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Bonds in moleculs

  1. May 4, 2013 #1
    Bonds in molecules

    What is the meaning of the bonds σ and π in molecules quantum mechanically?
    Last edited: May 4, 2013
  2. jcsd
  3. May 4, 2013 #2


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    Staff: Mentor

    Consider a molecular orbital in a diatomic molecule. The projection of the angular momentum of an electron in that orbital on the internuclear axis is designated by the quantum number ##\lambda##. In analogy with hydrogenic orbitals, the value of this quantum number is expressed with a letter according to
    | \lambda | = 0 \Rightarrow \sigma \\
    | \lambda | = 1 \Rightarrow \pi \\
    | \lambda | = 2 \Rightarrow \delta \\
    (note the absolute value, as the projection can be positive or negative).

    For polyatomic molecules, a similar concept is applied in LCAO-MO theory where the molecular orbitals are built two atoms at a time.

    An easy way to identify the value of ##| \lambda |## is to look along the bond and count the number of nodal planes. A ##\sigma## bond will look circular, a ##\pi## bond will be in the shape of a 8, similar to a p orbital in an atom.
  4. May 4, 2013 #3
    Thank you very much. I like to know how to calculate angular momentum in molecular orbitals. Could you please give me a reference for that?
  5. May 4, 2013 #4


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    Science Advisor

    Landau Lifgarbagez, Quantum Mechanics, has a good discussion of the states of diatomic molecules apt for physicists.
  6. May 4, 2013 #5
    Thank you. I will get it.
  7. May 5, 2013 #6
    Read also: Enrico Fermi "Molecules, Crystals and Quantum Statistics".
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