Synthetic Metals 155 (2005) 368–371

Photoinduced absorption and nonlinear optical propertiesof disubstituted polyacetylenes: Theory

Alok Shukla∗, Priya SonyPhysics Department, Indian Institute of Technology, Powai, Mumbai 400076, India

Available online 4 November 2005

Abstract

In this paper, we summarize results of our recent large-scale correlated calculations of nonlinear optical spectra and photoinduced absorption(PA) spectra of phenyl-disubstituted polyacetylenes (PDPA). Calculations were performed on oligomers of PDPA’s using correlated-electronPariser–Parr–Pople (P–P–P) model and configuration interaction (CI) methodology. Computed PA spectra are compared with the recent experimentsof Korovyanko et al., and good agreement is obtained between the two.© 2005 Elsevier B.V. All rights reserved.

Keywords: Semi-empirical models and model calculations; Organic semiconductors based on conjugated molecules; Other conjugated and/or conducting polymers

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. Introduction

Recently discovered conjugated polymer phenyl-disubs-ituted polyacetylenes (PDPA)[1] exhibits interesting opticalroperties such as laser action and photoluminescence (PL) with

arge quantum efficiency[2]. Observation of PL in these mate-ials was considered counter-intuitive because of their struc-ural similarities totrans-polyacetylene (t-PA). Since these earlyorks, a number of experimental studies of the optical proper-

ies of PDPA’s have been performed[3,4], including the recenteasurement of photoinduced absorption (PA) spectra of thisolymer[5].

Earlier we had theoretically studied the linear optical prop-rties of this material, and explained its PL in terms of reducedorrelation effects, as compared tot-PA, caused by substitutionf the phenyl rings in place of the side hydrogen atoms[6,7].owever, one of the major limitations of the linear optics is that

n centro-symmetric materials such as PDPA’s, it can connect theAg ground state only to the Bu type excited states, as per dipoleelection rules. Therefore, in order to probe the Ag type excitedtates, and higher energy Bu type excited states, it is necessary

[8], THG[9] and the PA spectra[10] of oligomers of PDPA’s. Incase of our theoretical PA spectra, we obtained good agreewith the recent experiments of Korovyanko et al.[5], and wereable to explain several peaks of the spectra in terms of impoexcited states of the material. In this paper, we present a ureview of these recent works of ours[8–10].

2. Theory

The unit cell of PDPA oligomers considered in this worpresented inFig. 1. Ground state geometry of PDPA’s, to the bof our knowledge, is still unknown. However, from a chempoint of view, it is intuitively clear that the steric hindrance wocause a rotation of the side phenyl rings so that they woulonger be co-planar with the polyene backbone of the polyThe extent of this rotation is also unknown, however, inprevious works[6,7], we argued that the steric hindrance effecan be taken into account by assuming that the phenyl rinthe unit cell are rotated with respect to they-axis by 30◦ in sucha manner that the oligomers still have inversion symmetr

o resort to either nonlinear spectroscopies such as the third-armonic generation (THG), two-photon absorption (TPA), orexcited state spectroscopy such as the PA. It is with this aim

n mind, recently, we performed theoretical studies of the TPA

the following, we will adopt the notation PDPA-n to denote aPDPA oligomer containingn unit cells of the type depicted inFig. 1.

The correlated calculations on oligo-PDPA’s were performedusing the Pariser–Parr–Pople (P–P–P) model Hamiltonian:

H

∗ Corresponding author.

379-6779/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.synthmet.2005.09.015

= HC + HP + HCP + Hee, (1)

A. Shukla, P. Sony / Synthetic Metals 155 (2005) 368–371 369

Fig. 1. The unit cell of PDPA. The phenyl rings are rotated with respect to they-axis, which is transverse to the axis of the polyene backbone (x-axis).

whereHC andHP are the one-electron Hamiltonians for the car-bon atoms located on thetrans-polyacetylene backbone (chain),and the phenyl groups, respectively, andHCP is the one-electronhopping between the chain and the phenyl units. The individuaterms can now be written as:

HC = −∑

〈k,k′〉,M(t0 − (−1)M �t)Bk,k′;M,M+1, (2a)

