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Molecular orbital wavefunctions

  1. Feb 7, 2008 #1
    [SOLVED] molecular orbital wavefunctions


    starting with

    Sz(total) = Sz1 + Sz2
    Sz(alpha) = +(1/2)hbar(alpha)
    Sz(beta) = -(1/2)hbar(beta)

    I first found the determinant and then simplified

    psi = 1/sqrt(2)psi(b)^2[alpha(1)beta(2) - alpha(2)beta(1)]


    Sz1psi = 1/sqrt(2)psi(b)^2[beta(2)(1/2)h(bar)alpha(1) + alpha(2)(1/2)h(bar)beta(1)]

    Sz1psi = 1/sqrt(2)psi(b)^2[-alpha(1)(1/2)h(bar)beta(2) - beta(1)(1/2)h(bar)alpha(2)]

    Sztotal = Sz1 + Sz2 = 0

    Can someone please verify if this is correct?
    I would appreciate it.
    thank you
  2. jcsd
  3. Feb 9, 2008 #2
    I realize it's hard to read without the LaTeX, but no one can check if it's correct or not?
  4. Feb 9, 2008 #3


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    yes it seems to be ok,

    learn LaTeX, it is worth it :)
  5. Feb 9, 2008 #4


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    I don't understand that result. Shouldn't the second term be negative since it's a beta?

    You means Sz2 I think here. But the second term should be positive since it's an alpha, no?
  6. Feb 9, 2008 #5
    No because when you multiply by the -(1/2)hbar, the beta portion (the second term) becomes a positive, the opposite goes for the alpha, I think, and yes it should be an Sz2.
  7. Feb 9, 2008 #6


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    you are absolutely right, my mistake. For some reason, when i replied to your post, I forgot about the Slater determinant and I was thinking about a symmetric wavefunction. Sorry about that.
  8. Feb 9, 2008 #7
    Thank you all for your help
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