3402
J. Phys. Chem. 1980, 84, 3402-3408
Reactions of Thermal H Atoms at Cryogenic Temperature below 77 K as Studied by ESR. Competitive H Abstraction from C2H8and H I in Rare-Gas Matrices Hachiro Muto, Kelchl Nunome, and Machio Iwasaki" Government Industrial Research Institute, Nagoya, Hlrate, Kita, Nagoya, Japan (Recelved: September 17. 1979; In Flnal Form: July 10, 1980)
Previously we have reported that thermal H atoms easily abstract H from C2H6 at cryogenic temperature below 77 K contrary to the ordinary postulate. To elucidate the nature of the reactions in the low-temperature solids, we have carried out further studies. In the present work the trapped hydrogen (HJ and iodine atoms (I,) produced by 4.2 K photolysis of HI (0.015-0.75 mol 5%) in Xe matrices containing a small amount of C2H6 (0.13-1.28 mol %) both have been detected by ESR and it has been shown that the H atoms detrapped at 35-50 K after the photolysis competitively abstract an H atom from either or HI forming C2H5 or I atoms, respectively, without a loss of H atoms by the reactions with other atoms and radicals. Although HI is known to be a good scavenger of thermal H atoms at ordinary temperature, thermal H atoms effectively react with C2H6 giving the rate constant ratio, k(HI)/k(C2H6),of -2 at 50 K. The results suggest that the reactions of H atoms are strongly diffusion controlled in the Xe matrices. It is also suggested that, as the diffusion velocity of H atoms becomes faster at higher temperature, the reaction with HI becomes more and more competitive, giving a higher rate-constant ratio.
Experimental Section The samples of Xe (>99.9%),Kr (>99.9%), and C2H6 (>99.7%) obtained from Takachiho Shoji and DI (>99.9%) from Merck Sharp & Dohme were used without further purification. The sample of HI obtained from Tokyo Kasei Kogyo as aqueous solutions was distilled in a vacuum line after being treated with phosphorus pentoxide. Gaseous mixtures of Xe (Kr), C2H6, and HI (DI) were prepared in a vacuum line by repeating condendation and evaporation several times. They were introduced into an ESR tube, only the tip of which was immersed in liquid is further confirmed by H atoms trapped after 4.2 K nitrogen, and then the frozen samples were slowly dephotolysis of HI (0.15 mol %) in Xe matrices containing posited in the bottom of the tube by gradually elevating 0.75 mol 70 of C2H6; that is, the H atoms detrapped at the liquid nitrogen level. The rapid quenching of the ~ around 35 K react with CzH6 with the efficiency of ~ 7 0 % ~gaseous mixture gave essentially the same results for Xe In the latter case, however, the problem may arise from matrices. To check the homogeneity of the frozen mixthe question of why H atoms do not react with HI more tures, we also prepared the samples at 4.2 K to ensure more favorably, preventing the efficient formation of C2H5 berapid condensation. It is confirmed that the same results cause the activation energy (0.5 kcal/mol) of H abstraction are obtaiiiql quantitatively from the different methods of from HI (eq 2) at ordinary temperatures is very low as preparation for Xe (mp 161 K) mixtures. However, for the k(HU Kr (mp 116 K) matrices it was difficult to prepare hoH. HI I. + Hz (2) mogeneous samples at 77 K, and the better results were obtained from the samples frozen a t 4.2 K. In addition, compared with H abstraction from C2H6.S Even if the to ensure good thermal conduction and equilibrium during reaction at such a low temperature proceeds by the tunnel the thermal annealing at elevated temperatures and the pr0cess,4'~the reaction with a lower activation energy may subsequent ESR measurements at 4.2 K, we filled the be faster.6 However, if the reaction of H atoms in such sample tubes with helium to -0.5 atm at 77 K (or 4.2 K) low-temperature solids is diffusion controlled as we have before sealing them In checking the undesirable efalready suggested in our previous paper^,^^^^^ the situation fects of helium gas