J. Phys. Chem. 1982, 86, 2359-2365
2350
Electronic and Vibrational Structures of Finite Polyenes Toklo Yamabe, Kazuo Akagl, Yukltoshl Tanabe, Kenlchl Fukul, Department of Hydrocarbon Ctmmistfy, Faculiy of Engineering, Kyoto Universliy, Kyoto, Japan
and Hldekl Shlrakawa Institute of Material Science, University of Tsukuba, Ibaraki, Japan (Received: March 24, 1981; I n Final Form: December 16, 1981)
Theoretical investigation of the electronic and vibrational structures of finite conjugated polyenes has been performed with MIND0/3 MO calculations. The results show that the increase of the charge density polarization generated by the electron loss is responsible for the enhancement of IR-active vibrational intensity, by which the three characteristic IR absorption bands observed in doped polyacetylene and &carotene can be reasonably rationalized. It is also found that the polarized charge distribution is achieved by the electronic rearrangement which tends to strengthen the electrostatic nature and to weaken the covalent nature of the finite polyene chain.
Introduction There is currently evidence that polyacetylene, (CH),, doped with an electron donor or acceptor exhibits high electric c~nductivityl-~ and characteristic optical properon which a great deal of physical and chemical attention has been focused during the past few years. In particular, the origin of the enhancement of three IR bands,w which provides fundamental information on the electronic and vibrational structures of the doped (CH),, has been an urgent subject of investigation. Recently, Street et aL6Sobserved from the measurement of Fourier transform IR transmission spectroscopy that a common feature in doping by halogens, silver salts, and h F 5is an electron transfer from the polyene to the dopant to yield an oxidized (CH), and a reduced form of the dopant. This has been confirmed to be in accord with the case where ,&carotene8tgis used instead of (CH),, which will be mentioned later. However, their subsequent argument7 that three IR bands observed in the oxidized polyene originate from the vibronic activation, i.e., the enhancement of the totally symmetric Raman-active AB vibrations in the IR spectrum,is not necessarily convincing. This is because such an interpretation is only an inference from the case of TCNE charge-transfer complexes or TCNQ salts, based on Ferguson and Matsen's charge density oscillation mechanism.'O Furthermore, the straightforward application of this mechanism to the in-
teracting system between (CH), and the dopant concerned here has not been theoretically established. Meanwhile, the doped @-carotenehas been revealed to behave similarly to the doped (CH), with respect to both electric c o n d u ~ t i v i t y and ~ ~ Jelectronic ~ absorption,lZwhich has naturally facilitated the use of a model system such as @-carotene.21Very recently, Harada et al.*v9observed three IR bands in alZ-trans-@-carotenedoped with I, or SO3 as well as in the doped (CH), and interpreted them as the "ungerade" vibrations of the positively charged parts in the polyene chain. From this experimental evidence for model systems, one may attribute the global feature of the doped (CH), to the changes of electronic and vibrational structures on the polyene segments of (CH),. For instance, the trans-(CH),, a thermally stable polyene, is known to be composed of various segments with 4 to ca. 100 conjugated double bonds.4 It is therefore expected that the essential nature of the potentiality to enhance three IR bands can be drawn by elucidating the electronic and vibrational structures of the finite polyenes in neutral and oxidized forms which correspond to the undoped and doped (with electron donors) polyene segments, respectively. Note that the dopant will be hereafter restricted to the electron acceptor such as Iz or h F , , unless otherwise stated. In connection with the electron transfer mentioned above, there arises another subject, Le., the mechanism by which electronic and nuclear rearrangements accompa-
