Free energy profile along a discretized reaction path via the hyperplane constraint force and torque

By employing mechanical work analogies, we derive a convenient computational approach for evaluation of the free energy profile (FEP) along some discretized path defined as a sequence of hyperplanes. A hyperplane is fully specified by any of its point and a tangent vector. The FEP is obtained as an integral of two components. The translational component of the free energy is computed by integrating the hyperplane constraint force. The rotational component is evaluated via the hyperplane torque. Both ingredients--the constraint force and the hyperplane torque-are evaluated on each hyperplane independently. The integration procedure utilizes a set of reference points defining a point of rotation on each hyperplane, and these points can be chosen before or after the sampling takes place. A shift in the reference points redistributes the FEP contributions between the translational and rotational components. For systems where the FEP is dominated by the potential energy differences, reference points residing on the minimum energy path present a natural choice. We demonstrate the validity of our approach on two examples, a simple two-dimensional (2D) potential, and a seven-atom Lennard-Jones cluster. In each case, we compare the numerical FEP with the harmonic approximation estimates. Our results for the 2D potential are also verified by the data available in the literature. In both cases, the rotational component of the FEP represents a sizable contribution to the total FEP, so ignoring it would yield clearly incorrect results.     

Electron reorganization in chemical reactions: Pair population analysis along concerted reaction path of allowed and forbidden pericyclic reactions

The recently proposed pair population analysis was applied to the study of electron reorganization in the course of chemical reactions. The studied reactions involved a series of pericyclic reactions, both forbidden and allowed, and attention was devoted mainly to the evaluation of the specific differences between the allowed reactions and the forbidden ones. It was demonstrated that while the mechanism of allowed reactions can be visualized as a simple cyclic shift of the bonds the electron reorganization in forbidden reactions is much more complex and involves the considerable changes in the character of the wave function during the process. © 1997 John Wiley & Sons, Inc.     

On the quadratic reaction path evaluated in a reduced potential energy surface model and the problem to locate transition states*

Knowledge of the location of saddle points is crucial to the study the chemical reactivity. Using a path following method defined in a reduced potential energy surface, and starting at either the reactant or product region, we propose an algorithm that locates the corresponding saddle point. The reduced potential energy surface is defined by the set of molecular geometry parameters, namely bond distances, bond angles, and dihedral angles that undergo the largest change for the reaction under consideration; the rest of the coordinates are forced to have a null gradient. Consequently, the proposed method can be seen as a new formulation of the distinguished coordinate method. The method is based on a quadratic model; consequently, it only requires the calculation of the energy and the gradient. The Hessian matrix is normally updated except in the first step and the steps where the resulting updated Hessian matrix is not adequate. Some examples are presented and analyzed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 387–406, 2001     

The maximum hardness and minimum polarizability principles as the basis for the study of reaction profiles

New and useful aspects of chemical reactivity as described by reactivity indexes and used in connection with the maximum hardness and minimum polarizability principles (MHP and MPP, respectively) are discussed and illustrated for two classical reactions in organic chemistry. They include the Beckmann rearrangement and the condensation reactions of -amino acids. The MPP appears as a more general rule than the MHP. Another relevant result is related to the usefulness of both empirical reactivity rules to predict the most probable reaction mechanism among two different pathways displaying very close values in activation energy (competitive pathways). This is illustrated for the condensation reaction of a series of -amino acids: while the accepted stepwise route follows both the MHP and MPP rules, the alternative concerted channel does not, yet its associated activation energy is slightly lower than that corresponding to the nonconcerted reaction mechanism.From the Proceedings of the 28th Congresco de Quimicos Teóricos de Expresión Latina (QUITEL 2002)     

DFT research on the dehydroxylation reaction of pyrophyllite 2. Characterization of reactants, intermediates, and transition states along the reaction path

