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I've just found this paper (J. Chem. Phys. 141, 174106 (2014)) that deals with the translational and rotational entropies in solution. The method is promising but, unfortunately, requires a modification in the frequency calculation that is not readily available on most quantum chemistry packages.

As such, my question is which methods explicitly calculate solvation contributions to free energies and how do they compare?

They naturally have something to do with a polarizable continuum (J. Phys. Chem. A 1998, 102, 11, 1995-2001), but which methods go beyond pure electrostatic/cavity/dispersion energies and deal with free energy in terms of entropies and enthalpies (as in the rigid rotor-harmonic oscillator approximation)? (I would rather avoid purely parameterized corrections as in, e.g., J. Phys. Chem. B 2009, 113, 18, 6378-6396.)

The problem of entropy

In terms of free energy contributions, one particularly significant contribution is entropy. Are there any readily available methods/theories for the rotational and translational contributions to enthalpy and entropy of solutes?

I am particularly interested in the fact that current successful methods (SMD, PCM, etc.) seem to adjust electronic energies using free energy terms, such as CPCM (which explicitly uses an equation derived by Pierotti from the hard-sphere theory for calculating the cavity free energy, J. Phys. Chem. A 1998, 102, 11, 1995-2001), or SMD (which uses purely parameterized terms that certainly include entropic contributions). As such, their temperature dependence likely wrong (or am I missing something?). This has been addressed in recent publications to some extent, such as in Catal. Sci. Technol., 2019,9, 5433-5440 and ACS Catal. 2019, 9, 8, 6803–6813.

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    $\begingroup$ I don't know this field very well, but I'm trying to clear up the un-answered queue. I know the COSMO method, do you think it's relevant here? $\endgroup$ Jun 16 '20 at 2:19
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    $\begingroup$ Are there two questions here? One of them is "which methods calculate the effect of solvents on free energies?" and the other one is "which methods provide translational and rotational contributions to solute free energies?" $\endgroup$ Jun 25 '20 at 17:33
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    $\begingroup$ I have now sent this question to a former colleague David Wilkins, who has worked much more in this area than I have. Let's hope you get an answer soon! $\endgroup$ Jun 26 '20 at 4:51
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    $\begingroup$ Just sent another reminder to Dave Wilkins, since I didn't receive an answer to my email on 26 June. Let's hope you get an answer. $\endgroup$ Jul 4 '20 at 14:02
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    $\begingroup$ Just throwing a couple of ideas out there: What about (i) doing a free energy perturbation or potential of mean force calculation as available in typical classical MD setups? For known salt systems in water, this is well studied and should result in decent results. (ii) Do a classical MD in explicit solvent for the solute of interest --> carve out solute core for QM --> run geometry optimization and frequency calculations. Of course do this over multiple snapshots from MD to capture averaged solvent effects. $\endgroup$
    – gogo
    Aug 14 '20 at 1:15
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Just throwing a couple of ideas out there:

(i) Perform a free energy perturbation or potential of mean force calculation as available in typical classical MD setups. For known salt systems in water, this is well studied and should result in decent results (e.g., Joung and Chaetham's paper).

(ii) Do a classical MD in explicit solvent for the solute of interest $\rightarrow$ carve out the solute core for QM $\rightarrow$ run geometry optimization and frequency calculations. Of course, do this over multiple snapshots from MD to capture averaged solvent effects

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    $\begingroup$ Haha, keep it coming ;) $\endgroup$
    – gogo
    Aug 14 '20 at 23:25

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