Milestoning with transition memory

Milestoning is a method used to calculate the kinetics and thermodynamics of molecular processes occurring on time scales that are not accessible to brute force molecular dynamics (MD). In milestoning, the conformation space of the system is sectioned by hypersurfaces (milestones), an ensemble of trajectories is initialized on each milestone, and MD simulations are performed to calculate transitions between milestones. The transition probabilities and transition time distributions are then used to model the dynamics of the system with a Markov renewal process, wherein a long trajectory of the system is approximated as a succession of independent transitions between milestones. This approximation is justified if the transition probabilities and transition times are statistically independent. In practice, this amounts to a requirement that milestones are spaced such that trajectories lose position and velocity memory between subsequent transitions. Unfortunately, limiting the number of milestones limits both the resolution at which a system's properties can be analyzed, and the computational speedup achieved by the method. We propose a generalized milestoning procedure, milestoning with transition memory (MTM), which accounts for memory of previous transitions made by the system. When a reaction coordinate is used to define the milestones, the MTM procedure can be carried out at no significant additional expense as compared to conventional milestoning. To test MTM, we have applied its version that allows for the memory of the previous step to the toy model of a polymer chain undergoing Langevin dynamics in solution. We have computed the mean first passage time for the chain to attain a cyclic conformation and found that the number of milestones that can be used, without incurring significant errors in the first passage time is at least 8 times that permitted by conventional milestoning. We further demonstrate that, unlike conventional milestoning, MTM permits milestones to be spaced such that trajectories do not have enough time to lose their velocity memory between successively crossed milestones.     

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.     

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.     

Revisiting the reaction of hydroxyl radicals with vicinal diols in water

The carbonyl products of the reactions of hydroxyl radicals with three vicinal diols (ethane-1,2-diol, propane-1,2-diol and butane-2,3-diol) have been identified and quantified. Hydroxyl radicals were produced by γ-radiolysis of N(2)O-saturated aqueous solutions. The reactions result in the formation of alkoxyl radicals (~15%) followed by β-fragmentation, and α-hydroxyl alkyl radicals that undergo H(2)O elimination. The latter process is part of a radical chain reaction at higher diol concentrations.     

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).     

Extending the fluctuation theorem to describe reaction coordinates

The fluctuation theorem describes the distribution of work done on small systems which have been pushed out of equilibrium in response to an external field. The theorem has recently been a subject of much interest for describing single-molecule experiments and simulations. In this communication, it is shown how the fluctuation theorem can be extended to describe fluctuations not only in the work done on a system, but also in a reaction coordinate. The extension explored in this work allows for a generalized derivation of Hummer and Szabo's expression (G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001)) for reconstructing the potential of mean force from nonequilibrium trajectories. The derivation demonstrates how implementation of this expression can be more easily facilitated. Atomistic simulations of a biomolecular system are presented which support these results.     

Probing structural evolution along multidimensional reaction coordinates with femtosecond stimulated Raman spectroscopy

Mapping out multidimensional potential energy surfaces has been a goal of physical chemistry for decades in the quest to both predict and control chemical reactivity. Recently a new spectroscopic approach called Femtosecond Stimulated Raman Spectroscopy or FSRS was introduced that can structurally interrogate multiple dimensions of a reactive potential energy surface. FSRS is an ultrafast laser technique which provides complete time-resolved, background-free Raman spectra in a few laser shots. The FSRS technique provides simultaneous ultrafast time (~50 fs) and spectral (~8 cm(-1)) resolution, thus enabling one to follow reactive structural evolutions as they occur. In this perspective we summarize how FSRS has been used to follow structural dynamics and provide mechanistic detail on three classical chemical reactions: a structural isomerization, an electron transfer reaction, and a proton transfer reaction.     

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.     

Determination of reaction coordinates via locally scaled diffusion map

We present a multiscale method for the determination of collective reaction coordinates for macromolecular dynamics based on two recently developed mathematical techniques: diffusion map and the determination of local intrinsic dimensionality of large datasets. Our method accounts for the local variation of molecular configuration space, and the resulting global coordinates are correlated with the time scales of the molecular motion. To illustrate the approach, we present results for two model systems: all-atom alanine dipeptide and coarse-grained src homology 3 protein domain. We provide clear physical interpretation for the emerging coordinates and use them to calculate transition rates. The technique is general enough to be applied to any system for which a Boltzmann-sampled set of molecular configurations is available.     

Automatic method for identifying reaction coordinates in complex systems

To interpret simulations of a complex system to determine the physical mechanism of a dynamical process, it is necessary to identify the small number of coordinates that distinguish the stable states from the transition states. We develop an automatic method for identifying these degrees of freedom from a database of candidate physical variables. In the method neural networks are used to determine the functional dependence of the probability of committing to a stable state (committor) on a set of coordinates, and a genetic algorithm selects the combination of inputs that yields the best fit. The method enables us to obtain the first set of coordinates that is demonstrably sufficient to specify the transition state of the C(7eq)--> alpha(R) isomerization of the alanine dipeptide in the presence of explicit water molecules. It is revealed that the solute-solvent coupling can be described by a solvent-derived electrostatic torque around one of the main-chain bonds, and the collective, long-ranged nature of this interaction accounts for previous failures to characterize this reaction.     

