Reproducing Hydrogen Molecule Hamiltonian in OpenFermion

I am learning quantum chemistry at the moment and I'm trying to understand the Hamiltonian generated by the [OpenFermion](https://www.google.com/search?as_q=openfermion) package. I'm now stuck at understanding how openfermion calculates the coefficients in second quantization Hamiltonians.


Take the for Hydrogen molecule for example. My understanding is that the coefficients



> 
> * $h\_{00}$, represents electron 1 in 1s orbit with spin up.
> * $h\_{11}$, represents electron 1 in 1s orbit with spin down.
> * $h\_{22}$, represents electron 2 in 1s orbit with spin up.
> * $h\_{33}$, represents electron 2 in 1s orbit with spin down.
> 
> 
> 


As the wavefunction of 1s orbits takes the form


$$\psi\_{1s}(r) = \frac{1}{\sqrt{\pi}}e^{-r}$$


The $h\_{ii}$ should be


\begin{equation}
2\pi \int\_0^{\infty}\int\_0^{\pi}\psi\_{1s}(r)\left(-\frac{1}{2}\nabla^2-\frac{1}{r}-\frac{1}{\sqrt{r^2+R^2-2r R\cos\theta}}\right)\psi\_{1s}(r)r^2 \sin\theta d\theta dr
= -1.07123
\end{equation}
when $R = 0.74$ Bohr radius, which does not match with openfermion's
\begin{align}
h\_{00} &= h\_{11} = -1.2524635735648988\\
h\_{22} &= h\_{33} = -0.47594871522096416
\end{align}


Can anyone tell me why I am wrong?