(1)H. Shuakawa, E.J. Louis, A. G. MacDiarmid, C. K. Chiang, and A. J. Heeger, J. Chem. SOC.,Chem. Commun., 578 (1977). (2)C. K.Chiang, M. A. Druy, S. G. Gau, A. J. Heeger, E. J. Louis, A. G. MacDiarmid, Y. W. Park, and H. Shirakawa, J. Am. Chem. SOC.,100, 1013 (1978). (3) H. Shirakawa, T. Sasaki, and S. Ikeda, Chem. Lett., 1113 (1978). (4)I. Harada, M. Tasumi, H. Shirakawa, and S. Ikeda, Chem. Lett., 1411 (1978). (5)C. R.Fincher, Jr., M. Ozaki, A. J. Heeger, and A. G. MacDiarmid, Phys. Reu. B, 19,4140 (1979);W. P.Su,J. R. Schrieffer,and A. J. Heeger, Phys. Reu. Lett., 42,1678 (1979). (6)T. C. Clarke and G. B. Street, Synth. Met., 1, 119 (7)J. F. Rabolt, T. C. Clarke, and G. B. Street, J. Chem. Phys., 71, 4614 (1979). (8)I. Harada, Y. Furukawa, M. Tasumi, H. Shirakawa, and S. Ikeda, J. Chem. Phys., 73,4746 (1980). (9)I. Harada, Y. Furukawa, M. Tasumi, H. Shirakawa, and S. Ikeda, Chem. Lett., 267 (1980). (10)E.E.Ferguson and F. A. Mataen, J.Chem. Phys., 29,105(1958); E.E.Ferguson and F. A. Mataen, J . Am. Chem. Soc., 82,3286(1960);E. E.Ferguson, J . Chem. Phys., 61, 257 (1964). (11)F. Inagaki, M. Tasumi, and T. Miyazawa, J. Raman Spectrosc., 3 , 335 (1975).
(12)H. Shirakawa and S. Ikeda, Polymer Reprints, Japan, 28, 465 (1979). (13)C.M. Huggins and 0. H. LeBlanc, Jr., Nature (London),186,552 (1960). (14)J. W. McIver and A. Komornicki, Chem. Phys. Lett., 10, 303 (1971). (15)J. Gerrat and J. M. Mills, J. Chem. Phys., 49,1719 (1969). (16)E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, 'Molecular Vibrations", McGraw-Hill, New York, 1955;S. Kato, H. Kato, and K. Fukui, J. Am. Chem. SOC.,99,684 (1977). (17)M. Tratterberg, Acta Chem. Scand., 22,628 (1968). (18)E.R.Lippincott and T. E. Kenny, J. Am. Chem. Soc., 84,3641 (1962).See also E.R. Lippincott, C. E. White, and J. P. Sibilia, J. Am. 80,2926 (1958). Chem. SOC., (19)J. A.Pople and D. P. Santry, J.Chem. Phys., 43,S136 (1965);44, 3289 (1966);M. S. Gordon, J.Am. Chem. SOC., 91,3122 (1969);S.Ehrenson and S. Seltzer, Theor. Chim. Acta, 20, 17 (1971). (20)J. H. Lupinski and C. M. Huggins, J. Phys. Chem., 66, 2221 (1962);J. H. Lupinski, ibid., 67,2725 (1963). (21)We have carried out a preliminary examination of the 8-carotene-I, complex, which was prepared according to the interface reaction presented in ref 20,and observed three characteristic IR bands located at 1456,1125,and 986 cm-' in this complex.
0022-365418212086-2359$0 1.2510
0 1982 American Chemical Society
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Yamabe et al.
The Journal of Physical Chemistry, Vol. 86,No. 13, 1982
nying the electron transfer from the polyene to the dopant affect the electronic distribution of the cationic polyene or polyene segment. This mechanism is of special interest from the viewpoint of the dynamic behavior of a polyene in the electronic ground state. The purposes of the present study are to elucidate the origin of the enhanced IR bands observed in (CH), or /3-carotene upon doping and to rationalize the role of dynamic rearrangement of electrons and nuclei in producing a resultant electronic distribution of the cationic polyene. For these aims, molecular orbital (MO) calculations by the MIND0/3 method are performed by using some finite polyenes which will be discussed in detail in the next section.
