a quantum-mechanical study of oxidized oligopyrroles

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A Quantum-Mechanical Study ofOxidized Oligopyrroles

¨TARMO TAMM, JURI TAMM, MATI KARELSONDepartment of Chemistry, University of Tartu, Jakobi St. 2, Tartu EE2400, Estonia

Received 17 April 1998; accepted 8 May 1998

ABSTRACT: The geometry and band-gap values of oligopyrroles of increasing chainŽlength were calculated using different semiempirical quantum-chemical methods AM1,

.PM3, SAM1, INDOr1 CI . The oxidative doping results in large changes in the geometryand conductive properties of oligomers. The properties of doped polypyrrole areextrapolated from the calculated data for oligomers. Q 1999 John Wiley & Sons, Inc. Int JQuant Chem 71: 101]109, 1999

Introduction

he relationship between the electronic struc-T ture and electrical properties of electricallyconducting polymers has been of substantial inter-

w x w xest 1 since their discovery in 1977 2 . Organicheterocyclic polymers have been given special at-tention, due to the stability of their chemical struc-

w xture and large variance of the conductivity. 1, 3Notably, the optical and electrical properties ofheterocyclic polymers have been studied using dif-ferent experimental techniques.

The computer-aided molecular design based onquantum-mechanical methods can be suggestivein the development of new polymeric materialswith better electrical conductivities. The calcula-tions at different levels of theory have been carried

Žout for various heterocyclic polymers for a re-

Correspondence to: M. Karelson.

w x.view, see 3 . In addition to the calculations onw xinfinite polymer chains, experimental 4, 5 and

w xtheoretical 6]8 studies of the respective oligomershave been reported. In the latter case, the proper-ties of the polymers have been predicted proceed-ing from the regular dependence of the corre-sponding properties of oligomers on their chain

Ž .length or the reciprocal value of the chain length .The electrical conductivity of neutral polymers

is expected to be directly related to their electronicstructure and, in particular, to the gap between the

Ž .conductive and valence band band gap . In theframework of the LCAO MO formalism, the bandgap of a polymer can be estimated using the ex-trapolation of the energy gap between the highest

Ž .occupied molecular orbital HOMO and the low-Ž .est unoccupied molecular orbital LUMO of the

w xrespective oligomers of increasing chain length 3 .As almost all conductive polymers are insula-

tors in the undoped form, it would be of specialinterest to study the influence of the electrochemi-

( )International Journal of Quantum Chemistry, Vol. 71, 101]109 1999Q 1999 John Wiley & Sons, Inc. CCC 0020-7608 / 99 / 010101-09

TAMM, TAMM, AND KARELSON

cal or chemical doping on the electronic structureand the related conductive properties of thesepolymers. It is known experimentally that the con-ductivity of most polymers is increased due to

w xeither oxidative or reductive doping 1, 3 . In thecase of chemical doping, the alkali metals are com-monly used as electron donors, and strong oxi-dants like AsF , SbF , FeCl , I , and Br , as elec-5 5 3 2 2

w x Žtron acceptors 9 . The doping level average charge.per polymer unit depends on the type of the

polymer, the polymerization conditions, and thew xsolvent used 1, 3, 10 .

The theoretical study of the influence of dopingon the electronic structure of polymers is a non-trivial task and requires a careful choice of theapproach. First, the doping can be modeled byheterocyclic oligomers that are forced to havequinoid-type bonds due to homolytically cleaved

w xheteroatom]hydrogen bonds 11 or additionalw xdouble-bond terminal groups 8 . Another possibil-

ity is to simulate the charge transfer by the addi-tion of some alkali metal ions close to the hetero-

w xcyclic rings 12 . Also, it is possible to investigatethe dications of heterocyclic oligomers, as pro-posed by Ehrendorfer and Karpfen in the case of

w xoligothiophenes 7 . The study of monocations issomewhat more complicated as it requires the useof a methodology suitable for the open-shell elec-tronic systems.

In the present work, the electronic properties ofoxidized polypyrrole have been studied using thesemiempirical calculations on oligopyrroles andthe subsequent extrapolation of properties to infi-nite chain length. The geometrical, energetic, andelectronic properties of the neutral and the oxi-dized oligopyrroles were calculated using severalsemiempirical methods, both at the SCF and CIlevels of theory.

