deletions | additions       diff --git a/Casida, Tamm-Dancoff, and excited-state forces.tex b/Casida, Tamm-Dancoff, and excited-state forces.tex  index 8516888..c9ae23e 100644  --- a/Casida, Tamm-Dancoff, and excited-state forces.tex  +++ b/Casida, Tamm-Dancoff, and excited-state forces.tex 
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\centering  \begin{tabular}{ccccc|c}  RPA & Petersilka & Tamm-Dancoff & Casida & Variational & Exp't \\ \hline  8.234 & 9.421 & 9.343 & 9.254 & 9.671 & 9.309  \\ 8.234 & 9.421 & 9.343 & 9.254 & 1.028 10.28  & 9.309  \\ 9.671 & 9.671 & 9.671 & 9.671 & 1.028 10.28  & 9.921  \\ 9.671 & 1.024 10.24  & 1.024 10.24  & 1.022 10.22  & 1.079 10.79  & 10.270  \\ 9.671 & 1.024 10.24  & 1.024 10.24  & 1.022 10.22  & 1.080 10.80  & 10.270  \\ 9.671 & 1.103 11.03  & 1.093 10.93  & 1.092 10.92  & 1.108 11.08  & 12.199  \\ \end{tabular}  \caption{  \label{tab:nitrogen_casida}  Calculated The first 6  excitation energies (in eV) for the N$_2$ molecule with different approximations to TDDFT in the electron-hole basis. The VWN LDA parametrization \cite{Vosko_1980} was used for the exchange-correlation functional, the  bond length is 1.098 \AA, the real-space grid was a sphere of radius 7.4 \AA with spacing 0.16 \AA, and 16 unoccupied states were used.} used. The experimental data is from Ref. \cite{Ben-Shlomo_1990}.}  \end{table}  % consider notation about spin-polarization elsewhere  For a non-spin-polarized system, the excitations separate into a singlet and a triplet subspace,  which are superpositions of singlet and triplet KS transitions:  \begin{align}