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Lee K, Lee S. Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics. J Chem Phys 2020; 153:044129. [PMID: 32752726 DOI: 10.1063/5.0016269] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders. Therefore, it would be interesting to see which effect dominates when the number density of B as well as the number density of the crowders increases. We will present an approximate theory that provides a reasonable account for the Brownian dynamics simulation results.
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Affiliation(s)
- Kyusup Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- Department of Chemistry, Seoul National University, Seoul 151-747, South Korea
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2
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Kasahara K, Sato H. Dynamics theory for molecular liquids based on an interaction site model. Phys Chem Chem Phys 2017; 19:27917-27929. [DOI: 10.1039/c7cp05423h] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.
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Affiliation(s)
- Kento Kasahara
- Department of Molecular Engineering
- Kyoto University
- Japan
| | - Hirofumi Sato
- Department of Molecular Engineering and Elements Strategy for Catalysts and Batteries (ESICB)
- Kyoto University
- Japan
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Kasahara K, Sato H. A theory of diffusion controlled reactions in polyatomic molecule system. J Chem Phys 2016; 145:194502. [DOI: 10.1063/1.4967400] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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4
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Seki K, Wojcik M, Tachiya M. Diffusion-mediated geminate reactions under excluded volume interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011131. [PMID: 22400536 DOI: 10.1103/physreve.85.011131] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Indexed: 05/31/2023]
Abstract
In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles, and the results are compared with those obtained by Monte Carlo simulations. In general, excluded volume interactions by the inert particles slow down the diffusive motion of reactants. However, when the initial concentration of the inert particles is uniform and high, we show that additional influence of interference between reaction and correlated diffusion accelerates the transient decay of the survival probability in the diffusion-controlled limit. We also study the escape probability for a nonuniform initial distribution of the inert particles by taking the continuous limit in space. We show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.
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Affiliation(s)
- Kazuhiko Seki
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, Higashi 1-1-1, Tsukuba, Ibaraki, 305-8565 Japan
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Litniewski M, Gorecki J. Computer investigations on the asymptotic behavior of the rate coefficient for the annihilation reaction A + A → product and the trapping reaction in three dimensions. J Chem Phys 2011; 134:244505. [DOI: 10.1063/1.3601343] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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6
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Seki K, Wojcik M, Tachiya M. Effects of excluded volume interaction and dimensionality on diffusion-mediated reactions. J Chem Phys 2011; 134:094506. [DOI: 10.1063/1.3560419] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dorsaz N, De Michele C, Piazza F, De Los Rios P, Foffi G. Diffusion-limited reactions in crowded environments. PHYSICAL REVIEW LETTERS 2010; 105:120601. [PMID: 20867619 DOI: 10.1103/physrevlett.105.120601] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2010] [Indexed: 05/29/2023]
Abstract
Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio R(s), the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing R(s), the encounter rate is substantially depressed and becomes even nonmonotonic for R(s)<<1. Concurrently with the saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction.
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Affiliation(s)
- N Dorsaz
- University of Fribourg, Adolphe Merkle Institute, CH-1723 Marly 1, Switzerland
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Kim JS, Yethiraj A. Crowding effects on association reactions at membranes. Biophys J 2010; 98:951-8. [PMID: 20303852 DOI: 10.1016/j.bpj.2009.11.022] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2009] [Revised: 11/01/2009] [Accepted: 11/04/2009] [Indexed: 11/25/2022] Open
Abstract
The effect of macromolecular crowding on the binding of ligands to a receptor near membranes is studied using Brownian dynamics simulations. The receptor is modeled as a reactive patch on a hard surface and the ligands and crowding agents are modeled as spheres that interact via a steep repulsive interaction potential. When a ligand collides with the patch, it reacts with probability p(rxn). The association rate constant (k(infinity)) can be decomposed into contributions from diffusion-limited (k(D)) and reaction-limited (k(R)) rates, i.e., 1/k(infinity) = 1/k(D) + 1/k(R). The simulations show that k(D) is a nonmonotonic function of the volume fraction of crowding agents for receptors of small sizes. k(R) is always an increasing function of the volume fraction of crowding agents, and the association rate constant k(infinity) determined from both contributions has a qualitatively different dependence on the macromolecular crowding for high and low values of the reaction probability p(rxn). The simulation results are used to predict the velocity of the membrane protrusion driven by actin filament elongation. Based on the simple model where the protrusive force on the membrane is generated by the intercalation of actin monomers between the membrane and actin filament ends, we predict that crowding increases the local concentration of actin monomers near the filament ends and hence accelerates the membrane protrusion.
