deletions | additions       diff --git a/Casida, Tamm-Dancoff, and excited-state forces.tex b/Casida, Tamm-Dancoff, and excited-state forces.tex  index c822325..8bbafed 100644  --- a/Casida, Tamm-Dancoff, and excited-state forces.tex  +++ b/Casida, Tamm-Dancoff, and excited-state forces.tex 
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The energy of a given excited state $k$ is a sum of the ground-state energy and the excitation energy: $E_k = E_0 + \omega_k$.  The force is then given by the ground-state force, minus the derivative of the excitation energy:  \begin{align}  F^{k}_{R_{i \alpha}} F^{k}_{i \alpha}  = -\frac{\partial E_k}{\partial R_{i \alpha}} = F_{R_{i \alpha}} F_{i \alpha}  - \frac{\partial \omega_k}{\partial R_{i \alpha}}\ . \end{align}  Using the Hellman-Feynman Theorem we find the last term without introducing any additional sums over unoccupied states.  In the particular case of the Tamm-Dancoff approximation we have