Response to Comment on a proposed method for finding barrier height distributions [J. Chem. Phys. 103,

Response to ‘‘Comment on a proposed method for finding barrier heightdistributions’’[J. Chem. Phys. 103, 1235 (1995)]John E. Straub and T. KeyesDepartmentofChemistry,BostonUniversity,Boston,Massachusetts02215D. ThirumalaiDepartmentofChemistryandBiochemistry,InstituteforPhysicalScienceandTechnology,UniversityofMaryland,CollegePark,Maryland20742~Received 19 January 1995; accepted 11April 1995!Several systems, such as proteins and glasses, are char- We choose a one-dimensional rough potential of a form9acterized by a complex potential energy surface, i.e., there originally studied by Zwanzig:are many minima that are separated by barriers of differing 2V~x!5x /21e cos~qx!. ~1!1–3heights spanning the entire gamut of energy scales. ForThispotentialconsistsofaquadratic‘‘background’’potentialthese systems, it is meaningful to characterize the distribu-which varies slowly compared with the sinusoidal ‘‘rough-tion of energy barriers,g(E), which is notoriously very dif-ness.’’ An effective Smoluchowski equation was proposedficult to compute. In several papers, we have proposed andfor coarse grained motion ~on the length scale greater thandeveloped related methods for calculation of g(E) from the1/q! which leads to the correct mean first passage time. Attemperature-dependent fraction f (T) of unstable ‘‘instanta-ulow temperatures, the effective diffusion constant is reduced4neous normal modes.’’We have obtained g(E) in peptidesfrom the original by an Arrhenius-like ...