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Affiliation(s)
- Jun Soo Kim
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin, USA
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Abstract
Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA.
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Dorsaz N, De Michele C, Piazza F, Foffi G. Inertial effects in diffusion-limited reactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104116. [PMID: 21389450 DOI: 10.1088/0953-8984/22/10/104116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.
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Affiliation(s)
- N Dorsaz
- Institute of Theoretical Physics and Institut Romand de Recherche Numérique en Physique des Matériaux, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
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Kim JH, Lee S, Lee J, Lee S. Kinetics of collision-induced reactions between hard-sphere reactants. J Chem Phys 2009; 131:164503. [DOI: 10.1063/1.3251144] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Uwabe A, Ueno M, Ibuki K. Molecular dynamics simulation of partially diffusion-controlled reaction between mono- and diatomic molecules. J Mol Liq 2009. [DOI: 10.1016/j.molliq.2008.07.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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14
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Kim JS, Yethiraj A. Effect of macromolecular crowding on reaction rates: a computational and theoretical study. Biophys J 2009; 96:1333-40. [PMID: 19217851 DOI: 10.1016/j.bpj.2008.11.030] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2008] [Accepted: 11/13/2008] [Indexed: 10/21/2022] Open
Abstract
The effect of macromolecular crowding on the rates of association reactions are investigated using theory and computer simulations. Reactants and crowding agents are both hard spheres, and when two reactants collide they form product with a reaction probability, p(rxn). A value of p(rxn) < 1 crudely mimics the fact that proteins must be oriented properly for an association reaction to occur. The simulations show that the dependence of the reaction rate on the volume fraction of crowding agents varies with the reaction probability. For reaction probabilities close to unity where most of encounters between reactants lead to a reaction, the reaction rate always decreases as the volume fraction of crowding agents is increased due to the reduced diffusion coefficient of reactants. On the other hand, for very small reaction probabilities where, in most of encounters, the reaction does not occur, the reaction rate increases with the volume fraction of crowding agents--in this case, due to the increase probability of a recollision. The Smoluchowski theory refined with the radiation boundary condition and the radial distribution function at contact is in quantitative agreement with simulations for the reaction rate constant and allows the quantitative analysis of both effects separately.
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Affiliation(s)
- Jun Soo Kim
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin, Madison, Wisconsin, USA
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Sun J, Weinstein H. Toward realistic modeling of dynamic processes in cell signaling: quantification of macromolecular crowding effects. J Chem Phys 2007; 127:155105. [PMID: 17949221 DOI: 10.1063/1.2789434] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
One of the major factors distinguishing molecular processes in vivo from biochemical experiments in vitro is the effect of the environment produced by macromolecular crowding in the cell. To achieve a realistic modeling of processes in the living cell based on biochemical data, it becomes necessary, therefore, to consider such effects. We describe a protocol based on Brownian dynamics simulation to characterize and quantify the effect of various forms of crowding on diffusion and bimolecular association in a simple model of interacting hard spheres. We show that by combining the elastic collision method for hard spheres and the mean field approach for hydrodynamic interaction (HI), our simulations capture the correct dynamics of a monodisperse system. The contributions from excluded volume effect and HI to the crowding effect are thus quantified. The dependence of the results on size distribution of each component in the system is illustrated, and the approach is applied as well to the crowding effect on electrostatic-driven association in both neutral and charged environments; values for effective diffusion constants and association rates are obtained for the specific conditions. The results from our simulation approach can be used to improve the modeling of cell signaling processes without additional computational burdens.
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Affiliation(s)
- Jian Sun
- Department of Physiology and Biophysics, Weill Medical College, Cornell University, 1300 York Avenue, New York, New York 10021, USA
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Dzubiella J, McCammon JA. Substrate concentration dependence of the diffusion-controlled steady-state rate constant. J Chem Phys 2007; 122:184902. [PMID: 15918760 DOI: 10.1063/1.1887165] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B2*. Comparisons to Brownian dynamics simulations excluding hydrodynamic interactions show excellent agreement up to bulk number densities of B2*rho0 < approximately = 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.
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Affiliation(s)
- J Dzubiella
- NSF Center for Theoretical Biological Physics (CTBP), University of California, San Diego, La Jolla, California 92093-0365, USA.
