Collision theory treatment of monomolecular and bimolecular gas reactions

An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).     

Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

A recently formulated continuum limit semiclassical initial value series representation (SCIVR) of the quantum dynamics of dissipative systems is applied to the study of vibrational relaxation of model harmonic and anharmonic oscillator systems. As is well known, the classical dynamics of dissipative systems may be described in terms of a generalized Langevin equation. The continuum limit SCIVR uses the Langevin trajectories as input, albeit with a quantum noise rather than a classical noise. Combining this development with the forward-backward form of the prefactor-free propagator leads to a tractable scheme for computing quantum thermal correlation functions. Here we present the first implementation of this continuum limit SCIVR series method to study two model problems of vibrational relaxation. Simulations of the dissipative harmonic oscillator system over a wide range of parameters demonstrate that at most only the first two terms in the SCIVR series are needed for convergence of the correlation function. The methodology is then applied to the vibrational relaxation of a dissipative Morse oscillator. Here, too, the SCIVR series converges rapidly as the first two terms are sufficient to provide the quantum mechanical relaxation with an estimated accuracy on the order of a few percent. The results in this case are compared with computations obtained using the classical Wigner approximation for the relaxation dynamics.     

A refined ring polymer molecular dynamics theory of chemical reaction rates

We further develop the ring polymer molecular dynamics (RPMD) method for calculating chemical reaction rates [I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005)]. We begin by showing how the rate coefficient we obtained before can be calculated in a more efficient way by considering the side functions of the ring-polymer centroids, rather than averaging over the side functions of the individual ring-polymer beads. This has two distinct advantages. First, the statistics of the phase-space average over the ring-polymer coordinates and momenta are greatly improved. Second, the resulting flux-side correlation function converges to its long-time limit much more rapidly. Indeed the short-time limit of this flux-side correlation function already provides a "quantum transition state theory" approximation to the final rate coefficient. In cases where transition state recrossing effects are negligible, and the transition state dividing surface is put in the right place, the RPMD rate is therefore obtained almost instantly. We then go on to show that the long-time limit of the new flux-side correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface. This is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.     

Transition probabilities of a string oscillator subject to impulsive collisions with a heavy mass point

Impulsive linear collisions between a string oscillator (a one-dimensional particle in a box) and a mass point are studied quantum mechanically. In the limit of a very heavy mass point (which corresponds classically to many collisions during a single encounter) the transition probabilities are determined exactly. The result permits a discussion of the mixed quantum-classical regime where the collider becomes almost classical while the oscillator remains quantum mechanical. While the average transition probabilities P(m-->n) are well reproduced by the Ehrenfest mean-field approximation, the prediction for the superimposed high-frequency resonance structure is qualitatively wrong for a genuine quantum oscillator. Only if the oscillator is also almost classical and if (m-n)2 square root(mu) < m, where mu is the mass ratio collider/oscillator, this structure is correctly predicted by the Ehrenfest approximation.     

分析化学中“检出限”的物理意义及测定方法探究

阐述了分析化学中各类分析方法的检出限的物理意义、测定方法及可能存在的问题,并论述了经典的检出限定义的局限性。在利用凝血酶适配体与凝血酶的特异性结合抑制Pt纳米颗粒对量子点荧光猝灭检测凝血酶和基于CuGeO_3纳米线和葡萄糖氧化酶(GOx)修饰的玻碳电极(GCE)生物传感器测定葡萄糖的分析方法中,由于测定信号与被检测物质浓度或浓度的对数成负相关关系,导致分析方法的检出限与经典的检出限测定产生一定的冲突,出现了测定精密度越高,检出限越差的异常情况。     

An upper limit to kinetic fragility in glass-forming liquids

The kinetic fragility of a liquid is correlated to the magnitude of enthalpy hysteresis in various glass-forming materials during thermal cycling across the glass transition. While the lower bound of liquid fragility is well known, there has been little research into the possibility of an inherent upper limit to fragility. In this paper, we present a theoretical argument for the existence of a maximum fragility and show that the correlation between fragility and enthalpy hysteresis allows for an empirical evaluation of the upper limit of fragility. This upper limit occurs as the enthalpy hysteresis involved in thermal cycling about the glass transition approaches zero, leading to m(max)≈175. This result agrees remarkably well with our previous estimate. The dynamics of maximum fragility liquids are discussed, and a critical temperature of ～1.5 T(g) (where T(g) is the glass transition temperature) is revealed where a transition from nonexponential to exponential structural relaxation occurs.     

