Origin of the Excited-State Absorption Spectrumof Polythiophene

Ras Baizureen Roseli, Patrick C. Tapping, and Tak W. Kee∗

Department of Chemistry, The University of Adelaide, South Australia 5005, Australia

E-mail: tak.kee@adelaide.edu.auPhone: +61-8-8313-5039

Abstract

The excited states of conjugated polymers playa central role in their applications in organicsolar photovoltaics. The delocalized excitedstates of conjugated polymers are short-lived(τ < 40 fs) but are imperative in the pho-tovoltaic properties of these materials. Pho-toexcitation of poly(3-hexylthiophene) (P3HT)induces an excited-state absorption band butthe transitions that are involved are not wellunderstood. In this work, calculations havebeen performed on P3HT analogues using non-linear response time-dependent density func-tional theory to show that an increase in theoligomer length correlates with the dominanceof the S1 → S3 transition. Furthermore, thepredicted transition energy shows an excellentagreement with experiment. The calculationsalso yielded results on intramolecular chargetransfer in P3HT due to the S1 → S3 transi-tion, providing insight into the mechanism ofexciton dissociation to form charge carriers.

Graphical TOC Entry

Keywords

P3HT, density functional theory, CAM-B3LYP,intramolecular charge transfer, exciton dissoci-ation

1

Organic solar cells are photovoltaic devicesconsisting of electron donor and acceptor semi-conducting materials with domain sizes of sev-eral nanometers.1,2 Photoexcitation of eitherthe donor or acceptor materials leads to thegeneration of molecular excitons, which subse-quently migrate to the donor-acceptor hetero-junction to undergo dissociation to form thehole and electron on the donor and acceptor, re-spectively.3,4 Owing to strong Coulombic forcesbetween the hole and electron, these species canstill interact across the heterojunction. For or-ganic solar cells that exhibit a significant ef-ficiency, including those composed of a conju-gated polymer (donor) and fullerene (acceptor),however, an effective charge separation at theheterojunction has been attributed to rapid dif-fusion of charges.5,6 In 2012, a study by Bakulinet al. suggested that delocalized states of theexciton play a role in the effective formationof separated charges.7 More recently, Gelinaset al. used a combination of ultrafast tran-sient absorption spectroscopy and modeling toshow that long-range charge separation requiresrapid motion of the hole and electron away fromthe heterojunction through delocalized statesof the exciton.8 Using the excited-state absorp-tion (ESA) band of blends of a number of con-jugated polymers and fullerene, it was shownthat electron-hole separation occurs with a timeconstant of <40 fs.8 Although the ESA bandof conjugated polymers is often used to revealinsight into the dynamics of excitons and sep-arated charges, the physical nature of the ab-sorption band, particularly the transitions thatare involved, is insufficiently understood.

Polythiophenes are some of the most widelystudied conjugated polymers in organic so-lar cells.9 Poly(3-hexylthiophene) (P3HT), asshown in Figure 1, is one of the most studiedconjugated polymers.10,11 Phenyl-C61-butyricacid methyl ester (PCBM) is typically usedalongside P3HT as an electron acceptor ina bulk-heterojunction organic photovoltaic de-vice.12 Regioregular P3HT can aggregate dueto face-to-face π–π stacking, resulting in crys-tallization and formation of nanofibers, whichhave long-range order.13,14 The use of P3HTnanostructures in organic photovoltaics has led

to an improved power conversion efficiencybecause of efficient exciton and hole trans-port.15–19

** *

*

Figure 1: (Top) Chemical structure of regioreg-ular P3HT. (Bottom) Two views of the opti-mized structure of the 3MT heptamer in theS1 state, showing a C−C−C−S dihedral angle(red asterisks on P3HT structure) of 0°.

The photophysical and photochemical prop-erties of P3HT have been studied with fem-tosecond laser spectroscopy to reveal exci-ton lifetime,20 torsional relaxation,21 exci-ton hopping,22,23 self localization,24,25 chargetransfer,26,27 charge generation,3,28,29 and exci-ton dissociation of P3HT.30,31 Excited-statepolythiophenes in solution exhibit a near-infrared (NIR) absorption band centered at1100 nm.20,32 This induced absorption band, oran ESA band,30,33 has been used to understandthe relaxation dynamics of P3HT and chargetransfer reaction with PCBM.27,28 The NIRESA band of P3HT films or aggregates hastwo components, that is, an exciton band at1200 nm, which is a major component at earlytime, and a hole-polaron band at 1000 nm whichis present several nanoseconds after charge sep-aration.20,27,34 Although there is vast literatureon the ESA band of P3HT, a detailed under-standing of the physical nature of this inducedabsorption band is still unavailable.

2

Recently, Ling et al. reported a computa-tional study on the ESA of a different set ofoligomers, namely, oligofluorenes, offering in-sight into the transitions that are involved.35

These authors performed nonlinear-responsetime-dependent density functional theory(TD-DFT) calculations using the Coulomb-attenuated Becke 3-Parameter (Exchange),Lee, Yang, and Parr (CAM-B3LYP) functionalon oligofluorenes ranging from the dimer toheptamer, showing that the NIR ESA band isdue to a dominant S1 → S5 transition. TheCAM-B3LYP functional has been employedin other recent computational studies of con-jugated oligomers, showing high-level perfor-mance in predicting the physical and chem-ical properties of these systems.36–42 In thisstudy, the electronic properties of the S1 ex-cited state of oligothiophenes are investigatedusing nonlinear-response TD-DFT. The com-putational methods used are shown in the Sup-porting Information (SI). The 3-hexylthiophene(3HT) oligomers are approximated using 3-methylthiophenes (3MT), as shown in Figure 1.We have performed calculations to show thatsubstitution of the hexyl side-chains of olig-othiophenes with methyl groups has negligibleinfluences on its electronic structure, as shownin Figure S1 in SI. In addition, we have alsoshown that the use of the CAM-B3LYP func-tional is crucial in obtaining the ESA spectrumthat agrees with experiment, as shown in FigureS2.

The optimized structure of the heptamer inthe S1 state is shown in Figure 1, highlightingthe planar arrangement with a C−C−C−S (redasterisks) dihedral angle of 0°. The optimizedstructure in the S0 state is given in Figure S3of SI, showing that the ground-state geometryis nonplanar with an average dihedral angle of∼30°. The structures of other oligomers arealso shown in Figure S3, which agree with thoseby Bhatta et al. on 3HT oligomers.43 In addi-tion, Figure S4 shows that the length of thealkyl side-chains plays a negligible role in theoptimized structure in the S1 state. In a verti-cal excitation, an electronic transition occursfrom the S0 to the S *

1 state, which exhibitsthe greatest Franck-Condon overlap with S0.

The subsequent relaxation from S *1 to S1 in-

duces planarization of the oligomers, which hasbeen observed spectroscopically as a spectralshift in both ultrafast transient absorption andphotoluminescence studies.21,25 The torsionalmotions occur rapidly (∼100 fs), lowering theexcited-state energy and increasing the effec-tive conjugation length of the oligomers, whichis evident in the changes of the C−C and C−−Cbond lengths in the S0 and S1 states. In the ex-cited state, the shortening of the C−C and cor-responding lengthening of the C−−C bonds arecharacteristics of the aromatic-to-quinoid liketransitions, indicating the presence of the exci-ton.44 Interestingly, while the trimer displays acomplete inversion to the quinoidal type geom-etry in the S1 state, this distortion remains lim-ited to the central region for larger oligomers,with a spatial extent of about three thiopheneunits. For the heptamer, however, the terminalthiophene rings in the S1 state exhibit similarbond lengths to those in the S0 state, suggest-ing that it can support localization of the exci-ton.45,46

Figure 2 shows the oscillator strengths of theESA peaks of 3MT oligomers as a function ofexcitation energy. The ESA spectrum of thetrimer has two contributions, that is, the S1 →S2 and S1 → S3 transitions with similar os-cillator strengths. In contrast, the ESA spec-tra of the tetramer and pentamer have threedifferent contributions, arising from the formertransitions and S1 → S5 transition. For thehexamer and heptamer, only the S1 → S2 andS1 → S3 transitions are the contributing tran-sitions. The S1 → S3 transition, however, hasa substantially higher oscillator strength thanthe S1 → S2 transition. Figure 2 also shows thesignificant increase in the oscillator strength ofthe S1 → S3 transition as the oligomer length-ens, with it being the dominant transition forthe heptamer. The effect of solvent on the ESAspectrum was also investigated and Figure S5in SI shows the insignificant difference betweenthe calculated ESA spectrum in tetrahydrofu-ran and vacuum.

The S1 → S3 ESA peak position of the hep-tamer is close to the experimental value ofP3HT, which is indicated by the dashed line

3

0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

S2

S3Heptamer

0.0

0.5

1.0 Hexamer

S2

S3

0.0

0.5

1.0 Pentamer

S2

S3

S5

0.0

0.5

1.0 Tetramer

S2

S3S5

0.0

0.5

1.0

1.5

Trimer

S2S3

Osc

illat

or S

tren

gth

ΔE (eV)

