Solvation free energy difference of alchemical transformation of K+ into Na+

From: Abhishek Kumar Singh (
Date: Tue Jan 10 2017 - 05:09:01 CST


I have alchemically transformed K+ to Na+ at the center of water boxes (40,
60 and 80 A edge length respectively) using NAMD software and CHARMM36
forcefield. A harmonic spring of force constant = 10 kcal/mol.A^-2 has been
applied throughout the transformation. Temp and Pressure has been kept at
310K and 1 atm respectively.
Free energy of alchemical transformation has been calculated using
thermodynamic integaration. The derivative has been computed as (∂G/∂λ) = ⟨
U(λ=1)- U)(λ=0) ⟩λ, where λ is the coupling parameter such that λ=1 and λ=0
are K+ and Na+ vdw parameters respectively. Free energy derivatives has
been computed for 11 λvdw values ( 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3,
0.2, 0.1 and 0.0). The area under the plot (derivate vs λ) gives me = -23.40,
-23.46 and -23.4
 kcal/mol for the box sizes of 40A, 60A and 80A respectively. I am
attaching alongwith the derivate vsλ values for 40A water box.

The standard CHARMM36 prm file actually states that the value should be
-18.6 kcal/mol.
So what can be reason for this difference. Is there any problem in this
procedure ?
Your suggestions are most welcome.


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