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Density functional study on the structures and vibrational spectra of the radical anion and cation of biphenyl
THEO CHEM ELSEVIER
Journal of Molecular Structure (Theochem) 424 (1998) 225-235
Density functional study on the structures and vibrational spectra of the radical anion and cation of biphenyl Kazuhiko Furuyaa-b, Hajime Toriib, Yukio Furukawab, Mitsuo Tasumib’* “Ashigara Research Laboratories, Fuji Photo Film Co. Ltd., 210 Nakanuma, Minami Ashigara, Kanagawa 250-01. Japan bDepartment of Chemistry School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Received 29 November 1996; accepted 3 1 March 1997
Abstract Density functional theory using the 6-3lG‘ basis set and two non-local exchange-correlation functionals (B-YLP and B3-LYP) has been applied to the calculations of the structures and vibrational spectra of the radical anion and cation, of biphenyl. The B3-LYP dihedral angles between the two phenyl rings are 5.8” and 19.5” for the radical anion and cation, respectively. Upon ionization, structural changes occur in the direction from benzenoid to quinoid. The unscaled vibrational frequencies calculated at the B-YLP/6-3 lG* level are mostly in agreement with the frequencies in the Raman spectra of the radical anion and cation of the normal and perdeuterated species reported in the literature. The calculations predict that both the radical anion and cation give rise to a very strong infrared band, and that this band arises from a mode in which the benzenoid-to-quinoid deformation occurs out of phase in the two phenyl rings. 0 1998 Elsevier Science B.V. Keywords:
Density functional calculations;
Vibrational
analyses; Biphenyl; Radical ions; Infrared intensities
1. Introduction Conjugated conducting polymers have attracted much attention from both fundamental and practical viewpoints because of their novel physical properties [l]. Poly(p-phenylene), which is one of conducting polymers, shows high electrical conductivities when doped with acceptors or donors, while it is an insulator in the undoped state [2]. To understand the optical and electrical properties of non-degenerate conjugated polymers such as poly(p-phenylene), polarons and bipolarons are proposed as elementary excitations, while polarons and solitons are conceivable in degenerate polymers such * Corresponding author
as Iruns-polyacetylene [ 11. A negative (positive) polaron and a negative (positive) bipolaron correspond to a radical anion (radical cation) and a dianion (dication), respectively. The formation of a polaron or a bipolaron is accompanied by structural changes over several phenylene rings and the appearance of localized electronic states. Studies of polarons and bipolarons are expected to lead to a deeper understanding of the optical and electrical properties of doped polymers. Vibrational spectroscopy has played an important role in studying the nature of polarons and bipolarons in conducting polymers [3,4], because different structural and spectral characteristics are expected for polarons and bipolarons. Zerbi and co-workers [5] have proposed the effective conjugation coordinate
0166-1280/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SOl66-1280(97)00153-X
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K. Furuva
et al./Journal
of MolecularStructure
theory to interpret dopingand photo-induced infrared absorptions in conjugated polymers including poly(p-phenylene) [6]. Two of the authors (YF and MT) have analyzed the Raman spectra of Na-doped poly(p-phenylene) on the basis of the Raman spectra of the radical anions and dianions of p-oligophenyls and have concluded that negative polarons and bipolarons are generated in Na-doped poly(p-phenylene) [7,8]. Quantum chemical calculations for the radical ions and divalent ions of p-oligophenyls are useful for studying polarons and bipolarons in poly(p-phenylene). Brtdas et al. [9] have calculated the structure of a complex between p-quaterphenyl and two Li atoms using the ab initio Hartree-Fock (HF) method with the minimal STO-3G basis set and a partial geometry optimization. Cuff et al. [lo] have calculated the structures of the divalent ions of p-terphenyl at the HF/3-21G level. Ehrendorfer and Karpfen [ 1 l] have calculated the structures of the divalent ions of p-oligophenyls consisting of up to 11 rings at the HF/3-21G level. They have also calculated the structures and vibrational spectra of the dications of a-oligothiophenes using the ab initio HF method [ 12- 141. The HF method incorporates electron exchange, but does not take electron correlation explicitly into account, whereas Shimoi and Abe [ 151 have shown that electron correlation is significant in the stability of polarons and bipolarons. Then, appropriate post-HF methods are required to deal with electron correlation. Irle and Lischka [16] have calculated the structures of the complexes of one or two alkali-metal atoms with p-oligophenyls (biphenyl and p-quaterphenyl) at the HF and Msller-Plesset perturbation levels. Rubio et al. [ 171 have calculated the structures and electronic spectra of the radical anion and cation of biphenyl using the complete active space selfconsistent field method (CASSCF) and multiconfigurational second-order perturbation approach (CASPT2). It is practically impossible to calculate the structures and vibrational frequencies of the radical ions and divalent ions of long-chain p-oligophenyls at such high theoretical levels. As an alternative, density functional theory (DFT) may be used, because one of the advantages of DFT lies in its ability to incorporate both electron exchange and correlation in treating large systems. Recently, we have pointed out the usefulness of the DFT method
(Theochem)
424 (1998) 225-235
to the studies of the radical anion and cation of biphenyl [ 181. In the present paper, we report in more detail the results of density functional calculations on the structures and vibrational properties of the radical anion and cation of biphenyl.
2. Method of calculation Density functional (DF) calculations of the structures and vibrational properties (harmonic frequencies, vibrational patterns, and infrared intensities) of biphenyl and its radical anion and cation were performed by using the Gaussian 94 suite of programs [ 191 on a Silicon Graphics Power Onyx workstation. Counter ions were not included in the calculations of the radical anion and cation. The 6-3 1G* basis set was used. Calculations were performed with two sets of functionals: (i) Becke’s exchange functional [20] in combination with the Lee-Yang-Parr correlation functional [21] (abbreviated as B-LYP) and (ii) Becke’s three-parameter hybrid method [22] using the Lee-Yang-Parr correlation functional (abbreviated as B3-LYP). While the normal grid was used for numerical calculations of two-electron integrals in the previous paper [ 181, the fine grid was used in the present calculations. Thus, results in this study are slightly different from those reported previously. Full geometry optimizations were performed under Dz symmetry for all the species. No imaginaryfrequency mode was found at the optimized structures. Calculated atomic displacements in each vibrational mode were depicted with the LXVIEW program [23].
3. Structures The numbering of atoms in biphenyl and its radical ions is shown in Fig. 1. The structural parameters calculated at the B-LYP/6-31G* and B3-LYPI 6-31G* levels for the neutral molecule are listed in Table 1, together with experimental values in the vapor phase [24]. Table 1 also shows the structural parameters calculated by Rubio et al. [ 171 at the CASSCF level. The DF calculations have shown that the neutral molecule has a twisted structure (D2 symmetry). The values of the torsional angle around
K. Furuya et d/Journal
Fig.
