Singlet and triplet energies of α-oligothiophenes: A spectroscopic, theoretical, andphotoacoustic study: Extrapolation to polythiopheneJ. Seixas de Melo, Luıs M. Silva, Luıs G. Arnaut, and R. S. Becker Citation: The Journal of Chemical Physics 111, 5427 (1999); doi: 10.1063/1.479825 View online: http://dx.doi.org/10.1063/1.479825 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/111/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linearacenes J. Chem. Phys. 131, 224321 (2009); 10.1063/1.3270190 Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition J. Chem. Phys. 122, 224901 (2005); 10.1063/1.1929731 Electronic structures and dynamics of the excited triplet states of α,ω-diphenylpolyynes J. Chem. Phys. 114, 1775 (2001); 10.1063/1.1331614 On the triplet–singlet energy gap of acetylene J. Chem. Phys. 112, 7008 (2000); 10.1063/1.481299 π-dimers of oligothiophene cations J. Chem. Phys. 112, 5353 (2000); 10.1063/1.481105

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Singlet and triplet energies of a-oligothiophenes: A spectroscopic,theoretical, and photoacoustic study: Extrapolation to polythiophene

J. Seixas de Melo,a) Luıs M. Silva, and Luıs G. ArnautChemistry Department, University of Coimbra, 3049 Coimbra, Portugal

R. S. BeckerInstituto de Tecnologia Quı´mica e Biologica, Rua da Quinta Grande 6, 2780 Oeiras, Portugaland Department of Chemistry, University of Arkansas, Fayetteville, Arkansas 72701

~Received 30 March 1999; accepted 28 June 1999!

The triplet state energies,ET(0 – 0), for the a-oligothiophenes (an’s! with n51 – 7, weredetermined and vary from 18 000 cm21 ~a2! to 13 000 cm21 ~a7!. The data were obtained fromspectroscopic and calorimetric measurements. It was found that the triplet energies decrease with theincrease ring number~n!, leveling off beginning with thea-oligothiophene withn55. A linearrelation was obtained for the triplet energy as a function of the reciprocal ofn. The data has allowedthe extrapolation to polythiophene (n5`) and the evaluation of its triplet energy~>10 000 cm21!.The energies~0–0! of the first singlet excited state ofn51 – 7 were also evaluated and again a linearrelation was found for theE@S1(0 – 0)# as a function of 1/n. The S12T1 energy splitting,DE(S12T1), was determined and also found to decrease with the increase in the number ring.Semiempirical molecular orbital theoretical calculations reproduce this same trend of decreasingDE(S12T1) with n. Extended FEMO theory was applied to the singlet and triplet energies as afunction of the number ofp electrons of the system. The data obtained are discussed regarding thelength of the chain needed for an effective conjugation similar to that of the polymer (n5`) andthe geometries of the singlet and triplet states of thea-oligothiophenes. ©1999 American Instituteof Physics.@S0021-9606~99!00236-6#

I. INTRODUCTION

Oligothiophenes have received a lot of attention in thepast two decades essentially due to the fact that thea-oligothiophene withn53, know asa-terthienyl (a-T),has been shown to be a potent photosensitizer.1,2 The highefficiency of singlet oxygen formation together with the highstability towards light ofa-T and some of its derivativesgave origin to a great number of studies involving its photo-dynamic behavior, see, for example,~Refs. 1–6!.

