Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1. N. Elsner, C. P. Royall, B. Vincent, and D. R. E. Snoswell, “Simple models for two-dimensional tunable colloidal crystals in rotating ac electric fields,” J. Chem. Phys. 130, 154901 (2009).
2. S. Jäger and S. H. L. Klapp, “Pattern formation of dipolar colloids in rotating fields: Layering and synchronization,” Soft Matter 7, 6606 (2011).
3. A. Prokop, J. Vacek, and J. Michl, “Friction in carborane-based molecular rotors driven by gas flow or electric field: Classical molecular dynamics,” ACS Nano 6, 19011914 (2012).
4. F. Ma, D. T. Wu, and N. Wu, “Formation of colloidal molecules induced by alternating-current electric fields,” J. Am. Chem. Soc. 135, 78397842 (2013).
5. P. Lidström, J. Tierney, B. Wathey, and J. Westman, “Microwave assisted organic synthesisa review,” Tetrahedron 57, 92259283 (2001).
6. K.-K. Ni, S. Ospelkaus, D. Wang, G. Quéméner, B. Neyenhuis, M. De Miranda, J. Bohn, J. Ye, and D. Jin, “Dipolar collisions of polar molecules in the quantum regime,” Nature (London) 464, 13241328 (2010).
7. Y. Zheng and F. L. H. Brown, “Single molecule counting statistics for systems with periodic driving,” J. Chem. Phys. 139, 164120 (2013).
8. W. H. Miller, “Beyond transition-state theory: A rigorous quantum theory of chemical reaction rates,” Acc. Chem. Res. 26, 174 (1993).
9. D. G. Truhlar, B. C. Garrett, and S. J. Klippenstein, “Current status of transition-state theory,” J. Phys. Chem. 100, 1277112800 (1996).
10. R. Hernandez, T. Bartsch, and T. Uzer, “Transition state theory in liquids beyond planar dividing surfaces,” Chem. Phys. 370, 270276 (2010).
11. R. G. Mullen, J.-E. Shea, and B. Peters, “Communication: An existence test for dividing surfaces without recrossing,” J. Chem. Phys. 140, 041104 (2014).
12. E. Pollak and P. Pechukas, “Transition states, trapped trajectories, and classical bound states embedded in the continuum,” J. Chem. Phys. 69, 1218 (1978).
13. P. Pechukas and E. Pollak, “Classical transition state theory is exact if the transition state is unique,” J. Chem. Phys. 71, 2062 (1979).
14. N. De Leon, M. A. Mehta, and R. Q. Topper, “Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory,” J. Chem. Phys. 94, 83108328 (1991).
15. T. Uzer, C. Jaffé, J. Palacián, P. Yanguas, and S. Wiggins, “The geometry of reaction dynamics,” Nonlinearity 15, 957 (2002).
16. G. S. Ezra, H. Waalkens, and S. Wiggins, “Microcanonical rates, gap times, and phase space dividing surfaces,” J. Chem. Phys. 130, 164118 (2009).
17. G. S. Ezra and S. Wiggins, “Phase-space geometry and reaction dynamics near index 2 saddles,” J. Phys. A 42, 205101 (2009).
18. H. Teramoto, M. Toda, and T. Komatsuzaki, “Dynamical switching of a reaction coordinate to carry the system through to a different product state at high energies,” Phys. Rev. Lett. 106, 054101 (2011).
19. A. Allahem and T. Bartsch, “Chaotic dynamics in multidimensional transition states,” J. Chem. Phys. 137, 214310 (2012).
20. C.-B. Li, A. Shoujiguchi, M. Toda, and T. Komatsuzaki, “Definability of no-return transition states in the high-energy regime above the reaction threshold,” Phys. Rev. Lett. 97, 028302 (2006).
21. H. Waalkens and S. Wiggins, “Direct construction of a dividing surface of minimal flux for multi-degree-of-freedom systems that cannot be recrossed,” J. Phys. A 37, L435L445 (2004).
22. U. Çiftçi and H. Waalkens, “Reaction dynamics through kinetic transition states,” Phys. Rev. Lett. 110, 233201 (2013).
23. J. Lehmann, P. Reimann, and P. Hänggi, “Surmounting oscillating barriers,” Phys. Rev. Lett. 84, 16391642 (2000).
24. J. Lehmann, P. Reimann, and P. Hänggi, “Surmounting oscillating barriers: Path-integral approach for weak noise,” Phys. Rev. E 62, 62826303 (2000).
25. J. Lehmann, P. Reimann, and P. Hänggi, “Activated escape over oscillating barriers: The case of many dimensions,” Phys. Status Solidi B 237, 5371 (2003).