of Molecular Structure (Theochem) 424 (1998) 225-235
I. Numbering of atoms.
the inter-ring C ,C, I bond, r(C2C ,C rC2,), calculated at the B-LYP/6-3 1G* and B3-LYP/6-3 lG* levels are 37.4” and 38.3”, respectively. The torsional angle in the vapor phase has been determined to be 44.4” by means of electron diffraction [24]. The CC bond lengths at the B3-LYP/6-31G* level are shorter than those at the B-LYP/6-31G* level by 0.007-0.012 .&. The ring CC bond lengths calculated at the B3-LYPI 6-31G* level are in good agreement with those observed. However, the C ,C ,I bond length calculated at the B-LYP/6-31G* level is in better agreement with that observed. The structural parameters calculated at the B-LYPI 6-31G* and B3-LYP/6-31G* levels for the radical Table I Structural
parameters
B-LYP
NCK3H3) W3C4W
a Ref. [17]. h Electron diffraction
anion are listed in Table 2. The crystal structures of bis(tetraglyme)rubidium biphenyl Rb+[CH30(CH&H20)&HJ2(C r2H1,$ [26], bis(tetraglyme)potassium biphenyl K+[CH30(CH2CH20)4CH3]I(C r2H lo)_ [27] and bis(triglyme)sodium biphenyl Na’[CH30(CH2CH20)3CHs]2(C1ZH10)[25] have been determined by means of X-ray diffraction, although structural parameters obtained have large uncertainties. The structural parameters of bis(triglyme)sodium biphenyl [25] are also shown in Table 2. The structural parameters calculated at the B-LYP/6-3 lG* and B3-LYP/6-3 lG* levels for the radical cation are listed in Table 3. The DF calculations have shown that the radical anion and cation have twisted structures (D2 symmetry). The values of the torsional angle around the C ,C I - bond calculated at the B-LYP/6-31G* and B3-LYP/6-31G* levels for the radical anion are 8.4” and 5.8”, respectively, and those for the radical cation are 20.5” and 19.5”, respectively. The calculated values of the torsional angle of the radical cation are considerably larger than those of the radical anion. Rubio et al. [ 171 have reported planar structures for the radical anion and cation, because they have optimized the geometries under the constraint of DZh symmetry. The CC bond lengths of the radical anion calculated at the B3-LYP/6-3 lG* level are in better agreement with the experimental
of neutral biphenyl Bond lengths/i
tiCzC IC I,CZ,) r(ClCl,) r(C ICz) r&K?) v(C,C,) r(CzHz) r(CiH,) r(C&) &CzC IC,) KICKI) &C2C1C4) B(CK.K,) WCICZHZ)
227
37.4 1.493 1.417 1.404 1.406 1.094 1.094 1.094 118.0 121.0 120.3 119.4 119.4 119.6 120.3
data [24].
and angles/deg B3-LYP 38.3 1.486 1.405 1.394 1.396 1.087 1.087 1.087 118.1 121.0 120.3 119.4 119.4 119.6 120.3
CASSCF” 44.3 1.492 1.405 1.399 1.399 1.077 1.077 1.077 118.4 120.9 120.2 119.4 119.7 119.7 120.3
EDb 44.4 1.507 1.404 I.395 1.396 1.102 I.102 1.102 119.4 119.9
228
Table 2 Structural parameters
K. Furuya et al./Journal ofMolecular
Structure (Theochem) 424 (1998) 225-235
of the radical anion of biphenyl Bond lengths/A and anglesideg B3-LYP
B-LYP
a A planar structure is assumed [ 171. b X-ray diffraction data obtained for bis(triglyme)sodium
biphenyl
values compared with those calculated at the B-LYPI 6-31G* level. As shown in Tables 2 and 3, the C,C,’ and CzC3 bonds are shortened and the C ,CZ and C3C4 bonds are lengthened on going from the neutral molecule to either the radical anion or cation. The shrinkage and elongation of these bonds are in fact observed for the radical anion. It can be concluded that the
X-ray b
0
5.8 1.439 1.441 1.383 1.410 1.087 1.092 1.088 114.2 122.6 121.8 117.0 119.3 118.7 121.5
8.4 1.45 I 1.451 1.394 1.421 1.095 1.099 1.095 114.3 122.6 121.7 117.1 119.3 118.8 121.4
Table 3 Structural parameters
CASSCF”
1.430 1.442 1.387 1.412 1.076 1.081 1.078 114.1 122.7 121.8 116.9 119.9 118.7 121.5
7.2 1.435 1.436 1.381 1.397
114.7 122.1 121.6 117.9
[25].
addition (or removal) of one electron to (or from) the neutral molecule leads to structural changes from benzenoid to quinoid. Similar structural changes are found in the structural parameters calculated at the CASSCF level [ 171, as shown in column 4 of Table 2 and column 4 of Table 3. Significant changes are found in the calculated bond angles of the radical
of the radical cation of biphenyl Bond lengths/l\ B-LYP
7(C&,C,C?,) r(CICI,) u(CIC2) r(C2C3) r(C3C4) tiC2H2) r(C3H3) 64H4)
e(C2CICh) e(C ,C2c1) e(c2w4) e(C3C4C5) WIC2H2) fw2C3H3) w3C4H4)
a A planar structure is assumed
20.5 I.456 1.442 1.390 1.419 1.091 1.092 1.093 117.8 120.9 120.0 120.3 119.9 120.1 119.8
[ 171.
and anglesideg B3-LYP 19.5 1.444 1.433 1.379 1.409 1.083 1.085 1.086 117.8 120.9 120.0 120.4 120.0 120.1 119.8
CASSCFa 0 1.433 1.435 1.381 1.409 1.071 1.075 1.076 117.1 121.3 120.2 119.9 120.6 119.8 120.0
K. Furuya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
Table 4 Calculated
and experimental
Mode”
a
frequencies
of neutral biphenyl-h 1oand -dlo hlo
v4 vs V6 y7 YE “9 “IO “II “I2 VI3
y14 “I5
229
dlo
Obsdb/cm-’
Calcd”/cm~
Obsdd/cm-’
Calcd’icm~’
1606 1505 1282 1186 1029 1003 964 838 740 405 307 55
1595 1506 1268 1192 1030 990 929 831 735 409 307 70
1578 1418 1192 872 841 962 788 654 693 355 300
1558 1403 1181 872 844 950 751 646 688 359 295 64
a The ylo. Y , ,, Y13and YI5 modes are correlated b In the vapor or solution phase [29-3 11. ’ At the B-LYP/6-3 lG* level. d In a solution [3 11.
with the au modes of the planar DZh structure.
anion. In particular, the C2C1C6 angle is reduced by 3.7” at the B-LYP/6-31G’ level and 3.9” at the B3-LYP/6-3 lG* level. This may be due to the repulsion between hydrogen atoms in the nearly planar structure of the radical anion [ 171. On the other hand, changes in the calculated bond angles on going from the neutral molecule to the radical cation are less than 1.0”.
4. Vibrational spectra The neutral molecule of biphenyl has 60 normal modes classified according to D2 symmetry: 1% + 13b l + 16bz + 16b3. The frequencies of the neutral molecule and its perdeuterated analog have been calculated and compared with the observed data reported in Refs. [28-311. The frequencies of the a modes calculated at the B-LYP/6-3 lG* level are listed in Table 4, together with those observed. It is noted that the vg mode is due to the inter-ring CC stretch. The ~10, v1 r, Y13and v,~ modes are correlated with the a, modes (out-of-plane vibrations) of the planar DZh structure. The root mean square deviations of unscaled B-LYP frequencies from the observed ones are 11.6 cm-’ and 12.0 cm-’ for biphenyl-h ,O and -dlo, respectively. Thus, the B-LYP/6-31G* method gives reliable frequencies without scaling.
4.1. Raman spectra of the radical anion and cation The Raman spectra of the radical anion of biphenyl [32-351 and its perdeuterated analog [34,35] have been reported. Eight bands of each species have been attributed to the totally symmetric fundamentals [33-351. The frequencies of the a modes calculated at the B-LYP/6-31G* level are listed in Table 5, together with the observed. The differences between the observed and unscaled B-LYP frequencies are less than 17 cm-’ and 19 cm-’ for biphenyl-h 10 and -dlo, respectively. Such agreement between the observed and unscaled B-LYP frequencies leads to a conclusion that the B-LYP/6-3 lG* method will be useful in assigning the observed Raman bands of the radical anions of long-chain p-oligophenyls. The calculated atomic displacements of v4-v9, vi2 and v14 of the radical anion are shown in Fig. 2. The v4 mode consists of the C2C3 (C&6) stretch (IRL in the notation of Tasumi et al. (TUN) [36]) and the inter-ring C iC ,’ stretch. The v5 mode consists of the ring stretch ( lR1?p, in the TUN notation) and the inter-ring CC stretch. The vg mode is due to the inter-ring CC stretch. The ~7 and v8 modes are due to the CH in-plane bends (1 HBI,” and lHB$, respectively, in the TUN notation). The vg, v12 and vi4 modes are due to the ring deformations (IRT, 1RT and IRZ,, respectively, in the TUN notation). The via, vi ,, vi3 and vi5 modes are correlated
K. Furuya et al./Journal ofMolecular Structure (Theochem) 424 (1998) 225-235
230
Table 5 Calculated
and experimental
frequencies
of the radical anion of biphenyl-h 10and -do
Mode”
hlo
dto
Obsdb/cm-’
Calcdc/cm-’
Obsdd/cmm’
1587 1493 1326 1201 1017 979 -
1604 1492 1310 1209 1000 966 849 724 709 414 322 38
1558
721 327 a The Y,a, Y, 1,YI3and Y15modes are correlated b In THF [32]. ’ At the B-LYP/6-31G’ level. d In ethanol [35].
