Steepest descent reaction path integration using a first-order predictor-corrector method

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor-corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.     

A combined explicit-implicit method for high accuracy reaction path integration

We present the use of an optimal combined explicit-implicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method, an explicit stabilized third order algorithm implemented in the code DUMKA3 and the traditional explicit fourth order Runge-Kutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.     

Automatic integration of the reaction path using diagonally implicit Runge-Kutta methods

The diagonally implicit Runge-Kutta framework is shown to be a general form for constructing stable, efficient steepest descent reaction path integrators, of any order. With this framework tolerance driven, adaptive step-size methods can be constructed by embedding methods to obtain error estimates of each step without additional computational cost. There are many embedded and nonembedded, diagonally implicit Runge-Kutta methods available from the numerical analysis literature and these are reviewed for orders two, three, and four. New embedded methods are also developed which are tailored to the application of reaction path following. All integrators are summarized and compared for three systems: the Muller-Brown [Theor. Chem. Acta 53, 75 (1979)] potential and two gas phase chemical reactions. The results show that many of the methods are capable of integrating efficiently while reliably keeping the error bound within the desired tolerance. This allows the reaction path to be determined through automatic integration by only specifying the desired accuracy and transition state.     

Theoretical study of dynamical properties on reaction path in molecular internal coordinates

The dynamical properties on reaction path (IRC) in internal coordinates have been obtained, which in. clude ω_K (frequencies orthogonal to IRC), L_K (vibrational modes), B_(KF) (coupling constants between the IRC and vibra tions orthogonal to it), B_(KL) (coupling constants between every two vibrations orthogonal to IRC). A set of theory of teac. tion path in molecular internal coordinates has been also constructed. The dynamical properties, including ω_K, B_(KF) B_(KL) of the reaction H~1O~2H~3 H~4→H~1O~2 H~3H~4 have been calculated, which explicitly explain the interaction, chang ing trend and contribution of each chemical bond (including bond angle) in the reaction.     

The reaction path intrinsic reaction coordinate method and the Hamilton-Jacobi theory

The definition and location of an intrinsic reaction coordinate path is of crucial importance in many areas of theoretical chemistry. Differential equations used to define the path hitherto are complemented in this study with a variational principle of Fermat type, as Fukui [Int. J. Quantum Chem., Quantum Chem. Symp. 15, 633 (1981)] reported in a more general form some time ago. This definition is more suitable for problems where initial and final points are given. The variational definition can naturally be recast into a Hamilton-Jacobi equation. The character of the variational solution is studied via the Weierstrass necessary and sufficient conditions. The characterization of the local minima character of the intrinsic reaction coordinate is proved. Such result leads to a numerical algorithm to find intrinsic reaction coordinate paths based on the successive minimizations of the Weierstrass E-function evaluated on a guess curve connecting the initial and final points of the desired path.     

Variational calculations of vibrational and vibration-rotational properties of ozone

Vibrational and vibration-rotational energy levels of ozone and its isotopic substitutes have been calculated variationally by the ladder operator method. Thirty vibrational band origins and rotational energies of vibrational ground states for these molecules have been given. The good agreement between the calculated results and the observed values shows that the calculation method is a promising one for variational studies of vibrational and vibration-rotational properties of nonlinear polyatomic molecules.     

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational M?ller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.     

The nature and properties of giant-orbital polymers

In the course of studying the properties of highly conjugated polymers, we found that long-range orbital delocalization conferred unexpected properties. The giant electronic orbitals made these materials electroactive yet very stable. A new mode of electronic polarizability, a giant nomadic polarization, resulted, making these organic polymers among the most polarizable materials ever observed. In addition, remanent magnetization, high conductivity, and unusual pressure sensitivity could be achieved. The giant-orbital concept opens new vistas of materials properties.     

