J. Phys. Chem. 1991, 95, 197-204
197
CIDNP and C IDEP Studies on Intramolecular Hydrogen Abstraction Reaction of Polymethylene-Linked Xanthone and Xanthene. Determination of the Exchange Integral of the Intermediate Biradlcals Kiminori Maeda,* Masahide Terazima, Tohru Azumi,* Department of Chemistry, Faculty of Science, Tohoku University, Sendai 980, Japan
and Yoshifumi Tanimotot Faculty of Pharmaceutical Sciences, Kanazawa University, Takara-machi, Kanazawa 920, Japan (Received: May 14, 1990)
Hydrogen abstraction reaction of a polymethylene-linkedsystem is investigated by using chemically induced dynamic nuclear and electron polarization (CIDNP and CIDEP) methods. The reaction scheme is determined from the CIDNP and CIDEP spectra of the unlinked xanthene and xanthone system. The exchange integral J between the two terminal radicals of the system is obtained from the simulation process by using the spin-correlated CIDEP theory modified with (a) the fast population relaxation between the central S-To mixed states, (b) the contribution from the triplet mechanism, and (c) hyperfine line dependent line width. The mechamism of the fast population relaxation and the dependence of the J value on the temperature and polymethylene chain length are discussed.
1. Introduction Since biradicals can be model systems of intermediate species of photochemical reactions, the nature of biradicals has attracted considerable attention recently. The mechanism of spin dynamics, the chain dynamics, the reactivities, and the exchange interaction between the two terminal radicals have been extensively studied by various methods, such as transient absorption,l magnetic field effect,, CIDEP,3 and CIDNP.4 The biradicals that have been investigated so far, however, are restricted to those created by Norrish type I photocleavage of cyclic On the other hand, for aromatic type biradicals, reaction scheme, magnetic properties, and spin dynamics remain unclear. In previous we have investigated the exchange interaction of biradicals created by the hydrogen abstraction reaction of xanthone from xanthene, a-(xanthene-2-carbonyloxy)-w-(xanthene-2-carbonyloxy)alkanes (referred hereafter to as XO-n-XH,; n = 2-6, 8 , IO, 12), by using the magnetic field effect on the biradical lifetimelOJ' and CIDEP method.12 During the course of the investigation, we have found that the CIDEP spectrum of the biradical from XO-1 2-XH2 should be interpreted by the spin-correlated radical pair CIDEP model proposed by Buckley et alei3and Closs et aI.l4 with a very fast population relaxation between the central two S-To mixed states.I2 The exchange integral (J)between the xanthyl radical (XH) and the hydroxyxanthyl radical (XOH) determined from the CIDEP spectrum at -60 O C is in the range 0 mT < -J < 0.18 mT. However, there remain several questions. First, the simulation spectrum could not be perfectly fitted to the observed spectrum at that time,12 and the origin of the distortion has not been understood. Second, whether or not the J value depends on temperature has not been clarified. Third, from the magnetic field effect on the biradical lifetime, the, dependence of the J value between the two terminal radicals (XOH and XH) on the chain length has been obtained qualitatively.I0 It has not been clear whether the chain length dependence of the J value can be measured quantitatively from the CIDEP spectrum. In this paper, first we try to clarify the reaction scheme of the hydrogen abstraction reaction of unlinked XO from XH, by using both the CIDEP and CIDNP methods. Second, on the basis of the results of the unlinked XO and XH2 system, the reaction scheme and the CIDNP spectrum of the linked XO-n-XH2 are interpreted. Third, the CIDEP spectra of XO-n-XH, !n = 3, 6 , 8, 12) are analyzed by considering the triplet mechanism in the
'
Present address: Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan.
biradical system and the hyperfine dependence of the line width. Fourth, from the simulation process, the J value between X H and XOH is determined a t various temperatures and for molecules of various chain lengths. Fifth and finally, the mechanism of the fast population relaxation in the spin-correlated CIDEP is discussed.
