional methods. Analysis of the dependence of the activation energy on conversion often permits the identification of the kinetic scheme for the process. This dependence may also be used to solve applied kinetic problems related to predicting the behavior of a substance outside the range of experimental temperatures. Methods for using this dependence for evaluating both the preexponential factor and the reaction model, as well as for detecting isokinetic relationships, have been discussed. Because all of these operations have a common origin in computing the dependence of the activation energy on conversion, isoconversional methods may be considered as a basis of a unified approach to kinetic processing of nonisothermal data. © 1996 John Wiley & Sons, Inc.     

A stochastic simulation of nonisothermal nucleation

The results of stochastic simulations of growth and evaporation of small clusters in vapor are reported. Energy dependent growth rates are determined from the monomer-cluster collision rate and decay rates are found from a detailed balance, with the equilibrium size and energy distribution of clusters calculated using the capillarity approximation and the equilibrium vapor pressure. These rates are used in simulations of two-dimensional random walks in size and energy space to determine the fraction of clusters in supersaturated vapor of size (i(min)+1) that reach a size i(max). By assuming that clusters of size i(min) are in equilibrium, this fraction can be related to the nonisothermal nucleation rate. The simulated rates show good agreement with the previously published analytical results. In the absence of an inert carrier gas, the nonisothermal nucleation rates are typically between 1% and 5% of the isothermal rates.     

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.     

Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid–gas reactions

Isoconversional methods, those using only one curve α = α(T) (α is the conversion degree and T is the temperature), and invariant kinetic parameter method were applied to estimate the kinetic parameters from the following nonisothermal data: (1) simulated TG curves for a single reaction; (2) TG curves for thermal degradation of PVC; and (3) TG curves for the dehydration of CaC₂O₄·H₂O. The results obtained by applying various methods for the same system are compared and discussed. Finally, a procedure of kinetic analysis is suggested. Its application could lead to kinetic parameter values that can be used to predict either α = α(t) curves for other heating rates or α = α(T) curves for isothermal conditions. © 2001 John Wiley & Sons, Inc. Int J chem Kinet 33: 564–573, 2001     

A new equation for modeling nonisothermal reactions

Based on previously reported approximations of the temperature integral, a new approximation $$\int {\exp ( - E/RT)dT = \frac{{RT^2 }}{E}} \left[ {\frac{{1 - 2(RT/E)}}{{1 - 5(RT/E)^2 }}} \right]\exp ( - E/RT)$$ has been proposed for modeling nonisothermal reactions. It has been found that the equation of Coats and Redfern deviates by less than 1 % from the exact solution forE/RT ratio greater than 23 and by less than 10% forE/RT ratio greater than 6. The exact solution was obtained independently by solving the exponential temperature integral numerically by the Simpson's rule and the Trapezoidal rule. The Gorbachev equation deviates by less than 0.1% forE/RT ratio greater than 41 and by less than 1 % forE/RT ratio greater than 11. The Li equation deviates by less than 0.1 % forE/RT ratio greater than 21 and by less than 1% forE/RT ratio greater than 9. The proposed equation deviates by less than 0.1% forE/RT greater than 7.     

Stress and heat flux for arbitrary multibody potentials: a unified framework

A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multibody potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the nonuniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the nonuniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the nonuniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multibody potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.     

Computer simulation studies of recombination of ions in multi-ion-pair ensembles

The problem of the diffusion-controlled recombination of ions for the case where initially two or more nonseparable pairs of oppositely charged ions are present in the system is treated by means of computer simulation. In the first stage, the calculations for the media with the short mean free paths of the free movement of ions between scattering events were performed (diffusion model). The results were compared with the results of the calculations of the electron-cation recombination in the systems characterized by long mean free path of electron between the scattering events. The scale of the deviations of the kinetics of the recombination process in the multi-pair clusters from the kinetics for the isolated pairs was estimated for both the diffusion case and the long mean free path case. The deviations of the multi-pair kinetics and escape probability from the corresponding single-pair results are significant.     

