The string method page

Publications

Zero temperature string method (ZTS) to compute minimum energy paths (MEPs)

String method for the study of rare events , W. E, W. Ren, and E.~Vanden-Eijnden, Phys. Rev. B: 66, 052301 (2002).
Simplified and improved string method for computing the minimum energy paths in barrier-crossing events. , W. E, W. Ren, and E. Vanden-Eijnden J. Chem. Phys.: 126,164103 (2007).

Zero temperature string method in collective variable space to compute minimum free energy paths (MFEPs)

String method in collective variables: Minimum free energy paths and isocommittor surfaces, L. Maragliano, A. Fischer, E. Vanden-Eijnden, and G. Ciccotti J. Chem. Phys.: 125,024106 (2006).
On-the-fly string method for minimum free energy paths calculation , L. Maragliano and E. Vanden-Eijnden Chem. Phys. Lett.: 446,182-190 (2007).

Finite temperature string method (FTS)

Finite temperature string method for the study of rare events W. E, W. Ren, and E. Vanden-Eijnden J. Phys. Chem. B: 109,6688-6693(2005).
Transition pathways in complex systems: Reaction coordinates, isocommittor surfaces, and transition tubes. , W. E, W. Ren, and E. Vanden-Eijnden Chem. Phys. Lett.: 413, 242-247 (2005).
Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide. , W. Ren, E. Vanden-Eijnden, P. Maragakis, and W. E J. Chem. Phys.: 123,134109 (2005).
Revisiting the finite temperature string method for the calculation of reaction tubes and free energies , E. Vanden-Eijnden and M. Venturoli J. Chem. Phys.: 130,194103 (2009).

Examples

The movies below show the evolution of the string on the Mueller potential using the zero-temperature string method (ZTS - top movie); and the evolution of the string on a rugged version of the Mueller potential using the finite-temperature string method (FTS - bottom movie). In both cases, there are 10 images along the string.

ZTS converges to the minimum energy path (MEP), which is the transition path of maximum likelihood at zero-temperature; FTS samples the transition tube at finite temperature.

The Matlab code illustrating the zero temperature string method (ZTS) on the Mueller potential can be downloaded from here.

The Matlab code illustrating the finite temperature string method (FTS) on the rugged Mueller potential can be downloaded from here.