Free-energy calculations - Theoretical Biophysics Group
Free-energy calculations - Theoretical Biophysics Group
Free-energy calculations - Theoretical Biophysics Group
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Reaction coordinate–based free-<strong>energy</strong> <strong>calculations</strong> A backdrop on potential of mean force <strong>calculations</strong><br />
Back transformation into Cartesian coordinates:<br />
dA(ξ)<br />
dξ<br />
= − 1<br />
<br />
1<br />
exp[−βU(x)] δ[ξ(x) − ξ]<br />
β Pξ<br />
<br />
× −β ∂U(x)<br />
<br />
1 ∂|J|<br />
+ dx<br />
∂ξ |J| ∂ξ<br />
The derivative of the free <strong>energy</strong> with respect to the order parameter may be expressed as a<br />
sum of configurational averages at constant ξ: 50<br />
50 CARTER ET AL. (1989); CHIPOT, POHORILLE (2007)<br />
dA(ξ)<br />
dξ =<br />
<br />
∂U(x)<br />
−<br />
∂ξ ξ<br />
1<br />
<br />
∂ ln |J|<br />
:= −〈Fξ〉ξ<br />
β ∂ξ ξ<br />
Chris Chipot <strong>Free</strong>-<strong>energy</strong> <strong>calculations</strong>
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