A new nonisothermal ion-exchange method for enrichment of solutions

A new dual temperature ion-exchange method for concentration and separation of solutes, the “swinging wave” method, was described. The method can be used for the reactant-free enrichment of solutions in microcomponents. The effectiveness of the method applied to the enrichment of bromides in sea water on a highly basic anion-exchange resin was demonstrated, and technological characteristics of this process were studied using computer simulation and experimental studies. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya No. 12, pp. 2166–2172, December, 1997.     

A constant entropy increase model for the selection of parallel tempering ensembles

The present paper explores a simple approach to the question of parallel tempering temperature selection. We argue that to optimize the performance of parallel tempering it is reasonable to require that the increase in entropy between successive temperatures be uniform over the entire ensemble. An estimate of the system's heat capacity, obtained either from experiment, a preliminary simulation, or a suitable physical model, thus provides a means for generating the desired tempering ensemble. Applications to the two-dimensional Ising problem indicate that the resulting method is effective, simple to implement, and robust with respect to its sensitivity to the quality of the underlying heat capacity model.     

A graph representation of molecular ensembles for polymer property prediction

Synthetic polymers are versatile and widely used materials. Similar to small organic molecules, a large chemical space of such materials is hypothetically accessible. Computational property prediction and virtual screening can accelerate polymer design by prioritizing candidates expected to have favorable properties. However, in contrast to organic molecules, polymers are often not well-defined single structures but an ensemble of similar molecules, which poses unique challenges to traditional chemical representations and machine learning approaches. Here, we introduce a graph representation of molecular ensembles and an associated graph neural network architecture that is tailored to polymer property prediction. We demonstrate that this approach captures critical features of polymeric materials, like chain architecture, monomer stoichiometry, and degree of polymerization, and achieves superior accuracy to off-the-shelf cheminformatics methodologies. While doing so, we built a dataset of simulated electron affinity and ionization potential values for >40k polymers with varying monomer composition, stoichiometry, and chain architecture, which may be used in the development of other tailored machine learning approaches. The dataset and machine learning models presented in this work pave the path toward new classes of algorithms for polymer informatics and, more broadly, introduce a framework for the modeling of molecular ensembles.

A graph representation that captures critical features of polymeric materials and an associated graph neural network achieve superior accuracy to off-the-shelf cheminformatics methodologies.     

A multidimensional pseudospectral method for optimal control of quantum ensembles

In our previous work, we have shown that the pseudospectral method is an effective and flexible computation scheme for deriving pulses for optimal control of quantum systems. In practice, however, quantum systems often exhibit variation in the parameters that characterize the system dynamics. This leads us to consider the control of an ensemble (or continuum) of quantum systems indexed by the system parameters that show variation. We cast the design of pulses as an optimal ensemble control problem and demonstrate a multidimensional pseudospectral method with several challenging examples of both closed and open quantum systems from nuclear magnetic resonance spectroscopy in liquid. We give particular attention to the ability to derive experimentally viable pulses of minimum energy or duration.     

Applicability of Kissinger model in nonisothermal crystallization assessed using a computer simulation method

The Kissinger method is one of the most popular approaches for determining kinetic parameters from the nonisothermal processes. The applicability of the Kissinger model in describing the nonisothermal crystallization was verified using the data of the simulated experiments with the given crystallization mechanism. The results show that the data of the Monte Carlo experiments for nonisothermal crystallization can be used to evaluate the nonisothermal crystallization model. The Kissinger model can be used to estimate the parameter of the activation energy of the nonisothermal crystallization from the DSC curves with the different heating rates, but unsuitable to obtain the parameter from the DSC curves with the different cooling rates.     

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net . The software is implemented in C++ and has been tested on Linux and OSX platforms. © 2013 Wiley Periodicals, Inc.     

