分子自发对称性破缺时的稳定构型
Stable configuration of a molecule as spontaneous symmetry breaking
摘要：
在没有外场作用的分子中，原子核的运动由原子核坐标的函数V决定。这个函数（势能）是两个项的总和：原子核之间的库仑排斥和电子有效势E，它由玻恩-奥本海默近似产生。在本文中，我们提出了一组坐标变换，它们是函数E和V的对称性。我们证明了动力学表示的公式，它在分子正常模式的对称性分析中具有根本的重要性，从这些对称性中得出。此外，我们证明了每个分子至少有一个正常模式属于全对称（因此拉曼活性）的点群的不可约表示的分子。接下来，我们使用V和E的对称性来分析某些分子类型的可能形状。我们应用Abud-Sartori-Michel定理和对称性适应的电子有效势展开。最后，我们导出了一个由键长预测双原子分子振动频率数量级的近似关系式。
英文摘要：
In a molecule subjected to no external fields, motion of nuclei is governed by a function V of nuclear coordinates. This function (potential energy) is a sum of two terms: Coulomb repulsion between nuclei and the electronic effective potential E which results from the Born-Oppenheimer approximation. In this paper we have presented a group of coordinate transformations which are the symmetries of functions E and V. We showed that the formula for dynamical representation, which has fundamental importance in the symmetry analysis of normal modes of a molecule, follows from these symmetries. In addition, we proved that every molecule has at least one normal mode belonging to the totally symmetric (and therefore Raman-active) irreducible representation of the point group of that molecule. Next, we used symmetries of V and E to analyze possible shapes of some molecule types. We applied both Abud-Sartori-Michel theorem and symmetry adapted expansion of the electronic effective potential around united atom. Finally, we derived an approximate relation which predicts order of magnitude of the vibration frequency from the bond length in a diatomic molecule.
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