No more gap-shifting: Stochastic many-body-theory based TDHF for accurate theory of polymethine cyanine dyes

We introduce an individually fitted screened-exchange interaction for the time-dependent Hartree-Fock (TDHF) method and show that it resolves the missing binding energies in polymethine organic dye molecules compared to time-dependent density functional theory (TDDFT). The interaction kernel, which can be thought of as a dielectric function, is generated by stochastic fitting to the screened-Coulomb interaction of many-body perturbation theory (MBPT), specific to each system. We test our method on the flavylium and indocyanine green dye families with a modifiable length of the polymethine bridge, leading to excitations ranging from visible to short-wave infrared. Our approach validates earlier observations on the importance of inclusion of medium range exchange for the exciton binding energy. Our resulting method, TDHF@vW, also achieves a mean absolute error on a par with MBPT at a computational cost on a par with local-functional TDDFT.