How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne⁶⁺, and Ne⁸⁺?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study suggested that functionals with few parameters provide more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne⁶⁺, and Ne⁸⁺ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science 2017, 355, 49-52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. In addition, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.