Model System and Method of Calculation The finite polyenes C1&,, and C9Hll*,both of which are of all-trans configuration, are adopted. The former is a closed-shell system with Czh symmetry, and the latter an open-shell system with CZusymmetry. As for the doped forms, we are concerned with the cation radical, Cl0Hi2+., and the monocation, C9Hll+,which are considered to be generated by the one-electron transfer from polyene segments to the dopant. In addition, the dication C10H122+ is also considered to be the heavily doped polyene segment. MO calculations of closed-shell and open-shell systems are carried out by using RHF and UHF MIND0/3 methods, respectively. The geometry optimizations and calculations of normal vibrations of these finite polyenes are performed by means of the energy-gradient method. That is, the equilibrium nuclear configuration is calculated with the variable metric optimization procedurei4for which the gradient of potential energy is obtained by the MIND 0 / 3 version of its SCF f0rma1ism.l~ The normal coordinates corresponding to the normal vibrations are given as the eigenvectors of the seqular equationi6 det [d2W/(dXiaxj)- K&j] = 0 . . K = a constant i , 3 = 1, 2, ..., 3N where W is the potential energy and Xi is the massweighted Cartesian coordinate. The masses (in atomic units) used for atoms are 1.0078 for H and 12.00 for C. The second derivatives of the potential energy, d2W/(dXiaxj), are obtained by the numerical differentiation of potential gradients. The IR intensity, Ai, is calculated with the numerical differentiation of the dipole moment, p, in the electronic ground state along each normal coordinate, Qi, by the following formula: Ai = ( N ~ / 3 ~ ' ) ( d p / d Q i ) ~ Throughout the present calculations, the origin of the Cartesian coordinate system is chosen at the center of gravity of finite polyene.
Results and Discussion First of all, it is worthwhile to examine the validity of the present MINDO/ 3 calculation.22 The optimized geometry and vibrational frequencies of trans-hexatriene, C6H8,are compared with the experimental data,"J8 as shown in Table I. It is seen from this table that the calculated bond distances are in good agreement with the experimental data,I7 although the bond angles tend to be overestimated by 9-10°. The calculated vibrational frequencies are found to be comparable to the experimental (22) Lasaga et al. recently reported the equilibrium geometries and vibrational frequencies of some finite polyenes on the basis of modified PPP MO calculations: A. C. Lasaga, R. J. Aerni, and M. Karplus, J . Chem. Phys., 73, 5230 (1980).
TABLE I: Experimental and Calculated Geometriesa and Vibrational Frequenciesb of trans-Hexatriene, C,H, exptlC calcd
c,-c* c*-c3 c344
IC,-C,-C3 IC,-C,-C,
1.337 1.458 1.368 121.7 124.4
1.330 1.462 1.347 131.1 130.8
exptld
calcd
exptld
calcd
A, Modee 1573 1791 1394 1325 1280 1232 1245 1203
1187 1128 444 347
1154 849 437 313
395
83
1166 1130 590 540
1151 885 468 136
475
414 189
exptld
calcd
3085 3054 3054 2989 1623
3547 3532 3428 3420 1885
990 928
937 850
B, Modee 897 764 758 501
3091 3040 3012 2959
3547 3532 3431 3421
B, Modef 1623 1857 1429 1356 1294 1258 1255 1202
1011 941
939 935
A, Mode 899 850 658 605
2 + ( C 2 hsymmetry)
Bond distances are in angstroms. Bond angles are in degrees. In units of cm-' . Reference 1 7 . Reference 18. e Raman-activemodes. IR-active modes.
values,I8 so far as the frequency region of 900-1400 cm-l (in experimental values) is concerned. This frequency region will be the focus of discussion in connection with the three characteristic IR bands. From these preliminary examinations, the present calculation is expected to afford sufficient results to permit a qualitative discussion. Electronic Structures of Finite Polyenes. Figure 1 describes the optimized geometries, bond energies, and P-bond orders of polyenes with Cl&lz and Cl&12+. forms. Upon one-electron loss, the length of the polyene chain tends to be contracted (shortened) while the bond alternation is weakened. A t the same time, the charge density of Cl0Hl2+.becomes more polarized; i.e., the positive and negative charges alternatively spread over the polyene chain, in comparison with the case of the neutral form. In addition, the dication form, Cl0H12+exhibits a more polarized charge distribution than CioHi2and Cl0Hl2+-,and its bond alternation is further weakened, as shown in Figure 2. Figure 3 shows the changes of electronic and geometrical structures due to the loss of one electron in the case of a finite polyene with an odd number of carbon atoms. Although the bond alternation is strengthened, the trend of which is the reverse of the case of a finite polyene with an even number of carbon atoms, both the contraction of the finite polyene and the increase of charge polarization are recognized as common features. It is understood from the analyses of atomic orbital contributions that the increase of charge polarization encountered in the cation form is mainly attributed to the polarization of the P atomic orbital of the carbon atom. Note that, although the polarization of the spin density, for instance in C&I!l. or C1,,Hl2+.,is much greater than that of the charge density, the spin density itself is not correlated with the IR intensity concerned here and hence will not be discussed further in the present study. Vibrational Analyses. Since the three observed IR bands are located at 1397, 1288, and 888 cm-' for the (CH)x-12system8 and at 1464, 1122, and 972 cm-l for the P-carotene-I2 system,9!21the corresponding normal vibra-
The Journal of Physical Chemistry, Vol. 86, No. 13, 1982 2361
Structures of Finite Polyenes
+o. 02 )Jet C h a r g e
-0.03
+0.02
9
5
Bond L e n g t h 1.3 2
+o.
+O. 04
Bond E n e r g y
+o.
02
cl-c2
c2-c3 c3-c4 cq-c5
24.59
16.69
23.77
0.96
0.28
0.92
02
C5'C6
1 6 . 8 5 23.70
(eW a-Bond O r d e r
(Spin Density) N e t Charge
(+O. 38)
( + 0 .35)
+0.09
+0.16
0.30
0.92
(+0.13)
+o .ll
Bond L e n g t h 2
-0.01
-0.03
-0.11
(-0.22)
(-0.14)
(-0.14)
cl-c2
c2-c3 c3-c4 c4-c5
0.84
0.45
n-aond O r d e r
0.66
E
6
4
1 0
C5-Cg
0.60
0.61
Figure 1. Electronic and geometrical structures of C,oH12 (upper) and CloHI2+- (lower).
N e t Charge
+ O . 38
+0.03
+0.17
3
1
9
5
Bond L e n g t h
-0.12
c2-c3 c3-c4 c4-c5
C1-C2
0.75
?T-Bond Order
-0.05
0.61
0.43
0.85
C5-Cs 0.31
Figure 2. Electronic and geometrical structures of CloHl,2+.
TABLE 11: IR-Active Vibrational Frequencies (em-' ) and Intensities of C,,,H,,, CIOH12+., and C,,H,, '+
vc< +
vc=ca,b
6 c-*a,d
SC-HQC
C,,H,,
1877 (0.004), 1816 (0.032) 1383 (0.034),1310 (0.053) 1236 (0.003),1219 (0.009),1200 (0.056), 1166 (0.072),1120 (0.086) 1665 (0.381),1517 (14.11) 1454 (0.229),1302 (0.154) 1230 (0.061). 1219 10.040). 1192 (0.516). C,,H,,+, .. .1183 (1.293),1125 (1.043) C,,H,,*+ 1728 (0.705),1609 (92.09) 1493 (9.664) 1230 (0.057),1218 (0.726),1187 (0.920), 1173 (3.648),1117 (1.221) a
Main assignment.
First band group.
Second band group.
Third band group.
TABLE 111: IR-Active Vibrational Frequencies (cm-' ) and Intensities of C,H,;and C,H,,+
C,H,;
1624 (0.001),1504 (0.003)
1336 (0.001),1316 (0.078) 1226 (0.001),1204 (0.022),1175 (0.031), 1157 (0.002),1118 (0.146) 1317 (0.268) 1243 (0.092),1211 (2.416),1198 (0.009), 1182 (4.387),1126 (0.299)
C,H,,+ 1790 (1.957),1578 (13.80), 1548 (100.4)' a
Main assignment.
* First band group.
C
Second band group.
Third band group.
' See the body of the manuscript.
2362
The Journal of Physical Chemistry, Vol. 86, No. 13, 1982
(Spin Density)
Yamabe et al.
