A master equation model for bimolecular reaction via multi-well isomerization intermediates

A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Activated escape from polarization pulling in fibre Raman amplifiers

Fluctuation-induced escape (FIE) from a metastable state with probability controlled by external force is a process inherent in many physical phenomena such as diffusion in crystals, protein folding, activated chemical reactions etc. [1-3]. In this work we present a novel example of FIE problem, considering a very practical nonlinear system recently emerged in the area of fibre telecommunications. Unlike the standard FIE problems where noise is time-dependent, in fibre Raman amplifier (FRA) the role of noise is played by frozen fluctuations of parameters (random birefringence) along the fibre span which result from the breaking of cylindrical symmetry during the fibre drawing [4-6]. The role of periodic forcing in this problem is played by the periodic fibre spinning, leading to key model that is formally similar to the time-domain equations for periodically forced escape [1-3]. © 2011 IEEE.

Prediction of absolute rate coefficients and product branching ratios for the C(P-3) plus allene reaction system

Complex chemical reactions in the gas phase can be decomposed into a network of elementary (e.g., unimolecular and bimolecular) steps which may involve multiple reactant channels, multiple intermediates, and multiple products. The modeling of such reactions involves describing the molecular species and their transformation by reaction at a detailed level. Here we focus on a detailed modeling of the C(P-3)+allene (C3H4) reaction, for which molecular beam experiments and theoretical calculations have previously been performed. In our previous calculations, product branching ratios for a nonrotating isomerizing unimolecular system were predicted. We extend the previous calculations to predict absolute unimolecular rate coefficients and branching ratios using microcanonical variational transition state theory (mu-VTST) with full energy and angular momentum resolution. Our calculation of the initial capture rate is facilitated by systematic ab initio potential energy surface calculations that describe the interaction potential between carbon and allene as a function of the angle of attack. Furthermore, the chemical kinetic scheme is enhanced to explicitly treat the entrance channels in terms of a predicted overall input flux and also to allow for the possibility of redissociation via the entrance channels. Thus, the computation of total bimolecular reaction rates and partial capture rates is now possible. (C) 2002 American Institute of Physics.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

Generation of nitrogen functionalities on activated carbons by amidation reactions and Hofmann rearrangement: Chemical and electrochemical characterization

Nitrogen functionalization of a highly microporous activated carbon (BET surface area higher than 3000 m2/g) has been achieved using the following sequence of treatments: (i) chemical oxidation using concentrated nitric acid, (ii) amidation by acyl chloride substitution with NH4NO3 and (iii) amination by Hoffman rearrangement. This reaction pathway yielded amide and amine functional groups, and a total nitrogen content higher than 3 at.%. It is achieved producing only a small decrease (20%) of the starting microporosity, being most of it related to the initial wet oxidation of the activated carbon. Remarkably, nitrogen aromatic rings were also formed as a consequence of secondary cyclation reactions. The controlled step-by-step modification of the surface chemistry allowed to assess the influence of individual nitrogen surface groups in the electrochemical performance in 1 M H2SO4 of the carbon materials. The largest gravimetric capacitance was registered for the pristine activated carbon due to its largest apparent surface area. The nitrogen-containing activated carbons showed the highest surface capacitances. Interestingly, the amidated activated carbon showed the superior capacitance retention due to the presence of functional groups (such as lactams, imides and pyrroles) that enhance electrical conductivity through their electron-donating properties, showing a capacitance of 83 F/g at 50 A/g.

Chemical reactions of double bonds in activated carbon:microwave and bromination methods

The reaction of localised C=C bonds on the surface of activated carbons has been shown to be an effective method of chemical modification especially using microwave-assisted reactions.

Regeneration of Activated Carbon by (Photo)-Fenton Oxidation

This work aims to study the adsorption of phenol on activated carbons (ACs) and the consecutive in situ regeneration of carbon by Fenton oxidation. Two different operations have been carried Out: (1) a batch procedure in order to investigate the influence of Fe(2+) and H(2)O(2) concentrations; (2) continuous fixed bed adsorption, followed by a batch circulation of the Fenton`s reagent through the saturated AC bed. to examine the efficiency of the real process. Two different activated carbons have been also studied: a both micro- and mesoporous AC (L27) and an only microporous One (S23). In the batch reactor the best conditions found for pollutant mineralization in the homogeneous Fenton system are not the best For AC regeneration: a continuous reduction of adsorption capacity of L27 is observed after 3 oxidations, due to the decrease of both AC weight and surface area. Higher concentration of Fe(2+) and lower concentration of H(2)O(2) (2 times the stoichiometry) lead to a 50% recovery of the initial adsorption capacity during at least four consecutive cycles for L27, while about 20% or less for S23. In the consecutive continuous adsorption/batch Fenton oxidation process, the regeneration efficiency reaches 30-40% for L27 after two cycles whatever the feed concentration and less than 10% for S23. A photo-Fenton test performed on L27 shows almost complete mineralization (contrary to ""dark"" Fenton) and further improves recovery of AC adsorption capacity although not complete (56% after two cycles).

