Wavepacket approach to the cumulative reaction probability within the flux operator formalism
Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Dirac -function representable as a localized Gaussian wavepacket. This functional form enables compu...
Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Dirac -function representable as a localized Gaussian wavepacket. This functional form enables compu...
A pseudospectral method for optimal control of open quantum systems
In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the pr...
In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the pr...
A diffusional bimolecular propensity function
J. Chem. Phys. 131, 164109 (2009); doi:10.1063/1.3253798
Published 27 October 2009
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We derive an explicit formula for the propensity function (stochastic reaction rate) of a generic bimolecular chemical reaction in which the reactant molecules move about by diffusion, as solute molecules in a bath of much smaller and more numerous solvent molecules. Our derivation assumes that the solution is macroscopically well stirred and dilute in the solute molecules. It effectively extends the physical rationale for the chemical master equation and the stochastic simulation algorithm from well-stirred dilute gases to well-stirred dilute solutions, with the former becoming a limiting case of the latter. This extension is important for cellular systems, where the solvent molecules are typically water and the solute (reactant) molecules are much larger organic structures, whose relatively low populations often require a discrete-stochastic formalism. In the course of our derivation, we illuminate some limitations on the ability of the classical diffusion equation to accurately describe how a diffusing molecule moves on spatial and temporal scales that are relevant to collision-induced chemical reactions.
©2009 American Institute of Physics
| History: | Received 1 September 2009; accepted 2 October 2009; published 27 October 2009 |
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REFERENCES (17)
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J. Phys. Chem. B 113, 1640 (2009) . - This result is most easily proved by appealing to the following well known theorem in random variable theory—a theorem that will be invoked in other contexts later in this paper. If N1 and N2 are statistically independent normal random variables with means µi and variances
(i=1,2), then N1±N2 will be the normal random variable with mean µ1±µ2 and variance
+
. So, taking the x-component of the velocity of an Si molecule to be Ni with µi=0 and
, the x-component of the velocity of an S1 molecule relative to an S2 molecule will be N1−N2, and that, by the theorem just stated, is a normal random variable with mean 0 and variance kBT(m
+m
)
![[equivalent]](http://scitation.aip.org/stockgif3/equiv.gif)
kBTm.
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- This invocation of the addition law of probability for mutually exclusive events is justified only if dt is infinitesimally small, since only then will the probability for more than one collision in dt be negligibly small.
- To the best of the author's knowledge, this result and its implications for trajectory simulation were first articulated by C. Gillespie (private communication), who discovered it numerically by carrying out a series of Monte Carlo simulation experiments using Eq. (8).
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