Theoretical study on the stability of double-decker type metal phthalocyanines, M(Pc)2 and M(Pc)2+ (M = Ti, Sn and Sc): a critical assessment on the performance of density functionals

Abstract

We report the results of theoretical calculations on the optimized structures and relative energies between the D_4d and D₂ symmetry structures for double-decker type phthalocyanine compounds, Ti(Pc)₂, Ti(Pc)₂⁺, Sn(Pc)₂, Sn(Pc)₂⁺, Sc(Pc)₂ and Sc(Pc)₂⁺, using eighteen types of functionals: B3LYP, B3PW91, B3P86, PBE1PBE, BHandHLYP, BPW91, BP86, M06, M06-2x, M06-HF, M06L, LC-BPW91, LC-ωPBE, CAM-B3LYP, B97D, ωB97, ωB97X and ωB97XD. Two phthalocyanine moieties are stacked in a face-to-face configuration in the D_4d structure, but they are stapled by two σ-bonds in the D₂ one. We found that the molecular symmetry of M(Pc)₂ and M(Pc)₂⁺ depends on the balance between stabilization due to electron delocalization and exchange repulsion of π-electrons in the phthalocyanine moieties. We assessed the performance of the well-established functionals to select the appropriate functional for calculations on M(Pc)₂ and M(Pc)₂⁺, and several important aspects came out. Generally, the hybrid GGA and hybrid meta-GGA functionals with 20–27% of the HF exchange term would give the molecular structures consistent with the experimental expectations for the double-decker type phthalocyanine compounds. Pure GGA and pure meta-GGA functionals (BPW91, BP86, M06L and B97D) have the tendency to overestimate the stability of the D_4d structure. On the other hand, functionals including HF exchange for 50% and over or including long-range corrections (BHandHLYP, M06, M06-2x, M06-HF, LC-BPW91, LC-ωPBE, CAM-B3LYP, ωB97, ωB97X and ωB97XD) tend to overestimate the stability of the D₂ structure. It should be emphasized that the B3LYP functional, one of the most commonly used hybrid GGA functionals with 20% HF exchange, cannot estimate the relative stability between the two molecular structures of Ti(Pc)₂ appropriately. The calculation for the systems considered in this article required well-balanced treatment of the HF exchange with the accompanied exchange–correlation functional. Thus, as has been pointed out rigorously and frequently, the selection of the functional is a crucial point for reliability of the calculations.