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The number of all two-electron integrals: $$ \tag{1} \langle \phi_1 \phi_2|\phi_3\phi_4 \rangle = \int d^3\mathbf r' \int d^3\mathbf r'' \, \phi_1(\mathbf r'') \, \phi_2(\mathbf r') \frac{1}{|\mathbf r' - \mathbf r''|} \, \phi_3(\mathbf r') \, \phi_4(\mathbf r''), $$ for $N$ number of basis funct...