218 research outputs found
Chemical Reaction Dynamics within Anisotropic Solvents in Time-Dependent Fields
The dynamics of low-dimensional Brownian particles coupled to time-dependent
driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have
been described through the use of a variant of the stochastic Langevin
equation. The rotational motion of the mesogens is assumed to follow the motion
of an external driving field in the linear response limit. Reaction dynamics
have also been probed using a two-state model for the Brownian particles.
Analytical expressions for diffusion and reaction rates have been developed and
are found to be in good agreement with numerical calculations. When the
external field driving the mesogens is held at constant rotational frequency,
the model for reaction dynamics predicts that the applied field frequency can
be used to control the product composition.Comment: 13 pages, 5 figure
Dissipating the Langevin equation in the presence of an external stochastic potential
In the Langevin formalism, the delicate balance maintained between the
fluctuations in the system and their corresponding dissipation may be upset by
the presence of a secondary, space-dependent stochastic force, particularly in
the low friction regime. In prior work, the latter was dissipated
self-consistently through an additional uniform (mean-field) friction [Shepherd
and Hernandez, J. Chem. Phys., 115, 2430-2438 (2001).] An alternative approach
to ensure that equipartition is satisfied relies on the use of a
space-dependent friction while ignoring nonlocal correlations. The approach is
evaluated with respect to its ability to maintain constant temperature for two
simple one-dimensional, stochastic potentials of mean force wherein the
friction can be evaluated explicitly when there is no memory in the barriers.
The use of a space-dependent friction is capable of providing qualitatively
similar results to those obtained previously, but in extreme cases, deviations
from equipartition may be observed due to the neglect of the memory effects
present in the stochastic potentials.Comment: 9 pages, 5 figures, to appear in J. Chem. Phy
Persistence of transition state structure in chemical reactions driven by fields oscillating in time
Chemical reactions subjected to time-varying external forces cannot generally
be described through a fixed bottleneck near the transition state barrier or
dividing surface. A naive dividing surface attached to the instantaneous, but
moving, barrier top also fails to be recrossing-free. We construct a moving
dividing surface in phase space over a transition state trajectory. This
surface is recrossing-free for both Hamiltonian and dissipative dynamics. This
is confirmed even for strongly anharmonic barriers using simulation. The power
of transition state theory is thereby applicable to chemical reactions and
other activated processes even when the bottlenecks are time-dependent and move
across space
Chemical reactions induced by oscillating external fields in weak thermal environments
Chemical reaction rates must increasingly be determined in systems that
evolve under the control of external stimuli. In these systems, when a reactant
population is induced to cross an energy barrier through forcing from a
temporally varying external field, the transition state that the reaction must
pass through during the transformation from reactant to product is no longer a
fixed geometric structure, but is instead time-dependent. For a periodically
forced model reaction, we develop a recrossing-free dividing surface that is
attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T.
Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for
single-mode sinusoidal driving, the stability of the time-varying transition
state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R.
Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous
work to the case of multi-mode driving waveforms. Excellent agreement is
observed between the rates predicted by stability analysis and rates obtained
through numerical calculation of the reactive flux. We also show that the
optimal dividing surface and the resulting reaction rate for a reactive system
driven by weak thermal noise can be approximated well using the transition
state geometry of the underlying deterministic system. This agreement persists
as long as the thermal driving strength is less than the order of that of the
periodic driving. The power of this result is its simplicity. The surprising
accuracy of the time-dependent noise-free geometry for obtaining transition
state theory rates in chemical reactions driven by periodic fields reveals the
dynamics without requiring the cost of brute-force calculations
The ontology of temperature in nonequilibrium systems
The laws of thermodynamics provide a clear concept of the temperature for an
equilibrium system in the continuum limit. Meanwhile, the equipartition theorem
allows one to make a connection between the ensemble average of the kinetic
energy and the uniform temperature. When a system or its environment is far
from equilibrium, however, such an association does not necessarily apply. In
small systems, the regression hypothesis may not even apply. Herein, we show
that in small nonequilibrium systems, the regression hypothesis still holds
though with a generalized definition of the temperature. The latter must now be
defined for each such manifestation.Comment: J.Chem.Phys. (in press); 23 pages, 3 figures, 1 tabl
The projection of a nonlocal mechanical system onto the irreversible generalized Langevin equation, II: Numerical simulations
The irreversible generalized Langevin equation (iGLE) contains a
nonstationary friction kernel that in certain limits reduces to the GLE with
space-dependent friction. For more general forms of the friction kernel, the
iGLE was previously shown to be the projection of a mechanical system with a
time-dependent Hamiltonian. [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)] In
the present work, the corresponding open Hamiltonian system is further
explored. Numerical simulations of this mechanical system illustrate that the
time dependence of the observed total energy and the correlations of the
solvent force are in precise agreement with the projected iGLE.Comment: 8 pages, 9 figures, submitted to J. Chem. Phy
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