2146
J. Phys. Chem. 1991, 95, 2146-2150
Pressure Effect on the Photoinduced Hydrogen Abstraction Reactions of Azanaphthalenes In Mixed Crystals of Durene Nagahiro Hoshi, Kimihiko Hara, Seigo Yamauchi,+and Noboru Hirota* Department of Chemistry, Faculty of Science, Kyoto University, Kyoto, 606, Japan (Received: August 15. 1990)
A pressure effect on the phosphorescence decay rate constants (kT) of quinoxaline and quinoline in mixed single crystals of durene-h14and durene-d14is observed up to 20 kbar. kT’s increase drastically under high pressure in the temperature region where measurable photoinduced hydrogen abstraction reactions are known to occur at 1 atm. This increase can be attributed to the enhancement of the reaction rate constants (km) of photoinduced hydrogen abstraction. The absolute values R and the slopes of the Arrhenius plots decrease as the applied pressure increases. The Arrhenius plots of kTR of ~ T increase at high pressures deviate from straight lines as they do at 1 atm, suggesting that tunneling remains important at high pressures. The pressure dependence of ~ T R ’ s can be explained reasonably well on the basis of the Siebrand model by taking account of the decrease of the tunneling distance and the increase of the vibrational energy of the low-frequency vibration with increasing pressure.
Introduction A number of studies on photoinduced hydrogen abstraction reactions in mixed organic crystals have been reported.’” In such systems, reactions occurring from excited triplet states cause drastic increases of the phosphorescence decay rate constants of the guest molecules in the high-temperature range. On the basis of the observation that the Arrhenius plots of the reaction rate constants deviate from straight lines and that large deuterium isotope effects are observed in the apparent activation energies, it has been suggested that tunneling plays an essential role in these reactions.’” When the tunneling distance decreases, the tunneling reaction rate constant is expected to increase drastically. By applying high pressure to a mixed crystal, one may expect to reduce the tunneling distance. If the phosphorescence decay rate constant (kT) is determined by the tunneling reaction rate constant, there should be a drastic pressure effect on kT. In fact, Beardslee and Offen reported a remarkable pressure effect on the kT of naphthalene in a mixed single crystal of durene.’ Recently, we suggested that the temperature dependence of kT in the naphthalene/durene system originally reported by Hirota and Hutchisons is due to hydrogen abstraction by triplet naphthalene from durene and that the pressure effect can be explained on the basis of the increased reaction rate constant caused by the decrease of the tunneling distance.6 In order to gain further insight into photoinduced hydrogen abstraction reactions in mixed organic crystals and to investigate the generality of the pressure effect on such reactions, we have studied the pressure effect on the reactions in azanaphthalene/durene systems. Pressure effects on reaction rate constants have been investigated extensively in liquid phase^.^*'^ There have been also some studies of pressure effects on tunneling reactions in solution,”J2 but a clear understanding of the pressure effect on a molecular level is difficult to obtain because of the lack of structural information in solution. In a mixed crystal where the orientation and the intermolecular distance of the reacting molecules are fixed, interpreting the pressure effect on the tunneling reaction is expected to be much easier than in solution. In this article, we first report the pressure effect on kT’s of quinoxaline and quinoline in mixed crystals of durene. Drastic increases of kT’sare observed by applying pressure in the temperature range where the measurable photoinduced hydrogen abstraction reactions occur at 1 atm. The increase of kT’S can be attributed to the increase of the reaction rate constants (kTR) originating from the decrease of the intermolecular distance. Arrhenius plots of ~ T R ’ s deviate from straight lines at high pressures as they do at 1 atm, indicating that tunneling remains
important at high pressures. Furthermore, it is shown that the slope of the Arrhenius plot decreases as the applied pressure increases. We next try to rationalize the observed pressure effect by calculating the km’s using the golden rule treatment proposed by Siebrand.I3 The observed trend of kTR can be explained reasonably well by the decrease of the tunneling distance and the increase of the vibrational energy of the low-frequency mode a t high pressure.
