The vibrational motion of N atom molecular system, moving on a potential energy surface, V(q) can be described by n = 3N -6 internal coordinates, q = [q 1 , q 2 , . . . q n ]. Considering the body-fixed (BF) Cartesian coordinates expressed as functions of the internal coordinates, x = x (q), i.e x α = x α (q 1 , . . . , q n ), α = 1, . . . 3N, the standard expression of the deformation part of the kinetic energy operator (KEO) in terms of the contravariant components of the metric tensor G ij (q) and with the Euclidean volume element, dν E , reads as :