Development of massive multilevel molecular dynamics simulation program,platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

New approximations of the temperature integral for nonisothermal kinetics

The accuracy and scope of application of previously reported approximations of the temperature integral were evaluated. The exact solution was obtained independently by solving the temperature integral numerically be Simpson's rule, the trapezoidal rule and the Gaussian rule. Two new approximations have been proposed: $$\begin{gathered} P(X) = e^{ - x} (1/X^2 )(1 - 2/X)/(1 - 5.2/X^2 ) \hfill \\ P(X) = e^{ - x} (1/X^2 )(1 - 2/X)/(1 - 4.6/X^2 ) \hfill \\ \end{gathered} $$ whereX=E/RT. The first equation gives higher accuracy, with a deviation of less than 1% and 0.1% from the exact solution forX≥7 andX≥10, respectively. The second equation has a wider scope of application, with a deviation of less than 1% forX≥4 and of less than 0.1% forX≥35.     

Remarks on “A new equation for modelling nonisothermal reactions”

The formula proposed by Agrawal [7] for the approximation of the temperature integral in non-isothermal kinetics is shown to be less accurate than several approximations proposed earlier that are of the same complexity. The domain of applicability of 10 approximate formulae is discussed.     

A novel methodological approach for the analysis of host-ligand interactions.

Traditional analysis of drug-binding data relies upon the Scatchard formalism. These methods rely upon the fitting of a linear equation providing intercept and gradient data that relate to physical properties, such as the binding constant, cooperativity coefficients and number of binding sites. However, the existence of different binding modes with different binding constants makes the implementation of these models difficult. This article describes a novel approach to the binding model of host-ligand interactions by using a derived analytical function describing the observed signal. The benefit of this method is that physically significant parameters, that is, binding constants and number of binding sites, are automatically derived by the use of a minimisation routine. This methodology was utilised to analyse the interactions between a novel antitumour agent and DNA. An optical spectroscopy study confirms that the pentacyclic acridine derivative (DH208) binds to nucleic acids. Two binding modes can be identified: a stronger one that involves intercalation and a weaker one that involves oriented outer-sphere binding. In both cases the plane of the bound acridine ring is parallel to the nucleic acid bases, orthogonal to the phosphate backbone. Ultraviolet (UV) and circular dichroism (CD) data were fitted using the proposed model. The binding constants and the number of binding sites derived from the model remained consistent across the different techniques used. The different wavelengths at which the measurements were made maintained the coherence of the results.     

FEM simulation of nonisothermal crystallization, 1 Crystallinity distribution on 2 D space

This work employs the relaxed Stefan model and Nakamura crystallization kinetics to describe the nonisothermal crystallization process of polymeric materials by finite element discretization method (FEM) simulation, giving the evolution of crystallinity distribution on 2 D space. Numerical results show that the final crystallinity and its distribution are mainly dependent on the cooling rate. Crystallinity decreases with increasing cooling rate, but the influence is negligible as long as the cooling rate is below a critical value (ca. 30°C·min^–1 for poly(ethylene terephthalate) (PET)). If the cooling rate is higher than this critical one, crystallinity drops sharply. It is also concluded that the crystallization behavior of polymeric samples in a mild cooling medium is quite different from that in a strong cooling medium. In the first case (for example, in silicon oil), crystallinity of the article is relatively high and its distribution is fairly uniform. During the initial short period, the crystallinity on the surface is higher than that on the inside. Crystallinity increases slowly with time, and finally, the crystallinity of the internal part exceeds the crystallinity on the surface. In the second case (for instance, in water), crystallinity is relatively low, and there is a serious gradient of crystallinity. The crystallinity on the surface reaches a very low equilibrium value in a short time and changes little afterwards. Although the crystallinity of the inside part can be improved by changing the shape of the polymeric article, the crystallinity on the surface essentially remains constant, which leads to a significant gradient. Geometrical shape and dimension of the article are also important to the crystallinity and its distribution, and the ratio of surface area to volume can be used as a rough index to estimate the shape/dimension influence on crystallinity. Except the coefficient of thermal conductivity, physical parameters of the polymeric material and kinetic parameters of crystallization show only weak effects compared to cooling conditions.