\begin{equation}
g^{Breit}\left(1,2\right)=-\frac{c{\alpha}_{1}\cdot c{\alpha}_{2}}{2c^{2}r_{12}}-\frac{\left(c{\alpha}_{1}\cdot\mathbf{r_{12}}\right)\left(c{\alpha}_{2}\cdot\mathbf{r}_{12}\right)}{2c^{2}r_{12}^{3}}
\end{equation}