Now, what does electron spin have to do with putting electrons into orbitals? The answer starts with the observation that electrons are all identical. In order to account for this, we have to be sure that no electrons are treated preferentially. In particular, this means that when we label electrons in wavefunctions, we have to make sure that we do so in such a way that all physical properties we calculate do not depend on which electron we call 1, which we call 2, and so on. This non-preferential labelling is called symmetrization. One way to ensure that numbering of electrons doesn't matter is to arrange things so that if we renumber electrons, then the wavefunction does not change. This requirement is actually too rigid. If we allow that the sign of the wavefunction might change, that would still be OK, since it is the square of the wavefunction that determines electron density, and when we square the wavefunction, any sign change disappears. So, there are two ways to symmetrize many-electron wavefunctions. Many- electron wavefunctions that have been adjusted so that the sign of the wavefunction does not change on relabelling any two electrons are said to be symmetric. Many-electron wavefunctions that have been adjusted so that the sign of the wavefunction does change on relabelling any two electrons are said to be antisymmetric. In considering the symmetry of many-electron wavefunctions with respect to exchange of electron labels, we have to consider both the spatial and spin parts of the wavefunction. One procedure is to write the wavefunction as a product of space and spin parts, and to consider the symmetry of each part separately. With this background, we can state one of the most profound aspects of quantum mechanics for the material world. It is known as the Pauli principle: The overall wavefunction--spatial and spin parts--must change sign if any two electrons are relabeled. That is, many-electron wavefunctions must be antisymmetric. More generally, the wavefunction of any quantum system composed of entities with half-odd intrinsic angular momentum(spin quantum number 1/2, 3/2, 5/2,... ) must be antisymmetric. The wavefunction of any quantum system composed of entities with integer intrinsic angular momentum must be symmetric. An example is photons, the packets of light energy. Photons have intrinsic spin 1, and so the wavefunction of a collection of photons must be symmetric with respect to the relabelling of any two photons. --

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