Quantitative assessment of the effect of basis set superposition error on the electron density of molecular complexes by means of quantum molecular similarity measures

The Chemical Hamiltonian Approach (CHA) method is applied to obtain Basis Set Superposition Error (BSSE)-free molecular orbitals at the Hartree–Fock (HF) and Density Functional Theory (DFT) levels of theory. To assess qualitatively the effect of the BSSE on the first-order electron density, we had previously applied Bader's analysis of the intermolecular critical points located on the electron density, as well as density difference maps for several hydrogen bonded complexes. In this work, Quantum Molecular Similarity Measures are probed as an alternative avenue to properly quantify the electronic relaxation due to the BSSE removal by means of distance indices between the uncorrected and corrected charge densities. It is shown that BSSE contamination is more important at the DFT level of theory, and in some cases, changes on the topology of the electron density are observed upon BSSE correction. Inclusion of diffuse functions have been found to dramatically decrease the BSSE effect in both geometry and electron density. The CHA method represents a good compromise to obtain accurate results with small basis sets