The role of carbon surface chemistry in N2O conversion to N2 over Ni catalyst supported on activated carbon

The effect of acidic treatments on N2O reduction over Ni catalysts supported on activated carbon was systematically studied. The catalysts were characterized by N-2 adsorption, mass titration, temperature-programmed desorption (TPD), and X-ray photoelectron spectrometry (XPS). It is found that surface chemistry plays an important role in N2O-carbon reaction catalyzed by Ni catalyst. HNO3 treatment produces more active acidic surface groups such as carboxyl and lactone, resulting in a more uniform catalyst dispersion and higher catalytic activity. However, HCl treatment decreases active acidic groups and increases the inactive groups, playing an opposite role in the catalyst dispersion and catalytic activity. A thorough discussion of the mechanism of the N2O catalytic reduction is made based upon results from isothermal reactions, temperature-programmed reactions (TPR) and characterization of catalysts. The effect of acidic treatment on pore structure is also discussed. (C) 1999 Elsevier Science B.V. All rights reserved.

Opposite roles of O-2 in NO- and N2O-carbon reactions: An ab initio study

Previous experimental studies showed that the presence of O-2 greatly enhances NO-carbon reaction while it depresses N2O-carbon reaction on carbon surfaces. A popular explanation for the rate increase is that the addition of O-2 results in a large number of reactive carbon-oxygen complexes, and decomposition of these complexes produces many more active sites. The explanation for the latter is that excess O-2 simply blocks the active sites, thus reducing the rate of N2O-carbon reaction. The contradiction is that O-2 can also occupy active sites in NO-carbon reaction and produce active sites in N2O-carbon reduction. By using ab initio calculation, we find that the opposite roles of O-2 are caused by the different manners of N2O and NO adsorption on the carbon surface. In the presence of excess O-2, most Of the active sites are occupied by oxygen groups. In the competition for the remaining active sites, NO is more likely to chemisorb in the form of NO2 and NO chemisorption is mon thermodynamically favorable than O-2 chemisorption. By contrast, the presence of excess O-2 makes N2O chemisorption much less thermally stable either on the consecutive edge sites or edge sites isolated by semiquinone oxygen. A detailed analysis and discussion of the reaction mechanism of N-2 formation from NO- and N2O-carbon reaction in the presence of O-2 is presented in this paper.

Automatic learning for the classification of chemical reactions and in statistical thermodynamics