W
v8
vg
672 315
1571 1393 1198 869 831 947 675 576 664 365 309 34
with the au modes of the planar Dzh structure.
with the a, modes (out-of-plane vibrations) of the planar structure. The observed and calculated frequencies of the inter-ring CC stretch (vg) of the neutral molecule of
1604 Cm-’
1412 1203 869 837 954
1000 cm-r
@)
v5
1492cm-r
(f)
966 cm.’
Cc)
v.5
1310 cm-’
(9) VI2
709 cm-]
W
VT
1209 cm-’
@I VM
322 cm-r
Fig. 2. Atomic displacements calculated at the B-LYP/6-31G’ for some of the a modes of the radical anion of biphenyl.
level
biphenyl-h,s are 1282 cm-’ and 1268 cm-‘, respectively; the observed and calculated frequencies of the corresponding mode of the radical anion are 1326cm-’ and 1310cm-‘, respectively (Tables 4 and 5). The upshift of the inter-ring CC stretch frequency on going from the neutral molecule to the radical anion is consistent with the structural changes in the direction from benzenoid to quinoid. Upon deuteration, mode mixing is changed significantly. The inter-ring CC stretch makes a smaller contribution to the vg mode of the radical anion of biphenyldIo. Thus, a smaller upshift of the vg band (from 1192 to 1203 cm-‘) is observed for biphenyl-d10 upon ionization. The Raman spectra of the radical cation of biphenyl [35,37,38] and its perdeuterated analog [35,38] have been reported. Nine bands of the normal species and seven bands of the perdeuterated species have been ascribed to the totally symmetric fundamentals [35,38]. The frequencies calculated at the B-LYPI 6-3 lG* level for the a modes are listed in Table 6, together with the observed. The calculated atomic displacements of v4-vg, vi2 and v14 of the radical cation (not shown) are very similar to those of the radical anion. The vro, vI1, ur3 and v15 modes are correlated with the a, modes (out-of-plane vibrations) of the planar DZh structure. The differences between the observed and calculated frequencies are less than
K. Furuya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
231
Table 6 Calculated
and experimental
frequencies
of the radical cation of biphenyl-h ,,, and -dlo
Mode”
a
h 10
v4 Q V6 v-i v8
yg VI0 “II “12
VI3 “I4
Calcd’km-’
Obsdb/cm-’
Calcd”/cm-
1615 1502 1342 1224 1018 989
1606 1486 1310 1219 1008 979 957 803 726 384 321 66
1579 1421
1568 1386 1200 878 840 950 778 629 681 336 306 60
737 391 334
VI5
a The Y10, Y, , , Y,i and Y,5modes are correlated b In acetonikile solutions [35,38]. ’ At the B-LYP/6-3 1G’ level.
dlo
Obsd bicm-’
882 847 958
688 329 -
with the a,, modes of the planar D2h structure.
23 cm-‘, except for V6of the normal species and v5 of the perdeuterated species. The inter-ring CC stretch makes contributions to these modes. The calculated v6 frequency for the radical cation of biphenyl is 32 cm-’ lower than that observed, whereas the calculated frequencies for neutral species and the radical anion are in better agreement with those observed. The calculated length of the inter-ring CC bond in the radical cation is longer than that in the radical anion (Tables 2 and 3). This is consistent with the result that the calculated frequency of the inter-ring CC stretch of the radical cation is lower than that of the radical anion. Actually, however, the observed wavenumber of the Raman band of the radical cation is higher than that of the radical anion. The origin of this discrepancy between the calculated and observed frequencies is not clear at present. Sasaki and Hamaguchi [35] have observed a weak band at 39 1 cm-’ in the Raman spectrum of the radical cation in an acetonitrile solution. They have interpreted that the presence of this band in the Raman spectrum results from a twisted structure (02 symmetry) of the radical cation, because the 391 cm-’ band corresponds to a Raman-inactive a, mode of the planar structure (&, symmetry). Their assignment has been confirmed by the present calculation. The corresponding band is not observed in the Raman spectrum of the radical anion [35]. The small deviation from a planar structure in the radical anion
(Table 2) suggests that the vt3 band of the radical anion might be too weak to be observed. 4.2. Infrared spectra of the radical anion and cation The present DF calculations predict that the frequencies and/or the intensities of the infrared bands of the radical anion and cation are significantly different from those of the neutral molecule, although the infrared spectra of the radical anion and cation have not been reported yet. Some important theoretical predictions are described below. The frequency calculated for each CH stretch (~~6, v,,, vts, vz9 or Vet) of neutral biphenyl is higher than that for the radical anion and lower than that for the radical cation, as shown in Table 7. The infrared intensities calculated for three CH stretching modes of the neutral molecule (vt6 and vt, of the b, species and ~29 of the b2 species) are strong. Experimentally, the CH stretches are strongly observed [29,31,39]. The infrared intensities of the CH stretches of the radical anion and cation are different from those of neutral biphenyl. The infrared intensity of each CH stretch of the neutral molecule is weaker than that of the radical anion and stronger than that of the radical cation. Similar features have been reported for the calculated CH stretching frequencies and intensities of the neutral and charged species of polycyclic aromatic hydrocarbons [40]. Gussoni et al. [41] have
K. Fumya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
232
Table 7 Calculated”
frequencies
and infrared intensities of the b-species modes due to the CH stretches and CH out-of-plane Radical anion
Neutral Mode
CH stretch b, “lb “I7 “I8 62 “29 “30 CH out-of-plane bi “53 “54 “55 “86
Freq./cm-’
3121 3107 3091 3117 3099 bend 954 885 730 692
a At the B-LYP/6-31G’
IR int. km molK’
Mode
48 42 9 68 14
b,
“lb “11
“IX
b?
“29 “Xl
bends
Radical cation Freq./cm-’
IR int. /km mol-’
3085 3072 3023 3092 3027
110 77 97 168 187
876 717 647 516
45 11 35
0
2 63 25
Mode
Freq./cm-’
“16 “17 “IX “29 “30
0
bl
IR int.1 km mol-’
3154 3143 3131 3161 3141
4 1 0 2 0
985 926 747 621
1 2 73 43
“53 “54 “55 “S6
level.
shown for neutral hydrocarbons that the intensity of a CH stretch depends on the atomic charge of the hydrogen atom. According to their theory, the intensity of a CH stretch can be expressed by the square of the sum of the equilibrium atomic charge of hydrogen and a charge-flux term. The former term has positive values and is sensitive to the conjugation of the adjacent CC bonds. The latter term has negative constant values. Then, as the atomic charge becomes small, the intensity of the CH stretch becomes strong. Let us assume that this rule can be applied to the neutral species, radical anion and radical cation of biphenyl. The Mulliken charges (which are viewed approximately as the atomic charges) of the hydrogen atoms are, O.lOOe-0.103e for the neutral species, O.O14e-0.043e for the radical anion, and O.l62e0.183e for the radical cation; the atomic charges decrease in the order of the radical cation, the neutral species and the radical anion. Thus, the infrared intensity of the CH stretch becomes strong in this order. This is consistent with the results of the present DF calculations. The 736 cm-’ and 700 cm-’ infrared bands observed for the neutral species in a solution [31] are assigned to v55 and v56, respectively. It is well known that these two bands are characteristic of the mono-substituted benzene ring. According to the results of the present DF calculations, the H3 (H3,), H4 (Hdf) and H5 (HS,) atoms move predominantly in phase ( 1HB,Op in the TUN notation [36]) for v55,
whereas the H2 (Hz,), H4 (H4f) and H6 (He,) atoms move predominantly in phase ( lRyp in the TUN notation) for v56 (not shown). On the other hand, the v54, us5 and v57 modes of the radical anion have considerable intensities (Table 7). The v55 mode of the radical anion is similar to the v56 mode of the neutral species. As shown in Fig. 3(a,b), the Hz (HZ,), H3 (H3,), H5 (H,,) and H6 (H6,) atoms move predominantly in phase in vs4; the H4 (H4,) atoms move predominantly in vs7. The CH out-of-plane modes of the radical anion are strikingly different from those of the neutral
(a)
vs4
7 17 cm-t
(d) v~
747 cm-t
(e) vs6
627 cm-t
l---=-l(b)
“57
576cm-*
(c)
VL9
1583cm-t
(f)
vts
1517 cm-t
Fig. 3. Atomic displacements calculated at the B-LYP/6-31G’ level. (a) 1~54,(b) “57, (c) v 19for the radical anion; (d) “s5. (e) “56. (f) “ts for the radical cation.
