- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Minimizing thermodynamic length to select intermediate states for free-energy calculations and replica-exchange simulations

Daniel K. Shenfeld1, Huafeng Xu1, Michael P. Eastwood1, Ron O. Dror1, and David E. Shaw1,2,*

  • 1D. E. Shaw Research, New York, New York 10036, USA
  • 2Center for Computational Biology and Bioinformatics, Columbia University, New York, New York 10032, USA

  • *Author to whom correspondence should be addressed. David.Shaw@DEShawResearch.com
PDF

Phys. Rev. E 80, 046705 – Published 19 October, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.046705

Abstract

In computational thermodynamics, a sequence of intermediate states is commonly introduced to connect two equilibrium states. We consider two cases where the choice of intermediate states is particularly important: minimizing statistical error in free-energy difference calculations and maximizing average acceptance probabilities in replica-exchange simulations. We derive bounds for these quantities in terms of the thermodynamic distance between the intermediates, and show that in both cases the intermediates should be chosen as equidistant points along a geodesic connecting the end states.

View figure in article

Corrections

22 October, 2009

Erratum

Publisher's Note: Minimizing thermodynamic length to select intermediate states for free-energy calculations and replica-exchange simulations [Phys. Rev. E 80, 046705 (2009)]

Daniel K. Shenfeld, Huafeng Xu, Michael P. Eastwood, Ron O. Dror, and David E. Shaw
Phys. Rev. E 80, 049904 (2009)

Article Text

References (23)

  1. P. Kollman, Chem. Rev. (Washington, D.C.) 93, 2395 (1993).
  2. C. H. Bennett, J. Comput. Phys. 22, 245 (1976).
  3. M. R. Shirts, E. Bair, G. Hooker, and V. S. Pande, Phys. Rev. Lett. 91, 140601 (2003).
  4. D. A. Pearlman and P. A. Kollman, J. Chem. Phys. 90, 2460 (1989).
  5. N. Lu and D. A. Kofke, J. Chem. Phys. 111, 4414 (1999).
  6. R. J. Radmer and P. A. Kollman, J. Comput. Chem. 18, 902 (1997).
  7. D. Wu and D. A. Kofke, J. Chem. Phys. 123, 084109 (2005).
  8. C. J. Geyer, in Computing Science and Statistics Proceedings of the 23rd Symposium on the Interface (American Statistical Association, New York, 1991), pp. 156–163.
  9. Y. Sugita, A. Kitao, and Y. Okamoto, J. Chem. Phys. 113, 6042 (2000).
  10. H. Fukunishi, O. Watanabe, and S. Takada, J. Chem. Phys. 116, 9058 (2002).
  11. R. Affentranger, I. Tavernelli, and E. E. D. Iorio, J. Chem. Theory Comput. 2, 217 (2006).
  12. D. J. Earl and M. W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005).
  13. D. A. Kofke, J. Chem. Phys. 117, 6911 (2002).
  14. C. Predescu, M. Predescu, and C. V. Ciobanu, J. Chem. Phys. 120, 4119 (2004).
  15. A. Kone and D. A. Kofke, J. Chem. Phys. 122, 206101 (2005).
  16. N. Rathore, M. Chopra, and J. J. de Pablo, J. Chem. Phys. 122, 024111 (2005).
  17. C. Predescu, M. Predescu, and C. V. Ciobanu, J. Phys. Chem. B 109, 4189 (2005).
  18. W. Nadler and U. H. E. Hansmann, Phys. Rev. E 76, 065701(R) (2007).
  19. F. Weinhold, J. Chem. Phys. 63, 2479 (1975).
  20. P. Salamon and R. S. Berry, Phys. Rev. Lett. 51, 1127 (1983).
  21. G. E. Crooks, Phys. Rev. Lett. 99, 100602 (2007).
  22. S.-I. Amari, Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics Vol. 28 (Springer-Verlag, Berlin, Heidelberg, 1985).
  23. H. G. Katzgraber, S. Trebst, D. A. Huse, and M. Troyer, J. Stat. Mech.: Theory Exp. (2006) P03018.

Outline

Information

Phys. Rev. E 80, 046705– Published 19 October, 2009
  • Received 1 July 2009
  • Corrected 22 October 2009
Creative Commons Logo

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation