- Email: [email protected]
Excited states absorptions in oligomers of PPV
Synthetic Metals 155 (2005) 439–442
Excited states absorptions in oligomers of PPV Haranath Ghosh R & D Block ‘A’, Centre for Advanced Technology, Indore 452013, India Available online 7 November 2005
Abstract Recent experimental studies based on pump-probe spectroscopy of phenyl-based polymers reveal quite different relaxation dynamics of low and high energy even parity states reached by photoinduced absorption (PA). One class of even parity states (mAg ) experiences ultrafast internal conversion to the lowest singlet state (1Bu ), whereas the other class (kAg ) in violation of the Vavilov–Kash’s rule undergoes a different pathway. We therefore investigate theoretically the nature of higher excited states, both even as well as odd parity states, for various sizes of oligomers of poly(paraphenylene vinylene) (PPV). We study Third Harmonic Generation (THG) of oligomers of PPV within a rigid band correlated Pariser–Parr–Pople (P–P–P) model Hamiltonian, using the -electron basis and the powerful multireference single and double configuration interaction (MRSDCI) method. We also use single–double–triple–quadruple configuration interaction (SDTQCI) in limited cases. We reconfirm the nature of (mAg ) states, which are responsible for the low energy PA band. We also show that in THG three kinds of one-photon states 1Bu , jBu and nBu (where j < n) appear whereas two kinds of even parity states 2Ag and mAg appears. While mAg absorptions appear just after the nBu , the 2Ag absorption peak appears immediately after the jBu absorptions. The later absorption features were not seen in case of linear chain materials like polydiaccetylene (PDA). © 2005 Elsevier B.V. All rights reserved. Keywords: Poly(phenylene vinylene) and derivatives; Models of non-linear phenomena; Many body and quasi-particle theories
With the discovery of electroluminescence in the conjugated semiconductor poly(para-phenylene vinylene) (PPV) the optical properties of the phenyl-based semiconductors have attracted wide attention. PPV and its derivatives have all pervasive applications in modern technologies, organic light emitting diodes (OLEDS) [1], lasers [2], photovoltaics and photodetectors [3]. Photophysics of PPV and its derivatives are governed by a series of alternating one-photon (Bu ) and two-photon (Ag ) optically allowed states. Fluorescence would usually occur from the lowest excited (1Bu ) state and its quantum yield is independent of excitation energy—Vavilov–Kasha rule. Although Vavilov–Kash rule is widely followed by lots of molecular systems, there are other competing processes like singlet exciton fission, exciton dissociation [5], which can take place and interfere with internal conversion (IC) [4]. Interplay of IC with exciton dissociation is currently a very intriguing subject in organic molecular systems. For example, two prominent bands of different classes of Ag states (mAg at lower energy and kAg at higher energies) are identified by various non-linear spectroscopic tools like two-photon absorption,
E-mail address: [email protected]. 0379-6779/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.synthmet.2005.09.032
transient photomodulation spectroscopies. Relaxation dynamics of these higher energy even parity states are closely monitored experimentally [6,7] and later on theoretically [8,9]. It was concluded from both experimental and theoretical studies that while the low energy two-photon state mAg that is reached by photoinduced absorption (PA) relaxes to the optical exciton by IC (as its time scale is <250 fs), whereas the higher energy twophoton allowed state (kAg ) decays (only partially) very slowly and possibly dissociates into polaron pairs. Other investigations that reveal similar observation of high energy two-photon state dissociation to polaron pair formation in PPV derivatives, polyfluorene, ladder type poly-(paraphenylene) (PPP) [10–13] and its oligomers makes these phenomena universal for phenylbased polymers. The presence of these two different classes of two-photon states were found by explicit theoretical calculations on phenylbased polymers [8,9] by us. Such different relaxation dynamics was attributed due to their specific electronic nature—mAg states are superpositions of one electron–hole and two electron–hole excitations between the highest delocalized valence-band and the lowest delocalized conduction-band states, but the kAg states have different two electron–hole contributions involving both delocalized and localized orbitals.
H. Ghosh / Synthetic Metals 155 (2005) 439–442
440
Therefore, it is a theoretical challenge to determine accurately many body wave functions of higher excited (both even as well as odd parity) states of PPV (and related materials) and finding various absorption spectra by means of non-linear optical processes (for sufficiently longer oligomers). Here, we choose Third Harmonic Generation (THG) process, as the THG intensity identifies both the one- and two-photon states. While the nature of one-photon states in PPV oligomers were studied earlier both theoretically as well as experimentally [16,27–29] but most of the theoretical results are singles configuration interaction (SCI) level. We shall show here that some of the higher excited Bu states have dominant double excitations in their wave functions. Therefore, accurate determination Bu states are in order. There appears two kinds of Ag states in the calculated THG spectra—2Ag and mAg and there characters are exactly same as was obtained earlier [8,9]. We note that the 2Ag peak was not observed earlier [6,7] has now been identified experimentally [25], this calculation predicts THG to be another experimental platform to find 2Ag peak. There appears three kinds of odd parity states in the THG spectra—1Bu , jBu and nBu ; nature of these excitons depend on the length and for larger lengths these excitons are mostly within delocalized bands. These observations are new in contrast to earlier detailed theoretical studies on polydiacetylenes [14] where 1Bu , nBu and mAg are found as essential states. We study various oligomers of PPV within a rigid band correlated -electron model like Pariser–Parr–Pople (P–P–P) model Hamiltonian, † † H =− tij (ciσ cjσ + cjσ ciσ ) + U ni↑ ni↓ ij,σ
+
PPV oligomers, we chose the hopping elements to be −2.2 eV for the single bond, and −2.6 eV for the double bond. As stated above, the correlated electron calculations were done using the MRSDCI approach, which is a powerful CI technique [18] that has been used previously for linear chain polyenes by Tavan and Schulten [19] as well as others [21], and by us to calculate the excited state ordering in polyphenylaccetylene and polydiphenylacetylenes [22]. The details of methodology behind the MRSDCI calculations are beyond the scope of this paper (see refs. [22,23,8]). In this calculation, we use full -electron basis set as well as a basis set with frozen most interior d3 orbitals (see ref. [17] for d3 orbitals) and show they are almost equivalent. With this we establish a method by which longer oligomers of PPV can be studied without any loss of generality. Fig. 1(a) is the result for PPV3 keeping all orbitals (i.e., using full -electron basis set and using MRSDCI method, whereas Fig. 1(b and c) represents that for PPV3-FRZ-d3 (PPV3 oligomer with freezed d3 orbitals) using MRSDCI and QCI methods, respectively. Two primary observations may be made from Fig. 1. First, accuracy of the QCI method is well known and by a closure look at Fig. 1(b and c) it is easily appreciable that MRSDCI method is as good (or better) as (than) QCI as there is no qualitative difference between these two figures. Second, d3 orbitals do not play any important contribution as far
i
Vij (ni − 1)(nj − 1)
(1)
i
where ij implies nearest neighbors, ciσ creates an electron of † spin σ on the pz orbital of carbon atom i, niσ = ciσ ciσ the num niσ is the total number ber of electrons with spin σ and ni = σ
of electrons on atom i. The parameters U and Vij are the on-site and long-range Coulomb repulsions, respectively, while tij is the nearest neighbor one-electron hopping matrix element that includes bond alternation and connectivity. The parameterization of the intersite Coulomb interactions is done in a manner similar to the Ohno parameterization [15] U −1/2 (1 + 0.6117R2i,j ) , (2) k where k is a parameter which has been introduced to account for the possible screening of the Coulomb interactions in the system [16,17,20]. We have examined both the standard Ohno parameters (U = 11.13 eV; k = 1.0), as well as a particular combination of U and k (U = 8.0 eV; k = 2.0) that was shown previously to be satisfactory at a semi-quantitative level for explaining the full wavelength dependent ground state absorption spectrum of PPV [16,17]. We shall hereafter refer to this second set of parameters (U = 8.0 eV; k = 2.0) as screened Ohno parameters. As far as the hopping matrix elements are concerned, we took t = −2.4 eV for the C C bond in benzene rings. For the vinylene linkage of the Vi,j =
