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Peierls distortion in trans polyacetylene: Evidence from infrared intensities
Solid State Communications, Vol. 56, No. 10, pp. 863-866, 1985. Printed in Great Britain.
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
PEIERLS DISTORTION IN TRANS POLYACETYLENE: EVIDENCE FROM INFRARED INTENSITIES C. Castiglioni and G. Zerbi Dipartimento di Chimica Industriale e Ingegneria Chimica del Politecnico, piazza L. da Vinci 32, Milano, Italy and M. Gussoni Istituto di Chimica Fisica dei Materiali, CNR, Genova, Italy
(Received 15 May 1985 by F. Bassani) It is shown that from the polarization properties of the infrared spectrum of oriented pristine trans polyacetylene clear evidence of Peierls distortion is obtained. Moreover, it is shown that during CH stretching and in-plane bending CC bonds develop relevant charge fluxes. Infrared intensity studies indicate the existence of an unusual charge mobility. PEIERLS DISTORTION or bond dimerisation in trans polyacetylene (PA) has been proposed with great certainty in the early theoretical works on this material [1]. Subsequent more extensive quantum mechanical calculations started weakening the original firm statement even reaching the proposal that the inclusions of electron correlation could remove bond dimerisation tending towards an undistorted chain [2]. The issue was so important for the understanding of the physical properties of this material that several experimental techniques were tried in order to reach the experimental quantitative proof on the real existence of bond dimerisation. The task was and is still not simple because of the intrinsic difficulty in handling this material. The most accurate electron diffraction [3] and n.m.r, experiments [4] on solid PA do suggest with fair reliability a dimerized structure with alternant single and double bonds. The experimental value of CC bond distances ( R c c = l . 4 4 A and R c c = l . 3 6 A ) indicate a relevant delocalisation of electrons (conjugation) between CC bonds. In a previous work [5] we have shown that simple optical selection rules for vibrational transitions in infrared and Raman are not sufficient in proving the existence of Peierl's distortion. Only when the selection rules and the theory of resonance enhancement in resonance Raman spectra are included evidence is found for bond dimerisation. We wish to point out and wish to show here that infrared spectroscopy alone can provide an independent evidence of bond dimerisation if the dichroic ratios of the infrared bands on stretch oriented samples are analyzed in terms of the theory of vibrational intensities. For this reason we have recorded the infrared spectra of highly oriented specimens of PA synthetized by 863
Assoreni [6]. The spectrum is reported in Fig. 1. In this paper we wish to elaborate on an apparent anomaly of the dichroic behavior of the C - H stretching motion at 3013 cm -1. This may appear to be inconsistent with the structure of stretch oriented polyacetylene. This is really not the case but provides us with an interesting structural information. Theory of infrared intensity allows to express the observed transition moment in terms of bond properties such as atomic equilibrium charges qO and charges fluxes aq/aQ. It becomes then possible to derive detailed information on the electrical properties of molecules from infrared absorption coefficients [8]. We apply this theory in this paper to PA to determine structure and electronic properties. It is at present well-known that if PA is a Peierl's undistorted system, its symmetry is D2h; if bond dimerisation occurs the symmetry is C2h (see Fig. 2). Let us examine the dichroic behaviour of the q = 0 infrared active phonon lines at 1015, 1292 or 1250 and 3013 cm -1 [9, 10]. The band at 1015 cm -1,unanimously assigned to the CH out-of-plane bending motion shows a strong perpendicular polarization, as required by symmetry for both point groups. However, in the actual spectrum a non negligible parallel component is observed which can be interpreted as due to the non complete alignment of the chains. An average angle ~ of orientation of the chains with respect to the drawing direction can be determined from the dichroic ratio of the out-ofplane band. Spectra of different samples with drawing ratio of 3.5 indicate that ~ = 24 °. On the contrary, the CH stretching band (3013 cm -1) shows a larger component in the parallel spectrum. For D2h symmetry, the dichroic ratio of the 3013cm -~ band should be exactly the same as that of the 1015 cm -~
864
Vol. 56, No. 10
PEIERLS DISTORTION IN TRANS POLYACETYLENE
f~
!
3,,oo
|
3,oo
2+bo
|
2~
2/oo
,9oo'
,6bo
,3'oo
,o;o
(;13,1- I
Fig. 1. Spectra of a sample of trans polyacetylene (drawing ratio 3.5) recorded with light linearly polarized parallel ( ) and perpendicular ( . . . . ) to the drawing axis: band and the parallel component should originate from the non-oriented chains. However, as shown in Fig. 1, the two bands have opposite dichroic behaviour. This fact forces us to reject the D2h structure. For C2h symmetry (Fig. 2) both aMY/aQstr and aMZ/~Q=tr may be nonvanishing. The angle formed by aM/aQ, tr with the chain axis can be evaluated from the dichroic ratio of the CH stretching band using the average angle = 24 ° obtained from the out-of-plane band. The value so obtained is O = 48 °*. This is a very important information generally unexpected, namely upon stretching the C - H bond an electronic rearrangement at the sp 2 carbon atom takes place such that the dipole changes occur at an angle of "" 48 ° with respect to the direction of the C - H bond. This result may be rationalized in two different ways: (a) i)M/~Qstr is directed along the CH bond (namely the stretching induces a charge repolarization only in the CH bond); in this case CH bonds must strongly deviate from the perpendicular to the chain axis, as suggested by Leising et al. [11]. However, a tilting angle of 48 ° is hard to be accepted for a system in sp 2 hybridization. (b) large fluxes of electronic charge take place along the chain during CH stretching vibration.
~M/~Q.tr as a function of electrooptical parameters (EOP) [12]. In this theory the dipole moment induced by the vibrations is represented in terms of local parameters such as equilibrium bond dipole moments and their variations with vibrational coordinates. One sees from Table l(a) that the parallel component of the CH stretching band is due to the combination A = (aMc--c/ arCH-- 3Mc=c/~)rCH); these parameters account for the redistribution of the electronic charge in the CC bonds, while CH stretches. Notice that in the case of an undimerized structure aMc_c/arcH = aMc=c/arcH for symmetry reasons and the aMZ/aQstr component vanishes. In Table l(a) we have also reported a numerical
-k
1015 cm -= Dzh perpendicular
C2h perpendicuLar
1292 o r 1 250 cm -~ poratLeL
parallel and perpendicular
3013 cm-~ perpendicular
paraLleL and perpendicuLar
In Table l(a) we have reported the expression of
* The occurrence of a large 0 angle has been first mentioned in [4b].
Fig. 2. Infrared-active modes of trans polyacetylene. The polarization of the bands in the dimerized structure (C2h) and in the undimerized one (D2h) are reported at the bottom.
PEIERLS DISTORTION IN TRANS POLYACETYLENE
Vol. 56, No. 10
865
Table 1. Expression of aM/aQi as a function of EOP; The equilibrium geometry adopted has CH bonds perpendicular to the chain axis. The values of EOP are reported in Debye for equilibrium parameters, Debye/rad for bending parameters and Debye/A for stretching parameters (1) Asymmetric CH stretching:
aMZ /aQstr = 1.270(aMc=C/arcn -- aMc-C/arca) aMY/aQ, tr = 0.733(2amCn/arcn- (aMc=C/arcn + aMC--C/arcrx))
abI
a~_~ r
A = (aMc=c/arci~ - aMc--C/arcn) # +-0.350 = (aMC=C/arci~ + aMc--C/arct.x) = - 0 . 2 0 4
(2) In plane CH bending i~MZ/itQinpl. = 1.406mC~o/r~ + 1.663(itMC=C/it~ + i~MC-C/a~) itMY/aQinpla = 0.960(aMC=Cli~o -- i~MC--C/a~o)
a.
b.
A = (aMC=C/a~o-aMc---C/a~o) = + 0.119
+ 0.073
= (aMc=c/a~o + aMc-C/a~o) = - 0.476
- 0.459
(3) Out of plane CH bending
aMX/aQopla = 1.466mCtIo /rOrI +
m cH° = 0.701
estimate [10] of the EOP of trans PA; the relevant values of A and ~ indicate the existence of highly mobile electrons along the CC chain, as one would expect in the presence of strongly conjugated CC bonds. The occurrence of a relevant flux of electrons along the chain clearly emerges also from the analysis of the behaviour of the two bands due to bending motions [10]. The assignment of the in.plane bending motion is still controversial: some authors [9, 10] have assigned this motion at 1292cm-t; however, Harada
et al. [9.c] and Galtier [9.d] reject this choice and assign the in-plane bending at 1250cm -I. From the viewpoint of intensity the two bands are practically identical. From the viewpoint of polarization properties the 1250 cm -1 band is more strongly polarized along the chain axis (012so = 2 8 °) than the 1292cm -1 band (tSt292 = 45°); however, a choice based on polarization properties cannot be made because also in this case any orientation aM/aQinola in the plane is allowed by symmetry.
866
PEIERLS DISTORTION IN TRANS POLYACETYLENE
In Table 1(b, c) we have reported the expressions of ~)M/~Qinp]a and aM/~Qopla in terms of electrooptical parameters. The large difference between the in.plane and the out-of-plane modes is due to the relevance of the combination ~ = (aMc-c/a + aMc=c/a ), which has opposite sign with respect to m ° [10]. As for the combination A = (aMc_c/a~o - aMc=c/a~o), its value is slightly different in the two possible assignment (Table l(b)); in any case the presence of nonvanishing value of A still indicates the occurrence of a dimerized structure. The relevant values of aMc--c/a~ and aMc=c/a~ inform us that the charge on the CC bonds is very mobile. In conclusion the polarization properties of the infrared spectrum of oriented pristine trans-polyacetylene indicates: (i) that the structure of the trans-polyacetylene chain is inequivocally dimerized; (ii) that the CC bonds develop very relevant charge fluxes during CH stretching vibration and during in-plane bendings. (iii)that the infrared intensity pattern may be related to an unusual charge mobility, probably related with the large conjugation of CC bonds.
Vol. 56, No. 10
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9a. b. c. d. 10. 11. 12.
H.C. Longuett-Higgins & L. Salem, Proc. Roy. Soc. London, A251, 172 (1959). W.P. Su, J.R. Schriffer & A.J. Heeger, Phys. Rev. B22, 2099 (1980). A.A. Ovchinnikov, A.E. Belinski, I.A. Misurkin & I.I. Ukraiskii, Int. J. Quant. Chem. 22, 761 (1982). S. Suhai, Chem. Phys. Lett. 96,619 (1983). J.C.W. Chien, Polyacetylene, Chap. 3, Academic Press, N.Y. (1984). T.C. Clarke, R.D. Kendvick & C.S. Yannoni, J. Phys. (Paris), 44, C3-369 (1983). G. Zannoni & G. Zerbi, Solid State Commun. 48, 871 (1983). U. Pedretti, G. Perego & G. Lugli, Italian Patent Appl. 22722 A/82 to Assoreni. M. Gussoni, P. Jona & G. Zerbi, J. Chem. Phys. 78, 6802 (1982). M. Gussoni, C. Castiglioni & G. Zerbi, J. Phys. Chem. 88, 600 (1984). H. Shirakawa & S.I. Ikeda, Polymer Journal, 2, 231 (1971). P. Piaggio, G. Dellepiane, L. Piseri, R. Tubino & C. Taliani, Solid State Commun. 50, 947 (1984). I. Harada, Y. Furukawa, T. Arakawa, H. Takeuchi & H. Shirakawa, Mol. Crystals Liq. Cryst., 117, 335 (1985). M. Galtier, M. Charbonnel, A. Montaner & J.L. Ribet,Polymer, 25, 1253 (1984). C. Castiglioni, M. Gussoni, M. Miragoli, G. Lugli & G. Zerbi, Spectro. Acta, 41A, 371 (1985). G. Leising, R. Uitz, B. Ankele. W. Ottinger & F. Stelzer, Mol. Crystals Liq. Cryst., 117,327 (1985). M. Gussoni, J. Mol. Struc., 113,323 (1984).