Pattern of separatrices and intrinsic reaction coordinates for degenerate thermal rearrangements

A structurally stable model of the standard adiabatic gradient field of the potential energy surface for certain pericyclic reactions is derived.These reactions are not subjected to the principles of orbital isomerism or to the Woodward-Hoffmann rules.Use is made of a principle established by Ariel Fernández and Oktay Sinanolu which precludes direct meta-IRC connections between transition states.It is shown that Jahn-Teller isomers of the singlet biradicals involved in the process are not interconvertible since the biradical configuration is not a transition state but a critical point with Hessian matrix with two negative eigenvalues.The topological features of the PES obtained by combinatorial methods are in full agreement with earlier results obtained from MINDO calculations.     

化学反应处理的计算模型

介绍了一种将同类反应上升为合成反应知识和在计算机上实现反合成分析的方法,反合成分析是合成设计中最关键的一步,在本工作中采用了基于谋略键寻找的合成设计方法。它有逻辑宜于在计算机上实现的优点。为了实现这个方法,我们首次提出了一种能中肯地描述合成反应的计算模型—反应知识的分类模型。这一模型由三条规则定义：规则A-反应类型;规则B-发生反应的外部条件;规则C-不适宜采用这个反应的情况;这种计算模型能够将海量反应数据中最重要最基本的信息提炼出来,转换成计算机能处理的知识。它也包含有反应适用范围的信息,从而提高了析分过程的外推能力。     

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.     

The determination of intrinsic reaction coordinates by density functional theory

The first implementation of the intrinsic reaction coordinate (IRC ) method within the density functional theory (DFT ) framework is presented. The implementation has been applied to four different types of chemical reactions represented by the isomerization process, HCN ? HNC (A); the S_N2 process, H^? + CH₄ ? CH₄ + H^? (B); the exchange process, H˙ + HX ? HX + H˙ (X ? F,Cl) (C); and the elimination process, C₂H₅Cl ? C₂H₄ + HCl (D). The present study presents for each process optimized structures and calculated harmonic vibrational frequencies for the reactant(s), the transition state, and the product(s) along with the IRC path connecting the stationary points. The calculations were carried out within the local density approximation (LDA ) as well as the LDA/NL scheme where the LDA energy expression is augmented by Perdew's and Becke's nonlocal (NL ) corrections. The LDA and LDA/NL results are compared with each other as well as the best available ab initio calculations and experimental data. For reaction (D), ab initio calculations based on MP 2 geometries and MP 4SDTQ energies have been added due to the lack of accurate published post-HF calculations on this process. A detailed discussion is provided on the efficiency of the IRC algorithms, the relative accuracy of the DFT and ab initio schemes, as well as the reaction mechanisms of the four reactions. It is concluded that the LDA/NL scheme affords the same accuracy as does the MP 4 method. The post-HF methods seem to overestimate activation energies, whereas the corresponding LDA/NL estimates are too low. The LDA activation energies are even lower than the LDA/NL counterparts. The incorporation of the IRC method into the DFT framework provides a promising and reliable tool for probing the chemical reaction path on the potential energy surfaces, even for large-size systems. IRC calculations by ab initio methods of an accuracy similar to the LDA/NL scheme, such as the MP 4 scheme, are not feasible. © John Wiley & Sons, Inc.     

One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions

For multidimensional activated rate processes controlled by diffusive crossing of a saddle point region, we show that a one-dimensional reaction coordinate can be constructed even when the diffusion anisotropy is arbitrary. The rate constant, found using the potential of mean force along this coordinate, is identical to that predicted by the multidimensional Kramers-Langer theory. This reaction coordinate minimizes the one-dimensional rate constant obtained using a trial reaction coordinate and is orthogonal to the stochastic separatrix, the transition state that separates reactants from products.     

Blue moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics.

We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic dynamics which, unlike the usual constrained molecular dynamics, introduces no bias. Finally, we give a new perspective on bias removal by using constrained molecular dynamics.     

Revisiting the reaction between diaminomaleonitrile and aromatic aldehydes: a green chemistry approach

The reaction between diaminomaleonitrile (DAMN) and aldehydes and the resulting monoimines are well known. Since the standard reaction conditions involve the use of toxic solvents (typically methanol), we have sought to apply green chemistry principles to this reaction by either using water as the solvent without any catalysts or employing "solvent-free" conditions. The monoimines derived from DAMN are of interest as precursors for obtaining different heterocyclic systems and linear polymers. The methodologies used have significant advantages with regards to cost and environmental considerations.