Fig. 1. Magnitude of the THG susceptibility χxxxx (−3ω; ω, ω, ω) in arbitrary units as a function of energy (in eV) for 3 units PPV oligomer (PPV3). (a) The calculated spectra for full -electron basis using MRSDCI method. (b) The THG intensity using MRSDCI method and with frozen d3 orbitals, whereas (c) represents the same as in (b) using SDTQCI method. (3)
H. Ghosh / Synthetic Metals 155 (2005) 439–442
Fig. 2. Magnitude of the THG susceptibility χxxxx (−3ω; ω, ω, ω) in arbitrary units as a function of energy (in eV) for 4 units PPV oligomer with freezed d3 orbitals (PPV4-FRZ-d3). A line width parameter Γ = 0.05 eV has been used. (3)
as THG intensity is concerned. Because all the figures in Fig. 1 are qualitatively very similar in terms of the nature of exciton causing the peak and its location. Fig. 1 has five distinct features, which are attributed to 1Bu , jBu , 2Ag , nBu and mAg , respectively, from lower to higher energies. The odd parity states (e.g., 1Bu , jBu and nBu ) appear for three-photon resonance, whereas the even parity states corresponding to two-photon state resonance. In case of PPV4 (Fig. 2), jBu peak is splitted. Detailed description of the excitonic nature of different absorption bands is beyond the scope of the present paper and will be made available soon [23]. As mentioned earlier, that the nature of 2Ag , mAg are already known from earlier studies [8,9] and therefore we shall not redescribe these wave functions. The jBu state mostly involves various d1 (d∗1 ) orbitals but has weak equal and opposite in signs d1 → l* contribution. These are single excitations. It also has weak double excitation contribution like (d1 → d∗1 ) (l → l* ). The nBu involves dominantly various single and double excitations between the delocalized bands involving d1,2 as well with weaker double excitation involving lowest delocalized and localized bands. Finally, motivated by the recent experimental observations of PA in phenyl-based organic -conjugated polymers [6,7,10,11] together with successful theoretical explanation [8] we presented correlated theory of Third Harmonic Generation in this paper. It was predicted experimentally that two classes of even parity states exists and relaxation dynamics of these two classes of states are quite different, the mAg one relaxes back to the lowest excited state according to Vavilov–Kasha rule, whereas the kAg classes of states do not relax back to the lowest excited state and thereby do not participate in luminescence. This is also accompanied by charge separation [10,30]. This observation therefore is bound to have immense technological importance as far as brightness of OLED systems are concerned. Earlier we demonstrated that the difference in two classes of Ag states are due to their different electronic nature—mAg states are superpositions of one electron–hole and two electron–hole excitations between
441
the delocalized valence-band and the delocalized conductionband states, but the kAg states differ in two electron–hole contributions involving both delocalized and localized orbitals. Understanding these experimental observations pose stiff challenges to theoretical studies—theoretical study must be based on long enough oligomer to mimick realistic situation together with accurate many body calculation. This requires enormous computer memory and time, and it was realized [8] that anything more than PPV4 with full -electron basis is very difficult. This calls for an appropriate scheme so that longer oligomer lengths can be studied. In this paper, we have described the ‘Frozend3 ’ orbital scheme. We showed that ‘Frozen-d3 ’ orbital scheme is good enough comparing the results of the same with full electron basis set. This is done for PPV3 and PPV4 oligomers. This lead us to carry on for higher size oligomers of PPV based on ‘Frozen-d3 ’ along with ‘essential state mechanism’, which reduces the dimension greatly. Details of exact contributions of various CSF’s for higher excited state absorptions along with detailed characters of various THG features will be available shortly [23]. Briefly, in the longer chain limit (PPV6 onwards) all the features in the THG involves various excitations among delocalized orbitals only—perhaps this observation makes earlier studies [32,21] justified where only d1 –d∗1 bands are kept in the basis set. However, in all cases (smaller to longer PPV oligomers) delocalized orbitals play dominant role, whereas jBu states contain delocalized–localized excitations comparable to that of