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DFT oligomer approach to vibrational spectra of poly(p-phenylenevinylene)
Vibrational Spectroscopy 40 (2006) 149–154 www.elsevier.com/locate/vibspec
DFT oligomer approach to vibrational spectra of poly( p-phenylenevinylene) Kotaro Honda a, Yukio Furukawa a,*, Hiroyuki Nishide b a
Department of Chemistry, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan b Department of Applied Chemistry, School of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan Received 22 January 2005; received in revised form 23 March 2005; accepted 30 March 2005 Available online 6 June 2005
Abstract Experimental Raman and infrared spectra of poly( p-phenylenevinylene) have been analyzed on the basis of the normal coordinate calculations based on the density functional theory method at the B3LYP/cc-pVDZ level for a model oligomer. Vibrational modes corresponding to optically active modes of an infinite polymer chain have been selected from the calculated results. On the basis of these normal vibrations, the observed vibrational spectra of poly( p-phenylenevinylene) have been explained successfully. The angles between the calculated transition dipole moment vectors and the polymer axis for some infrared bands agree with those derived from observed infrared dichroic spectrum. # 2005 Elsevier B.V. All rights reserved. Keywords: Density functional theory; Infrared spectroscopy; Raman spectroscopy; Poly( p-phenylenevinylene)
1. Introduction Thin films (thickness, less than 100 nm) of poly( pphenylenevinylene) (PPV) and its derivatives are incorporated as the active materials of organic electronic devices such as light-emitting diodes and field-effect transistors [1,2]. The performance of the polymer electronic devices depends on the molecular structure and the orientation of polymer chains, which may be elucidated by vibrational spectroscopy [3]. The orientation analysis based on infrared spectroscopy requires the transition dipole moment vector of each infrared band. For high-symmetry compounds symmetry determines the directions of the transition dipole moment vectors. On the other hand, for low-symmetry compounds the directions of the transition dipole moments can be determined from the polarization measurements of single crystals or oriented samples and the quantum-chemical calculations at high levels. Since the conjugated polymers used in organic electronic devices have low symmetry in most cases, the * Corresponding author. Tel.: +81 3 3208 7022; fax: +81 3 3208 7022. E-mail address: [email protected] (Y. Furukawa). 0924-2031/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.vibspec.2005.03.007
quantum-chemical calculations are useful in determining the transition dipole moments of infrared bands. The Raman and infrared spectra [4–8] of PPV and the polarized infrared spectra [4,7] of oriented PPV films have been reported. The observed infrared and Raman spectra have been analyzed on the basis of the spectra of PPVoligomers [5–7] and empirical normal coordinate calculations [9]. However, further studies are necessary for the complete assignments of the observed spectra of PPV. The vibrational assignments enable us to elucidate the molecular structure and the orientation of polymer chains from the observed spectra such as infrared reflection–absorption spectra of electronic devices fabricated with the thin films of PPV and its derivatives [10]. Density functional theory (DFT) calculations are very useful for predicting vibrational frequencies of large molecules in good accuracy. The infrared and Raman spectra of PPV oligomers, trans-stilbene [11], 1,4-distyrylbenzene [12], and 4,40 distyrylstilbene, have been assigned on the basis of DFT calculations. Structural parameters calculated by the DFT method for trans-stilbene also agree well with experimental values [11]. However, it is impossible to calculate vibrational frequencies of an infinite PPV chain by using the DFT method
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K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154 Table 1 Calculated bond lengths and angles for the central part of mPV4 ˚ Bond length/A Bond angle/8 r(C1C2) r(C2C3) r(C3C4) r(C4C7) r(C7C8) r(C2H9) r(C3H10) r(C7H13) r(C8H14)
Fig. 1. (a) Chemical structure of an oligomer (mPV4) and (b) numbering of atoms for the central part.
at present. Because of high performance of computers, it is not difficult for us to perform the normal coordinate calculations of very long oligomers by means of the DFT method. In this study, we have made the normal coordinate calculation of a long oligomer having five phenylene rings and four vinylene moieties (abbreviated as mPV4, Fig. 1a). We analyzed the calculated atomic displacements in the vibrational modes of the oligomer. On the basis of the analysis, we have assigned the observed infrared and Raman spectra of PPV. We have compared the calculated transition dipole moments of some bands with those derived from a polarized infrared measurement in the literature.
2. Calculations The harmonic frequencies, atomic displacements, infrared intensities, and Raman intensities for mPV4 were calculated by the DFT method at the B3LYP/cc-pVDZ level. The Gaussian 03 program package [13] was used. Full geometry optimization was performed under C2h symmetry. The oligomer takes the planar structure except methyl groups with the trans configuration for all C C bonds. No imaginary frequencies were obtained. The calculated vibrational frequencies were scaled uniformly by a factor of 0.978. Calculated atomic displacements in each vibrational mode were depicted with the LXVIEW program [14].
