Phase-space reaction network on a multisaddle energy landscape: HCN isomerization

By using the HCN/CNH isomerization reaction as an illustrative vehicle of chemical reactions on multisaddle energy landscapes, we give explicit visualizations of molecular motions associated with a straight-through reaction tube in the phase space inside which all reactive trajectories pass from one basin to another, with eliminating recrossing trajectories in the configuration space. This visualization provides us with a chemical intuition of how chemical species "walk along" the reaction-rate slope in the multidimensional phase space compared with the intrinsic reaction path in the configuration space. The distinct nonergodic features in the two different HCN and CNH wells can be easily demonstrated by a section of Poincare surface of section in those potential minima, which predicts in a priori the pattern of trajectories residing in the potential well. We elucidate the global phase-space structure which gives rise to the non-Markovian dynamics or the dynamical correlation of sequential multisaddle chemical reactions. The phase-space structure relevant to the controllability of the product state in chemical reactions is also discussed.     

A new way of probing reaction networks: analyzing multidimensional parameter space

Technically relevant partial oxidation reactions represent complex reaction networks. Establishing a kinetic model for a system of multiple consecutive and parallel reaction steps is a challenging goal. The synthesis of acrylic acid by oxidation of propane using MoVTeNb mixed oxide as catalyst is such a reaction network. In an on-going study, a 10- fold parallel reactor set-up is used to vary systematically reaction conditions in a broad range over a single, well-defined MoVTeNb oxide. Selectivity and product yield in a multidimensional parameter space can give insight into the reaction network. Apparent activation energies and reaction orders of propane are derived for several conditions. Optimum reaction conditions within the investigated parameter space are specified. The results presented within this contribution contain about 200 data points measured in steady states each corresponding to reaction conditions that differ in temperature, contact time, and propane feed concentration. The fact that this data was collected in less than two months shows clearly the advantage of parallel screening of reaction conditions for mechanistic studies.     

Controlled subnanosecond isomerization of HCN to CNH in solution

We report a study of control of the HCN-->CNH isomerization in a liquid Ar solution. We show, using molecular dynamics simulations, nearly complete conversion from HCN to CNH can be achieved in solution on the subnanosecond time scale without requiring laser pulse shaping or molecular alignment. The mechanism of the isomerization reaction involves multiphoton rovibrational excitation on the ground electronic state potential energy surface coupled with rapid rovibrational relaxation in solution. The results demonstrate the important role of rotation-vibration coupling in multiphoton excitation of small molecules and constitute the first realistic computational demonstration of fast, robust, and high-yield laser field manipulation of solution-phase molecular processes.     

Including anharmonicity in the calculation of rate constants. 1. The HCN/HNC isomerization reaction

A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.     

SCF CI potential energy surfaces for the HCN α HCN isomerisation reaction

We report X ¹A' and 2 ¹A' potential energy surfaces for HCN. Thermal isomerisation on the ground-state surface is discussed. An avoided crossing between X ¹A' and 2 ¹A' suggests alternative isomerisation mechanisms via this excited state. The X¹A'-2¹A' interaction may also allow the formation of CN(X ²Σ⁺) in photodissociation of XCN molecules.     

Effect of intramolecular energy transfer on the rate of unimolecular isomerization: HCN --HNC

This paper reports calculations of the rate of isomerization of HCN - HCN based on the theory of Gary and Rice as extended by Zhao and Rice. The major task is to determine the effect of intramolecular energy transfer on the prediction of the rate of isomerization. Both the full three-dimensional (3D) system and the reduced two-dimensional (2D) system obtained from freezing CN bond at 1.159 A are analyzed to check the validity of the freezing bond approximation. Meanwhile, RRKM rates are calculated to test RRKM choice of the transition state by comparing to Gary-Rice three-state model. The comparison shows that the rates from 2D model and 3D model are differing up to 20% with 2D rates consistently larger. The intramolecular energy transfer modifies the isomerization rate for HCN system up to 30% that is modestly small by the expectation. The isomerization rate predicted from RRKM theory is greater than those of Gary-Rice three-state model theory up to 65%, and it overstimates the rates under all consider     

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5-2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.     

