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

TL;DR

This paper presents a new stochastic, system-specific screened-exchange interaction for the TDHF method, improving accuracy in modeling polymethine cyanine dyes by capturing missing binding energies with computational efficiency comparable to TDDFT.

Contribution

Introduction of a system-specific, stochastic fitted screened-exchange interaction kernel for TDHF, enhancing accuracy for organic dyes while maintaining low computational cost.

Findings

Accurately predicts binding energies in polymethine dyes.

Achieves mean absolute error comparable to MBPT.

Maintains computational cost similar to TDDFT.

Abstract

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 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 (Flav) and indocyanine green (ICG) dye families with a modifiable length of the polymethine bridge, leading to excitations ranging from the visible to short-wave infrared (SWIR). Our approach validates earlier observations on the importance of inclusion of medium range exchange for the exciton binding energy. Our resulting method, TDHF@$v_W$, also achieves a mean absolute error on par with MBPT at a computational cost on par with local-functional TDDFT.