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The Hessian of potential energy at a mechanical equilibrium, expressed in specified displacement coordinates. It determines restoring forces to first order. Combining it with the mass matrix gives the dynamical matrix whose eigenvalues are squared mode angular frequencies.

A linear combination of atomic displacements adapted to an irreducible representation of a molecular point group. Symmetry coordinates reduce the dynamical matrix into independent symmetry blocks; several coordinates in the same block can still mix.