Electrostatic potentials in systems periodic in one, two, and three dimensions

We consider the electrostatic potential in a unit cell containing N point charges Q(j) with positions r(j) inside the cell. The cell is replicated periodically in one, two, and three dimensions. The purpose is to give representations for the potential which contain only lattice sums which are absolutely convergent and uniformly convergent in the sampling position r. These representations are derived using variants of the Ewald method and are primarily intended for use in evaluating the accuracy of any algorithm to evaluate electrostatic energies and forces in simulations of dense matter, rather than necessarily for use of themselves in simulations. In reduced dimensionality the Ewald representations can be numerically inefficient and other representations are also provided with careful specification which allows two forms to be used for the potential functions in order to improve numerical performance. These mixed representations may be satisfactory in simulations.     

Quantum trajectories in complex phase space: multidimensional barrier transmission

The quantum Hamilton-Jacobi equation for the action function is approximately solved by propagating individual Lagrangian quantum trajectories in complex-valued phase space. Equations of motion for these trajectories are derived through use of the derivative propagation method (DPM), which leads to a hierarchy of coupled differential equations for the action function and its spatial derivatives along each trajectory. In this study, complex-valued classical trajectories (second order DPM), along which is transported quantum phase information, are used to study low energy barrier transmission for a model two-dimensional system involving either an Eckart or Gaussian barrier along the reaction coordinate coupled to a harmonic oscillator. The arrival time for trajectories to reach the transmitted (product) region is studied. Trajectories launched from an "equal arrival time surface," defined as an isochrone, all reach the real-valued subspace in the transmitted region at the same time. The Rutherford-type diffraction of trajectories around poles in the complex extended Eckart potential energy surface is described. For thin barriers, these poles are close to the real axis and present problems for computing the transmitted density. In contrast, for the Gaussian barrier or the thick Eckart barrier where the poles are further from the real axis, smooth transmitted densities are obtained. Results obtained using higher-order quantum trajectories (third order DPM) are described for both thick and thin barriers, and some issues that arise for thin barriers are examined.     

Extrusion computations in three dimensions

The present paper considers the problem of predicting extrudate shapes from asymmetrical dies for Newtonian and non-Newtonian fluids. The flow is fully three-dimensional and an exploration of finite elements and boundary elements is made with a view to finding accurate, stable and economical schemes. A number of finite elements are compared and we conclude that some of the Fortin elements are most useful on the grounds of computational overhead and solution accuracy. These have been used to investigate some symmetrical (square dies) and asymmetrical (unequal lip) planar and general L-shaped die flows for Newtonian fluids. The question of predicting regions of plug flow is addressed for materials with a yield stress in the three-dimensional case. Finally, we show that an unconstrained extrudate may, in absence of gravity, describe a helix in space as the most general result.     

Phase transfer and rhodium (I) catalyzed isomerization of allylaromatics and cognate systems

Summary Allylaromatics undergo isomerization by the use of chlorodicarbonylrhodium(I) dimer as the metal catalyst and phase transfer catalysis conditions [benzene or methylene chloride as the organic phase, aqueous NaOH, and a quarternary ammonium salt as the phase transfer catalyst]. Isomerization of allyl amines and sulfones occurred as well, but the rhodium(I) complex was not required in the latter case.     

Analytical Hartree–Fock gradients with respect to the cell parameter for systems periodic in three dimensions

Analytical Hartree–Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of three-dimensional periodicity. The code is based on Gaussian-type orbitals, and the summation of the Coulomb energy is performed with the Ewald method. It is shown that a high accuracy of the cell gradient can be achieved.     

