On invariance of the Mulliken substituent-induced charge changes in quantum-chemical calculations of different levels

A comparative analysis of the electron density distributions derived from the B3LYP DFT and RHF calculations with a diversity of basis sets from the minimal to the 6-311+G(2df,2p) one has been carried out for benzene and monosubstituted benzenes. The π and σ substituent-induced charge changes (SCC) on the non-ipso carbon atoms of the benzene ring have been determined in the framework of the Mulliken approach. It has been found that the π SCC obtained with all theoretical models examined are linearly related among them. The π SCC calculated in the framework of minimal and, separately, split valence bases, are the same within every class of calculations. In their absolute values the split valence π SCC are approximately half as much again ones obtained at the minimal bases, i.e. going from the minimal to the split valence bases the sensitivity of the Mulliken atomic charges to substitution rises. The behaviour of the Mulliken σ SCC calculated at the minimal and double split valence basis sets is nearly the same as of the π ones. But the Mulliken triple split valence σ SCC increase dramatically, their values become physically unjustified and basis set dependent. The reason is that the σ overlap populations of the benzene ring CC bonds of monosubstituted benzenes in the triple split valence calculations have unphysical negative values, which, being added to atomic populations to produce the gross σ atomic populations, lead to physically unjustified magnitudes of the latters and of the atomic σ SCC. A comparison with the literature experimental data has shown that the Mulliken SCC obtained at the double split B3LYP/6-31G∗∗ and /6-31G levels can be applied in correlations with experimental and theoretically calculated substituent effects.