Quantum chemical reaction dynamics on a highly parallel supercomputer

Summary In this paper we describe the solution of the quantum mechanical equation for the scattering of an atom by a diatomic molecule on a high-performance distributed-memory parallel supercomputer, using the method of symmetrized hyperspherical coordinates and local hyperspherical surface functions. We first cast the problem in a format whose inherent parallelism can be exploited effectively. We next discuss the practical implementation of the parallel programs that were used to solve the problem. The benchmark results and timing obtained from the Caltech/JPL Mark IIIfp hypercube are competitive with the CRAY X-MP, CRAY 2 and CRAY Y-MP supercomputers. These results demonstrate that such highly parallel architectures permit quantum scattering calculations with high efficiency in parallel fashion and should allow us to study larger, more complicated chemical systems. Future extensions to this approach are discussed.Work performed in partial fulfillment of the requirements for the Ph.D. degree in Chemistry at the California Institute of Technology.Contribution number 8209     

Exact quantum mechanical vibration-rotation kinetic energy operator of four-particle system in various coordinates

The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.     

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.     

处理量子反应散射的负虚数势方法

处理量子反应散射的负虚数势方法蔡宇民，胡旭光，李前树（西安石油学院化学工程系．西安，７１００６１）（吉林大学理论化学研究所，长春，１３００２３）关键词反应散射，反应几率，光学势近年来，处理反应散射问题的各种严格的和近似的量子力学方法发展迅速［１～５］...     

An internal coordinate invariant reaction pathway

In this work we show that some properties of a potential energy surface are not independent of the choice of the coordinate frame. So the reaction pathway often described as steepest descent way does not correspond to an invariant curve under coordinate transformations. We propose an internal intrinsic reaction pathway by using some quasi-dynamical considerations (like instantaneous internal acceleration). Our work precises the intrinsic-reaction coordinates of Fukui to any set of 3N-6 internal parameters. Finally, from the equations of motion we deduce the form of the normal reaction coordinates frame anywhere along the postulated reaction pathway.     

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates

We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH(3) molecule and N(2)H(5) (-) ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH(3), the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N(2)H(5) (-), the centroid IRC is largely deviated from the "classical" IRC, and the free energy barrier is reduced by the quantum effects even more drastically.     

Time-dependent quantum dynamics of reactive scattering and the calculation of product quantum state distributions — A study of the collinear F+H2(v=0) → HF(v′)+H reaction

Summary A new method for the calculation of partial cross sections in the time-dependent quantum theory of molecular reactive scattering processes is discussed. Preliminary calculations are presented which clearly illustrate the power of the method. They show how all the partial cross sections associated with a single initial quantum state may be computed over a very wide energy range from a single propagation of a prepared wavepacket. The resonance behaviour is obtained without difficulty and the energies of the reactive scattering resonances are exactly reproduced.     

Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

LCAC-SW quantum scattering dynamic study on the ion-pair formation process

LCAC-SW method has been extended to study the reaction dynamics for ion-pair formation processes. M X2→-M X2- reaction system involves two potential energy surfaces, i.e., the covalence state (M X2) and the ionic state (M X2-) and their crossing effect. The working equations for calculating state-to-state probability have been derived based on the above two-state model. Satisfied results of collinear state-to-state probabilities for K I2→K I2- ion-pair formation system have been obtained.     

A new set of bending Td symmetry coordinates for MX4 molecules

The conventional set of T_d symmetry coordinates for the bending modes of MX₄ molecules can lead to ambiguous geometries when displacements from equilibrium are large. It is proposed here to use internal coordinates that are haversines of the bending angles divided by their sum. The A₁ representation becomes a constant, enabling recovery of the bending angles unambiguously, analytically, and without approximation. © 2013 Wiley Periodicals, Inc.     

