# What types of energies can be determined by molecular dynamics in gas phase or explicit solvents?

For molecular dynamics in the gas phase I've seen that electronic energy can be determined and also decomposed in kinetic and potential energy. I've also seen that we can include ZPE. But can we determine (changes in) $\Delta H$, $\Delta S$ and $\Delta G$?

And how about explicit solvent systems? In particular I'm interested if it's possible to determine the free energy of activation and the entropy of activation for reactions in explicit solvent systems. Is it possible to determine such energies for the whole system or even for only the reacting molecules (if that makes sense to do)?

To add: I'm talking about using QM (DFT) for the molecular dynamics. Not molecular mechanics.

## 1 Answer

First, whether you use DFT or molecular mechanics to get your energies and forces doesn't really matter. If you have equations of motion, forces, and energies then you have the dynamics necessary to sample an ensemble and from there you should be able to get any physical observable you desire.

It is often very difficult to determine free energy changes using straight up molecular dynamics. The reason for this is that even very fast reactions are rare events when compared to typical molecular motions such as vibrations and rotations. For this reason, many methods have been developed to determine free energies without having to run simulations long enough to get good sampling of reactions. Usually, this is not possible anyways.

First, you may wish to read about umbrella sampling. Umbrella sampling, as a general idea, does not sample a trajectory on the potential energy surface determined the potential energy of the system (your output from DFT if you like), but rather, a harmonic potential energy is added to the system as well. This has the effect of lifting the molecule out of the potential well it may be stuck in so that sampling of rare events like reactions becomes much more common.

It is not obvious at all that any physically meaningful quantities should be able to be derived from this new system where the potential energy is constantly being modified. Yet, surprisingly and rather beautifully, it is possible. You should probably see ref. [1] and the citations therein.

The second way to do this I will mention is so-called meta-dynamics. The conceptual idea here is to first define the so-called "collective variables" of the system. These are literally any variables which can be used to describe the properties of a system. Typically one would choose some set of internal coordinates, particularly for a gas-phase system as you describe. However, my understanding is that it is also possible to choose various other coordinates such as intermolecular distances. One could imagine this being quite useful if you are interested in something like radial distribution functions in some hard-to-sample region.

Using these collective variables, again, a biasing potential is applied to the system, but this potential is said to be "history-dependent" in the sense that the form of the biasing potential might change based on what parts of the free energy landscape have already been seen. This differs from umbrella sampling where the potential is always harmonic and the rate at which the potential is biased and how extreme the bias is, is chosen by the user. You should see ref. [2] and references therein for more details on metadynamics.

So, yes, it is possible and even fairly routine to calculate free energies, enthalpies, entropies and pretty much anything else from molecular dynamics simulations. However, just because it is routing does not mean these methods are perfect. It can be very hard to measure error with these sorts of methods because one does not generally know the correct answer particularly for dynamical processes. That is, if your aim is to study details of dynamics which can't be observed experimentally, then it is very hard to know if the dynamics under your biased potential mean much beyond the fact they should give you pretty good ensemble averages. Also, there is the inherent subjectivity in metadynamics involved in choosing collective variables which has been known to cause problems. How many variables are enough and which ones?

Hopefully that is about what you were looking for.

I don't address the differences between explicit solvent and gas-phase much because these methods will work in any context (even implicit solvent) for which forces and energies can be supplied.

[1]: Kästner, J. (2011). Umbrella sampling. Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(6), 932-942.

[2]: Barducci, A., Bonomi, M., & Parrinello, M. (2011). Metadynamics. Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(5), 826-843.

• Thanks for your answer.If I understand it correct the first problem is to actually get constructive trajectories but once we got them we can calculate pretty much anything we want? or do we need a distribution between constructive and non constructive trajectories? The reactions I'm looking at are extremely fast (no enthalpy barrier, fully entropy controlled) and time in the transition state zone should be quite close to that of a C-C vibration. There are examples using normal mode sampling at the transition state and propagate it forward and in reverse to get mainly constructive trajectories.
– DSVA
Nov 7, 2017 at 13:14
• Once you have a trajectory, you can calculate anything at all that statistical mechanics allows you to calculate, which is basically anything. The difficulty comes from getting enough sampling to actually have reliable averages. As for your specific case, it's hard to know what would work without more information (do you have an advisor?). I think that either need described could be used for this because your problem will be getting sufficient sampling of such a quick event, so you have to force the system to stay near the transition state. Nov 7, 2017 at 21:05
• thanks that's what I wanted to hear. I just wanted to get sure about some of the absolute basics before I approach the people who have the knowledge to run such calculations. They have done it before for similar systems and got several hundred trajectories but they mostly looked at hydrogen bonds during the reaction and not thermodynamic values.
– DSVA
Nov 7, 2017 at 21:25