Ab Initio Implementation of the Frenkel–Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates

Abstract

A fragment-based method for computing vertical excitation energies of molecular clusters is introduced based on an ab initio implementation of a Frenkel-Davydov exciton model consisting of singly excited monomer basis states. Our strategy is to construct and diagonalize the exact Hartree-Fock Hamiltonian in such a basis. Matrix elements between nonorthogonal determinants are computed via the corresponding orbital transformation and the resulting generalized eigenvalue problem is solved to determine collective excitation energies and wave functions. The basis may be expanded to include higher-lying fragment excited states in order to account for interfragment polarization effects. Absolute errors of ≲0.1 eV (relative to supersystem methods) are achievable for systems such as water clusters and crystalline arrays of organic chromophores such as pentacene and napthalenediimide. Preliminary tests for a nine-chromophore subunit of an organic nanotube suggest that it is possible to target the optically bright state, even when it is a high-lying excitation, by using carefully selected basis states. The highly parallel nature of this method provides a foundation for further developments to treat collective excitations in large molecular assemblies.

A model hamiltonian tuned toward high level ab initio calculations to describe the character of excitonic states in perylenebisimide aggregates

“…However, the dimer model, where only two dye molecules out of a larger aggregate are explicitly considered, was employed successfully to obtain parameters of the FE–CT model . Further developments of these models incorporate coarse‐gaining strategies for the determination of coupling parameters between FE and partially also CT‐configurations …”

“…[24,44,54,56,57] Further developments of these models incorporate coarse-gaining strategies for the determination of coupling parameters between FE and partially also CT-configurations. [20,[58][59][60][61] Due to its potential of interpreting excited states, the amount of FE and CT excitation character is of high interest and several useful tools have been developed for this purpose. [22,[62][63][64][65] Among these FE-CT analysis approaches, the approach of Liu et al [22] sticks out as it provides not only the amount of FE and CT character of the excited state but also the energies and coupling parameters of the configurations of a FE-CT model Hamiltonian.…”

EXAT: EXcitonic analysis tool

“…[20] Since then the exciton model has been applied to systems of increasing complexity and in particular it has been successfully used to predict the CD spectra of proteins, [21][22][23][24] pigmentprotein complexes, [25][26][27] and nucleic acids. [28][29][30][31] In most applications, quantum mechanical (QM) methods have been used to determine the fundamental quantities of the exciton model, with various approaches for the calculation of exciton couplings, [21,23,[32][33][34][35][36][37][38][39][40] and possibly extending the model to charge-transfer (CT) states. [41] The QM version of the exciton model is particularly interesting as, in principle, it is parameterfree; however, the quality of the results strongly depends on the level of QM theory adopted to describe the subunits and their interactions.…”

Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver

“…Choosing these parameters empirically to match experiment or other reference data is the crux of the phenomonological Frenkel-Davydov exciton model [60,61]. Recently, we introduced a new ab initio exciton model approach [45][46][47][48][49], in which the parameters of the exciton model are determined explicitly by high-level ab initio computations on the isolated monomers, under the assumption of sufficient monomer separations to relax the fermionic antisymmetry constraint. We have extended the ab initio exciton model to treat full non-adiabatic dynamics through the development of analytical gradients/coupling vectors [46,47] and have increased the basis set to include both local and charge-transfer excitations [47].In this ab initio exciton model the Hamiltonian matrix elements in Equation 8 all have distinct physical origins: E is the mean-field energy, Z A is roughly (half) of the difference between the ground and excited state energy of monomer A, X X AB is the transition-dipole-transitiondipole interaction and ZZ AB is the difference-dipoledifference-dipole interaction between monomers A and B, and X Z AB and ZX AB are transition-dipole-differencedipole interaction cross terms.…”