where ℎ �⃗ are the formation enthalpies of products in energy per atom (ℎ 0 is the enthalpy of formation of the starting compound, ℳ or 𝒞𝒞), and 𝒔𝒔 = (𝑠𝑠 1 ���⃗, … , 𝑠𝑠 𝑛𝑛 ���⃗) is a matrix whose column vectors are the stoichiometric coefficients for the elements to be conserved, divided by the total number of atoms (whether conserved or not), for each compound. The corresponding vector of normalized stoichiometric coefficients for the starting compound, ℳ or 𝒞𝒞, is denoted 𝑠𝑠 0 ���⃗ . Only the stoichiometric constraints expressed by entries in 𝒔𝒔 are imposed, and by omitting the row corresponding to an element (e.g., oxygen) no stoichiometric constraint is imposed.