Optimum Exchange for Calculation of Excitation Energies and Hyperpolarizabilities of Organic Electro-optic Chromophores

Abstract

Organic electro-optic (OEO) materials integrated into silicon-organic hybrid devices afford significant improvements in size, weight, power, and bandwidth performance of integrated electronic/photonic systems critical for current and next generation telecommunication, computer, sensor, transportation, and defense technologies. Improvement in molecular first hyperpolarizability (β), and in turn electro-optic activity, is crucial to optimizing device performance. Common hybrid density functional theory (DFT) methods, while attractive due to their computational scaling, often perform poorly for optical properties in systems with substantial intramolecular charge-transfer character, such as OEO chromophores. This study evaluates the utility of the long-range corrected (LC) DFT methods for computation of the molecular second-order nonlinear optical response. We compare calculated results for a 14-molecule benchmark set of OEO chromophores with the corresponding experimentally measured β and one-photon absorption energy, λmax. We analyze the distance dependence of the fraction of exact exchange in LC-DFT methods for accurately computing these properties for OEO chromophores. We also examine systematic tuning of the range-separation parameter to enforce Koopmans'/ionization potential theorem. This tuning method improves prediction of excitation energies but is not reliable for predicting the hyperpolarizabilities of larger chromophores since the tuning parameter value can be too small, leading to instabilities in the computation of βHRS. Additionally, we find that the size dependence of the optimal tuning parameter for the ionization potential has the opposite size dependence of optimal tuning parameter for best agreement with the experimental λmax, suggesting the tuning for the ionization potential is unreliable for extended conjugated systems.

Structural Progression in Clusters of Ionized Water, (H2O)n=1–5+

“…Similarly, the 5A−5D gap is 1.27 kcal/mol with MPW1K, compared to 1.20 kcal/mol with the benchmark EOM method, although other isomers exhibit larger errors. Whether this accuracy continues in much larger systems, where the optimal fraction of HF exchange in density functionals is known to vary, 119 remains to be determined. The method, therefore, is not sufficient for numerical benchmark accuracy (and may not be sufficient to distinguish isomers which are close in energy) but the overall energy landscape for small clusters is reproduced nicely.…”

DFT predictions of the oxidation potential of organic dyes for opto-electronic devices

“…For all the used functionals, equilibrium geometries were computed only for the most stable conformer of each dye. Indeed at variance with dipole moments [41][42][43], ionization energies are known to exhibit a marginal dependence on conformations [22].…”

“…Low-exchange hybrid GGA functionals are expected to provide reliable predictions of oxidation free energies only for donor-acceptor dyes possessing a short bridge, for which no delocalization is expected upon ionization, possibly because in that case localizing solvation effects are sufficient to balance the self-interaction error [22]. Finally high exchange and range separated GGA functionals are not a practical choice for oxidation free energies because the restricted open shell formalism has to be adopted for unpaired electron species to prevent an unphysical energy lowering due to spin contamination.…”

“…1, all of them undergo single electron oxidation. Most of them are donoracceptor (DA) conjugate chromophores such as the tricyanofuran amine 12 which exhibits non linear optical activity [20][21][22], amino oligoenes 1-5 [23], coumarine and perylene dyes (13,16) used so far as sensitizers for dye sensitized solar cells (DSSC) [24,25].…”

Density-functional errors in ionization potential with increasing system size

“…Indeed, our recent study of ω tuning of charge-transfer chromophores showed that the size-dependent trends in the Koopmans' optimized ω were opposite to those that gave the best agreement with experimental excitation energies. 52 The present work investigates the relationships between molecular size, delocalization error, accuracy of the computed ionization potential, and the effectiveness of ω tuning, for a series of gas-phase organic molecules. The results show that the delocalization error introduces a systematic underestimation of the IP that increases with system size and that the computed IP is also not size-extensive.…”