Part of the solution of the matrix equation of
normal coordinate analysis,
\(\boldsymbol{G\!F\!L} = \boldsymbol{L \lambda}\). Each element
\(L_{ik}\) of
\(\boldsymbol{L}\) is a vibrational eigenvector, and gives the change in internal coordinate
\(R_{i}\) during unit change in the
normal coordinate \(Q_{k}\), as shown in matrix form by
\(\boldsymbol{R} = \boldsymbol{LQ}\), i.e.,
\(L_{ik} = \partial R_{i}/\partial Q_{k}\).
Eigenvectors are sometimes expressed in terms of symmetry coordinates or Cartesian coordinates.
Note:
SI unit: \(\pu{kg^{-1/2}}\). Common unit: \(u^{-1/2} = \pu{2.45400E13 kg^{-1/2}}\).
Source:
PAC, 2021, 93, 647. 'Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)' on page 768 (https://doi.org/10.1515/pac-2019-0203)