HP = −t0∑

〈µ,ν〉,MBµ,ν;M,M, (2b)

and

HCP = −t⊥∑

〈k,µ〉,MBk,µ,;M,M. (2c)

In the equation above,k, k′ are carbon atoms on the polyenebackbone,µ, ν the carbon atoms located on the phenyl groups,M a unit consisting of a phenyl group and a polyene carbon,〈· · ·〉implies nearest neighbors andBi,j;M,M′ = ∑

σ(c†i,M,σcj,M′,σ +h.c.). Matrix elementst0, and t⊥ depict one-electron hops.In HC, �t is the bond alternation parameter arising due toelectron–phonon coupling. InHCP, the sum overµ is restrictedto atoms of the phenyl groups that are directly bonded to backbone carbon atoms.Hee depicts the electron–electron repulsionand can be written as:

H

w heC Ohnr

V

whereκi,j,M,N depicts the dielectric constant of the system whichcan simulate the effects of screening,U the on-site repulsionterm andRi,j is the distance in̊A between theith carbon and thejth carbon. For Coulomb parameters, we chose the “screenedparameters” of Chandross et al.[11] with valuesU = 8.0 eV andκi,i,M,M = 1.0, andκi,j,M,N = 2.0. For hopping matrix elements,we usedt0 = 2.4 eV, t⊥ = 1.4 eV, and�t = 0.168 eV. For per-forming many-body calculations, we used the multi-referencesingles–doubles CI (MRSDCI) method, details pertaining towhich can be found in our earlier works[7–9]. Both longitudinal(χ(3)

xxxx) and transverse (χ(3)yyyy) components corresponding to the

TPA and THG spectra were computed using the sum-over-statesmethod.

3. Calculation and results

Next, we present the results of our MRSDCI calculations per-formed on oligomer PDPA-5. Choice of the PDPA-5 was due tothe fact that in both thin film and solution based experimentalsamples of PDPA, the mean conjugation length is believed to bebetween five to seven repeat units[4]. In Figs. 2–5, we present,respectively, the TPA, the THG and the PA spectra from the1Bu and the 2Ag excited states. From the selection rules, it isobvious that in the TPA and 1Bu–PA spectra only Ag type statescontribute, in 2Ag–PA spectrum only Bu-type states contribute,w sc O)p s of ass ciTs gt esm .C from

Fχ enedp ed fora

ee = U∑

i

ni↑ni↓ + 1

2

∑

i=j

Vi,j(ni − 1)(nj − 1), (3)

here i and j represent all the atoms of the oligomer. Toulomb interactions are parameterized according to the

elationship:

i,j = U

κi,j

(1 + 0.6117R2i,j)

1/2, (4)

l

-

o

hile in the THG spectrum both the Ag and the Bu excited stateontribute. It is widely believed that the nonlinear optical (NLroperties of conjugated polymers can be described in termmall number excited states called “essential states”[12]. Thesetates consist of 1Bu, mAg andnBu states (m andn are generi

ntegers) and make strong contributions to the TPA (mAg) andHG (1Bu,mAg,nBu) spectra. For the case of polyenes,mAg hastrong coupling to the 1Bu state, whilenBu has strong couplino themAg state[12]. Thus, one would expect that in polyenAg will also lead to a strong peak in the 1Bu–PA spectrumonsistent with the essential state mechanism, it is clear

ig. 2. Comparison of imaginary parts ofχ(3)xxxx(−ω; ω, −ω, ω) (solid lines) and

(3)yyyy(−ω; ω, −ω, ω) (dashed lines) of PDPA-5 computed using the screarameters and the MRSDCI method. A linewidth of 0.05 eV was assumll the levels.

370 A. Shukla, P. Sony / Synthetic Metals 155 (2005) 368–371

Fig. 3. Comparison of∣∣χ(3)

xxxx(−3ω; ω, ω, ω)∣∣ (solid lines) and∣∣χ(3)

yyyy(−3ω; ω, ω, ω)∣∣ (dashed lines) of PDPA-5 computed using the

screened parameters and the MRSDCI method. A linewidth of 0.05 eV wasassumed for all the levels.