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
PEIERLS DISTORTION IN TRANS POLYACETYLENE: EVIDENCE FROM INFRARED INTENSITIES C. Castiglioni and G. Zerbi Dipartimento di Chimica Industriale e Ingegneria Chimica del Politecnico, piazza L. da Vinci 32, Milano, Italy and M. Gussoni Istituto di Chimica Fisica dei Materiali, CNR, Genova, Italy
(Received 15 May 1985 by F. Bassani) It is shown that from the polarization properties of the infrared spectrum of oriented pristine trans polyacetylene clear evidence of Peierls distortion is obtained. Moreover, it is shown that during CH stretching and in-plane bending CC bonds develop relevant charge fluxes. Infrared intensity studies indicate the existence of an unusual charge mobility. PEIERLS DISTORTION or bond dimerisation in trans polyacetylene (PA) has been proposed with great certainty in the early theoretical works on this material [1]. Subsequent more extensive quantum mechanical calculations started weakening the original firm statement even reaching the proposal that the inclusions of electron correlation could remove bond dimerisation tending towards an undistorted chain [2]. The issue was so important for the understanding of the physical properties of this material that several experimental techniques were tried in order to reach the experimental quantitative proof on the real existence of bond dimerisation. The task was and is still not simple because of the intrinsic difficulty in handling this material. The most accurate electron diffraction [3] and n.m.r, experiments [4] on solid PA do suggest with fair reliability a dimerized structure with alternant single and double bonds. The experimental value of CC bond distances ( R c c = l . 4 4 A and R c c = l . 3 6 A ) indicate a relevant delocalisation of electrons (conjugation) between CC bonds. In a previous work [5] we have shown that simple optical selection rules for vibrational transitions in infrared and Raman are not sufficient in proving the existence of Peierl's distortion. Only when the selection rules and the theory of resonance enhancement in resonance Raman spectra are included evidence is found for bond dimerisation. We wish to point out and wish to show here that infrared spectroscopy alone can provide an independent evidence of bond dimerisation if the dichroic ratios of the infrared bands on stretch oriented samples are analyzed in terms of the theory of vibrational intensities. For this reason we have recorded the infrared spectra of highly oriented specimens of PA synthetized by 863
Assoreni [6]. The spectrum is reported in Fig. 1. In this paper we wish to elaborate on an apparent anomaly of the dichroic behavior of the C - H stretching motion at 3013 cm -1. This may appear to be inconsistent with the structure of stretch oriented polyacetylene. This is really not the case but provides us with an interesting structural information. Theory of infrared intensity allows to express the observed transition moment in terms of bond properties such as atomic equilibrium charges qO and charges fluxes aq/aQ. It becomes then possible to derive detailed information on the electrical properties of molecules from infrared absorption coefficients [8]. We apply this theory in this paper to PA to determine structure and electronic properties. It is at present well-known that if PA is a Peierl's undistorted system, its symmetry is D2h; if bond dimerisation occurs the symmetry is C2h (see Fig. 2). Let us examine the dichroic behaviour of the q = 0 infrared active phonon lines at 1015, 1292 or 1250 and 3013 cm -1 [9, 10]. The band at 1015 cm -1,unanimously assigned to the CH out-of-plane bending motion shows a strong perpendicular polarization, as required by symmetry for both point groups. However, in the actual spectrum a non negligible parallel component is observed which can be interpreted as due to the non complete alignment of the chains. An average angle ~ of orientation of the chains with respect to the drawing direction can be determined from the dichroic ratio of the out-ofplane band. Spectra of different samples with drawing ratio of 3.5 indicate that ~ = 24 °. On the contrary, the CH stretching band (3013 cm -1) shows a larger component in the parallel spectrum. For D2h symmetry, the dichroic ratio of the 3013cm -~ band should be exactly the same as that of the 1015 cm -~
864
Vol. 56, No. 10
PEIERLS DISTORTION IN TRANS POLYACETYLENE
f~
!
