Normal mode analysis has been employed to characterize fundamental phenomena in diverse scientific disciplines, including the identification of molecular vibrations in chemistry and their peak assignments in infrared and Raman spectra. The vibrational modes are traditionally determined from the potential energy surface under the harmonic approximation. Here, we introduce a methodology called Expanded Moment of Inertia Tensor, EMIT, which can extract a complete set of normal coordinates from the molecular geometry at any point in phase space. Its principle lies in the conservative expansion of the angular momentum within the rigidbody framework. This method provides normal modes that resemble those obtained from group theory and show their efficacy by accurately reproducing all characteristic frequencies in the vibrational spectra of ${\mathrm{NO}}_2^{-}$ and ${\mathrm{NO}}_3^{-}$ in aqueous solution. Not only this geometry-based method of normal mode determination looks promising in many fields, but it also inspires us to view known molecular quantities in physics differently.

正态模式分析已用于表征各种科学学科中的基本现象，包括化学中分子振动的识别以及红外和拉曼光谱中的峰分配。传统上，振动模式是在谐波近似下根据势能面确定的。在这里，我们介绍了一种称为惯性张量的扩展矩量（EMIT）的方法，该方法可以从相空间中任意点的分子几何结构中提取出完整的法线坐标集。其原理在于刚体框架内角动量的保守扩展。这种方法提供的正常模态类似于从群论中获得的模态，并通过准确地再现振动光谱中的所有特征频率来显示其功效。${\mathrm{没有}}_2^{--}$ 和 ${\mathrm{没有}}_3^{--}$在水溶液中。这种基于几何的法线模式确定方法不仅在许多领域看起来很有希望，而且还启发我们以不同的方式看待物理学中的已知分子量。