(-0.43)
(-0.59)
(-0.59)
+o . 0 4
+o .02
+o . 0 2
N e t Chdrqe
2
4
(+O. 54)
6
8
( + O . 71)
( + O . 69)
cl-c2 c2-c3 c3-c4 c4-c5 0.85
n-Bond O r d e r
N e t Charge
0.40
0.66
-0.08
0.54
-0.16
2
-0.16 e
6
4
Bond L e n g t h 1 . 3 1
+0.14
Bond E n e r g y
(ev) n-Bond
Order
+0.29
+ O . 34
24.34
16.96
22.46
18.83
0.91
0.39
0.74
0.57
Figure 3. Electronic and geometrical structures of CBHl,. (upper) and C9H,,+ (lower).
tions are selected keeping in mind that the calculated vibrational frequencies in this region tend to be overestimated by ca. 100-200 cm-'. The IR-active normal vibrations in this region are found to belong to b, and bz modes for finite polyenes with C% and Czv symmetries, respectively. In Tables TI and I11 are summarized the vibrational frequencies and relative IR intensities, ( d p / dQJZ. According to the locations of these vibrations, they can be separated into three groups of vibrations which are abbreviated as the first, second, and third groups. Although each vibration in these tables contains contributions from several internal coordinate displacements, one may characterize the vibration by focusing on the internal vibrational mode which makes the greatest contribution. Thus, the first group is mainly assigned to the C=C stretching vibration (uc4), the second to the mixed vibration (vC4 + 6C--H) including the C-C stretching (vC4) and in-plane C-H bending (6c-H) vibrational modes, and the third to the aCVH vibration. Table I1 indicates that, upon the loss of one electron, the u c = and vc-c + 8C-H vibrations tend to shift toward the lower and higher frequencies, respectively, whereas the aCpH vibrations are not so changed as expected. Simultaneously, the intensities of vibrations in C1&I12+.,especially those of v0-C vibrations, are largely enhanced. Three typical kinds of vibrational modes are illustrated in Figures 4 and 5. Table I1 further indicates that the loss of two electrons affords, in general, greater vibrational intensities than the loss of one electron. Such enhancement of IR-active vibrations is also found in the relation between CgHl1. and C9Hll+,as shown in Table 111. In this case, however, both the uC4 and uC+ + ~ C - H vibrations tend to shift toward the higher frequency, which is different from the case of Cl&Il2+-against Cl&I1p In particular, the vibration of 1548 cm-' in C$I1,+, which is the most enhanced vibration, has shifted re-
I
I
I
I
/
I
I
t
1 5 1 7 cm-l
I
I
1454 cm-'
/ 1125 ex-'
Figure 4. Relatlve magnitudes and directions of displacement vectors in IR-active normal vibrations of C,,,H,,+..
markably to the higher frequency and is located at the region of the first band group. Furthermore, this vibration has the nature of not only the vc-c and 6C-H modes but
The Journal of Physical Chemisfry, Vol. 86, No. 13, 1982 2363
Structures of Finite Polyenes
I
I
I
I
I
TABLE IV: Analyses of Stabilization Energies (eV) for C,H,,+ and ClOHlZ2+ C,Hll+
C10H122+
One-Center 43.66 -17.48 9.93 36.11
A EAU AE A J AEAK
1790 cm-l
sum (AEA)
58.43 -29.15 11.14 40.42
Two-Center
A EA-B(covalent) A EA, (electrostatic)
sum (AEA-B)
A
sum
-0.06 6.68 -4.04 1.43 4.07
net charge
+ 0.27
-0.10 9.90 -7.75 2.04 4.39
AEAU
AEAJ AEAK
sum
c 3
c4
c,
t0.28 2.55 0.72 0.70 3.97
-0.15 9.82 -7.57 2.08 4.33
t 0.36
-0.02 10.55 -7.96 2.06 4.65
t 0.19
C9H11'
t0.12 1.98 1.23 0.59 3.80
AEAK
