The notion of hypersurface is used to stress the multidimensionality of
PESs. In a molecular system consisting of N atomic nuclei, the number of the independent coordinates that fully determine the
PES is equal to 3N - 6 (or 3N - 5 if the system is linear).
Source:
PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1938 (https://doi.org/10.1351/pac199971101919)