This paper investigates Monte Carlo techniques for construction of compact wave functions for the internal atomic motion of the D3O+ ion. The polarization force field models of Stillinger et al. and of Ojamae et al. were used. Initial pair product wave functions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair product wave functions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair product wave functions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair product wave functions, the traditional variational theorem permits identification of wave function features with significant potential for further optimization. The most important explicit correlation variable found for the D3O+ ion was the vector triple product r(OD1) . (r(OD2) X r(OD3)). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wave function with an error of 5-6% in the zero point energy.