We can make the combinatorial space of multi-component compounds more tractable by introducing chemical constraints. We choose to work with the first 103 elements of the Periodic Table (from H to Lr). This pool of atomic building blocks is expanded into 421 species when the accessible oxidation states are considered. For instance, Fe(II) and Fe(III) are both formed from the element Fe, but exhibit distinct physicochemical properties such as the black pigment Fe(II)O and the red antiferromagnet Fe(III)2O3.