Hamiltonian:
$$ \begin{align} \hat{H} &= \frac{\hat{p}_1^2}{2} + v[\hat{x}_1] + \frac{\hat{p}_2^2}{2} + v[\hat{x}_2] + \frac{\kappa}{\sqrt{(\hat{x}_1-\hat{x}_2)^2 + a^2}} \tag{7}\\ &\equiv h[\hat{p}_1,\hat{x}_1] + h[\hat{p}_2,\hat{x}_2] + u[\hat{x}_1,\hat{x}_2] \tag{8} \end{align} $$Energy states:
$$ \begin{equation} \vert\Phi_k\rangle = \sum_{i < j} C_{ij, k}\frac{\vert \varphi_i \varphi_j\rangle - \vert \varphi_j \varphi_i\rangle}{\sqrt{2}}, \tag{9} \end{equation} $$(Slater basis)