Correspondence of canonical and microcanonical rate constants using variational transition state theory for simple bond fissions (original) (raw)
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The Journal of Physical Chemistry C, 2014
A simple three-state model for the dynamics of the singlet fission (SF) process is developed. The model facilitates the analysis of the relative significance of different factors, such as electronic energies, couplings, and the entropic contributions. The entropic contributions to the rates are important; they drive the SF process in endoergic cases (such as tetracene). The anticipated magnitude of entropic contributions is illustrated by simple calculations. By considering a series of three acenes (tetracene, pentacene, and hexacene), we explained the experimentally observed 3 orders of magnitude difference in the rate of SF in tetracene and pentacene and predicted that the rate in hexacene will be slightly faster than in pentacene. This trend is driven by the increased thermodynamic drive for SF (Gibbs free energy difference of the initial excitonic state and two separated triplets). The model also explains experimentally observed fast SF in 5,12diphenyltetracene. Consistently with the experimental observations, the model predicts weak temperature dependence of the multiexciton formation rate in tetracene as well as a reduced rate of this step in solutions and in isolated dimers.
Variational RRKM calculation of thermal rate constant for C–H bond fission reaction of nitro methane
Arabian Journal of Chemistry, 2017
The present work provides quantitative results for the rate constants of unimolecular C-H bond fission reactions in the nitro methane at elevated temperatures up to 2000 K. In fact, there are three different hydrogen atoms in the nitro methane. The potential energy surface for each C-H bond fission reaction of nitro methane was investigated by ab initio calculations. The geometry and vibrational frequencies of the species involved in this process were optimized at the MP2 level of theory, using the cc-pvdz basis set. Since C-H bond fission channel is a barrierless reaction, we have used variational RRKM theory to predict rate coefficients. By means of calculated rate coefficients at different temperatures, the Arrhenius expression of the channel over the temperature range of 100-2000 K is k(T) = 5.9E19 * exp(À56274.6/T).
Russian Journal of Physical Chemistry A, 2013
The present work provides quantitative results for the rate of unimolecular carbon-hydrogen bond fission reaction of benzene and nitro benzene at elevated temperatures up to 2000 K. The potential energy surface for each C-H (in the ortho, meta, and para sites) bond fission reaction of nitro benzene was investigated by ab initio calculations. The geometry and vibrational frequencies of the species involved in this process were optimized at the MP2 level of theory, using the cc-pvdz basis set. Since C-H bond fission channel is barrier less reaction, we have used variational RRKM theory to predict rate constants. By means of calculated rate constant at the different temperatures, the activation energy and exponential factor were determined. The Arrhenius expression for C-H bond fission reaction of nitro benzene on the ortho, meta and para sites are k(T) = 2.1 × 10 17 exp(-56575.98/T), k(T) = 2.1 × 10 17 exp(-57587.45/T), and k(T) = 3.3 × 10 16 exp(-57594.79/T) respectively. The Arrhenius expression for C-H bond fission reaction of benzene is k(T) = 2 × 10 18 exp(59 343.48.18/T). The effect of NO 2 group, location of hydrogen atoms on the substituted benzene ring, reaction degeneracy, benzene ring resonance and tunneling effect on the rate expression have been discussed.
Markov Models of Molecular Kinetics
Encyclopedia of Biophysics, 2013
Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.
Variational transition-state theory
Accounts of Chemical Research, 1980
Annu. Rev. Phys. Chem. 1984.35:159-189. Downloaded from arjournals.annualreviews.org by University of Minnesota-Law Library on 01/09/07. For personal use only.
Rare events in many-body systems: reactive paths and reaction constants for structural transitions
2012
This PhD thesis deals with the study of fundamental physics phenomena, with applications to nuclear materials of interest. We have developed methods for the study of rare events related to thermally activated structural transitions in many body systems. The first method involves the numerical simulation of the probability current associated with reactive paths. After deriving the evolution equations for the probability current, a Diffusion Monte Carlo algorithm is implemented in order to sample this current. This technique, called Transition Current Sampling was applied to the study of structural transitions in a cluster of 38 atoms with Lennard-Jones potential (LJ-38). A second algorithm, called Transition Path Sampling with local Lyapunov bias (LyTPS), was then developed. LyTPS calculates reaction rates at finite temperature by following the transition state theory. A statistical bias based on the maximum local Lyapunov exponents is introduced to accelerate the sampling of reactiv...
Error analysis and efficient sampling in Markovian state models for molecular dynamics
2005
In previous work, we described a Markovian state model (MSM) for analyzing molecular-dynamics trajectories, which involved grouping conformations into states and estimating the transition probabilities between states. In this paper, we analyze the errors in this model caused by finite sampling. We give different methods with various approximations to determine the precision of the reported mean first passage times. These approximations are validated on an 87 state toy Markovian system.
Calculation of reaction constants using Transition Path Sampling with a local Lyapunov bias
2011
We propose an efficient method to compute reaction rate constants of thermally activated processes occurring in many-body systems at finite temperature. The method consists in two steps: first, paths are sampled using a transition path sampling (TPS) algorithm supplemented with a local Lyapunov bias favoring diverging trajectories. This enhances the probability of observing rare reactive trajectories between stable states during relatively short simulations. Secondly, reaction constants are eventually estimated from the unbiased fraction of reactive paths, yielded by an appropriate statistical data analysis tool, the multistate Bennett acceptance ratio (MBAR) package. In order to test our algorithm, we compute reaction constants for structural transitions in LJ38, a well studied Lennard-Jones cluster, comparing our results to values previously reported in the literature. Additionally, we apply our method to the calculation of reaction rates for vacancy migration in an {\alpha}-Iron ...
Markov models of molecular kinetics: Generation and validation
Chemical Physics, 2011
Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.
Microscopic Phase-Space Exploration Modeling of ^{258}Fm Spontaneous Fission
Physical review letters, 2017
We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of ^{258}Fm can be well reproduced using simple assumptions on the quantum collective phase space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory with pairing. This approach goes beyond the mean-field theory by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation, as well as prescission particle emission, are obtained. We conclude that fluctuations of the TKE and mass are ...