Methodology

The extrapolation from the calculated propertiesof oligomers of increasing chain length was usedas a basic method to assess the properties of therespective doped polymers. This approach has beenfrequently used for the theoretical examination of

w xheterocyclic polymers 8, 11, 13 as it allows, inprinciple, to apply any contemporary quantum-chemical method designed for the low molecular

weight systems. In some cases, the poor conver-gence of the property value as the oligomer sizeis increased may limit the applicability of thismethod. However, in most cases, the dependenceof a given property on the reciprocal of the chain

Ž .length 1rN of oligomers is linear and gives aconfident estimate of the respective property forthe polymer.

The calculations were carried out using theŽ . w xsemiempirical AM 1 Austin model 1 14 , PM3

Ž . w x Žparametric method 3 15 , and SAM1 semi ab. w xinitio method 1 16 methods. The program pack-

w xages MOPAC 6.0 and Ampac 5.0 16 were used.AM1 and PM3 have proved to predict reliably thebond lengths and valence angles in heterocyclesand heterocyclic oligomers consisting of first- and

w xsecond-row elements 17, 18 . In order to obtain amore adequate description of the electronic prop-erties by taking into account possible electron cor-relation effects, the INDOrCI calculations werealso carried out on oligomers using the ZINDO

w x95.1 program package 19 . The optimized geome-tries of compounds obtained from AM1, PM3, andSAM1 calculations were used in the INDOrCIcalculations. The limited CI space included twoHOMOs and two LUMOs per monomer unit. Suchscaling should somewhat correct for the size-in-

w xconsistency error of the CI method 13 . The lowestCI calculated transition energies were taken as ameasure of the band gap in these oligomers.

The geometries of all oligomers were fully opti-w xmized. In contrast to some other work 7, 12 , no

constraints to the geometry optimization ofoligomers by forcing the planar symmetry were

X Ž X.applied in this work. Only a,a or 2,2 -linkedoligomers were considered in both anti and syn

Ž .conformations Scheme 1 . The oxidative dopingŽ .p-doping was modeled by removing two elec-

Ž .2qtrons from the oligomers, resulting in Py dica-nŽ .tions Py s pyrrole . All dications were treated as

closed-shell systems.

SCHEME 1. Anti- and syn-bipyrroles.

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OXIDIZED OLIGOPYRROLES

Results and Discussion

GEOMETRY

It is still controversial if polypyrrole exists onlyin the anti form or if some extent of the synconformation is also populated at experimentalconditions. The anti form has been found to beenergetically more favorable, but some experimen-tal evidence about the presence of the syn form

w xhas also been reported 20 . Our calculations usingAM1 and SAM1 parametrizations indicate that theanti conformation is energetically favored by about1]1.5 kcalrmol per pyrrole unit. Also, as no pla-narity was forced on the oligomer geometries, theAM1 and SAM1 calculated syn oligomers tend to

w Ž .become helical as their length increases Fig. 1 aŽ .xand b . The calculations with PM3 starting from

the syn form geometry even failed to find therespective energetic minimum as in most cases theoligomers rotated from the initial syn geometry tothe more favorable anti form. In some cases, thesame behavior was also observed using the AM1and SAM1 geometry optimization. Thus, our fur-ther calculations were restricted to the anti confor-mation of the oligomers.

The results of calculations indicate that the con-ductive properties may substantially depend onthe geometric structure of the polymers. A signifi-cant part of the conductivity of heterocyclic poly-mers is expected to rise from the charge transferalong the C—C bonds, both inside the rings andbetween them. In cases where the polymeric chainhas a more aromatic nature as a whole, the delo-calization of electrons over neighboring rings isincreased and the polymer has higher conductivityas compared to the polymer with more aromaticheterocyclic rings and less electron delocalizationbetween them.

