How many shades of grey? On the proximity of density functional approximation to ab initio method via calculations of electric multipole moments

The wide spreading of the application of Density Functional Approximation via its represtnatives, i.e. the Density Functionals (DFs), in almost all the fields of computational chemistry is globally witnessed. Therefore, it is believed that an evaluation of their performance in tedious calculations will offer useful insights to both users and developers. As such calculations we chose the prediction of electric multipole moments of first to fourth order, namely dipole ( µ α /ea 0 ), quadrupole ( Θ α β / e a 0 2 ) , octupole ( Ω α β γ / e a 0 3 ) and hexadecapole ( Φ α β γ δ / e a 0 4 ) . Values at both ab initio up to the highly accurate couple cluster with singles and doubles (reference values) as well as different flavors of DFs: hybrid, GGA, double hybrid, long range corrected, including dispersion correction, both hybrid and long range corrected and some from the Minessota family. The target set is a group of 10 molecules of C 2 ν symmetry. The results were further analyzed with the root mean square deviation (RMSD) method as to find the method that is the most proximal to reference CCSD. The functionals PBE1PBE, CAM-B3LYP and B2PLYP seem to survive the proximity test, whereas B97D, M05, M06 and M08 provide results that are the least proximal to CCSD ones.