They have revealed potentially important characteristicsfor nonlinear optics applications, prototypes of electronic de-vices such as light-emitting diodes, field-effect transistors,electronic semiconducting materials, and potential electrolu-minescent devices like optical switches.6–14 Relating to thelast consideration,a-oligothiophenes are generally being in-vestigated as model compounds of the conjugated polymer,the polythiophene,7 since it is considered an excellent semi-conducting material when doped.10

The photophysical properties ofa-oligothiophenes andpolythiophene, ap-conjugated polymer, have been inten-sively studied and in particular the excited-state dynamics ofsinglet and triplet states since their properties are closelyconnected with the luminescence efficiency which is obvi-ously related to the efficiency of electroluminescentdevices.7–9,13–15The energy of the lowest singlet and tripletstate ofa-oligothiophenes has been intensely studied in re-

cent years.6–9,14–22The absence of phosphorescence of thesecompounds, most probably due to a very efficient internalconversion from the triplet to the ground state6 calls for al-ternative techniques to measure their triplet energies. A con-sequence of this is that no absolute and reliable triplet ener-gies have been made for the oligothiophenes in general. Theone exception is an estimate made by Scaiano and co-workers fora3 using the solvent induced heavy atom effectto promote theS0→T1 transition.23

The possibility of studying thean’s or alkyl-substitutedan’s in solution, contrary to the polythiophenes, made thema preferential target and a model for polythiophenes.8,13

a-sexythienyl~a6! was reported to be the first organic com-pound displaying semiconducting properties.14

The focus of many spectral and photophysical studiesof an’s, has been the nature and state energy order of thetwo lowest singlet excited states6,24,25 ~because they areinteresting analogues of polyenes26!, and their tripletenergies.16,17,19–21,27The assignment of the first singlet ex-citedp, p* state has been done for oligothiophenes up to andincluding n57. The lowest state was established to be the~1!1 Bu-like state.6 The suffix ‘‘like’’ is applied because theexact molecular symmetry is not known, but takingan’s asplanar and in thetrans ~or anti! conformation, they belong toC2v andC2h symmetry group.8

Time-resolved photoacoustic calorimetry~PAC! is apowerful tool for studying the energetics and lifetimes ofphotoinduced transients in solution.28 This technique mea-sures the heat released following the absorption of a pulse of

a!Author to whom correspondence should be addressed. Electronic mail:sseixas@cygnus.ci.uc.pt

JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 12 22 SEPTEMBER 1999

54270021-9606/99/111(12)/5427/7/$15.00 © 1999 American Institute of Physics

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light by the sample. The amount of heat deposited in thesystem depends on the enthalpies of the reactions and theirquantum yields. Additionaly, the time scale of the heat depo-sition can be related to the lifetimes of the reactingspecies.28,29

In our work we obtained the triplet energies for a largenumber of oligothiophenes and found a linear relation be-tween the triplet energy and the reciprocal of the number ofthiophene rings in thean’s. This gives us access to the trip-let energy expected for oligothiophenes withn.7 as well asfor the polythiophene polymer withn5`. We also mea-sured theS1-T1 energy splitting,DE(S1-T1), and found it todecrease with an increase in the number of rings. Semiempir-ical molecular orbital calculations using the AM1~Ref. 30!method agree with this trend.

II. EXPERIMENT

Thea-oligothiophenes were obtained and purified as de-scribed elsewhere.6 O-hydroxybenzophenone~2-HBP! andb-carotene~both from Aldrich! were used as received.

The solvents used were of spectroscopic or equivalentgrade. 1,4-dioxane was purified by the following procedure.It was made react with FeSO4 for 48 h and then a HClsolution~37% w/w! in water~1:10! was added. At this stagethe solution turns yellow pale. The solution was refluxed for12 h, and KOH pellets were added until two clear phaseswere observed and the pale yellow color vanished. Aftercooling, more KOH pellets were added and left stirring overmore 12 h. Finally the organic phase was fractionally dis-tilled over sodium.

The concentrations of the solutions ranged from131025 to 1026 M.

