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.

本研究中，我们注意到，在对属于C2v点群（Point Group）的分子（例如水分子）的振动与分子轨道（Molecular Orbitals）标记为B1和B2时，相关文献存在歧义现象。经对多部教材与多篇学术文章的调研发现，该歧义由来已久且延续至今，已成为师生产生误解、耗费时间的根源之一。这表明，针对Cnv、Dn及Dnh点群（n=2、4、6）的相关研究场景中，提请学生注意文献中存在的此类歧义至关重要。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，至今仍未得到广泛遵循。