Restoring rotational symmetry of multicomponent wavefunctions with nuclear orbitals

In this work, we present a non-orthogonal configuration interaction (NOCI) approach to address the rotational corrections in multicomponent quantum chemistry calculations where hydrogen nuclei and electrons are described with orbitals under Hartree-Fock (HF) and density functional theory (DFT) frameworks. The rotational corrections are required in systems such as diatomic (HX) and nonlinear triatomic molecules (HXY), where localized broken-symmetry nuclear orbitals have a lower energy than delocalized orbitals with the correct symmetry. By restoring rotational symmetry with the proposed NOCI approach, we demonstrate significant improvements in proton binding energy predictions at the HF level, with average rotational corrections of 0.46 eV for HX and 0.23 eV for HXY molecules. For computing rotational excitation energies, our results indicate that HF kinetic energy corrections are consistently accurate, while discrepancies arise in total energy predictions, primarily from an incomplete treatment of dynamical correlation effects. Rotational energy corrections in multicomponent DFT calculations, using the epc17-2 proton-electron correlation functional, lead to an overestimation of proton binding energies. This is as a result of double-counting of proton-electron correlation effects in the off-diagonal NOCI terms. As a correction, we propose a scaling scheme that effectively adjusts the proton-electron correlation contributions, bringing our results into close agreement with reference CCSD(T) data. The scaled rotational corrections, on average, increase the epc17-2 proton binding energy predictions by 0.055 eV for HX and 0.025 eV for HXY and yield average deviations of 1.0 cm-1 for rotational transitions.