Figure 2: Calculated ESA peaks for 3MToligomers. The excitation energies correspondto the transitions from the S1 state to a higher-lying Sn excited state, where n ranges from 2to 5. The vertical dashed line indicates the ex-perimental ESA peak position of P3HT.30

in Figure 2. Furthermore, the S1 → S3 energygap of 3MT oligomers shows a red shift witholigomer length, as shown in SI (Figure S6), ex-hibiting a 1/n dependence, where n is the num-ber of repeating units. This dependence hasbeen observed for oligothiophenes47–49 and sug-gests that only a minor decrease in the S1 → S3

energy gap is expected for any oligomers longerthan the heptamer. Therefore, the heptamersystem is sufficiently large to yield quantita-tive results for comparison with experiment. Inthis case, the experimental ESA peak positionof P3HT chains is 1.17 eV and the predictedvalue for the heptamer (1.22 eV) differs by only<0.1 eV, showing a good agreement.30,32 Thisresult is similar to a previous study by Linget al., in which the predicted and experimentalESA peaks of polyfluorenes differ by <0.2 eV.35

In order to demonstrate the agreement, Fig-ure 3 shows the experimentally measured ESAspectrum of P3HT30 and the calculated spec-trum of the heptamer. The calculated spec-trum was broadened using a Gaussian functionwith a best-fit full width at half maximum of0.36 eV. The difference between the two spec-tral peaks in Figure 3 is 0.07 eV. In the inset ofFigure 3, the calculated spectrum is shifted bythis minor energy difference, showing an excel-lent agreement to the experimental spectrum.30

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Energy (eV)

Nor

mal

ized

osc

illat

or s

tren

gth

(a.u

.) CalculatedExperimental

0.9 1.0 1.1 1.2 1.3

Figure 3: ESA spectra of P3HT from exper-iment (red),30 and as calculated for the 3MTheptamer (black). The inset shows an excel-lent agreement between the spectra when thecalculated spectrum is shifted by −0.07 eV.

The reproduction the ESA spectrum of P3HTusing such a simplified system and relatively

4

nonresource intensive computational method isinitially surprising, given that the accurate cal-culation of the ground-state absorption spec-trum of conjugated polymers can be challeng-ing.39,50 In solution, thermal and solvent ef-fects cause the polymer to adopt a random-coil geometry with a wide distribution of inter-monomer angles and dihedrals. Consequently,the ground-state chromophores are highly dis-ordered, and thus defining a chromophore pre-cisely is a complex task.51–53 Furthermore, theabsorption spectrum is not solely due to anysingle chromophore but is composed of an en-semble of chromophores with a variety of envi-ronments and geometries. Choosing a represen-tative selection of chromophores is a challenge,even before considering a suitable method andthe associated computational costs. To ad-dress these obstacles, simulation of the opticalproperties of conjugated polymers is often per-formed using classical methods to obtain thepolymer geometry and simplified quantum me-chanical methods with the ability to scale tosystems with hundreds or thousands of chro-mophores.49,54,55 In contrast with the ground-state S0 geometry, the excited S1 state of P3HTis more ordered and well defined. As shownin Figure S3 and S4 in SI, the S1 state adoptsa planar geometry, regardless of the side-chainsubstituents. While the vertical S0 → S *

1 exci-tation involves ∼20 thiophene units of a highlydisordered chain, the exciton localizes to 5–10monomeric units, driving the planarization ofthe chromophore site. Similar to the ground-state absorption, the ESA is also due to an en-semble of chromophores but in this case eachindividual chromophore can be sufficiently de-scribed as a planar oligothiophene of 5 to 10monomeric units.

The excellent agreement between the mea-sured ESA spectrum of P3HT and that of the3MT heptamer calculated using TD-DFT withthe CAM-B3LYP functional is consistent witha previous study.35 Ling et al. showed that TD-DFT calculations using CAM-B3LYP produceESA spectra that exhibit agreement with exper-iment,35 demonstrating the importance of ac-counting for the long-range contributions to theelectronic exchange interactions. In addition to

excited-state properties, CAM-B3LYP includescharge-transfer contributions to electronic ex-citations. The application of CAM-B3LYP onpredicting the charge-transfer properties of theexcited states of a 3MT oligomer is discussedbelow. Additional results and further discus-sion on the choice of functional may be foundin SI.

To reveal insight into the charge transfer char-acter of the S1 → S3 transition, we turn to theelectron density change involved in this tran-sition. The electron density difference, ∆ρ(r),between the excited state and ground state canbe evaluated as

∆ρ(r) = ρexcited(r)− ρground(r) (1)

where ρexcited(r) and ρground(r) are the electrondensities of the excited and ground states atposition r. There is, however, no direct methodto calculate the electron density changes of theS1 → S3 transition. Therefore, eq 2 is used torelate the electron density changes of the S1 →S3 transition to those of the S0 → S1 and S0 →S3 transitions.

∆ρS1→S3(r) = ∆ρS0→S3(r)−∆ρS0→S1(r) (2)

This approach provides an indirect route to ob-taining the electron density change between theS1 and S3 states. On the basis of eq 1, an in-crease in electron density corresponds to more“electron” character, while a decrease in elec-tron density corresponds to more “hole” char-acter.

Figure 4 shows the electron density differ-ence calculated for the S1 → S3 transition ofthe heptamer. The increase in electron den-sity is concentrated in the middle region of theoligomer, with the corresponding decrease oc-curring along the oligomer’s ends, as indicatedby the black arrows in Figure 4. The middle re-gion of the 3MT heptamer undergoes a “switch”in the electron and hole positions in compari-son with both the S0 → S1 and S0 → S3 tran-sitions (SI, Figure S7). An increase in electrondensity occurs at the central sulfur atom forboth the S0 → S1 and S0 → S3 transitions. Forthe S1 → S3 transition, however, the same sul-

5

fur atom shows an electron density decrease,indicating charge movement, or intramolecu-lar charge transfer, along the backbone of theoligomer. This “switch” has also been observedby Denis et al. for the S1 → Sn transition com-pared with the S0 → S1 transition for fluo-rene homopolymers and fluorene-based copoly-mers.56 The electron density difference for theS1 → S3 transition of other oligomers exhibitsa similar behavior and is shown in Figure S8 inSI. The intramolecular charge transfer charac-ters were also investigated using a natural tran-sition orbital analysis and the results are shownin SI (Figure S9).

Figure 4: Electron density difference of the3MT heptamer for the S1 → S3 transition,where the violet and turquoise regions repre-sent the increase and decrease, respectively, inelectron density. The arrows serve to highlightthe movement of charge. The isosurface valueused to visualize the electron density difference

is 0.0005 �A−3

The intramolecular charge transfer process isa primary indicator of the capacity for an exci-ton to dissociate into free charge carriers. Ex-perimentally, we have used transient absorptionspectroscopy to demonstrate charge carrier gen-eration in P3HT chains through targeted pho-toexcitation of the ESA band.30 We have useda femtosecond pump-push-probe technique toisolate the relaxation processes and products ofthe higher-lying Sn state. The computationalwork presented here offers new insight, confirm-ing that charge carrier generation occurs on iso-lated polymer chains through an intramolecu-lar charge-transfer intermediate. In the experi-ment, the visible pump-pulse vertically excitesP3HT from the ground-state to form the S *

1

singlet exciton. The high-energy exciton thenundergoes relaxation within ∼100 fs to the S1

state. The NIR push-pulse is tuned to match

the ESA band, further exciting the S1 exciton toa high-energy state, Sn. From the results in thisstudy (Figure 2), we can now assign the previ-ously unknown Sn state to S3. From the S3 statethe exciton rapidly relaxes back to S1, but in theexperiment ∼11% of the S3 exciton populationdirectly returns to the ground-state rather thanback through S1. This phenomenon was at-tributed to dissociation of the exciton into elec-tron and hole-polaron charge carriers. We havenow shown that such dissociation on isolatedchains is possible due to the charge transfer na-ture of the S3 state, where the movement ofelectrons occurs predominantly from the outerregions to the center of the chromophore. Be-cause the separated electrons and holes are stillspatially restricted to a single P3HT chain,geminate recombination occurs rapidly, result-ing in a direct return to the S0 ground-state.

In short, we have used nonlinear response TD-DFT to gain insight into the ESA band of P3HTin the NIR region. Computational studies us-ing the CAM-B3LYP functional have been con-ducted on the 3MT oligomers ranging from thetrimer to heptamer to show that the ESA bandcorresponds to the S1 → S3 transition. The os-cillator strength of this transition increases as afunction of oligomer length and it becomes thedominant transition of the 3MT heptamer. Thepredicted energy of the S1 → S3 transition ex-hibits an excellent agreement with experiment.The results also reveal the charge transfer char-acter of the S1 → S3 transition, which is consis-tent with experimental results on exciton disso-ciation because of optical pumping of the singletexciton.

Acknowledgement This research was un-dertaken with the assistance of resources pro-vided at the Phoenix High Performance Com-puting service at the University of Adelaide.We acknowledge the assistance of Mr. Rohan J.Hudson in the DFT calculations and Dr. DavidM. Huang for his comments and suggestions forthis manuscript.

6

Supporting Information Avail-

able

(1) Computational methods, (2) influence ofside-chain substituents, functional, and solva-tion on computed excited state transitions,(3) geometry of 3HT and 3MT trimers, 3MTtetramer to heptamer optimized in S0 and S1

states, (4) calculated S1 → S3 transition en-ergies with 3MT oligomer length, (5) electrondensity difference of 3MT heptamer for S0 →S1 and S0 → S3 transitions, and S1 → S3 tran-sitions for 3MT trimer to hexamer, (6) natu-ral transition orbitals of the S0 → S1 and S0

→ S3 transitions of the 3MT heptamer, (7)input commands to compute excited state ab-sorptions using Dalton2016 software, (8) Carte-sian coordinates for all molecular structures.

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