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Potential Energy Surface

  1. Nov 16, 2011 #1

    jgens

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    Gold Member

    1. The problem statement, all variables and given/known data

    Estimate the ground-state potential energy surface for H2+ using the first-order perturbative change in the energy.

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I can calculate the first-order correction to the energy using the fact that [itex]E^1_0 = \langle \mathrm{1s}_A |V| \mathrm{1s}_A \rangle[/itex]. In particular,

    [tex]E_0^1 = \int_{-\infty}^{\infty}\overline{\mathrm{1s}}_A V \mathrm{1s}_A\mathrm{d}\mathbf{r} = \int_{-\infty}^{\infty}\overline{\mathrm{1s}}_A\left( \frac{1}{R} - \frac{1}{r_B}\right)\mathrm{1s}_A = e^{-2R}\left(1+\frac{1}{R}\right)[/tex]

    However, I'm having trouble getting from the first-order correction in the energy to obtaining a potential energy surface. Can anyone help with this?
     
  2. jcsd
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