Fig. 4. PA spectrum of PDPA-5 from its 1Bu state, computed using the MRSDCImethod. Only the peaks in the experimental energy region have been labeled.linewidth of 0.15 eV was assumed.

Fig. 5. PA spectrum of PDPA-5 from its 2Ag excited state, computed using theMRSDCI method. A linewidth of 0.15 eV was assumed.

the figures that themAg state leads to strong peaks in the lon-gitudincal components of the TPA and THG spectra, as wellas to the 1Bu–PA spectra, consistent with the observation thatthe low-lying excitations in oligo-PDPA’s are essentially basedon the polyene backbone. In polyenesnBu state does not cou-ple strongly to the 2Ag state, and therefore, will be invisiblein their 2Ag–PA spectra. However, in oligo-PDPA’s it couplesrather strongly to the 2Ag state leading to the most intense peakin their 2Ag–PA spectra. We also note that the 2Ag state con-tributes a rather strong peak in the longitudinal THG spectrumof PDPA’s, which is quite unlike the case of polyenes where itdoes not contribute at all.

Additionally, we notice from the figures that the essentialstates contributing to transverse components of the TPA andTHG spectramyAg andkyAg, corresponding to interaction ofy-polarized photons, are distinct and are placed at higher energiesas compared to their longitudinal counterparts. In the experi-mental PA spectra of oligo-PDPA’s, Korovyanko et al. obtainedtwo features namely PA1 (1.1–1.2 eV) and PA2 (2.0 eV) in1Bu–PA spectra, and only one prominent feature PAg (1.7 eV)in the 2Ag–PA spectra. Upon comparingFig. 4 to the exper-imental spectrum[5], we identify themAg state of PDPA-5located at 1.19 eV with the experimental feature PA1. We pre-dict that the PA1 transition will basically correspond to anx-polarized photon. Regarding the PA2 feature, we have two pos-sible candidates—m A (1.72 eV) andkA (2.17 eV). Our cal-c ery -pc )i -t avef o ourr

4

PA,T lighto lts ont sultsc , ourr tativea put toa suredo ns ont

A

ento

R

A

y g gulations predictmyAg to have mixed polarization with strong-component, whilekAg will be mainlyx-polarized. Upon comaring the experimental 2Ag–PA spectrum withFig. 5, we con-lude that the first peak corresponding to thenBu state (1.59 eVs a very good description of feature PAg. We predict this feaure to bex-polarized. For a discussion of the many-particle wunctions of all these excited states, we refer the reader tecent works[8–10].

. Conclusions and future directions

In conclusion, we have presented calculations of the THG, and PA spectra of oligo-PDPA’s and analyzed them inf essential state mechanism. Since, no experimental resu

he TPA and THG spectra of these materials exist, our reould be tested in future experiments. On the other handesults on the PA spectra are found to be in very good quantigreement with the experimental results. These could ben even more stringent test in which the PA-spectra is mean the oriented samples, and compared with our predictio

he polarization of the photons absorbed.

cknowledgement

This work, in part, was supported by the DST (Governmf India) grant SP/S2/M-10/2000.

eferences

[1] K. Tada, et al., Jpn. J. Appl. Phys. 34 (Part 2) (1995) L1087.[2] I. Gontia, et al., Phys. Rev. Lett. 82 (1999) 4058.

A. Shukla, P. Sony / Synthetic Metals 155 (2005) 368–371 371

[3] R. Hidayat, et al., Phys. Rev. B 61 (2000) 10167.[4] I. Gontia, et al., Phys. Rev. B 66 (2002) 075215.[5] J. Korovyanko, et al., Phys. Rev. B 67 (2003) 035114.[6] A. Shukla, et al., Phys. Rev. Lett. 83 (1999) 3944.[7] H. Ghosh, et al., Phys. Rev. B 62 (2000) 12763.

[8] A. Shukla, Chem. Phys. 300 (2004) 177.[9] A. Shukla, Phys. Rev. B 69 (2004) 165218.

[10] P. Sony, A. Shukla, Phys. Rev. B 71 (2005) 165204.[11] M. Chandross, et al., Phys. Rev. B 55 (1997) 1497.[12] S.N. Dixit, et al., Phys. Rev. B 43 (1991) 6781.