Interactive companion to Figure 4

How Good Is DFT for Solid-Liquid Interfaces? A Comparison With the Random-Phase Approximation for Water on Graphene

Solid-liquid interfaces are notoriously hard to simulate accurately. Different force fields and DFT functionals can give very different pictures of how water structures, wets, and moves near a surface, and until now there has been no high-accuracy reference to say which picture is closer to right. In the paper we use RPA as that reference at the graphene-water interface, folding structural, dynamical, and spectroscopic agreement into one overall score by averaging six observables with equal weight. This page lets you set the weighting yourself, for whichever property matters most for your use case.

How scoring works

Setting the weights in the console recomputes the individual scores, the overall score, and the structure and dynamics scores, reproducing Figure 4B, 4C, 4D and Figure S11 of the Supporting Information. Everything on the page is scored against RPA/QZ. The reference can be changed in the console, including to experiment, which is measured for the VSFG spectra alone.

All six observables share one measure of agreement. For a profile or a spectrum it compares the two curves point by point, d = 1 − Σ|a − b| / Σ(|a| + |b|), and for a scalar such as the friction coefficient or a VSFG peak position it is the same expression on a single pair of numbers. It is symmetric in the two arguments and bounded by 0 and 1, so no observable is scored on a scale of its own and swapping which level of theory plays the reference does not change the size of the disagreement.

Fig. 4C

Overall Score

Overall score for each XC approximation, obtained by averaging over all individual observable scores and sorted from best to worst. Hatching indicates the dispersion correction and error bars give the propagated standard error.

Fig. 4D

Structure and Dynamics Scores

Dynamics score plotted against structure score for all XC approximations considered, each averaged over the observables assigned to that group in the console. Marker shape indicates the functional family. Most functionals fall below the diagonal, indicating that a faithful description of interfacial dynamics is generally harder to achieve than one of interfacial structure.

Fig. 4B

Individual Scores

Individual scores for representative XC approximations, grouped by family and decomposed by observable. Bar height gives the score and bar width gives the weight assigned to that observable, so an observable at zero weight collapses to a hairline.

Fig. S11

Full Breakdown

Heatmap of individual scores for every XC approximation considered, together with the group mean for each category. Rows are sorted by overall score. Column headers carry the current weight, and Δ gives how many places an XC approximation has moved relative to equal weighting.

Score [%]

50to100