delocalized orbitals. Since mAg states have weak delocalized–localized excitations and mAg states strongly dipole couple to nBu states, the latter states are thereby expected to contain delocalized–localized excitations as well. Given that there exists two different classes higher energy even parity states, appropriate determination of odd parity states are also essential—although there are lots of exploration in these directions but most of the theoretical studies are confined up to SCI level. We showed that while SCI is adequate for low energy odd parity states but not for the higher energy Bu s that involve strong double excitations. Therefore, we study Third Harmonic Generation which gives information about both the even and odd parity state, of oligomers of PPV within a rigid band correlated Pariser–Parr–Pople model Hamiltonian, using the -electron basis and the powerful multireference single and double configuration interaction (MRSDCI) method. We have specifically shown that this method is as strong as QCI. We also show that in THG three kinds of one-photon states 1Bu , jBu and nBu (where j < n) appear whereas two kinds of even parity states 2Ag and mAg appear. We have categorically described all these excitons using the above mentioned many body calculations. While mAg absorptions appear just after the nBu , the 2Ag appears immediately after the nBu absorptions. In obtaining THG spectrum a low line width parameter Γ = 0.05 eV has been used. However, experimental line width parameter could be much larger than this one and one may miss some of the absorption peaks as there could be overlap between jBu and the 2Ag as well as nBu and mAg . In literature, Γ values as large as 0.3 eV has been used [17], if such a large Γ value is employed here, one may end up only one broad peak (or possibly two), as is seen in one of the earlier experiments [31]. In case of linear
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H. Ghosh / Synthetic Metals 155 (2005) 439–442
chain materials like polydiaccetylene (PDA) it was shown earlier [14] that 2Ag is not an essential state for THG and electroabsorption. However, PPV being emissive material 2Ag has higher energy than the 1Bu and hence the cancellation effect may not occur. Furthermore, from calculated THG intensity for PPV5 and PPV6 (not included here) the feature due to 2Ag is quite pronounced enough and possibly experimentally detectable. Acknowledgements I thank Professor Sumit Mazumdar for letting me use his computer and various useful discussions and Professor Alok Shukla for crucial numerical helps and discussions. This paper is dedicated to the 60th birthday of Dr. Kailash Chander Rustagi who did pioneering work in the field of non-linear optics of organics. Finally, specific comment by Professor S. Ramasesha that excited states are delocalized, is considered here by considering larger number of excited states. References [1] C.W. Tang, S.A. Van Slyke, Appl. Phys. Lett. 51 (1987) 913. [2] N. Tessler, G.J. Denton, R.H. Friend, Nat. (Lond.) 382 (1996) 695. [3] G. Yu, J. Gao, J.C. Hummelen, F. Wudl, A.J. Heeger, Science 270 (1995) 1789. [4] S.V. Frolov, Ch. Kloe, S. Berg, G. Thomas, B. Balogg, Chem. Phys. Lett. 326 (2000) 558. [5] M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals and Polymers, Oxford University Press, New York, 1999. [6] S.V. Frolov, Z. Bao, M. Wohlgenannt, Z.V. Vardeny, Phys. Rev. Lett. 85 (2000) 2196. [7] S.V. Frolov, Z. Bao, M. Wohlgenannt, Z.V. Vardeny, Phys. Rev. B 65 (2001) 205209.
[8] A. Shukla, H. Ghosh, S. Mazumdar, Phys. Rev. B 67 (2003) 245203, and references therein. [9] A. Shukla, H. Ghosh, S. Mazumdar, Synth. Met. 141 (2004) 59. [10] C. Gadermaier, G. Cerullo, G. Sansone, G. Leising, U. Scherf, G. Lanzani, Phys. Rev. Lett. 89 (2002) 117402. [11] C. Gadermaier, G. Cerullo, M. Zavelani-Rossi, G. Sansone, G. Lanzani, E. Zojer, A. Pogantsch, D. Beljonne, Phys. Rev. B 67 (2003) 245203. [12] V.I. Klimov, D.W. McBranch, N. Barahkov, J. Ferraris, Phys. Rev. B 58 (1998) 7654. [13] B. Kraabel, V.I. Klimov, R. Kohlman, S. Xu, H.L. Wang, D.W. McBranch, Phys. Rev. B 61 (2001) 8501. [14] D. Guo, S. Mazumdar, S.N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, N. Peyghambarian, Phys. Rev. B 48 (1993) 1433. [15] K. Ohno, Theor. Chim. Acta 2 (1964) 219. [16] M. Chandross, S. Mazumdar, M. Liess, P.A. Lane, Z.V. Vardeny, M. Hamaguchi, K. Yoshino, Phys. Rev. B 55 (1997) 1486. [17] M. Chandross, S. Mazumdar, S. Jeglinski, X. Wei, Z.V. Vardeny, E.W. Kwock, T.M. Miller, Phys. Rev. B 50 (1994) 