1.411 1.389 1.413 1.462 1.355 1.092 1.093 1.095 1.095
u(C6C1C2) u(C1C2C3) u(C2C3C4) u(C3C4C7) u(C4C7C8) u(C3C2H9) u(C2C3H10) u(C8C7H13) u(C7C8H14)
117.0 121.1 121.9 119.0 127.1 118.9 119.2 118.6 118.6
methyl groups. This result is consistent with the previous results concerning PPV oligomers [11,12]. The calculated bond lengths and angles for the central part of mPV4 are listed in Table 1. The numbering of atoms is shown in Fig. 1b. The phenylene ring has a center of inversion. The C1C2, C2C3, and C3C4 bond lengths of the phenylene ring are ˚ , respectively; the phenylene ring 1.411, 1.389, and 1.413 A deforms from benzenoid to quinoid structure slightly. In poligophenyls, phenyl and phenylene rings take benzenoid structures [15]. The C6C1C2 angle (1178) is smaller than 1208, whereas the C1C2C3 and C2C3C4 angles are larger than 1208. The lengths of the vinylene C4C7 and C7C8 bonds are ˚ , respectively. These bonds are thus 1.462 and 1.355 A regarded as the single and double bonds, respectively. 3.2. Normal vibrations The factor group of a planar infinite PPV chain is isomorphous to the point group C2h. The repeating unit of the PPV chain consists of 14 atoms. The vibrational irreducible representation at the zone center (q = 0) is as follows: 14ag + 6bg + 6au + 12bu. The molecule of mPV4 contains 74 atoms. The 216 normal vibrations of mPV4 with C2h symmetry are distributed: 72ag + 36bg + 37au + 71bu. In both cases, the modes belonging to the ag and bu symmetries are in-plane vibrations, and those belonging to the bg and au symmetries out-of-plane vibrations. The ag and bg vibrations are Raman active, whereas the au and bu vibrations are infrared active. The vibrational modes of benzene derivatives have been discussed on the basis of the Wilson notation [16] for a long time. Hrenar et al. [12] have demonstrated that vibrational modes of PPV oligomers are significantly different from those of benzene. However, in this paper we will discuss the vibrational modes by using the Wilson notation, because the use of the Wilson notation is useful in understanding the vibrations of benzene derivatives. The calculated atomic displacements of all the vibrations will be sent on request.
3. Results and discussion 3.3. Raman spectrum 3.1. Structure No imaginary values in the calculated frequencies indicate the planar structure of mPV4 without the terminal
The 1064 nm excited FT-Raman spectrum of a PPV film and the calculated Raman spectrum of mPV4 are shown in Fig. 2a and b, respectively. The Raman bands observed at
K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154
Fig. 2. (a) Observed Raman spectrum of a PPV film and (b) calculated Raman spectrum of mPV4.
1624, 1581, 1546, 1328, 1301, 1193, 1171, 886, 661, 634, and 328 cm1 are attributed to n4(ag)–n14(ag) of PPV, respectively, as described below. From the calculated normal vibrations of mPV4, we have selected the bands corresponding to the optically-active vibrations of PPV on the basis of the Raman intensities and atomic displacements of vibrational modes. For example, the strongest band observed at 1581 cm1 is correlated with the calculated 1592 cm1 band; the 1581 cm1 band is attributed to n5(ag) of PPV. The calculated atomic displacements in the 1592 cm1 mode are shown in Fig. 3. This is assigned to the mixture of vinylene C C stretch and the ring stretch (8a in the Wilson notation). In each of optically-active vibrations of an infinite polymer chain, every repeating unit has the same vibrational phase. In other words, the phase difference d between the neighboring two units is equal to zero, or the wavenumber q is equal to zero in a dispersion curve. The vibrations of a long-chain oligomer may be classified by the phase difference d. The phase difference of the vibrations of a long oligomer having n repeating units may be expressed by m/(n + 1) (m = 1, 2,. . ., n) for each mode [17]. The 1/(n + 1) mode has no node in the sequence of the vibrational phases. As shown in Fig. 3, no node is found in the atomic displacements in the 1592 cm1 mode. When the frequency dispersion of the vibrational branch of the polymer chain is small, the frequency of the 1/(n + 1) mode for the long oligomer is very close to that of the corresponding optically-active vibration of the polymer. Raman studies [5–7] of PPV and oligomers have shown that frequency dispersions of the vibrational modes for PPV are small. Thus, the Raman band observed at 1581 cm1 is ascribed to n5(ag) of PPV. We have assigned
Fig. 3. Calculated atomic displacements in the 1592 cm1 mode of mPV4.
