Molecular normal coordinate ($Q_i$)

A mass-weighted displacement coordinate along an eigenvector of the molecular harmonic force-constant matrix after rigid translations and rotations are removed. An orthonormal normal-mode basis gives kinetic energy $\frac{1}{2}{\sum }_i{P}_i^2$ and harmonic potential $\frac{1}{2}{\sum }_i{\omega }_i^2{Q}_i^2$. This use of normal coordinate concerns molecular vibrations, rather than normal coordinates of a spacetime metric.