26. R. S. Maier and D. L. Stein, “Noise-activated escape from a sloshing potential well,” Phys. Rev. Lett. 86, 39423945 (2001).
27. M. I. Dykman, B. Golding, and D. Ryvkine, “Critical exponent crossovers in escape near a bifurcation point,” Phys. Rev. Lett. 92, 080602 (2004).
28. M. I. Dykman and D. Ryvkine, “Activated escape of periodically modulated systems,” Phys. Rev. Lett. 94, 070602 (2005).
29. G. T. Craven, T. Bartsch, and R. Hernandez, “Persistence of transition state structure in chemical reactions driven by fields oscillating in time,” Phys. Rev. E 89, 040801R (2014).
30. A. E. Orel and W. H. Miller, “Collision induced absorption spectra for gas phase chemical reactions in a high power IR laser field,” J. Chem. Phys. 72, 51395144 (1980).
31. V. Y. Argonov and S. V. Prants, “Theory of dissipative chaotic atomic transport in an optical lattice,” Phys. Rev. A 78, 043413 (2008).
32. G. Orlandi, P. Palmieri, and G. Poggi, “An ab initio study of the cis-trans photoisomerization of stilbene,” J. Am. Chem. Soc. 101, 34923497 (1979).
33. D. H. Waldeck, “Photoisomerization dynamics of stilbenes,” Chem. Rev. 91, 415436 (1991).
34. J. Quenneville and T. J. Martínez, “Ab initio study of cis-trans photoisomerization in stilbene and ethylene,” J. Phys. Chem. A 107, 829837 (2003).
35. I. N. Levine, Physical Chemistry (McGraw-Hill, 2002).
36. L. P. Kadanoff and C. Tang, “Escape from strange repellers,” Proc. Natl. Acad. Sci. U.S.A. 81, 12761279 (1984).
37. R. T. Skodje and M. J. Davis, “Statistical rate theory for transient chemical species: Classical lifetimes from periodic orbits,” Chem. Phys. Lett. 175, 92100 (1990).
38. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, 1998), Vol. 9.
39. T. Bartsch, R. Hernandez, and T. Uzer, “Transition state in a noisy environment,” Phys. Rev. Lett. 95, 058301 (2005).
40. T. Bartsch, T. Uzer, and R. Hernandez, “Stochastic transition states: Reaction geometry amidst noise,” J. Chem. Phys. 123, 204102 (2005).
41. T. Bartsch, T. Uzer, J. M. Moix, and R. Hernandez, “Identifying reactive trajectories using a moving transition state,” J. Chem. Phys. 124, 244310 (2006).
42. F. Revuelta, T. Bartsch, R. M. Benito, and F. Borondo, “Communication: Transition state theory for dissipative systems without a dividing surface,” J. Chem. Phys. 136, 091102 (2012).
43. T. Bartsch, F. Revuelta, R. M. Benito, and F. Borondo, “Reaction rate calculation with time-dependent invariant manifolds,” J. Chem. Phys. 136, 224510 (2012).
44. S. Kawai, A. D. Bandrauk, C. Jaffé, T. Bartsch, J. Palacián, and T. Uzer, “Transition state theory for laser-driven reactions,” J. Chem. Phys. 126, 164306 (2007).
45. P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, and G. Vattay, Chaos: Classical and Quantum (Niels Bohr Institute, Copenhagen, 2012), see

Data & Media loading...


Article metrics loading...



When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product—for example, an energy barrier—becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition state. Specifically, strong agreement is observed between the difference in the Floquet exponents describing stability of the transition state trajectory, which defines a recrossing-free dividing surface [G. T. Craven, T. Bartsch, and R. Hernandez, “Persistence of transition state structure in chemical reactions driven by fields oscillating in time,” Phys. Rev. E , 040801(R) (2014)], and the rates calculated by simulation of ensembles of trajectories. This result opens the possibility to extract rates directly from the intrinsic stability of the transition state, even when it is time-dependent, without requiring a numerically expensive simulation of the long-time dynamics of a large ensemble of trajectories.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd