J . Phys. Chem. 1989, 93, 1713-1718 symmetric top. Thus, our results concerning ro values of DMA are consistent with the work of Nathanson and McClelland. In the case of the C, probes used here, however, a quantitative prediction of the evolution of ro using Nathanson and McClelland’s theory would be difficult (if feasible) because of the complicated flexibility of the molecules. On average, the conformation of C, probes should be rather globular, and recovering an approximate linearity similar to this predicted for both oblate and prolate ellipsoids is plausible. VI. Conclusion
In this paper, we have explored different aspects of the fundamental anisotropy and particularly its behavior as a function of temperature. Our study has shown the existence of two types of behaviors for ro: at low temperature (Le., when the medium is frozen) ro may be considered a constant quantity whereas at
1713
high temperature it decreases linearly with the temperature. It is worth noticing that, in general, experimental studies take place in the high-temperature range owing to the lifetime of the fluorophores. Moreover, for a fluorophore such as anthracene, both the nature and the length of the substituents and the medium affect the value of the fundamental anisotropy. Thus, techniques such as fluorescence polarization under continuous excitation in equilibrium or nonequilibrium, which consider ro as a constant quantity, are able to predict only qualitatively the evolution of the mobility of the medium as a function of external parameters (temperature, pressure, etc.). Time-resolved techniques are necessary for a quantitative study of the mobility. Acknowledgment. We are indebted to F. Costa-Torro, B. Jasse, and C. K. Yeung for the synthesis of the probes used in this study. Registry No. Cl0, 98876-32-5; C12, 118043-87-1;CI6,98876-34-7.
Exciton Coupling in Bis(phthalocyaninato)tin(I V ) Osamu Ohno, Naoto Ishikawa, Hideyo Mafsuzawa, Youkoh Kaizu, and Hiroshi Kobayashi* Department of Chemistry, Tokyo Institute of Technology, 0-okayama, Meguro- ku, Tokyo 152, Japan (Received: August 26, 1987; In Final Form: June 27, 1988)
Exciton coupling in a face-to-face stacking dimer, bis(phthalocyaninato)tin(IV), gives rise to a remarkable splitting not only of the Q band but also of the B band. The absorption spectrum of the stacking dimer exhibits a prominent splitting of the Q band between 13 X lo3 and 16 X lo3 cm-’ and a remarkable blue shift of the B band up to 30 X IO3 cm-’ with a lower wavenumber tail extending to 22 X lo3 cm-’. The observed splitting can be theoretically reproduced on the basis of the molecular-orbital calculations which extensively take into account electronic correlation effects. In principle, the splitting is attributable to both Coulomb and exchange interactions in the exciton coupling. However, the exchange interaction is negligibly small as compared with the Coulomb interaction even in such a close stacking distance of 2.7 A. The lowest excited states (Q and B excited states) of metallophthalocyanines are ascribed predominantly to single excited configurations ‘(6e, 2alJ and ‘(6e, 4a2J, whose transition moments are parallel and of comparable magnitude. The exciton coupling in the phthalocyanine dimer of a face-to-face stacking conformation yields a remarkable splitting of the Q band and also an increase in the total intensity of the B band in contrast with the diminished interaction in the Q band of the corresponding porphyrin dimers, which shows only a minute splitting of the Q band and a redistribution of intensity within the component B bands. The energy of the charge-resonancetransition between phthalocyaninemolecules in the dimer is theoreticallyevaluated on the same principle applied to the exciton interaction. The lowest charge-resonanceexcitation is predicted at a lower energy than that of the lowest excited singlet state observed as Q band. The lack of fluorescence in the dimer phthalocyanine can be attributed to a rapid relaxation in the low-lying dipole-forbidden charge-resonance state.
-
-
Introduction
A prominent splitting of the Q band is observed in bis(phthalocyaninato)tin(IV) ((Pc)zSn), which is a “face-to-face” stacking dimer. The splitting is ascribed to the exciton coupling interaction strikingly enhanced in the intense phthalocyanine Q band in contrast with the diminished interaction in the weak porphyrin Q band. The Dddstacking structure of the dimer has been characterized by X-ray crystallographic study’ and less definitely by a Mossbauer spectrum.2 A similar splitting of the Q band has been observed with lanthanide diphthalocyanines, [ ( P C ) ~ Y ~and ] - [(PC)~LU]-,~ for example, indicating their closely stacking configurations in contrast with the less resolved splitting in the p o x 0 dimer ( P C S ~ ) ~ O The . ~ distances between two phthalocyanine moieties in D,, symmetry of (Pc),Sn, (Pc)&u (1) Bennett, W. E.; Broberg, D. E.; Baenziger, N. C. h o r g . Chem. 1973, 12, 930.
(2) O’Rourke, M.; Curran, C. J . Am. Chem. SOC.1970, 92, 1501. (3) (a) Corker, G. A,; Grant, B.; Clecak, N. J. J . Electrochem. SOC.1979, 126, 1339. (b) L‘Her, M.; Cozien, Y.; Courtot-Coupez, J. C. R. Acad. Sci. (Paris) 1985, 300,487. ( c ) Markovitsi, D.; Tran-thi, T.; Even, R.; Simon, J. Chem. Phys. Lett. 1987, 137, 107. (4) Ciliberto, E.; Doris, K. A.; Pietro, W. J.; Reisner, G. M.; Ellis, D. E.; Fragala, I.; Herbstein, F. H.; Ratner, M. A,; Marks, T. J. J. Am. Chem. SOC. 1984, 106, 7748.
(oxidized form), and (PcSi)zO are 2.70,l2.69,5 and 3.32 A,4 respectively. Absorption spectra of the p o x 0 dimers such as ( T P P S C ) ~ ~ ~~ (TPP; 5,10,15,20-tetraphenylporphyrin)and ( O E P S C ) (OEP; 2,3,7,8,12,13,17,18-octaethylporphyrin) exhibit a remarkable blue shift of the B band with a lower wavenumber tail extending down to 22 X lo3 cm-I which arises from an exciton coupling in the B band of the stacked porphyrin dimers.6 On the other hand, the Q band is blue-shifted only to a lesser extent in the porphyrin dimers. Similar spectral behavior has been found with (TPPA1)z07 and (TPPNb)z03.8 The forbidden Q and allowed B excited states of metalloporphyrins are mostly described by a 50-50 admixture of the lowest two excited configurations in accidental degeneracy whose transition moments are parallel and of comparable magnitude. Thus the exciton coupling in the stacking porphyrin dimer yields a sizable splitting only in the allowed B band with redistribution of spectral intensity within the B-band manifold. On the other hand, the lowest excited states of metallophthalocyanines ~
~
~~
( 5 ) DeCian, A,; Moussavi, M.; Fischer, J.; Weiss, R. Inorg. Chem. 1985,
24, 3162. ( 6 ) Gouterman, M.; Holten, D.; Lieberman, E. Chem. Phys. 1977.25, 139. ( 7 ) Kaizu, Y.; Misu, N.; Tsuji, K.; Kaneko, Y.;Kobayashi, H. Bull. Chem. SOC.Jpn. 1985, 58, 103. (8) Ohno, 0.;Kaizu, Y.;Kobayashi, H. J. Chem. Phys. 1985,84, 1779.
0022-3654/89/2093-1713$01.50/00 1989 American Chemical Society
1714 The Journal of Physical Chemistry, Vof. 93, No. 5, 1989
Ohno et al.
are ascribed predominantly to single lowest excited configurations with comparable transition moments. The exciton coupling in the phthalocyanine dimers results in not only a remarkable splitting of the Q band but also an increase of intensity of the higher energy component B band. A blue shift and broadening of the Q band observed with phthalocyanine in sublimed thin film crystals must be attributable to a rather complicated exciton coupling between a range of neighboring chromophores in the crystal^.^ Recently the coupling has also been described on covalently linked phthalocyanine oligomers in open and closed conformations.1° In this paper, we present a discussion on the exciton coupling band of the stacking dimer (Pc),Sn. Absorption spectra of the So far, however, the exciton dimer have been coupling in the stacking dimer has never been discussed.
Experimental Section ( P C ) ~ Swas ~ prepared by reaction of dichloro(phtha1ocyaninato)tin(IV) (PcSnCl,) and disodium phthalocyanine (PcNa2) according to the with some modification. A freshly ground mixture of PcSnCl, (0.50 g) and PcNa, (0.47 g) was placed in a flask and dried in an oven for 3 h at 110 “C. To this flask was added dried 1-chloronaphthalene (20 mL), and the mixture was refluxed for 90 min under nitrogen atmosphere. By vacuum distillation, the solution was condensed. After the residual was washed with a small amount of benzene, the complex was extracted with benzene in a Soxhlet apparatus. The extract was loaded onto an alumina column (Merck alumina 90) and eluted with benzene. The complex thus obtained was further purified by chromatography on an alumina column using benzene as eluent. ( P C ) ~used S ~ for spectral measurements was obtained from the eluate by vacuum evaporation of the solvent. Benzene used for extraction and chromatography was purified by distillation after dried over CaC12 and then CaH2. Anal. Calcd for C,H32N16Sn (M, 1143.8): C, 67.21; H, 2.82; N, 19.59. Found: C, 67.46; H, 2.56; N, 19.68. PcSnClz and PcNa, were prepared and purified by literature methods.14 PcAlCl was obtained from Pfaltz and Bauer Inc. and purified by sublimation. Absorption as well as second-derivative absorption spectra were measured on a Hitachi spectrophotometer 330. Magnetic circular dichroism (MCD) spectra were taken on a JASCO spectropolarimeter J-5OOC in an external magnetic field set at 1 T. Luminescence emission as well as excitation spectra were measured on a Hitachi spectrofluorometer 850 equipped with a Hamamatsu Photonics photomultiplier R928. Solvents used for spectral measurements were ethanol, toluene, and 1-chloronaphthalene purified by distillation just before the measurements.
Results end Discussion Absorption and MCD spectra of (Pc),Sn in toluene are shown in Figure 1B. A remarkable splitting of the Q band is observed with the sandwich phthalocyanine dimer. The B band also shows a notable blue shift with a longer wavelength tail extending to about 22 X lo3 cm-’. A-term MCD dispersion^'^ appear in the Q and B bands (Figure lB(II1)). It should be noted that the MCD dispersion is observed in each of the split exciton bands. Absorption and emission spectra of monomer PcSnClz and PcAlCl a r e also presented in Figures lA(1) and 2(I), respectively. The monomeric phthalocyanines emit intense fluorescence, while the dimer exhibits no detectable emission. MCD spectrum of PcSnC12 in 1-chloronaphthalene shows A-term dispersions in the absorption (9) (a) Sarp, J. H.; Lardon, M. J . Phys. Chem. 1968, 72, 3230. (b) Shechtman, B. H.; Spicer, W. E. J . Mol. Specrrosc. 1970, 33, 28. (c) Hollebone, B. R.; Stillman, M. J. J . Chem. Soc., Faraday Trans. 2 1978,74,2107. (d) Davidson, A. T. J . Chem. Phys. 1982, 77, 168. (10) Lever, A. B. P.; Hempstead, M. R.; Leznoff, C. C.; Liu, W.; Melnik, M.; Nevin, W. A.; Seymour, P. Pure Appl. Chem. 1986, 58, 1467. (1 1) Whalley, M. J . Chem. SOC.1961, 866. (12) Edwards, L.; Gouterman, M. J . Mol. Specfrosc. 1970, 33, 292. (13) Kenney, M. E.; Kroenke, W. J. Inorg. Chem. 1964, 3, 251. (14) Barrett, P. A.; Dent, C. E.; Linstead, R.P. J . Chem. Soc. 1936, 1719. (15) Stephens, P. J.; Suetaak, W.; Schatz, P. N. J . Chem. Phys. 1966,44, 4592.
I 30
20
10
10
20
30
Navenbmberl 103c,-
Wavenumber / l o 3 cm-’
(I), second-derivative absorption (11)” and MCD (111) spectra (under a magnetic field set at 1 T) of PcSnC12 (A) in 1-chloronaphthalene and the dimer (Pc)$n (B)in toluene. Fluorescence emission (- - -) observed with PcSnClz is also presented in (A(1)). For comparison, absorption spectrum of monomeric PcSnCI2 is also presented with the spectrum of the dimer in (B(1)). The splitting is observed with the dimer ( P c ) ~ Snot ~ only in Q but also in B bands. Figure 1. Absorption (-)
(-a)
31
I (I)
I
1
10
20
30
40
50
Wavenumberl 103cm-’
Figure 2. Absorption (-), emission (- - -) (I), second-derivative absorption (II), and MCD (111) spectra (under 1-T magnetic field) of PcAlCl in ethanol.
bands at 14.3 X lo3 and 14.9 X lo3cm-’, while it shows B-term maxima in the absorption bands at 16.4 X lo3, 16.6 X lo3, and 17.1 X lo3 cm-l which are also detected by the second-derivative absorption spectrum (Figure 1A). These B-term maxima have been observed with the other metallophthalocyanines.I6 Another weak absorption band is present to the red of the B band around 23 X lo3 cm-I. PcAlCl in ethanol exhibits rather clearly the corresponding weak absorption bands in the region (Figure 2). These bands are also detected by excitation spectra of the fluorescence from the Q state, and thus they are ascribed to the phthalocyanine moiety but not to some possible impurities. The B band exhibits an A-term MCD dispersion, while the weak bands to the red of the B band exhibit B-term extrema. These weak bands between Q and B bands, which show B-term MCD extrema, may be attributable to the low-lying (n, T * ) excitations in phthal~cyanine.l’-’~ However, it should be noted that the in(16) (a) Stillman, M. J.; Thomson, A. J. J . Chem. Soc., Faraday Trans. 2 1974, 70,790. (b) Stillman, M. J.; Thompson, A. J. J. Chem. Soc., Faraday Trans. 2 1974, 70, 805. (c) Nyokong, N.; Gasyna, Z.; Stillman, M. J. Inorg. Chem. 1987, 26, 1087. (17) Henriksson, A,; Roos, B.; Sundbom, M. Theor. Chim. Acta 1972,27, 303. (18) Schaffer, A. M.; Gouterman, M.; Davidson, E. R. Theor. Chim. A d a 1973, 30, 9.
Exciton Coupling in Bis(phthalocyaninato)tin(IV)
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1715
(n)
(1)
I
0 - -1 - -2
configurations were taken into account for the configuration-interaction calculation. Table I summarizes the calculated excitation energies and oscillator strengths of the excited singlet states of the metallophthalocyanine monomer. By use of the Nishimoto interaction (model a, e2/[2a R])21 instead of the original Nishimoto-Mataga formula (model b, e2/[n the best reproduction of the observed excited singlets was obtained. The lowest allowed excited states of metallophthalocyanines are described mostly by single configurations such as '(6e,+-2ai,) or I(6eg+4a2,) (four-orbital model) in contrast with the 50-50 configuration-interaction admixtures of the corresponding excited configurations in metalloporphyrins. The calculation on the same principle was also performed on metalloporphyrins. The results are in good agreement with those observed by spectroscopy and obtained by the screened-potential molecular-orbital c a l c ~ l a t i o n . ~ ~ The present calculation on the excited states of monomeric metallophthalocyanine reconfirms the conclusion of earlier molecular-orbital calculations: the lowest excited states lE, and 2E,, are mostly described by single configurations '(6e,+2al,) and '(6e,+4a2,) (four-orbital model), respectively, while there is a sequence of the symmetry-allowed but actually forbidden E, (6eg+3 b2J, (6eg+3a2,), and excited configurations (7eg+2a '(6e,+2bl,) within 10 X lo3 cm-' higher energy than '(6e,+ 4a2u).26 Model b of the present work predicts planar oscillator excited states lE, (f= 0.15; f is the oscillator strength evaluated with transition velocity operator fi/m,; fi, momentum operator; me, mass of electron), 2E, (f = 0.04), 3E, (f = 0.62), 4E, cf = 0.23), and 5E, (f= 0.09) at 14.1 X IO3, 30.7 X lo3, 31.0 X lo3, 33.1 X lo3, and 34.7 X lo3 cm-', respectively, which well correspond to the results of C I calculation by Gouterman and his students: Q (f= 0.16), B (f= 0.79), and N (f= 0.18 for closely spaced two states) at 15 X IO3, 30 X lo3, and 35 X lo3 cm-', respectively. In the present calculation, we released the traditional zero-differential overlap assumption in one-electron and twoelectron terms. This alters the relative weights of excited configurations in the configuration interaction. Nevertheless, our model b, which is based on the empirical parameters determined by the same principle, well reproduced the results obtained by Gouterman group except that ours predicts weakly allowed second excited state 2E, mainly made of '(7e,+-2a1,) at a lower energy region than the strongly allowed third excited state 3E, mostly attributable to I(6eg+4a2,) (Table Ib). It should be noted that the intensity of the B-band manifold is granted almost exclusively from the '(6e,+4a2,) excited configuration regardless of the presence of other weakly allowed excited configurations in the same energy region, even if the diffuse B band is to be ascribed to a complex of closely spaced excited states. Model c, in which the shielding effect due to electronic correlation is taken into account only to a lesser extent, yields only a poor reproduction of the observed excitation energies as is usually encountered in the molecular-orbital calculations of porphyrin spectra. The model predicts two weakly allowed excited states 2E, (mainly attributable to '(7eg+-2al,)) and 3E, ('(6e,+3a2,); '(6e,+3b2,)) to the red of the strongly allowed 4E, ('(6eg74a2,)) (Table IC); however, the intensities of 2E, and 3E, are originated from containing '(6e,+-4a2,,). Model a, which is prescribed by taking much electron correlation effect so as to well describe the excited states of polarizable porphyrin macrocycles, yields I E , (f=0.21), 2E, (f= 0.89), 3E, (f=0.10), 4E, (f= O.OO), and 5E, (f= 0.04) at 14.2 X lo3, 26.3 X lo3, 28.8 X lo3, 29.5 X lo3, and 29.6 X lo3 cm-'. As Table Ia shows, lE, and 2E, are mostly attributable to single excited configurations I( 6eg+2alu) and I (6eg+4a2,), respectively. An observed diffuse band at around (25-32) X lo3 cm-' is ascribed to a manifold of closely spacing excited states 2-5E!,,. The observed oscillator strengths of PcAlCl in ethanol are 0.24 and 0.79 at the 15 X lo3 and (25-32) X lo3 cm-I bands, respectively. Since the
+
- -3 - -4
- -5
in
1
1
f j
f 1
f
0
05 0
05 0
05
" I L L -
Figure 3. HOMOS and LUMOs (I) and lowest singlet excited states (11) calculated by the models of Nishimoto (a), Nishimoto-Mataga (b), and Ohno (c).
-
tensities of these bands are as high as t lo4 and the absorption bands are observed even in concentrated acidic media. As the molecular-orbital calculation described later predicts, there are a sequence of the forbidden or weakly allowed '(*,a*)excited states between Q and B bands and also one in the region of the B band. The forbidden transitions can be granted intensities from the allowed Q and B states by vibronic couplings and exhibit B-term MCD extrema. In the present work, however, the exciton coupling of the allowed planar degenerate oscillators in metallophthalocyanine that exhibit A-term MCD dispersions is discussed. The welectron system of D4*metallophthalocyanine was calculated by the semiempirical SCMO-CI method taking into account all the non-nearest-neighbor interactions. The present calculation did not assume the traditional zero-differential overlap.20 The molecular geometry was the one previously assumed.'* The charge on the central metal ion was assumed to be neutralized by charge donation from the coordinated nitrogens. One-electron overatomic core integrals are given by
where Zp is the empirical valence-state ionization potential, -Z,(kklpp) is the attraction term due to the charge (zk) on the core k in terms of the two-electron integral (kklpp), 0 "(S,/FPo) is a parameter adjusted so as to reproduce the (T, a 9 transitions of benzene and pyrazine, and S, and S", are the overlap integrals of the a bonds in phthalocyanine and of the reference C C and C N bonds in benzene and pyrazine, respectively. Two-electron interactions between two centers at a distance R were evaluated from the formula prescribed by Nishimoto (e2/[2a R]),2i NishimotwMataga (e2/[a R])?2and Ohno (eZ/[a2 R2]1/2)?3 while the one-center interaction e2/a was empirically determined by the atomic term values.24 The other multicenter interactions are approximated by the equation
+
+
+
Figure 3 (I) presents the highest occupied and the lowest vacant orbitals and the energy levels of the lowest excited states of metallophthalocyanine. The lowest 84 (a,a*)one-electron excited (19) Huang, T.; Rieckhoff, K. E.; Voigt, E. M. J . Phys. Chem. 1981,85, 3322. (20) Pariser, R.; Parr, R. G. J . Chem. Phys. 1953, 21, 466, 767. (21) Tomono, K.; Nishimoto, K. Bull. Chem. SOC.Jpn. 1976, 49, 1179. (22) Mataga, N.; Nishimoto, K. Z.Phys. Chem. (Munich) 1957, 13, 140. (23) Ohno, K. Theor. Chim.Acta 1964, 2, 219. (24) Weiss, C.; Kobayashi, H.; Gouterman, M. J. Mol. Spectrosc. 1965, 16, 415.
+
(25) Sekino, H.; Kobayashi, H. J . Chem. Phys. 1987.86, 5045. See also Sekino, H.; Kobayashi, H. J . Chem. Phys. 1981, 75, 3477. (26) McHugh, A. J.; Gouterman, M.; Weiss, C. Theor. Chim.Acta 1972, 24, 346.
1716 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Ohno et al.
TABLE I: Excited Sinelet States of Metallophthalocvanine Calculated bv the Models of Nishimoto (a). Nishimoto-Mataea (b). and Ohno (c) model aa ;/io3 cm-I
model b" t/103 cm-'
HGWC t/103 cm-'
model cL? f(p)b
;/io3 cm-'
f(p)b
f
obsd (PcAICl in EtOH) ;/io3 cm-' f
wave function 14.16 23.97 26.10 26.33 28.68 28.75 28.77 28.81 28.95 29.18 29.54 29.54 29.60
(a) lE,, = 0.96716e,,+2al,) + 0.24116e,,+-4a2,) + 0.06016e,+3a2,) - 0.03413bl,+-5e,,) + ... lBl, = 0.98913bIu+2alU)+ 0.08614b2,+4a2,) - 0.049~6eg,+4e8,) 0.04916eg,+4e,,) ... 1B2, = -0.99214b2,+2alu) - 0.053~6egy+-5eg,)- 0.05316e,,+-5e,,) + ... 2E,, = 0.89316e8,+-4a2,) - 0.23616e,,+-2al,) - 0.24616e,,+-3b2,) 0.19316e,,+-3azu) + ... 1A2, = 0.59916egy+-4eg,)- 0.59916e,,+-4e,,) + 0.29716egy+5egr) - 0.297(6e,+5e8,) ... lAl, = 0.676/6ep+-5e8,) + 0.676)6e,,+5eg,) - 0.124)6egX+-4e,) - 0.124~6e,,+-4e,,) + ... 2B2, = 0.500~6egy~4eg,) + 0.500~6e,,+4e,,) 0.480~6egy+-5eg,) 0.48016e,,+-5e,,) ... 3E,, = -0.821~6e,,+3b2,) + 0.38416e,,+-3a2u) - 0.28916e,+-4a2,) - 0.20217e,,+-2al,) + ... 2A2, = -0.63416e,,+-5egX) + 0.63416egx+5e,,) 0.25716egy+4eg,) - 0.25716e,,+-4egY) ... 2Bl, = 0.67916eg,+-4e,) - 0.67916e8,+4e,,) - 0.13516eg,+-5e,,) 0.13516e,,+-5e8,) + ... 4E,, = 0.73216eg,+3a2y) 0.420~6eg,+-2bl,) + 0.40917e,,+2aI,) 0.189)6e,,+-lal,) + ... 3B1, = 0.68916e8,~5e,,) - 0.68916e,,+5eg,) + 0.132~6e8,+4e8,) - 0.132)6egY+5e,,) ... 5E,, = -0.86317e,,+2al,) + 0.377(6e,,+-2bl,) + 0.24816e8,+-3b2,,) + 0.16816eg,+- 3a2,) + .
0.21 0.93 forbidden forbidden 0.89 2.10 forbidden forbidden forbidden 0.10 0.21 forbidden forbidden 0.000 0.002 forbidden 0.038 0.058
14.10 24.79 27.20 30.69 31.03 3 1.63 32.34 32.71 33.08 33.70 33.96 34.48 34.75
(b) lE,, = -0.94916e,,+-2al,) + 0.29116e,+-4a2,) + 0.05513bl,+-4e,,) - 0.052~3bl,+5e,,) + ... 1 BI, = -0.993)3bl,+-2al,) + 0.07914b2,+4a2,) - 0.03317em+5e,) 0.03317e,+5esy) + ... lB2, = 0.98514b2,+-2alu) + 0.100~3bl,+-4a2,) - 0.06516egy+-5e,) - 0.065(6e,+-5egY) ... 2 K x = -0.838~7egy+-2al,) - 0.31416egx+4a2,,) + 0.30116e,+-3b2,) - 0.26216e,,+3a2,) + ... 3Eu, = -0.69416e,+-4a2,) - 0.49817egY+-2a,,) - 0.344(6eg,+3a2,) - 0.23616e,,+2al,) ... lA2, = -0.888(5a2,+-2alu) 0.25416e,+5eg,) - 0.254~6e,,+-5e,,) + ... 2B2, = 0.52416eg,+5e,) + 0.52416e,+5egY) 0.41416e,,+-4eg,) + 0.41416e,+-4eg,) + ... 2A2, = 0.519~6egy+-5eg,) - 0.51916e,+-5egY) + 0.44815a2,+-2alu) + ... 4E,, = 0.63916e,+3b2,) + 0.47116e,+-4a2,) - 0.44916e,,+3a2,) + 0.238)6e,,+2bI,) ... lAl, = 0.51416e,+-Se8,) + 0.514~6e,,+-Se,,) - 0.39516eg,+-4e,,) - 0.39516e8,+-4e,,) + ... 2Bl, = 0.66816eg,+-4eg,) - 0.66816eg,+-4e,,) + 0.217~3b,,+lal,) + ... 3A2, = 0.52816eg,+-4e,) - 0.$2816e,+4e8,) - O.36116eg,+5e,) + 0.36116e,,+5e8,) ... 5E,, = -0.55016e,,+-3a2,) - 0.503)6e,,+2bl,) - 0.33616e,,+-3b2,) - 0.329~6egy+-laIu) + ...
0.15 0.92 forbidden forbidden 0.04 0.17 0.62 1.81 forbidden forbidden forbidden 0.23 0.74 forbidden forbidden forbidden 0.08 0.20
13.73 23.92 26.98 30.33 3 1.30 35.90 36.02 36.23 38.62 39.12 39.42 40.25 41.59
lE,, = -0.94516e8,+-2al,) - 0.28216eg,+4a2,) + 0.0S2~3bl,+-4e,,) - 0.06416e8,+-3a2,) + ... lBl, = -0.99613blu+2al,) + 0.06114bzu+-4aZu)+ 0.028(7e,,+-4e,,) - 0.028)7egY+-4e,,) + ... 1B2, = -0.97814b2,+-2alU) - 0.081~6egy+-5eg,)- 0.081~6e,,+5e,,) - 0.1 1913blu+4a2,) + ... 2E,, = 0.980~7egy+2al,) + 0.10816e,+3b2,) - 0.06716e,+3a2,) + 0.062~3bl,+-5e,,) + ... lA2, = 0.97515a2,+-2alu) + 0.11816e,+5eg,) - 0.1 1816eg,+-5e,,) + ... 2B2, = 0.540)6egy+5eg,) + 0.540)6eg,+-5e,) + 0.30516egy+4eg,) + 0.305~6e,,+-4e,,) + ... 3E,, = -0.64216egx+3a2,) + 0.59516e,,+-3b2,) + 0.32413bl,+-5e,,) - 0.19316ep+-4a2,) + ... 2A2, = 0.59516e8,+5e,) - 0.59516e,+5eg,) - 0.370(3b,,+3b2,) - 0.19615a2,+-2a,,) + ... 4E,, = -0.76916egX+-4a2,,) - 0.370)6e,,+-2bl,) - 0.23716e,+-3b2,) + 0.23516e,,+-2alu) + ... 1A,, = -0.49016eg,+-4e,) - 0.49016e,,+4e,,) + 0.31316e,+-5em) + 0.3 13)6e8,+-5e,,) + ... 2Bl, = -0.60116e,+4e,) + 0.60116eg,+-4e,) - 0.316~3blu+lal,) + ... 5E,, = 0.42816e,,+2blu) - 0.414~6egy+lal,) - 0.37516e,+-4a2") + 0.31314b2u+-5egx)+ ... 3A2, = 0.54416eg,+-4e,) - 0.54416e8,+-4e,,) + 0.39516e,,+-3egX) - 0.39516eg,+-3e,,) + ...
+ +
+ +
+
+
+
+
+
+
+
+ + +
+
+ +
+
+
+
(c)
0.14 1.09 forbidden forbidden 0.03 0.07 forbidden forbidden 0.03 0.11 forbidden 0.48 2.13 forbidden forbidden 0.17 0.55 forbidden
"The predominant configurations are given in parentheses. *The oscillator strengthsf(p) andf(d) are evaluated with the transition velocities and the transition dipoles, respectively. From ref 26.
excited configuration ](6e,+-4a2,) is an almost exclusive source of intensity of the B-band manifold, the oscillator strength evaluated from the observed total absorption intensity at around (25-32) X l o 3 cm-' is compared with the calculated. Figure 3(II) shows the absorption spectra observed with PcAlCl in ethanol and calculated by models a, b, and c. Model a well reproduces the observed spectrum including the benzenoid bands appearing in (40-50) X lo3 cm-'.26 Figure 2(II) shows the second-derivative absorption spectrum of PcAlCl in ethanol measured in the present work. The minima observed in the second-derivative
spectra correspond to the absorption maxima. In addition to the forbidden character bands at (17-18) X lo3 and (21-22) X lo3 cm-I, the second-derivative spectrum shows twin minima, at (23-24) X l o 3 cm-' in a weakly allowed band to the red of the B-band manifold. Model b predicts a weakly allowed excited state 2Eu cf = 0.04) at 30.7 X lo3 cm-' to the lower energy side of a manifold of 3E, cf = 0.62), 4E, cf = 0.23), and 5E, cf = 0.09) at 31.0 X IO3, 33.1 X IO3, and 34.7 X IO3 cm-I, but the calculated excitation energies are rather high compared with the observed. Model a reasonably characterizes the B-band manifold as a
Exciton Coupling in Bis(phthalocyaninato)tin(IV)
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1717
TABLE 11: Calculated Exciton-Coupling Interactions in the Phthalocyanine Dimer of D M Symmetry"
Coulomb interaction
exchange interaction
(6eh4afu14a;u6e:x) = -(6e&4atu14a!u6e:y) = (6ety4a&14a!u6eL) = (6ety4af.14a;u6e:y) = 446.7 cm-' -(6etx4afu12ayu6eL)= -(6etx4atu12ayu6eiy) = (6e~x2afu(4a!u6e~x) = (6etx2afu(4a!u6e:y) = (6ety4a$u12ayu6e:x)= -(6ety4afu(2ayu6e:y)= -(6ety2afu14a!u6eL) = (6ety2afu(4a!u6e:y) = 656.2 cm-' (6etx2af,,l2a~,,6e:J = -(6etx2afu12ayu6e:y) = (6ety2afu12ayu6eL) = (6ety2afu12ayu6e:y) = 920.1 cm-l
(6etx6eL14a!u4a$u) = -(6e$6e:y14a;u4afu) = (6ety6e:x14a!u4afu) = (6ety6e:y14a;u4afu) = 1 1.18 cm-' -(6etx6eL12ayu4a$u)= -(6eh6e:y(2ayu4afu) = (6etx6e:x14a;u2afu) = (6eh6e;y14a!u2afu) = (6etY6e:J2a~,,4afu)= -(6ety6e:y12a~u4afu)= -(6ety6eL14a!u2afu) = (6ety6e:y14a!u2afu) = 0.40 cm-' (6etx6e:x12a~u2afu) = -(6etx6e:y12a~u2at\,) = (6ety6e:x12ayu2afu)= (6ety6e:y12ayu2afu) = 28.86 cm-'
'Calculated by the model of Nishimoto (a) complex of 2E, (f = 0.89), 3E, (f = 0. lo), 4E, (f = O.OO), and 5E, (f= 0.04) at 26.3 X lo3, 28.8 X lo3, 29.5 X lo3, and 29.6 X lo3 cm-l being superposed by a sequence of underlying forbidden excited states. As Table Ia shows, there are forbidden (a,a*) excited states of Blp and B2, symmetry between Q and B bands and a series of forbidden excited states of A,,, A2,, Bl,, and B2, symmetry in the B-band manifold. These nondegenerate forbidden excited states can borrow their intensities by e, vibrational modes from the strongly allowed Q and B planar oscillators and give rise to B-term MCD extrema. A transition-state DV Xcu calculation of P c S ~ ( O H )which ~,~ can partly take into account the effect of excitation-induced countermigration of the electrons not directly involved in the excitation, predicts the (a,a*)electronic excitations '(6eg+2al,), ](6eg+4a2,), I(6eg+3b2,,), I(6e +3a2,) at 14.9 X lo3, 22.6 X lo3, 26.8 X lo3, and 28.5 X lo3 cm-9 and an (n, a*)excitation at 22.6 X lo3 cm-I, respectively. The method yielded a surprisingly good reproduction of the energies of the excited configurations without the use of the empirical parameters. The calculation concludes that the intensity of the (n, a*)transition is too weak to cause a broadening of the (25-30) X lo3 cm-I band, although the details of the calculation of spectral intensities are not given. The Q state of metallophthalocyanine can be described mostly by a single configuration '(6eg+-2al,) as concluded by the present calculation. However, the spectral profile of the B band can be reproduced by the configuration-interaction admixing of closely spacing excited configurations '(6eg+4a2,), i(7eg+2alu), I(6eg+3b2,), 1 ( 6 e g ~ ? a 2 uand ) , '(6eg+2bl,) but not by a superposition of the individual contributions of closely spaced but noninteracting excited configurations. These excited configurations of E, symmetry are symmetry-allowed but actually forbidden except '(6eg+4a2,), which is exclusively allowed. In such a situation, the interaction between the excited configurations does not result in sufficient admixing; however, the interaction redistributes the oscillator strength mostly originated from '(6e,+4a2,) between the interacting excited states and yields the diffuse B-band profile observed at -(25-32) X lo3 cm-I. The exciton-coupling interaction between the excited singlets I1(j+a)A), Ii(k+b)B) localized on partners A and B in the dimer is given by
+
( '(j+a)A(fili(k+b)B) = -(jAkB(bBaA) 2(jAaAlbBkB)
The lowest excited states of metallophthalocyanine are degenerate. Thus all the component interactions of the degenerate oscillators of Q and B bands in the dimer should be taken into account. Because of the small overlap between the a orbitals of two stacked phthalocyanines in an interplanar distance of 2.7 A,' (S,(C,C) = 0.09 and S,(N,N) = 0.04 for two coaxial carbon and nitrogen 2p, orbitals, respectively), an electrostatic interaction between two overlap charges (jAkB) and (bBaA)may be ignored. If it is the case, the exciton coupling is attributed to the Coulomb interaction (jAaAlbBkB) between two transition charges (jAaA)and (bBkB). The Coulomb interaction between two transition charges may be approximated by the interaction of two transition dipoles mA = (jAlm(aA)and mB' = (kB(mlbB)on partners A and B:
where RAB= R A - RE,RAB= (R-1, and R A and RB are the position vectors of two phthalocyanine centers in the dimer. The transition moments mA and m i are determined by the observed absorption intensities according to the relationship ~('(j+a)lm10)12 = (1.42189
X
10-3)J-c,a(ij) dij/ijja (au2)
where l'(j+a)) and 10) are the wave functions of excited and ground states, g is the degeneracy of the excited state, and are the molar absorption coefficient of absorption maximum at ijJa. The transition moments of Qo,o and B bands are evaluated from the Gaussian best fits of the observed with monomeric PcSnC12. Coulomb interactions of the transition dipoles predict the splittings 18.1 X lo3 and 18.9 X lo3 cm-' for the Q and B bands in the dimer, respectively. However, these are much greater than those observed in the Q and B bands, 3.1 X lo3 and 3.9 X lo3 cm-l. In the Q band the exciton coupling yields a weak band and an intense band around 13 X lo3 and 16 X lo3 cm-I, respectively. On the other hand, the exciton interaction results in a blue shift of the intense-component B band up to 30 X lo3 cm-I with a lower wavenumber tail for the weak-component B band extending to 22 X lo3 cm-' as presented in Figure 1B. The splittings of the Q and B bands in the dimer are calculated for the Coulomb interactions between the excitations localized on each partner on the basis of molecular-orbital calculation. The intermolecular overatomic Coulomb interactions between two partner Phthalocyanine molecules can be approximated by e2/ [2a + R], $/[a + R], or $/[a2 + R2]'I2. The splittings in the stacked dimer of Ddd symmetry were calculated as follows: 3.34 X lo3 cm-' (Q band); 4.39 X lo3 cm-' (B band) by e2/[2a R], 4.84 X lo3 cm-I (Q); 6.50 X lo3 cm-' (B) by e2/[a R], 8.35 X lo3 cm-' (Q); 7.88 X lo3 cm-' (B) by e2/[a2 + R2]i/2,respectively. The Nishimoto formula, which extensively takes into account electronic correlation effect, yields a good reproduction of t h e observed splittings: 3.1 X lo3 cm-' (Q) and 3.9 X lo3 cm-I (B). So far we have ignored the exchange terms (jAkBlbBaA) assuming that the overlap between the a orbitals of two stacked phthalocyanine moieties is less significant. The exchange terms are rewritten as a linear combination of the overatomic twoelectron interactions
+
+
J- J - x , * ~ ~ ~ x , * ~ ~ ) ~ ~drl~ dT2 / ~ =1 (p*rlsq*) 2~~,~~~xs~~ +
which are evaluated as a Coulomb interaction e2/[2a R(pr,qs)] (R(pr,qs) = IR,, - RqJ) of the overlap charges S,, and S,, placed at the midpoints of the p and r centers (R,,) and of the q and s centers (&J,respectively. The formula yields a good reproduction of the theoretical values. The overatomic exchange interactions of coaxial a oritals on the partners A and B are evaluated as = 0.045 eV and (NA*NBINB*NA)= 0.009 eV, (CA*CBICB*CA) while the corresponding STO-3G values are 0.090 and 0.023 eV, respectively. Thus the calculated Davydov splittings are corrected for the exchange interactions. The calculation on the Nishimoto formula results in the splitting of 3.26 X lo3 and 4.35 X lo3 cm-' for Q and B bands. This indicates the contribution of exchange terms is sufficiently small and negligible. Table I1 presents the calculated Coulomb and exchange interactions in the exciton (jAaA)bBkB) = {(mA'mB') - ~(~A.RA,)(~B"RAB)/RA~~)/RAB~ coupling.
Ohno et al.
1718 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 TABLE 111: Observed and Calculated Transition Diooles m and Oscillator Streneths f of PcSnCI,. PcAICI. and (PchSn ~ _ _ _ _ ~~
calcda
obsd
PcSnCI2
Q band
B band PcAlCl Q band B band ( P C ) ~ S ~ Q..band'
Q+ bandc B band
Iml/au
lmI2/au2
Im(p)l/aub
2.3 2.4 2.3 3.0 1.6 2.2 3 1
5.3 5.8 5.2 9.0 2.6 4.8
2.2 (2.2) 3.3 (3.0)
13.7
(1.8) (4.1)
obsd
Im(d)l/aub 4.6 (4.7) 5.1 (5.0)
(5.5) (8.0)
calcd'
f
f(P)d
0.24 0.48 0.24 0.79 0.10 0.20 1.25
0.21 (0.22) 0.89 (0.75)
0.93 (0.95) 2.10 (2.07)
(0.16) (1.50)
(1.46) (5.70)
a The values in parentheses were obtained by taking into account only the lowest one-electron excited configurations between 4a2,, 2al,, and 6egx,y - E,) instead of orbitals. *The transition dipoles m(p) were evaluated with the transition velocities according to m(p) -ihe('Cica)lB/m,l0)/(Ej those obtained by direct integration of m(d) = ( ' ( j ~ a ) l ~ e i l O 'Q) . and Q+ bands correspond to the lower and higher energy exciton Q band of (Pc)*Sn. dThe oscillator strengthsf(p) and Ad) were evaluated with the transition velocities and the transition dipoles, respectively.
Table 111 indicates the observed transition dipoles (m = and oscillator strengths cf = (4.319 X 10-9).f5a(F) d'v) of the monomer and dimer metallophthalocyanines with theoretically calculated values. The transition dipole moments can be evaluated by use of transition velocity ('(j-a)lp/m,lO) and also by direct integration of ('(j+-a)leilO). The calculated values given in Table 111 were obtained on the basis of molecular-orbital calculations by use of the Nishimoto interaction. The results obtained by means of transition velocity always give a good reproduction of the observed. As seen in Table 111, the observed intensity of the Q band attributable to each phthalocyanine moiety of the dimer is much reduced from that of the monomer, while that of the B band of the dimer exceeds than that of the monomer. The exciton coupling gives rise to a redistribution of transition moment between the Q and B states in the dimer. In fact, the sum (mQI2+ lm& attributable to each phthalocyanine chromophore is conserved; 10.6 au2 (dimer) and 11.1 au2 (monomer). The lowest excited states of metallophthalocyanine are predominantly described as single configurations '(6eg+2aI,) and I(6eg-4a2,,), whose transition moments are parallel and of comparable magnitude. The interaction between the Q and B excited states in the dimer increases the intensity of the higher energy component band (B band) in the face-to-face stacking conformation. In the case of metalloporphyrin, the first-order configuration interaction between the lowest two excited configrations in accidental degeneracy whose transition moments are parallel and of comparable magnitude yields the forbidden Q and allowed B excited states in the monomer. Thus the coupling in the dimer between the weak Q and strong B oscillators yields no appreciable increase in the resultant intensity of the B band even in a stacking conformation. Figure 4 shows the exciton splitting energies calculated with varied orientational angles of stacking phthalocyanine molecules from D4d to D4,,symmetry. The calculations on the molecularorbital basis can reproduce fairly well the observed exciton coupling but give the values slightly altered with the conformation. However, the dipole-dipole interaction model yields an identical value of splitting regardless of whether the dimer is in D4hor D4d conformation. The energy of charge-resonance transition between phthalocyanine molecules in the dimer was also calculated on the same principle applied to the exciton coupling in the present work. The energy of the excited state that arises from the intermolecular charge transfer from the orbital laA) of partner A to the orbital liB) of partner B is given by ( l(j-a)lmlO))
ECR=
e(j)
-
+
€(a) - (aAaAbBjB) (i)(aAjBtjBaA)
B band
4 5 7
p
44
Q band
35
'I: 36 3 5
34
34
33
3 3
i3
3 2r 1
0
r 60
30
90
e / degree Figure 4. Exciton splitting energies calculated by varying the orientation angle (0) of stacking phthalocyanine molecules.
where 2 and 0 in (i) stand for the singlet and triplet states, respectively. The configuration interaction between the intermolecular charge transfer (lie) laA))and the counter chargetransfer (liA) laB)) excitations is given by
-
-
-(jBjAlaeaA)
+ (i)(aAjBFAaB)
However, these interactions as well as (aAjeueaA)could be ignored because of the vanishingly small interaction between two overlap charges. The energy of the lowest charge-resonance state was evaluated on the basis of the Nishimoto approximation to be 10.6 X lo3 cm-I in the dimer of Da symmetry with a stacking distance of 2.7 A. It should be noted that the calculated charge-resonance state is lower than the lowest excited singlet in the phthalocyanine dimer and the lack of fluorescence in the dimer is attributable to a rapid relaxation in this particular low-lying charge-resonance state (with closely spaced singlet and triplet components) which cannot be detected by absorption and emission measurements because of the dipole-forbidden nature. In contrast with the phthalocyanine dimer, the p-oxo-bridged porphyrin dimers such as ( T P P S C ) ~(TPPA1)20,7 ~,~ and (TPPNb)2038emit rather intense fluorescence from the lowest excited singlet. The calculation on the same principle as applied to the phthalocyanine dimer predicts the charge-resonance state of the oxo dimers in a 4.7-A interporphyrin distance at 18.5 X lo3cm-I, which is higher than the lowest excited singlet at 17 X lo3 cm-I. Registry No. (Pc),Sn, 12581-75-8.