in the sample tubes, we further conmay become quite different. fumed that the results are the same as those obtained from To reach a proper understanding of the reactions of H the sample in an evacuated tube. The sample tubes used atoms in the low-temperature solids, we have further were of 4-mm diameter, and essentially the same results studied the behavior of H atoms and their competition were also obtained from the sample tubes of 2-mm diamreactions with C2H6and HI in rare-gas matrices below 77 eter. K. The results indicate that H-atom reactions in Xe The photolysis by 2537-A light from a low-pressure matrices are strongly diffusion controlled, giving a small mercury lamp (a conventional spiral type) was performed k(HI)/k(C&) ratio, although H atoms react with both in an insertion ESR Dewar, during which the sample tube C2HG and HI. This is further confirmed by the increase was rotated to ensure homogeneous decomposition of HI. of the signal from iodine atoms produced by reaction 2.9 The rate of the decomposition in the mixture containing The present results support our previous interpretation 0.15 mol % HI was estimated to be -1 X 10l6 spin rnin-l of the low-temperature irradiation effect in some alkanes per centimeter of height from the yield of trapped H atoms and their m i x t u r e ~ . ~ , ~ , ~ J ~ J ~
Hydrogen atoms produced by radiolysis or photolysis have long been postulated to be unreactive with alkanes at low temperatures if they are thermalized, because the activation energies of H abstraction by H atoms at ordinary temperatures are several kcal/mol. Contrary to this postulate we have recently obtained ESR evidence that thermal H atoms trapped at 4.2 K in CH4 containing 0.5 mol % of CzH6 efficiently abstract H from C2H6 forming C2H5 (eq 1) when they are detrapped at 10-20 K.lv2 This
+
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0022-3654/80/2084-3402$0 1.0010
0 1980 American Chemical Soclety
Competitive H Abstraction from C2H6 and HI
The Journal of Physical Chemistry, Vol. 84, No. 25, 1980 3403
0.5
c
Flgure 1. ESR spectra of the Xe/C2H6 (0.13 mol %)/HI (0.13 mol %) mixture measured (a) after 4.2 K photolysis for 8 min, (b) after annealing at 50 K for 1 min, and (c) after annealing at 77 K for 1 min. ESR measurementswere made at 4.2 K with the same gain using the microwave power of (3 pW and the modulation width of 4 G.
and ethyl radicals. Some of the experiments were also performed by using longer-wavelength light from the high-pressure mercury lamp (Ushio, 500 W). The rate of photolytic decomposition is -0.07 of the low-pressure mercury lamp. The ESR spectra were measured by a Varian E-12 spectrometer with 100-kHz field modulation. The signals from a single crystal of ruby mounted on the cavity wall were used as a monitor of the spectrometer conditions. The ESR spectra were digitized by a Nicolet 1070 signal averager and then transferred into a Hewlett-Packard 9825A computer, by which the double integration and other spectral analyses have been performed. The thermal annealings of the samples below 77 K were performed by pulling the sample tube up above the liquid-helium level in the insertion-type Dewar used for the ESR measurements. The annealing temperatures were measured by a Scientific Instrument 1875CK digital thermocouple. Because of the temperature gradient above the liquid-helium level and of the specimen size, the specimen temperature during the thermal annealing has a range of -&3 K at -30-50 K. The annealing at 77 K was performed by transferring the sample tube into a liquid-nitrogen Dewar, the requiring time for the transfer being less than 1 s.
1
L UVilbphation time
8dn
Flgure 2. Buildup of H, and C2H5 with illumination time. The buildup curves are normalized so as to give the same initial increase of y. The concentrations (mol YO)of c2H6 and HI in the Xe matrices are as follows: (A) 1.0 and 0.15; (0) 0.75 and 0.25; ( 0 )0.75 and 0.40; and (X) 0.13 and 0.13, respectively.