K. Furuya et al/Journal
Table 8 Calculated”
frequencies
and infrared intensities of biphenyl
Neutral
“19 “20 "21 "22
“13 “24 “27 bz
“31 y32
“33 “34 "35 "36
“41 "44
Freq./cm-’
IR int./ km mol-’
Mode
1601 1489 1183 1041 996 984 608
11 22 0 2 5 0 8
b,
1567 1433 1341 1285 1166 1079 624 127
4 5 1 3 0 5 0 0
bz
233
and its radical ions
Radical anion
Mode
b,
of Molecular Structure (Theochem) 424 (1998) 225-235
“19 "20 "21 "22 "23 "24 "27 "31 "32
“33 "34 "35 "36
“40 "44
Radical cation Freq./cm-’
IR int./ km mol-’
Mode
1583 1458 1171 992 979 932 581
405 0 43 61 34 120 2
b,
1481 1391 1344 1232 1101 1062 622 149
0 33 28 1 7 2 0 0
b2
“19 "20 "21 "22 "23 "2s "21
“?I "32 "33 "34
“35 "36
“41 “44
Freq./cm-’
IR int./ km mol.’
1571 1457 1192 1003 985 950 597
336 55 32 9 7 83 21
1511 1417 1362 1262 1159 1095 590 147
18 22 17 3 5 8 3 0
a At the B-LYP/6-3 1G’ level.
species. The infrared intensities calculated for two CH out-of-plane bending modes of the radical cation (vs~ and v56 of the b3 species) are strong, as shown in Table 7. The DF calculations indicate that the H3 (Hjf), H4 (H4,) and H5 (H5f) atoms move predominantly in phase (lHBip in the TUN notation [36]) for vs5, whereas the H2 (H2,), H4 (H+) and H6 (H6,) atoms move predominantly in phase ( lRyP in the TUN notation) for v5& as shown in Fig. 3(d,e). The calculated atomic displacements of v55 and v56 of the radical cation are quite similar to those of vs5 and v56, respectively, of the neutral species. In the results calculated for the radical anion and cation, some of the 6, modes are strong in infrared intensity, as shown in Table 8. In particular, the vlg modes of the radical anion and cation have strong intensities. Transition dipole moments associated with the b, modes are parallel to the molecular long axis. The calculated atomic displacements of vi9 (b, species) of the radical anion and cation are shown in Fig. 3(c) and Fig. 3(f), respectively. In these modes, the two phenyl rings deform out of phase in the direction from benzenoid to quinoid; the C2C3 and C&6 bonds stretch (shrink), whereas the C,C2, C3C4, C4C5 and C&I bonds shrink (stretch). It is noted that the v4 mode of the radical anion and cation (a species,
Fig. 2(a)) is the corresponding in-phase mode. Strong infrared intensities of vi9 of the radical anion and cation can be interpreted in terms of the vibronic theory, as described below. The infrared absorption intensity of a fundamental vibrational transition, Z,i ..-$, can be expressed [42] in the harmonic approximation as Igl.--go OZKg1 IcclgO)12
(1)
where He is the electronic Hamiltonian; p is the dipole moment operator; I@) and Igl) represent the vibronic wavefunctions of the ground electronic state with vibrational quantum numbers 0 and 1, respectively; Q is the normal coordinate; 1s”) and Iso)indicate the electronic wavefunctions of the ground and excited electronic states at the equilibrium structures, respectively; I$ and E,” are the energies of these states; w is the frequency of the normal vibration. From Eq. (2), one can understand that the infrared intensity of a vibrational band results from the vibronic coupling
234
K. Furuya et al./Journnl of Molecular Structure (Theochem) 424 (1998) 225-235
between the ground and excited electronic states. Strong infrared intensities come from the electronic states satisfying the following conditions: (1) the transition energy, l$ - ,$, is small; (2) the matrix element of the dipole moment operator, (s”lplgo>, is large (allowed transition); (3) the matrix element of the vibronic coupling operator, (go l(aZ!Z$aQ)Ols?, is large. The radical anion and cation of biphenyl give rise to two strong electronic absorption bands in the visible region: 15 300 and 24 400 cm-’ for the radical anion and 14 200 and 25 800 cm-’ for the radical cation [43]. These absorption bands are polarized parallel to the molecular long axis [43]. On the other hand, neutral biphenyl gives rise to a long-axis polarized band at 39 700 cm-’ [44]. The electronic spectra of the radical anion and cation have been studied by means of the CASPT2 method on the assumption that the radical anion and cation have planar structures [ 171. The lower and higher energy bands of the radical anion are due to the 1 *Bls - 1 *BsU and 2 2B2, - 1 *BjU transitions, respectively; the lower and higher energy bands of the radical cation are due to the 1 *Bs,, - 1 *B2, and 2 2B3U- 1 *B2, transitions, respectively. According to Eq. (2) the symmetry consideration ((go 1(aHdaQ)ols’) # 0) leads us to the conclusion that the excited electronic states mentioned above can give intensities to the b Iu vibrational modes. The b,, modes are correlated with the b, modes of a twisted structure. The transition dipole moments associated with the b,, or 6, modes are parallel to the molecular long axis. Among the 6, modes, the v l9 mode is probably effective for the vibronic mixing. The matrix elements of the vibronic coupling operator for the radical anion and cation should be larger than that for the neutral species. Thus, the strong infrared intensities associated with v19 are considered to originate from the visible electronic absorptions, although further experimental and theoretical studies are required for a more quantitative analysis. Doped conjugated polymers give rise to infrared absorptions due to vibrational transitions and electronic absorptions in the region from visible to infrared, which are associated with high electrical conductivities [ 11. Thus, studies on the intensities in the infrared absorption spectra of charged oligomers and doped polymers may lead us to a better understanding of high electrical conductivities in doped polymers.
5. Conclusions The structures and vibrational spectra of the radical anion and cation of biphenyl have been studied by using DF calculations with the B-LYP and B3-LYP exchange-correlation functionals and the 6-3 lG* basis set. The results obtained are as follows. (1) The radical anion and cation have twisted structures. The B-LYP (B3-LYP) dihedral angles between two phenyl rings are 8.4” (5.8”) and 20.5” (19.5”) for the radical anion and cation, respectively. Ionization induces structural changes in the phenyl rings in the direction from benzenoid to quinoid. (2) The vibrational frequencies calculated at the B-LYP/6-31G* level are in fair agreement with observed frequencies in the Raman spectra reported in the literature. The frequency of the inter-ring CC stretch is sensitive to the structural changes from benzenoid to quinoid. The B-LYP/6-3 lG* method will be useful in assigning the vibrational spectra of the radical ions of long-chain p-oligophenyls. (3) Infrared intensities calculated for the CH stretches of the radical cation are anomalously weak, whereas infrared intensities calculated for the CH stretches of the radical anion are stronger than those for the corresponding modes of the neutral molecule. These intensity features have been interpreted by the Mulliken charges on the hydrogen atoms. (4) The radical anion and cation are expected to give rise to a very strong infrared band attributed to the ring CC stretch where the two phenyl rings deform out of phase in the direction from benzenoid to quinoid. The strong intensity of the band probably comes from the excited electronic states associated with the visible absorptions through vibronic coupling.
Acknowledgements One of the authors (KF) thanks Mr. J. Hayashi, director and general manager of the Ashigara Research Laboratories, for allowing KF to publish the results of calculations in this paper. Thanks are also due to Mrs. M. Kobayashi for her help in data processing.