The C—C bond lengths of a pyrrole nonamercalculated using the three different methods are

Žpresented in Figure 2 n is the relative position ofa C—C bond with respect to the central C—C

.bond of the oligomer .The PM3-calculated bond lengths tend to be

shorter inside the heterocyclic rings as comparedto the bonds between the heterocycles in the poly-mer chain. Therefore, the PM3 results predict aless aromatic nature of the heterocycle chain and,consequently, a smaller delocalization of electronsalong the chain. The SAM1-calculated bond lengths

FIGURE 1. AM1-optimized nonamer of syn-pyrrole: topand side views.

are, on average, longer than the respective bondlengths obtained using other two parametrizations.Also, there is a significantly smaller differencebetween the SAM1 calculated interring bondlengths and the bond lengths inside the rings.

The oxidative doping strongly affects the C—CŽbond alternation cf. Fig. 3 for pyrrole nonamer

.dication . Notably, a similar behavior has beenw xreported for the polythiophene 7 . The AM1- and

PM3-calculated bond lengths of doped oligomersare very similar, whereas the SAM1 method pre-dicts somewhat longer bonds and a larger varianceof bond lengths. Both the AM1 and PM3 results

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 103


FIGURE 2. C—C bond lengths of the pyrrole nonamer( ) ( ) ( )calculated using a AM1, b PM3, and c SAM1

methods.FIGURE 3. C—C bond lengths of the pyrrole nonamer

( ) ( ) ( )dication calculated using a AM1, b PM3, and cSAM1 methods.

VOL. 71, NO. 1104


indicate a more quinoid character of the centralpart of the oligomer, whereas the terminal partsremain more aromatic.

ENERGETICS

The heats of formation of oligopyrroles of differ-ent chain length calculated using the differentmethods are presented in Table I. As discussedabove, the results for the oligomeric systems withthe syn geometry must be treated with caution.During the optimization, some systems have ro-tated back to the anti conformation, which indi-cates the absence of a local minimum at the synconformation. The PM3 results are expected to bethe closest to the experimental energies, since thecalculated heat of formation of the pyrrole

Ž 0 .monomer D H s 27.11 kcalrmol compares fa-f

vorably with the respective experimental valueŽ 0 . w xD H s 25.88 kcalrmol 21 .f

The calculated heats of formation of the pyrroleoligomer dications are given in the Table II. In thiscase, the shortest oligomers were neglected as thedoping levels corresponding to the dications would

w xbe unrealistically high 22 .The stabilizing effect of each additional pyrrole

unit in the oligomeric dications is reflected by thedecrease of the double ionization energies, D, ofthe respective neutral oligomers as the chain length

Ž .is increased cf. Table II . The small change in theŽ .stabilization energy y0.96 kcalrmol calculated

with the PM3 method for the decamer and non-

amer dication suggests that further addition ofpyrrole units to the oligomer has little stabilizingeffect. Therefore, the extension of the bipolaronicperturbation along the chain cannot be much largerthan 10]12 pyrrole rings, and the correspondingdoping level is in the order of 0.2.

ELECTRONIC PROPERTIES

The ionization potential and the band gap areboth important electronic properties that are re-lated to the intrinsic conductivity of polymers. Theionization potential corresponds to the affinity of a

Ž .polymer or oligomer to the p-doping. The bandgap is directly related to the conductivity of semi-conductors. In the present work, both propertiesfor oligopyrroles were examined. The plot of ion-ization potentials as a function of the reciprocal ofchain length is given in Figure 4.

The results presented in Figure 4 indicate thatthe AM1 and PM3 methods perform quite simi-larly while the SAM1 parametrization gives signif-icantly lower ionization potential values and also adifferent slope of the dependence on the reciprocalof the chain length. The comparison of the calcu-lated ionization potentials of a pyrrole monomer

Ž .with the experimental value Table III , however,indicates that the SAM1 method is closest to theexperiment. Nevertheless, the ionization potentialcalculated using AM1 and PM3 methods does notdeviate substantially from the respective experi-mental value.

TABLE I( )AM1, PM3, and SAM1 calculated heats of formation of oligopyrroles in anti and syn conformations kcal ///// mol .

