General N-body Non-adiabatic Wave function

As we have suggested recently [68] the technique involving separation of the CM motion and representation of the wave function in terms of explicitly correlated gaussians is not only limited to non- adiabatic systems with coulombic interactions, but can also also extended to study assembles of particles interacting with different types of two- and multi-body potentials. In particular, with this approach one can calculate the vibration-rotation structure of molecules and clusters. In all these cases the wave function will be expanded as symmetry projected linear combinations of the explicitly correlated fa of eqn.(29) multiplied by an angular term, Y M. 

Here Vr is an appropriate permutational symmetry projection operator for the desired state, T, and YfcM is a product of coupled solid harmonics labeled by the total angular momentum quantum numbers L and M. Permutational symmetry is handled using projection methods in the same manner as described for the potential expansion in the previous section. Again, the reader is referred to the references for details[9,10,12], 

YkM is a vector coupled product of solid harmonics[69] given by the Clebsch-Gordon expansion, 

Cobes and R. Seiler, Quantum Dynamics of Molecules, ed. R. G. Woolley, Plenum Press, New York, 1980, p. 435. 

Martinez, R. Seiler and X. Wang, Commun. Math.Phys. 143 (1992) 607. 

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