2ob;;:6
(b)
or
10
L
Results Initial Yields of Httrand C2H5. Shown in Figure l a is a typical example of the ESR spectrum obtained from Xe/C2H6 (0.13 mol %)/HI (0.13 mol %) after photolysis at 4.2 K for 8 min. The outer spectrum due to trapped H atoms (H,) exhibits superhyperfine structures arising from the coupling with lz9Xeand lalXe as is reported by Foner et al.12 The central spectrum is due to C2H5formed during the photolysis by the reaction of H with C2H6. The spectral interpretation will be given in a later section. The total yield of H, and C2H5 was nearly the same as the H, yield in Xe/HI ( O X 3 mol %) mixtures without C2H,. The rates of C2H5 and H, production both decrease with illumination time as shown in Figure 2. As the decrement of the Htr production is higher than that of C2H5, the relative yield of C2H5to H, increases with time. Therefore, the initial value of [C2H5]/([Htr]+ [C2H5])is plotted against the C2H6concentration in Figure 3a. As is seen, it increases linearly with the C2H6 concentration up to 1 mol %, the fraction of C2H5being less than 0.14 in this concentration range. It is to be noted that the slope of this linear relation is ind!ependent of the HI concentration up
2
5
0
-4 0
30
a
0.1
0.2rnol%
0.4
0.5 (HI)
0.7
Flgure 3. Initial yield of C2H5 vs. (a) C2H6 and (b) HI concentrations. The ordinate in (a) is the initial value of Yo [C2H5]/([H,]4- [C,H,]) interpobtedto zero iiiumination time. The ordinate in (b) is Yo/[C2H6], that Is,the slope of the llnear relation in (a). The concentrations (mol %) of C2H6 and HI In the Xe mixtures are as follows: (1) 0.13 and 0.13; (2) 0.2 and 0.dk (3) 0.75 and 0.75; (4) 0.75 and 0.4; (5) 0.75 and 0.25; (0) 1.0 and 0.15; (7) 1.28 and 0.013; and (8) 1.28 and 0.064, respectively.
to 0.75 mol % as shown in Figure 3b. ESR Spectra of Trapped I Atoms (Itr).As is already reported, I, produced by 4.2 K photolysis of HI in Xe matrices gives an ESR spectrum with a clear axial pattern which extends over 5000 G.9 It, in the Xe/C2H6/HImixtures gave a similar axial pattern with an increasing line width depending upon the C,H6 concentration. The initial I, yield estimated from the spectral simulation was only a few percent of [H,] + [C2H5]for the samples with [HI] = 0.015-0.4. Thiia is greatly short of the expected amounts, since the initial production of I atoms must be equal to that of H atoms, and further the additional I atoms are expected to be formed from reaction 2 during the photo-
3404
The Journal of Physical Chemistry, Vol. 84, No. 25, 1980
Muto et al.
(a)
[ [trJ
1
I
7'
0.51
\
/Vi 42
"
25
20
30
35
LO
11.0
fi
"'I
\
i 5 50 & ') annealing temperature
75 K
Figure 4. (a) The decay of H, (0)and the growths of C2Hs(0) and I, (X) in the Xe/C2Hs(0.13 mol %)/HI (0.13 mol %) mixture by the successive annealing at 20-77 K each for 1 min, where the initial yield of [Hb] [C,H,] Is normalized to 1.0 and the amount of [I,,] Is 50 K given in an arbitrary unit (see text). (b) Increments of C2Hs(0)and I ,(X) vs. decrement of H!, in the temperature ran e of 45-50 K. The 35 K ordinate, y, is the fractional Increase defined by![R] r - [R]~s]I{[RIso 0.4 1.0 [Hl]/[C2Hsl 2 .o [R]46), where [R] TI [R]4C, and [RISOare the amounts of C2HSor I,, at T , 45, and 50 K, respectively. The abscissa, x , is the fractional Flgure 5. (a) The efficiency of the hydrogenatom reaction wlth CAS decrease defined by W,L5- [HvlTJ4[H!,145- [H,,ld, where [&IT9 plotted against the [HI]/[C2He] ratio (0)at 50 K, (X) at 35 K, and (A) and [H+,lsOare the amounts of H, at T, 45, and 50 K, reat 77 K (see text). (b) A linear relation between en-' and the [HI]/ spectively. [C&ie] ratio (see eq 5 in the text). Ths concentrations (mol % ) of CAe and HI In the Xe mixtures are as follows: (1) 1.28 and 0.013; (2) 0.75 lysis. As will be discussed in a later section, we came to and 0.015; (3) 0.92 and 0.013; (4) 2.0 and 0.15; (5) 1.0 and 0.15; (8) 0.75 and 0.15; (7) 0.3 and 0.15; (8) 0.13 and 0.064; (9) 0.13 and 0.13; the conclusion that the species giving a clear axial pattern (10) 0.75 and 0.75; and (11) 0.2 and 0.4, respectlvely. is only a minority of the trapped I atoms. It is likely that
