A benchmark dataset for ground-state protonic densities and energies

In this work, we present a benchmark set of protonic densities and energies aimed at testing and validating quantum chemical methods. In particular, we discuss the use of said data for benchmarking multicomponent calculations and the choice of nuclear basis functions. We selected 28 systems, spanning varying degrees of symmetry and acidity, from strongly acidic protons up to hydrides. The reference data were constructed through variational calculations on computed 1-particle potentials, fitted from Born-Oppenheimer 3D-grids. The chemical variety allows for more general fitting of electron-proton correlation functionals and/or basis sets for use in multicomponent calculations. As an illustration, we use the dataset to evaluate nuclear basis functions. Instead of fitting exponents to self-consistent numerical calculations, we evaluate different sets by observing how well the reference densities can be directly fitted. The basis sets under analysis are all based on Gaussian functions, for which we show the importance of higher-angular momentum (at least d-type functions). We also present a procedure for basis-set construction based on vibrational theory. Finally, we propose two series of nuclear basis sets, vc1-PBnZ and vc1-PBnZ+t, and recommend the latter for routine multicomponent calculations.