Industrial application of catalytic systems for n-heptane isomerization

The ideal gasoline must have a high pump octane number, in the 86 to 94 range, and a low environmental impact. Alkanes, as a family, have much lower photochemical reactivities than aromatics or olefins, but only the highly branched alkanes have adequate octane numbers. The purpose of this work is to examine the possibilities of extending the technological alternative of paraffin isomerization to heavier feedstocks (i.e., n-heptane) using non-conventional catalytic systems which have been previously proposed in the literature: a Pt/sulfated zirconia catalyst and a molybdenum sub-oxide catalyst. Under the experimental conditions at which these catalysts have been evaluated, the molybdenum sub-oxide catalyst maintains a good activity and selectivity to isomerization after 24 h, while the Pt/sulfated zirconia catalyst shows a higher dimethylpentanes/methylhexanes ratio, probably due to a lower operating temperature, but also a high formation of cracking products, and presents signs of deactivation after 8 h. Though much remains to be done, the performance of these catalysts indicates that there are good perspectives for their industrial application in the isomerization of n-heptane and heavier alkanes.     

Quantum‐matter photonic framework perspective of chemical processes: Entanglement shifts in HCN/CNH isomerization

A complete electro‐nuclear (EN) basis set and quantum electrodynamics bases in photon number scheme combines to form photonic bases sets. The EN q‐states can hence be modulated by appropriate external electromagnetic sources. Quantum determinants for HCN/CNH isomerization within photonic bases are elaborated that rationalize quantum state changes as if it were an apparent unimolecular process. Topologic label of base states permit linking with those obtained with semiclassic schemes. A comparison of results leads to conclude that both schemes can turn out to be complementary. The q‐scheme yielding more detailed information that the semiclassic one as expected. © 2015 Wiley Periodicals, Inc.     

光敏电子转移异构反应中的盐效应

本文利用四正丁基四氟硼酸铵为探针, 研究了顺式芪和四环烷的9,10-二氰基蒽敏化光异构化的反应机理, 加入四正丁基四氟硼酸铵明显加快顺式芪的异构反应而减慢四环烷的反应。荧光猝灭及激光闪光光解实验证明四正丁基四氟硼酸铵能促进电荷分离过程而生成离子自由基对。从而证实顺式芪的异构化反应是经由离子自由基的历程, 而四环烷则是通过激基复合物机理。     

Perturbation theory without wave function for multidimensional systems

A new method to obtain perturbation corrections to the eigenvalues of multidimensional quantummechanical models is developed. It consists of rearranging the Rayleigh-Schrodinger perturbation theory so that any coefficient of the perturbation series is obtained from a simple and compact recursion relationship. The Zeeman effect in hydrogen and the hydrogen molecule-ion are used to illustrate the procedure.     

Quantum tunneling dynamics in multidimensional systems: a matching-pursuit description

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method.     

Integrin clustering in two and three dimensions

Integrins are transmembrane proteins that allow cells to bind to their external environment. They are the primary regulators of cell-matrix interactions, with direct roles in cell motility and signaling, which in turn regulate numerous physiological processes. Under common experimental conditions, integrins tend to cluster for sturdy and effective binding to extracellular matrix molecules. These clusters often evolve into focal adhesions, which regulate downstream signaling. However, integrin clusters are more pronounced and have longer lifetimes in two-dimensional assays than in more realistic three-dimensional environments. While a number of models and theoretical approaches have focused on integrin binding and diffusion, the reasons for the differences between two- and three-dimensional clustering have remained elusive. In this study, we model an individual cluster attached to a two-dimensional collagen film and attached to collagen fibers of various sizes in three-dimensional matrices. We then discuss how our results explain differences in size and lifetime, and how they hint at reasons for other differences between the two environments. Further, we make predictions regarding the stability of clusters based on different overall intracellular conditions. Our results show good agreement with experiments and provide a quantitative basis for understanding how matrix dimensionality and structure regulate integrin behavior in environments that mimic in vivo conditions.