14702. [18] R.J. Buenker, S.D. Peyerimhoff, Theor. Chim. Acta 35 (1974) 33. [19] P. Tavan, K. Schulten, Phys. Rev. B 36 (1987) 4337. [20] C.W.M. Castleton, W. Barford, J. Chem. Phys. 117 (2002) 3570. [21] D. Beljonne, Habilitation Thesis, Universit´e de Mons-Hainaut, Belgium, 2001. [22] H. Ghosh, A. Shukla, S. Mazumdar, Phys. Rev. B 62 (2000) 12763. [23] H. Ghosh, unpublished. [25] C.X. Sheng, Z.V. Vardeny, Preprint, 2003. [27] M.J. Rice, Yu.N. Gartstein, Phys. Rev. Lett. 73 (1994) 2504. [28] Y. Shimoi, S. Abe, Synth. Met. 78 (1996) 219. [29] D. Comoretto, G. Dellepiane, F. Marabelli, J. Cornil, D. dos Santos, J. Br´edas, D. Moses, Phys. Rev. B 62 (2000) 10173. [30] A. K¨ohler, D.A. dos Santos, D. Beljonne, Z. Suhai, J.-L. Br´edas, A.B. Holmes, A. Kraus, K. M¨ullen, R.H. Friend, Nature 392 (1998) 903. [31] A. Mathy, K. Ueberhofen, R. Schenk, H. Gregorius, R. Garay, K. M¨ullen, C. Bubeck, Phys. Rev. B 53 (1996) 4367. [32] M.Y. Lavrentiev, W. Barford, S.J. Martin, H. Daly, R.J. Bursill, Phys. Rev. B 59 (1999) 8650.
Excited states absorptions in oligomers of PPV Haranath Ghosh R & D Block ‘A’, Centre for Advanced Technology, Indore 452013, India Available online 7 November 2005
Abstract Recent experimental studies based on pump-probe spectroscopy of phenyl-based polymers reveal quite different relaxation dynamics of low and high energy even parity states reached by photoinduced absorption (PA). One class of even parity states (mAg ) experiences ultrafast internal conversion to the lowest singlet state (1Bu ), whereas the other class (kAg ) in violation of the Vavilov–Kash’s rule undergoes a different pathway. We therefore investigate theoretically the nature of higher excited states, both even as well as odd parity states, for various sizes of oligomers of poly(paraphenylene vinylene) (PPV). We study Third Harmonic Generation (THG) of oligomers of PPV within a rigid band correlated Pariser–Parr–Pople (P–P–P) model Hamiltonian, using the -electron basis and the powerful multireference single and double configuration interaction (MRSDCI) method. We also use single–double–triple–quadruple configuration interaction (SDTQCI) in limited cases. We reconfirm the nature of (mAg ) states, which are responsible for the low energy PA band. We also show that in THG three kinds of one-photon states 1Bu , jBu and nBu (where j < n) appear whereas two kinds of even parity states 2Ag and mAg appears. While mAg absorptions appear just after the nBu , the 2Ag absorption peak appears immediately after the jBu absorptions. The later absorption features were not seen in case of linear chain materials like polydiaccetylene (PDA). © 2005 Elsevier B.V. All rights reserved. Keywords: Poly(phenylene vinylene) and derivatives; Models of non-linear phenomena; Many body and quasi-particle theories
With the discovery of electroluminescence in the conjugated semiconductor poly(para-phenylene vinylene) (PPV) the optical properties of the phenyl-based semiconductors have attracted wide attention. PPV and its derivatives have all pervasive applications in modern technologies, organic light emitting diodes (OLEDS) [1], lasers [2], photovoltaics and photodetectors [3]. Photophysics of PPV and its derivatives are governed by a series of alternating one-photon (Bu ) and two-photon (Ag ) optically allowed states. Fluorescence would usually occur from the lowest excited (1Bu ) state and its quantum yield is independent of excitation energy—Vavilov–Kasha rule. Although Vavilov–Kash rule is widely followed by lots of molecular systems, there are other competing processes like singlet exciton fission, exciton dissociation [5], which can take place and interfere with internal conversion (IC) [4]. Interplay of IC with exciton dissociation is currently a very intriguing subject in organic molecular systems. For example, two prominent bands of different classes of Ag states (mAg at lower energy and kAg at higher energies) are identified by various non-linear spectroscopic tools like two-photon absorption,
E-mail address: [email protected]. 0379-6779/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.synthmet.2005.09.032