0DHf

AM1 SAM1 PM3aN anti syn anti syn anti

1 39.88 35.96 27.112 80.60 81.70 70.20 71.48 50.863 121.62 123.58 104.36 107.35 74.774 162.63 165.57 138.43 142.04 98.655 203.66 207.53 172.49 177.28 122.536 244.70 249.54 206.54 206.39 146.437 285.91 291.58 240.73 240.44 170.528 326.77 332.09 274.66 281.50 194.209 367.81 374.14 308.71 316.78 218.09

10 408.84 417.18 342.77 352.72 241.99

a No stable structure corresponding to the syn conformation of oligomers was obtained using PM3 parametrization.



TABLE IIAM1-, PM3-, and SAM1-calculated heats of formation of oligopyrrole dications and neutral oligomers and

( )the respective double ionization energies, D , of the latter in kcal ///// mol .

AM1 PM3 SAM1

DH DH DHf f f

a b c d a b c d a b c dN + 2 0 D Step + 2 0 D Step + 2 0 D Step

5 573.11 203.66 369.55 505.70 122.54 383.16 490.32 172.49 317.816 605.88 244.70 361.18 y8.26 521.72 146.43 375.29 y7.87 514.53 206.54 307.99 y9.827 642.08 285.91 356.17 y5.01 540.84 170.52 370.32 y4.97 542.00 240.73 301.26 y6.728 679.41 326.77 352.64 y3.53 561.36 194.20 367.15 y3.17 571.58 274.66 296.92 y4.349 718.90 367.81 351.09 y1.55 583.66 218.09 365.57 y1.58 602.63 308.71 293.92 y3.01

10 758.69 408.84 349.85 y1.24 606.60 241.99 364.61 y0.96 634.60 342.77 291.84 y2.08

a, b Total ionic charge on the oligomer.c (( 2 +) ( )The D value is calculated as DH Py y DH Py in kcal / mol.f N f Nd ( 2 +) ( 2 + )The step value if calculated as DH Py y DH Py in kcal / mol and reflects the stabilization due to the additional pyrrolef N f N + 1unit.

The band gap of polypyrrole has been a subjectof interest both experimentally and theoreticallyw x11]13 . In the present work, the band gaps of

Ž .pyrrole oligomers E were calculated as the en-gergy difference between the highest occupiedmolecule orbital and the lowest unoccupiedmolecule orbital:

E s E y E .g LUMO HOMO

The calculated band gaps and HOMO and LUMOenergies of oligopyrroles of different chain lengthand geometries are presented in Table IV. Thesedata indicate that the anti conformers have some-

FIGURE 4. Dependence of the AM1, PM3, and SAM1( )ionization potentials I on the reciprocal of the neutralp

( )pyrrole oligomer chain length 1 / N .

what smaller calculated band gaps than those ofthe corresponding syn conformers. The results forthe syn conformers did not reveal systematicchanges in the molecular orbital energies due tothe irregularities in the geometry of the corre-sponding oligomers. The band gap values ob-tained using the SAM1 parametrization were thelowest and the closest to the experimental value

Ž . w xfor the polymer 2.2]2.8 eV 3 . The main reasonfor the overestimation of band gap values bysemiempirical calculations at the SCF level is ex-pected to be due to the neglect of the electron

w xcorrelation effects 13 . Also, the electron correla-tion may affect the bond alteration and electronic

w xstructure in conjugated polymers 23]25 . In orderto examine these effects, the INDOrCI calculationswere carried out for all the studied oligomers. Thegeometries were taken from the results of theAM1, PM3, and SAM1 calculations. However, ithas to be noted that the resulting INDOrCI excita-tion energies were rather insensitive of the initial

Ž .geometry Fig. 5 .The oxidation changes substantially the band

structure of oligopyrroles. The resulting HOMO

TABLE IIIIonization potential of pyrrole obtained withdifferent methods.

Method

Exp.[ ]AM1 PM3 SAM1 21

I 8.66 8.93 8.40 8.22p

VOL. 71, NO. 1106


(FIGURE 5. Dependence of E calculated using INDOg)/ CIS on the reciprocal of chain length of neutral

oligopyrroles. The geometries of oligomers were takenas AM1- and PM3-optimized geometries.

and LUMO energies of the pyrrole oligomer dica-Ž .tions are lower more negative than those of the

neutral oligomers. As the shift to more negativevalues of the energy is larger for LUMOs, the bandgap for dications becomes smaller as compared

Žto the respective neutral oligomers Table IV and.Fig. 6 .

