Abstract
The reaction rate in a condensed phase is retarded by solvent friction and deviates from the transition state theory (TST) in a highly viscous solvent. The Z/E isomerization kinetics of 4-dimethylamino-4′-nitroazobenzene in solution have been experimentally analyzed in a wide range of pressure in our previous studies. Herein the non-TST behaviors of the rate constant were theoretically modelled by means of Kramers’ theory and its extensions and by molecular dynamics (MD) simulations. The Z/E isomerization takes place in milliseconds or longer and so is not reachable by normal MD simulations. The accelerated MD method was employed to simulate the rare events using a biased isomerization potential barrier.
Similar content being viewed by others
References
Schröder, J., Troe, J.: Elementary reactions in the gas–liquid transition range. Ann. Rev. Phys. Chem. 38, 163–190 (1987)
Asano, T., Furuta, H., Sumi, H.: Two-step mechanism in single-step isomerizations. Kinetics in a highly viscous liquid phase. J. Am. Chem. Soc. 116, 5545–5550 (1994)
Cosstick, K., Asano, T., Ohno, N.: Pressure effects on thermal isomerizations in highly viscous media. The first clear-cut example of viscosity-induced retardation of “slow” thermal reactions. High Press. Res. 11, 37–54 (1993)
Asano, T., Furuta, H., Hofmann, H.-J., Cimiraglia, R., Tsuno, Y., Fujio, M.: Mechanism of thermal Z/E isomerization of substituted N-benzylideneanilines. Nature of the activated complex with an sp-hybridized nitrogen atom. J. Org. Chem. 58, 4418–4423 (1993)
Sumi, H., Asano, T.: Is isomerization in highly viscous solvents under pressure understandable with the idea of frequency-dependent friction? Chem. Phys. Lett. 240, 125–129 (1995)
Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)
Hänggi, P., Talkner, P., Borkovec, M.: Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990)
Northrup, S.H., Hynes, J.T.: Short range caging effects for reactions in solution. I. Reaction rate constants and short range caging picture. J. Chem. Phys. 71, 871–883 (1979)
Go, N., Taketomi, H.: Respective roles of short- and long-range interactions in protein folding. Proc. Natl. Acad. Sci. USA 75, 559–563 (1978)
Grubmüller, H.: Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys. Rev. E 52, 2893–2906 (1995)
Voter, A.F.: A method for accelerating the molecular dynamics simulation of infrequent events. J. Chem. Phys. 106, 4665–4677 (1997)
Hamelberg, D., Mongan, J., McCammon, J.A.: Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. J. Chem. Phys. 120, 11919–11929 (2004)
Case, D.A., Darden, T.A., Cheatham III, T.E., Simmerling, C.L., Wang, J., Duke, R.E., Luo, R., Walker, R.C., Zhang, W., Merz, K.M., Roberts, B., Hayik, S., Roitberg, A., Seabra, G., Swails, J., Goetz, A.W., Kolossváry, I., Wong, K.F., Paesani, F., Vanicek, J., Wolf, R.M., Liu, J., Wu, X., Brozell, S.R., Steinbrecher, T., Gohlke, H., Cai, Q., Ye, X., Wang, J., Hsieh, M.-J., Cui, G., Roe, D.R., Mathews, D.H., Seetin, M.G., Salomon-Ferrer, R., Sagui, C., Babin, V., Luchko, T., Gusarov, S., Kovalenko, A., Kollman, P.A.: AMBER 12. University of California, San Francisco (2012)
Pierce, L.C.T., Salomon-Ferrer, R., de Oliveira, C.A.F., McCammon, J.A., Walker, E.C.: Routine access to millisecond time scale events with accelerated molecular dynamics. J. Chem. Theory Comp. 8, 2997–3002 (2012)
Asano, T., Crosstick, K., Furuta, H., Matsuo, K., Sumi, H.: Effects of solvent fluctuations on the rate of thermal Z/E isomerization of azobenzenes and N-benzylideneanilines. Bull. Chem. Soc. Jpn. 69, 551–560 (1996)
Asano, T., Matsuo, K., Sumi, H.: Effects of solvent fluctuations on the rate of the thermal Z/E isomerization of N-benzylideneanilines in a highly viscous liquid hydrocarbon. Bull. Chem. Soc. Jpn. 70, 239–244 (1997)
Asano, T., Okada, T.: Further kinetic evidence for the competitive rotational and inversional Z-E isomerization of substituted azobenzenes. J. Org. Chem. 51, 4454–4458 (1986)
Kono, H., Ohga, Y., Asano, T.: Dynamic solvent effects on the fading of a merocyanine formed from a spironaphthoxazine. A case of a strong coupling between chemical and medium coordinate. Phys. Chem. Chem. Phys. 6, 2260–2266 (2004)
Goto, Y., Takahashi, T., Ohga, Y., Asano, T., Hildebrand, M., Weinberg, N.: Dynamic solvent effects on the thermal cyclization of a hexadienone formed from a diphenylnaphthopyran: an example of a system with distinctly separate medium and chemical contributions to the overall reaction coordinate. Phys. Chem. Chem. Phys. 5, 1825–1830 (2003)
Pollak, E.: Classical and quantum rate theory for condensed phases. In: Schwartz, S.D. (ed.) Theoretical Methods in Condensed Phase Chemistry, pp. 1–46. Kluwer Academnic Publishers, Dordrecht (2000)
Grote, R.F., Hynes, J.T.: Reactive modes in condensed phase reactions. J. Chem. Phys. 74, 4465–4475 (1981)
Pollak, E., Grabert, H., Hänggi, P.: Theory of activated rate processes for arbitrary frequency dependent friction: solution of the turnover problem. J. Chem. Phys. 91, 4073–4087 (1989)
Tucker, S., Tuckerman, M., Berne, B., Pollak, E.: Comparison of rate theories for generalized Langevin dynamics. J. Chem. Phys. 95, 5809–5826 (1991)
Xin, Y., Doshi, U., Hamelberg, D.: Examining the limits of time reweighting and Kramers’ rate theory to obtain correct kinetics from accelerated molecular dynamics. J. Chem. Phys. 132, 224101 (2010)
Doshi, U., Hamelberg, D.: Extracting realistic kinetics of rare activated processes from accelerated molecular dynamics using Kramers’ theory. J. Chem. Theor. Comp. 7, 575–581 (2011)
Hamelberg, D., Shen, T., McCammon, J.A.: Examining the limits of time reweighting and Kramers’ rate theory to obtain correct kinetics from accelerated molecular dynamics. J. Chem. Phys. 122, 241103 (2005)
Basilevsky, M.V., Ryaboy, V.M., Weinberg, N.N.: Kinetics of chemical reactions in condensed media in the framework of the two-dimensional stochastic model. J. Phys. Chem. 94, 8734–8740 (1990)
Agmon, N., Hopfield, J.J.: Transient kinetics of chemical reactions with bounded diffusion perpendicular to the reaction coordinate: intramolecular processes with slow conformational changes. J. Chem. Phys. 78, 6947–6959 (1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shigemitsu, Y., Ohga, Y. Accelerated Molecular Dynamics Study of Z/E Isomerization of Azobenzene: Kramers’ Theory Validation. J Solution Chem 43, 1746–1754 (2014). https://doi.org/10.1007/s10953-014-0237-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10953-014-0237-5