We consider an implementation of umbrella sampling in which the pertinent range of states is subdivided into small windows that are sampled consecutively and linked together. This allows us to simulate without a weight function or to extrapolate the results to the neighboring window in order to estimate a weight function. Additionally, we present a detailed error analysis in which we demonstrate that the error in umbrella sampling is controlled and, in the absence of sampling difficulties, independent of the window sizes. In this case, the efficiency of our implementation is comparable to a multicanonical simulation with a very good weight function, which in our scheme does not need to be known ahead of time. The analysis also allows us to detect sampling difficulties such as correlations between adjacent windows and provides a test of equilibration. We exemplify the scheme by simulating the liquid–vapor coexistence in a Lennard-Jones system.
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15 June 2004
Research Article|
June 15 2004
Calculation of free energy through successive umbrella sampling
J. Chem. Phys. 120, 10925–10930 (2004)
Article history
Received:
October 23 2003
Accepted:
March 18 2004
Citation
Peter VirnauMarcus Müller; Calculation of free energy through successive umbrella sampling. J. Chem. Phys. 15 June 2004; 120 (23): 10925–10930. https://doi.org/10.1063/1.1739216
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