We delineate the dehydroxylation reaction of pyrophyllite in detail by localizing the complete reaction path on the free energy surface obtained previously by Car-Parrinello molecular dynamics and the implemented metadynamics algorithm ( Molina-Montes et al. J. Phys. Chem. B 2008, 112, 7051 ). All intermediates were identified, and a transition state search was also undertaken with the PRFO algorithm. The characterization of this reaction and the atomic rearrangement in the intermediates and products at quantum mechanical level were performed for the two reaction paths found previously: (i) direct dehydroxylation through the octahedral hole (cross mechanism) or between contiguous hydroxyl groups (on-site mechanism) and (ii) two-step dehydroxylation assisted by apical oxygens for each of the two steps. New intermediates were found and determined structurally. The structural variations found for all intermediates and transition states are in agreement with experimental results. The formation of these structures indicates that the dehydroxylation process is much more complex than a first-order reaction and can explain the wide range of temperatures for completing the reaction, and these results can be extrapolated to the dehydroxylation of other dioctahedral 2:1 phyllosilicates.     

Structure and stability of XeF6 isomers: density functional theory study and the maximum hardness principle

The geometrical configurations of the four possible isomers with C_3v, O_h, C_s and C_2v symmetry on the potential energy surface of the XeF₆ molecule are optimized by using DFT-LDA/NL. Their relative energies, vibration frequencies, electronic chemical potential and hardness have been calculated. It is found that the C_2v configuration has one imaginary frequency. The relative energies of the four isomers increase in order of C_3v, O_h, C_s and C_2v, and the hardness values in same order. The isomer stability obeys the maximum hardness principle (MHP), while their hardness values are very close to each other. It is quite evident that the very close hardness is the main reason for the structure fluxionality of XeF₆.     

Gas-phase properties and Fukui indices of sulfine (CH2SO). Potential energy surface and maximum hardness principle for its protonation process. A density functional study

Gas-phase thermochemical properties of sulfine (CH₂SO) and the potential energy surface of its protonation process were studied by the density functional method employing different exchange-correlation potentials. All calculations showed that the most stable protonated isomer is planar with the proton bonded to the oxygen atom in a trans arrangement of the skeleton. Three transition states were located that allow interconversion between the different isomers. Hardnesses and Fukui indices were calculated to follow the reactivity trend along the protonation path and to explain the preference for a particular protonation site on neutral sulfine. Proton affinity, gas-phase basicity and heat of formation values, obtained for the first time fully quantum mechanically, agree well with those derived by a recent mass spectrometry experimental study. Good agreement between density functional theory and previous high-level theoretical and experimental data was also found for the heat of formation of sulfine and its most stable protonated form. Received: 12 October 1998 / Accepted: 24 November 1998 / Published online: 16 March 1999     

Computing the chemical reaction path with a ray-based fast marching technique for solving the Hamilton-Jacobi equation in a general coordinate system

This article presents a ray-based fast marching approach for solving the static Hamilton-Jacobi equation. The approach is very general and can be used for both orthogonal and non-orthogonal coordinate system. The method is unconditionally stable, algorithmatically simple and highly accurate. As an application, we use the method to compute different types of reaction path. Specifically, we consider the path for which the change in action or time is less than that of all other conceivable paths connecting two states. Such reaction paths are efficiently evaluated by back-tracing on the least-action or least-time surfaces. The method is illustrated by applying it to the collinear reactions, F + H₂ →HF + H and HF + H→H + FH.     

Stopped-flow electrospray ionization mass spectrometry: a new method for studying chemical reaction kinetics in solution

In this work a new mass spectrometry based method for monitoring the kinetics of chemical reactions in solution is described. A stopped-flow mixing instrument is coupled to an electrospray ionization (ESI) mass spectrometer via a novel type of interface. Chemical reactions are initiated by rapid mixing of two reactant solutions. The mixture is instantaneously transferred to a reaction tube where the kinetics can be monitored in real-time by ESI mass spectrometry. With the current setup, a time window from 2.5 to 36 seconds after mixing of the reactants can be monitored. The experimental setup is used to study the kinetics of acetylcholine hydrolysis under alkaline conditions as a function of pH. The intensities of reactant (acetylcholine) and product (choline) ions are monitored simultaneously as a function of time. The reaction is carried out under pseudo-first-order conditions and the intensity-time curves are well described by single exponentials. The rate constants determined from these fits compare favorably with previous data from the literature.     