Massively parallel spin–orbit configuration interaction

We describe a new approach to incorporating quantum effects into chemical reaction rate theory using quantum trajectories. Our development is based on the entangled trajectory molecular dynamics method for simulating quantum processes using trajectory integration and ensemble averaging. By making dynamical approximations similar to those underlying classical transition state theory, quantum corrections are incorporated analytically into the quantum rate expression. We focus on a simple model of quantum decay in a metastable system and consider the deep tunneling limit where the classical rate vanishes and the process is entirely quantum mechanical. We compare our approximate estimate with the well-known WKB tunneling rate and find qualitative agreement.     

Equilibrium limit of diffusion equation for interacting particles: are bifurcations and multiplicity of correlation functions an artifact or real?

The structure of a fluid is analyzed by taking the equilibrium limit of a diffusion equation including the Giacomin-Lebowitz term for intermolecular interactions. This equation represents the differential mass balance in fluids with the Metropolis algorithm for fluxes; it allows a new qualitative yet analytical approximation for the direct correlation function over the entire range of fluid densities and temperatures. This approximation is analogous to a classical Ono-Kondo model for adsorption if the distribution of molecules around a central molecule is viewed as the adsorption of molecules on a central molecule. While this model qualitatively predicts known behavior for both gas and liquid phases, approaching a phase transition (e.g., condensation of gas into liquid) results in a bifurcation and multiplicity of the direct correlation function. The model predicts a sequence in the transformation of correlation functions from that of a gas to that of a liquid. This sequence starts with the appearance of an isolated loop in the direct correlation function, indicating states that are stable but cannot be achieved without perturbation of the system. However, the system seems to sense its proximity to a phase transition and reflects the distance to the phase boundary by the size and shape of this isolated loop in the direct correlation function. At lower temperatures, this loop merges with the gas-phase peak, indicating that clusters can form spontaneously. Then, these clusters grow into a high-density (liquid) phase. The notion of bifurcations and multiplicity in correlation functions is an unusual and controversial concept. Certainly, it is unexpected and raises important questions: (a) if such a behavior is not real, why does the diffusion equation predict such behavior, i.e., is it a mathematical artifact or is it due to conflicting physical assumptions? (b) if this behavior is real, how does one interpret it at a molecular level? Here, we present some interpretations, but they are open for discussion.     

Electron tunneling dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an anharmonic bath is found in a time-dependent Hartree approximation. The general expression is presented in terms of medium Keldysh functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation where the rate constant does not exhibit an activation dependence at high temperatures. The reorganization energy E(r) and the renormalized reaction heat epsilon are expressed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that E(r) and epsilon are temperature dependent.     

Quantum theory of chemical bond formation processes in condensed systems: studies towards exploration of electrochemical dark and photoprocesses on semiconductors

Quantum theoretical models of chemical bond formation and partial charge transfer processes in condensed systems, and their extension to processes in electronic non-equilibrium are investigated in this paper with a view to further exploration of electrochemical and photoelectrochemical kinetics on semiconductors. Electrochemical dark and photocurrents on n-III-V-semiconductors are correlated with calculated transition probabilities for atom-group transfer over larger distances (80 to 240 pm), leading to a first estimate of potential surface shapes compatible with experiment. Some specific problems connected with transition probability calculations for heavy-particle transfer in strong anharmonic potentials are considered in detail, including approximation of Franck-Condon transitions in arbitrary potentials by their classical limit.     

Mixed quantum-classical description of spectroscopy of dissipative systems

Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.     

Statistical mechanics and fluid structure

In the axiomatic approach to the derivation of statistical mechanics the theory is based upon the equations of motions of classical mechanics (Hamilton equations). Since these equations are unstable with respect to initial conditions, in the time τ ≈ 10^?12 s they generate chaos in the system of atoms and molecules. This chaos can be described by only probability theory laws. The laws of this theory are introduced into statistical mechanics as the second postulate. However, for both postulates (i.e., Hamilton equations and probability theory laws) to be compatible with each other, about one and a half ten of additional requirements defining in detail the matter model underlying the theory must be imposed on the system. This report analyzes only the restrictions imposed by probability theory. The main of them are: a transition to the thermodynamic limit, the condition of correlation attenuation, and a short-range character of the interaction potential. The matter model formulated based on these restrictions is a continuous medium in which a correlation sphere with a small radius R ≈ 10^?7 cm (physical point) is submerged. It is submerged in an infinite thermostat, the particles of which behave as the ideal gas relative to the particles forming the correlation sphere. Here all macroscopic parameters of matter in this physical point are determined by the state of the correlation sphere. Thus formulated model determines the macro- and microscopic structure of matter, and finally, results in thermodynamic and hydrodynamic equations.     