Notably, the relationship between E and 1rNgfor dications of oligopyrroles is not linear, whichmakes an extrapolation to the infinite chain lengthless precise. However, the error from nonlinearityshould be moderate as the extrapolated value is

FIGURE 6. Dependence of AM1-, PM3-, andSAM1-calculated E on 1 / N of pyrrole oligomergdications.

close to the calculated points. The band gap isagain substantially overestimated using the AM1,PM3, and SAM1 semiempirical methods. TheINDOrCI calculations accounting for electroncorrelation were performed for dications and therespective results are presented in Table VI andFig. 7.

The comparison of the results with those forundoped oligomers shows that the shift of energylevels and the decrease of the band gaps due tooxidative doping is much smaller if the correlationeffects are taken into account. The extrapolatedvalues of band gaps for the oxidized oligopyrroles

Ž . Ž .are in the order of 0.5 eV SAM1 to 1.1 eV AM1 .These values correspond to the rather high con-

TABLE IV( )Calculated frontier molecular orbital energy levels and band gaps of anti-oligopyrroles eV .

AM1 PM3 SAM1

N HOMO LUMO E HOMO LUMO E HOMO LUMO Eg g g

4 y7.402 y0.0955 7.307 y7.617 y0.2017 7.415 y6.425 0.5683 6.9945 y7.324 y0.2125 7.112 y7.530 y0.3009 7.229 y6.267 0.5008 6.7686 y7.279 y0.2891 6.990 y7.479 y0.3644 7.115 y6.164 0.4620 6.6267 y7.249 y0.3408 6.909 y7.448 y0.4074 7.041 y6.093 0.4426 6.5368 y7.231 y0.3804 6.851 y7.423 y0.4394 6.984 y6.040 0.4247 6.4649 y7.219 y0.4091 6.809 y7.408 y0.4626 6.945 y6.001 0.4165 6.417

10 y7.210 y0.4309 6.779 y7.397 y0.4796 6.987 y5.971 0.4112 6.383



TABLE V( )Calculated energy levels and band gaps of oligopyrrole dications eV .

AM1 PM3 SAM1

N HOMO LUMO E HOMO LUMO E HOMO LUMO Eg g g

5 y13.389 y8.294 5.095 y13.605 y8.634 4.971 y11.879 y7.276 4.6046 y12.623 y7.858 4.765 y12.839 y8.214 4.624 y11.085 y6.875 4.2117 y12.047 y7.553 4.494 y12.266 y7.934 4.332 y10.496 y6.584 3.9139 y11.221 y7.172 4.049 y11.404 y7.569 3.835 y9.675 y6.228 3.447

10 y10.884 y7.059 3.825 y11.032 y7.492 3.541 y9.365 y6.123 3.242

FIGURE 7. INDO / CIS calculated band gaps of pyrroleoligomer dications using the AM1-, PM3-, andSAM1-optimized geometries.

ductivity of the oxidatively doped polypyrrole andcompare very favorably with the respective experi-mental estimates.

The straightforward comparison of the resultsobtained by theoretical calculations with the exper-

imental conductivities is not trivial. First, differentmethodology has been used for the conductivitymeasurements and the polypyrrole films have beendeposited under different conditions. Thus, theexperimental conductivities are spread over a wide

y1 wrange from several to several hundred S cm 22,x26, 27 . An indirect possibility to estimate the band

gap arises from the visrNIR absorption informa-tion. The main absorption peak of doped polypyr-

w xrole at 600]650 nm 27 corresponds to the bandgap in the order of 1.9]2.1 eV. The band-gapvalues calculated with the CI method for the pyr-role oligomer dications in this work comparefavorably with the values given above. The extrap-olated values for the infinite chain length are un-derestimated. This effect may be due to the struc-tural impurities and mislinkages in the real poly-mer, resulting in a wide absorption peak and largerband gap.

In conclusion, our results suggest that thesemiempirical quantum-chemical methodologywith the inclusion of electron correlation effectscan give reliable information about the details ofthe geometrical and electronic structure of dopedconductive heterocyclic polymers.

