Systematic Error Estimation for Chemical Reaction Energies

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.