This Thesis describes the application of automatic learning methods for a) the classification of organic and metabolic reactions, and b) the mapping of Potential Energy Surfaces(PES). The classification of reactions was approached with two distinct methodologies: a representation of chemical reactions based on NMR data, and a representation of chemical reactions from the reaction equation based on the physico-chemical and topological features of chemical bonds. NMR-based classification of photochemical and enzymatic reactions. Photochemical and metabolic reactions were classified by Kohonen Self-Organizing Maps (Kohonen SOMs) and Random Forests (RFs) taking as input the difference between the 1H NMR spectra of the products and the reactants. The development of such a representation can be applied in automatic analysis of changes in the 1H NMR spectrum of a mixture and their interpretation in terms of the chemical reactions taking place. Examples of possible applications are the monitoring of reaction processes, evaluation of the stability of chemicals, or even the interpretation of metabonomic data. A Kohonen SOM trained with a data set of metabolic reactions catalysed by transferases was able to correctly classify 75% of an independent test set in terms of the EC number subclass. Random Forests improved the correct predictions to 79%. With photochemical reactions classified into 7 groups, an independent test set was classified with 86-93% accuracy. The data set of photochemical reactions was also used to simulate mixtures with two reactions occurring simultaneously. Kohonen SOMs and Feed-Forward Neural Networks (FFNNs) were trained to classify the reactions occurring in a mixture based on the 1H NMR spectra of the products and reactants. Kohonen SOMs allowed the correct assignment of 53-63% of the mixtures (in a test set). Counter-Propagation Neural Networks (CPNNs) gave origin to similar results. The use of supervised learning techniques allowed an improvement in the results. They were improved to 77% of correct assignments when an ensemble of ten FFNNs were used and to 80% when Random Forests were used. This study was performed with NMR data simulated from the molecular structure by the SPINUS program. In the design of one test set, simulated data was combined with experimental data. The results support the proposal of linking databases of chemical reactions to experimental or simulated NMR data for automatic classification of reactions and mixtures of reactions. Genome-scale classification of enzymatic reactions from their reaction equation. The MOLMAP descriptor relies on a Kohonen SOM that defines types of bonds on the basis of their physico-chemical and topological properties. The MOLMAP descriptor of a molecule represents the types of bonds available in that molecule. The MOLMAP descriptor of a reaction is defined as the difference between the MOLMAPs of the products and the reactants, and numerically encodes the pattern of bonds that are broken, changed, and made during a chemical reaction. The automatic perception of chemical similarities between metabolic reactions is required for a variety of applications ranging from the computer validation of classification systems, genome-scale reconstruction (or comparison) of metabolic pathways, to the classification of enzymatic mechanisms. Catalytic functions of proteins are generally described by the EC numbers that are simultaneously employed as identifiers of reactions, enzymes, and enzyme genes, thus linking metabolic and genomic information. Different methods should be available to automatically compare metabolic reactions and for the automatic assignment of EC numbers to reactions still not officially classified. In this study, the genome-scale data set of enzymatic reactions available in the KEGG database was encoded by the MOLMAP descriptors, and was submitted to Kohonen SOMs to compare the resulting map with the official EC number classification, to explore the possibility of predicting EC numbers from the reaction equation, and to assess the internal consistency of the EC classification at the class level. A general agreement with the EC classification was observed, i.e. a relationship between the similarity of MOLMAPs and the similarity of EC numbers. At the same time, MOLMAPs were able to discriminate between EC sub-subclasses. EC numbers could be assigned at the class, subclass, and sub-subclass levels with accuracies up to 92%, 80%, and 70% for independent test sets. The correspondence between chemical similarity of metabolic reactions and their MOLMAP descriptors was applied to the identification of a number of reactions mapped into the same neuron but belonging to different EC classes, which demonstrated the ability of the MOLMAP/SOM approach to verify the internal consistency of classifications in databases of metabolic reactions. RFs were also used to assign the four levels of the EC hierarchy from the reaction equation. EC numbers were correctly assigned in 95%, 90%, 85% and 86% of the cases (for independent test sets) at the class, subclass, sub-subclass and full EC number level,respectively. Experiments for the classification of reactions from the main reactants and products were performed with RFs - EC numbers were assigned at the class, subclass and sub-subclass level with accuracies of 78%, 74% and 63%, respectively. In the course of the experiments with metabolic reactions we suggested that the MOLMAP / SOM concept could be extended to the representation of other levels of metabolic information such as metabolic pathways. Following the MOLMAP idea, the pattern of neurons activated by the reactions of a metabolic pathway is a representation of the reactions involved in that pathway - a descriptor of the metabolic pathway. This reasoning enabled the comparison of different pathways, the automatic classification of pathways, and a classification of organisms based on their biochemical machinery. The three levels of classification (from bonds to metabolic pathways) allowed to map and perceive chemical similarities between metabolic pathways even for pathways of different types of metabolism and pathways that do not share similarities in terms of EC numbers. Mapping of PES by neural networks (NNs). In a first series of experiments, ensembles of Feed-Forward NNs (EnsFFNNs) and Associative Neural Networks (ASNNs) were trained to reproduce PES represented by the Lennard-Jones (LJ) analytical potential function. The accuracy of the method was assessed by comparing the results of molecular dynamics simulations (thermal, structural, and dynamic properties) obtained from the NNs-PES and from the LJ function. The results indicated that for LJ-type potentials, NNs can be trained to generate accurate PES to be used in molecular simulations. EnsFFNNs and ASNNs gave better results than single FFNNs. A remarkable ability of the NNs models to interpolate between distant curves and accurately reproduce potentials to be used in molecular simulations is shown. The purpose of the first study was to systematically analyse the accuracy of different NNs. Our main motivation, however, is reflected in the next study: the mapping of multidimensional PES by NNs to simulate, by Molecular Dynamics or Monte Carlo, the adsorption and self-assembly of solvated organic molecules on noble-metal electrodes. Indeed, for such complex and heterogeneous systems the development of suitable analytical functions that fit quantum mechanical interaction energies is a non-trivial or even impossible task. The data consisted of energy values, from Density Functional Theory (DFT) calculations, at different distances, for several molecular orientations and three electrode adsorption sites. The results indicate that NNs require a data set large enough to cover well the diversity of possible interaction sites, distances, and orientations. NNs trained with such data sets can perform equally well or even better than analytical functions. Therefore, they can be used in molecular simulations, particularly for the ethanol/Au (111) interface which is the case studied in the present Thesis. Once properly trained, the networks are able to produce, as output, any required number of energy points for accurate interpolations.

Waste recovery into activated carbon for water purification from heavy metals

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Química Pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecn