# Potential Energy Surface

1. Nov 16, 2011

### jgens

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 $E^1_0 = \langle \mathrm{1s}_A |V| \mathrm{1s}_A \rangle$. In particular,

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

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?