This relationship must have been essential in the local creation of the table I’ve included above, which lacks some scientific merit, but is intrinsically tied to the folklore surrounding Soulcasting. An emerald can be used to create food—and thus is traditionally associated with a similar Essence. Indeed, on Roshar there are considered to be ten elements; not the traditional four or sixteen, depending upon local tradition.
Curiously, these gemstones seem tied to the original abilities of the Soulcasters who were an order of Knights Radiant—but they don’t seem essential to the actual operation of the Investiture when performed by a living Radiant. I do not know the connection here, though it implies something valuable.
Soulcasters, the devices, were created to imitate the abilities of the Surge of Soulcasting (or Transformation). This is yet another mechanical imitation of something once only available only to a select few within the bounds of an Invested Art. The Honorblades on Roshar, indeed, may be the very first example of this—from thousands of years ago. I believe this has relevance to the discoveries being made on Scadrial, and the commoditization of Allomancy and Feruchemy.