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the experimental infrared and Raman spectra of PPV on the basis of the calculated normal vibrations of mPV4 in the same way. Although significant mode mixing in the sequence of vibrational displacements makes choices of the 1/(n + 1) modes difficult in some bands, we selected most probable bands from the calculated modes. The selected bands are shown with thick solid lines, and the others with thin solid lines in Fig. 2b. The selected frequencies are listed in Table 2. The bands corresponding to n12(ag) and n14(ag) are not clear in the calculated vibrations because of large mode mixing. The calculated 644 cm1 band is tentatively correlated to n12(ag). The calculated 293 cm1 band is tentatively correlated to n14(ag), whereas the calculated 347 cm1 band may be attributed to n14(ag) instead to the 293 cm1 band. The Raman band observed at 959 and 860 cm1 are attributed to n21(bg) and n22(bg), respectively. In the previous paper [5], YF et al. have assigned the 959 cm1 Raman band Table 2 Assignments of the observed vibrational bands of PPV Species No. Calcd/cm1 Obsd/cm1 Mode ag
n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14
3124 3099 3075 1650 1592 1549 1314 1291 1194 1163 883 644 632 293
– – – 1624 1581 1546 1328 1301 1193 1171 886 661 634 328
au
n15 n16 n17 n18 n19 n20
980 957 840 558 403 220
966 – 838 556 – –
Vinyl CH op-bend CH op-bend (17a) CH op-bend (11) Ring op-deform (16b) Ring op-deform (16a) Skeletal op-deform
bg
n21 n22 n23 n24 n25 n26
960 880 820 706 313 107
959 860 – – – –
CH op-bend (5) Vinyl CH op-bend CH op-bend (10a) Skeletal op-deform (4) Rotational Skeletal op-deform
bu
n27 n28 n29 n30 n31 n32 n33 n34 n35 n36 n37 n38
3122 3097 3082 1517 1425 1353 1272 1206 1108 1000 794 435
3110 3077 3024 1519 1424 1340 1271 1211 1107 1014 784 430
CH str CH str Vinyl CH str Vinyl C C str, ring str (8a) Ring str (8a), vinyl C C str Ring str (8b) Vinyl CH ip-bend, CH ip-bend CH ip-bend, vinyl CH ip-bend C–C str CH ip-bend (9a) Ring str (1), C–C str Ring ip-deform (6b) Ring ip-deform (6a) Rotational
CH str CH str Vinyl CH str Ring str and ip-deform (19a) Ring str and ip-deform (19b) Vinyl CH ip-bend, ring str (14) Ring str (13) Vinyl CH ip-bend CH ip-bend (18b) CH ip-bend (18a) Ring ip-deform (12) Skeletal ip-deform
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K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154
Fig. 4. Calculated atomic displacements of the central part of mPV4 in some calculated modes corresponding to n4, n5, n6, and n10 of PPV.
Fig. 5. (a) Observed infrared spectrum of a PPV film and (b) calculated infrared spectrum of mPV4.
to the in-phase CH op-bend that is infrared-active mode n15(au) because the observed Raman wavenumber is very close to infrared one. In this study, the 959 cm1 band is tentatively attributed to n21(bg) because the calculated wavenumber is in good agreement with the observed. However, further studies are requisite for the complete assignment of this band. In the calculated band corresponding to n23(bg), the atomic displacements of the terminal rings are different from those of other three rings. The calculated 820 cm1 band is tentatively correlated to n23(bg). The bands observed at 1415 and 406 cm1 are not attributed to fundamentals. The 1415 cm1 band may be attributed to the branch of n31(bu) or the combination of n7(ag) and n26(bg). The origin of the 406 cm1 band is not known. The atomic displacements of the central part of mPV4 for the bands attributed to n4(ag), n5(ag), n6(ag) and n10(ag) are shown in Fig. 4. The n4(ag) as well as n5(ag) modes are assigned to the mixture of the C C stretch and the ring stretch (8a) in the Wilson notation. These two modes have opposite phases in these two stretches. In the displacements of n5(ag) the two stretches occur along bond alternation. According to Zerbi’s theory, the contribution of the effective conjugation coordinate is the largest for this mode [8]. The n6(ag) mode is assigned to a ring CC stretch (8b). The n10(ag) mode is assigned to a CH ip-bend (9a).
of large mode mixing. The calculated 220 cm1 band is tentatively correlated to n20(au). The infrared bands observed at 3110, 3077, 3024, 1519, 1424, 1340, 1271, 1211, 1107, 1014, 784, and 430 cm1 are attributed to n27(bu)–n38(bu), respectively. The calculated bands corresponding to n34(bu) and n38(bu) are not obvious owing to large mode mixing. The calculated 1206 and 435 cm1 bands are tentatively correlated to n34(bu) and n38(bu), respectively. The atomic displacements of the central part of mPV4 for the bands attributed to n29(bu), n30(bu), n31(bu), and n37(bu) are shown in Fig. 6. The n29(bu) band is assigned to a CH stretch of the vinyl group whereas the n27(bu) and n28(bu) bands to CH stretches of the phenylene rings. The n30(bu) and n31(bu) bands are assigned to the 19a and 19b modes in the Wilson notation, respectively. The n37(bu) band is assigned to the ring in-plane deform (12 mode).
