The chart of the elements provides a striking representation of the periodic law. The construction of an analogous periodic system of diatomic molecules has tantalized several investigators over the span of a century. There have been different approaches to the construction. In this chapter, while not denigrating other approaches, we consider the one which is solidly based on the chart of the elements. In its most general form it is a direct product of the element chart (considered as a matrix) with itself; it can be represented therefore as a four-dimensional architecture. Finding data imprinted in the element chart is trivial; finding digital data in a complex four-dimensional geometrical structure is not difficult with indexing, but in this chapter we present a semi-visual method to supplement the indexing process. We also submit a semi-visual representation of a search for new data based on surface fitting of fixed-group diatomics. The presentation of the semi-visual method begins with a very simple case in which the element chart is imagined to have just four elements and then extends to its development in the hyperstructure with main-group and transition-metal molecules. The addition of lanthanoid and actinoid molecules would present no serious difficulty.