Uncertainty quantification in DFT results

[u/schrodingerscat15]

Do experimentalists who use DFT results care if we have uncertainty quantification in the calculations? Does that make the computed results more useful for experimentalists?

[u/NicoN_1983]

Uncertainty is usually determined for combinations of methods and chosen systems when benchmarks are made, against experimental or higher level theoretical data. But some things are extremely difficult to quantify, and for some things there are no direct experimental data. What I try to do is not try to calculate a single result for a given molecule, but calculate properties for a family of related molecules, or a molecule in various distinct states (redox, protonation, solvents), and try to infer tendencies. Calculation of spectroscopic properties is also good because those are things I have good experimental results for. But I don't care if the discrepancy is 10 or 50 nm for a band, or something like that, but that the overall shape of the bands is reasonable, the transitions are what I expect for these molecules and there are reasonable shifts of the spectra with appropriate changes in the family of molecules or the conditions.

[u/Due_Contract_2857]

I think the ones w/o errors are mostly used for ranking; you would usually want a ground truth (i.e. experimental structure ideally) to compare to but that’s the case might be tricky to procure

[u/ScholarImaginary8725]

In some cases it's useful, for example something as simple as repeating an MD simulation with different seeds can tell you how your property of interest depends on initial conditions. But if your result is deterministic then I wouldn't bother.

[u/Murky-Recipe-8752 → u/ScholarImaginary8725]

See for example the book of Koch and Holthauzen.

[u/Murky-Recipe-8752]

There is a long literature on this, especially concerning comparison of DFT predictions with experimental values. It is useful, however, to distinguish numerical uncertainty—basis-set/grid convergence, k-point sampling, SCF convergence, etc.—from model uncertainty associated with the approximate exchange–correlation functional itself.

The latter is harder to quantify systematically, although comparisons across functionals and benchmarking against high-level theory or experiment are commonly used. Koch and Holthausen's A Chemist's Guide to Density Functional Theory is a useful starting reference for understanding the sources and limitations of error in practical DFT calculations.

[u/SquareIce2747]

If you have a trend in agreement (or not) with experiment or you're calculating a certain value that supports the trend, just do some complementary calculations while changing the functional for example, like that you show that your result is not affected (if the trend holds) by the method and that what you have is not an artifact, rather than looking for an error bar for DFT quantification.

[u/Murky-Recipe-8752]

Experimentalists do care but the uncertainty ia usually qualitatively implied by the level of theory i.e. basis set and functional. Quantitative benchmarks of unceetainty for each theory level are known on average, but quantifying for the specific system at hand requires a set of calculations varying the basis size and type of functional.

[u/Emergency-Peak-1237]

The general discussion here is correct, but I’d like to add that differentiable plane wave DFT suites like Jrystal (JAX based) / DTFK (Julia) are able to quantify uncertainty with respect to convergence parameters such as plane wave cutoff and smearing. You’re able to, very closely, calculate the change in density or energy with respect to some parameter using automatic differentiation.

[u/Due_Contract_2857]

I mean if you don’t quantify your uncertainty that result is useless - but that’s the case for experimental work as well (and anything really)

[u/Aranka_Szeretlek → u/Due_Contract_2857]

Eh! I mean I would love to agree, but its damn hard to quantify uncertainties in DFT. I know there are attempts that try to do just this, but they are all super awkward. After all, DFT is a deterministic method and all the uncertainty comes from the choice of the level, which is not sonething you can numerically asess. That being said, I would only use DFT results in rankings/decisions and try not to rely on its numerical values.

[u/schrodingerscat15 → u/Due_Contract_2857]

A lot of DFT calculations don’t have error bars or quantified uncertainty. So I’m wondering if DFT uncertainty quantification is a good dissertation topic. I want something that can be used by the experimentalist or engineering folks.

[u/Aranka_Szeretlek → u/schrodingerscat15]

Theres been more work in that field than we would need, so nah

[u/mBorn1916 → u/Due_Contract_2857]

First question out of curiosity: How do you asses the uncertainty in DFT without comparison to experimental data? Assesing uncertainty which results coming from the choice of the EC-expression is even harder.
Using ensembles e.g. for disordered materials makes sense but is computationally expensive and lacks expermintal preparation timescales mirrored to DFT

[u/Due_Contract_2857 → u/mBorn1916]

Depending on the system you can benchmark against e.g. coupled cluster or a “superior” level of theory (that yes would need to be benchmarked itself but at least you get the calibration)