Basis set superposition error: effects of atomic basis set optimization on value of counterpoise correction

Using the DFT method, we simulated the adsorption of a single hydrogen molecule on pristine low-dimensional carbon nanomaterials: carbon nanotubes (CNT), en-yne (CEY), and graphdiyne (GDY). For wave function decomposition, we employed two approaches: localized pseudoatomic orbitals (SIESTA package) and plane waves (VASP package). For CNT, CEY, GDY, and bulk carbon (graphite), we optimized atomic basis sets. Delta test of used DFT packages showed a good agreement for carbon: $\Delta_C = 0,36$ meV/atom. We demonstrated that after atomic basis set optimization the value of counterpoise (CP) correction of basis set superposition error (BSSE) in calculations of hydrogen adsorption energies reduces. Moreover, this CP correction could be by several times bigger than the corrected hydrogen adsorption energy. Therefore, to obtain reasonable results in weakly interacting systems, CP-corrected adsorption energies in the optimized PAOs are needed. In considered systems, hydrogen adsorption energies, which were calculated in this way, agree with the energies obtained using the BSSE-free plane-wave basis set.