Role of Geometric Distortion and Polarization in Localizing Electronic Excitations in Conjugated Polymers

Abstract

Five different Density Functional Theory (DFT) models (ranging from pure GGA to long-range-corrected hybrid functionals) were used to study computationally the nature of the self-trapped electronic states in oligophenylene vinylenes. The electronic excitations in question include the lowest singlet (S1) and triplet (T1(†)) excitons (calculated using Time Dependent DFT (TD-DFT) method), positive (P(+)) and negative (P(-)) polarons, and the lowest triplet (T1) states (computed with the Self-Consistent Field (SCF) scheme). The polaron formation (spatial localization of excitations) is observed only with the use of range-corrected hybrid DFT models including long-range electronic exchange interactions. The extent of localization for all studied excitations is found to be invariant with respect to the size of the oligomer chain in their corresponding optimal geometries. We have analyzed the interdependence between the extent of the geometrical distortion and the localization of the orbital and spin density, and have observed that the localization of the P(+) and P(-) charged species is quite sensitive to solvent polarization effects and the character of the DFT functional used, rather than the structural deformations. In contrast, the localization of neutral states, S1 and T1(†), is found to follow the structural distortions. Notably, T1 excitation obtained with the mean field SCF approach is always strongly localized in range-corrected hybrid DFT models. The molecular orbital energetics of these excitations was further investigated to identify the relationship between state localization and the corresponding orbital structure. A characteristic stabilization (destabilization) of occupied (virtual) orbitals is observed in hybrid DFT models, compared to tight-binding model-like orbital filling in semilocal GGA functionals. The molecular and natural orbital representation allows visualization of the spatial extent of the underlying electronic states. In terms of stabilization energies, neutral excitons have higher binding energies compared to charged excitations. In contrast, the polaronic species exhibit the highest solvation energies among all electronic states studied.

Resonance Raman Spectra of a Perylene Bis(dicarboximide) Chromophore in Ground and Lowest Triplet States

“…All implied correlations indicated within each row are best matches for normal modes of model compounds 2 and 3, or between S 0 and T 1 states. Calculated frequencies are scaled by 0.972. excited states have been found to localize on a single unit in other conjugated systems, 53 including ethyne-linked porphyrin oligomers that are analogous to 1. 54−56 The fact that triplet excitons are localized in the latter systems on the relatively slow time scale of EPR spectroscopy implies that localization on the faster (fs) time scale of resonance Raman scattering is even more probable.…”

Singlet and triplet excitons and charge polarons in cycloparaphenylenes: a density functional theory study

“…The effect of solvent is included in a framework of the conductor-like polarizable continuum model (CPCM) using the experimentally relevant dichloromethane solvent (e r = 9.02) as implemented in the Gaussian 09 package. 27,38,39 Therefore, one has to use long-range corrected hybrid functionals in order to capture the correct physics. 2,13 It is important to stress that the popular GGA and hybrid (with the modest 20-25% fraction of orbital exchange) functionals such as PBE1 36 (also called PBE) and B3LYP 37 tend to smear the charges over the entire molecule and strongly delocalize the optical excitations.…”

“…As shown previously, 27 gas-phase calculations do not yield correct excited state geometries for singlet excitons and predict vanishing oscillator strength for fluorescence even in larger [n]CPPs in contrast to experimental observations. 38,39 Among the multiple kernels available, 35,[40][41][42][43] we chose the simple CAM-B3LYP model where the fraction of orbital exchange varies between 20% and 65% on short and long distances, respectively, whereas the intermediate region is smoothly described using the standard error function with parameter 0.33. 27,38,39 Therefore, one has to use long-range corrected hybrid functionals in order to capture the correct physics.…”

Self-Trapping of Excitons, Violation of Condon Approximation, and Efficient Fluorescence in Conjugated Cycloparaphenylenes

“…[9]CPP and larger hoops show localization in the excited state. We further note that B3LYP functional and lack of solvent model mostly used in the previous TD-DFT calculations of CPPs 5,13,17 proved to be deficient to model experimentally observed excitation localization phenomena in conjugated polymers and was unable to reproduce deformed structures 27,28 appearing due to exciton self-trapping. 33−36 Subsequently, previously reported results for excited state geometries are qualitatively different from ours (e.g., see Supporting Information Table S1 and Figure S1).…”