To mimic the experimental absorption spectrum within this formalism, a damping term is typically included in Eq. ( ). This effectively incorporates a finite lifetime of the excited state in the response function, which produces a broadening in the absorption spectrum peaks . The damping factor used in this tutorial on naphthalene is 0.01 fs -1 (see left panel of Fig. ). This approach gives the polarizability along the direction of the initially applied field, and the full polarizability tensor is obtained from three independent time propagations where the only quantity that is altered is the direction of the external electric field. The average of the polarizability along the three Cartesian axes is taken as the absorption spectrum of naphthalene, as shown in the right-hand side of Fig. .