When we look at the binding energy spectrum of an element, we see peaks originating from various atomic orbitals. If the atom changes in chemical state, the peak positions shift around. For example, the 2p and 2s peaks of Si shift to a higher binding energy in SiO2. But when a molecule is formed the atomic orbitals combine to form molecular orbitals. For example, the Si signals in SiO2 are no longer actually coming from 2s and 2p orbitals (I suspect they are due to non-bonding molecular orbitals formed by lone pair electrons from oxygen), yet we continue to give them these labels. Why?
It is of course correct that strictly spoken all states observed in XPS are mixed-atom states and no longer isolated atomic orbitals. For valence bond energy ranges that are observed in UPS you will rarely find an "atomic orbital" notation but rather a MO state notation building on individual DFT or WF calculations.
In the case of Si2x you have states that are not in the valence band but that are of course close to it, but those states are still pretty much dominated by that single orbital and therefore it is widely considered appropriate to leave the "simple atomic name" which building on their proximity to the atomic orbital binding energy is a quite decent approximation to reality and allows for a much more convenient assignment than introducing a new notation every time.
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