Systematic Error Estimation for Chemical Reaction Energies

Abstract

For a theoretical understanding of the reactivity of complex chemical systems, accurate relative energies between intermediates and transition states are required. Despite its popularity, density functional theory (DFT) often fails to provide sufficiently accurate data, especially for molecules containing transition metals. Due to the huge number of intermediates that need to be studied for all but the simplest chemical processes, DFT is, to date, the only method that is computationally feasible. Here, we present a Bayesian framework for DFT that allows for error estimation of calculated properties. Since the optimal choice of parameters in present-day density functionals is strongly system dependent, we advocate for a system-focused reparameterization. While, at first sight, this approach conflicts with the first-principles character of DFT that should make it, in principle, system independent, we deliberately introduce system dependence to be able to assign a stochastically meaningful error to the system-dependent parametrization, which makes it nonarbitrary. By reparameterizing a functional that was derived on a sound physical basis to a chemical system of interest, we obtain a functional that yields reliable confidence intervals for reaction energies. We demonstrate our approach on the example of catalytic nitrogen fixation.

The Exploration of Chemical Reaction Networks

“…For instance, electronic structure models are likely to be based on fast semiempirical (97) or density-functional theory (98) methods, which can be affected by surprisingly large errors for specific structures (see Refs. (99,100,101) for examples). Without proper uncertainty quantification, explorations based on such data will be inherently unreliable.…”

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

“…Chemists also want reliable forecasts for exotic conditions,43 not only for well‐trod paths. And even for those, there may be occasional surprises.…”

“…At the end of the day,any weather-forecasting model has to be tested against reality,a nd success for one season or region is no guarantee for further successful predictions. Chemists also want reliable forecasts for exotic conditions, [43] not only for well-trod paths.And even for those,there may be occasional surprises.Inthe end, there is no way around some experimental benchmarking.T he benefits of this practice are obvious,w hen one looks back at the development of electronic-structure methods.Even though quantum chemists will often find shortcomings in their methods when performing theory/theory benchmarks,i ti su sually the hard test against experiment that brings about ac hange in practice.A recent example of this is the description of dispersion forces. Although conventional DFT functionals were well known to fail in the description of weakly bound van der Waals complexes, [44] until about ten years ago al arge community regarded this as am inor inconvenience for computational studies on "realistic" systems.L ooking at the interaction curves of rare-gas dimers was not convincing enough, and it was uncertain whether these small contributions would cancel out or add up.Areal change only came about when aseries of benchmark studies with increasing system sizes,supported by experimental evidence,u nequivocally showed that the DFT Figure 2.…”

Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes

“…By contrast, structure discovery through exploration requires system-focused uncertainty quantification in order to be reliable. 36 While some machine learning methods provide error estimates for such system-focused, rolling approaches, in most studies applying statistical learning to investigate chemical systems the focus is placed on the prediction accuracy (e.g., refs. [48][49][50][51][52][53][54][55][56][57][58][59][60][61].…”

“…9,11,18,19,23,32,33 Even if accurate reference data for given molecular structures were available, one could not assume the error of a DFT result to be transferable to the close vicinity of that particular region of chemical space. 11,13,14,[34][35][36] Finally, even if one had some upper bound on the error of a calculated property, this bound would be so large that subsequent analyses, such as kinetic studies, would be rendered meaningless. 37 If, however, an error estimate of each result was known, the value of any approximate DFT approach would be dramatically increased as it would flag those results to be considered with caution.An assigned uncertainty would allow one to judge whether conclusions drawn from the data are valid or not.A few methods have been developed that aim at providing systematic error estimates for individual DFT results.…”