Unravelling the reaction path of rhodium-MonoPhos-catalysed olefin hydrogenation

The mechanism of the asymmetric hydrogenation of methyl (Z)-2-acetamidocinnamate (mac) catalysed by [Rh(MonoPhos)(2)(nbd)]SbF(6) (MonoPhos: 3,5-dioxa-4-phosphacyclohepta[2,1-a:3,4-a']dinaphthalen-4-yl)dimethylamine) was elucidated by using (1)H, (31)P and (103)Rh NMR spectroscopy and ESI-MS. The use of nbd allows one to obtain in pure form the rhodium complex that contains two units of the ligand. In contrast to the analogous complexes that contain cis,cis-1,5-cyclooctadiene (cod), this complex shows well-resolved NMR spectroscopic signals. Hydrogenation of these catalyst precursors at 1 bar total pressure gave rise to the formation of a bimetallic complex of general formula [Rh(MonoPhos)(2)](2)(SbF(6))(2); no solvate complexes were detected. In the dimeric complex both rhodium atoms are ligated to two MonoPhos ligands but, in addition, each rhodium atom also binds to one of the binaphthyl rings of a ligand that is bound to the other rhodium metal. Upon addition of mac, a mixture of diastereomeric complexes [Rh(MonoPhos)(2)(mac)]SbF(6) is formed in which the substrate is bound in a chelate fashion to the metal. Upon hydrogenation, these adducts are converted into a new complex [Rh(MonoPhos)(2){mac(H)(2)}]SbF(6) in which the methyl phenylalaninate mac(H)(2) is bound through its aromatic ring to rhodium. Addition of mac to this complex leads to displacement of the product by the substrate. No hydride intermediates could be detected and no evidence was found for the involvement at any stage of the process of complexes with only one coordinated MonoPhos. The collected data suggest that the asymmetric hydrogenation follows a Halpern-like mechanism in which the less abundant substrate-catalyst adduct is preferentially hydrogenated to phenylalanine methyl ester.     

An analytic hindered rotor model for calculating microcanonical variational unimolecular rate constants from reaction path properties

A model is proposed for performing microcanonical variational transition state theory calculations which incorporates ideas from vibrator and flexible variational transition state models. Vibrational frequencies, moments of inertia, and potential energy for the variational transition state are found by reaction path following as for the vibrator model. However, the transitional modes are treated as hindered rotors using an analytic potential and an analytic density of states, which are fit to barriers for hindered rotation determined from reaction path following. The model proposed here differs from the flexible transition state model in that the density of states for the transitional modes is analytic and transitional modes and external rotational angular momenta are uncoupled. For the H + CH₃ ? CH₄ system, rate constants calculated with this new model are only 6–23% smaller on average from those of the flexible transition state model for values of total angular momentum which correspond to average rotational temperatures of 0–2000 K. Harmonic frequencies calculated for the transitional modes from the hindered rotor Hamiltonian are in good agreement with the exact values found by a reaction path analysis. © 1994 John Wiley & Sons, Inc.     

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H(2)O and NH(3). The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined.     

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.     

Ab initio study of the reaction path of the reaction HNCO+CN

HNCO is a convenient photolytic source of NCO and NH radicals for laboratory kinetics studies of elementary reaction[1] and plays an important role in the combustion and atmosphere chemistry. It can re- move deleterious compounds rapidly from exhausted ga…     

The Pictet-Spengler reaction in nature and in organic chemistry

Alkaloids are an important class of natural products that are widely distributed in nature and produced by a large variety of organisms. They have a wide spectrum of biological activity and for many years were used in folk medicine. These days, alkaloids also have numerous applications in medicine as therapeutic agents. The importance of these natural products in inspiring drug discovery programs is proven and, therefore, their continued synthesis is of significant interest. The condensation discovered by Pictet and Spengler is the most important method for the synthesis of alkaloid scaffolds. The power of this synthesis method has been convincingly proven in the construction of stereochemicaly and structurally complex alkaloids.     

A hybrid potential reaction path and free energy study of the chorismate mutase reaction.

We present a combination of two techniques--QM/MM statistical simulation methods and QM/MM internal energy minimizations--to get a deeper insight into the reaction catalyzed by the enzyme chorismate mutase. Structures, internal energies and free energies, taken from the paths of the reaction in solution and in the enzyme have been analyzed in order to estimate the relative importance of the reorganization and preorganization effects. The results we obtain for this reaction are in good agreement with experiment and show that chorismate mutase achieves its catalytic efficiency in two ways; first, it preferentially binds the active conformer of the substrate and, second, it reduces the free energy of activation for the reaction relative to that in solution by providing an environment which stabilizes the transition state.