$d ^{(2)}$ to rewrite $ \langle \Psi _{b} | \hat{U} | \Psi _{b} \rangle - \langle \Phi _{b} | \hat{U} | \Phi _{b} \rangle$ or $\langle \Psi _{b} | \hat{U} | \Psi _{b} \rangle - \langle \Phi ^{\prime} _{b} | \hat{U} | \Phi _{b} ^{\prime} \rangle$ as $\int _{ {\bf r} ^{\prime},{\bf r} ^{\prime \prime} \in \Omega} d ^{3} r ^{\prime} d ^{3} r ^{\prime \prime} U ( | {\bf r} ^{\prime} - {\bf r} ^{\prime \prime} | ) [ \langle {\bf r} ^{\prime} | \rho ^{(1)} | {\bf r} ^{\prime \prime } \rangle \langle {\bf r} ^{\prime \prime} | d ^{(2)} | {\bf r} ^{ \prime } \rangle + \langle {\bf r} ^{\prime} | \rho ^{(1)} | {\bf r} ^{\prime } \rangle \langle {\bf r} ^{\prime \prime} | d ^{(1)} | {\bf r} ^{\prime \prime } \rangle] $. We can take $I= |A\rangle \langle A| + | B \rangle \langle B| $ in Eq. (3) to introduce $d ^{(2)}$ on $\mathbb{C} ^{2} _{ \Omega} $. The operator $d ^{(2)}$ comes from the factor $ | \alpha _{c} | ^{2} \langle \Psi _{c} | \hat{U} | \Psi _{c} \rangle$ when we calculate $\langle \Psi _{b} | \hat{U} | \Psi _{b} 