A coherent discrete variable representation method on a sphere.

The coherent discrete variable representation (ZDVR) has been extended for constructing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two-dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenvalues and exponential convergence with increasing ZDVR basis size.