Welcome to the physically based shading in Cycles, I hope you will find your new materials to be the secret weapon to stunningly realistic renderings!
Gem materials have each their own absorption and/or light dispersion, this is especially true for diamond which have a very charateristic refraction pattern. You can alter the "purity" of the gem by dialing in the amount of absorption and its colour.
Jade material uses a complex SSS/reflection setup, allowing you to tweak the overall polishing
Studio setup included, HDRI from www.hdrihaven.com released as CC0