3.4. Infrared spectrum The infrared spectrum of a PPV film and the calculated infrared spectrum of mPV4 are shown in Fig. 5a and b, respectively. The infrared bands observed at 966, 838, and 556 cm1 are attributed to n15(au), n17(au), and n18(au), respectively. The n15(au) band is assigned to the in-phase CH op-bend of the vinylene group. The n17(au) band is assigned to the in-phase CH op-bend of the phenylene ring. The calculated band corresponding to n20(au) is not clear because
Fig. 6. Calculated atomic displacements of the central part of mPV4 in some calculated modes corresponding to n29, n30, n31, and n37 of PPV. Dotted lines show the polymer axis. Dashed-and-dotted lines mean the directions of transition dipole moments.
K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154 Table 3 Observed and calculated polarizations of some infrared bands No.
Obsd/cm1
n29(bu) n30(bu) n31(bu) n15(au) n17(au) n37(bu) n18(au)
3024 1519 1424 966 838 784 556
Ref. [3]
This study
R = Ak/A?
u/8
u/8
0.19 0.033 1.95 16 14 0.021 26
30 9 64 84 83 3 90
23 1 49 90 90 4 90
Bradley et al. [4] have obtained the angle between the polymer chain axis and the transition dipole moment of each infrared band from the polarized infrared spectrum of a highly oriented PPV film. The results reported are listed in the forth column of Table 3. From the results calculated for mPV4, the angle between the molecular chain axis and the transition dipole moment of each band has been calculated; the results are shown in the fifth column of Table 3. The calculated transition dipole moment vectors of the other infrared modes will be sent on request. The calculated angles are in fairly good agreement with those reported. The calculated angle for n29(bu) is 238, which is quite different from the value of 768 expected from the atomic displacements of vinyl H atoms in this mode (see Fig. 6). This deviation is caused by the charge flux induced by the vinyl CH stretch along the polymer chain [4,18]. A similar effect has been found for the CH stretch band of transpolyacetylene [18]. Charge fluxes are associated with delocalization of p-electrons. The charge-flux effect is included in the DFT calculations. The infrared bands observed at 1629, 1596, 1302, 1194, 1180, 888, 856, and 560 cm1 are not attributed to fundamentals. The 1629 cm1 band is possibly attributed to the n5(ag) branch or the combination, n12(ag) + n15(au) = 661 + 966 = 1627 or n9(ag) + n38(bu) = 1623. The 1596 cm1 band is possibly attributed to the n5(ag) branch or the combination, n10(ag) + n38(bu) = 1171 + 430 = 1601. The 1302 cm1 band is tentatively attributed to the n7(ag) branch or the combination, n11(ag) + n38(bu) = 886 + 430 = 1316. The 1194 cm1 band is attributed to the n10(ag) branch. The 1180 cm1 band is attributed to the n10(ag) branch or the combination, n13(ag) + n18(au) = 634 + 556 = 1190. The 888 cm1 band is possibly attributed to the combination, n14(ag) + n18(au) = 328 + 556 = 884. The origins of the 856 cm1 band and the 560 cm1 peak are unknown.
4. Conclusions The normal coordinate calculations based on the DFT method at the B3LYP/cc-pVDZ level have been performed for a methyl-capped poly( p-phenylenevinylene) oligomer having four vinylene groups and five phenylene rings. The observed infrared and Raman spectra of poly( p-phenyle-
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nevinylene) have been analyzed on the basis of the calculated results. The 15 infrared and 12 Raman bands have been attributed to fundamental vibrations. The calculated transition dipole moments of some bands show fairly good agreements with those derived from the infrared dichroic measurements in the literature. The DFT calculation incorporates the effect of charge flux associated with conjugated p-electrons in the infrared-active vinyl CH stretch. The DFT oligomer approach presented in the present paper will be powerful method for the orientation analyses of low-symmetry PPV derivatives showing high performance in organic light-emitting diodes.
Acknowledgements This work was supported in part by the Grant-in-Aid for Scientific Research (A) (No. 16205004) and the 21COE ‘‘Practical Nano-Chemistry’’ from the Ministry of Education, Culture, Sports, Science, and Technology
References [1] J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P.L. Burns, A.B. Holmes, Nature 347 (1990) 539. [2] R.H. Friend, G.J. Denton, J.J.M. Halls, N.T. Harrison, A.B. Holmes, A. Ko¨hler, A. Lux, S.C. Moratti, K. Pichler, N. Tessler, K. Towns, H.F. Wittmann, Solid State Commun. 102 (1997) 249. [3] Y. Furukawa, in: J.M. Chalmers, P.R. Griffiths (Eds.), Handbook of Vibrational Spectroscopy, vol. 4, John Wiley and Sons, Chichester, 2002, pp. 2483–2495. [4] D.D.C. Bradley, R.H. Friend, H. Lindenberger, S. Roth, Polymer 27 (1986) 1709. [5] Y. Furukawa, A. Sakamoto, M. Tasumi, J. Phys. Chem. 93 (1989) 5354. [6] A. Sakamoto, Y. Furukawa, M. Tasumi, J. Phys. Chem. 96 (1992) 1490. [7] I. Orion, J.P. Buisson, S. Lefrant, Phys. Rev. B 57 (1998) 7050. [8] E. Mulazzi, A. Ripamonti, J. Wery, B. Dulieu, S. Lefrant, Phys. Rev. B 60 (1999) 16519. [9] B. Tian, G. Zerbi, K. Mu¨llen, J. Chem. Phys. 95 (1991) 3198. [10] Z.-F. Guo, Y. Yang, Appl. Phys. Lett. 80 (2002) 148. [11] H. Watanabe, Y. Okamoto, K. Furuya, A. Sakamoto, M. Tasumi, J. Phys. Chem. A 106 (2002) 3318. [12] T. Hrenar, R. Mitric, Z. Meic, H. Meier, U. Stalmach, J. Mol. Struct. 661–662 (2003) 33. [13] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G.
