We present accurate potential energy surfaces for Ar-HF, Ar-H2O, and Ar-NH3 from the supermolecular calculations using Moller-Plesset perturbation theory up to the complete fourth-order (MP4) and efficient basis sets containing bond functions. Preliminary calculations on Ar-HF are given to show the usefulness of bond functions and the stability of the results with respect to the change of the basis set. Detailed MP4 calculations on Ar-HF with a fixed HF bond length of r=[r](v=0) give a global potential minimum with a well depth of 200.0 cm(-1) at the position R=3.470 Angstrom, theta=0 degrees (linear Ar-H-F), a-secondary minimum with a well depth of 88.1 cm(-1) at R=3.430 Angstrom, theta=180 degrees (linear Ar-F-H); and a potential barrier of 128.3 cm(-1) that separats the two minima near R=3.555 Angstrom, theta=90 degrees (T shaped). Further calculations on the three main configurations of Ar-HF with varying HF bond length are;performed to obtain vibrationally averaged well depths for v=0, 1, 2, and 3. Our primary-wells are about 15 cm(-1) higher than those of Hutson’s H6(4,3,2) potential for v=0, 1, 2, and 3, and our minimum distances are about 0.05 Angstrom longer. Extensive MP2 calculations (R=3.1-5.0 Angstrom); and brief MP4 calculations (near the radial minimum) are performed for the intermolecular potentials of Ar-H,O and Ar-NH3 with the monomers held fixed at equilibrium geometry. For Ar-H,O, MP4 calculations give a single global minimum with a well depth of 130.2 cm(-1) at R=3.603 Angstrom, theta=75 degrees, phi=0 degrees, along with barriers of 22.6 and 26.6 cm(-1) for in-plane rotation at theta=0 degrees and 180 degrees respectively, and a barrier of 52.6 cm(-1) for out-of-plane rotation at theta=90 degrees, phi=90 degrees. All these are in good agreement with experiment, especially with Cohen and Saykally’s AW2 potential. The dependence of the Ar-H2O potential on an OH bond length is calculated to study the effect from excitation of the bond stretching vibration and the result agrees well with the red shift observed. For Ar-NH3, MP4 calculations give a single global minimum with a well depth of 130.1 cm(-1) at R=3.628 Angstrom, theta=90 degrees, phi=60 degrees, along with barriers of 55.2 and 38.0 cm(-1) for end-over-endrotation at theta=0 degrees and 180 degrees, respectively, and a barrier of 26.6 cm(-1) for rotation about NH3 symmetry axis at theta=90 degrees, phi=0 degrees. All these are in good agreement with experiment and Schmuttenmaer et al. AA1 potential. The effects on potential from the change of the normal NH3 pyramidal geometry to the planar geometry are calculated and the results indicate that the Sigma states with tunneling motion perpendicular to the radial coordinate remain virtually unchanged from free NH3 whereas the Pi states with tunneling motion parallel to the radial coordinate have the tunneling motion nearly quenched. Comparisons of the potentials for the systems from Ar-HF, Ar-H2O, to Ar-NH3 are made to reveal the periodic trends of bonding and structure in the van der Waals complexes.