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lecture notes6

The ordering of orbitals is 2p u 2p g

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Unformatted text preview: the s€ wave function must be antisymmetric, giving spin pin S=0. Thus the term symbol is 1 Σ + . g Ground state of HeH+: This molecule has two electrons, and like H2 they both occupy the lowest € orbital. However, there is no parity symmetry in this molecule, so the term symbol is 1 Σ + . More generally, all molecules in which each energy level is completely filled have fully paired electrons (S=0), an equal number in positive and negative angular momentum orbitals (Λ=0), and have term symbols 1 Σ + (homonuclear) or 1 Σ + g (heteronuclear). This is analogous to noble gas structures (although the close spacing of molecular orbitals may make such species much more reactive than noble gases!). Examples include CO, CS, N2, etc. € € Ground state of O2: The O2 molecule has orbitals formed from the symmetric and antisymmetric linear combinations of the atomic orbitals on each O atom. The ordering of orbitals is: 2p σu ____ 2p πg ____ ____ 2p πu ____ ____ 2p σg ____ 2s σg ____ 2s σu ____ 1s σu ____ 1s σg ____ The 16 electrons fill the lowest orbitals, with two unpaired electrons in the πg orbital. Thus the parity symmetry will be g. Hund’s rules tell us that the electrons will go into the higher ­spin (S=1) state, so the orbital wave function must be antisymmetric. Since both the m=+1 and −1 orbitals have one electron, Λ=0. Finally, the antisymmetric combination of the πg orbitals has − symmetry. Thus the term symbol is 3 Σ− . g Excited states of O2: The lowest excited states of O2 will have the electrons in S=0, so they occupy € ymmetric combination of the π orbitals. This may be either a case of bo...
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