The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic techniques such as linear absorption and circular dichroism. In order to compare calculated Hamiltonians to experiments, a lineshape theory is needed, which takes into account the coupling of the excitons with inter- and intramolecular vibrations. This coupling is normally introduced in a perturbative way through the cumulant expansion formalism, and further approximated by assuming a Markovian exciton dynamics, for example with the modified Redfield theory.<br><br>Here we present an implementation of the full cumulant expansion (FCE) formalism [Ma and Cao, <i>J. Chem. Phys.</i> <b>2015</b>, 142, 094106 ] to efficiently compute absorption and circular dichroism spectra of molecular aggregates beyond the Markov approximation, without restrictions on the form of the exciton-phonon coupling. By employing the LH2 system of purple bacteria as a challenging test case, we compare the FCE lineshapes with the Markovian lineshapes obtained with the modified Redfield theory, showing that the latter present a much poorer agreement with experiments. The FCE approach instead accurately describes the lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the FCE approach will become a valuable tool for accurately comparing model exciton Hamiltonians with optical spectroscopy experiments.
Cumulant expansion for systems with large spins