Absorption and fluorescence spectra were recorded in aShimadzu UV-2100 and SPEX Fluorog spectrometer, re-spectively. Our PAC apparatus was recently described.29 ThePAC cell follows the front-face design with a dielectric mir-ror protecting the transducer from the light impinging on thecell.31 This minimizes the background and increases the sen-sitivity of the measurements. The sample and reference so-lutions flow with a 1 ml /min rate through a 0.11 mm thickcell, where they are irradiated with an unfocused PTI dyelaser ~model PL2300!, pumped by a N2 laser working at afrequency of 2 Hz, or directly with the N2 laser. The olig-othiophenesa2 and a3 were irradiated atlexc5337 nm,whereasa4, a5, anda7 were irradiated atlexc5421 nm. Ina typical PAC experiment, we first match the absorbances ofthe reference~2-HBP or trans-b-carotene! and sample solu-tions at the excitation wavelength~337 or 421 nm!. The ab-sorbances of the solutions employed are in the 0.3–0.7 rangeat the excitation wavelength. Then, 100 acoustic waves ofthe sample, reference and pure solvent are collected and av-eraged in the same experimental conditions. Four sets of av-eraged sample, reference, and solvent waves are used fordata analysis at a given laser intensity, and four laser inten-sities are employed in each experiment. The different laserintensities are obtained by interposing neutral density filterswith transmissions in the 30%–100% range~79%, 57.7%,and 32.6% when usinglexc5337 nm and 73.5%, 48.8%, and27.2% forlexc5421 nm). All the sample, reference, and sol-

vent solutions were deaerated by continuously bubbling N2

during the course of the experiment ensuring by that waythat all the samples were kept continuously free of O2. Thepure solvent signal was scaled by the fraction of light ab-sorbed by the sample in the PAC cell~typically 5%! andsubtracted from the sample and reference signals before dataanalysis. We use the Marquardt program previouslydescribed32 to deconvolute the sample and reference signals.The photoacoustic calorimetry references were chosen be-cause they convert all light energy absorbed into thermalenergy in a time much shorter than the transducer oscillationfrequency~2.25 MHz!.

The semiempirical MO~using the AM1 Hamiltonian30!calculations were performed in a Silicon Graphics Inc O2workstation using theMOPAC6.0 version running in Cerius2

~from Molecular Simulations Incorporated-MSI! environ-ment. In all the cases configuration interaction involving 100~5 HOMO and 5 LUMO! configurations was used.

A program based on Marquardt’s algorithm33 was usedfor the adjustments performed with Eq.~9! in the discussionof FEMO theory.

III. RESULTS AND DISCUSSION

Time-resolved PAC gives the fraction of heat released innonradiative processes, as well as the decay times associatedwith such processes. In the case ofa-oligothiophenes, thefractions of heat released can be conveniently divided into afast and slow step (f1 andf2). The fast step has a lifetimeshorter than 1 ns (t1<1 ns), and includes the internal con-version fromSn to S1(f IC1

), the internal conversion fromS1

to S0(f IC2), the intersystem crossing to the triplet manifold

(f ISC1), and the relaxation of the spectroscopically formed

ground state species~see Fig. 1!. The thermal energy re-leased in the fast step is therefore given by

FIG. 1. Simplified Jablonski-type diagram illustrating the deactivation pro-cesses occurring after the excitation with a pulse laser (Eabs) of the an’s.Radiative deactivation,Ef ~fluorescence! andEp ~phosphorescence!; radia-tionless deactivation, IC1, internal conversionSn;;→S1 , IC2, internalconversion S1;;→S0 , ISC1, intersystem crossingS1;;→Tn;;→T1 , ISC2, intersystem crossingT1;;→S0 . The decay timest8, t9, andt- are associated with the IC1, IC2, and ISC1 processes and can be roughlyconsidered to be identified with the experimental lifetime obtained fromPAC, t1 . The lifetimet2 is associated with the ISC2 process. The fractionof dissipated radiationless energy in the PAC experiment is given by theparametersf1 andf2 ~see text!.

5428 J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 de Melo et al.

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f1•Ehn5~ESn2ES1

!•f IC11ES1

f IC21~ES1

2ET1!

•f ISC11DErfF . ~1!