2. Experimental Section The experimental method is similar to that reported previou~ly.'~ Briefly, for the CIDNP experiments, a 100-MHz FT-NMR spectrometer (JEOL FX-100) was used. Samples were irradiated by a 500-W ultrahigh-pressure Hg arc lamp from one side of the NMR probe. The diameter of the sample tube was 5 mm. The solution was deoxygenated by the nitrogen-bubbling method. CIDEP studies were carried out on an Ar-bubbled solution by using a flow system and an excimer laser (XeCI, 308 nm) as a light source. The CIDEP apparatus and flow systems of the solution were similar to those reported by Akiyama et a1.I6
(1) Johnston, L. J.; Scaiano, J. C. Chem. Rev. 1989, 89, 521. (2) Steiner, U. E.; Ulrich, T. Chem. Reu. 1989, 89, 51. Closs, G. L.;
Forbes, M. D. E. In Kinetics and Spectroscopy of Carbenes and Biradicals; Mathew, S. P., Ed.; Plenum: New York, 1990. (3) Closs, G. L.; Forbes, M. D. E. J . Am. Chem. SOC.1987, 109. 6185. (4) Kanter, F. J. J.; Hollander, J. A.; Huizer, A. H.; Kaptein, R. Mol. Phys. 1977, 34, 857. (5) Kanter, F. J. J.; Kaptein, R. J . Am. Chem. SOC.1982, 104, 4759. (6) Wang, J.; Doubleday, C.; Turro, N. J. J . Am. Chem. SOC.1989, 1 1 1 , 3962. ( 7 ) Wang, J.; Doubleday, C.; Turro, N. J. J . Phys. Chem. 1989, 93,4780. (8) Zimmt, M. B.; Doubleday, C.; Turro, N. J. J . Am. Chem. Soc. 1986. 108, 3618. (9) Tsentalovich, Y. P.; Yurkovskaya, A. V.; Sagdeev, R. Z.; Obynochny, A. A.; Purtov, P.A.; Shargodsky, A. A. Chem. Phys. 1989, 139, 307. (10) Tanimoto, Y.; Takashima, M.; Hasegawa, K.; Itoh, M. Chem. Phys. Lett. 1987, 137, 330. (1 1) Tanimoto, Y.; Takashima, M.; Itoh, M. Bull. Chem. Soc. Jpn. 1989, 62, 3923. (1 2) Terazima, M.; Maeda, K.; Azumi, T.; Tanimoto, Y.;Okada, N.; Itoh, M. Chem. Phys. Lett. 1989, 164, 562. (13) Buckley, C. D.; Hunter, D. A.; Hore, P. J.; Mclauchlan, K. A. Chem. Phys. Lett. 1987, 135, 307. (14) Closs, G. L.; Forbes, M. D. E.; Norris, J. R. J . Phys. Chem. 1987, 91, 3592. (1 5 ) Terazima, M.; Maeda, K.; Sugawara, M.; Takahashi, S.; Azumi, T. J . Chem. SOC.,Faraday Trans. 1990, 86, 253. (16) Akiyama, K.; Tero-Kubota, S.;Ikegami, Y.;Ikenoue, T. J. Phys. Chem. 1985,89, 339.
0022-365419 112095-0197%02.50/0 0 1991 American Chemical Society
198 The Journal of Physical Chemistry. Vol. 95, No. 1, 1991
Maeda et at.
Xanthene and xanthone were purified by recrystallization from ethanol. The method of synthesis of polymethylene-linked molecules (XO-n-XH,; n = 3,6, 12, 16) was published e1sewhere.l' Chloroform was used as solvent for the CIDEP experiments, and its deuterated compound was used for the CIDNP experiments. 3. Calculation Method of the Spin-Correlated Radical Pair CIDEP Spectrum 3.1. Effect of the Population Relaxation between the Central Two S-To Mixed States. In a previous paper,l2 we have shown that the CIDEP spectrum of the polymethylene-linked X H and XOH should be interpreted by the spin-correlated radical pair CIDEP theory and the fast population relaxation between the central S-To mixed states. The principle will be described briefly. Under the high-field approximation, the matrix elements of the spin-correlated radical pair spin Hamiltonian in the singlet-triplet basis are given by IT+)
'=(: /w-J
0
IT-)
ITo)
IS)
0 -J
O
Q
O 0
Q
J
0
0
0
-w-J
\
with
+ ab)
(2a)
Q = Y2(wa - wb)
(2b)
w
=
!!2(0a
where wa and wb are the frequencies of the ESR transitions of AH and XOH radicals, respectively. The eigenstates, I*"), and eigenvalues, w,, of the Hamiltonian are described as follows.
I*,)
= IT+)
= cos 61s) (q3) = -sin 61s)
WI
=-J+w
+ sin OITo) + cos BITo)
= IT..)
w4 =
w2 =
Q w3 = -Q
Q=J+Q
(4)
and tan 20 = Q / J (5) Under the assumption that the initial populations of the three triplet sublevels are equal and none in the singlet state, the populations of the eigenstates at time t are given byI2 (6a)
Y3
P2 =
y3 sinZ6 exp(-k,(cos2
0)t)
(6b)
P3 =
Y3 cosz 6 exp(-k,(sin2
0)t)
(6C)
p4
=
x
(64
where k, is the rate constant for the radical recombination from the singlet state of the biradicals. Because the intensity of the ESR line is represented by the product of the transition probability and the population difference between the states connected by the transition, the relative intensities are described by -Il2 =
I24
=
- I l 3 = 134=
y3 sin2 6(l - sin2 6 exp[-kr(cos2 O ) t ] l Y3 cosz 6(l - cos2 6 exp[-kr(sin2
(7a)
6 ) t ] ) (7b)
As discussed in the previous paper, the observed CIDEP spectrum
of XOH-n-XH cannot be reproduced by using this formula. We have assumed the fast population relaxation between the 9zand *3states; that is, the populations of the eigenstates are given by ( 17) Chemically Induced Magnetic Polarization; Muus, L. T.,Atkins, P. W., Mclauchlan, K . A., Pedersen, J . B., Eds.; Reidel: Dordrecht, 1977.