+
-
the spectra from the majority are smeared out by the incomplete and irregular quenching of the orbital angular momentum by the surroundings as has been postulated for a long time.l8 It was not possible to estimate the smeared spectral component over more than 5000 G by the integration of the entire spectrum. However, the ESR signal with the clear axial pattern could be used as a relative measure of the amount of I,, as will be shown in the following section. Reaction of Detrapped H Atoms with c2H6 and HI. When the sample was annealed at 35-50 K,14 the signal of Ht, decreased with the concomitant increase of the c2Hs signal. A typical example of the spectral changes is shown in Figure lb. The decay of Ht, and the growth of CZH, by the successive annealing for 1 min at each temperature from 20-55 K are shown in Figure 4 for the Xe/C2H6 (0.13 mol %)/HI (0.13 mol %) mixtures. It is clear that CzH6 is formed from the reaction of the detrapped H atoms with C2Hs. The efficiency of the reaction with CZH6, that is, the ratio of the increment of C,H, to the decrement of Hk, is dependent upon HI concentration as shown in Figure 5a. It is to be noted that the efficiency increases to 1.0 in the limit of zero HI concentration. This suggests that all of the detrapped H atoms react with CzHBwithout a loss of recombination. As shown in Figure 6, the signal of Itr also increased concomitantly with the decrease of Ha.In addition, the signals from C2H6and I,, increased with the same rate as that of the decrease of the H,, signal as shown in Figure 4b. This clearly indicates that the detrapped H atoms react not only with CzH6 but also with HI forming I atoms. Temperature Change of the Efficiency. When the thermal annealing is performed successively at each temperature, stepwise decay of Ht, starts at -35 K, and the prolonged annealing at 35 K is accompanied by the decrease of 10-15% of Htr. The decay rate of Htrsuddenly increases at -50 K, and H, decays out within 1min above
I 1000
t
,/I4
I
I 1500
(I_,
I
1
\ I , 2000 G
I
,
I'
I
Flgure 0. ESR spectra of I, atoms in the Xe/C2He(0.13 mol %)/HI YO)mixture measured (a) after 4.2 K photolysis for 8 mln, (b) after annealing at 50 K for 1 mh, and (c) after anneailng at 77 K for 1 mln. The three low-field hyperfine lines of the perpendicular component are given. The measurementswere made at 4.2 K with the same gain using the mlcrowave power of 10 mW and the modulation width of 4 G. (0.13 mol
50 K. Although there is a trend that the efficiency of the reaction of H with CzH6 at 50 K is slightly lower than that at 35 K, a marked lowering of the efficiency was not observed when the sample was annealed at 50 < T < 77 K in the helium atmosphere in the Dewar. Since the decay of the entire Ht, took place within 1min at temperatures above 50 K, it is likely that most of the detrapped H atoms
Competitive H Abstraction from C2H, and HI
reacted with C2H6 and HI before the thermal equilibrium was reached, giving an efficiency similar to that at 50 K. On the other hand, when the annealing was performed at 77 K in the liquid-nitrogen Dewar for 1 min by rapidly transferring the sample from the liquid-helium Dewar, marked lowering of the efficiency was observed as shown in Figure 5a. In this case, however, there is a possibility that a part of C2H5 was lost by the temperature rise above 77 K during the transfer, making the efficiency lower. In any event, it is not possible to raise the specimen temperature without passing through the intermediate temperature, so that there is a possibility that a part of the detrapped H atoms has reacted with C2H6 before the thermal equilibrium1is reached, making the efficiency still higher even in this case. For these reasons, it is difficult to obtain a reliable value for the efficiency at 77 K. We feel that the actual officiency would be considerably lower at 77 K if the instant temperature rise is achieved. Spectral Changes of It,. Shown in Figure 6 are the three low-field hyperfine lines associated with the perpendicular