also the vc+ mode, where the contribution of the latter mode is comparable to that of the former mode (Figure 5). Hence, it may be rather reasonable to regard this vibration as one of the component vibrations in the first band group. The vibrational structures thus obtained for cation forms provide a spectral feature with respect to the relative intensity and the bandwidth; i.e., the first band group (very strong, broad), the second (weak, sharp), and the third (strong, very broad). This is consistent with the observed features of IR spectra for doped (CH),7p8 and doped P-~arotene.~ It should be noted that the broadness of the observed vibrational bands7p8may be attributed to the unresolvable component vibrations of various cationic polyene segments as well as those of each band group of one cationic segment described here. The resultant enhancement of IR-active vibrations can be reasonably explained by the remarkable polarization of charge density originating from the loss of one or two electrons as mentioned in the previous section. That is, the increase of the charge polarization causes the increase of the differentiation rate of the dipole moment in terms of the molecular displacement along the asymmetrical normal vibration. Electronic and Nuclear Rearrangements. Now let us consider the electronic and nuclear rearrangements occurring after the electron transfer from the polyene to the dopant. It is of interest to clarify how these rearrangement affect the electronic distribution and stabilization of the polyene cation. Here, the following polyenes of C a l l + and C O ~ , , I - Iforms ~ ~ ~ +are discussed for simplicity, since both of them are closed-shell systems. According to the FrankCondon principle, the nuclear rearrangement is assumed to occur after the electronic rearrangement is accomplished. In Figures 6 and 7, E::; and E$nt)stand for the
19.17
C2
Cl
AEAU
Flgure 5. Relative magnitudes and directions of displacement vectors In IR-actlve normal vibrations of CgHll+.
16.96
TABLE V: Analyses of One-Center Stabilization Energies (eV) for C9Hll+and CIOH122+
net charge AEAU
1 2 1 1 cm-I
-22.72 1.47 -21.25
Total A E , ~ ~ ( = AtE&EA-,) A
1548 cm-l
I
-20.35 1.20 -19.15
1.55 1.79 0.67 4.01
CIOH1Z2+
t0.35 3.03 0.25 0.82 4.10
2.63 0.87 0.83 4.33
6.98 -3.87 1.36 4.47
TABLE VI: Analyses of Two-Center Stabilization Energies (eV) in Terms of C=C, C-C, and C-H Bonds of C,H,,' and C,,H,, '+
C=C
C-C
C-H
C9H11'
Covalent) AEA-B(electrostatic) AE,-B(
sum
AEA-B(COValent) AEA-B(electrostatic) sum
c
1
-2.58
-4.89
-2.23
t 0.06
t 0.97
t 0.25
-2.52
-3.93
-1.98
-0.85
-2.12 -0.21 -2.54
3 12 l+
-7.73 1.46 -6.27
t
t 1.23
t0.39
total energies of the cation form calculated on the basis of the optimized geometry of the neutral form (CgHll. or Cl0HlZ),with and without SCF calculation, respectively. The latter corresponds to the condition at the time when one or two electrons are lost, and the former when the electronic rearrangement is accomplished. E?;:). stands for the total energy of the cation form calculated with respect to the optimized geometry of itself with SCF calculation, and it corresponds to the condition when both electronic and nuclear rearrangements are ended. It is apparent from these figures that the stabilization energy due to the electronic rearrangement @Eele)is much greater than that due to the nuclear one (AE,,). While the charge distribution of the neutral form is, as expected, maintained at the time when one or two electrons are lost, the final charge distribution of the cation form is almost constructed even after the electronic rearrangement is accomplished. Therefore, in order to obtain deeper insight, the elecwas divided into onetronic stabilization energy (Ai?,,,) center (a,) and two-center terms, and these two terms were further divided into several kinds of physicochemical terms,lg as summarized in Tables IV-VI. Table IV indicates that, although the two-center term behaves as the destabilizing factor because of the large decrease of the covalent nature, the stabilization of the one-center
2384
The Journal of Physical Chemisty, Vol. 86, No. 13, 1982
+0.22
+O . 0 5
Yamabe et al.
+o. 22
+0.30
+0.05
0 E (int)
-
+o . o o
+o.
