We present results on the energetics of the hydrogen bridges for the Guanine-Cytosine pair obtained in a DNA fragment consisting of three stacked base pairs in the B-DNA conformation. The wave function computations on the 87 atom system are all-electron ab initio SCF-MO computations obtained with a basis set of 1032 primitive gaussian functions contracted to 315. Even if the results are only preliminary, one can tentatively advance conclusions relative to the molecular field effect of stacked base-pairs on the potential energy surface for a hydrogen bond. These computations have been performed with a modified version of our molecular program, which uses an IBM 4341 host and six to ten attached array processors (FPS-164) in parallel. The strategy to convert the program from sequential to parallel is briefly outlined and comparisons with our parallel system are made with a present-day "vector" super-computer. From these studies, we conclude that if one adopts the "parallel" approach presented and tested here, much larger chemical systems than previously are now amenable to all-electron ab initio computations.