From the Four-OrbitalModel to the Three-Orbital Model:Parameterizing the Q x / Q y -Band Energiesin Phthalocyanines and Their Analogues Using Symmetry-Adapted PerturbationTheory

Here, we summarize the general use of the symmetry-adapted perturbation theory (SAPT) toward empirical prediction of the energy (and splitting when present) of the Qx- and Qy-bands in a large variety of substituted phthalocyanines (Pcs) and their analogues (i.e., tetraazaporphyrins (TAPs), naphthalocyanines (Ncs), and anthracocyanines (Acs)). It was shown that SAPT can be used as a reliable and quick empirical tool for the accurate (within 0.05 eV) estimation of both Qx- and Qy-band energies and splittings. Simple empirical rules for a 24 nm redshift per added benzene ring at the β,β′-positions (96 nm rule going from TAP to Pc to Nc to Ac) and 30, 15, 8, 5, and 4 nm rules for redshift per added amino, thiol, alkoxy, aryl, and alkyl group at the α-position of the phthalocyanine core, respectively, were established. The SAPT accuracy was tested against the data from more time-consuming and resource-intensive time-dependent density functional theory (TDDFT) calculations for several series of compounds.