Y6
exp(-!hkrr)
(8b)
p3
=
1/6
exp(-!hkrt)
(8c)
=
x
(84
By use of these formulas, the observed CIDEP spectrum can be almost perfectly reproduced,I2 but still slight deviation remains. 3.2. Triplet Mechanism in the Spin-Correlated Radical Pair CIDEP Spectrum. The precursor of this hydrogen abstraction reaction is a triplet. In this case the polarization of the triplet sublevels in the precursor molecule may remain in the intermediate radicals. This is the triplet mechanism observed frequently in the conventional CIDEP spectrum. Although there has been no report on that mechanism in the biradical system, we try to interpret the net emissive component of the observed spectrum with using the triplet mechanism in the spin-correlated radical pair CIDEP. The net polarization due to the triplet mechanism in the spincorrelated radical pair CIDEP spectrum is taken into account in a similar way as the case of the conventional CIDEP mechanism. According to the theory proposed by Wong et a]., the populations of the 9,and q4states under the participation of the triplet mechanism are given byI8
(3c) (34
=
Here we neglect the small difference in the Boltzmann population of the central two states. Then the relative intensity of each ESR line is given by
(3b)
-J - w
@a)
Y3
p2
p4
(3a)
where
PI =
PI =
P, =
y3
+a
(1 Oa)
P4 =
y3
-a
(lob)
In the simulation process, a! is used for a fitting parameter. 3.3. Hyperfine Line Dependence of Line Width. The effect of hyperfine line dependent line width is taken into account in the following way. According to the theory proposed by Carrington,19 the ESR line width is proportional to the term given by Aw
a
(PBBZk,+4 + CM;ab,@)(PLsB&4 I
+ CM/4+4) (1 1) I
where gab and aib are the anisotropic terms of g tensor and hyperfine coupling tensor, respectively, and MIis the eigenvalue of the nuclear spin. Since a& is proportional to the isotropic hyperfine coupling constant, a', for aromatic organic substances, the line width is given by Aw = A
+ B(xM;al) + C(xM;al)z 1
i
(12)
We used A , B, and C as the parameters to fit the calculated spectrum to the observed spectrum. This effect becomes apparent when the anisotropies in the g tensor and the hyperfine interaction fluctuate by the molecular Brownian tumbling, and these fluctuations induce the spin-spin relaxation effectively. 4. Results and Discussion 4.1. Unlinked Xanthone and Xanthene System. 4.1 .a. CIDEP Measurement. Figure la shows the CIDEP spectrum of xanthone and xanthene (0.01 M) in chloroform at room temperature recorded at 0.5 ps after the laser excitation. The observed emission/absorption (E/A) pattern is interpreted by the multiplet effect of the radical pair mechanism for the triplet precursor. No distortion from the E/A pattern indicates that the net polarization (18) Wong, S. K.;Hutchinson, D. A.; Wan, J. K.S.J . Chem. Phys. 1973, 58, 985. (19) Carrington, A.; Longuet-Higgins, H. C. Mol. Phys. 1962, 5 , 447.
Polymethylene-Linked Xanthone and Xanthene
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Magnetic f ield/mT Figure 1. ClDEP spectrum of the hydrogen abstraction reaction XO from XH2 in chloroform: (a) observed spectrum of 0.01 M XO and XH2 at room temperature, (b) simulation spectrum with fwhm = 0.03 mT, (c) observed spectrum of 0.02 M XO and XH2 at -10 "C,(d) simulation with fwhm = 0.03 mT and RPM:TM = 1:0.85.
due to the Ageffect of the radical pair mechanism and the triplet mechanism are both negligibly small under this condition. The observed spectrum.can be simulated in terms of two intermediate radicals, XH and XOH (Figure lb), with fwhm = 0.03 mT. For the simulation spectrum, the reported hyperfine coupling constants of the individual radicals are used.% The difference of the gvalues between XOH and XH is too small to be determined from the ClDEP spectrum. We used the same g value (2.00331) for the two radicals. The ClDEP spectrum indicates that the hydrogen abstraction reaction of XO from XH, is the only photochemical reaction for this system. At higher concentration of XO and XH2 (0.02 M) in chloroform, the CIDEP spectrum also shows E/A pattern but with additional net emissive character (E*/A) (Figure IC) at -10 OC. (20) Wilson, R. J . Chem. Soc. 1968, 13, 1581 (B). Davidson, R. S.; Younis, F. A. J . Chem. Soc., Chem. Commun. 1967, 826. Sevilla, M. D.; Vincow, G. J . Phys. Chem. 1968, 72, 3635. Lunazzi, L.; Mangini, A.; Placcucci, G.; Vincenti, C. J . Chem. Soc., Perkin Trans. 1972, 1700.
2
1 ppm
0
Figure 2. NMR spectra of xanthone and xanthene (0.01 M) in chloroform-d at room temperature: (a) before the light irradiation, (b) during the irradiation, (c) dark condition after about 1-min irradiation.
This feature does not depend on temperature between -10 OC and room temperature. Since every peak can still be assigned to the hyperfine structure of XH and XOH, the hydrogen abstraction reaction of XO from XH2 should be the dominant photochemical reaction also at this higher concentration. Therefore, the Ag effect of the radical pair mechanism in this radical pair system is revealed to be negligibly small from the symmetric E/A pattern of the CIDEP spectrum at 0.01 M (Figure la), and the emissive net polarization should come from the triplet mechanism. The appearance of the net polarization due to the triplet mechanism at this higher concentration can be explained as follows. The hydrogen abstraction reaction occurs from the triplet state of xanthone. The net polarization due to the triplet mechanism is expected to appear if the reaction rate is faster than the rate of the spin-lattice relaxation between the triplet spin sublevels. Under the dilute conditions (0.01 M), the reaction rate of the hydrogen abstraction is slower than that of the spin-lattice relaxation and the triplet mechanism does not appear in the CIDEP spectrum. The increase of the concentration causes more frequent collisions of xanthone and xanthene molecules. Therefore, the reaction rate is predicted to increase with the increase of the concentration. When the reaction rate becomes faster than that of the spin-lattice relaxation at the higher concentration, the triplet mechanism is expected to appear in the CIDEP spectrum. Figure Id is the simulation spectrum with the contribution of the triplet mechanism (45% relative to the radical pair mechanism). The appearance of the net polarization due to the triplet mechanism at the higher concentration will be a clue to the discussion of the net polarization of the polymethylene-linked system later. 4.1 .b. CIDNP Measurement. The CIDNP spectrum of the xanthone and xanthene system is shown in Figure 2. The peaks between 6 and 8 ppm are due to aromatic ring H, and they are too congested to be analyzed. Therefore, we focus our attention on the isolated peaks around 4 ppm. The singlet peak at 4.0 ppm (peak 3) is assigned to the methylene proton of xanthene. Peak 2, which does not show CIDNP and grows with the irradiation time, was assigned to the methine proton of dixanthene. At 4.15 ppm the enhanced absorption was observed (peak 1) and assigned to the methine proton of hydroxydi~anthene.'~~~' This enhanced absorption is due to the Ag effect in the radical pair theory. The Ag effect is proportional to the external magnetic field; hence, the appearance of the Ag effect, which cannot be observed in the ESR measurement (about 330 mT), is not surprising because of the higher external magnetic field (about 2.5 T) of N M R measurement. From the absorptive polarization of this peak, the sign of Ag value can be determined by using the Kaptein rule2Zas (21) Takacs, M.; Kertesz, P.; Toth, G.; Vajda, J. H. Arch. Pharm. 1976, 309, 735. (22) Kaptein, R. J . Am. Chem. SOC.1971, 94, 6251.
200 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 1
16 31 35 Irradiation time dependence of the three peaks of the CIDNP spectrum (Figure 2) around 4 ppm. Figure 3.
follows, although the information on Ag is unavailable from the CIDEP spectrum. Hydroxydixanthene is the geminate recombination product. The precursor of this reaction is revealed to be the triplet state from the CIDEP spectrum (vide supra). The hyperfine coupling constant of the methine proton is negatiye. Therefore, the g value of XOH should be greater than that of X H from the Kaptein rule.22 The time evolutions of those three peaks under the light irradiation are shown in Figure 3. The intensities of peak 3 (xanthene) and peak 1 (CIDNP of hydroxydixanthene) decrease, and that of peak 2 (dixanthene) increases with the irradiation time. When the reaction is completed (after 35 min), peak 1 disappears completely. This fact indicates that hydroxydixanthene is the unstable product. The similar instability of the recombination product between XH and hydroxysemiquinone radicals has been o b ~ e r v e d . ' ~Schonberg *~~ et al. have suggested the existence of the equilibrium between the product (hydroxydixanthene) and the reactants (xanthone and xanthene) with i r r a d i a t i ~ n .The ~ ~ disppearance of the hydroxydixanthene (Figure 3) supports their suggestion. 4.l.c. Reaction Scheme. On the basis of the CIDNP and CIDEP spectra described above, the reaction scheme for the hydrogen abstraction reaction can be summarized as shown in Figure 4. XO abstracts the hydrogen of ninth position of XH2 and forms the radical pair. The geminate recombination product from this radical pair shows CIDNP by the nuclear spin selective intersystem crossing and the spin selective recombination reaction.22 The escaped product (dixanthene) is observed with the NMR method. During the course of the diffusion process of the radical pair, CI.DEP due to the radical pair mechanism is created in XOH and XH. The geminate recombination product, hydroxydixanthene, is an unstable product which dissociates by the light irradiation. 4.2. Poiymethylene-Linked System. 4.2.a. CIDNP Measurement. (I) X012-XH2 The CIDNP spectrum of XO-1 2-XH2 in chloroform at room temperature is shown in Figure 5. An enhanced absorption is observed at 4.28 ppm, and this peak is safely assigned to the cage product between XOH and XH on the analogy of the CIDNP spectrum of unlinked xanthone and xanthene system (Figure 2). In contrast to the case of unlinked XH2 and XO system, the spectrum becomes broader after the long irradiation of light. The broadening may come either from polymerization of XOH-12-XH by intermolecular reaction or by various side reactions with the solvent molecule. However, the similarity of the CIDNP spectrum (Figures 2 and 5 ) indicates that the reaction schemes of the linked XO-12-XH2 and the unlinked XH2 and XO system are similar. (2) XO-6-XH2 and XO-3-XH2. Figure 6a is the CIDNP spectrum of XO-6-XH2 under the same conditions of Figure 5. At 4.3 and 3.7 ppm, two enhanced absorption peaks were observed. (23) Maruyama, K.;Otsuki, T.; Takuwa, A.; Arakawa, S. Bull. Chem. SOC.Jpn. 1913, 46, 2470.
(24) SchBnberg, A.; Mustafa, A. J . Chem. SOC.1945, 551.
Maeda et al. The polarization of enhanced absorption indicates that these peaks are due to the geminate recombination products. Further, since the intensity ratio of these two peaks is independent of the initial concentration of the sample, the possibility that these peaks are due to intermolecular reaction products can be ignored. Therefore, we conclude that there are two kinds of geminate recombination products. We regard these products as the stereoisomers shown in Figure 7. The fact that only one enhanced absorption peak is observed in the XO-12-XH2 case (Figure 5 ) may be explained by the difference of the stabilities of these stereoisomers. Probably, the long polymethylene chain allows the preferential formation of the stabler isomer. Figure 6b is the CIDNP spectrum of XO-3-XH2. Although the spectrum is similar to the spectrum of XO-6-XH2, the CIDNP intensity is more intense than that of XO-6-XH2. This is explained as follows. The CIDNP intensity is determined by the competition between the geminate recombination reaction and the nuclear spinjattice relaxation, and the collision frequency between XH and XOH is expected to increase with the decrease of polymethylene chain length. Therefore, the shorter the chain length is, the stronger the CIDNP intensity is expected. 4.2.6. CIDEP Measurement. The above-discussed CIDNP studies show that the main photochemical reaction mechanism of the polymethylene-linked molecules (XO-n-XH2) is the hydrogen abstraction reaction whose reaction scheme should be analogous to that shown in Figure 4. In the sections follow, we will determine the J value of these polymethylene-linked biradicals from the CIDEP spectrum. (1) XO-12-XH2. Figure 8a shows the CIDEP spectrum of XO-12-XH2 at -60 "C recorded at 0.3 ps after the laser irradiation. As discussed in the previous paper,I2 this CIDEP spectrum cannot be interpreted either by the conventional radical pair mechanism or by the triplet mechanism. The calculated spectrum based on the spin-correlated radical pair CIDEP m e c h a n i ~ m ' ~ cannot reproduce the observed spectrum either. We have found that the observed CIDEP sperctrum can be reproduced only when the populations of the \kk2and \k3 states are equal (P2 = P3).We may conceive of two possible origins for equal populations. One is the fast population consumption from the q2and \k3 states (P2 = P3 = 0), and the other is the fast population relaxation between \k2 and \k3 ( P 2 = P3 # 0). In the previous paper, we have denied the consumption mechanism in view of the finding that the observed spectrum cannot be simulated by using eqs 6 and 7 with the experimentally determined upper limit value of the geminate recombination rate constant (kr). Furthermore, we should point out that the former mechanism can be excluded by the observation of CIDNP. Under the high magnetic field, CIDNP is explained by S-To mixing mechanism, and the nuclear spin selective intersystem crossing between S and To states and the electron spin selective chemical reaction in the radical pair are responsible for the CIDNP. For the appearance of CIDNP due to the S-To mixing mechanism, the geminate recombination should compete with the radical scavenging by solvent or interbiradical reaction as a spin-sorting mechanism. Therefore, if the population of 92 and \k3 is consumed before the CIDEP measurement (0.3 ps after the laser excitation), the population of 9,and \k4 should be also empty (PI= P2 = P3 = P4 0). Then, CIDEP of XOH-n-XH should not be observed, and this prediction contradicts the experimental fact. On the basis of these considerations, we conclude that the fast population relaxation between q2and 93is the origin of the observed CIDEP spectrum. The mechanism of the fast population relaxation will be considered in section 4.3. The calculated spectrum, which takes account of the fast population relaxation (Figure 3 in ref 12), however, was not perfectly fitted to the observed spectrum. First, the spectrum shows the net emissive polarization. The net emissive polarization may arise either from the S-T- mixing or from the triplet mechanism. In several biradical systems, the net emissive polarization have been observed in CIDNP4 and CIDEP3 spectra and they are interpreted by the S-T- mixing. However, in this case, since the energy difference between S and T- states (-0.5 mT) is much smaller than the electron spin Zeeman energy (-330
-
Polymethylene-Linked Xanthone and Xanthene
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 201
L
I
fl sc
I
st&
L
L
C I-DEP , C-ID E P
a
IISC
I
.............h y
% CEO C I DNP
Figure 4. Reaction scheme of the hydrogen abstraction reaction of xanthone from xanthene.
b)
d)
I
1
1
I
9
0
7
6
I
,
I
I
I
5 4 3 2 1 CHEMICAL SHlF T/ ppm
I
0 9
6
7
6
Figure 5. NMR spectra of XO-12-XH2 (0.01 M) in chloroform-d at room temperature: (a) before the light irradiation, (b) during the irra-
5 4 3 2 1 CHEMICAL S H I F T / ~ P ~
0
diation. mT), the contribution of S-T-mixing to CIDEP is considered to be negligible. On the other hand, the net emissive polarization due to the triplet mechanism is observed in the free xanthone and xanthene system at higher concentration (0.02 M) (Figure IC) because of the fast hydrogen abstraction reaction compared with the electron spin-lattice relaxation. For the polymethylene-linked system, the distance between XO and XH, is much shorter than that of the free system of 0.02 M solution and the hydrogen abstraction reaction is expected to be much faster. Therefore, the triplet mechanism is more plausible for the origin of net polarization in the XO-n-XH, case. Second, even after subtracting the net polarization from the CIDEP spectrum, the spectrum shows distortion from the expected point symmetric pattern. We find that the distortion is interpreted by the hyperfine dependent line width. The unsymmetric pattern is satisfactorily interpreted by the hyperfine dependent line width. By taking account of all these effects (the spin-correlated radical pair CIDEP mechanism, the fast population relaxation, the triplet mechanism, and the hyperfine line dependent line width) as described in section 3, the observed spectrum can be reproduced well with -0.0 mT > J > -0.1 8 mT. For the magnetic properties of XOH and XH, the g value determined from the CIDEP spectrum of the free X.0 and XH, system and the hyperfine coupling constants of XOH and X H without the proton at the joint of polymethylene chain are used.20 The J value, the relative contribution of the triplet mechanism (a),and the parameters for line width ( A , B, C) are used for the fitting parameters. Figure 8b is an example of the simulation spectrum with J = -0.1 mT, A = 0.35 mT, B = 0.06, C = 0.03 mT-I, and a = 6.5
bl
I
I
I
I
9
0
7
6
I
1
,
I
5 4 3 2 CHEMICAL SHIFT/pp,
I
I
1
0
Figure 6. NMR spectrum of (a) XO-6-XH2 (0.01 M) in chloroform-d at room temperature: (a) before the light irradiation, (b) during the irradiation, (c) XO-3-XH2 (0.01 M) in chloroform-dat room temperature before the light irradiation, (d) during the irradiation.
Figure 7. Possible two stereoisomers of the recombination products from the intermediate biradical of XOH-n-XH.
202 The Journal of Physical Chemistry, Vol. 95, No. I, 1991
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. b)
in
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M a g n e t i c f ield/mT Figure 9. CIDEP spectrum of XO-12-XH2 (0.005 M) in chloroform: (a) observed spectrum at -10 OC and delay time 1.0 ps, (b) simulation spectrum with the parameters J = -0.26 mT, A = 0.28 mT, B = 0, C = 0 m T ’ , and a = 4.6 X 10”. L 326
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330
Magnetic field/mT Figure 8. CIDEP spectrum of XO-12-XH2 (0.005M) in chloroform: (a) observed spectrum at -60 OC and delay time 0.3 ps; (b) simulation spectrum for (a) with the parameters J = -0.1 mT, A = 0.35 mT, E = 0.06, C = 0.03 mT’,and a = 6.5 X 10”; (c) the observed spectrum at -60 “C and delay time 1 .O p s , (d) simulation spectrum for (c) with J = - 0 . 1 mT, A = 0.27 mT, E = 0.04 mT, C = 0.0 mT”, and a = 3.3 X X For the simulation process, we use k, = 0 s-l because the exact value of k , cannot be measured even by using the flash photolysis methods1*and, furthermore, the shape of the simulation spectrum does not depend on the value of k,. The k, value determines the absolute signal intensity, which we cannot measure. As a consequence of the condition of k, = 0 s-l, however, the absolute value of a determined from the simulation process does not have physical meaning. The finite value of a only means that the triplet mechanism exists in the spin-correlated radical pair CIDEP. When the different Jvalue is used, we should use different values for the other parameters ( A , B, C, a ) in order to reproduce the observed CIDEP spectrum. The agreement between the calculated and observed CIDEP spectra is very good. Since the emissive and absorptive peaks of the spin-correlated radical pair CJDEP cancel each other at small IJI. the signal intensity is expected to be small for small 14. Therefore, although the spectral shape can be reproduced with a rather wide range of J (-0.0 mT > J > -0.18 mT), we believe that the upper limit
of IJI is the most appropriate value for describing the CIDEP spectrum. Figure 8c shows the CIDEP spectrum recorded at 1 .Ops after the laser excitation at -60 OC. This spectrum is presented in order to see the delay time dependence. The spectrum becomes slightly sharper than that recorded at 0.3 p s (Figure 8a). Figure 8d is the simulation spectrum for the observed spectrum (Figure 8c; -60 O C , delay time 1.Ops). It is possible to simulate the spectrum with -0.0 mT > J > -0.18 mT. When we used J = -0.1 mT, the other parameters should be A = 0.27 mT, B = 0.04, C = 0.0 m T ’ , and LY = 3.3 X After 1 .O ps, the shape of the CIDEP spectrum does not depend on the delay time. Even at 3.0 ps, the CIDEP spectrum due to the radical pair mechanism and the triplet mechanism with J = 0 mT cannot be observed. The CIDEP spectrum at higher temperature (-10 “C)is shown in Figure 9a. The observed spectrum cannot be reproduced with the J value from -0.0 to -0.18 mT. For the simulation, we should use the larger absolute J value (-0.23 to -0.28 mT). Figure 9b is an example of simulation spectrum with J = -0.26 mT, A = 0.28 mT, B = 0, and C = 0 mT-’. At this higher temperature the hyperfine line dependent line width disappeared. This disappearance may be due to the effect of the very rapid molecular tumbling to average the anisotropies of the hyperfine coupling constant and the g value. Several relationships between the J value and the distance between the radical center have been r e p ~ r t e d . ~ ~ -Generally, ~’ the J value increases with the decrease of the distance. The fact that the J value increases with the increase of temperature indicates that the distance between the two radicals becomes small at high temperature. The shrinking of polymethylene chain at high temperature has been reported for diamagnetic molecules2* Flory et reported that the end-to-end distance of polymethylene chains depends on the viscosity, and several calculations (25) Kanter, F. J. J.; Sagdeev, R. Z . ; Kaptein, R. Chem. Phys. Lett. 1978, 58, 334. (26) Herring, C.; Flicker, M. Phys. Reo. 1964, 134, A362. (27) Shulten, K.; Bittl, R. J . Chem. Phys. 1986, 84, 5155. (28) Flory, P. J . Statistical Mechanics of Chain Molecules; Wiley: New York, 1969. (29) Flory, P. J.: Cifferi, A.; Chiang, R. J . Am. Chem. Soc. 1961.83, 1023.
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 203
Polymethylene-Linked Xanthone and Xanthene TABLE I: Upper and Lower Limits of IJI with Which the Observed ClDEP Spectra of XO-n-XH(n = 3,6,8, 12) Can Be Simulated" n temp/OC IJll,.,ImT IJl,,,,,ImT 3
-40
6
-60 -60
8
-40
12
-60 -10 -60
0.00 0.00
0.7 0.7
0.28 0.23 0.00 0.23
0.38 0.28 0.20 0.28 0.18
0.00
I
I
a)
.
ffl
n
a
326
327
328
329
330
M a g n e t i c field/mT
331
"All of the J values are negative.
also support the ~ h r i n k i n g . ~ ~For , ~ 'photochemical intermediate biradicals. Wang et aL6 have suggested the similar temperature dependence from the decay rate of the intermediate triplet biradicak6 Thus, although the temperature dependence of the end-to-end distance has been observed in several examples, we believe that this paper presents a new method to observe explicitly the temperature dependence of end-to-end distance for the intermediate polymethylene-linked biradicals. (2) XO-6-XH2 and XO-3-XH2. Figure 10a is the CIDEP spectrum of XO-6-XH,. The spectrum is broader than that of XO-12-XH2. The broadening may be explained by the short distance between the terminal radicals. If the radical-to-radical distance is short, the fluctuation of J due to the motion of polymethylene chain and the electron spin dipole-dipole interaction become large. The large fluctuation makes the CIDEP spectrum broad. Further, since the separation between the emissive and the absorptive hyperfine line due to the J splitting becomes large under the large IJI value, the large separation of the J splitting also contributes to the broadness of the CIDEP spectrum. Figure 10b is the simulation spectrum for the observed spectrum (Figure loa) of XO-6-XH2 ( J = -0.3 mT, A - 0.4 mT, B = 0, C = 0 mT-'). A similar calculated spectrum can be obtained with J = -0.28 to -0.38 mT. Figure 1Oc is the CIDEP spectrum of XO3-XH2and simulation spectrum with J = -0.6 mT, A = 0.3 mT, B = 0, and C = 0 mT-' (Figure 10d). We could also simulate the spectrum with -0 mT > J > -0.7 mT. 4.2.c. Chain Length Dependence of J . The upper and lower limits of J with which the observed CIDEP spectra of XO-n-XH, (n = 3, 6, 8, 12) can be simulated are summarized in Table I. As shown in the table, a rather wide range of J can be used to reproduce the CIDEP spectra and we cannot specify a single J value to characterize the molecule and the experimental conditions, such as temperature. Actually, in a solution phase, the J value should be distributed over a wide range depending upon the biradical conformation, which determines the distance between the terminal radicals. Therefore, the wide distribution of J is not unexpected. However, we consider that the biradical which possesses the upper limit of IJI in the table mainly contributes to the spin-correlated radical pair CIDEP, because the CIDEP intensity for the small IJ1 value should be weak as discussed in section 4.2.b. Table I shows that the upper limit of IJI decreases with the increase of the polymethylene chain length. Tanimoto et al.IO have reported that the magnetic field effect on the lifetimes of XO-n-XH2 (n = 2-6, 8, IO, 12) depends on the polymethylene chain length n. Chain length dependence has been interpreted by the increase of IJI with the decrease of n. Our interpretation of the ClDEP study also indicates that the IJ1 value increases with the decrease of the chain length. However, the dependence of the J value is not so remarkable to explain the large chain length dependence of the magnetic field effect on the biradical lifetime. The J value which is determined by the magnetic field effect and CIDEP method including that by the CIDNP method will be published elsewhere.32 4.3. Origin of the Fast Population Relaxation. In this section, the possible origins of the fast population relaxation between the (30) Abe, A,; Jernigan, R. L.; Flory, P. J . J . Am. Chem. SOC.1966, 88, 631. (31) Lal, M.; Spencer, D. Mol. Phys. 1971, 22, 649. (32) Maeda, K.; Terazima, M.; Azumi, T. To be published.
I
I 326
1
I
327
326
329
330
331
I 326
327
328
329
330
I 331
326
327
326
326
330
331
M a g n e t i c field/mT
wI
M a g n e t i c field/mT
M a g n e t i c f ield/mT Figure 10. CIDEP spectrum of XO-6-XH2 (0.005 M) in chloroform: (a) observed spectrum at -60 O C and delay time 1.0 ps, (b) simulation spectrum with the parameters J = -0.3 mT, A = 0.4 mT, B = 0, C = 0 m T ' , and a = 3.3 X (c) observed spectrum at -40 O C and delay time 1.0 ps; (d) the simulation spectrum with the parameters J = -0.6 mT, A = 0.3 mT, B = 0, C = 0 mT', and a = 4.9 X IO-).