K. Furuya et al./Journal ofMolecular
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Journal of Molecular Structure (Theochem) 424 (1998) 225-235
Density functional study on the structures and vibrational spectra of the radical anion and cation of biphenyl Kazuhiko Furuyaa-b, Hajime Toriib, Yukio Furukawab, Mitsuo Tasumib’* “Ashigara Research Laboratories, Fuji Photo Film Co. Ltd., 210 Nakanuma, Minami Ashigara, Kanagawa 250-01. Japan bDepartment of Chemistry School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Received 29 November 1996; accepted 3 1 March 1997
Abstract Density functional theory using the 6-3lG‘ basis set and two non-local exchange-correlation functionals (B-YLP and B3-LYP) has been applied to the calculations of the structures and vibrational spectra of the radical anion and cation, of biphenyl. The B3-LYP dihedral angles between the two phenyl rings are 5.8” and 19.5” for the radical anion and cation, respectively. Upon ionization, structural changes occur in the direction from benzenoid to quinoid. The unscaled vibrational frequencies calculated at the B-YLP/6-3 lG* level are mostly in agreement with the frequencies in the Raman spectra of the radical anion and cation of the normal and perdeuterated species reported in the literature. The calculations predict that both the radical anion and cation give rise to a very strong infrared band, and that this band arises from a mode in which the benzenoid-to-quinoid deformation occurs out of phase in the two phenyl rings. 0 1998 Elsevier Science B.V. Keywords:
Density functional calculations;
Vibrational
analyses; Biphenyl; Radical ions; Infrared intensities
1. Introduction Conjugated conducting polymers have attracted much attention from both fundamental and practical viewpoints because of their novel physical properties [l]. Poly(p-phenylene), which is one of conducting polymers, shows high electrical conductivities when doped with acceptors or donors, while it is an insulator in the undoped state [2]. To understand the optical and electrical properties of non-degenerate conjugated polymers such as poly(p-phenylene), polarons and bipolarons are proposed as elementary excitations, while polarons and solitons are conceivable in degenerate polymers such * Corresponding author
as Iruns-polyacetylene [ 11. A negative (positive) polaron and a negative (positive) bipolaron correspond to a radical anion (radical cation) and a dianion (dication), respectively. The formation of a polaron or a bipolaron is accompanied by structural changes over several phenylene rings and the appearance of localized electronic states. Studies of polarons and bipolarons are expected to lead to a deeper understanding of the optical and electrical properties of doped polymers. Vibrational spectroscopy has played an important role in studying the nature of polarons and bipolarons in conducting polymers [3,4], because different structural and spectral characteristics are expected for polarons and bipolarons. Zerbi and co-workers [5] have proposed the effective conjugation coordinate
0166-1280/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SOl66-1280(97)00153-X
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et al./Journal
of MolecularStructure
theory to interpret dopingand photo-induced infrared absorptions in conjugated polymers including poly(p-phenylene) [6]. Two of the authors (YF and MT) have analyzed the Raman spectra of Na-doped poly(p-phenylene) on the basis of the Raman spectra of the radical anions and dianions of p-oligophenyls and have concluded that negative polarons and bipolarons are generated in Na-doped poly(p-phenylene) [7,8]. Quantum chemical calculations for the radical ions and divalent ions of p-oligophenyls are useful for studying polarons and bipolarons in poly(p-phenylene). Brtdas et al. [9] have calculated the structure of a complex between p-quaterphenyl and two Li atoms using the ab initio Hartree-Fock (HF) method with the minimal STO-3G basis set and a partial geometry optimization. Cuff et al. [lo] have calculated the structures of the divalent ions of p-terphenyl at the HF/3-21G level. Ehrendorfer and Karpfen [ 1 l] have calculated the structures of the divalent ions of p-oligophenyls consisting of up to 11 rings at the HF/3-21G level. They have also calculated the structures and vibrational spectra of the dications of a-oligothiophenes using the ab initio HF method [ 12- 141. The HF method incorporates electron exchange, but does not take electron correlation explicitly into account, whereas Shimoi and Abe [ 151 have shown that electron correlation is significant in the stability of polarons and bipolarons. Then, appropriate post-HF methods are required to deal with electron correlation. Irle and Lischka [16] have calculated the structures of the complexes of one or two alkali-metal atoms with p-oligophenyls (biphenyl and p-quaterphenyl) at the HF and Msller-Plesset perturbation levels. Rubio et al. [ 171 have calculated the structures and electronic spectra of the radical anion and cation of biphenyl using the complete active space selfconsistent field method (CASSCF) and multiconfigurational second-order perturbation approach (CASPT2). It is practically impossible to calculate the structures and vibrational frequencies of the radical ions and divalent ions of long-chain p-oligophenyls at such high theoretical levels. As an alternative, density functional theory (DFT) may be used, because one of the advantages of DFT lies in its ability to incorporate both electron exchange and correlation in treating large systems. Recently, we have pointed out the usefulness of the DFT method
(Theochem)
424 (1998) 225-235
to the studies of the radical anion and cation of biphenyl [ 181. In the present paper, we report in more detail the results of density functional calculations on the structures and vibrational properties of the radical anion and cation of biphenyl.
2. Method of calculation Density functional (DF) calculations of the structures and vibrational properties (harmonic frequencies, vibrational patterns, and infrared intensities) of biphenyl and its radical anion and cation were performed by using the Gaussian 94 suite of programs [ 191 on a Silicon Graphics Power Onyx workstation. Counter ions were not included in the calculations of the radical anion and cation. The 6-3 1G* basis set was used. Calculations were performed with two sets of functionals: (i) Becke’s exchange functional [20] in combination with the Lee-Yang-Parr correlation functional [21] (abbreviated as B-LYP) and (ii) Becke’s three-parameter hybrid method [22] using the Lee-Yang-Parr correlation functional (abbreviated as B3-LYP). While the normal grid was used for numerical calculations of two-electron integrals in the previous paper [ 181, the fine grid was used in the present calculations. Thus, results in this study are slightly different from those reported previously. Full geometry optimizations were performed under Dz symmetry for all the species. No imaginaryfrequency mode was found at the optimized structures. Calculated atomic displacements in each vibrational mode were depicted with the LXVIEW program [23].
3. Structures The numbering of atoms in biphenyl and its radical ions is shown in Fig. 1. The structural parameters calculated at the B-LYP/6-31G* and B3-LYPI 6-31G* levels for the neutral molecule are listed in Table 1, together with experimental values in the vapor phase [24]. Table 1 also shows the structural parameters calculated by Rubio et al. [ 171 at the CASSCF level. The DF calculations have shown that the neutral molecule has a twisted structure (D2 symmetry). The values of the torsional angle around
K. Furuya et d/Journal
Fig.
of Molecular Structure (Theochem) 424 (1998) 225-235
I. Numbering of atoms.
the inter-ring C ,C, I bond, r(C2C ,C rC2,), calculated at the B-LYP/6-3 1G* and B3-LYP/6-3 lG* levels are 37.4” and 38.3”, respectively. The torsional angle in the vapor phase has been determined to be 44.4” by means of electron diffraction [24]. The CC bond lengths at the B3-LYP/6-31G* level are shorter than those at the B-LYP/6-31G* level by 0.007-0.012 .&. The ring CC bond lengths calculated at the B3-LYPI 6-31G* level are in good agreement with those observed. However, the C ,C ,I bond length calculated at the B-LYP/6-31G* level is in better agreement with that observed. The structural parameters calculated at the B-LYPI 6-31G* and B3-LYP/6-31G* levels for the radical Table I Structural
parameters
B-LYP
NCK3H3) W3C4W
a Ref. [17]. h Electron diffraction
anion are listed in Table 2. The crystal structures of bis(tetraglyme)rubidium biphenyl Rb+[CH30(CH&H20)&HJ2(C r2H1,$ [26], bis(tetraglyme)potassium biphenyl K+[CH30(CH2CH20)4CH3]I(C r2H lo)_ [27] and bis(triglyme)sodium biphenyl Na’[CH30(CH2CH20)3CHs]2(C1ZH10)[25] have been determined by means of X-ray diffraction, although structural parameters obtained have large uncertainties. The structural parameters of bis(triglyme)sodium biphenyl [25] are also shown in Table 2. The structural parameters calculated at the B-LYP/6-3 lG* and B3-LYP/6-3 lG* levels for the radical cation are listed in Table 3. The DF calculations have shown that the radical anion and cation have twisted structures (D2 symmetry). The values of the torsional angle around the C ,C I - bond calculated at the B-LYP/6-31G* and B3-LYP/6-31G* levels for the radical anion are 8.4” and 5.8”, respectively, and those for the radical cation are 20.5” and 19.5”, respectively. The calculated values of the torsional angle of the radical cation are considerably larger than those of the radical anion. Rubio et al. [ 171 have reported planar structures for the radical anion and cation, because they have optimized the geometries under the constraint of DZh symmetry. The CC bond lengths of the radical anion calculated at the B3-LYP/6-3 lG* level are in better agreement with the experimental
of neutral biphenyl Bond lengths/i
tiCzC IC I,CZ,) r(ClCl,) r(C ICz) r&K?) v(C,C,) r(CzHz) r(CiH,) r(C&) &CzC IC,) KICKI) &C2C1C4) B(CK.K,) WCICZHZ)
227
37.4 1.493 1.417 1.404 1.406 1.094 1.094 1.094 118.0 121.0 120.3 119.4 119.4 119.6 120.3
data [24].
