Geometric description of chemical reactions

We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a 2-dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this in the particular cases of a reaction with only two species corresponding to either two ideal gases or two van der Waals gases. We then consider the case of a reaction with an arbitrary number of species. The initial equilibrium state of the geodesic is determined by the initial conditions of the reaction. The final equilibrium state, which follows from a thermodynamic analysis of the reaction, is shown to correspond to a coordinate singularity of the thermodynamic metric which describes the equilibrium manifold.     

Overreact,an in silico lab: Automative quantum chemical microkinetic simulations for complex chemical reactions

Today's demand for precisely predicting chemical reactions from first principles requires research to go beyond Gibbs' free energy diagrams and consider other effects such as concentrations and quantum tunneling. The present work introduces overreact, a novel Python package for propagating chemical reactions over time using data from computational chemistry only. The overreact code infers all differential equations and parameters from a simple input that consists of a set of chemical equations and quantum chemistry package outputs for each chemical species. We evaluate some applications from the literature: gas-phase eclipsed-staggered isomerization of ethane, gas-phase umbrella inversion of ammonia, gas-phase degradation of methane by chlorine radical, and three solvation-phase reactions. Furthermore, we comment on a simple solvation-phase acid–base equilibrium. We show how it is possible to achieve reaction profiles and information matching experiments.     

A new extension of the polarizable continuum model: Toward a quantum chemical description of chemical reactions at extreme high pressure

A quantum chemical method for studying potential energy surfaces of reactive molecular systems at extreme high pressures is presented. The method is an extension of the standard Polarizable Continuum Model that is usually used for Quantum Chemical study of chemical reactions at a standard condition of pressure. The physical basis of the method and the corresponding computational protocol are described in necessary detail, and an application of the method to the dimerization of cyclopentadiene (up to 20 GPa) is reported. © 2015 Wiley Periodicals, Inc.     

Redox reactions: inconsistencies in their description

The paper is aimed at defining reduction, oxidation, and redox reactions based both on the oxidation number and charge changes in reacting species. It is rationalized that the processes of oxidation and reduction, usually occurring simultaneously, can occur also as independent processes. It is explained that in balancing chemical equations of redox reactions the “gain” or “loss” of electrons should be understood as changes in oxidation number. A formal expressions “+n e^?” and “?n e^?” represent in reality a decrease and increase in oxidation number by n units, respectively.     

The characteristic polynomial of a chemical graph

We list uses of, and the computational methods for the characteristic polynomial of a (chemical) graph. Pour computational methods are singled out for more detailed presentation. These are the graphical methods of Sachs, the recurrence formulae for several classes of simple graphs, the method based on Ulam subgraphs, and the Le Verrier — Faddeev — Franic recursive method. The latter method appears, at present, to be the most efficient procedure for the computation of the characteristic polynomials of graphs of sizes with up to even a few hundred sites.Dedicated to Dennis H. Rouvray, the friend and one of the foremost popularizers of chemical graph theory in our time.Research supported by the Robert A. Welch Foundation of Houston, Texas, USA.     

A graph theory method for determining the basis of homodesmic reactions for acyclic chemical compounds

One of the techniques for theoretically determining enthalpies of formation of organic compounds is the method of homodesmic reactions. In this work, a graph theory interpretation of acyclic chemical compounds was presented, and an algorithm for constructing a basis of homodesmic reactions was developed, which makes it possible to use a homodesmic approach to calculating the enthalpy of formation. Using the developed algorithm was exemplified by building the basis of homodesmic reactions for the butyramide molecule.     

Mechanism-based chemical understanding of chiral symmetry breaking in the Soai reaction. A combined probabilistic and deterministic description of chemical reactions

The experimentally observed distribution of enantiomers in the Soai reaction is interpreted in this Article on the basis of a chemical mechanism using a newly developed stochastic kinetic method, accelerated Monte Carlo simulation combined with deterministic continuation and symmetrization. The method is in principle suitable for handling large mechanisms with realistic particle numbers and could be useful for any case where the kinetics of a process shows inherent random fluctuations. The mechanism shows how a slow initial reaction combined with efficient and highly enantioselective autocatalysis can give rise to chiral symmetry breaking under completely nonchiral external conditions.     

On the description of reactions in solution

A formulation for diffusion-influenced reactions in solution is given in which reactive and translational contributions are separated, steady state rate-limiting step formulations are generalized to the dynamical case and the influence of different experimental initial conditions is isolated.     

Consistency of a set of chemical reactions

It is a useful feature of many general chemical kinetics programs that the user's reaction scheme is tested as far as possible before a calculation is started. Attempts are made to answer the question: How far can a reaction scheme be tested for consistency, with respect to mass conservation, without knowing the molecular weights of the species involved? It is found that this problem can be transformed so that it is solvable by the standard methods used in linear programming.     

