- #1
jgens
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Homework Statement
Estimate the ground-state potential energy surface for H2+ using the first-order perturbative change in the energy.
Homework Equations
N/A
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?