[gmx-users] Bennet error in FEP-calculations for charged ligands.

[Artem Shekhovtsov]

Hi all!
I encountered an error in my relative free energy calculations and do not
know how to fix it.
Molecules for which I want to carry out calculations contain a carboxyl
group.
To validate the protocol, I tried to run the fep-calculations of symmetric
molecules for which the change in free energy will be zero.
During validation, I was faced with the fact that the convergence error for
charged ligands greatly exceeds that for neutral ones.
For example, for the case of m-methyl benzoic acid [O-]C(= O)c1cc(C)ccc1:
Mutation (-CH3 + H) for one meta position (-H + CH3) for another meta
position relative to the carboxyl group.

Ionized acid (solvent leg, 5 ns):
point      0 -      1,   DG 28.74 +/-  0.02
point      1 -      2,   DG 53.79 +/-  0.41
point      2 -      3,   DG 27.76 +/-  2.45
point      3 -      4,   DG 18.51 +/-  2.95
point      4 -      5,   DG  8.80 +/-  0.79
point      5 -      6,   DG  4.04 +/-  0.07
point      6 -      7,   DG -0.06 +/-  0.04
point      7 -      8,   DG -2.62 +/-  0.33
point      8 -      9,   DG -8.95 +/-  0.27
point      9 -     10,   DG -23.89 +/-  1.61
point     10 -     11,   DG -29.32 +/-  1.29
point     11 -     12,   DG -54.15 +/-  0.08
point     12 -     13,   DG -28.79 +/-  0.03

total      0 -     13,   DG -6.12 +/-  3.19

Unionized acid (solvent leg, 5 ns):
point      0 -      1,   DG  0.08 +/-  0.01
point      1 -      2,   DG -6.88 +/-  0.10
point      2 -      3,   DG -14.69 +/-  0.05
point      3 -      4,   DG -21.07 +/-  0.03
point      4 -      5,   DG -13.21 +/-  0.02
point      5 -      6,   DG -7.46 +/-  0.02
point      6 -      7,   DG -0.09 +/-  0.03
point      7 -      8,   DG  7.37 +/-  0.02
point      8 -      9,   DG 13.24 +/-  0.03
point      9 -     10,   DG 21.15 +/-  0.06
point     10 -     11,   DG 14.72 +/-  0.03
point     11 -     12,   DG  6.98 +/-  0.07
point     12 -     13,   DG -0.05 +/-  0.01

total      0 -     13,   DG  0.09 +/-  0.22

For a neutral molecule containing a charged carboxyl and amino groups
([O-]C(=O)c1cc(C)c([NH3+])cc1) the error is small:
point      0 -      1,   DG -4.65 +/-  0.01
point      1 -      2,   DG -19.95 +/-  0.04
point      2 -      3,   DG -28.67 +/-  0.13
point      3 -      4,   DG -57.84 +/-  0.19
point      4 -      5,   DG -44.18 +/-  0.08
point      5 -      6,   DG -26.84 +/-  0.05
point      6 -      7,   DG  0.10 +/-  0.20
point      7 -      8,   DG 26.92 +/-  0.06
point      8 -      9,   DG 44.28 +/-  0.13
point      9 -     10,   DG 57.79 +/-  0.13
point     10 -     11,   DG 28.68 +/-  0.09
point     11 -     12,   DG 19.98 +/-  0.12
point     12 -     13,   DG  4.66 +/-  0.03

total      0 -     13,   DG  0.28 +/-  0.21

Adding Na and Cl ions to ([O-]C(=O)c1cc(C)c([NH3+])cc1) does not cause an
increase in error.
point      0 -      1,   DG -4.61 +/-  0.01
point      1 -      2,   DG -19.96 +/-  0.07
point      2 -      3,   DG -28.68 +/-  0.04
point      3 -      4,   DG -57.67 +/-  0.04
point      4 -      5,   DG -44.24 +/-  0.01
point      5 -      6,   DG -26.91 +/-  0.04
point      6 -      7,   DG  0.03 +/-  0.03
point      7 -      8,   DG 26.89 +/-  0.03
point      8 -      9,   DG 44.20 +/-  0.08
point      9 -     10,   DG 57.75 +/-  0.09
point     10 -     11,   DG 28.65 +/-  0.06
point     11 -     12,   DG 20.02 +/-  0.05
point     12 -     13,   DG  4.67 +/-  0.01

total      0 -     13,   DG  0.12 +/-  0.18

FEP-part of *.mdp:
free-energy               = yes
sc-power                  = 1
sc-alpha                  = 0.5
sc-coul                   = yes
fep-lambdas               = 0.0 0.01  0.05  0.1  0.2  0.3   0.4  0.6   0.7
0.8  0.9  0.95 0.99  1.0
coul-lambdas              = 0.0 0.01  0.05  0.1  0.2  0.3   0.4  0.6   0.7
0.8  0.9  0.95 0.99  1.0
vdw-lambdas               = 0.0 0.01  0.05  0.1  0.2  0.3   0.4  0.6   0.7
0.8  0.9  0.95 0.99  1.0

What is the reason of such error and how I can fix it?

mdp, itp, gro, xvg files by link -
https://drive.google.com/open?id=1MiepOQb2QAZ9rclpY13owCnl8QWcTHnf
Ready to provide any additional information.

Thank you,
Shekhovtsov Artem