When should we use explicit solvent molecules in QM calculations?

Recently I have talked with several people about the use of explicit solvent molecules in QM calculations. I will summarize my personal thoughts here, it might be not fully correct, or even might be completely wrong. So any comments are welcome via the email in the left side bar.

Ok, what is the short answer from me? I might say it’s “I do not know” as clearly it’s very system-dependent, using explicit solvent molecules might be very helpful for some reactions while might be trivial for some calculations. Here I want to separate my thoughts into two parts: calculations of chemical properties and calculations of reactions.

Properties (pKa, Redox Potential, etc)

For the calculations of the chemical properties including pKa, redox potential and so on. What matters is the contribution from the solvation free energy, i.e., the polarity of the molecule is usually not much changed, so the explicit interactions between solute and solvent can be expected to be cancelled out largely. In quantum chemistry, people use the implicit solvent models with QM methods (usually DFT methods because it’s relatively cheap). For the correct calculations of the solvation free energies within the framework of implicit solvent models, this comment 2010 JPCA paper is a good material to read.

So what’s the core message of the above paper, I think it’s using the implicit solvent models as how they were designed. Beacuse of the parameterization, sometimes explaining things physically becomes hard. For example, for the SMD model, if we check the original parameterization, we can see for most molecules, explicit solvent molecules are not included explicitly but the solvation free energy of it are reproduced via tuning other parameters. So when these tuned parameteres are fixed in computational softwares, then should we add the explicit solvent molecules?

It is a question I asked myself earlier and by doing pKa calculations of a broad set of molecules, I found using explicit solvent molecules for anions are pretty helpful but for cations and neutral species, it might be not helpful at all. For more details, you can read my 2019 JPCA paper. How does this happen? Actually I have to admit that I am not 100% sure but I think it’s related with the fact that the errors of anions are much larger than others. Another point is that many experimental solvation free energies in MNSOL data base used to develop SMD were obtained by reproducing the experimental pKa/redox values, thus how to use SMD correctly for redox potential/pKa is closely related with how SMD was originally developed to reproduce those experimental pKa/redox values.

I have not conducted tests for redox potential or other chemical properties but I think the same conclusion is expected.

Reactions

For chemical reactions, we still need to separate them into at least two classes. The first one is where explicit solvent molecules can work as a part of the reaction, for example, for some systems, water can work as a bridge for proton transfer. In this case, definitely you need to add solvent molecules in.

For other systems, the solvent is just solvent/medium, which means there’s no bonding breaking or forming itself. Then we might need to consider if the solute-solvent interactions are enough to change the kinectis of the reaction (for example, the reaction with a polar TS involved). This is not only related with the calculation of solvation free energy but more, i.e., even in gas-phase, when the solute-solvent interaction is large, it should be not ignored. Sometimes I think chemical intuition from experimental chemists are really helpful.

Summary & Directions Forward?

So a few points here:

(1) If you are using SMD to calculate pKa/redox potential, then the protocols we presented in my 2019 JPCA paper might be good one to follow;

(2) If you are using PCM or other solvation models to calculate pKa/redox potentials, then what I recommend is to find a set of molecules (with clearly defined experimental results) whose structures are pretty close with one you want to model and then test if using explicit solvent moelcules are helpful;

(3) For reactions without bond breaking/forming of solvent molecules, we recommend to use explicit solvent molecules with SMD model for the following cases:

reactions of anions;

reactions with polar TS involved where the solute-solvent interactions can help stablize the TS

reactions of open-shell species and charge-separate state, see here for some related content in the page of Prof. Wolfram Sander;

some reactions for which explicit solvent effects are widely known important, for example, the Diels-Alder reaction.

keep updating

For other cases, you can test but I think the effects might be small;

(4) The number of solvent molecules is another issue, I think having a convergence test might be necessary and system-dependent. It’s simiar with the tests on the size of QM region in QM/MM calculations. Modelling all molecules at QM level is not pratical while at which point to separate the QM and MM (or continuum medium for implicit solvent models) is a problem depending on the nature of the systems.

(5) The theoretical level is another factor needs to be considered, I suggested using different functional/basis set to see how the choice of theoretical level can affect the results.

I am planning to have a study about testing the effects of explicit solvent molecules in chemical reactions. The work might be pretty expensive if we intend to include as many chemical reactions types (at least those important ones) as possible. Another problem might be we do not have well-defined experimental activation barrier for many reactions in solution phase compared with the experimental pKa/redox potentials.

But clearly, we are at a stage where more details about solvation dynamics should be considered in reaction modelling. For example, the JACS paper of Prof. Daniel Singleton published recently is absolutely excellent one to read, especially for readers having a background of non-equilibrium solvation knowledge like me. I hope I can have a chance to explore this aspect in the future.