transient photomodulation spectroscopies. Relaxation dynamics of these higher energy even parity states are closely monitored experimentally [6,7] and later on theoretically [8,9]. It was concluded from both experimental and theoretical studies that while the low energy two-photon state mAg that is reached by photoinduced absorption (PA) relaxes to the optical exciton by IC (as its time scale is <250 fs), whereas the higher energy twophoton allowed state (kAg ) decays (only partially) very slowly and possibly dissociates into polaron pairs. Other investigations that reveal similar observation of high energy two-photon state dissociation to polaron pair formation in PPV derivatives, polyfluorene, ladder type poly-(paraphenylene) (PPP) [10–13] and its oligomers makes these phenomena universal for phenylbased polymers. The presence of these two different classes of two-photon states were found by explicit theoretical calculations on phenylbased polymers [8,9] by us. Such different relaxation dynamics was attributed due to their specific electronic nature—mAg states are superpositions of one electron–hole and two electron–hole excitations between the highest delocalized valence-band and the lowest delocalized conduction-band states, but the kAg states have different two electron–hole contributions involving both delocalized and localized orbitals.
H. Ghosh / Synthetic Metals 155 (2005) 439–442
440
Therefore, it is a theoretical challenge to determine accurately many body wave functions of higher excited (both even as well as odd parity) states of PPV (and related materials) and finding various absorption spectra by means of non-linear optical processes (for sufficiently longer oligomers). Here, we choose Third Harmonic Generation (THG) process, as the THG intensity identifies both the one- and two-photon states. While the nature of one-photon states in PPV oligomers were studied earlier both theoretically as well as experimentally [16,27–29] but most of the theoretical results are singles configuration interaction (SCI) level. We shall show here that some of the higher excited Bu states have dominant double excitations in their wave functions. Therefore, accurate determination Bu states are in order. There appears two kinds of Ag states in the calculated THG spectra—2Ag and mAg and there characters are exactly same as was obtained earlier [8,9]. We note that the 2Ag peak was not observed earlier [6,7] has now been identified experimentally [25], this calculation predicts THG to be another experimental platform to find 2Ag peak. There appears three kinds of odd parity states in the THG spectra—1Bu , jBu and nBu ; nature of these excitons depend on the length and for larger lengths these excitons are mostly within delocalized bands. These observations are new in contrast to earlier detailed theoretical studies on polydiacetylenes [14] where 1Bu , nBu and mAg are found as essential states. We study various oligomers of PPV within a rigid band correlated -electron model like Pariser–Parr–Pople (P–P–P) model Hamiltonian, † † H =− tij (ciσ cjσ + cjσ ciσ ) + U ni↑ ni↓ ij,σ
+
PPV oligomers, we chose the hopping elements to be −2.2 eV for the single bond, and −2.6 eV for the double bond. As stated above, the correlated electron calculations were done using the MRSDCI approach, which is a powerful CI technique [18] that has been used previously for linear chain polyenes by Tavan and Schulten [19] as well as others [21], and by us to calculate the excited state ordering in polyphenylaccetylene and polydiphenylacetylenes [22]. The details of methodology behind the MRSDCI calculations are beyond the scope of this paper (see refs. [22,23,8]). In this calculation, we use full -electron basis set as well as a basis set with frozen most interior d3 orbitals (see ref. [17] for d3 orbitals) and show they are almost equivalent. With this we establish a method by which longer oligomers of PPV can be studied without any loss of generality. Fig. 1(a) is the result for PPV3 keeping all orbitals (i.e., using full -electron basis set and using MRSDCI method, whereas Fig. 1(b and c) represents that for PPV3-FRZ-d3 (PPV3 oligomer with freezed d3 orbitals) using MRSDCI and QCI methods, respectively. Two primary observations may be made from Fig. 1. First, accuracy of the QCI method is well known and by a closure look at Fig. 1(b and c) it is easily appreciable that MRSDCI method is as good (or better) as (than) QCI as there is no qualitative difference between these two figures. Second, d3 orbitals do not play any important contribution as far
i
Vij (ni − 1)(nj − 1)
(1)
i
where ij implies nearest neighbors, ciσ creates an electron of † spin σ on the pz orbital of carbon atom i, niσ = ciσ ciσ the num niσ is the total number ber of electrons with spin σ and ni = σ
