According to Pauli's principle, two electrons in an orbital cannot have the same spin.
Does this mean, for example, that two hydrogen atoms, each with one electron, will not covalently bond to H2 if their electrons happen to have the same spin? Because then there would be two electrons in the sigma orbital with the same spin.
In general, in the covalent bond between two atoms with an even number of valence electrons (for example C-C, Mg-S, Si-O), is one electron with up spin and one from the other atom with down spin taken for the bond orbital?
Wouldn't this then lead to major restrictions when drawing Lewis structures, for example?