A differential fluctuation theorem

We derive a nonequilibrium thermodynamics identity (the "differential fluctuation theorem") that connects forward and reverse joint probabilities of nonequilibrium work and of arbitrary generalized coordinates corresponding to states of interest. This identity allows us to estimate the free energy difference between domains of these states. Our results follow from a general symmetry relation between averages over nonequilibrium forward and backward path functions derived by Crooks [Crooks, G. E. Phys. Rev. E 2000, 61, 2361-2366]. We show how several existing nonequilibrium thermodynamic identities can be obtained directly from the differential fluctuation theorem. We devise an approach for measuring conformational free energy differences, and we demonstrate its applicability to the analysis of molecular dynamics simulations by estimating the free energy difference between two conformers of the alanine dipeptide model system. We anticipate that these developments can be applied to the analysis of laboratory experiments.     

Using internal coordinates to describe photoinduced geometry changes in MLCT excited states

A resonance Raman intensity analysis of the metal-to-ligand charge-transfer (MLCT) transition for the rhenium compound Re(2-(2'-pyridyl)quinoxaline)(CO)(3)Cl (RePQX) is presented. Photoinduced geometry changes are calculated, and the results are presented using the vibrational normal modes and the redundant internal coordinates. A density functional theory calculation is used to determine the ground-state nonresonant Raman spectrum and a transformation matrix that transforms the redundant internal coordinates into the normal modes. The normal modes nu(37) (rhenium coordination sphere distortion) and nu(75) (ligand skeletal stretch) show the largest photoinduced geometry change (Delta = 1.0 and 0.7, respectively). A single carbonyl mode is enhanced in the resonance Raman spectra. Time-dependent density functional theory is used to calculate excited-state geometry changes, which are subsequently used to determine the signs of the photoinduced normal mode displacements. Transforming to internal coordinates reveals that all the CO bond lengths are displaced in the excited state. The Re-C and C-C ligand bond lengths are also displaced in the excited state. The results are discussed in terms of a simple one-electron picture for the electronic transition. Many bond angles and torsional coordinates are also displaced by the metal-to-ligand charge transfer, and most of these are associated with the rhenium coordination sphere. It is demonstrated that using internal coordinates presents a clear picture of the geometry changes associated with photoinduced electron transfer in metal polypyridyl systems.     

Continuum composition models to describe multicomponent reaction kinetics

Some principles of the construction of kinetic models for multicomponent processes of oil-refining and petrochemistry are suggested in terms of the continuum mixture composition concepts. The results of computer simulation of industrial gasoline fraction hydrocracking processes are presented.

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Extensions to the likelihood maximization approach for finding reaction coordinates

This paper extends our previous work on obtaining reaction coordinates from aimless shooting and likelihood maximization. We introduce a simplified version of aimless shooting and a half-trajectory likelihood score based on the committor probability. Additionally, we analyze and compare the absolute log-likelihood score for perfect and approximate reaction coordinates. We also compare the aimless shooting and likelihood maximization approach to the earlier genetic neural network (GNN) approach of Ma and Dinner [J. Phys. Chem. B 109, 6769 (2005)]. For a fixed number of total trajectories in the GNN approach, the accuracy of the transition state ensemble decreases as the number of trajectories per committor probability estimate increases. This quantitatively demonstrates the benefit of individual committor probability realizations over committor probability estimates. Furthermore, when the least squares score of the GNN approach is applied to individual committor probability realizations, the likelihood score still provides a better approximation to the true transition state surface. Finally, the polymorph transition in terephthalic acid demonstrates that the new half-trajectory likelihood scheme estimates the transition state location more accurately than likelihood schemes based on the probability of being on a transition path.     

On the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics: Application to O + CS2 → SO + CS

