deletions | additions       diff --git a/Casida, Tamm-Dancoff, and excited-state forces.tex b/Casida, Tamm-Dancoff, and excited-state forces.tex  index 24145d0..f1e9e06 100644  --- a/Casida, Tamm-Dancoff, and excited-state forces.tex  +++ b/Casida, Tamm-Dancoff, and excited-state forces.tex 
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\end{equation}  and  \begin{multline}  \left<\varphi_c \varphi_v \left| \frac{\partial \hat{A}}{\partial R_{i \alpha}} \right| \varphi_{c'} \varphi_{v'} \right> &= =  \left<\varphi_c \left| \frac{\partial \hat{H}}{\partial R_{i \alpha}} \right| \varphi_{c'} \right> \delta_{vv'} \\\nonumber  - \left<\varphi_v \left| \frac{\partial \hat{H}}{\partial R_{i \alpha}} \right| \varphi_{v'} \right> \delta_{cc'}  + \left<\varphi_c \varphi_v \left| \hat{K}_{\rm xc} \frac{\partial \rho}{\partial R_{i \alpha}} \right| \varphi_{c'} \varphi_{v'} \right>\,.  \end{multline}