A new exact quantum mechanical rovibrational kinetic energy operator for penta-atomic systems in internal coordinates

The concrete molecule-fixed (MF) kinetic energy operator for penta-atomic molecules is expressed in terms of the parameterδ, the matrix element G_(?), and angular momentum operator (?). The applications of the operator are also discussed. Finally, a general compact form of kinetic energy operator suitable for calculating the rovibrational spectra of polyatomie molecules is presented.     

Information-theoretic analysis of quantum mechanical reaction cross sections

Information theory is used to analyze quantum mechanical rotation excitation probabilities for the hydrogen exchange reaction. A linear rotational surprisal is found, and the entropy deficiency of the product rotational distribution is computed.     

Quantum wave packet study of the insertion reaction S+H2

S(¹D)+H₂→SH+H reaction at zero total angular momentum has been studied by using a time-dependent quantum real wave packet method. State-to-state and state-to-all reactive scattering probabilities for a broad range of energy are calculated. The probabilities show many sharp peaks that ascribed to reactive scattering resonances. The density plots of the wave function shows that the reaction presents a pure insertion pathway.     

F+H2→HF+H反应的全量子态分辨的散射动力学研究

A crossed molecular beams, state-to-state scattering study was carried out on the F+H2→HF+H reaction at the collision energy of 5.02 kJ/mol, using the highly sensitive H atom Rydberg tagging time-of-flight method. All the peaks in the TOF spectra can be clearly assigned to the ro-vibrational structures of the HF product. The forward scattering of the HF product at v′=3 has been observed. The small forward scattering of the HF product at v′=2 has also been detected. Detailed theoretical analysis is required in order to fully understand the dynamical origin of these forward scattering products at this high collision energy.     

氯分子束与InP(100)表面反应散射的角分布研究

采用角分辨分子束散射技术研究了Cl_2与InP(100)表面热反应和激光诱导反应产物的角分布. 对于热反应, 由调制分子束和可转动四极质谱仪测得产物离子InCl~+、InCl_2~+、PCl~+、PCl_2~+和P_4~+的角分布, 都可用cos~(1.5)θ函数报合. 对于紫外(355 nm)激光诱导反应, 由飞行时间质谱法测得主要产物离子的角分布明显地偏离Knudsen定律. 其中In~+, InCl~+和InCl_2~+的角分布可用α·cosθ+(1-α)cos~nθ函数拟合, 其中α和n为拟合参数, 对于不同的产物离子有不同的数值. 由实验测得的脱附粒子的通量和能量在表面法线方向有明显地聚集现象, 可以认为产物从表面上脱附的机理, 除了热脱附之外, 还有非热脱附以及在表面附近脱附粒子的碰撞效应.     

The choice of internal coordinates in complex chemical systems

This article presents several considerations for the appropriate choice of internal coordinates in various complex chemical systems. The appropriate and black box recognition of internal coordinates is of fundamental importance for the extension of internal coordinate algorithms to all fields where previously Cartesian coordinates were the preferred means of geometry manipulations. Such fields range from local and global geometry optimizations to molecular dynamics as applied to a wide variety of chemical systems. We present a robust algorithm that is capable to quickly determine the appropriate choice of internal coordinates in a wide range of atomic arrangements. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

The reaction force. A scalar property to characterize reaction mechanisms

The reaction force is a global property of a chemical reaction that arises when applying the Hellmann–Feynmann theorem to the potential energy surface that links reactants, products and transition states. In the present work, the reaction force is defined rigorously from the cartesian components coming out from all forces exerted over each atom of a molecular system during the chemical reaction; it is demonstrated that the reaction force is a scalar property. An erratum to this article can be found at     

Finding all possiblea priori mechanisms for a given type of overall reaction

The method, presented for finding all thea priori possible mechanisms of a certain number of steps for a given type of overall reaction, is applied to finding the possible two-step mechanisms for: overall reactions of the type of molecular rearrangements, and of the type of molecular associations. Many examples from organic, physical or biochemistry are given such as mutarotation of glucose, Henry-Michaelis-Menten enzyme mechanism, rearrangements of halogenoamines, hydration of epoxides, etc. The approach provides a systematics for otherwise diverse mechanisms. Alexander von Humboldt Senior Scientist Awardee, West Germany. Predoctoral Research Assistant, Yale University 1973–1974. Then at the Roswell Park Memorial Institute, Department of Experimental Therapeutics, Buffalo, New York 14203.     

