Optimized attenuated interaction: Enabling stochastic Bethe-Salpeter spectra for large systems

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.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations

We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.