indeed reveals a contribution to the change in total energy due to the change of the wave functions $\Phi_j$.
However, provided that the $\Phi_j$ are eigenstates of $H$, it is easy to show that the last two terms cancel each other and in the special case of $H=T+V$ the force is given by
\begin{equation}
indeed reveals a contribution to the change in total energy due to the change of the wave functions $\Phi_j$.
However, provided that the $\Phi_j$ are eigenstates of $H$, it is easy to show that the last two terms cancel each other and in the special case of $H=T+V$ the force is given by
\begin{equation}