and angles/deg B3-LYP 38.3 1.486 1.405 1.394 1.396 1.087 1.087 1.087 118.1 121.0 120.3 119.4 119.4 119.6 120.3
CASSCF” 44.3 1.492 1.405 1.399 1.399 1.077 1.077 1.077 118.4 120.9 120.2 119.4 119.7 119.7 120.3
EDb 44.4 1.507 1.404 I.395 1.396 1.102 I.102 1.102 119.4 119.9
228
Table 2 Structural parameters
K. Furuya et al./Journal ofMolecular
Structure (Theochem) 424 (1998) 225-235
of the radical anion of biphenyl Bond lengths/A and anglesideg B3-LYP
B-LYP
a A planar structure is assumed [ 171. b X-ray diffraction data obtained for bis(triglyme)sodium
biphenyl
values compared with those calculated at the B-LYPI 6-31G* level. As shown in Tables 2 and 3, the C,C,’ and CzC3 bonds are shortened and the C ,CZ and C3C4 bonds are lengthened on going from the neutral molecule to either the radical anion or cation. The shrinkage and elongation of these bonds are in fact observed for the radical anion. It can be concluded that the
X-ray b
0
5.8 1.439 1.441 1.383 1.410 1.087 1.092 1.088 114.2 122.6 121.8 117.0 119.3 118.7 121.5
8.4 1.45 I 1.451 1.394 1.421 1.095 1.099 1.095 114.3 122.6 121.7 117.1 119.3 118.8 121.4
Table 3 Structural parameters
CASSCF”
1.430 1.442 1.387 1.412 1.076 1.081 1.078 114.1 122.7 121.8 116.9 119.9 118.7 121.5
7.2 1.435 1.436 1.381 1.397
114.7 122.1 121.6 117.9
[25].
addition (or removal) of one electron to (or from) the neutral molecule leads to structural changes from benzenoid to quinoid. Similar structural changes are found in the structural parameters calculated at the CASSCF level [ 171, as shown in column 4 of Table 2 and column 4 of Table 3. Significant changes are found in the calculated bond angles of the radical
of the radical cation of biphenyl Bond lengths/l\ B-LYP
7(C&,C,C?,) r(CICI,) u(CIC2) r(C2C3) r(C3C4) tiC2H2) r(C3H3) 64H4)
e(C2CICh) e(C ,C2c1) e(c2w4) e(C3C4C5) WIC2H2) fw2C3H3) w3C4H4)
a A planar structure is assumed
20.5 I.456 1.442 1.390 1.419 1.091 1.092 1.093 117.8 120.9 120.0 120.3 119.9 120.1 119.8
[ 171.
and anglesideg B3-LYP 19.5 1.444 1.433 1.379 1.409 1.083 1.085 1.086 117.8 120.9 120.0 120.4 120.0 120.1 119.8
CASSCFa 0 1.433 1.435 1.381 1.409 1.071 1.075 1.076 117.1 121.3 120.2 119.9 120.6 119.8 120.0
K. Furuya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
Table 4 Calculated
and experimental
Mode”
a
frequencies
of neutral biphenyl-h 1oand -dlo hlo
v4 vs V6 y7 YE “9 “IO “II “I2 VI3
y14 “I5
229
dlo
Obsdb/cm-’
Calcd”/cm~
Obsdd/cm-’
Calcd’icm~’
1606 1505 1282 1186 1029 1003 964 838 740 405 307 55
1595 1506 1268 1192 1030 990 929 831 735 409 307 70
1578 1418 1192 872 841 962 788 654 693 355 300
1558 1403 1181 872 844 950 751 646 688 359 295 64
a The ylo. Y , ,, Y13and YI5 modes are correlated b In the vapor or solution phase [29-3 11. ’ At the B-LYP/6-3 lG* level. d In a solution [3 11.
with the au modes of the planar DZh structure.
anion. In particular, the C2C1C6 angle is reduced by 3.7” at the B-LYP/6-31G’ level and 3.9” at the B3-LYP/6-3 lG* level. This may be due to the repulsion between hydrogen atoms in the nearly planar structure of the radical anion [ 171. On the other hand, changes in the calculated bond angles on going from the neutral molecule to the radical cation are less than 1.0”.
4. Vibrational spectra The neutral molecule of biphenyl has 60 normal modes classified according to D2 symmetry: 1% + 13b l + 16bz + 16b3. The frequencies of the neutral molecule and its perdeuterated analog have been calculated and compared with the observed data reported in Refs. [28-311. The frequencies of the a modes calculated at the B-LYP/6-3 lG* level are listed in Table 4, together with those observed. It is noted that the vg mode is due to the inter-ring CC stretch. The ~10, v1 r, Y13and v,~ modes are correlated with the a, modes (out-of-plane vibrations) of the planar DZh structure. The root mean square deviations of unscaled B-LYP frequencies from the observed ones are 11.6 cm-’ and 12.0 cm-’ for biphenyl-h ,O and -dlo, respectively. Thus, the B-LYP/6-31G* method gives reliable frequencies without scaling.
4.1. Raman spectra of the radical anion and cation The Raman spectra of the radical anion of biphenyl [32-351 and its perdeuterated analog [34,35] have been reported. Eight bands of each species have been attributed to the totally symmetric fundamentals [33-351. The frequencies of the a modes calculated at the B-LYP/6-31G* level are listed in Table 5, together with the observed. The differences between the observed and unscaled B-LYP frequencies are less than 17 cm-’ and 19 cm-’ for biphenyl-h 10 and -dlo, respectively. Such agreement between the observed and unscaled B-LYP frequencies leads to a conclusion that the B-LYP/6-3 lG* method will be useful in assigning the observed Raman bands of the radical anions of long-chain p-oligophenyls. The calculated atomic displacements of v4-v9, vi2 and v14 of the radical anion are shown in Fig. 2. The v4 mode consists of the C2C3 (C&6) stretch (IRL in the notation of Tasumi et al. (TUN) [36]) and the inter-ring C iC ,’ stretch. The v5 mode consists of the ring stretch ( lR1?p, in the TUN notation) and the inter-ring CC stretch. The vg mode is due to the inter-ring CC stretch. The ~7 and v8 modes are due to the CH in-plane bends (1 HBI,” and lHB$, respectively, in the TUN notation). The vg, v12 and vi4 modes are due to the ring deformations (IRT, 1RT and IRZ,, respectively, in the TUN notation). The via, vi ,, vi3 and vi5 modes are correlated
K. Furuya et al./Journal ofMolecular Structure (Theochem) 424 (1998) 225-235
230
Table 5 Calculated
and experimental
frequencies
of the radical anion of biphenyl-h 10and -do
Mode”
hlo
dto
Obsdb/cm-’
Calcdc/cm-’
Obsdd/cmm’
1587 1493 1326 1201 1017 979 -
1604 1492 1310 1209 1000 966 849 724 709 414 322 38
1558
721 327 a The Y,a, Y, 1,YI3and Y15modes are correlated b In THF [32]. ’ At the B-LYP/6-31G’ level. d In ethanol [35].