-
-
central two S-To mixed states compared with that between the other states (\k] (\k,,\k3) \k4) are discussed. We consider that there are two possible candidates for the origin of the fast relaxation. FIrst, the very fast population relaxation is due to the large fluctuation of J and the small energy gap between the two states. If the spin-lattice relaxation is induced by the time-fluctuated Hamiltonian, the relaxation rate between states a and b is expressed by33
where 7, is the correlation time of the fluctuation of the perturbation, (dab is the frequency between the states a and b, and V a b is the time average value of (alV(t)lb). V(t) is the time-dependent perturbation which causes the population relaxation. This (33) Slichter, C. P. Principles of Magnetic Resonance; Springer-Verlag: Berlin, 1978.
204 The Journal of Physical Chemistry, Vol. 95, No. I, 1991
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the populations of the \k2 and \k3 states are equal according to eqs 6b and 6c. However, if there still remains coherence between the two states, the populations of qzand q3become unequal again
-
5. Conclusion The reaction scheme of the hydrogen abstraction reaction of xanthene from xanthone is determined by using the CIDNP and CIDEP methods. On the basis of the result!, the nature of the polymethylene-linked aromatic biradicals (XH-n-XOH) is investigated. The observed CIDEP spectra can be reproduced completely by the spin-correlated radical pair CIDEP theory with the very fast population relaxation between the central two S-To mixed states, the triplet mechanism, and the hyperfine dependent line width. Even after the sufficient long delay time, the CIDEP spectrum of the escaped radicals cannot be observed. From the simulation of the CIDEP spectrum, the value of the exchange integral (J)between X H and XOH is determined. The IJI value increases with the increase of the temperature and with decrease of the chain length.
time-dependent perturbation may be the exchange integral for the q2 q3relaxation and the anisotropic terms of hyperfine coupling and g tensor for the (qz,'P3) q4relaxation. The fluctuation is caused by molecular motion in the solution. Although we do not know the absolute value of (Vab),the fluctuation of J is expected to be larger than that of hfc and g tensors because the J value fluctuates exponentially with the radical-radical distance. According to the distribution calculation of the biradical conformation, we find that the J value can be fluctuated from 60 to 0 mT for XO- 1 2-XH2 when the distribution is divided into 20 segments with equal areas3* Therefore, the relaxation between \k2 and q3is expected to be much faster than that between the other states. Moreover, in the magnetic field of X-band ESR spectrometer (about 330 mT), the energy gap between \k2 and \k3 is several hundredths of the Zeeman energy of the radicals. Therefore, even if ( Vab)for q2 q3and \k, ('Pz,'P3) q4 are the same magnitude, the spin-lattice relaxation time between q2and J13 should be shorter than that between the other states as shown below. At -60 OC, the viscosity of chloroform is 1.7 mP. When we assume that the terminal radicals diffuse freely as the separated radicals (XO and XH) and that the diameter of the radicals is 3 A, the rotational correlation time ( T ~ of ) the radicals is calculated to about 7 X lo-" s by using Einstein's relation. By use of the energy gap (wab = 330 mT for q , (\k2,'kl) q4and Wab = 2 mT for q2 q3), T ~ and . eq 13, the relaxation process between q2and q3is predicted to be one-tenth as fast as that between the other states. From the lifetimes of the CIDEP signal, the spin-lattice relaxation time between (q2,q3 (\k4 is determined to -500 ns. Therefore, the relaxation time between and this rate is q2and \k3 is estimated about 50 ns, and this rate is fast enough for the observation of the CIDEP spectrum which is to be explained by the relaxation model even at 300 ns after the laser irradiation. The second possible origin of the fast population relaxation is the dephasing mechanism between the S-To mixed states at IJI = 0. When the distance between the terminal radicals is sufficiently large, the exchange integral can be neglected (14 = 0) and
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Maeda et al.
- -
- -
-
after the biradical comes back to the IJI > 0 region, where the spin-correlated radical pair CIDEP is created. On the other hand, if the coherence is lost at IJI = 0, the populations of Pzand q3 remain equal even after the J value becomes finite. According to the distribution calculation of the biradical c ~ n f o r m a t i o n , ~ ~ biradical should be in the IJI = 0 region almost of all the time. Therefore, it is not unexpected if the dephasing, which is usually faster than the spin-lattice relaxation, occurs at IJI = 0 within 0.3 p s after the biradical creation.
Acknowledgment. We are much indebted to Proffesor Y. Ikegami, Professor S. Tero-Kubota, and Dr. K. Akiyama of the Chemical Research Institute of Non-Aqueous Solutions, Tohoku University, for allowing us to use their CIDEP apparatus. We also express our thanks to Fujinomiya Research Laboratories of Fuji Photo Film Co., Ltd., for the gift of the sample. The present research was supported by a Grant-in-Aid for Scientific Research (No. 62430001) from the Japanese Ministry of Education, Science and Culture.
