A NUMERICALLY EXACT FULL-DIMENSIONAL CALCULATION OF RO-VIBRATIONAL LEVELS OF WATER DIMER

_x000d_ _x000d_ We have developed a new method for computing numerically exact rovibrational levels of a Van der Waals dimer_x000d_ with flexible monomers and applied it to water dimer, a 12-dimensional cluster._x000d_ %_x000d_ The method uses basis functions that are products of an inter-monomer function and an intra-monomer function._x000d_ The inter-monomer function is a product of Wigner functions, used to study dimers within the rigid monomer_x000d_ approximation. The intra-monomer functions are monomer vibrational wavefunctions._x000d_ %_x000d_ When the coupling between inter- and intra-monomer coordinates is weak, this new basis is very efficient _x000d_ and only a few monomer vibrational wavefunctions are necessary. The product structure of the basis makes it efficient to use the Lanczos algorithm _x000d_ to calculate eigenvalues and eigenfunctions of the Hamiltonian matrix._x000d_ In particular, potential matrix-vector products are evaluated, without storing the potential on a full-dimensional grid,_x000d_ by adapting the F-matrix idea previously used to compute _x000d_ rovibrational levels of 5-atom and 6-atom molecules _x000d_ with a contracted basis and an iterative eigensolver.footnote{X.-G. Wang and T. Carrington Jr. J. Chem. Phys. {bf 119}, 101 (2003) and {bf 129}, 234102 (2008).}_x000d_ %_x000d_ %_x000d_ We have obtained numerically exact and converged inter-monomer energy levels and compare these with results _x000d_ obtained using the 6D + 6D adiabatic approach on the CCpol-8sf {em ab initio} potential energy surface.footnote{C. Leforestier, K. Szalewicz, and A. van der Avoid, J. Chem. Phys. {bf 137}, 014305 (2012).}_x000d_ %_x000d_ We have also obtained the water bend levels and their shifts. We compare with results of the previous adiabatic calculation and experiment._x000d_ _x000d