We explore the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics. These coordinates provide the natural extension to polyatomic systems of the familiar atom—diatom model of “rolling a marble” on a skewed and scaled potential surface in that they reduce the kinetic energy of an arbitrary system to one equivalent to that of a single mass point moving in 3N - 3 dimensions. For any given number of atoms, usually several distinct types of mass scaled cluster coordinates can be introduced, all of which are interrelated by orthogonal transformations, and many of which are convenient for describing trajectory motion in one or more arrangement channels. We illustrate these points by an application to the collinear O + CS₂ → SO + CS reaction. For this system, the reagent to product coordinate transformation is conveniently described in terms of two Euler angles α and β, for which β is analogous to the atom—diatom skew angle, and α determines how the reagent vibrational normal modes relate to the product degrees of freedom. Examination of trajectory behavior indicates that the rather small value of π - α (21.7°) leads to a rather clean correlation between CS₂ asymmetric stretch motion and product CS vibrational motion, and between CS₂ symmetric stretch and a combination of SO stretch and product translation. This explains why symmetric stretch mode excitation enhances the O + CS₂ reaction rate more efficiently than asymmetric stretch mode excitation. We also find for O + CS₂ (and many other reactions for which the unbroken bond does not significantly change its length during the reaction) that the reagent and product segments of the minimum energy path are coplanar. This means that a natural partitioning of the reaction dynamics exists in which motions parallel to this plane tend to be active in promoting the reaction whereas motions perpendicular tend to be inactive. A study of trajectory motions and product state energy partitioning for O + CS₂ confirms this.     

Generating reaction coordinates by the Pauling relation

The Pauling relation of bond order and bond length together with the BEBO postulate are utilized to generation reaction coordinates on potential energy surfaces of simple exchange reactions. A generalization of the Pauling relation where the constant is dependent on the equilibrium separation is proposed.     

Mapping the reaction coordinates of enzymatic defluorination

The carbon-fluorine bond is the strongest covalent bond in organic chemistry, yet fluoroacetate dehalogenases can readily hydrolyze this bond under mild physiological conditions. Elucidating the molecular basis of this rare biocatalytic activity will provide the fundamental chemical insights into how this formidable feat is achieved. Here, we present a series of high-resolution (1.15-1.80 ?) crystal structures of a fluoroacetate dehalogenase, capturing snapshots along the defluorination reaction: the free enzyme, enzyme-fluoroacetate Michaelis complex, glycolyl-enzyme covalent intermediate, and enzyme-product complex. We demonstrate that enzymatic defluorination requires a halide pocket that not only supplies three hydrogen bonds to stabilize the fluoride ion but also is finely tailored for the smaller fluorine halogen atom to establish selectivity toward fluorinated substrates. We have further uncovered dynamics near the active site which may play pivotal roles in enzymatic defluorination. These findings may ultimately lead to the development of novel defluorinases that will enable the biotransformation of more complex fluorinated organic compounds, which in turn will assist the synthesis, detoxification, biodegradation, disposal, recycling, and regulatory strategies for the growing markets of organofluorines across major industrial sectors.     

Obtaining reaction coordinates by likelihood maximization

We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.     

Applicability of one-stage chemical reaction kinetic equation to describe non-isothermal destruction processes

The applicability of the traditional kinetic power equation to describe the thermal destruction of solids, and in particular polymers, is discussed. It is shown that in the majority of cases the use of such an equation is reasonable, even though the true mechanism of the process under study is either obscure or so complex that it cannot be analytically described in detail. In such cases the effective rather than the true kinetic parameters are obtained and provide certain useful information on the process. The fixed conversion temperature dependence on the heating rate is analyzed with examples on the model process and the thermal degradation of an epoxy binder.     

Path-integral virial estimator based on the scaling of fluctuation coordinates: application to quantum clusters with fourth-order propagators

We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite-difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat-capacity calculations of the (H(2))(22) and Ne(13) clusters at low temperature using the fourth-order Takahashi-Imada [J. Phys. Soc. Jpn. 53, 3765 (1984)] and Suzuki [Phys. Lett. A 201, 425 (1995)] propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite-difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.     

Extending Pummerer reaction chemistry. Application to the oxidative cyclization of indole derivatives

Treatment of 2-(phenylsulfinyl)indoles bearing a pendant nucleophile at C(3) with Tf(2)O/lutidine triggers a Pummerer-like cyclization to furnish 3,3-spirocyclic-2-(phenylthio)indolenine products, which can, in turn, be hydrolyzed to 3,3-spirocyclic oxindoles. [reaction: see text]     

Extending Pummerer reaction chemistry. Application to the oxidative cyclization of tryptophan derivatives

The diastereoselective oxidative cyclization of a beta-oxygenated tryptophan derivative is reported. This process, which utilizes a new variant of the Pummerer reaction, may have application in TMC-95A synthesis.     

Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem

We focus on the non-equilibrium two-bath spin-boson model, a toy model for examining quantum thermal transport in many-body open systems. Describing the dynamics within the noninteracting-blip approximation equations, applicable, e.g., in the strong system-bath coupling limit and/or at high temperatures, we derive expressions for the cumulant generating function in both the Markovian and non-Markovian limits by energy-resolving the quantum master equation of the subsystem. For a Markovian bath, we readily demonstrate the validity of a steady-state heat exchange fluctuation theorem. In the non-Markovian limit a "weaker" symmetry relation generally holds, a general outcome of microreversibility. We discuss the reduction of this symmetry relation to the universal steady-state fluctuation theorem. Using the cumulant generating function, an analytic expression for the heat current is obtained. Our results establish the validity of the steady-state heat exchange fluctuation theorem in quantum systems with strong system-bath interactions. From the practical point of view, this study provides tools for exploring transport characteristics of the two-bath spin-boson model, a prototype for a nonlinear thermal conductor.     

Revisiting and computing reaction coordinates with Directional Milestoning

The method of Directional Milestoning is revisited. We start from an exact and more general expression and state the conditions and validity of the memory-loss approximation. An algorithm to compute a reaction coordinate from Directional Milestoning data is presented. The reaction coordinate is calculated as a set of discrete jumps between Milestones that maximizes the flux between two stable states. As an application we consider a conformational transition in solvated adenosine. We compare a long molecular dynamic trajectory with Directional Milestoning and discuss the differences between the maximum flux path and minimum energy coordinates.     

Computing time scales from reaction coordinates by milestoning

An algorithm is presented to compute time scales of complex processes following predetermined milestones along a reaction coordinate. A non-Markovian hopping mechanism is assumed and constructed from underlying microscopic dynamics. General analytical analysis, a pedagogical example, and numerical solutions of the non-Markovian model are presented. No assumption is made in the theoretical derivation on the type of microscopic dynamics along the reaction coordinate. However, the detailed calculations are for Brownian dynamics in which the velocities are uncorrelated in time (but spatial memory remains).     

On the fluctuation theorem for the dissipation function and its connection with response theory

Recently, there has been considerable interest in the fluctuation theorem (FT). The Evans-Searles FT shows how time reversible microscopic dynamics leads to irreversible macroscopic behavior as the system size or observation time increases. We show that the argument of this FT, the dissipation function, plays a central role in nonlinear response theory and derive the dissipation theorem, giving exact relations for nonlinear response of classical N-body systems that are more widely applicable than previous expressions. These expressions should be verifiable experimentally. When linearized they reduce to the well-known Green-Kubo expressions for linear response.     

On the application of mean value theorem to reaction kinetics over inhomogeneous surfaces

Monolithic materials have been widely used for over 20 years as catalyst supports in the abatement of emissions from mobile and stationary sources. They have been most successfully used for applications where high volumetric flow rates and potential for thermal shock are required. Their use is expected to further increase as new applications are found. This paper describes three new catalytic technologies which require a monolithic support; 1) the diesel oxidation catalyst commercialized in 1994 and 2) NO_x abatement with hydrocarbons in lean environments and 3) catalytically supported thermal combustion both of which are currently under development.     

Extending pummerer reaction chemistry. Application to the total synthesis of (+/-)-dibromoagelaspongin

The sponge metabolite dibromoagelaspongin was synthesized in 16 steps from imidazole. The route features two successive oxidative cyclizations with complete control of regiochemistry to deliver the unusual triaminomethane core of the target. These oxidative cyclizations likely resulted from Pummerer-like processes on the imidazole-2-sulfoxide (sulfide) precursors.     

A systematic treatment of three-dimensional quantum mechanical reaction coordinates

Summary The rigorous, collinear, canonical point transformation method with hyper-hyperbolic coordinates is extended to the infinite central mass problem in three dimensions. The initial transformation performed is (x_A, y _A, z _A, x _C, y _C, z _C) (, , , r, R, ), where (, , ) are the Euler angles; r and R are the AB and BC interatomic distances, respectively, and is the angle between r and R. A second transformation is then performed to (, , , , , ), where is the reaction coordinate mimicking the reaction path, and is the vibrational coordinate of the diatom. The transformed spaces are all one-to-one mappings from the original spaces, and thus do not have any three-to-one regions. The transformed momenta and Hamiltonians are derived, and are Hermitian in their respective transformed spaces.