Experimental data from vibrationally and rotationally resolved laser induced fluorescence experiments have been used to produce potential energy surfaces (PES) for the excited (A) over tilde(2) Sigma(+) states of the AR.SH and Kr.SH van der Waals complexes. This was done using a potential energy functional form first suggested by Bowman and co-workers [J. Phys. Chem. 94, 2226, 8858 (1990); Chem. Phys. Lett. 189, 487 (1992)] for Ar.OH/D. A discrete variable representation (DVR) of the vibration-rotation Hamiltonian was used in combination with the implicitly restarted Lanczos method and sequential diagonalization truncation (SDT) of the DVR Hamiltonian. This approach takes advantage of the sparseness of the DVR Hamiltonian and the reduced order of the SDT representation. This combination of methods greatly reduces the amount of computational time needed to determine the eigenvalues of interest. This is important for the determination of the PES that results from minimizing the difference between the experimental and theoretically predicted values for the vibronic energy levels and their corresponding rotational constants. In addition this procedure was helpful in assigning the absolute vibrational quantum numbers for the deuterated species for which less experimental data was available. Flats of the calculated wavefunctions corresponding to various experimentally vibronic bands indicate that these states sample regions of the PES from 0 degrees, where the hydrogen atom is closest to the rare gas atom, to approximately the saddle point, near the T-shaped configuration. As a result this region of thr surface is determined accurately whereas the region of the PES around 180 degrees, corresponding to the sulfur atom being closest to the rare gas atom, is determined only qualitatively. (C) 1997 American Institute of Physics.