TABLE VIINDO ///// CIS calculated band gaps of neutral pyrrole oligomers and the respective dications using the AM1-,

( )PM3-, and SAM1-optimized geometries eV .

AM1 PM3 SAM1

N 0 +2 0 +2 0 +2

5 2.73 1.92 2.77 2.03 2.76 1.956 2.61 1.78 2.65 1.79 2.64 1.717 2.53 1.68 2.57 1.61 2.57 1.538 2.48 1.60 2.51 1.50 2.50 1.40

VOL. 71, NO. 1108


References

1. Skotheim, T. A., Ed.; Handbook of Conducting Polymers;Marcel Dekker: New York, 1986]88; Vols. 1 and 2.

2. Chiang, C. K.; Fincher, C. R.; Park, Y. W.; Heeger, A. J.;Shirakawa, H.; Louis, E. J.; Gau, S. C.; MacDiarmid, A. G.Phys Rev Lett 1977, 39, 1098.

3. Andre, J. M.; Delhalle, J.; Bredas, J. L. Quantum Chemistry´ ´Aided Design of Organic Polymers for Molecular Electron-ics; World Scientific: Singapore, 1991.

4. Raymond, D. E.; Harrison, D. J. J Electroanal Chem 1993,355, 115.

5. Fichou, D.; Teulade-Fichou, M.-P; Horowitz, G.; Demanze,Ž .F. Adv Mater 1977, 9 1 75.

6. Musso, G. F.; Dellepiane, G.; Cuniberti, C.; Rui, M.; Borgh-esi, A. Synth Met 1995, 72, 209.

7. Ehrendorger, Ch.; Karpfen, A. J Phys Chem 1994, 98, 7492.8. Karpfen, A.; Kertesz, M. J Phys Chem 1991, 95, 7680.9. Roth, S.; Bleier, H.; Pukacki, W. Faraday Discuss Chem Soc

1989, 88, 223.10. Satoh, M.; Kaneto, K.; Yoshino, K. Synth Met 1986, 14, 289.11. Jurimae, T.; Standberg, M.; Karelson, M. Int J Quantum¨ ¨

Chem 1995, 54, 369.

12. Bredas, J. L.; Themans, B.; Fripiat, J. G.; Andre, J. M. Phys´ ´ ´Rev B 1984, 29, 6761.

13. Karelson, M.; Zerner, M. C. Chem Phys Lett 1994, 224, 213.14. Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P.

J Am Chem Soc 1985, 107, 3902.15. Stewart, J. J. P. J Comput Chem 1989, 10, 209.

Ž16. AMPAC 5.0 Q 1994 Semichem, 7128 Summit, Shawnee, KS.66216 .

17. Distefano, G.; Jones, D.; Guerra, M.; Favaretto, L.; Modelli,A.; Mengali, G. J Phys Chem 1991, 95, 9746.

18. Dobado, J. A.; Molina, J.; Espinosa, M. R. Theochem 1994,303, 205.

Ž .19. Ridley, J.; Zerner, M. Theor Chim Acta Berl 1973, 32, 111.20. Cui, C. X.; Kertesz, M. Phys Rev B 1989, 40, 9661.21. Scott, D. W.; Berg, W. T.; Hossenlopp, I. A.; Hubbard, W.

N.; Messerly, J. F.; Todd, S. S.; Dousling, D. R.; McCullough,J. P.; Waddington, G. J Phys Chem 1967, 71, 2263.

22. Merz, A.; Haimerl, A.; Owen, J. Synth Met 1988, 25, 89.23. Beljonne, D.; Bredas, J. L. Phys Rev B 1994, 50, 2841.´24. Choi, C. H.; Kertesz, M.; Karpfen, A. J Chem Phys 1997,

107, 6712.¨25. Champagne, B.; Deumens, E.; Ohrn, Y. J Chem Phys 1997,

107, 5433.26. Schiavon, G.; Setran, S.; Zotti, G. Synth Met 1989, 32, 209.27. Li, Y.; Imaeda, K.; Inokuchi, H. Polym J 1996, 28, 559.


a quantum-mechanical study of oxidized oligopyrroles

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