Cyclic peptides containing even numbers of alternating D- and L-amino acids adopt a symmetric ring structure with NH and CO amide functions approximately perpendicular to the average plane of the ring. This results in hydrogen-bonded, beta-sheet like tubular ensembles by coaxial stacking of rings in which adjacent strands are oriented antiparallel to one another. Starting from a molecular mechanics minimum energy configuration having the C-4 symmetry reported for similar structures, an optimized monomer geometry which retained that symmetry was obtained using density functional theory (DFT). The geometry of the monomer is quite similar to that of stable polypeptides and proteins and the calculated gas-phase harmonic vibrational frequencies are quantitatively reasonable. Two monomers were then brought together coaxially, with adjacent strands arranged antiparallel, creating a dimer of D-4 symmetry. Dimer energy was then minimized with respect to ring separation along, and relative rotation of one ring with respect to the other about, the common C-4 axis. The interstrand separation in this dimer model is reasonable in comparison with experimental values reported for stable beta-sheet polypeptides and proteins as are the harmonic vibrational frequencies. An approximation to the harmonic N-H ... O stretching frequency calculated for this dimer model was also physically reasonable by comparison to the interchain motion calculated for beta-sheet polypeptides from analysis of experimental vibrational frequencies. Though synthesis of the molecules in this study has not been reported, they serve as excellent models for the analysis of ring structure and for isolating the role of backbone-backbone hydrogen bonds in the stacking process for similar assemblies. This study provides theoretical support for experimental work on more complex systems, and the DFT calculations are among the largest ever for the study of molecular systems using double valence single polarization basis sets.