+o.oo
0
-
A E e l e- E(int)
+o .oo
00
SCF E (int)
= 1 6 . 9 6 eV
+0.12
+0.36
+0.28
-0.06
-0.15
-0.08
-0.06
-0.15
+o . 3 4
+O .29
+O . 1 4
+0.12
+0.28
-0.16
+O. 29
-0.16
= 1.60 e V
+O . 1 4
-0.08
Flgure 6. Analysis of charge distribution of C9H,,+.
+O. 25
+O. 31
+0.19
+O. 0 5
+0.13
+ O m1 3
+O. 25
+0.05
+o.
+0.31
19
0 AEele = E ( i n t )
-
ESCF
(int)
= 1 9 . 1 7 eV +O. 2 7
+o.
+0.35
19
-0.10
-0.02
ESCF
(int) -0.10
+o
-0.02
+o.
,19
35
+0.27
SCF AEgeo = E ( i n t )
+O. 38
+O. 33
-0.12
+0.17
-0.05
+O. 1 7
+0.37
ESCF
(opt)
= 1 . 2 3 eV
-0.12
-0.05
-
+0.33
Figure 7. Analysis of charge distribution of C,oH,,2+
term overwhelms the destabilization of the two-center numbers. Thus, the stabilization due to the electronic term. This results in the stabilization of the polyene cation rearrangement comes from the strengthening of the electrostatic nature in the polyene chain, which is accounted after the electronic rearrangement. Simultaneously, it is for by the core and Coulombic terms being essentially understood that this one-center stabilization energy is electrostatic. The above argument is more clearly visudominated by the core (AE,) and exchange (aAK) terms and that the former is predominantly contributive. Table alized in the two-center term, as shown in Tables IV and V shows the interesting correlation between the net charges VI. Therein, the weakening of the covalent nature is more and some energy terms. While the core and Coulombic drastic than the stengthening of the electrostatic one, ( A E M ) terms at the positively charged carbon atoms are which as a consequence yields the destabilization energy stabilized, those at the negatively charged ones are largely of the two-center term, commonly in the monocation and stabilized and destabilized, respectively (except at the C5 dication forms. atom in CloH122+).These results can be rationalized by Conclusion considering the electronic distribution characterized 85 the charge polarization where the x-electron density is prefThe electronic and vibrational structures of (CH), and erably accumulated at the carbon atoms with even numdoped (CH), are investigated on the basis of finite polybers in the polyene cation, whereas the a-electron density enes. From the present study, the following concluding remains almost unchanged. Such an electron distribution, remarks can be drawn. therefore, leads to the increases of both the one-center (1)The one- or two-electron transfer from the polyene attractive energies between nuclei and surrounding elecsegment in (CH), to the electron-accepting dopant causes trons and the one-center repulsive energies between eleca charge polarization, whereby the positive and negative trons, especially in terms of the carbon atoms with even charges are alternately spread over the polyene chain. This
J. Phys. Chem. 1982, 86,2365-2369
charge polarization remarkably enhances the IR-active vibrations to yield the intense vibrational bands which can be classified into three band groups. The relative intensity and broadness of these band groups evaluated here are in good accord with the global features of IR spectra observed in the doped species of (CH), and p-carotene. (2) The electronic distribution characterized as the charge polarization in the polyene cation is almost constructed after the electronic rearrangement which tends to strengthen the electrostatic nature and to weaken the covalent nature in the polyene chain, before the subsequent occurrence of the nuclear rearrangement. Indeed, the
2385
stabilization energy due to the electronic rearrangement is much greater than that of the nuclei, and the former is predominantly attributed to the increase of the one-center attractive energies between nuclei and their surrounding electrons.
Acknowledgment. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan and by a Grant-in-Aid from the Japan Society for the Promotion of Science. The computations were carried out on a FACOM M200 at the Data Processing Center, Kyoto University.
