Exciton Absorption Spectra by Linear Response Methods: Application to Conjugated Polymers

The theoretical description
of the time-evolution of excitons requires,
as an initial step, the calculation of their spectra, which has been
inaccessible to most users due to the high computational scaling of
conventional algorithms and accuracy issues caused by common density
functionals. Previously (J. Chem. Phys. 2016, 144, 204105), we developed a simple method that
resolves these issues. Our scheme is based on a two-step calculation
in which a linear-response TDDFT calculation is used to generate orbitals
perturbed by the excitonic state, and then a second linear-response
TDDFT calculation is used to determine the spectrum of excitations
relative to the excitonic state. Herein, we apply this theory to study
near-infrared absorption spectra of excitons in oligomers of the ubiquitous
conjugated polymers poly­(3-hexylthiophene) (P3HT), poly­(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene)
(MEH-PPV), and poly­(benzodithiophene-thieno­[3,4-b]­thiophene) (PTB7). For P3HT and MEH-PPV oligomers, the calculated
intense absorption bands converge at the longest wavelengths for 10
monomer units, and show strong consistency with experimental measurements.
The calculations confirm that the exciton spectral features in MEH-PPV
overlap with those of the bipolaron formation. In addition, our calculations
identify the exciton absorption bands in transient absorption spectra
measured by our group for oligomers (1, 2, and 3 units) of PTB7. For
all of the cases studied, we report the dominant orbital excitations
contributing to the optically active excited state–excited
state transitions, and suggest a simple rule to identify absorption
peaks at the longest wavelengths. We suggest our methodology could
be considered for further developments in theoretical transient spectroscopy
to include nonadiabatic effects, coherences, and to describe the formation
of species such as charge-transfer states and polaron pairs.