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.