Experimental Section Quinoxaline (Qx) was purified by vacuum sublimation and quinoline (Q) by vacuum distillation. Durene-h,, (D’h14) was recrystallized from ethanol followed by column chromatography and zone refining. Durene-d14 (D-d,,) purchased from MSD Isotopes was used as received. Mixed single crystals were grown from melts containing about 0.1 mol % guest molecules by the standard Bridgman method. Pressure is applied with a high-pressure cell similar to Drickamer’s type l i 4 as described elsewhere.” It has two windows at 90’ and uses NaCl both as a pressure-transmitting fluid and as windows. The NaCl windows consist of three parts with different diameters, from the inside of the cell, 0.7, 1.2, and 1.7 mm diameter. The outer jacket is made of steel of nickel, chrome, molybdenum (SNCM) hardened to HRC 45-50. The inner cell is made of steel YAG 300 hardened to HRC 60. The carboloy pistons are jacketed with the SNCM jacket. The pressure calibration was based on the shift of the R , fluorescence line of ruby (1) Prass, B.; Colpa, J. P.; Stehlik, D. Chem. f h y s . 1989, 136, 187. (2) Prass, B.; Colpa, J. P.; Stehlik, D. J . Chem. fhys. 1988,88, 191, and
references therein. (3) Yamauchi, S.; Terazima, M.; Hirota, N . J . f h y s . Chem. 1985, 89, 4804. (4) Hoshi, N.; Yamauchi, S.;Hirota. N . J . Phys. Chem. 1988,92.6615. ( 5 ) Hoshi, N.; Yamauchi, S.;Hirota, N. J . fhys. Chem. 1990.94,7523. ( 6 ) Hoshi, N.; Yamauchi, S.; Hirota, N. Chem. fhys. Lerr. 1990,169,326. (7) Beardslee, R. A.; Offen, H. W. J . Chem. Phys. 1970, 52, 6016. (8) (a) Hirota, N.; Hutchison, Jr., C. A. J . Chem. fhys. 1967, 46, 1561. (b) Harrigan, E. T.; Hirota, N . J . Chem. fhys. 1968, 49, 2301. (9) Asano, T.; Le Noble, W. J . Chem. Reu. 1978, 78, 407. (IO) Sasaki, M.; Osugi, J. Yuki Gosei Kuguku 1983.41, 692. ( 1 1 ) (a) Isaacs, N . S.;Javaid, K.; Rannala, E. J . Chem. SOC.,ferkin Trans. 2 1978,709. (b) Isaacs, N. S.; Javaid, K. J. Chem. Soc., ferkin Tram. 2 1979, 1583. (12) Sugimoto, N.; Sasaki, M.; Osugi, J. J . Am. Chem. SOC.1983, 105, 7676. (13) Siebrand, W.; Wildman, T. A.; Zgierski, M. Z. J . Am. Chem. Sm. 1984, 106,4083, 4089. (14) Fitch, R. A.; Slykhouse, T. E.; Drickamer, H. G. J . Opt. SOC.Am. 1957,47, 1015. (15) Hara, K.; Katou, Y.; Osugi, J. Bull. Chem. Soc. Jpn. 1983.56, 1308.
‘Present address: Chemical Research Institute of Non-aqueous Solutions, Tohoku University, Katahira, Sendai, 980, Japan.
0022-365419 1 12095-2146S02.50,IO 0 1991 American Chemical Society I
,
1
Hydrogen Abstraction Reactions of Azanaphthalenes I.( kr/S" I
8
0
100-
I
I
0
A O
0 A 0 m
T/
0
c
0 0 A
1
A b
o
OA
. . .. . 04.mrrrA**z
0
-1
'2e *
0
-150 -100
-50
0
50 Ti%
Figure 2. (a) Pressure and temperature dependence of the phosphorescence decay rate constant (kT)of quinoline in durene-h,,: ( 0 )at 1 atm; (A)at IO kbar; ( 0 )at 20 kbar. (b) Pressure and temperature dependence of the phosphorescence decay rate constant (kT)of quinoline in durene-d14:( 0 )at 1 atm; (A)at IO kbar; (W) at 20 kbar.
