Computing excited OH stretch states of water dimer in 12-D using contracted intermolecular and intramolecular basis functions

Due to the ubiquity and importance of water, water dimer has been intensively studied. Computing the (ro-)vibrational spectrum of water dimer is challenging. The potential has 8 wells separated by low barriers which makes harmonic approximations of limited utility. A variational approach is imperative, but difficult because there are 12 coupled vibrational coordinate. In this paper, we use a product contracted basis, whose functions are products of intramolecular and intermolecular functions computed using an iterative eigensolver. An intermediate matrix $\bs{F}$ facilitates calculating matrix elements. Using $\bs{F}$, it is possible to do calculations on a general potential without storing the potential on the full quadrature grid. We find that surprisingly many intermolecular functions are required. This is due to the importance of coupling between inter- and intra-molecular coordinates. The full $G_{16}$ symmetry of water dimer is exploited. We calculate, for the first time, monomer excited stretch states and compare $P(1)$ transition frequencies with their experimental counterparts. We also compare with experimental vibrational shifts and tunnelling splittings. Surprisingly, we find that the the largest tunnelling splitting, which does not involve interchange of the two monomers, is smaller in the asymmetric stretch excited state than in the ground state. Differences between levels we compute and those obtained with a [6+6] adiabatic approximation [Leforestier et al. J. Chem. Phys. {\bf{137}} 014305 (2012) ] are $\sim 0.6$ cm$^{-1}$ for states without monomer excitation, $\sim 4$ cm$^{-1}$ for monomer excited bend states, and as large as $\sim 10$ cm$^{-1}$ for monomer excited stretch states