The last term in Eq.~1! is related with the contribution of theground state species relaxation, within the studied time win-dow, to the thermal energy dissipated in the lifetimet1 . Theenergy ofS1 , ES1

, is therefore a joint contribution of therelaxation termplus the energy of fluorescence given byEn max ~the energy at the maximum fluorescence intensitytaken as the gaussian center of the fluorescence band!, ES1

5En max1DEr .The second heat released occurs on a much longer time

scale (t2.10ms) and is associated with the radiationlessprocesses originating from the lowest triplet state. In the ab-sence of O2 and phosphorescence, we have

f2Ehn5ET1f ISC1

. ~2!

In the equations above,f represents the quantum yield of theprocesses illustrated in Fig. 1, andEhn is the energy of thelaser (Ehn584.84 kcal mol21 at 337 nm and Ehn

567.91 kcal mol21 at 421 nm!. The adequacy of the two-component, four parameter kinetic model to interpret the ex-perimental photoacoustic waves can be assessed from thecomparison between the experimental wave of the sample~E-wave! and the wave calculated with the fitted parameter~C-wave!, Fig. 2.

The difference between theE- andC-waves is typically1/100 of the amplitude of the waves. For thea-oligothiophenes under consideration the singlet lifetimes areall shorter than 1 ns, ranging from 46 ps~a2! to 0.85 ns~a7!.6,24 The formation of the triplet state is very fast for thetime resolution of our experiments and it is therefore accept-able to set the lifetime of the first exponential decay tot1

51 ns. For these and other studies29 it was seen that shortervalues fort1 do not introduce any change of the other pa-rameters in the deconvolution procedure.

The energy of the laser light absorbed (Ehn) is dissi-pated by radiative and radiationless processes. The first aremeasured by fluorescence and the latter by PAC. The equa-tion relating such is given by

Ehn5EF1Ehn~f11f2!, ~3!

where EF is the integrated radiative energy of the singletstate ~fluorescence!, f1 and f2 are the fractions of laserenergy released as thermal energy in the lifetimest1 andt2 ,respectively~see Fig. 1!.

The energy lost by fluorescence is given by

EF5E EF~ n !•I F~ n !

I 0dn, ~4!

whereI F and I 0 are the intensities of emitted and absorbedlight. If we approximate the emission band to a Gaussianshape, we can simplify Eq.~4! to

EF5En max•fF . ~5!

In the case ofan’s it is known that the internal conversionfrom S1 to the ground statef IC2

is essentially negligiblesincefT1fF>1 ~Ref. 6! and that onlyS1 emits radiation(f IC1

51). Thus, Eq.~1! can be simplified and rearranged to

fT•ET5~12f1!•Ehn2fF•En max. ~6!

In Table I we present the experimental values obtained byPAC, the fluorescence parameters as well as the triplet quan-tum yields6 needed to determine the triplet energies accord-ing to Eq.~6!. Equation~2! with f ISC1

5fT gives us a moredirect access to the triplet energies,ET . However, the 2.25MHz transducer does not accurately integrate heat decaywith lifetimes longer than a few microseconds and the errorassociated with the experimental measurement off2 is muchlarger than that of the measurement off1 .

The extrapolation of the spectroscopic properties of thean’s to polythiophene is one of the most interesting andpursued goals.6–9,14,16,19–22,34,35This happens because of thedifficulty in characterizing the solid~polythiophene polymer!since unsubstituted oligothiophenes withn>6 are verypoorly soluble.

Figure 3 presents several plots concerning the spectro-scopic triplet and singlet energies as a function of the recip-rocal of the thiophene number of rings ina-oligothiophenes.

The singlet energies presented in Fig. 3 were obtained attemperatures of 77 and 293 K.34 The 0–0 energies were ob-tained from the intersection of normalized absorption andfluorescence spectra.6,34 There is no significant difference be-tween the fits obtained at 77 and 293 K.

Oligothiophenes of longer chain, ranging froma6 toa11 ~actually 6,7,9, and 11! sensitize C60 by energy transfergenerating the triplet-state of C60.