m
1
TABLE I: Pressure DepeaaoaCe of tbe Phospbomcence Decay Rite Constant (kT)of Quinoxrline/Dureae (Qx/D) rad Quinollne/hvcae (QD) Qx1D-h Qxpd,, Q1D-h Qpdl4
i
0
I
I
59 11c Figure 1. (a) Pressure and temperature dependence of the phosphorescence decay rate constant (kT)of quinoxaline in durene-h,,: ( 0 )at 1 atm; (A) at 10 kbar; ( 0 ) at 20 kbar. (b) Pressure and temperature dependence of the phosphorescence decay rate constant (kT)of quinoxaline in durenc-d14: ( 0 )at 1 atm; (A) at IO kbar; (W) at 20 kbar. at 694.2 nm as determined at the NBS (0.75 cm-I/kbar). Mixed crystals were made into pellets of about 0.3 mm thickness. They were placed between the half cylinders of NaC\ single crystals and inserted into the sample hole of the high-pressure cell (3.2 mm diameter). NaCl has relatively low shear strength and acts as a reasonably good hydrostatic medium for optical purposes. In this system pressure is considered to be applied uniformly to a three-dimensional crystal.16J7 The tempertaure was controlled as follows. The high-pressure cell was surrounded by a Bakelite box to keep the temperature constant. Liquid nitrogen was poured between the high-pressure cell and the Bakelite box to cool it down to -170 "C. Then, the high-pressure cell was warmed naturally to room temperature. The temperature is determined with an uncertainty of 1 1 OC below -50 OC and 10.5 O C above -40 OC. Above room temperature, hot air was blown into the holes made at the four comers of the high-pressure cell to raise the temperature. The temperature was monitored by a Cu-constantan thermocouple placed near the sample hole. Dry nitrogen gas was flowed to the NaCl windows to prevent condensation. Guest molecules were irradiated with a XeCl excimer laser (308 nm; 10 Hz)whose light was aligned strictly with the NaCl windows of the high-pressure cell. Phosphorescence emission was transmitted by an optical fiber, whose output was collected with convex lenses and guided directly into an EMI9502B photo(16) Maisch, W.G.;Drickamer, H.G. J. Phys. Chem. Solids 1958,5,328. (17)Jacobs, 1. S.Phys. Rcu. 1954, 93,993.
k,(l atm)/s-' k,(10 kbar)/s" k,(2O kbar)/s-'
-3OOC
-140OC
21.7 81.1
4.50
182
5.10
4.83
-10 OC -2OOC -140 OC 8.2 3.6 1.20 11 17 1.25 18 60 1.30
50 OC 7.1 45.4 66.9
multiplier. The phosphorescence decay rate constants were measured by using a mechanical shutter. The phosphorescence decays were stored in a Kawasaki Electronica MR5OE transient memory and averaged with a Kawasaki Electronica TMC700 averager system. Because of relatively weak phosphorescence intensities, the decay rate constants determined under high pressure are estimated to have uncertainties up to 20%.
Results and Discussion Figure 1 shows the pressure and temperature dependence of the phosphorescence decay rate constant (kT)of Qx in a single crystal of durene. In D-hl4, kT increases drastically as the applied pressure increases at temperatures above -100 O C where a measurable photochemical reaction occurs at 1 atm.s The values of kT at -30 O C and different pressures are given in Table I. On the other hand, the pressure dependence of kT is small at low temperatures (below -1 10 "C) where kT is independent of temperature and no measurable photochemical reaction occurs as seen from Table I. The temperature a t which the temperature dependence of kT appears shifts to lower values as the applied pressure increases (-60 "C at 1 atm, -75 O C at 10 kbar, -90 OC at 20 kbar). In D-dI4,the pressure dependence of kT is smaller than that in D-hI4. The values of kT at -10 OC are given in Table I. At low temperatures where no measurable photochemical reaction occurs, k+s in D-dl4 have almost the same values as those in D-hI4 at any pressure. Figure 2 shows the pressure and temperature dependence of kT of Q in a single crystal of durene. As is the case in Qx/D, the pressure dependence of kT in D-hI4is drastic in the temperature range where measurable photoinduced hydrogen abstraction occurs at 1 atm.s The values of kT at -20 O C are given in Table I. The temperature at which kT begins to increase moves down to lower
Hoshi et al.
