Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?

This work provides a self-consistent extension of the recently proposed density-based basis-set correction method for wave-function electronic-structure calculations [J. Chem. Phys. 149, 194301 (2018)]. In contrast to the previously used approximation where the basis-set correction density functional was a posteriori added to the energy from a wave-function calculation, here the energy minimization is performed including the basis-set correction. Compared to the non-self-consistent approximation, this allows one to lower the total energy and change the wave function under the effect of the basis-set correction. This work addresses two main questions: i) What is the change in total energy compared to the non-self-consistent approximation, and ii) can we obtain better properties, namely dipole moments, with the basis-set corrected wave functions? We implement the present formalism with two different basis-set correction functionals and test it on different molecular systems. The main results of the study are that i) the total energy lowering obtained by the self-consistent approach is extremely small, which justifies the use of the non-self-consistent approximation, and ii) the dipole moments obtained from the basis-set corrected wave functions are improved, being already close to their complete-basis-set values with triple-zeta basis sets. Thus, the present study further confirms the soundness of the density-based basis-set correction scheme.