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Different levels of theoretical methods have been used to study a novel stable cyleophane 1,8- [1,8-naphthalenediylbis(4'.4-biphenyldivl)] naphthalene. It was concluded that HF/3-21g* was the most efficient method for the system, which could well reproduce the experimental structure. In addition, HF/3-21g*//B3LYP/3-21g* calculations explained the experimental observation that the cyclophane was much easier to be oxidized to the corresponding radical cation than its related compound 1, 8-bisphenyl-naphthalene. It was proposed that the more effective pi-pi and pi-cation interactions in the radical cation of the cyclophane caused the above behavior.