of electrons on atom i. The parameters U and Vij are the on-site and long-range Coulomb repulsions, respectively, while tij is the nearest neighbor one-electron hopping matrix element that includes bond alternation and connectivity. The parameterization of the intersite Coulomb interactions is done in a manner similar to the Ohno parameterization [15] U −1/2 (1 + 0.6117R2i,j ) , (2) k where k is a parameter which has been introduced to account for the possible screening of the Coulomb interactions in the system [16,17,20]. We have examined both the standard Ohno parameters (U = 11.13 eV; k = 1.0), as well as a particular combination of U and k (U = 8.0 eV; k = 2.0) that was shown previously to be satisfactory at a semi-quantitative level for explaining the full wavelength dependent ground state absorption spectrum of PPV [16,17]. We shall hereafter refer to this second set of parameters (U = 8.0 eV; k = 2.0) as screened Ohno parameters. As far as the hopping matrix elements are concerned, we took t = −2.4 eV for the C C bond in benzene rings. For the vinylene linkage of the Vi,j =
Fig. 1. Magnitude of the THG susceptibility χxxxx (−3ω; ω, ω, ω) in arbitrary units as a function of energy (in eV) for 3 units PPV oligomer (PPV3). (a) The calculated spectra for full -electron basis using MRSDCI method. (b) The THG intensity using MRSDCI method and with frozen d3 orbitals, whereas (c) represents the same as in (b) using SDTQCI method. (3)
H. Ghosh / Synthetic Metals 155 (2005) 439–442
Fig. 2. Magnitude of the THG susceptibility χxxxx (−3ω; ω, ω, ω) in arbitrary units as a function of energy (in eV) for 4 units PPV oligomer with freezed d3 orbitals (PPV4-FRZ-d3). A line width parameter Γ = 0.05 eV has been used. (3)
as THG intensity is concerned. Because all the figures in Fig. 1 are qualitatively very similar in terms of the nature of exciton causing the peak and its location. Fig. 1 has five distinct features, which are attributed to 1Bu , jBu , 2Ag , nBu and mAg , respectively, from lower to higher energies. The odd parity states (e.g., 1Bu , jBu and nBu ) appear for three-photon resonance, whereas the even parity states corresponding to two-photon state resonance. In case of PPV4 (Fig. 2), jBu peak is splitted. Detailed description of the excitonic nature of different absorption bands is beyond the scope of the present paper and will be made available soon [23]. As mentioned earlier, that the nature of 2Ag , mAg are already known from earlier studies [8,9] and therefore we shall not redescribe these wave functions. The jBu state mostly involves various d1 (d∗1 ) orbitals but has weak equal and opposite in signs d1 → l* contribution. These are single excitations. It also has weak double excitation contribution like (d1 → d∗1 ) (l → l* ). The nBu involves dominantly various single and double excitations between the delocalized bands involving d1,2 as well with weaker double excitation involving lowest delocalized and localized bands. Finally, motivated by the recent experimental observations of PA in phenyl-based organic -conjugated polymers [6,7,10,11] together with successful theoretical explanation [8] we presented correlated theory of Third Harmonic Generation in this paper. It was predicted experimentally that two classes of even parity states exists and relaxation dynamics of these two classes of states are quite different, the mAg one relaxes back to the lowest excited state according to Vavilov–Kasha rule, whereas the kAg classes of states do not relax back to the lowest excited state and thereby do not participate in luminescence. This is also accompanied by charge separation [10,30]. This observation therefore is bound to have immense technological importance as far as brightness of OLED systems are concerned. Earlier we demonstrated that the difference in two classes of Ag states are due to their different electronic nature—mAg states are superpositions of one electron–hole and two electron–hole excitations between
