Correction to “Free Energy Reconstruction in Bidirectional Force

Chem. B , 2016, 120 (28), pp 7037–7037. DOI: 10.1021/acs.jpcb.6b06166. Publication Date (Web): July 7, 2016. Copyright © 2016 American Chemical Soc...
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Addition/Correction pubs.acs.org/JPCB

Correction to “Free Energy Reconstruction in Bidirectional Force Spectroscopy Experiments: The Effect of the Device Stiffness” Simone Marsili and Piero Procacci* J. Phys. Chem. B 2010, 114 (7), 2509−16. DOI: 10.1021/jp908663z In eq 7 there is a missing term in the logarithm argument. The free energy profile Gm(r) of the system should be defined with respect to an immaterial reference distance r* as ⎛ Z (r ) ⎞ Gm(r ) = −kBT ln⎜ m ⎟ ⎝ Zm(r*) ⎠

(1)

−βH(x)

where Zm(r) = ∫ e δ[r − r(x)] dx. Equation 6 can be thus worked out as follows: P(r |λ) =

∫ e−β{H(x) + V [r(x) − λ]}δ[r − r(x)] dx

= e βG(λ)

Z(λ )

∫ e−βH(x)e−βV [r(x) − λ)]δ[r − r(x)] dx

Zm(r ) * βG(λ) −βV (r − λ) Zm(r ) e =e Zm(r ) * Zm(r ) * = e βG(λ)e−βV (r − λ)e−βGm(r)Zm(r ) *

Zm(r ) *

(2)

Equation 7 must be therefore corrected as P(r |λ) Zm(r ) (3) * When free energy dif ferences are evaluated with eq 3 (as done in eq 14), the Zm(r*) term cancels out so that the results in the paper are unaffected by the correction. G(λ) = Gm(r ) + V (r − λ) + kBT ln

Published: July 7, 2016 © 2016 American Chemical Society

7037

DOI: 10.1021/acs.jpcb.6b06166 J. Phys. Chem. B 2016, 120, 7037−7037