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Unformatted text preview: of H2+, molecules have multiple electrons and hence have a total value of the angular momentum projected onto the internuclear axis. This is denoted by the quantum number Λ. If Λ=0, then reflection through a plane containing the nuclei will multiply the overall wave function by either +1 or −1; that level of the molecule is then denoted as either “+” or “−.” Note that a single electron in a σ orbital always has + symmetry, so H2+ can have no Λ=0,− levels. Also note that Λ≠0 levels are doubly degenerate (reflection can always give a state with −Λ). € Finally, in a multielectron molecule, the electrons may have unpaired spins, and hence have a quantum number S denoting the total spin of the electrons. For closed
shell molecules, S=0, but radicals (e.g. CH), odd
electron species (e.g. NO), and paramagnetic even
electrion species (e.g. O2) have nonzero electron spin. All of these symmetry properties are designated by the molecular term symbol, which is of the form 2 S +1Λ±u,g . The electron spin is treated in the same way as for atoms; the orbital angular momentum (projected onto the internuclear axis) is denoted with a Greek letter (Σ, Π, Δ, etc.); and the ± superscript applies only to Σ levels. Examples of term symbols are as follows. €
Ground state of H2+: The single electron is in the lowest
energy orbital, which has no nodes and is a σ orbital. It is symmetric under parity (which exists since H2+ is homonuclear), so this is a g orbital, and with a single electron there is a + symmetry. The lone electron has spin S=½. Thus the term symbol is 2 Σ + . g
Ground state of H2: Now there are two electrons, both in the lowest σg orbital. Their orbital wave function is symmetric, so...
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 Winter '08
 Sargent,A

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