The expectation value of the kinetic energy expressed in atomic units for electron \( i \) is

$$ \langle \hat{K}_i \rangle = -\frac{1}{2}\frac{\langle\Psi|\nabla_{i}^2|\Psi \rangle}{\langle\Psi|\Psi \rangle}, $$ $$ \begin{equation} \tag{11} K_i = -\frac{1}{2}\frac{\nabla_{i}^{2} \Psi}{\Psi}. \end{equation} $$ $$ \begin{align} \frac{\nabla^2 \Psi}{\Psi} & = \frac{\nabla^2 ({\Psi_{D} \, \Psi_C})}{\Psi_{D} \, \Psi_C} = \frac{\nabla \cdot [\nabla {(\Psi_{D} \, \Psi_C)}]}{\Psi_{D} \, \Psi_C} = \frac{\nabla \cdot [ \Psi_C \nabla \Psi_{D} + \Psi_{D} \nabla \Psi_C]}{\Psi_{D} \, \Psi_C}\nonumber\\ & = \frac{\nabla \Psi_C \cdot \nabla \Psi_{D} + \Psi_C \nabla^2 \Psi_{D} + \nabla \Psi_{D} \cdot \nabla \Psi_C + \Psi_{D} \nabla^2 \Psi_C}{\Psi_{D} \, \Psi_C}\nonumber\\ \tag{12} \end{align} $$ $$ \begin{align} \frac{\nabla^2 \Psi}{\Psi} & = \frac{\nabla^2 \Psi_{D}}{\Psi_{D}} + \frac{\nabla^2 \Psi_C}{ \Psi_C} + 2 \frac{\nabla \Psi_{D}}{\Psi_{D}}\cdot\frac{\nabla \Psi_C}{ \Psi_C} \tag{13} \end{align} $$