Quantum instanton evaluation of the thermal rate constants and kinetic isotope effects for SiH4+H-->SiH3+H2 reaction in full Cartesian space

The quantum instanton calculations of thermal rate constants for the gas-phase reaction SiH4+H-->SiH3+H2 and its deuterated analogs are presented, using an analytical potential energy surface. The quantum instanton approximation is manipulated by full dimensionality in Cartesian coordinate path integral Monte Carlo approach, thereby taking explicitly into account the effects of the whole rotation, the vibrotational coupling, and anharmonicity of the reaction system. The rates and kinetic isotope effects obtained for the temperature range of 200-1000 K show good agreements with available experimental data, which give support to the accuracy of the underlying potential surface used. In order to investigate the sole quantum effect to the rates, the authors also derive the classical limit of the quantum instanton and find that it can be exactly expressed as the classical variation transition state theory. Comparing the quantum quantities with their classical analogs in the quantum instanton formula, the authors demonstrate that the quantum correction of the prefactor is more important than that of the activation energy at the transition state.     

The freezing transition of a hard sphere fluid subject to the Percus-Yevick approximation

A classical density functional theory is applied to the calculation of the fluid-solid transition for hard spheres, using the Percus-Yevick (PY) direct correlation function. Three algebraic conditions are established for the coexistence densities and the Lindemann parameter. The terms neglected in the present analysis are small and the present theory, in our eyes, is essentially an exact solution given the PY approximation. No fluid-solid transition is found for the bcc lattice, whereas for expanded fcc lattices, the agreement with previous density functional theory-based theories is good.     

Path integral based calculations of symmetrized time correlation functions. I

In this paper, we examine how and when quantum evolution can be approximated in terms of (generalized) classical dynamics in calculations of correlation functions, with a focus on the symmetrized time correlation function introduced by Schofield. To that end, this function is expressed as a path integral in complex time and written in terms of sum and difference path variables. Taylor series expansion of the path integral's exponent to first and second order in the difference variables leads to two original developments. The first order expansion is used to obtain a simple, path integral based, derivation of the so-called Schofield's quantum correction factor. The second order result is employed to show how quantum mechanical delocalization manifests itself in the approximation of the correlation function and hinders, even in the semiclassical limit, the interpretation of the propagators in terms of sets of guiding classical trajectories dressed with appropriate weights.     

Field-theoretic model of inhomogeneous supramolecular polymer networks and gels

We present a field-theoretic model of the gelation transition in inhomogeneous reversibly bonding systems and demonstrate that our model reproduces the classical Flory-Stockmayer theory of gelation in the homogeneous limit. As an illustration of our model in the context of inhomogeneous gelation, we analyze the mean-field behavior of an equilibrium system of reacting trifunctional units in a good solvent confined within a slit bounded by parallel, repulsive walls. Our results indicate higher conversions and, consequently, higher concentrations of gel following the gelation transition near the center of the slit relative to the edges.     

Liquid-vapor density profiles from equilibrium limit of diffusion equation for interacting particles

Liquid-vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.     

5,10-CH+-THF向邻苯二胺转移一碳单元反应的理论研究

叶酸辅酶在酶催化的一碳单元转移过程中具有重要的作用,已有大量的实验及实验模拟对其生物学功能进行了研究分析.本文用PM3半经验方法对5,10-CH⁺-THF向邻苯二胺转移一碳单元的反应进行了理论研究.结果表明,5,10-CH⁺-THF中的咪唑啉环有两种开环方式,从而使得该反应可以通过两种途径实现,每一种途径都经历了6个反应步骤,其中包括限制速度的两次质子转移步骤.优化计算了每个步骤所有可能的中间体和过渡态的结构和能量,并通过比较分析得到了各反应阶段的最优中间体和过渡态结构.