Excitonic Configuration Interaction: Going Beyond the Frenkel Exciton Model

Abstract

We present the excitonic configuration interaction (ECI) method — a fragment-based analogue of the CI method for electronic-structure calculations of the multichromophoric systems. It can also be viewed as a generalization of the exciton approach which (i) allows embedding via point charges with arbitrary values in the site-state calculation, (ii) includes multi-local excitation (MLE) products of site states in the excitonic basis, in addition to the ground-state (GS) and local excitation (LE) products, and (iii) takes into account all contributions to the full-system Hamiltonian matrix elements within the strong-orthogonality assumption. Regarding (i), we present the excitonic analogue of the Hartree-Fock method — called the EHF approach — which finds the embedding charges that minimize the energy of the GS product. In (ii), one can restrict the excitation rank of the employed excitonic basis, which results in truncated-CI-like expansions (ECIS includes GS and LE products, ECISD additionally includes two-fragment excitation, etc.). The expressions for the matrix elements in (iii) are obtained within McWeeny’s group function theory, generalized to accommodate the flexible embedding in (i). We assess the performance of ECI by computing absorption spectra of two multichromophoric systems. The first system, a metal-free guanine quadruplex, has the chromophores connected via hydrogen bonds (a supramolecular complex). The second system, a guanine quadruplex with a central Mg-cation, additionally exhibits metal–ligand bonds between some chromophores. It is shown that the accuracy of ECI strongly depends on the chosen embedding charges and ECI expansion. The most accurate combinations — ECIS or ECISD with EHF embedding — yielded spectra that qualitatively and quantitatively agree with full-system direct calculations, with RMSDs of the excitation energies around 20 meV or 100 meV, respectively, for the first and second test system. We also show that ECISD based on CIS site-state calculations can predict states of dominant MLE character that would be inaccessible in a full-system CIS calculation.