I have a reaction where a gas at high pressure and a solution with all kinds of species is involved. How do I take pressure correctly into account to get reasonable values for $G$?

Do I calculate thermochemical corrections at the given temperature and pressure (frequency calculations) and then add additional corrections for concentration ($\Delta G = RT ln(p)$, where $p$ is (partial) pressure or mole fraction)? Or should I calculate the thermochemical corrections at the given temperature, but standard pressure? For the additional term, should I use the overall pressure of the gas, and the mole fraction of the species in solution, or should I check for the solubility of the gas at given temperature and pressure in the solvent?

Usually, I would approach it this way:

Geometry optimization at lower level of theory, then computation of $G$ as the sum of:

1 single point energy at higher level

2 $G$ thermodynamic corrections (at 298.15 K and 1 bar)

3 $G_{solv}$ corrections from COSMOtherm (at infinite dilution)

4 $\Delta G_p = RT ln(p)$, where $p$ is either the molar fraction of the compound in solution or the partial pressure in gas phase

This works quite well, however, I'm not sure how to adjust the different terms when dealing with non-standard conditions. I think that as only dissolved gas participates in the reaction, I should be interested in this as a reference point for $\Delta G_r$, etc., but with what temperature/pressure do I then calculate 2? And do I take the pressure of gas above the solution in 4 or the molar fraction of gas in solution?

  • $\begingroup$ I am not sure to understand in detail your question, can you expand a little more?. Normally standard thermodynamic functions in gas phase is what we trivially calculate, but if there is a strong interaction between molecules (different from chemical reaction) it can be not useful. $\endgroup$ – user1420303 Apr 6 '16 at 14:56
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    $\begingroup$ There are two complexities to this. 1. Determining the free energy of a pure component at a specified temperature and a high pressure beyond the ideal gas region and 2. Starting with the free energy of the pure components at the same total temperature and pressure and determining the free energy of the mixture. Are you familiar with the concept of fugacity? Do you know how to do the first step using dG=VdP at constant T. $\endgroup$ – Chet Miller Apr 6 '16 at 19:45
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    $\begingroup$ I tried to clarify the problem - does that help? It's true that strong interactions between the molecules have an impact, especially at higher pressures/concentrations, but I think this can be neglected in my case. $\endgroup$ – snurden Apr 7 '16 at 6:57
  • $\begingroup$ That's a very interesting question. What about using a dynamical approach? $\endgroup$ – Felipe S. S. Schneider Jan 30 '17 at 15:45

If you want to calculate chemical equilibrium for the system, here's how to proceed. 1. Specify (make an assumption about) the list of chemical species present in the system. 2. For each species, either get from thermochemical tables (e.g., JANAF) or calculate the usual standard state ideal-gas chemical potentials at 1 bar from QM. 3. Either use existing or develop force fields (FFs) for the system species (first in pure species form and then use a combining rule for the interspecies FFs) 4. Calculate reaction equilibrium among the species using the Reaction Ensemble Monte Carlo algorithm (W.R. Smith and B. Triska, JCP 100, 3019-3027 (1994), DOI:10.1063/1.466443; Molec. Simulation, 34(2), 119-146 (2008) DOI: 10.1080/08927020801986564

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    $\begingroup$ This doesn't answer the OP's query. You might want to amend your answer to address the question. $\endgroup$ – Todd Minehardt Apr 7 '16 at 18:18
  • $\begingroup$ I assumed that a constraint was that system be at equilibrium, in which case G(T,P) is at a minimum. If not, then the usual expressions for G=\sum mu_i*n_i would be used. This requires the chemical potentials to be calculated at a given composition, which arise from mu_i = mu_i(IG) + mu_i(ex). The latter requires either an equation of state or excess chemical potential simulations. $\endgroup$ – WRSmithGuelph Apr 7 '16 at 21:50

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