3,,oo
|
3,oo
2+bo
|
2~
2/oo
,9oo'
,6bo
,3'oo
,o;o
(;13,1- I
Fig. 1. Spectra of a sample of trans polyacetylene (drawing ratio 3.5) recorded with light linearly polarized parallel ( ) and perpendicular ( . . . . ) to the drawing axis: band and the parallel component should originate from the non-oriented chains. However, as shown in Fig. 1, the two bands have opposite dichroic behaviour. This fact forces us to reject the D2h structure. For C2h symmetry (Fig. 2) both aMY/aQstr and aMZ/~Q=tr may be nonvanishing. The angle formed by aM/aQ, tr with the chain axis can be evaluated from the dichroic ratio of the CH stretching band using the average angle = 24 ° obtained from the out-of-plane band. The value so obtained is O = 48 °*. This is a very important information generally unexpected, namely upon stretching the C - H bond an electronic rearrangement at the sp 2 carbon atom takes place such that the dipole changes occur at an angle of "" 48 ° with respect to the direction of the C - H bond. This result may be rationalized in two different ways: (a) i)M/~Qstr is directed along the CH bond (namely the stretching induces a charge repolarization only in the CH bond); in this case CH bonds must strongly deviate from the perpendicular to the chain axis, as suggested by Leising et al. [11]. However, a tilting angle of 48 ° is hard to be accepted for a system in sp 2 hybridization. (b) large fluxes of electronic charge take place along the chain during CH stretching vibration.
~M/~Q.tr as a function of electrooptical parameters (EOP) [12]. In this theory the dipole moment induced by the vibrations is represented in terms of local parameters such as equilibrium bond dipole moments and their variations with vibrational coordinates. One sees from Table l(a) that the parallel component of the CH stretching band is due to the combination A = (aMc--c/ arCH-- 3Mc=c/~)rCH); these parameters account for the redistribution of the electronic charge in the CC bonds, while CH stretches. Notice that in the case of an undimerized structure aMc_c/arcH = aMc=c/arcH for symmetry reasons and the aMZ/aQstr component vanishes. In Table l(a) we have also reported a numerical
-k
1015 cm -= Dzh perpendicular
C2h perpendicuLar
1292 o r 1 250 cm -~ poratLeL
parallel and perpendicular
3013 cm-~ perpendicular
paraLleL and perpendicuLar
In Table l(a) we have reported the expression of
* The occurrence of a large 0 angle has been first mentioned in [4b].
Fig. 2. Infrared-active modes of trans polyacetylene. The polarization of the bands in the dimerized structure (C2h) and in the undimerized one (D2h) are reported at the bottom.
PEIERLS DISTORTION IN TRANS POLYACETYLENE
Vol. 56, No. 10
865
Table 1. Expression of aM/aQi as a function of EOP; The equilibrium geometry adopted has CH bonds perpendicular to the chain axis. The values of EOP are reported in Debye for equilibrium parameters, Debye/rad for bending parameters and Debye/A for stretching parameters (1) Asymmetric CH stretching:
aMZ /aQstr = 1.270(aMc=C/arcn -- aMc-C/arca) aMY/aQ, tr = 0.733(2amCn/arcn- (aMc=C/arcn + aMC--C/arcrx))
abI
a~_~ r
A = (aMc=c/arci~ - aMc--C/arcn) # +-0.350 = (aMC=C/arci~ + aMc--C/arct.x) = - 0 . 2 0 4
(2) In plane CH bending i~MZ/itQinpl. = 1.406mC~o/r~ + 1.663(itMC=C/it~ + i~MC-C/a~) itMY/aQinpla = 0.960(aMC=Cli~o -- i~MC--C/a~o)
a.
b.
