deletions | additions       diff --git a/Casida, Tamm-Dancoff, and excited-state forces.tex b/Casida, Tamm-Dancoff, and excited-state forces.tex  index f1e9e06..ce24ecd 100644  --- a/Casida, Tamm-Dancoff, and excited-state forces.tex  +++ b/Casida, Tamm-Dancoff, and excited-state forces.tex 
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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  \begin{equation}  \frac{\partial \omega_k}{\partial R_{i \alpha}} &= =  \left< x_k \left| \frac{\partial \hat{A}}{\partial R_{i \alpha}} \right| x_k \right>\ , \end{equation}  and  \begin{multline}