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the delocalized valence-band and the delocalized conductionband states, but the kAg states differ in two electron–hole contributions involving both delocalized and localized orbitals. Understanding these experimental observations pose stiff challenges to theoretical studies—theoretical study must be based on long enough oligomer to mimick realistic situation together with accurate many body calculation. This requires enormous computer memory and time, and it was realized [8] that anything more than PPV4 with full -electron basis is very difficult. This calls for an appropriate scheme so that longer oligomer lengths can be studied. In this paper, we have described the ‘Frozend3 ’ orbital scheme. We showed that ‘Frozen-d3 ’ orbital scheme is good enough comparing the results of the same with full electron basis set. This is done for PPV3 and PPV4 oligomers. This lead us to carry on for higher size oligomers of PPV based on ‘Frozen-d3 ’ along with ‘essential state mechanism’, which reduces the dimension greatly. Details of exact contributions of various CSF’s for higher excited state absorptions along with detailed characters of various THG features will be available shortly [23]. Briefly, in the longer chain limit (PPV6 onwards) all the features in the THG involves various excitations among delocalized orbitals only—perhaps this observation makes earlier studies [32,21] justified where only d1 –d∗1 bands are kept in the basis set. However, in all cases (smaller to longer PPV oligomers) delocalized orbitals play dominant role, whereas jBu states contain delocalized–localized excitations comparable to that of delocalized orbitals. Since mAg states have weak delocalized–localized excitations and mAg states strongly dipole couple to nBu states, the latter states are thereby expected to contain delocalized–localized excitations as well. Given that there exists two different classes higher energy even parity states, appropriate determination of odd parity states are also essential—although there are lots of exploration in these directions but most of the theoretical studies are confined up to SCI level. We showed that while SCI is adequate for low energy odd parity states but not for the higher energy Bu s that involve strong double excitations. Therefore, we study Third Harmonic Generation which gives information about both the even and odd parity state, of oligomers of PPV within a rigid band correlated Pariser–Parr–Pople model Hamiltonian, using the -electron basis and the powerful multireference single and double configuration interaction (MRSDCI) method. We have specifically shown that this method is as strong as QCI. We also show that in THG three kinds of one-photon states 1Bu , jBu and nBu (where j < n) appear whereas two kinds of even parity states 2Ag and mAg appear. We have categorically described all these excitons using the above mentioned many body calculations. While mAg absorptions appear just after the nBu , the 2Ag appears immediately after the nBu absorptions. In obtaining THG spectrum a low line width parameter Γ = 0.05 eV has been used. However, experimental line width parameter could be much larger than this one and one may miss some of the absorption peaks as there could be overlap between jBu and the 2Ag as well as nBu and mAg . In literature, Γ values as large as 0.3 eV has been used [17], if such a large Γ value is employed here, one may end up only one broad peak (or possibly two), as is seen in one of the earlier experiments [31]. In case of linear
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chain materials like polydiaccetylene (PDA) it was shown earlier [14] that 2Ag is not an essential state for THG and electroabsorption. However, PPV being emissive material 2Ag has higher energy than the 1Bu and hence the cancellation effect may not occur. Furthermore, from calculated THG intensity for PPV5 and PPV6 (not included here) the feature due to 2Ag is quite pronounced enough and possibly experimentally detectable. Acknowledgements I thank Professor Sumit Mazumdar for letting me use his computer and various useful discussions and Professor Alok Shukla for crucial numerical helps and discussions. This paper is dedicated to the 60th birthday of Dr. Kailash Chander Rustagi who did pioneering work in the field of non-linear optics of organics. Finally, specific comment by Professor S. Ramasesha that excited states are delocalized, is considered here by considering larger number of excited states. References [1] C.W. Tang, S.A. Van Slyke, Appl. Phys. Lett. 51 (1987) 913. [2] N. Tessler, G.J. Denton, R.H. Friend, Nat. (Lond.) 382 (1996) 695. [3] G. Yu, J. Gao, J.C. Hummelen, F. Wudl, A.J. Heeger, Science 270 (1995) 1789. [4] S.V. Frolov, Ch. Kloe, S. Berg, G. Thomas, B. Balogg, Chem. Phys. Lett. 326 (2000) 558. [5] M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals and Polymers, Oxford University Press, New York, 1999. [6] S.V. Frolov, Z. Bao, M. Wohlgenannt, Z.V. Vardeny, Phys. Rev. Lett. 85 (2000) 2196. [7] S.V. Frolov, Z. Bao, M. Wohlgenannt, Z.V. Vardeny, Phys. Rev. B 65 (2001) 205209.
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