A = (aMC=C/a~o-aMc---C/a~o) = + 0.119
+ 0.073
= (aMc=c/a~o + aMc-C/a~o) = - 0.476
- 0.459
(3) Out of plane CH bending
aMX/aQopla = 1.466mCtIo /rOrI +
m cH° = 0.701
estimate [10] of the EOP of trans PA; the relevant values of A and ~ indicate the existence of highly mobile electrons along the CC chain, as one would expect in the presence of strongly conjugated CC bonds. The occurrence of a relevant flux of electrons along the chain clearly emerges also from the analysis of the behaviour of the two bands due to bending motions [10]. The assignment of the in.plane bending motion is still controversial: some authors [9, 10] have assigned this motion at 1292cm-t; however, Harada
et al. [9.c] and Galtier [9.d] reject this choice and assign the in-plane bending at 1250cm -I. From the viewpoint of intensity the two bands are practically identical. From the viewpoint of polarization properties the 1250 cm -1 band is more strongly polarized along the chain axis (012so = 2 8 °) than the 1292cm -1 band (tSt292 = 45°); however, a choice based on polarization properties cannot be made because also in this case any orientation aM/aQinola in the plane is allowed by symmetry.
866
PEIERLS DISTORTION IN TRANS POLYACETYLENE
In Table 1(b, c) we have reported the expressions of ~)M/~Qinp]a and aM/~Qopla in terms of electrooptical parameters. The large difference between the in.plane and the out-of-plane modes is due to the relevance of the combination ~ = (aMc-c/a + aMc=c/a ), which has opposite sign with respect to m ° [10]. As for the combination A = (aMc_c/a~o - aMc=c/a~o), its value is slightly different in the two possible assignment (Table l(b)); in any case the presence of nonvanishing value of A still indicates the occurrence of a dimerized structure. The relevant values of aMc--c/a~ and aMc=c/a~ inform us that the charge on the CC bonds is very mobile. In conclusion the polarization properties of the infrared spectrum of oriented pristine trans-polyacetylene indicates: (i) that the structure of the trans-polyacetylene chain is inequivocally dimerized; (ii) that the CC bonds develop very relevant charge fluxes during CH stretching vibration and during in-plane bendings. (iii)that the infrared intensity pattern may be related to an unusual charge mobility, probably related with the large conjugation of CC bonds.
Vol. 56, No. 10
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9a. b. c. d. 10. 11. 12.
H.C. Longuett-Higgins & L. Salem, Proc. Roy. Soc. London, A251, 172 (1959). W.P. Su, J.R. Schriffer & A.J. Heeger, Phys. Rev. B22, 2099 (1980). A.A. Ovchinnikov, A.E. Belinski, I.A. Misurkin & I.I. Ukraiskii, Int. J. Quant. Chem. 22, 761 (1982). S. Suhai, Chem. Phys. Lett. 96,619 (1983). J.C.W. Chien, Polyacetylene, Chap. 3, Academic Press, N.Y. (1984). T.C. Clarke, R.D. Kendvick & C.S. Yannoni, J. Phys. (Paris), 44, C3-369 (1983). G. Zannoni & G. Zerbi, Solid State Commun. 48, 871 (1983). U. Pedretti, G. Perego & G. Lugli, Italian Patent Appl. 22722 A/82 to Assoreni. M. Gussoni, P. Jona & G. Zerbi, J. Chem. Phys. 78, 6802 (1982). M. Gussoni, C. Castiglioni & G. Zerbi, J. Phys. Chem. 88, 600 (1984). H. Shirakawa & S.I. Ikeda, Polymer Journal, 2, 231 (1971). P. Piaggio, G. Dellepiane, L. Piseri, R. Tubino & C. Taliani, Solid State Commun. 50, 947 (1984). I. Harada, Y. Furukawa, T. Arakawa, H. Takeuchi & H. Shirakawa, Mol. Crystals Liq. Cryst., 117, 335 (1985). M. Galtier, M. Charbonnel, A. Montaner & J.L. Ribet,Polymer, 25, 1253 (1984). C. Castiglioni, M. Gussoni, M. Miragoli, G. Lugli & G. Zerbi, Spectro. Acta, 41A, 371 (1985). G. Leising, R. Uitz, B. Ankele. W. Ottinger & F. Stelzer, Mol. Crystals Liq. Cryst., 117,327 (1985). M. Gussoni, J. Mol. Struc., 113,323 (1984).