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Systematic Error Estimation for Chemical Reaction Energies

For the 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 re-parameterization. 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 because we can then assign a stochastically meaningful error to the system-dependent parametrization that makes it non-arbitrary. By re-parameterizing 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 at the example of catalytic nitrogen fixation.