Albumin molecularly imprinted polymer with high template affinity — Prepared by systematic optimization in mixed organic/aqueous media

An approach using systematic optimization for the formation of an albumin molecularly imprinted polymer (MIP), able to separate albumin from proteins in solution, has been prepared by imprinting albumin using a copolymer comprising 3-dimethylaminopropyl methacrylate and tetraethylene glycol dimethacrylate in a mole ratio of 1 to 8. Cytochrome c, lysozyme and myoglobin were used in competitive re-binding experiments to compete with the polymer's native template with all protein species present at 0.0004 g mL^− 1. The effects of: monomer to crosslinker mole ratio, polymerization temperature and time were investigated. It was found that the addition of water 6.04%, into the pre-polymerization albumin-monomer complex enhanced the adsorption capacity and selectivity of the resulting MIP from 2.18 × 10^− 3 to 6.02 × 10^− 3 g g-MIP^− 1 and 83.5% to 98.7%, respectively. These results also showed that the MIP possessed high selectivity and adsorption capacity with respect to albumin in comparison with interfering species also present in solution. Polymerization temperature, time and the water content of the pre-polymerization mixture were all shown to have significant effects on the resulting albumin-MIP's performance. However, their influence on the polymer's affinity for the potentially interfering species was negligible. Additionally, higher polymerization temperatures (> 38 °C) and extended polymerization times (> 60 h) increased monomer conversion as determined by HPLC, but decreased the selectivity and adsorption capacity of the MIP. An optimized MIP, with very high selectivity and 6.37 × 10^− 3 g g-MIP^− 1 template re-adsorption capacity was obtained using the following polymerization conditions: 0.125 mole ratio of monomer to crosslinker, 6.04 wt.% water content with respect to the mass of the monomer complex, 60 h polymerization time at 38 °C, and with 0.47% albumin in the pre-polymerization monomer complex. Finally, the functions of polymerization temperature, time and the significance of the water content in the albumin-monomer complex are also discussed.     

Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results

This article presents a quasiclassical trajectory (QCT) method for determining the cumulative reaction probability (CRP) as a function of the total energy. The method proposed is based on a discrete sampling using integer values of the total and orbital angular momentum quantum numbers for each trajectory and on the development of equations that have a clear counterpart in the quantum mechanical (QM) case. The calculations comprise cumulative reaction probabilities at a given total angular momentum J, as well as those summed over J. The latter are used to compute QCT rate constants. The method is illustrated by comparing QCT and exact QM results for the H+H2, H+D2, D+H2, and H+HD reactions. The agreement between QCT and QM results is very good, with small discrepancies between the two data sets indicating some genuine quantum effects. The most important of these involves the value of the CRP at low energies which, due to the absence of tunneling, is lower in the QCT calculations, causing the corresponding rate constants to be smaller. The second is the steplike structure that is clearly displayed in the QM CRP for J = 0, which is much smoother in the corresponding QCT results. However, when the QCT density of reactive states, i.e., the derivatives of the QCT CRP with respect to the energy, is calculated, a succession of maxima and minima is obtained which roughly resembles those found in the QM calculations, although the latter are considerably sharper. The analysis of the broad peaks in the QCT density of reactive states indicates that the distributions of collision times associated with the maxima are somewhat broader, with a tail extending to larger collision times, than those associated with the minima. In addition, the QM and QCT dynamics of the isotopic variants mentioned above are compared in the light of their CRPs. Issues such as the compliance of the QCT CRP with the law of microscopic reversibility, as well as the similarity between the CRPs for ortho and para species in the QM and QCT cases, are also addressed.