Electronic Excited States of Linear Conjugated Polyenes Toklo Yamabe;
Kazuo Akagl, Tooru Matsul, Kenlchl Fukul,
Depaltment of Hydrocarbon Chemistry, Faculty of Englneerlng, Kyoto University, Kyoto, Japan
and Hldekl Shlrakawa Instfiute of Material Science, University of Tsukuba, Ibaraki. Japan (Received: March 26, 1981; In Final Form: September 15, 7981)
The low-lying electronically allowed excited states of conjugated polyenes are studied on the basis of several kinds of finite polyenes. Molecular orbital calculations are carried out by means of Pariser-Parr-Pople (PPP) and Longuet-Higgins and Pople (LHP) methods including all singly excited configuration interactions (CI) in order to evaluate the excitation energies and oscillator strengths of the finite polyenes employed here. The results well account for the absorption bands in the visible and near-infrared regions observed for the neat and doped species of polyacetylene, (CH),, and @-carotene.
Introduction that polyacetylene, (CH),, Since the crucial has an ability to form highly conductive derivatives with several kinds of dopant species was presented, much of the subsequent research has been directed toward such optical properties as the electronic absorption band in the nearinfrared region3s4and characteristic IR bands observed in doped (CH)x.5-8 This is because explorations of these properties can be expected not only to afford valuable information on electronic and vibrational structures of the doped (CH), itself but also to provide an insight into the mechanism generating the aforementioned high electric conductivity. The current evidencegJOthat the doped p-carotene exhibits behavior similar to that of the doped (1)H. Shirakawa, E.J. Louis, A. G. MacDiarmid, C. K. Chiang, and A. J. Heeger, J. Chem. Soc., Chem. Commun., 578 (1977). (2)C. K.Chiang, M. A. Druy, S. G. Gau, A. J. Heeger, E. J. Louis, A. G. MacDiarmid, Y. W. Dark, and H. Shirakawa, J.Am. Chem. SOC.,100, 1013 (1978). (3)H. Shirakawa, T. Saeaki, and S. Ikeda, Chem. Lett., 1113 (1978). (4)I. Harada, M. Tasumi, H. Shirakawa, and S. Ikeda, Chem. Lett., 1411 (1978). (5) C. R. Fincher, Jr., M. Ozaki, A. J. Heeger, and A. G. MacDiarmid, Phys. Reu. B, 19,4140(1979). (6)W.P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Reu. Lett., 42, 1678 (1979). (7)T. C. Clarke and G. B. Street, Synth. Met., 1, 119 (1979/80). (8) J. F. Rabolt, T. C. Clarke, and G. B. Street, J. Chem. Phys., 71, 4614 (1979). (9)H.Shirakawa and S. Ikeda, Polymer Reprints, Japan, 28, 465 (1979). (IO) I. Harada, Y. Furukawa, M. Tasumi, H. Shirakawa,and S. Ikeda, Chem. Lett., 267 (1980). 0022-3654/82/2086-2365$01.25/0
(CH), has suggested that (CH), assumed to have an infinite polyene chain could be described as the assembly of finite polyenes or segments with various chain length^.^ In the previous study" based on finite polyene models, it has been rationalized that the origin of the enhancement of three IR bands in the doped species of (CH), or pcarotene is the remarkable increase of the polarization produced by the electron transfer from the polyene segment to the dopant. Therefore the present study will be devoted to the subject of optical properties in doped (CH),.394 That is, while truns-(CH), shows an intense and broad absorption band in the visible region (Amm = 2.05 eV), the doping of trans-(CH), with iodine (Iz)provides a new band in the near-infrared region (Amm = 0.74 eV), together with the visible band which is slightly shifted toward the lowerenergy side. The appearance of this new band has also been observed in the case of ~ i s - ( C H ) , . ~Ini ~spite of extensive studies centered around experimental approaches, the identification of such a new band has not yet been settled. It is therefore desirable to pursue theoretical studies based on refined models. To do this, it is helpful to reexamine the spectroscopic feature of the new band in question. It is apparent that this band has an absorption intensity comparable to that of the visible band inherent to (CHI,, indicating that both of these bands are ascribed not to be electronically forbidden transitions but (11)T. Yamabe, K.Akagi, T. Tanabe, K. Fukui, and H. Shirakawa,
J.Phys. Chem., preceding article in this issue. 0 1982 American Chemical Society
