Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene

Abstract

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

Double‐buffered, heterogeneous CPU + GPU integral digestion algorithm for single‐excitation calculations involving a large number of excited states

“…We have reported a hybrid CPU + GPU algorithm for efficient digestion of two‐electron integrals with a large number of density‐like matrices, by appealing to the intrinsically data‐parallel nature of this operation. This effort specifically targets the ab initio exciton model that we developed previously, for which the digestion step proves to be a significant bottleneck. For synthetic benchmarks on real systems, we demonstrate speedups of over 6× as compared to a CPU‐only algorithm running on the same hardware, and speedups of 2–6× for calculations using the AIFDEM on real systems.…”

“…Pursuing the first of these strategies, we have recently introduced a novel method for computing excited‐state properties of extended molecular aggregates . Our method is based on the old idea of an exciton model, originally due to Frenkel and Davydov, but is a fully ab initio realization of this model that we therefore dub the ab initio Frenkel‐Davydov exciton model (AIFDEM) .…”

“…The computationally intensive part of an AIFDEM calculation involves formation of a Hamiltonian whose matrix elements are given by where The notation and underlying theory is explained more fully in Ref. []. Briefly, we define the contraction of matrices R and S as where in this work, at least one of R or S is always a symmetric matrix.…”

“…These approximations make sense in the context of the photosynthetic light‐harvesting complex examined in Ref. [], where the individual chromophores are well separated, but may be problematic in densely packed molecular crystals and aggregates, and in molecular liquids, which are the applications that we have so far targeted using the AIFDEM . GPU acceleration reported in Refs.…”

Mechanism of Spin-Exchange Internal Conversion: Practical Proxies for Diabatic and Nonadiabatic Couplings

“…36 Such practical difficulty to calculate NACs has led to a search for suitable proxies to replace them. For instance, researching an SF reaction, Morrison and Herbert took the direct product of monomeric states as the wave function basis within the ab initio Frenkel-Davydov exciton model, 37 to calculate the adiabatic state and NAC, instead of the direct calculation of the entire dimer system. 38 In another study, Feng, Luzanov, and Krylov proposed a proxy for NAC based on the reduced one-particle transition between initial and final adiabatic states and used it to evaluate the NAC strength variation with different intermolecular arrangements.…”