Hello,
I am doing umbrella sampling of a 20 mer poly(acrylic acid) chain
with the end-to-end distance as reaction coordinate.
Now, I computed the PMF using two approaches:
1) Computing the Force-Extension relation and integrate the curve
using the trapezoidal rule
2) Using the weighted histogram analysis method
I am getting two quite similar looking curves, but in case of WHAM, the free energy is about 28 kJ/mol larger compared to the PMF obtained via direct integration.
Can someone please say me, why this is the case?
Could it be, that the direct integration is an approximation and if yes, what is there approximated?
Best regards
The WHAM result should be more accurate. Integration methods introduce bias during integrating the partial derivatives while WHAM uses direct reweighting, which is in principle more accurate if your window spacing is fine.
I notice that the difference between free energy difference is quite huge in your case, 28 kJ/mol. Normally this indicates that there is something wrong with your implementation of the algorithm. The integration bias should not be such large.
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