20,21 Since the triplet en-ergy of C60 (1.57 eV,12 663 cm21) ~Ref. 19! lies below thatof an’s 1–7 ~see Table I! the foregoing results20,21 are ingood agreement with ours regarding the limits of the tripletenergies of longer chain oligothiophenes.

For a3, a value of 13 890 cm21 ~720 nm! exists forT1

which was determined from theS0→T1 transition;23 no otherexperimental values seem to exist forT1 energies ofa-oligothiophenes. This value can be compared to ours of

FIG. 2. PAC waves fora3 in dioxane at 293 K. Shown as the insert is thelegend of the waves.Ecalc, calculated wave;E exp, experimental acousticwave; Res* 10, residuals times 10~see text for more details!.

5429J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 Extrapolation to polythiophene

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15 533 cm21 ~644 nm! ~see Table I!, displaying a differenceof 1643 cm21. In one of the works,16 advanced levels oftheory are compared to some experimental published data.Triplet energies that are reported are those obtained fromdirect experiment23 ~only one! and from reported data ofT2T maxima fora3 anda4.36 The latter is a highly question-able procedure since it is quite clear that at leasta3 anda4have more than one T-T absorption band in the spectralregions examined.6 A value for the polythiophene triplet en-ergy, 1.49 eV~>12 018 cm21!,16 was obtained by extrapola-tion and compared with theory.16 This is very close to ourvalue for a7 and considerably above our value fora` ~seeTable I!. Clearly this procedure~triplet energies obtainedfrom so-calledT1→Tn absorption maxima! is not a rationalway to obtain triplet state energies. Despite all these facts,we decided to use our previousT1→Tn data in order tosimply compare the possible energies obtained fora` by socalledT1→Tn absorption maxima with those of others.

Our T12Tn data6 in Fig. 3 give a very different slopethan the one reported for theT1(0-0) energy obtained byPAC and consequently, the extrapolated obtained value forT1 of a` is very different depending on which correlation isconsidered. It should also be noticed that theT12Tn linear-ization, made whena1 is excluded, puts theT12Tn maximafor a` with a energy value that is lower than the one pre-dicted for T1(0 – 0). This clearly cannot be possible andthereforea1 should be considered, although its inclusionleads to a much poorer linear fit (R50.97). All other fitspresented in Fig. 3 have correlation factors>0.99, includingT12Tn maxima when the value fora1 is excluded. Others15

have obtained for poly-~3-octylthiophene! an overall maxi-mum of theT2T absorption band at 800 nm~12 500 cm21!.If we consider our fit in Fig. 3 forT12Tn ~max!, includinga1 ~-3-3-3-3-line!, the extrapolated value has exactly thissame value.

It is instructive to compare our study of the singlet andtriplet state energy of thean’s with the determinations pub-lished by Belleteˆte et al.37,38 They made a joint theoretical~using semiempirical AM1 and INDO/S MO calculations!and experimental~basically from singlet absorption data inseveral solvents! study to elucidate the conformational be-havior of a2 anda3 in the S0 and S1 states. From theorythey predicted the energies of theS1 andT1 state ofa2 to be29 733 cm21 and 10 771 cm21, respectively. As a conse-quence of the type of study and data used, no experimentaltriplet data was obtained. Fora3, the predicted values were24 402 cm21 for S1 and 9894 cm21 for T1 .38 Comparison ofthese values with those reported~in Table I! shows theS1

energies are in good agreement. However this same is nottrue for theT1 energies. Belleteˆte et al.38 calculate tripletenergy values as a function of the rotational angle betweenrings. They agree with our experimental results fora2 anda3 when the angle is'60° for a2 and '75° for a3 ~seeTable I and Ref. 38! which are obviously unrealistic distor-tions to have any validity.

