The symmetrical geometries of 1,3-cyclobutadiene (CB) and substitutional vacancies in crystalline fee Ar allow purely ab initio MO estimations to be made for the stabilization energies of several symmetric trapping sites in the Ar/CB matrix system at the MP2/6-311++G(2d,2p) [denoted HI-MO] level of theory. The single-substitutional vacancy supports the most stable trapping site in the HI-MO Ar/CB system. It was examined by filling an Ar-13 vacancy of the HI-MO Ar lattice with a symmetrical CB:Ar-12 kernel cluster, with dilation of the kernel cluster opposed by a symmetrical HI-MO lattice distortion PEI: derived for the purpose. In addition, various supplemental HI-MO stabilization energies were computed. Slightly displacing the four nearest-neighbor Ar atoms coplanar with CB from square-planar geometry shows this site distortion PEF is very soft. The results suggest fluxional behavior for the Ar atoms near the CB guest molecule and the soft trapping site environment provides access to equivalent global PES minima for the two valence isomers of CB. The fast automerization coordinate of CB acts in the presence of slow lattice coordinates to account for the unique spectroscopic observations on Ar/CB reported from the laboratories of J. Michl. These show (a) that CB automerizes at a rate greater than or equal to 10(3) s(-1) in cold matrices; (b) that equal populations exist for the matrix-isolated vicinally dilabeled (C-13 or D) CB valence isomers; and (c) that the automerization ZP energy levels of matrix-isolated CB are separated by an amount Delta greater than or equal to 35 cm(-1). Trapping sites for CB based on multiple Ar vacancies are not only computed to be less stable than the SS site, but they are unable to support a satisfactory explanation for the experimental observations.