• Möbius strip;
  • porphyrin;
  • electron;
  • first hyperpolarizability;
  • spin contamination

Möbius strip has attracted extensive interest due to its one-side structure, special physical and chemical properties. A new extended porphyrin with Möbius structure has been synthesized (Stępień et al., Angew. Chem. Int. Ed. 2007, 46, 7869). In this work, an electron is injected into Möbius to form Möbius anion. For Möbius, four methods (B3LYP, BHandHLYP, CAM-B3LYP, and LC-BLYP) obtain the similar first hyperpolarizability (β0). However, for Möbius anion, four methods obtain very different β0 values (ranging from 9.85 × 103 to 8.33 × 105 au). Moreover, the β0 values of Möbius anion are larger than those of Möbius. Why? The considerable variation (ranging from 0.8162 to 1.7630) of spin contamination (S2) of open-shell Möbius anion captures our attention. To probe the relationship between S2 and β0, the β0 values of Möbius anion were calculated using 23 methods. Interestingly, the Hartree-Fock (HF) composition increases from 0 to 50, the S2 value ranges from 0.7522 to 1.3372, and the β0 value increases from 4.3 × 103 to 7.36 × 104 au. Further, methods are “dissected” to investigate the effect of HF composition on the S2. © 2014 Wiley Periodicals, Inc.