A constrained approach to multiscale stochastic simulation of chemically reacting systems

Cotter, Simon L.; Zygalakis, Konstantinos C.; Kevrekidis, Ioannis G.; Erban, Radek

doi:doi:10.1063/1.3624333

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Dispersion energy evaluated by using locally projected occupied and excited molecular orbitals for molecular interaction

The dispersion terms are evaluated with the perturbation theory based on the locally projected molecular orbitals. A series of model systems, including some of the S22 set, is examined, and the calculated binding energies are compared with the published results. The basis set dependence is also examined. The dispersion energy correction is evaluated by taking into account the double excitations only of the dispersion type electron configurations and is added to the 3rd order single excitation pe...

Accurate predictions of the energetics of silicon compounds using the multireference correlation consistent composite approach

Theoretical studies, using the multireference correlation consistent composite approach (MR-ccCA), have been carried out on the ground and lowest lying spin-forbidden excited states of a series of silicon-containing systems. The MR-ccCA method is the multireference equivalent of the successful single reference ccCA method that has been shown to produce chemically accurate (within ±1.0 kcal mol−1 of reliable, well-established experiment) results. The percentage contributions of the SCF configurat...

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.

Article Outline

INTRODUCTION
AN ILLUSTRATIVE EXAMPLE
1. Invariant measure of the illustrative example
CONDITIONAL STOCHASTIC SIMULATION ALGORITHM
1. Choice of fast and slow variables for the CSSA
CONSTRAINED MULTISCALE ALGORITHM
APPLICATION OF CMA TO MODEL
1. One-dimensional slow variable: Choice of variables
2. Two-dimensional slow variable: Choice of variables
STOCHASTIC “BIFURCATION DIAGRAMS”
1. CMA for the bistable example
2. Analysis of parameter dependence
CHOOSING A SUITABLE LENGTH OF SIMULATION
DISCUSSION

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KEYWORDS and PACS

Keywords

Fokker-Planck equation, molecular dynamics method, reaction kinetics, stochastic processes

PACS

82.20.Uv

Stochastic theories of rate constants
05.10.Gg

Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
05.40.-a

Fluctuation phenomena, random processes, noise, and Brownian motion

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.3624333

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

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$abstract.society.value is a Member of CrossRef

American Institute of Physics

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