The following example (pdf file) demonstates the gradient vectors and Hessian matrices for the system

HOCl --> TS --> HClO

in the internal coordinates r(ClO), r(OH), and theta(HOCl).

Note that the eigenvalues and eigenvectors are obtained by diagonalization of the Hessian, but these are NOT related
to the vibrational frequencies and normal modes of the molecule since no mass scaling has been performed. These
only show the 2nd derivative matrix in a coordinate system where the Hessian is diagonal. The eigenvectors just define
this coordinate system in terms of the original internal coordinates.


Example

Fancier version of same data