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DFT oligomer approach to vibrational spectra of poly( p-phenylenevinylene) Kotaro Honda a, Yukio Furukawa a,*, Hiroyuki Nishide b a
Department of Chemistry, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan b Department of Applied Chemistry, School of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan Received 22 January 2005; received in revised form 23 March 2005; accepted 30 March 2005 Available online 6 June 2005
Abstract Experimental Raman and infrared spectra of poly( p-phenylenevinylene) have been analyzed on the basis of the normal coordinate calculations based on the density functional theory method at the B3LYP/cc-pVDZ level for a model oligomer. Vibrational modes corresponding to optically active modes of an infinite polymer chain have been selected from the calculated results. On the basis of these normal vibrations, the observed vibrational spectra of poly( p-phenylenevinylene) have been explained successfully. The angles between the calculated transition dipole moment vectors and the polymer axis for some infrared bands agree with those derived from observed infrared dichroic spectrum. # 2005 Elsevier B.V. All rights reserved. Keywords: Density functional theory; Infrared spectroscopy; Raman spectroscopy; Poly( p-phenylenevinylene)
1. Introduction Thin films (thickness, less than 100 nm) of poly( pphenylenevinylene) (PPV) and its derivatives are incorporated as the active materials of organic electronic devices such as light-emitting diodes and field-effect transistors [1,2]. The performance of the polymer electronic devices depends on the molecular structure and the orientation of polymer chains, which may be elucidated by vibrational spectroscopy [3]. The orientation analysis based on infrared spectroscopy requires the transition dipole moment vector of each infrared band. For high-symmetry compounds symmetry determines the directions of the transition dipole moment vectors. On the other hand, for low-symmetry compounds the directions of the transition dipole moments can be determined from the polarization measurements of single crystals or oriented samples and the quantum-chemical calculations at high levels. Since the conjugated polymers used in organic electronic devices have low symmetry in most cases, the * Corresponding author. Tel.: +81 3 3208 7022; fax: +81 3 3208 7022. E-mail address: [email protected] (Y. Furukawa). 0924-2031/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.vibspec.2005.03.007
quantum-chemical calculations are useful in determining the transition dipole moments of infrared bands. The Raman and infrared spectra [4–8] of PPV and the polarized infrared spectra [4,7] of oriented PPV films have been reported. The observed infrared and Raman spectra have been analyzed on the basis of the spectra of PPVoligomers [5–7] and empirical normal coordinate calculations [9]. However, further studies are necessary for the complete assignments of the observed spectra of PPV. The vibrational assignments enable us to elucidate the molecular structure and the orientation of polymer chains from the observed spectra such as infrared reflection–absorption spectra of electronic devices fabricated with the thin films of PPV and its derivatives [10]. Density functional theory (DFT) calculations are very useful for predicting vibrational frequencies of large molecules in good accuracy. The infrared and Raman spectra of PPV oligomers, trans-stilbene [11], 1,4-distyrylbenzene [12], and 4,40 distyrylstilbene, have been assigned on the basis of DFT calculations. Structural parameters calculated by the DFT method for trans-stilbene also agree well with experimental values [11]. However, it is impossible to calculate vibrational frequencies of an infinite PPV chain by using the DFT method
150
K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154 Table 1 Calculated bond lengths and angles for the central part of mPV4 ˚ Bond length/A Bond angle/8 r(C1C2) r(C2C3) r(C3C4) r(C4C7) r(C7C8) r(C2H9) r(C3H10) r(C7H13) r(C8H14)
Fig. 1. (a) Chemical structure of an oligomer (mPV4) and (b) numbering of atoms for the central part.
at present. Because of high performance of computers, it is not difficult for us to perform the normal coordinate calculations of very long oligomers by means of the DFT method. In this study, we have made the normal coordinate calculation of a long oligomer having five phenylene rings and four vinylene moieties (abbreviated as mPV4, Fig. 1a). We analyzed the calculated atomic displacements in the vibrational modes of the oligomer. On the basis of the analysis, we have assigned the observed infrared and Raman spectra of PPV. We have compared the calculated transition dipole moments of some bands with those derived from a polarized infrared measurement in the literature.
