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## Coordinates and Basis set

We use the standard body-fixed (BF) Jacobi coordinates , , and , which are the length of the distance vector between H and the center-of-mass of O, the length of the O internuclear distance , and the angle between and , respectively. The overall rotation of the complex with respect to a space fixed (SF) coordinate system is given by 3 Euler angles, collectively denoted by .

Good quantum numbers are the total angular momentum quantum number, , the projection of onto the SF -axis, , and the parity of the wave function under inversion of the SF nuclear coordinates, . We expand the wave function as a function of these quantum numbers. We use a sinc-DVR[52] with wrapped'' basis functions[53] and for the and coordinates, respectively.

For the angular coordinate, as in previous work, we employ a basis of parity adapted angular basis functions, . Here, is the rotational angular momentum of O and is the projection of both and on . The basis functions are defined as

 (1)

are associated Legendre functions in the phase convention of Condon and Shortley.[54] The are normalized Wigner D-matrices and are defined as
 (2)

with the D-matrices in the passive convention for rotations.[55,56]

This results in the following expression for the wave functions :

 (3)

is equal to 0 or 1, depending on the spectroscopic parity[57,58] . Because of the permutation inversion symmetry of the O molecule, only odd rotational states are allowed in Eq. (3).[59]

Since all calculations are independent of , we drop the superscript from now on.

Next: Hamiltonian, Propagation, and Analysis Up: Theory and Computational details Previous: Theory and Computational details
Anthony J. H. M. Meijer 2000-10-05