By analyzing absorption and fluorescence data fora32a6, Yanget al.22 used a correlation of the 0–0 vibrationalenergies (S1←S0) with 1/d ~whered stands for the numberof double bonds! to predict theE0 – 0 for the S1←S0 transi-tion for a polythiophene with infinite conjugation to be'16 290 cm21. This value is intermediate between our pre-diction based on data atT5293 K (17 290 cm21) and T577 K (15 305 cm21). A value of 2.1 eV~16 938 cm21! wasreported for theS1(0 – 0) energy of the polythiophene film39

by absorption techniques. For poly~3-octylthiophene! film avalue of 2.07 eV~16 667 cm21! exists.40 Also for the poly-mer it is reported that photochemical polymerization ofa2an a3 generates different types of polymers.41 For this lightinduced polymerization, polymers with 50 and 20 units~fora2 anda3 polymers, respectively! were obtained giving rise

TABLE I. Spectroscopic and calorimetric data for thean’s in dioxane at 293 K. See text for more details.

anEn max

~Hz! (31014) fTa

(12f1)Ehn

~kcal/mol!FTET

~kcal/mol!tT

a

~ms!ET(0 – 0)c

~cm21!DES-T

c

~cm21!Es(0 – 0)~293 K!

Es(0 – 0)~77 K!

a1 ¯ ¯ ¯ ¯ 28 200b 11 600 39 800a2 8.19 0,94 49.71660.987 48.39 146 18 003 11 937 29 940 29 673a3 7.04 0,93 45.72960.483 41.30 108 15 533 10 043 25 576 25 149a4 6.41 0,71 40.63860.620 29.626 48 14 594 8 511 23 105 22 573a5 5.99 0,60 41.22161.688 23.76 29 13 854 7 815 21 669 21 094a6 5.74 0,60 d d

¯ ¯ ¯ 20 582 19 838a7c 5.54 0,60 40.13560.541 22.17 >15 12 923 7 275 20 198 19 589a`~1/n relation!

¯ ¯ ¯ ¯ ¯ 9 988 5 257 or 7 302e 17 290 15 305

a`~FEMO!

11 525( l 520.418)

3 582 15 107( l 51.347)

aValues from Ref. 6.bValue obtained from the on-set of the phosphorescence spectrum since this is the only oligothiophene presenting phosphorescence emission. See textandRef. 6.

cEstimated assumingFT512FF . Due to the accuracy obtained for theFT values Ref. 6, the triplet energy values and consequently theDE(S12T1) shouldonly contain two significant values, that isET(0 – 0) would be 28 200 cm21 ~for a1!, 18 000 cm21 ~a2!, 16 000 cm21 ~a3!, 15 000 cm21 ~a4!, 14 000 cm21

~a5!, 13 000 cm21 ~a7! and 10 000 cm21 for a`. However we decide to use the obtained values~with five significant values! because the calorimetric valuesdo present a large accuracy.

dCompound not soluble in this solvent at the concentration level required to have a clear photoacoustic signal.eFirst value is the one extrapolated and obtained in Fig. 4; second value obtained from the difference betweenET(0 – 0) andEs(0 – 0) values at 293 K in thetable.

fa7 is actually a dibutyl substituted oligothiophene~Ref. 6!.

5430 J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 de Melo et al.

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to 2.23 and 0.64 eV for the energies, respectively, of theS1

and T1 states of thea2-generated polymer and of 2.01 and0.64 eV, respectively for theS1 andT1 energies of thea3-generated polymer.41 For poly~3-alkylthiophene! an estimatefor the triplet state energy of 1.57–1.72 eV exists.19

A report of a3 and polymer phosphorescence, claimsthat the spectra ofa3 is identical to that of the polymer andis wavelength dependent.17 As discussed elsewhere6 theseare questionable results because the triplet energy of thea3monomer and the polymer should not be identical. In addi-