分子体系的高压化学反应

在高压(一万到百万大气压)下物质的组成、结构、化学反应都可以发生前所未知的巨大变化。运用高压合成目标产物,表征高压下的物质结构与反应过程是高压化学研究的主要问题。一般而言,高压下不饱和化合物倾向于聚合形成高密度饱和共价键体系;反应中分子与原子扩散严重受限,常形成亚稳态化合物;反应物的空间晶体结构、官能团性质、反应体系的温度、静水压效果都对反应有显著影响。对高压下分子化学反应的研究需要综合运用晶体学、谱学、化学等实验手段和热力学、动力学等方面的理论计算相互验证,进而建立理论,深入极端条件化学的星辰大海。     

Deviation from a maxwellian distribution in chemical reactions

It is shown that Enskog and Chapman's method of solving the gaskinetic equation is not applicable to perturbations in the Maxwellian distribution due to chemical reaction. The method is extended to finite perturbations of the equilibrium distribution function in the high-energy region. Detailed calculations for given reaction crosssections show that the distribution function and the reaction rate may differ substantially from the equilibrium ones.     

On the accuracy of a localised description of chemical bonding

The applicability and accuracy of a localised picture of chemical bonding is examined on the basis of the projection approach to orbital localisation. The condition for maximal localisation is chosen to minimize the fluctuation in a number of electrons per bond. In this respect this treatment resembles the loge theory but differs from it in that it works with individual localised chemical bonds instead of loges.     

On the evaluation of the characteristic polynomial of a chemical graph

The evaluation of the characteristic polynomial of a chemical graph is considered. It is shown that the operation count of the Le Verrier–Faddeev–Frame method, which is presently considered to be the most efficient method for the calculation of the characteristic polynomial, is of the order n⁴. Here n is the order of the adjacency matrix A or equivalently, the number of vertices in the graph G. Two new algorithms are described which both have the operation count of the order n³. These algorithms are stable, fast, and efficient. A related problem of finding a characteristic polynomial from the known eigenvalues λ_i of the adjacency matrix is also considered. An algorithm is described which requires only n(n ? 1)/2 operations for the solution of this problem.     

Machine learning for in silico virtual screening and chemical genomics: new strategies

Support vector machines and kernel methods belong to the same class of machine learning algorithms that has recently become prominent in both computational biology and chemistry, although both fields have largely ignored each other. These methods are based on a sound mathematical and computationally efficient framework that implicitly embeds the data of interest, respectively proteins and small molecules, in high-dimensional feature spaces where various classification or regression tasks can be performed with linear algorithms. In this review, we present the main ideas underlying these approaches, survey how both the "biological" and the "chemical" spaces have been separately constructed using the same mathematical framework and tricks, and suggest different avenues to unify both spaces for the purpose of in silico chemogenomics.     

Rectifying a misbelief: Frank Harary's role in the discovery of the coefficient-theorem in chemical graph theory

It is shown that the formula relating the coefficients of the characteristic polynomial of a graphG to certain structural features ofG (which in mathematical chemistry is traditionally referred to as the Sachs theorem) is a straightforward and relatively easily inferable corollary of an earlier result by Frank Harary.     

An investigation of the quantum chemical description of the ethylenic double bond in reactions: II. Insertion of ethylene into a titanium–carbon bond

Insertion of ethylene into the Ti–methyl bond in TiH₂CH⁺₃ is chosen as a model reaction for investigating the performance of a range of contemporary quantum chemical models in polymerization studies. Basis set effects are investigated at the self-consistent-field level, covering Hartree–Fock, pure DFT, and hybrid DFT. In agreement with findings in part I of this study, the basis set sensitivity of ethylene is shown to introduce a bias in computed energetics, amounting to 2–3 kcal/mol when DZP bases are used to compute the overall heat of monomer insertion. The geometry of stationary points relevant to the insertion reaction is determined using hybrid density functional theory. Based on these structures, the energy profile of the insertion reaction is computed using a range of popular quantum chemical approximations. The methods include Hartree–Fock and Møller–Plesset (MP) perturbation theory up through the fourth order in spin-restricted, spin-unrestricted, and spin-projected formalisms. Furthermore, configuration-interaction-based methods are included, of which the top level method is singly and doubly excited coupled clusters with a perturbative estimate of the contribution from triply excited configurations added [CCSD(T)]. The performance of the methods just mentioned, as well as three pure density functional and three hybrid density functional methods, are compared with respect to “best” relative energies, defined through extrapolation of CCSD(T) correlation energies according to the PCI scheme of Siegbahn and coworkers. Even though the MP series show poor convergence, spin-projected MP2, as well as two pure DFT methods (BPW91, BP86) and PCI-78 based on the MCPF method, show similar and very good agreement with best relative energies for the insertion reaction. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 947–960, 1998     

Independence of chemical reactions

Up to this time the existence of physically true dependences between elementary reactions has been a returning question. The goal of this paper is to show that the real elementary reactions of a mechanism are practically independent. Introducing the concept of the space-time volume of a reaction (the reciprocal of the reaction rate) it is shown that, except for extremely fast processes (explosions), the reactions form very dilute systems. This systems must be ideal in the sense that interactions between elementary processes are very rare. The system exhibits some analogies with a dilute gas or solution. The extents of interactions can be calculated and the limits of independence estimated in this way.

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