Information characterizing the (X) over tilde (2)Pi state of the R.SH (R=Ne,Ar,Kr) complexes has been obtained from two complementary experimental techniques. The spin-vibronic energy levels have been determined by wavelength resolved fluorescence spectroscopy subsequent to laser excitation of specific vibrational levels of the (A) over tilde (2)Sigma(+) state. In addition, several "hot" bands from excited spin-vibronic levels of (X) over tilde (2)Pi Ne.SH have been observed and assigned. The experimental data have been used to construct a simple model for the ground state potential energy surface for each complex. These models show that the most stable conformation for each complex is linear H-bonded, but the barrier to isomerization to the S-bonded complex is quite low. The overall bonding is somewhat weaker and more isotropic than the corresponding hydroxyl complexes.