2. Calculations The harmonic frequencies, atomic displacements, infrared intensities, and Raman intensities for mPV4 were calculated by the DFT method at the B3LYP/cc-pVDZ level. The Gaussian 03 program package [13] was used. Full geometry optimization was performed under C2h symmetry. The oligomer takes the planar structure except methyl groups with the trans configuration for all C C bonds. No imaginary frequencies were obtained. The calculated vibrational frequencies were scaled uniformly by a factor of 0.978. Calculated atomic displacements in each vibrational mode were depicted with the LXVIEW program [14].
1.411 1.389 1.413 1.462 1.355 1.092 1.093 1.095 1.095
u(C6C1C2) u(C1C2C3) u(C2C3C4) u(C3C4C7) u(C4C7C8) u(C3C2H9) u(C2C3H10) u(C8C7H13) u(C7C8H14)
117.0 121.1 121.9 119.0 127.1 118.9 119.2 118.6 118.6
methyl groups. This result is consistent with the previous results concerning PPV oligomers [11,12]. The calculated bond lengths and angles for the central part of mPV4 are listed in Table 1. The numbering of atoms is shown in Fig. 1b. The phenylene ring has a center of inversion. The C1C2, C2C3, and C3C4 bond lengths of the phenylene ring are ˚ , respectively; the phenylene ring 1.411, 1.389, and 1.413 A deforms from benzenoid to quinoid structure slightly. In poligophenyls, phenyl and phenylene rings take benzenoid structures [15]. The C6C1C2 angle (1178) is smaller than 1208, whereas the C1C2C3 and C2C3C4 angles are larger than 1208. The lengths of the vinylene C4C7 and C7C8 bonds are ˚ , respectively. These bonds are thus 1.462 and 1.355 A regarded as the single and double bonds, respectively. 3.2. Normal vibrations The factor group of a planar infinite PPV chain is isomorphous to the point group C2h. The repeating unit of the PPV chain consists of 14 atoms. The vibrational irreducible representation at the zone center (q = 0) is as follows: 14ag + 6bg + 6au + 12bu. The molecule of mPV4 contains 74 atoms. The 216 normal vibrations of mPV4 with C2h symmetry are distributed: 72ag + 36bg + 37au + 71bu. In both cases, the modes belonging to the ag and bu symmetries are in-plane vibrations, and those belonging to the bg and au symmetries out-of-plane vibrations. The ag and bg vibrations are Raman active, whereas the au and bu vibrations are infrared active. The vibrational modes of benzene derivatives have been discussed on the basis of the Wilson notation [16] for a long time. Hrenar et al. [12] have demonstrated that vibrational modes of PPV oligomers are significantly different from those of benzene. However, in this paper we will discuss the vibrational modes by using the Wilson notation, because the use of the Wilson notation is useful in understanding the vibrations of benzene derivatives. The calculated atomic displacements of all the vibrations will be sent on request.
3. Results and discussion 3.3. Raman spectrum 3.1. Structure No imaginary values in the calculated frequencies indicate the planar structure of mPV4 without the terminal
The 1064 nm excited FT-Raman spectrum of a PPV film and the calculated Raman spectrum of mPV4 are shown in Fig. 2a and b, respectively. The Raman bands observed at
K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154
Fig. 2. (a) Observed Raman spectrum of a PPV film and (b) calculated Raman spectrum of mPV4.
1624, 1581, 1546, 1328, 1301, 1193, 1171, 886, 661, 634, and 328 cm1 are attributed to n4(ag)–n14(ag) of PPV, respectively, as described below. From the calculated normal vibrations of mPV4, we have selected the bands corresponding to the optically-active vibrations of PPV on the basis of the Raman intensities and atomic displacements of vibrational modes. For example, the strongest band observed at 1581 cm1 is correlated with the calculated 1592 cm1 band; the 1581 cm1 band is attributed to n5(ag) of PPV. The calculated atomic displacements in the 1592 cm1 mode are shown in Fig. 3. This is assigned to the mixture of vinylene C C stretch and the ring stretch (8a in the Wilson notation). In each of optically-active vibrations of an infinite polymer chain, every repeating unit has the same vibrational phase. In other words, the phase difference d between the neighboring two units is equal to zero, or the wavenumber q is equal to zero in a dispersion curve. The vibrations of a long-chain oligomer may be classified by the phase difference d. The phase difference of the vibrations of a long oligomer having n repeating units may be expressed by m/(n + 1) (m = 1, 2,. . ., n) for each mode [17]. The 1/(n + 1) mode has no node in the sequence of the vibrational phases. As shown in Fig. 3, no node is found in the atomic displacements in the 1592 cm1 mode. When the frequency dispersion of the vibrational branch of the polymer chain is small, the frequency of the 1/(n + 1) mode for the long oligomer is very close to that of the corresponding optically-active vibration of the polymer. Raman studies [5–7] of PPV and oligomers have shown that frequency dispersions of the vibrational modes for PPV are small. Thus, the Raman band observed at 1581 cm1 is ascribed to n5(ag) of PPV. We have assigned
Fig. 3. Calculated atomic displacements in the 1592 cm1 mode of mPV4.
