CARTESIAN AXIS AND PLANE CONVENTIONS IN Cnv SYMMETRY GROUPS

In this work, we call the attention to the ambiguity found in the literature when labeling vibrations and molecular orbitals as B1 and B2 for molecules belonging to the C2v point group as, for example, the water molecule. A survey of several books and some articles shows that this ambiguity comes from a long time ago and persists today, being a source of misunderstanding and a waste of time for students and teachers. It means that, in the case of the point groups Cnv, Dn, and Dnh (n = 2, 4, 6), it is very important to draw students’ attention to this ambiguity that exists in the literature. It is unfortunate that the recommendation made by Mulliken, more than sixty years ago, to always place the water molecule in the yz plane, has not been followed.

本研究提请关注当前文献中的一处歧义：针对属于C₂ᵥ点群的分子（例如水分子），对其振动模式与分子轨道(molecular orbitals)标记为B₁和B₂时存在标准不统一的问题。经对多部教材与多篇学术文章的调研发现，该歧义由来已久且至今仍持续存在，成为师生群体中产生误解、浪费时间的诱因。这意味着，对于Cₙᵥ、Dₙ及Dₙₕ点群（n=2、4、6）而言，提醒学生关注文献中存在的此类歧义十分必要。令人遗憾的是，六十余年前马利肯（Mulliken）提出的“始终将水分子置于yz平面内”的建议，至今仍未得到遵循。