Minimal basis CI of H2 dissociation
Using Szabo and Ostlund's notation (page 85):

\begin{align}
J_{ij} &amp;= (\psi_i\psi_i|\psi_j\psi_j)&amp;
\text{and}&amp;&amp;
K_{ij} &amp;= (\psi_i\psi_j|\psi_i\psi_j)\tag1\label{integrals}
\end{align}

For minimal basis set $\ce{H2}$ (page 162):

\begin{align}
\psi_1 &amp;= [2(1+S_{12})]^{-1/2}(\phi_1+\phi_2)&amp;
\text{and}&amp;&amp;
\psi_2 &amp;= [2(1-S_{12})]^{-1/2}(\phi_1-\phi_2)\tag2\label{minimal}
\end{align}

Substitute equation $\eqref{minimal}$ into $\eqref{integrals}$, set $S_{12}$ and any integral involving both $\phi_1$ and $\phi_2$ to zero (large $R$) and you see that

$$J_{11} = K_{12} = \frac{1}{2}(\phi_1\phi_1|\phi_1\phi_1)$$

Remember that $(\phi_1\phi_1|\phi_1\phi_1)=(\phi_2\phi_2|\phi_2\phi_2)$ since you are dealing with a homonuclear diatomic.