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Ibuki K, Ueno M. Analysis of Short-Time Transient Dynamics of a Diffusion-Controlled Reaction in a Hard-Sphere Fluid Based on Fokker–Planck–Kramers Equation. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2006. [DOI: 10.1246/bcsj.79.1509] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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18
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Lee J, Yang S, Kim J, Lee S. An efficient molecular dynamics simulation method for calculating the diffusion-influenced reaction rates. J Chem Phys 2006; 120:7564-75. [PMID: 15267669 DOI: 10.1063/1.1687680] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a molecular dynamics (MD) simulation method for calculating the diffusion-influenced reaction rates in the limit of low reactant concentrations. To calculate the reaction rate coefficient, we use MD trajectories of a nonreactive equilibrium system that are initiated with a pair of reactant molecules in reactive configuration. Hence reaction systems involving complicated reactant molecules with geometrically restricted reactivities can be treated with comparable efficiency as the simple hard-sphere reaction system. Compared to the similar MD method proposed by Van Beijeren, Dong, and Bocquet [J. Chem. Phys. 114, 6265 (2001)], the present method has a couple of advantages. First, reactions involving more general sink functions can be treated. Second, more accurate results can be obtained when the reaction probability upon collision is less than unity. As an application, we investigate the effects of nondiffusive dynamics and hydrodynamic interaction of reactants on the reaction rate.
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Affiliation(s)
- Jinuk Lee
- School of Chemistry and Molecular Engineering, and Center for Molecular Catalysis, Seoul National University, Seoul 151-747, South Korea
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19
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Ibuki K, Ueno M. Application of Fokker-Planck-Kramers equation treatment for short-time dynamics of diffusion-controlled reaction in supercritical Lennard-Jones fluids over a wide density range. J Chem Phys 2006; 124:134506. [PMID: 16613460 DOI: 10.1063/1.2183769] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
The validity of a Fokker-Planck-Kramers equation (FPKE) treatment of the rate of diffusion-controlled reaction at short times [K. Ibuki and M. Ueno, J. Chem. Phys. 119, 7054 (2003)] is tested in a supercritical Lennard-Jones fluid over a wide density range by comparing it with the Langevin dynamics and molecular dynamics simulations and other theories. The density n range studied is 0.323n(c)< or =n< or =2.58n(c) and the temperature 1.52T(c), where n(c) and T(c) are the critical density and temperature, respectively. For the rate of bimolecular reactions, the transition between the collision-limited and diffusion-limited regimes is expected to take place in this density range. The simulations show that the rate constant decays with time extensively at high densities, and that the magnitude of decay decreases gradually with decreasing density. The decay profiles of the rate constants obtained by the simulations are reproduced reasonably well by the FPKE treatment in the whole density range studied if a continuous velocity distribution is used in solving the FPKE approximately. If a discontinuous velocity distribution is used instead of the continuous one, the FPKE treatment leads to a rate constant much larger than the simulation results at medium and low densities. The rate constants calculated from the Smoluchowski-Collins-Kimball (SCK) theory based on the diffusion equation are somewhat smaller than the simulation results in medium and low densities when the intrinsic rate constant is chosen to adjust the steady state rate constant in the low density limit to that derived by the kinetic collision theory. The discrepancy is relatively small, so that the SCK theory provides a useful guideline for a qualitative discussion of the density effect on the rate constant.
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Affiliation(s)
- Kazuyasu Ibuki
- Department of Molecular Science and Technology, Faculty of Engineering, Doshisha University, Kyo-Tanabe, Kyoto 610-0321, Japan.