2148 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 (a)
(a)
,
3.0
5.0
4.0
6.0 1'1,103~4
\
loll loo,
10.4 \
3.0
1
A'
4.0
5.0
I
6.0
3.0
1t1O3K1 Figure 3. (a) Arrhenius plot of the reaction rate constant ( ~ T R )of quinoxaline in durene-h14at 1 atm (0),at 10 kbar (A),and at 20 kbar (0). Solid lines show the results of the tunneling calculation. (b) Ar-
rhenius plot of the reaction rate constant ( ~ T R )of quinoxaline in durene-d14at 1 atm (O), at 10 kbar (A),and at 20 kbar (m). Solid lines show the results of the tunneling calculation. values as the pressure increases (-20 "C at 1 atm, -50 "C at 10 kbar, -70 O C at 20 kbar). The pressure dependence of kT in D-dl4 a t 50 O C is also given in Table I. At low temperature where no measurable photoinduced hydrogen abstraction occurs, kT's in D-h14 have almost the same values as those in D d 1 4 at any pressure. On the basis of the fact that the drastic increase of kT is observed in the temperature range where measurable photoinduced hydrogen abstraction occurs at 1 atm in both Qx/D and Q/D, the pressure effect on kT is considered to be due to the increase of the reaction rate constant (kTR). When a photochemical reaction occurs from a triplet state, the phosphorescence decay rate constant (k,) is written as
k~ = ~
+
T G ~ T R
where kTGand kTRrepresent the intramolecular decay rate constant and the photochemical reaction rate constant, respectively. By analogy with the case at 1 atm,u we regard km as temperature independent even at high pressures. From the temperature-independent kT at low temperatures, we set kTOof Qx 4.5 s-l at 1 atm, 4.83 s-I at 10 kbar, and 5.10 s-l a t 20 kbar. As for Q, kTG is set to be 1.20 s-I at 1 atm, 1.25 s-] at 10 kbar, and 1.30 s-I at 20 kbar. We subtract these kTG'S from kT'S to obtain kTR'S. Figure 3 shows the Arrhenius plots of these km's of Qx/D. As the applied pressure increases, the absolute value of km increases, but the slope of the Arrhenius plot decreases in both D-h14and D-dl4. The Values of k T R at -30 O C and different pressures are given in Table 11. The Arrhenius plots deviate from straight lines a t all pressures. Figure 4 shows the Arrhenius plots Of kTR'S Of Q/D. The pressure effect on k T R is qualitatively similar to that of Qx. The values of k T R at -30 OC are given in Table 11. The slopes of the
I
I
I
4.0
5.0
6.0
1 0 3 K1
Figure 4. (a) Arrhenius plot of the reaction rate constant ( k T R ) of quinoline in durene-h14at 1 atm (0),at 10 kbar (A), and at 20 kbar (0).
Solid lines show the results of the tunneling calculation. (b) Arrhenius plot of the reaction rate constant (kTR) of quinoline in durene-d14at 1 atm (O), at 10 kbar (A),and at 20 kbar (m). Solid lines show the results of the tunneling calculation. TABLE I 1 Pressure Dependence of the Reaction Rate Constant ( k m ) of Wnoxafim/Durew (Ox/D) and opinoliw/Durene (O/D)
km(l atm)/s-l kTR(10 kbar)/s-' kTR(20kbar)/s-'
QxID-hi4 Qx/D-d14 QID-hi4 QID-di4 -30 OC -30 OC -30 OC 50 O C 17.2 0.80 1.33 7.10 73.3 177
1.43 3.09
9.50 28.2
45.4 66.9
Arrhenius plots of Q are almost the same as those of Qx a t all pressures, which indicates that the orientation and intermolecular distance of Q in durene remain almost the same as those of Qx at high pressure. The Arrhenius plots again deviate from straight lines at all pressures. The deviation of the Arrhenius plots from straight lines is characteristic of tunneling.I8 It is therefore suggested that tunneling plays an important role in the photoinduced hydrogen abstraction in Qx/D and Q/D at high pressures as it does a t 1 atm. When pressure is applied to an organic crystal, the intermolecular distance generally decreases. Based on an X-ray diffraction study of a TTF-TCNQ crystal at high pressures, the intermolecular distance is estimated to decrease by about 0.2 A at 20 kbar.I9 If tunneling is important in the photoinduced hydrogen abstraction, a small decrease of the tunneling distance is expected to give rise to a decrease of the slope of the Arrhenius plot and a drastic increase of the reaction rate constant.I3 Our experimental results show these characteristics. We now try to calculate the pressure and temperature dependences of kTRusing the method proposed by Siebrand et al. which Caldin, E. Chem. Rm. 1969, 69, 135. (19) Filhof, A. Acto Crystollogr.1981, 837, 1225. (18)
