[gmx-users] Solvation free energy and standard states

[Wang Ruixing]

Hello gmx-users,

I was trying to learn how to calculate solvation free energy using Gromacs and to relate the results to experimental values. I found multiple tutorials listed below:

  1.  http://www.gromacs.org/Documentation/Tutorials/Free_energy_of_solvation_tutorial
  2.  http://www.alchemistry.org/wiki/GROMACS_4.6_example:_Direct_ethanol_solvation_free_energy
  3.  http://www.mdtutorials.com/gmx/free_energy/

The tutorial 1 uses fep-lambda, which turns off electrostatic and vdw interactions simutaneously. The tutorial 2 uses both coul-lambda and vdw-lambda, turning off coulombic first and then followed by vdw interactions. The tutorial 3 seems assuming the coulombic part has been calculated already, and only use vdw-lambda to turn off vdw interactions.
Is it generally better to turn off electrostatic and vdw interactions separately as did in tutorial 2, and as oppose to tutorial 1?  For tutorial 3, as said above, does it mean the result obtained at the end (-9.13 kJ/mol) is not the solvation free energy of methane, since the electrostatic interaction is not considered?

Next, I want to relate the calculated solvation free energy with exeperimental air/water partition coefficients. Consider ethanol as an example, which is studied in tutorial 2.
I found the partition coefficient of ethanol in water from this paper<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1025.998&rep=rep1&type=pdf> (10.1093/jat/7.4.193). Its natural log (lnK) is 8.439 at 298.15 K. The solvation free energy can be calculated by dG=-RTlnK = -20.70 kJ/mol. Since the definition of partition coefficient uses concentration for both phases (that is, K=c(aq)/c(g) ), this dG should correspond to this process: Ethanol (1M,gas) -> Ethanol (1M,sol), where the standard state of gas phase is 1M instead of the usually used 1atm.
I also used QM to calculate the solvation free energy of ethanol (using Gaussian, SMD solvent model, M052X/6-31g(d) level). The result is -21.12 kJ/mol which is consistent with the above value. The standard state of gas phase is 1M in QM calculation (as pointed out in 10.1021/jp107136j). This could confirm that the dG calculated by partition coefficient indeed use 1M as the gas phase standard state.

The result from tutorial 2 is dG = -17.684kJ/mol using MBAR method. I believe the difference is due to different standard states, since apparently the process of the simulation is not 1M->1M. Theoretically, the dG of the equation Ethanol (1M,gas) -> Ethanol (1M,sol) represents the free energy change of moving 1 mole ethanol molecules from gas phase into solution phase, while the concentrations of both phases remain unchanged. However, the A->B states of the simulation are (1 ethanol in gas phase + pure water) -> (nothing in gas phase + 1 ethanol in water). It seems impossible not to change concentration of both phases during the simulation.. I have no idea how to convert the dG from simulation into standard states of 1M->1M. How should I do this?

Sorry for the long writing. I want to include more details and to make sure I'm not misunderstanding anything.

Any help would be appreciated. Thanks!


Best regards,
Ruixing Wang
Phd Student
University of Maryland