Truncated, correlated, wave function methods either produce imaginary frequencies (in the extreme case) or nonphysically low frequencies in out-of-plane motions for carbon and adjacent atoms when the carbon atoms engage in π bonding. Cyclopropenylidene is viewed as the simplest aromatic hydrocarbon, and the present as well as previous theoretical studies have shown that this simple molecule exhibits this behavior in the two out-of-plane bends (OPBs). This nonphysical behavior has been treated by removing nearly linear dependent basis functions according to eigenvalues of the overlap matrix, by employing basis sets where the spd space saturatation is balanced with higher angular momentum functions, by including basis set superposition/incompleteness error (BSSE/BSIE) corrections, or by combining standard correlation methods with explicitly correlated methods to produce hybrid potential surfaces. However, this work supports the recently described hypothesis that the OPB problem is both a method and a basis set effect. The correlated wave function’s largest higher-order substitution term comes from a π → π* excitation where constructive interference of both orbitals artificially stabilizes the OPB. By employing schema to overcome this issue, the symmetric OPB ν₉ is the predicted to be the second-brightest transition, and it will be observed very close to 775 cm^–1. However, more work from the community is required to formulate better how carbon atoms interact with their adjacent atoms in π-bonded systems. Such bonds are ubiquitous in all of chemistry and beyond.

中文翻译：

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克服简单芳香族中平面外运动相关性的失败：c -C ₃ H _2的振动振动量子化学分析

当碳原子与π原子键合时，截断的相关波函数方法会在碳和相邻原子的平面外运动中产生假想的频率（在极端情况下）或非物理的低频。环丙烯基被认为是最简单的芳烃，目前以及以前的理论研究表明，该简单分子在两个平面外弯曲（OPB）中表现出这种行为。这种非物理行为已通过以下方法解决：通过根据重叠矩阵的特征值去除几乎线性相关的基函数，并通过使用spd的基集来解决该非物理行为。通过包括基集叠加/不完全误差（BSSE / BSIE）校正，或通过将标准相关方法与显式相关方法结合以产生混合势面，可以通过较高的角动量函数来平衡空间饱和。但是，这项工作支持了最近描述的OPB问题既是方法又是基集效果的假设。相关波函数最大的高阶替换项来自π→π*激发，其中两个轨道的相长干涉人为地使OPB稳定。通过采用模式来克服这个问题，对称OPBν ₉是预测为第二亮过渡，并且将非常接近观察到775厘米^-1。但是，需要更多的社区工作来更好地阐明碳原子如何在π键系统中与其相邻原子相互作用。这样的键在所有化学反应中都是无处不在的。