Decomposition of dinitrosyl iron complex with thioformaldehyde ligands in water: reaction mechanisms and the role of chemical hardness of ligands

The mechanisms of hydrolysis of a model cationic dinitrosyl iron complex with a prototypic thioformaldehyde ligand have been studied using the density functional theory and polarizable continuum water model. The free-energy calculations have predicted that the associative mechanism of the thioformaldehyde ligand removal has a ～34 kJ mol^-1 lower activation barrier in water than the dissociative mechanism. The additional estimates of chemical hardness have provided useful qualitative characterization of the thio ligands binding.     

Topochemical polymerization of a diarylbutadiyne derivative in the gel and solid states

A diarylbutadiyne derivative was synthesized using a few steps and gelified in aromatic solvents. The gel prepared at low concentration is made of micrometers-long nanofibrils as shown by scanning electron microscopy. XRD of the dried gel shows sharp features, revealing a well-organized material. A topochemical reaction was performed on the dried gel, and a polydiacetylene presenting reversible thermochromism properties was obtained.     

A new approximate method for the stochastic simulation of chemical systems: the representative reaction approach

We have developed two new approximate methods for stochastically simulating chemical systems. The methods are based on the idea of representing all the reactions in the chemical system by a single reaction, i.e., by the “representative reaction approach” (RRA). Discussed in the article are the concepts underlying the new methods along with flowchart with all the steps required for their implementation. It is shown that the two RRA methods {with the reaction as the representative reaction (RR)} perform creditably with regard to accuracy and computational efficiency, in comparison to the exact stochastic simulation algorithm (SSA) developed by Gillespie and are able to successfully reproduce at least the first two moments of the probability distribution of each species in the systems studied. As such, the RRA methods represent a promising new approach for stochastically simulating chemical systems. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2012     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

On the usefulness of generalised quantum chemical valence parameters in monitoring the course of a chemical reaction: A case study of the photochemical decomposition of HNO in excited states

A variant of the orthogonal gradient method of orbital optimization in the INDO-MCSCF framework has been used to study the photochemical decomposition of the HNO molecule into H + NO in the lowest^1.3A″ states. A complete geometry optimization has been carried out at all points of the reaction path which appears to be almost barrierless. The one-electron density matrix extracted from the optimized wavefunction at each point has been used to generate the relevant sets of quantum chemical valence parameters. A sharp transition is noted in the N-H bond order and hydrogen free valence index when plotted as functions of r_NH. This enables us to locate the transition region easily.     

Periodical forcing for the control of chaos in a chemical reaction

Control of the chaotic behavior of a chemical system can be achieved perturbing periodically some control parameters of the system. This procedure based on external forcing, which is based on the phenomenon of resonance, can change a chaotic behavior into a periodical one by means of the application of a sinusoidal perturbation. In this paper, the influence of a periodical modulation added to the parameter controlling the oxygen adsorption rate in a cellular automaton (CA) model studying CO oxidation is analyzed. This CA model considers the oxidation reaction of CO on a catalytic surface, taking into account the catalyst temperature variation in order to analyze the reaction time oscillatory behavior. Simulations of the CA model exhibit chaotic and quasiperiodical behaviors, and it can be shown that the periodical forcing strategy can suppress the chaotic dynamics by means of the stabilization of periodical solutions.     

Development of a new file search system for nuclear magnetic resonance spectra: Production of an Enlarged Data Base and Search Test

A practical search system for proton n.m.r. spectra is reported. The coding rules and search algorithms are described in detail. Data for 8000 spectra have been converted into a computer-readable file from printed charts. Several search tests are used to evaluate the usefulness of the search system, and various effects of experimental conditions such as different instruments, frequencies and solvents on recall efficiency are described. The results presented indicate that the system should be applicable to routine analytical work.