Moran Damian, Simmonett Andrew C, Leach Franklin E, Allen Wesley D, Schleyer Paul V R, Schaefer Henry F
Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602, USA.
J Am Chem Soc. 2006 Jul 26;128(29):9342-3. doi: 10.1021/ja0630285.
Planar (D6h) benzene has one (1181i cm-1, b2g) and three (1844i cm-1, b2g; 462i cm-1, e2u) imaginary vibrational frequencies at the MP2/6-311++G(d,p) and MP2/6-311++G levels of theory, respectively! The spurious frequencies correspond to D3d chair (b2g) and C2v boat (e2u) out-of-plane distortions. Numerous, similar examples where planar benzene is not a minimum are documented at the MP2, MP3, and CISD levels with popular Pople-type basis sets, while the RHF, B3LYP, and BLYP methods exhibit no such problems. We show that, in the sp and spd atomic-orbital limits of MP2 theory, benzene is nonplanar. The observed failure of electron correlation methods with unbalanced basis sets to predict planar minima is not unique to benzene but is also found for other pi-delocalized molecules, including pyridine, naphthalene, anthracene, the cyclopentadienyl and indenyl anions, and the tropylium cation. Detailed mathematical analysis reveals that an insidious, geometry-dependent, two-electron basis set incompleteness error (BSIE) is responsible for the problem and that balanced, correlation-consistent constructions of basis sets are generally required to ensure reliable predictions for arenes with correlated wave functions.
平面（D6h）苯在MP2/6 - 311++G(d,p)和MP2/6 - 311++G理论水平下分别有一个（1181i cm-1，b2g）和三个（1844i cm-1，b2g；462i cm-1，e2u）虚振动频率！这些虚假频率分别对应于D3d椅式（b2g）和C2v船式（e2u）的面外畸变。在MP2、MP3和CISD水平下，使用流行的Pople型基组记录了许多类似的例子，其中平面苯不是能量最低点，而RHF、B3LYP和BLYP方法不存在此类问题。我们表明，在MP2理论的sp和spd原子轨道极限下，苯是非平面的。观察到的电子相关方法在使用不平衡基组时无法预测平面最低点的情况并非苯所特有，在其他π离域分子中也存在，包括吡啶、萘、蒽、环戊二烯基和茚基阴离子以及环庚三烯正离子。详细的数学分析表明，一个隐蔽的、与几何结构相关的双电子基组不完全性误差（BSIE）是导致该问题的原因，并且通常需要平衡的、相关一致的基组构建来确保对具有相关波函数的芳烃进行可靠预测。
