Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S-8 rings, on the interaction between a pair of such rings, and the reaction between one S-8 ring and the triplet diradical S-8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid-liquid phase transition. The results of these simulations will be presented in Part II. (C) 2003 American Institute of Physics.