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the experimental infrared and Raman spectra of PPV on the basis of the calculated normal vibrations of mPV4 in the same way. Although significant mode mixing in the sequence of vibrational displacements makes choices of the 1/(n + 1) modes difficult in some bands, we selected most probable bands from the calculated modes. The selected bands are shown with thick solid lines, and the others with thin solid lines in Fig. 2b. The selected frequencies are listed in Table 2. The bands corresponding to n12(ag) and n14(ag) are not clear in the calculated vibrations because of large mode mixing. The calculated 644 cm1 band is tentatively correlated to n12(ag). The calculated 293 cm1 band is tentatively correlated to n14(ag), whereas the calculated 347 cm1 band may be attributed to n14(ag) instead to the 293 cm1 band. The Raman band observed at 959 and 860 cm1 are attributed to n21(bg) and n22(bg), respectively. In the previous paper [5], YF et al. have assigned the 959 cm1 Raman band Table 2 Assignments of the observed vibrational bands of PPV Species No. Calcd/cm1 Obsd/cm1 Mode ag
n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14
3124 3099 3075 1650 1592 1549 1314 1291 1194 1163 883 644 632 293
– – – 1624 1581 1546 1328 1301 1193 1171 886 661 634 328
au
n15 n16 n17 n18 n19 n20
980 957 840 558 403 220
966 – 838 556 – –
Vinyl CH op-bend CH op-bend (17a) CH op-bend (11) Ring op-deform (16b) Ring op-deform (16a) Skeletal op-deform
bg
n21 n22 n23 n24 n25 n26
960 880 820 706 313 107
959 860 – – – –
CH op-bend (5) Vinyl CH op-bend CH op-bend (10a) Skeletal op-deform (4) Rotational Skeletal op-deform
bu
n27 n28 n29 n30 n31 n32 n33 n34 n35 n36 n37 n38
3122 3097 3082 1517 1425 1353 1272 1206 1108 1000 794 435
3110 3077 3024 1519 1424 1340 1271 1211 1107 1014 784 430
CH str CH str Vinyl CH str Vinyl C C str, ring str (8a) Ring str (8a), vinyl C C str Ring str (8b) Vinyl CH ip-bend, CH ip-bend CH ip-bend, vinyl CH ip-bend C–C str CH ip-bend (9a) Ring str (1), C–C str Ring ip-deform (6b) Ring ip-deform (6a) Rotational
CH str CH str Vinyl CH str Ring str and ip-deform (19a) Ring str and ip-deform (19b) Vinyl CH ip-bend, ring str (14) Ring str (13) Vinyl CH ip-bend CH ip-bend (18b) CH ip-bend (18a) Ring ip-deform (12) Skeletal ip-deform
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K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154
Fig. 4. Calculated atomic displacements of the central part of mPV4 in some calculated modes corresponding to n4, n5, n6, and n10 of PPV.
Fig. 5. (a) Observed infrared spectrum of a PPV film and (b) calculated infrared spectrum of mPV4.
to the in-phase CH op-bend that is infrared-active mode n15(au) because the observed Raman wavenumber is very close to infrared one. In this study, the 959 cm1 band is tentatively attributed to n21(bg) because the calculated wavenumber is in good agreement with the observed. However, further studies are requisite for the complete assignment of this band. In the calculated band corresponding to n23(bg), the atomic displacements of the terminal rings are different from those of other three rings. The calculated 820 cm1 band is tentatively correlated to n23(bg). The bands observed at 1415 and 406 cm1 are not attributed to fundamentals. The 1415 cm1 band may be attributed to the branch of n31(bu) or the combination of n7(ag) and n26(bg). The origin of the 406 cm1 band is not known. The atomic displacements of the central part of mPV4 for the bands attributed to n4(ag), n5(ag), n6(ag) and n10(ag) are shown in Fig. 4. The n4(ag) as well as n5(ag) modes are assigned to the mixture of the C C stretch and the ring stretch (8a) in the Wilson notation. These two modes have opposite phases in these two stretches. In the displacements of n5(ag) the two stretches occur along bond alternation. According to Zerbi’s theory, the contribution of the effective conjugation coordinate is the largest for this mode [8]. The n6(ag) mode is assigned to a ring CC stretch (8b). The n10(ag) mode is assigned to a CH ip-bend (9a).
of large mode mixing. The calculated 220 cm1 band is tentatively correlated to n20(au). The infrared bands observed at 3110, 3077, 3024, 1519, 1424, 1340, 1271, 1211, 1107, 1014, 784, and 430 cm1 are attributed to n27(bu)–n38(bu), respectively. The calculated bands corresponding to n34(bu) and n38(bu) are not obvious owing to large mode mixing. The calculated 1206 and 435 cm1 bands are tentatively correlated to n34(bu) and n38(bu), respectively. The atomic displacements of the central part of mPV4 for the bands attributed to n29(bu), n30(bu), n31(bu), and n37(bu) are shown in Fig. 6. The n29(bu) band is assigned to a CH stretch of the vinyl group whereas the n27(bu) and n28(bu) bands to CH stretches of the phenylene rings. The n30(bu) and n31(bu) bands are assigned to the 19a and 19b modes in the Wilson notation, respectively. The n37(bu) band is assigned to the ring in-plane deform (12 mode).
