Canonical-Ensemble Response from Spin-Adapted Time-Dependent Density Functional Theory

Abstract

Low-lying electronic states of different spins can be thermally populated in open-shell molecules, allowing optical absorption to begin from several initial states. We formulate their canonical optical response using the electronic levels and one-body matrices of spin-adapted time-dependent density functional theory. Boltzmann populations determine the contribution of each initial state, while transition density matrices determine its coupling to the final states. Absorption and stimulated emission then give the temperature-dependent strength of every allowed transition. Transition matrices are evaluated from the calculated first-order excitation amplitudes, with the additional mixed second-order electronic response omitted by this approximation identified explicitly. The resulting response function provides spin-resolved polarizabilities and absorption spectra with definite total spin assigned to each participating electronic state. Applications to diradicals provide a qualitative interpretation of their temperature-dependent absorption spectra.