The Journal of Physical Chemistry, Vol. 9S, No. 6, 1991 2149
Hydrogen Abstraction Reactions of Azanaphthalenes
TABLE 111: Panmeters Used in the Tunneling Calculation: (a) Quinoxaline/Durene, (b) QuinohdDurene
hw( C-H)/cm-I
hw( N-H)/cm-l AH/cm-' (a) Quinoxaline/Durene
Qx/D-h14(1 atm) Qx/D-d14(I atm) Qx/ D-h I 4( 10 kbar) Qx/D-d14(IO kbar) Qx/D-h 14(20kbar) Qx/D-d14(20kbar)
2770 2100 2770 2100 2770 2100
3090 2180 3090 2180 3090 2180
Q/D-hdl atm) QID-dl4(I atm) Q/D-h14(10kbar) Q/D-d14(IO kbar) Q/D-h14(20kbar) Q/D-d14(20kbar)
2770
3000 2120 3000 2120 3000 2120
16000 16000 16000 16000 16000 16000
hQ/cm-l
TD/A
J/cm-l
210 200 230 210 250 230
1.39 1.39 1.34 1.34 1.3 1.3
98 98 150 150 180 180
210 200 230 210 250 230
1.39 1.39 1.34 1.34 1.3 1.3
16 16 26 26 35 35
(b) Quinoline/Durene 2100 2770 2100 2770 2100
treats tunneling on the basis of Fermi's golden rule.', We present a brief outline of this treatment for the Qx/D system. The main vibrations that promote tunneling are assumed to be a high-frequency stretching vibration of hydrogen (x)and a low-frequency vibration of the lattice or the atomic group that includes the transferring hydrogen (A). By use of the wave functions of these vibrations, the reaction rate constant is given for a pair of vibrational levels of the reactant (0,V) and the product (w,W) as ~ T R , ~ . v .= ~.w
r is the reaction coordinate of the hydrogen and R is the distance between the C atom of durene and the N atom of Qx. and R are their equilibrium values, respectively. u and ware vibrational quantum numbers of the C-H modes in the reactant and product, respectively. Vand Wdenote those of the low frequency modes. J is an interaction operator that induces tunneling. J is assumed to be proportional to the overlap integral of the electronic wave functions of the carbon in durene and the nitrogen in quinoxaline between which the hydrogen transfer occurs and is written as
= J explS./ao(R - IRIM ' where {is an orbital exponent, a. is the Bohr radius, and li is the interaction at the equilibrium position. The density of states in the product ( p ) is represented by a Gaussian function. The reaction rate constants kTRu,v,w,w are summed over all the vibrational levels w and Wof the product to obtain the rate constant for a vibrational level u,V in the reactant. J
The observed rate constant is now given by a thermal average over u and Vlevels as
where Eu,vis the sum of the vibrational energies of the C-H and the low-frequency modes. The following parameters are used in the calculation. w(C-H) is the vibrational frequency of the C-H mode of durene. w(N-H) is the vibrational frequency of the N-H mode of the intermediate quinoxalinyl radical. These are calculated from the IR data and the orientation in the single crystal. AH is the exothermic energy of the reaction, which is calculated with the AM1 method20 (AMPAC QCPE No. 523). We fix these w(C-H), w(N-H), and AH in the calculation of kTR. R is the frequency of the lattice or the atomic group vibration that promotes tunneling. We assumed R to be the Ph-CH, bending vibration of durene. R and the other parameters, I and R, are varied so that the calculated klR's fit satisfactorily to the experimental values. The tunneling distance (TD) is equal to R - 2{, where { is the bond length of the C-H and N-H bond and is taken to be 1.1 A. The results (20) Dewar, M. J. S.;Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. Soc. 1905, 107, 3902.