tion our data show thatT1 states of these to be>8000 cm21

different.In Fig. 4 the singlet–triplet splitting energy is presented,

again as a function of 1/n. Contrary to what might be ex-pected, as we have noted above,DE(S12T1) does not havea constant value, rather it decreases asn increases. If weexclude thiophene we obtain a good linear fit that predictstheDE(S12T1) to be equal to 5257 cm21 for polythiophenewheren5`, see Fig. 4. This value is not equal to the oneobtained if we simply subtract the values obtained for theenergies ofS1 andT1 obtained by extrapolation~see Table Iand Fig. 3!, which in that case is equal to 7302 cm21. Aprobable cause for the difference is the fact that for the de-termination of the energies ofS1 and T1 for the poly-thiophene, Fig. 3, all data includinga1, were used while forthe DE(S12T1) vs 1/n plot, Fig. 4,a1 was excluded. Thequestion that arises is whether the value ofDE(S12T1) de-creases until it reaches the value of 5257 cm21 for n5` or,if the value begins to level off froma5 ~7815 cm21! througha7 ~7275 cm21! anda` ~7302 cm21!. Taking into consider-ation the observations made earlier regarding the nonexclu-sion of a1 in the correlation ofT12Tn maxima, we aretempted to conclude that the value of 7302 cm21 forDE(S12T1) of a` is probably more justified.

It is generally accepted that theory fails to predict accu-rate triplet energies. Nonetheless in the present case, as canbe seen in Fig. 5, our results indicate that good predictionsare seen regarding the trend in theenergy splittingbetweenS1 andT1 .

In Fig. 6 we present an energy diagram for the singletand triplet 0–0 energies of the oligothiophenesn51 – 7 andthe value obtained by extrapolation for polythiophene. Thisplot shows the decrease in the energy of the first singlet andtriplet excited states asn increases.

FIG. 3. Plots of energies of the lowest triplet and singlet states obtainedfrom spectroscopic and calorimetric data for thea-oligothiophenes (n51 – 7). ~a! Plots as a function of 1/n. All the experimental data wereobtained atT5293 K except where mentioned. For theT12Tn(max) datatwo linearizations are shown including~3-3! a1 data and excluding~•••!a1 data.~b! plot of theT1(0 – 0) energies as a function ofn and 1/n.

FIG. 4. Singlet–triplet energy splitting as a function of 1/n for thean’s 1–7obtained from data in Table I and Fig. 3. The presented linear fit is obtainedwhen the value fora1 is excluded.

5431J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 Extrapolation to polythiophene

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IV. EXTENDED FEMO THEORY APPLIED TO THEa-OLIGOTHIOPHENES

The previous fits of the 0–0 singlet and triplet state en-ergies have predicted the expected behavior for a oligoth-iophene of infinite chain length. These are however simpleempirical relations and a further interpretation of them isrestricted to the values of the energies for the polythiophenea` himself. Polyenes constitute a classical example of howthe FEMO theory is successfully applied. Oligothiophenescan be considered as polyenes with a fixed skeleton, derivedfrom the rigidity that the thiophene ring and inter-ring bond-ing brings to the overall structure. For polyene type mol-ecules, Kuhn derived an expression relating theDE ofHOMO and LUMO orbitals with the number ofp electronsof the system,42,43

DE5h2

8mL2 ~N11!1V0S 121

ND , ~7!

whereh is Planck’s constant,m is the electron mass,L is thechain length~or more exactly the extension of thep conju-

gated system!, N is the number ofp electrons, andV0 is aconstant value. This formula was first applied to severalspectroscopic properties of the oligothiophenes (n52 – 6) byRentschet al.24 These authors have used the expression ofL5(N11)d to define the electron box length, withd51.4 Å. This is in fact the crucial parameter to be defined.According to Taubmann the effective length of the conju-gated chain cannot just be taken as to be the distance be-tween the two terminal carbon atoms.44 It has beenproposed44 that the effective length,L, of the moleculeshould be given by

L5~N1 l !d, ~8!

where l is a parameter to be adjusted andd is an averagedC–C and CvC bond length, usually considered to be 1.40 Åfor polyenes.42,43Our average for the bond length taken fromAM1 individual C–C and CvC distances in the chain is1.4025 Å, which matches perfectly with the one obtained forpolyenes. Substituting Eq.~8! into Eq. ~7! one obtains

DE5h2

8md2

~N11!

