Mapping potential energy surfaces

Journal of Chemical Physics

Volumn 121, Issue 3, 2004, Pages 1193-1200

  Wu, Yudong ^a   Schmitt, Jeffrey D ^b   Car, Roberto ^a  

^a PRINCETON UNIVERSITY   (United States)

^b TARGACEPT INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE-GRAINED SPACE; FREE ENERGY SURFACES; NON-MARKOVIAN DYNAMICS; POTENTIAL ENERGY SURFACE (PES);

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONFORMATIONS; CONSTRAINT THEORY; FREE ENERGY; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MONTE CARLO METHODS; POTENTIAL ENERGY; SURFACE PROPERTIES;

MOLECULAR DYNAMICS;

EID: 3242880241     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1765651     Document Type: Article

References (20)

1. H. Eyring and A. E. Stem, Chem. Rev. (Washington, D.C.) 24, 2 (1939).
2. G. Torre and J. Valleau, J. Comput. Phys. 23, 187 (1977).
3. H. Grubmüller, Phys. Rev. E 52, 2893 (1995).
4. A. F. Voter, J. Chem. Phys. 106, 4665 (1997).
5. A. F. Voter, Phys. Rev. Lett. 78, 3908 (1997).
6. A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002).
7. C. W. Gear, I. G. Kevrekidis, and C. Theodoropoulos, Comput. Chem. Eng. 26, 941 (2002).
8. R. Martoňák, A. Laio, and M. Parrinello, Phys. Rev. Lett. 90, 075503 (2003).
9. The LP approach requires only knowledge of the local gradient on the PES and therefore we only compare it with unbiased approaches that are strictly force based. The fact that the method needs only the local gradient and not the Hessian is an important advantage when dealing with descriptions of the PES, like, e.g., the one given by density functional theory, where first derivatives are readily available but second derivatives are not. An efficient scheme to find transition states, based on local gradients only, is the dimer method [G. Henkelman and H. Jonsson, J. Chem. Phys. 111, 7010 (1999)]. This scheme, however, does not necessarily find the lowest transition state(s), nor does it provide a global interpolation of the PES. We do not make comparison with the dimer method here.
10. E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989).
11. The LP method is especially efficient to explore basins of the PES that are located near the starting configuration. For instance, in Ref. 8 the method is used to find phase transitions. A few important phases are rapidly sampled but the entire space is not.
12. For example, in Fig. 1 of Ref. 6, a model ID potential is constructed to show the evolution of the total energy surface as the number of metady-namics steps increases. After 320 steps of metadynamics, all three local minima are filled and the total potential, given by the sum of the energy surface and the bias potential, becomes flat in most regions.
13. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
14. D. E. Elmore and D. A. Dougherty, J. Org. Chem. 65, 742 (2000).
15. W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, Jr., D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, and P. A. Kollman, J. Am. Chem. Soc. 117, 5179 (1995).
16. For a general introduction to Monte Carlo methods, please see, e.g., M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley, New York, 1986), Vol. I.
17. S. Nose, Mol. Phys. 52, 256 (1984); S. Nose, J. Chem. Phys. 81, 511 (1984).
18. S. Nose, Mol. Phys. 52, 256 (1984); S. Nose, J. Chem. Phys. 81, 511 (1984).
19. G. Henkelman, B. P. Uberuaga, and H. Jonsson, J. Chem. Phys. 113, 9901 (2000).
20. W. E. W. Ren and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002).