Water from first principles?

A paper in Science this week claims to present a new, improved effective pair potential for water calculated from first principles, which works well both for water dimers and for the bulk liquid. I was a little puzzled by this, since there has been plenty of previous work in this area and it wasn’t immediately clear what the new trick was here that had enabled the claimed improvements. Having been asked to write about the work for Chemistry World, I contacted two experts in this field. Both were strongly critical of the paper.

First, the general context, which is nicely explained by one of my advisers:

“Modeling intermolecular interactions in water in terms of simple pair potentials is difficult because these potentials miss the cooperative effects of the H bonds. These are important: it is because of these effects that the “dipole” moment of a molecule in condensed phase is greatly enhanced compared to that of a molecule in gas phase (here I put dipole in quotes because this quantity cannot be unambiguously defined in condensed phase). Compared to simple liquids water has a much more open structure dictated by the underlying H-bond network.

Popular empirical potentials for water try to model the basic physics underlying H bonds interactions, which are largely of electrostatic origin in terms of interactions between point charges spatially located in a way that mimics, albeit very approximately, the charge distribution in the water molecule. These potentials are tuned to reproduce a number of properties of the liquid but have limited transferability to different environments as they miss the cooperative effects mentioned above.”

Existing classical potentials for water describe well the structure of the liquid (even very well I would say!). The difficulty with this approach, apart from the issue of transferability, is that we also need to describe the interaction between water and other molecules, material systems etc. in order to model solvation, interfacial water, confined water etc. In addition, there are properties such as the dielectric properties that depend on the actual electronic structure of the molecules in a given environment. Furthermore water molecules can dissociate. A good potential for the intermolecular interaction does not tell us everything.”

But in terms of the Science paper by Bukowski et al., he says:

“I am not too impressed by the contribution of Bukowski et al. They show that an extremely good potential for the dimer (a pair potential) is not sufficient for a good description of the liquid, as one could have expected. Including non-additive many body effects they obtain a more decent agreement with the experimental liquid structure. Interestingly, and to some extent unexpectedly (at least to me), simple polarization effects seem to be doing most of the job. However, in the end they have just another rigid water potential which, judging from their pair correlation function, appears to be almost as good as the best existing rigid empirical potentials for water. Of course conceptually it is not the same thing: the potential of Bukowski et al. is not tuned to reproduce experiment but is derived from accurate quantum mechanical calculations on the dimer (and in the most accurate case also on the trimer). This is an important achievement but difficult to generalize to a wide range of possible contexts, including e.g. flexible molecules, solvation effects, hydrophobic and hydrophilic conditions, confinement, systems other than water, etc. Keeping the attention on the liquid structure, I do not think that this potential gives us a better insight than what we already know on the structure of the H bond network in water.

I do not think that the work of Bukowski et al. goes anywhere beyond ab-initio molecular dynamics on the flight. [This is the kind of approach used by Dominik Marx, Roberto Car and others.] The latter models water in terms of nuclei and electrons, the former in terms of rigid intermolecular potentials. The latter produces flexible molecules by construction and describes in detail the interplay between electronic structure and nuclear dynamics. As such ab-initio molecular dynamics on the flight is applicable to the most general range of situations, including for instance proton transfer effects (the Grotthus mechanism) that are not allowed by any rigid classical intermolecular potential (whether ab-initio or empirical!). The main limitation of ab-initio molecular dynamics on the flight, apart from numerical cost, is due to the limited accuracy of existing approximations of density functional theory, but as these improve or if highly efficient and more accurate electronic structure methods are established, immediately this progress could be transferred to the accuracy of ab-initio molecular dynamics on the flight. It is not so with the method of Bukowski et al. which cannot go beyond the accuracy provided by a simple polarization approximation of the non additive many-body effects. The only system that Bukowski et al. describe better than ab-initio MD on the flight is the potential of the water dimer, for which they rely on the most accurate available quantum chemical methods. Some of this accuracy is lost when they go to condensed phase. Judging from their current results, they do not have a better description of liquid water than that provided by existing empirical potential. Overall, the insight on a number of properties, structural, electronic etc. provided by ab-initio MD (on the flight) is vastly superior.”