~N1 l !2 1V0S 121

ND . ~9!

In Fig. 7 we present the obtained fits for the singlet andtriplet energies as a function of the number ofp electrons~N! according to Eq.~9!. The adjustments made gave perfectfits when the adjustment is made with three fitting param-eters@(h2/8md2),l , andV0#. The values obtained, forV0 andl, for a` can be seen in Table I. At this stage, two pointsneed attention. First of all we will consider the limiting valuefor DE. For a box of infinite length theDE should be equalto V0 , i.e., for L→` we get DE>V0 . For the poly-thiophene, theE0 – 0 of the singlet state should be in the 2.0–2.1 eV ~16 100–17 000 cm21! range ~average between the

FIG. 5. Comparison between the trend of theDE(S12T1) obtained experi-mentally~see Fig. 4 and Table I! and the one predicted by the semiempiricalmethod AM1.

FIG. 6. Experimental energies~0–0! for the lowest excited singlet and trip-let excited states,S1 andT1 , as a function ofn. The extrapolated value fora` is obtained from the plot in Fig. 3.

FIG. 7. Experimental energies~0–0! for the lowest excited singlet~h! andtriplet ~s! excited states,S1 and T1 , as a function of the number ofpelectrons~N!. The lines associated with the data are obtained from the fittingto Eq. ~9!.

5432 J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 de Melo et al.

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values found in the literature for the polymer, see textabove!. From Table I what we see is that the predicted valueE0 – 0 for polythiophene from FEMO theory is slightly lower~>15 100 cm21!. We believe that this signifies that the effec-tive conjugation length of oligomers of medium size repre-sent the polythiophene. In fact a singlet energy of 16 900cm21 is attained forN578 which is equivalent to having anoligomer of 20 thiophene units.

The second consideration regards the obtained values forl. Using Kuhn’s relation, Rentschet al.24 set l 51 thus,L5(N11)d. This equation was also used by us but we didnot find any acceptable fits. This and the fact that the valuesfor l are different depending on the experimental data used( l 520.418 for the triplet energy relation andl 511.347 forthe singlet! leads us to conclude that the effective length ofthe box depends on the geometry of the molecule. This pointhas been stressed before and discussed elsewhere in terms ofa quinoidal type structure for the first singlet excited stateand a structure with more single bond character, and there-fore with a higher degree of rotational freedom between thethiophene rings for theT1 state.6

V. CONCLUDING REMARKS

In this work we have measured the energy of the lowesttriplet state in thea-oligothiophenes (an) using time-resolved photoacoustic measurements and other spectro-scopic parameters~absorption and fluorescence!. These ener-gies range from 18 000 cm21 ~a2! to >13 000 cm21 ~a7!.This approach is valuable when there is clear evidence forlong-lived triplets but no phosphorescence emission has beendetected. This is an alternative and more direct approachthan the determination of the quenching constants with mol-ecules of known triplet energy. It requires however, knowl-edge of the triplet quantum yields.

We have shown that the triplet energies increase linearlywith the reciprocal ofn. The same happens with the energyorigin ~0–0! of the lowest singlet excited states. This allowedus to predict the triplet and singlet state energies for thepolymer, the polythiophene of>10 000 cm21. We also ob-tained a value for the energy difference between the lowestsinglet excited state,S1 and the tripletT1 , the S–T energysplitting, for the an’s. This is not constant asn changes.Again, a linear behavior was found when this energy wasconsidered as a function of 1/n.

ACKNOWLEDGMENTS

This work was supported by FCT Project No. PRAXIS/PCEX/C/QUI/108/96 and PRAXIS 2/2.1/QUI/411/94. J.S.M.acknowledges A. C. Pais for his kind help regarding thefitting procedures.

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5433J. Chem. Phys., Vol. 111, No. 12, 22 September 1999 Extrapolation to polythiophene

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