Accuracies of the One-Electron and On-Top Two-Electron Densities Obtained with the Full Configuration-Interaction Employing Commonly Used Basis Sets

Accuracy studies of the one-electron density, the two-electron on-top density, and the on-top ratio were conducted. The ground-state wave function of the dihydrogen molecule was approximated by a linear combination of explicitly correlated Gaussian functions, and the results juxtaposed with those stemming from the full Configuration Interaction (CI) method with commonly used correlation-consistent orbital basis sets. As these quantities are employed in a broad spectrum of different formalisms and usually derived from wave function approximations typically assessed solely in terms of energy convergence, this research demonstrates that the energy error alone cannot serve as the sole criterion for establishing a foundation for reliable conclusions concerning even the simplest two-electron systems. Relative error amounting to ca. 1% may be achieved and maintained for one-electron density in full-CI calculations, while the accuracy of the on-top two-electron density is affected by excessively high errors. Even with very large basis sets, those errors are not lowered to less than approximately 15%, but even that is possible only in the proximity of the nuclei. The obtained results indicate that the on-top ratio values never exceed 1 for the considered systems, as was suggested in the literature.