That squares with my second adviser, who says:

“I'm very disappointed such a paper is appearing in Science. First, it gives an incredibly misleading account of the existing ab-initio literature on water, almost entirely based on DFT, and it omits a very recent quantum chemistry work (by S. Xantheas, JCP). Second, it "sells" a quantum chemistry based ab-initio potential as giving excellent agreement with experiment, when the agreement the authors find is not much better than what is already out there, in my opinion, using DFT based methods. This Science work just has different kind of disagreement with experiments, w.r.t. those found with DFT, but overall it is not much better (actually it is a little worse); most importantly: this work does NOT solve any of the open problems out there on the structure and/or properties of water.

Let me elaborate a bit on these points.

1) Account of the existing ab-initio literature. In the last ~ 15 years, most of the ab-initio simulations (no fit to or input from experiment) of water have been performed using Density Functional Theory (DFT) based methods, and they have been carried out mainly with two functionals (so call gradient corrected energy functionals, BLYP and PBE). Both of these functionals have been believed to give good agreement with experiment for several years (specifically until ~ 2004). However the good agreement with experiment did NOT came from a good performance of the theory but was somehow fortuitous, due to numerical inaccuracies in the solution of the Kohn-Sham equations (DFT equations) for the electrons. In 2004, Schwegler et al. (JCP 2004) and Grossman et al. (JCP 2004) pointed out these inaccuracies and showed that water correlation functions (g(r)--also discussed in the Science report) are over-structured and diffusion too slow (w.r.t. to experiment), when the numerics is done right and numerical inaccuracies are removed. The fortuitous agreement with experiment there had nothing to do with a fortuitous choice of functionals, as stated by the present authors. It had to do with numerics adopted in integration techniques. Those results were later confirmed by Sit and Marzari (JCP 2005), Serra and Artacho (several papers appeared in JCP) and others (none of these papers are mentioned in the Science report). So the introduction of this Science paper carelessly dismisses an approach (ab-initio simulations based on DFT) that, although not in full quantitative agreement with experiment, can describe well the salient, qualitative features of liquid water. On top of this, at the end of the paper the reader realizes that such a dismissed approach gives an agreement with experiment which is similar to the one found by the authors (Actually, I'd like to claim that DFT gives a more consistent agreement with experiment than the one presented in the Science paper--see below).

I also note that in the introduction of this paper dispersion forces in water are declared "non negligible", with no reference and no discussion. There is no clear experimental and/or theoretical evidence to support this statement. It may well be so, but nobody knows right now.

2) Agreement with experiment found here, wrt to existing ab-initio simulations based on DFT. I believe that overall the g(r)s found here are not in better agreement with experiment than those described by DFT ( see original papers). Note that they get right the first peak of g(r) but not the second, implying that their angular distribution (if they had computed it!) is quite inaccurate. Their diffusion coefficient is in agreement with experiment, but admittedly (see their own statement), this agreement may be fortuitous as they neglected proton quantum effects of the monomer, and flexibility of the monomer. Most importantly: the coordination number they find is an overestimate of what is accepted in the field as a reasonable number extracted from experiment. They find 5.6 and they compared it with 4.8, when the accepted value in the field is more like 4.3/4.5. Whatever number you consider, their value is a big overestimate, giving a liquid over-coordinated with respect to experiment and with too many hydrogen bonds. Their computed internal energies are worst that those obtained with empirical potentials.”

Not encouraging, then. And in any event, in terms of understanding hydration, the messages were as follows:

Adviser 1: “I cannot predict what would be the result of applying the scheme of Bukowski et al. to studying hydrophobic hydration. In hydrophobic hydration there is not just water but also the hydrophobic substance (unless this is the vacuum). Since their potential should be more transferable than standard empirical potentials, it should describe better the water close to a hydrophobic solute. In principle, however, all the interactions need to be included and treated with comparable accuracy. In our study of solvated methane both the water and the methane molecules have deformable electronic clouds that play an important role in the outcome of the calculation. These effects are described to some extent in terms of polarization effects by Bukowski et al., but they should also construct a methane-methane and a methane-water potential and include polarization effects beyond pure water in order to tackle the solvation problem.”

Adviser 2: “Even if the authors found the best ab-initio potential for liquid water fitted to ab-initio gas phase data, if they wanted to describe solvation they would have to start all over again, as they would have to do the fitting to gas phase water containing the solvated molecule or they would have to add other pieces to the potential. This is why fitted potential (whatever they are fitted to: ab-initio data, experiment, etc.) will always have serious drawbacks. If you want to study systems that have not been fitted, containing other entities, well... here you go, you have to start again with your fit.”


So there it is. I don’t like dumping on a paper, but this one has come out in a very high-profile journal where it will get a lot of recognition. So I thought it is only right to put the record straight.