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Litniewski M, Gorecki J. Molecular dynamics tests of the Smoluchowski–Collins–Kimball model for fluorescence quenching of spherical molecules. Phys Chem Chem Phys 2004. [DOI: 10.1039/b308680a] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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21
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Naumann W. Short-time kinetics of an irreversible bimolecular solution reaction: Asymptotic prediction by a non-Markovian Smoluchowski approach. J Chem Phys 2003. [DOI: 10.1063/1.1569472] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Ibuki K, Nishiguchi F, Ueno M. Improved Velocity Distribution Applied to Fokker–Planck–Kramers Equation Treatment for Dynamics of Diffusion-Controlled Reactions in Two Dimensions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2003. [DOI: 10.1246/bcsj.76.261] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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23
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Yang S, Han H, Lee S. An Efficient Brownian Dynamics Method for Evaluating Inertial Dynamic Effects on Diffusion-Influenced Reactions. J Phys Chem B 2001. [DOI: 10.1021/jp0102419] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Seongeun Yang
- School of Chemistry and Molecular Engineering, and Center for Molecular Catalysis, Seoul National University, Seoul 151-747, South Korea
| | - Heekyung Han
- School of Chemistry and Molecular Engineering, and Center for Molecular Catalysis, Seoul National University, Seoul 151-747, South Korea
| | - Sangyoub Lee
- School of Chemistry and Molecular Engineering, and Center for Molecular Catalysis, Seoul National University, Seoul 151-747, South Korea
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24
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Van Beijeren H, Dong W, Bocquet L. Diffusion-controlled reactions: A revisit of Noyes’ theory. J Chem Phys 2001. [DOI: 10.1063/1.1350642] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Ibuki K, Ueno M. Test of a Fokker-Planck-Kramers equation treatment for short-time dynamics of diffusion-controlled reactions by molecular dynamics simulation in Lennard-Jones fluids. J Mol Liq 2001. [DOI: 10.1016/s0167-7322(01)00130-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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26
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Lee J, Sung J, Lee S. Excluded volume effects on the diffusion-influenced reaction: The many-particle kernel approach. J Chem Phys 2000. [DOI: 10.1063/1.1318738] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Yang M, Lee S, Shin KJ. Kinetic theory of bimolecular reactions in liquid. I. Steady-state fluorescence quenching kinetics. J Chem Phys 1998. [DOI: 10.1063/1.475368] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Dong W. Long-time tail effect of the velocity correlation on diffusion-controlled reactions. J Chem Phys 1997. [DOI: 10.1063/1.475286] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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30
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Ibuki K, Ueno M. Effect of potential of mean force on short-time dynamics of a diffusion-controlled reaction in a hard-sphere fluid. J Chem Phys 1997. [DOI: 10.1063/1.474902] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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31
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32
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Ibuki K, Ueno M. Improved treatment of inertia and non-Markovian effects on short-time dynamics of diffusion-controlled reaction based on generalized diffusion equation. J Chem Phys 1997. [DOI: 10.1063/1.474045] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Song TT, Hwang YS, Su TM. Recombination Reactions of Atomic Chlorine in Compressed Gases. 3. Molecular Dynamics and Smoluchowski Equation Studies with Argon Pressure up to 6 kbar. J Phys Chem A 1997. [DOI: 10.1021/jp962305z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- T.-T. Song
- Department of Chemistry, National Taiwan University, Taipei, Taiwan, R. O. C., and The Institute of the Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan, R. O. C
| | - Y.-S. Hwang
- Department of Chemistry, National Taiwan University, Taipei, Taiwan, R. O. C., and The Institute of the Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan, R. O. C
| | - T.-M. Su
- Department of Chemistry, National Taiwan University, Taipei, Taiwan, R. O. C., and The Institute of the Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan, R. O. C
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34
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Bandyopadhyay T. Electronic excitation transfer in Lennard-Jones fluid: Comparison between approaches based on molecular dynamics simulation and the many-body Smoluchowski equation. J Chem Phys 1997. [DOI: 10.1063/1.473897] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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35
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Ibuki K, Ueno M. A Generalized Fokker–Planck Equation Treatment of Inertia and Non-Markovian Effects on the Short-Time Dynamics of a Collision-Induced Reaction. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1997. [DOI: 10.1246/bcsj.70.543] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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36
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Maciejewski A, Sikorski M, Augustyniak W, Fidecka M. The quenching of short-lived S2 states of aromatic thioketones by hydrocarbons. I. Important contributions of the transient effect from steady-state measurements. J Photochem Photobiol A Chem 1996. [DOI: 10.1016/1010-6030(95)04199-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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37
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Bandyopadhyay T. Light intensity effects on diffusion‐influenced fluorescence quenching in a hard‐sphere liquid: Molecular dynamics simulation and the many‐body Smoluchowski equation approach. J Chem Phys 1995. [DOI: 10.1063/1.468771] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Dong W, Andre JC. Diffusion‐controlled reactions. II. An approach based on a generalized diffusion equation. J Chem Phys 1994. [DOI: 10.1063/1.468183] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Zhou H, Szabo A. Comparison between molecular dynamics simulations and the Smoluchowski theory of reactions in a hard‐sphere liquid. J Chem Phys 1991. [DOI: 10.1063/1.461616] [Citation(s) in RCA: 63] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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