Christophe Iung

LSDSMS - Montpellier II - Place Eugene Bataillon - Case 14, FRANCE

This communication aims to present a general method that enables one to build kinetic energy operators in getting rid of the heaviness of differential calculus. In the present formulation [1,2], the system is described by any set of n vectors (Jacobi, Valence, Radau,... vectors). We will show how the kinetic energy can be written in terms of the (n-1) angular momenta associated to the (n-1) vectors and the total angular momentum J [3].
Application of such an approach [4] has been done for studying the ammonia spectroscopy [5]. We will show also show how this formalism can be adapted in order to study  semi-rigid molecules. In this latter case, our formalism provides a very compact, simple expression of the kinetic energy in terms of the BF projection of vector J  and the conguate momenta associated to the spherical coordinates of the vectors chosen in order to parametrize the molecule.
 

[1] "Vector Parametrization of the N-atom problem in quantum mechanics : I - Jacobi coordinates",
      F. Gatti, C. Iung, M. Menou, Y. Justum, A. Nauts et X. Chapuisat,  J. Chem. Phys., 108, 8804 (1998).
[2]  "Vector Parametrization of the N-atom problem in quantum mechanics : II - Coupled-angular-momentum spectral representation four four-atom systems"
       F. Gatti, C. Iung,  M. Menou, et X. Chapuisat, J. Chem. Phys. 108, 8821 (1998).
[3]  "Vector Parametrization of the N-atom problem in quantum mechanics with non orthogonal Coordinates"
       C. Iung, F. Gatti, A. Viel et X. Chapuisat,  Phys. Chem.  Chem. Phys., 1, 3377 (1999) .
[4]   "Vector Parametrization of the N-atom problem in quantum mechanics : III- Separation into two subsystem : Application to NH3",
        F. Gatti, J. Chem. Phys,111, 7225 (1999)
[5]   "Fully Coupled 6D Calculations of the Ammonia Vibration-Inversion-Tunnelling State with a Split Hamiltonian Pseudo-Spectral Approach"
       F. Gatti, C. Iung, C. Leforestier et X. Chapuisat