What chemicals can save / attract energy / electricity?

I think all of them do that to a greater or lesser degree... Because of the obvious stability of matter we forget that all elements are radioactive, and that in giving up a neutron for example, they will also give up a proton, and electrons(s)... And in the process of gaining mass they may lose or gain a charge... If you are looking for simple solutions, then they have been discovered and are in battery forms already...

I was thinking about something more crystal like chemical, like sodium sulphate.

well then, re you interested in phase changes only? or are you interested in higher forms of energy lije Fido spoke of.
Glaubers is a favorite for phase change thermal masses and ot works pretty good is you fill a whole house with it.