Dependence of the substituent energy on the level of theory

Most often, the substituent effects are described using rather troublesome Hammett constants. Quite recently, it has been proposed to use the so-called substituent energy, which is based on total energies of the X-substituted polycyclic aromatic hydrocarbon and phenyl. This article concerns the influence of the applied level of theory (i.e., both the basis set and the method) on the determined values of the substituent energies. For this purpose, the energies of the NH₂ and NO₂ groups in 16 unique positions of naphthalene, anthracene, tetracene, phenanthrene, and pyrene were calculated using 10 different basis sets and 23 various exchange-correlation functionals representing the entire Jacob's Ladder, from local, through gradient- and meta-gradient-corrected, to hybrid and double-hybrid ones. Additionally, using even larger 6-311++G(2df,2p) basis set, the energies of NH₂ , NO₂ , CN, and Cl were also computed. Both the basis set and the method used have little effect on the substituent energy if the substituent is in the benzene-like position. On the contrary, the effect of the level of theory is pronounced especially in the case of the most spatially crowded 4-substituted phenanthrene. Substituent energies have been shown to be very useful theoretical parameters describing the proximity effect in the substituted derivatives of polycyclic aromatic hydrocarbons.