W
v8
vg
672 315
1571 1393 1198 869 831 947 675 576 664 365 309 34
with the au modes of the planar Dzh structure.
with the a, modes (out-of-plane vibrations) of the planar structure. The observed and calculated frequencies of the inter-ring CC stretch (vg) of the neutral molecule of
1604 Cm-’
1412 1203 869 837 954
1000 cm-r
@)
v5
1492cm-r
(f)
966 cm.’
Cc)
v.5
1310 cm-’
(9) VI2
709 cm-]
W
VT
1209 cm-’
@I VM
322 cm-r
Fig. 2. Atomic displacements calculated at the B-LYP/6-31G’ for some of the a modes of the radical anion of biphenyl.
level
biphenyl-h,s are 1282 cm-’ and 1268 cm-‘, respectively; the observed and calculated frequencies of the corresponding mode of the radical anion are 1326cm-’ and 1310cm-‘, respectively (Tables 4 and 5). The upshift of the inter-ring CC stretch frequency on going from the neutral molecule to the radical anion is consistent with the structural changes in the direction from benzenoid to quinoid. Upon deuteration, mode mixing is changed significantly. The inter-ring CC stretch makes a smaller contribution to the vg mode of the radical anion of biphenyldIo. Thus, a smaller upshift of the vg band (from 1192 to 1203 cm-‘) is observed for biphenyl-d10 upon ionization. The Raman spectra of the radical cation of biphenyl [35,37,38] and its perdeuterated analog [35,38] have been reported. Nine bands of the normal species and seven bands of the perdeuterated species have been ascribed to the totally symmetric fundamentals [35,38]. The frequencies calculated at the B-LYPI 6-3 lG* level for the a modes are listed in Table 6, together with the observed. The calculated atomic displacements of v4-vg, vi2 and v14 of the radical cation (not shown) are very similar to those of the radical anion. The vro, vI1, ur3 and v15 modes are correlated with the a, modes (out-of-plane vibrations) of the planar DZh structure. The differences between the observed and calculated frequencies are less than
K. Furuya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
231
Table 6 Calculated
and experimental
frequencies
of the radical cation of biphenyl-h ,,, and -dlo
Mode”
a
h 10
v4 Q V6 v-i v8
yg VI0 “II “12
VI3 “I4
Calcd’km-’
Obsdb/cm-’
Calcd”/cm-
1615 1502 1342 1224 1018 989
1606 1486 1310 1219 1008 979 957 803 726 384 321 66
1579 1421
1568 1386 1200 878 840 950 778 629 681 336 306 60
737 391 334
VI5
a The Y10, Y, , , Y,i and Y,5modes are correlated b In acetonikile solutions [35,38]. ’ At the B-LYP/6-3 1G’ level.
dlo
Obsd bicm-’
882 847 958
688 329 -
with the a,, modes of the planar D2h structure.
23 cm-‘, except for V6of the normal species and v5 of the perdeuterated species. The inter-ring CC stretch makes contributions to these modes. The calculated v6 frequency for the radical cation of biphenyl is 32 cm-’ lower than that observed, whereas the calculated frequencies for neutral species and the radical anion are in better agreement with those observed. The calculated length of the inter-ring CC bond in the radical cation is longer than that in the radical anion (Tables 2 and 3). This is consistent with the result that the calculated frequency of the inter-ring CC stretch of the radical cation is lower than that of the radical anion. Actually, however, the observed wavenumber of the Raman band of the radical cation is higher than that of the radical anion. The origin of this discrepancy between the calculated and observed frequencies is not clear at present. Sasaki and Hamaguchi [35] have observed a weak band at 39 1 cm-’ in the Raman spectrum of the radical cation in an acetonitrile solution. They have interpreted that the presence of this band in the Raman spectrum results from a twisted structure (02 symmetry) of the radical cation, because the 391 cm-’ band corresponds to a Raman-inactive a, mode of the planar structure (&, symmetry). Their assignment has been confirmed by the present calculation. The corresponding band is not observed in the Raman spectrum of the radical anion [35]. The small deviation from a planar structure in the radical anion
(Table 2) suggests that the vt3 band of the radical anion might be too weak to be observed. 4.2. Infrared spectra of the radical anion and cation The present DF calculations predict that the frequencies and/or the intensities of the infrared bands of the radical anion and cation are significantly different from those of the neutral molecule, although the infrared spectra of the radical anion and cation have not been reported yet. Some important theoretical predictions are described below. The frequency calculated for each CH stretch (~~6, v,,, vts, vz9 or Vet) of neutral biphenyl is higher than that for the radical anion and lower than that for the radical cation, as shown in Table 7. The infrared intensities calculated for three CH stretching modes of the neutral molecule (vt6 and vt, of the b, species and ~29 of the b2 species) are strong. Experimentally, the CH stretches are strongly observed [29,31,39]. The infrared intensities of the CH stretches of the radical anion and cation are different from those of neutral biphenyl. The infrared intensity of each CH stretch of the neutral molecule is weaker than that of the radical anion and stronger than that of the radical cation. Similar features have been reported for the calculated CH stretching frequencies and intensities of the neutral and charged species of polycyclic aromatic hydrocarbons [40]. Gussoni et al. [41] have
K. Fumya et al./Journal of Molecular Structure (Theochem) 424 (1998) 225-235
232
Table 7 Calculated”
frequencies
and infrared intensities of the b-species modes due to the CH stretches and CH out-of-plane Radical anion
Neutral Mode
CH stretch b, “lb “I7 “I8 62 “29 “30 CH out-of-plane bi “53 “54 “55 “86
Freq./cm-’
3121 3107 3091 3117 3099 bend 954 885 730 692
a At the B-LYP/6-31G’
IR int. km molK’
Mode
48 42 9 68 14
b,
“lb “11
“IX
b?
“29 “Xl
bends
Radical cation Freq./cm-’
IR int. /km mol-’
3085 3072 3023 3092 3027
110 77 97 168 187
876 717 647 516
45 11 35
0
2 63 25
Mode
Freq./cm-’
“16 “17 “IX “29 “30
0
bl
IR int.1 km mol-’
3154 3143 3131 3161 3141
4 1 0 2 0
985 926 747 621
1 2 73 43
“53 “54 “55 “S6
level.
shown for neutral hydrocarbons that the intensity of a CH stretch depends on the atomic charge of the hydrogen atom. According to their theory, the intensity of a CH stretch can be expressed by the square of the sum of the equilibrium atomic charge of hydrogen and a charge-flux term. The former term has positive values and is sensitive to the conjugation of the adjacent CC bonds. The latter term has negative constant values. Then, as the atomic charge becomes small, the intensity of the CH stretch becomes strong. Let us assume that this rule can be applied to the neutral species, radical anion and radical cation of biphenyl. The Mulliken charges (which are viewed approximately as the atomic charges) of the hydrogen atoms are, O.lOOe-0.103e for the neutral species, O.O14e-0.043e for the radical anion, and O.l62e0.183e for the radical cation; the atomic charges decrease in the order of the radical cation, the neutral species and the radical anion. Thus, the infrared intensity of the CH stretch becomes strong in this order. This is consistent with the results of the present DF calculations. The 736 cm-’ and 700 cm-’ infrared bands observed for the neutral species in a solution [31] are assigned to v55 and v56, respectively. It is well known that these two bands are characteristic of the mono-substituted benzene ring. According to the results of the present DF calculations, the H3 (H3,), H4 (Hdf) and H5 (HS,) atoms move predominantly in phase ( 1HB,Op in the TUN notation [36]) for v55,
whereas the H2 (Hz,), H4 (H4f) and H6 (He,) atoms move predominantly in phase ( lRyp in the TUN notation) for v56 (not shown). On the other hand, the v54, us5 and v57 modes of the radical anion have considerable intensities (Table 7). The v55 mode of the radical anion is similar to the v56 mode of the neutral species. As shown in Fig. 3(a,b), the Hz (HZ,), H3 (H3,), H5 (H,,) and H6 (H6,) atoms move predominantly in phase in vs4; the H4 (H4,) atoms move predominantly in vs7. The CH out-of-plane modes of the radical anion are strikingly different from those of the neutral
(a)
vs4
7 17 cm-t
(d) v~
747 cm-t
(e) vs6
627 cm-t
l---=-l(b)
“57
576cm-*
(c)
VL9
1583cm-t
(f)
vts
1517 cm-t
Fig. 3. Atomic displacements calculated at the B-LYP/6-31G’ level. (a) 1~54,(b) “57, (c) v 19for the radical anion; (d) “s5. (e) “56. (f) “ts for the radical cation.