16000 16000 16000 16000 16000 16000
of the tunneling calculations are shown by the solid lines in Figures 3 and 4. At any pressure, the experimental results are fitted quite well despite the crudeness of the model. We set parameter values as shown in Table 111. The changes of the values required to explain the pressure effect are considered to be reasonable as explained in the following. In both Qx/D and Q/D, we assume that the frequency of the intramolecular hydrogen vibration (o(C-H), w(N-H)) is pressure independent. This is reasonable because the applied high pressure increases the frequency of the intramolecular vibration much less than that of the lattice vibration.21 We calculated w's by using the IR data and the configuration of the guest molecules determined by ESR22 and ENDOR.23 For Qx/D-h14, w(C-H) = 2770 cm-' and w(N-H) = 3090 cm-I. For Qx/D-d14, w(C-D) = 2100 cm-I and w(N-D) = 2180 cm-I. Since the orientation of Q in a durene single crystal is not so different from that of Qx, we use w(C-H) = 2770 cm-' and w(N-H) = 3000 cm-' for Q/D-h14, o(C-D) = 2100 cm-l and o(N-D) = 2120 cm-I for Q/D-d14. AH is calculated with the AM1 method to be 16000 cm-l in both Qx/D and Q/D. Because AH is not considered to be pressure dependent, we set AH constant. The other parameters (R, TD, J) are considered to be pressure dependent. The frequency of the low-frequency vibration (Q) is assumed to increase slightly with pressure. Though R is assumed to be the Ph-CH, bending vibration of durene in the present model, some lattice vibrations are expected to contribute to the tunneling reaction in reality.I3J4 An applied high pressure usually increases the frequencies of such lattice vibrations.*' The calculation should reflect such an increase of the frequency. We set the following values: in D-hI4,R is 210 cm-I at 1 atm, 230 cm-I at 10 kbar, and 250 cm-I at 20 kbar. In D-d14, Q is considered to be less than in D-hi4 at all pressures, because the reduced mass of the vibration increases. T D should decreaes with applied pressure. T D is taken to be 1.39 A at 1 atm, 1.34 A at 10 kbar, and 1.3 A at 20 kbar. Because neither the lattice constants nor the geometries of the molecules in durene crystals have been studied under high pressure, the real values of T D cannot be obtained. The assumed reduction of TD is, however, considered to be reasonable on the basis of the fact that the net intermolecular distance of the TTF-TCNQ crystal decreases by about 0.2 A at 20 kbar.19 On the basis of the experimental result that the slope of the Arrhenius plot of Q is almost the same as that of Qx, the orientation of Q is assumed to be the same as that of Qx in a durene single crystal even at high pressure. Therefore, Q should have the same value of Q and TD as Qx. The tunneling interaction should increase with pressure, at the equilibrium position because the decrease of the intermolecular distance results in the
(a
(21) (a) Cottle, A. C.; Lewis, W.F.; Batchelder, D. N. J. Phys. Chem. 1978, 1 1 , 605. (b) Hangyo, M.; Itakura, K.; Nakashima, S.;Mitsuishi, A,; Matsuda, H.; Nakanishi, H.; Kato, M.; Kurata, T. Solid Sfofe Commun. 1986, 60, 739. (22) Vincent, J. S.; Maki, A. H. J . Chem. Phys. 1%1,39,3088; 1965.42, 865. (23) Blok, H.; Kooter, J. A.; Schmidt, J. Chem. Phys. L r r r . 1975, 30, 160. (24) Fuke, K.; Kaya, K. J . Phys. Chem. 1989, 93, 614.
2150 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
increase of the overlap integral of the electronic wave functions. Since host deuteration is not likely to affect TD and 3, we set TD and J equal in both D-h14and D-dI4. The pressure dependence of kTRcan be explained qualitatively as follows. When the intermolecular distance decreases at a high pressure, the overlap integral of the vibrational wave functions increases to give rise to a great enhancement of kTR. The overlap integral of the vibrational wave functions at a low energy level is enhanced more than that at a high energy level, so that the ratio of the tunneling reaction rate constants between the high and low energy levels decreases. This gives rise to a decrease of the slope of the Arrhenius plot at a high pressure. Furthermore, the vibrational energy of the intermolecular vibration contributing to tunneling increases at high pressures, which results in a decrease of the number of the vibrational levels within a certain energy range. This also gives rise to a decrease of the slope of the Arrhenius plot. Here we give a few remarks on the Siebrand model used in this calculation. This model assumes that only a single low-frequency vibration contributes to tunneling other than the vibration of
Hoshi et al. transferring hydrogen. This assumption is, of course, an oversimplification, because there can be other low-frequency modes that can promote tunneling in the examined temperature range.’T2 The fact that the calculated kTR’sunderestimate the experimental ones at low temperature (Figure 3) indicates that some vibrational modes with much lower energy may contribute to tunneling. Furthermore, anharmonicities of the vibrations were also neglected in the calculation and this is probably the reason why the tunneling distances required to fit the data are rather small. Despite these limitations, this model, however, can reproduce the pressure and temperature dependence of kTR reasonably well by ‘changing parameter values appropriately. It seems that this model represents the essence of the tunneling reaction. In summary, we can account for the drastic changes of the absolute values and the slopes of the Arrhenius plots of kTRin azanaphthalene/durene at high pressures on the basis of the tunneling reaction. Acknowledgment. We thank Dr. Tatsuhisa Katoh of our department for lending optical fibers.
