Nuclear gradients for the excited state are state-of-the-art in many program codes, so that the general procedure will only be outlined in short to discuss modifications that are necessary for ADMM and sTDA kernels. To avoid the computational cost of calculating the first-order response of the MO coefficients and to take into account the geometry dependence of the AOs, the Lagrangian of Eq. ( ) needs to be extended by means of two additional constraints and thus is given as,