Y. Justum et al., N-ATOM MOLECULAR-SYSTEMS - BUNCH OF RELATIVE POSITION VECTORS, LOCAL COORDINATES AND QUANTUM-MECHANICAL KINETIC-ENERGY OPERATORS, Chemical physics, 223(2-3), 1997, pp. 211-237
After elimination of the centre of mass translation, a vector parametr
ization for an N-atom molecular system, consisting of N-1 relative pos
ition vectors, is used. Sets of 3N-6 local coordinates well suited for
describing the system are introduced: they are all made up of the N-1
vector lengths, N-2 planar angles of vector pairs and N-3 dihedral an
gles for vector triplets. In addition, three Euler angles describe the
orientation of the body-fixed frame: the first two angles allow one t
o orient the z-BF axis, either parallel to one vector or perpendicular
to the plane of two vectors; the third angle is for rotation around z
, completing the link between the molecule (i.e. the vectors) and the
BF axes. The three Euler angles, together with the 3N-6 local coordina
tes, make up a set of N-1 triplets of spherical coordinates for the re
lative position vectors, with respect to various frames. This property
is used to derive exact expressions of general quantum mechanical kin
etic energy operators, and also to propose a polyspherical-harmonics r
epresentation in which the kinetic energy matrix may take a relatively
simple form (i.e. prediagonalized to a large extent). (C) 1997 Elsevi
er Science B.V.