Chemical Reactions Using a Non-Equilibrium Wigner Function Approach
Departamento de Física Teórica I, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
Author to whom correspondence should be addressed.
Academic Editors: Giorgio Sonnino and Adom Giffin
Received: 13 July 2016 / Revised: 14 September 2016 / Accepted: 13 October 2016 / Published: 19 October 2016
A three-dimensional model of binary chemical reactions is studied. We consider an ab initio quantum two-particle system subjected to an attractive interaction potential and to a heat bath at thermal equilibrium at absolute temperature
. Under the sole action of the attraction potential, the two particles can either be bound or unbound to each other. While at
, there is no transition between both states, such a transition is possible when
(due to the heat bath) and plays a key role as
approaches the magnitude of the attractive potential. We focus on a quantum regime, typical of chemical reactions, such that: (a) the thermal wavelength is shorter than the range of the attractive potential (lower limit on T
) and (b)
does not exceed the magnitude of the attractive potential (upper limit on T
). In this regime, we extend several methods previously applied to analyze the time duration of DNA thermal denaturation. The two-particle system is then described by a non-equilibrium Wigner function. Under Assumptions (a) and (b), and for sufficiently long times, defined by a characteristic time scale D
that is subsequently estimated, the general dissipationless non-equilibrium equation for the Wigner function is approximated by a Smoluchowski-like equation displaying dissipation and quantum effects. A comparison with the standard chemical kinetic equations is made. The time τ
required for the two particles to transition from the bound state to unbound configurations is studied by means of the mean first passage time formalism. An approximate formula for τ
, in terms of D
and exhibiting the Arrhenius exponential factor, is obtained. Recombination processes are also briefly studied within our framework and compared with previous well-known methods.
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MDPI and ACS Style
Álvarez-Estrada, R.F.; Calvo, G.F. Chemical Reactions Using a Non-Equilibrium Wigner Function Approach. Entropy 2016, 18, 369.
Álvarez-Estrada RF, Calvo GF. Chemical Reactions Using a Non-Equilibrium Wigner Function Approach. Entropy. 2016; 18(10):369.
Álvarez-Estrada, Ramón F.; Calvo, Gabriel F. 2016. "Chemical Reactions Using a Non-Equilibrium Wigner Function Approach." Entropy 18, no. 10: 369.
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