3.4. Infrared spectrum The infrared spectrum of a PPV film and the calculated infrared spectrum of mPV4 are shown in Fig. 5a and b, respectively. The infrared bands observed at 966, 838, and 556 cm1 are attributed to n15(au), n17(au), and n18(au), respectively. The n15(au) band is assigned to the in-phase CH op-bend of the vinylene group. The n17(au) band is assigned to the in-phase CH op-bend of the phenylene ring. The calculated band corresponding to n20(au) is not clear because
Fig. 6. Calculated atomic displacements of the central part of mPV4 in some calculated modes corresponding to n29, n30, n31, and n37 of PPV. Dotted lines show the polymer axis. Dashed-and-dotted lines mean the directions of transition dipole moments.
K. Honda et al. / Vibrational Spectroscopy 40 (2006) 149–154 Table 3 Observed and calculated polarizations of some infrared bands No.
Obsd/cm1
n29(bu) n30(bu) n31(bu) n15(au) n17(au) n37(bu) n18(au)
3024 1519 1424 966 838 784 556
Ref. [3]
This study
R = Ak/A?
u/8
u/8
0.19 0.033 1.95 16 14 0.021 26
30 9 64 84 83 3 90
23 1 49 90 90 4 90
Bradley et al. [4] have obtained the angle between the polymer chain axis and the transition dipole moment of each infrared band from the polarized infrared spectrum of a highly oriented PPV film. The results reported are listed in the forth column of Table 3. From the results calculated for mPV4, the angle between the molecular chain axis and the transition dipole moment of each band has been calculated; the results are shown in the fifth column of Table 3. The calculated transition dipole moment vectors of the other infrared modes will be sent on request. The calculated angles are in fairly good agreement with those reported. The calculated angle for n29(bu) is 238, which is quite different from the value of 768 expected from the atomic displacements of vinyl H atoms in this mode (see Fig. 6). This deviation is caused by the charge flux induced by the vinyl CH stretch along the polymer chain [4,18]. A similar effect has been found for the CH stretch band of transpolyacetylene [18]. Charge fluxes are associated with delocalization of p-electrons. The charge-flux effect is included in the DFT calculations. The infrared bands observed at 1629, 1596, 1302, 1194, 1180, 888, 856, and 560 cm1 are not attributed to fundamentals. The 1629 cm1 band is possibly attributed to the n5(ag) branch or the combination, n12(ag) + n15(au) = 661 + 966 = 1627 or n9(ag) + n38(bu) = 1623. The 1596 cm1 band is possibly attributed to the n5(ag) branch or the combination, n10(ag) + n38(bu) = 1171 + 430 = 1601. The 1302 cm1 band is tentatively attributed to the n7(ag) branch or the combination, n11(ag) + n38(bu) = 886 + 430 = 1316. The 1194 cm1 band is attributed to the n10(ag) branch. The 1180 cm1 band is attributed to the n10(ag) branch or the combination, n13(ag) + n18(au) = 634 + 556 = 1190. The 888 cm1 band is possibly attributed to the combination, n14(ag) + n18(au) = 328 + 556 = 884. The origins of the 856 cm1 band and the 560 cm1 peak are unknown.
4. Conclusions The normal coordinate calculations based on the DFT method at the B3LYP/cc-pVDZ level have been performed for a methyl-capped poly( p-phenylenevinylene) oligomer having four vinylene groups and five phenylene rings. The observed infrared and Raman spectra of poly( p-phenyle-
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nevinylene) have been analyzed on the basis of the calculated results. The 15 infrared and 12 Raman bands have been attributed to fundamental vibrations. The calculated transition dipole moments of some bands show fairly good agreements with those derived from the infrared dichroic measurements in the literature. The DFT calculation incorporates the effect of charge flux associated with conjugated p-electrons in the infrared-active vinyl CH stretch. The DFT oligomer approach presented in the present paper will be powerful method for the orientation analyses of low-symmetry PPV derivatives showing high performance in organic light-emitting diodes.
Acknowledgements This work was supported in part by the Grant-in-Aid for Scientific Research (A) (No. 16205004) and the 21COE ‘‘Practical Nano-Chemistry’’ from the Ministry of Education, Culture, Sports, Science, and Technology
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