K. Furuya et al/Journal
Table 8 Calculated”
frequencies
and infrared intensities of biphenyl
Neutral
“19 “20 "21 "22
“13 “24 “27 bz
“31 y32
“33 “34 "35 "36
“41 "44
Freq./cm-’
IR int./ km mol-’
Mode
1601 1489 1183 1041 996 984 608
11 22 0 2 5 0 8
b,
1567 1433 1341 1285 1166 1079 624 127
4 5 1 3 0 5 0 0
bz
233
and its radical ions
Radical anion
Mode
b,
of Molecular Structure (Theochem) 424 (1998) 225-235
“19 "20 "21 "22 "23 "24 "27 "31 "32
“33 "34 "35 "36
“40 "44
Radical cation Freq./cm-’
IR int./ km mol-’
Mode
1583 1458 1171 992 979 932 581
405 0 43 61 34 120 2
b,
1481 1391 1344 1232 1101 1062 622 149
0 33 28 1 7 2 0 0
b2
“19 "20 "21 "22 "23 "2s "21
“?I "32 "33 "34
“35 "36
“41 “44
Freq./cm-’
IR int./ km mol.’
1571 1457 1192 1003 985 950 597
336 55 32 9 7 83 21
1511 1417 1362 1262 1159 1095 590 147
18 22 17 3 5 8 3 0
a At the B-LYP/6-3 1G’ level.
species. The infrared intensities calculated for two CH out-of-plane bending modes of the radical cation (vs~ and v56 of the b3 species) are strong, as shown in Table 7. The DF calculations indicate that the H3 (Hjf), H4 (H4,) and H5 (H5f) atoms move predominantly in phase (lHBip in the TUN notation [36]) for vs5, whereas the H2 (H2,), H4 (H+) and H6 (H6,) atoms move predominantly in phase ( lRyP in the TUN notation) for v5& as shown in Fig. 3(d,e). The calculated atomic displacements of v55 and v56 of the radical cation are quite similar to those of vs5 and v56, respectively, of the neutral species. In the results calculated for the radical anion and cation, some of the 6, modes are strong in infrared intensity, as shown in Table 8. In particular, the vlg modes of the radical anion and cation have strong intensities. Transition dipole moments associated with the b, modes are parallel to the molecular long axis. The calculated atomic displacements of vi9 (b, species) of the radical anion and cation are shown in Fig. 3(c) and Fig. 3(f), respectively. In these modes, the two phenyl rings deform out of phase in the direction from benzenoid to quinoid; the C2C3 and C&6 bonds stretch (shrink), whereas the C,C2, C3C4, C4C5 and C&I bonds shrink (stretch). It is noted that the v4 mode of the radical anion and cation (a species,
Fig. 2(a)) is the corresponding in-phase mode. Strong infrared intensities of vi9 of the radical anion and cation can be interpreted in terms of the vibronic theory, as described below. The infrared absorption intensity of a fundamental vibrational transition, Z,i ..-$, can be expressed [42] in the harmonic approximation as Igl.--go OZKg1 IcclgO)12
(1)
where He is the electronic Hamiltonian; p is the dipole moment operator; I@) and Igl) represent the vibronic wavefunctions of the ground electronic state with vibrational quantum numbers 0 and 1, respectively; Q is the normal coordinate; 1s”) and Iso)indicate the electronic wavefunctions of the ground and excited electronic states at the equilibrium structures, respectively; I$ and E,” are the energies of these states; w is the frequency of the normal vibration. From Eq. (2), one can understand that the infrared intensity of a vibrational band results from the vibronic coupling
234
K. Furuya et al./Journnl of Molecular Structure (Theochem) 424 (1998) 225-235
between the ground and excited electronic states. Strong infrared intensities come from the electronic states satisfying the following conditions: (1) the transition energy, l$ - ,$, is small; (2) the matrix element of the dipole moment operator, (s”lplgo>, is large (allowed transition); (3) the matrix element of the vibronic coupling operator, (go l(aZ!Z$aQ)Ols?, is large. The radical anion and cation of biphenyl give rise to two strong electronic absorption bands in the visible region: 15 300 and 24 400 cm-’ for the radical anion and 14 200 and 25 800 cm-’ for the radical cation [43]. These absorption bands are polarized parallel to the molecular long axis [43]. On the other hand, neutral biphenyl gives rise to a long-axis polarized band at 39 700 cm-’ [44]. The electronic spectra of the radical anion and cation have been studied by means of the CASPT2 method on the assumption that the radical anion and cation have planar structures [ 171. The lower and higher energy bands of the radical anion are due to the 1 *Bls - 1 *BsU and 2 2B2, - 1 *BjU transitions, respectively; the lower and higher energy bands of the radical cation are due to the 1 *Bs,, - 1 *B2, and 2 2B3U- 1 *B2, transitions, respectively. According to Eq. (2) the symmetry consideration ((go 1(aHdaQ)ols’) # 0) leads us to the conclusion that the excited electronic states mentioned above can give intensities to the b Iu vibrational modes. The b,, modes are correlated with the b, modes of a twisted structure. The transition dipole moments associated with the b,, or 6, modes are parallel to the molecular long axis. Among the 6, modes, the v l9 mode is probably effective for the vibronic mixing. The matrix elements of the vibronic coupling operator for the radical anion and cation should be larger than that for the neutral species. Thus, the strong infrared intensities associated with v19 are considered to originate from the visible electronic absorptions, although further experimental and theoretical studies are required for a more quantitative analysis. Doped conjugated polymers give rise to infrared absorptions due to vibrational transitions and electronic absorptions in the region from visible to infrared, which are associated with high electrical conductivities [ 11. Thus, studies on the intensities in the infrared absorption spectra of charged oligomers and doped polymers may lead us to a better understanding of high electrical conductivities in doped polymers.
5. Conclusions The structures and vibrational spectra of the radical anion and cation of biphenyl have been studied by using DF calculations with the B-LYP and B3-LYP exchange-correlation functionals and the 6-3 lG* basis set. The results obtained are as follows. (1) The radical anion and cation have twisted structures. The B-LYP (B3-LYP) dihedral angles between two phenyl rings are 8.4” (5.8”) and 20.5” (19.5”) for the radical anion and cation, respectively. Ionization induces structural changes in the phenyl rings in the direction from benzenoid to quinoid. (2) The vibrational frequencies calculated at the B-LYP/6-31G* level are in fair agreement with observed frequencies in the Raman spectra reported in the literature. The frequency of the inter-ring CC stretch is sensitive to the structural changes from benzenoid to quinoid. The B-LYP/6-3 lG* method will be useful in assigning the vibrational spectra of the radical ions of long-chain p-oligophenyls. (3) Infrared intensities calculated for the CH stretches of the radical cation are anomalously weak, whereas infrared intensities calculated for the CH stretches of the radical anion are stronger than those for the corresponding modes of the neutral molecule. These intensity features have been interpreted by the Mulliken charges on the hydrogen atoms. (4) The radical anion and cation are expected to give rise to a very strong infrared band attributed to the ring CC stretch where the two phenyl rings deform out of phase in the direction from benzenoid to quinoid. The strong intensity of the band probably comes from the excited electronic states associated with the visible absorptions through vibronic coupling.
Acknowledgements One of the authors (KF) thanks Mr. J. Hayashi, director and general manager of the Ashigara Research Laboratories, for allowing KF to publish the results of calculations in this paper. Thanks are also due to Mrs. M. Kobayashi for her help in data processing.
K. Furuya et al./Journal ofMolecular
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