Blue Moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics

Giovanni Ciccotti, Raymond Kapral, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. [Mol. Phys. 1997, 90, 925] for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic dynamics which, unlike the usual constrained molecular dynamics, introduces no bias. Finally, we give a new perspective on bias removal by using constrained molecular dynamics.

Original languageEnglish (US)
Pages (from-to)1809-1814
Number of pages6
Issue number9
StatePublished - Sep 5 2005


  • Blue Moon sampling
  • Constrained stochastics dynamics
  • Free energy
  • Mean force
  • Reaction coordinates

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry


Dive into the research topics of 'Blue Moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics'. Together they form a unique fingerprint.

Cite this