spectrum of Ikg There are at least two components in the Ib signal having slighitly different g values. The higher-field component with a narrower line width increases by thermal annealing at 35-50 K and then disappears at >50 K, leaving the lower-field component with a broader line width as shown in Figure 6. The results indicate that the higher-field componlent corresponds to It, produced by the reaction H + HI H2 + I. If the H2 molecule is trapped close to the I atoms, the strong axial field exerted by H2 may give rise to a well-resolved axial feature of the higher-field component of the I,, s p e ~ t r u m .Since ~ I,, giving the lower-field component and CzH5are stable even at 77 K, the disappearance of the higher-field component at >50 K does not always mean the decay of I,. When the I atom is trapped in the crystalline defect such as the substitutional vacancy with the absence of H2,weak perturbations which are slightly different from site to site may smear out the I,, spectrum because of the incomplete quenching of the orbital degeneracy of the I atoms.9J3 So, the disappearance of the higher-field component may be due to the escape of H2 above 50 K. The lower-field component might be ascribed to I,, formed by photolytic decomposition of HI. Although the origin of the axial field giving the lower-field component is not clear, one of the possibilities is photolysis of a dimeric HI giving I,, with a neighboring HI molecule. Spectral Change of C2HP In relation to the spectral change of I,, it may be noteworthy that the spectrum of C2H5 was also changed irreversibly by the annealing at temperature above 50 K, leaving the amount of C2H5 unchanged (see Figure 1c). Although the details will be given elsewhere,15the spectrum observed before the change can be interpreted in terrns of the CH3group which undergoes tunneling rotation at 4.2 K giving a typical splitting of the A and E lines.16 On the other hand, the spectrum after the annealing above 50 K is due to the conventional C2H5 radicals" in which the CH3 group undergoes classical hopping rotation giving the ordinary hyperfine structure. The irreversible change in the rotation of the CH3 group suggests that some chianges take place in the surroundings affecting the height of the hindering potential barrier of the CH3 group in C'ZHg. Since C2H5 is formed by the reaction H + C2H6*,.- H2 + C2HS,trapping of H2 close to C2H5and its escape a t >50 K might be the cause of this irreversible change. This is quite analogous to the spectral interpretation of the changes in the It, signals. Since the higher-field component of the I,, spectrum disappears simultaneouslyat the same temperature, it is plausible that
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The Journal of Flhysical Chemistry, Vol. 84, No. 25, 1980 3405
0.5
I / 0.5
(y,]
1.0
Figure 7. Fractionisl decay of D, vs. that of I-&in the Xe mixture containing both HI and DI. The thermal annealings were made in the temperature range of 50-55 K.
the changes in the environment result in the disappearance of the It, signal. Photolysis at 77 K. To obtain additional information on the H-atom reaction at 77 K, we have performed the photolysis of Xf?/CzH6 (0.75 mol %)/HI (0.15 mol %) under conditionri similar to those of the photolysis at 4.2 K using the same Dewar filled by liquid nitrogen. The results indicate that the initial C2H5 yield is -'/lo of that in the photolysis ,at 4.2 K. Although the spectra of Ht,were not detected, the It signal was observed when the spectra were measured at 4.2 K following the photolysis at 77 K. It is to be noted that the I,, spectrum obtained from the 77 K photolysis is only the lower-field component. This is consistent with the fact that the high-field component formed from H -t. HI reactions disappears at >50 K. The yield of I,, in the photolysis at 77 K is comparable with that a t 4.2 K followed by the annealing at temperatures above 55 K. This suggests that nearly the same number of H atoms are photolytically produced at 77 K as that at 4.2 K. If this is the case, C2H5 formed during the 77 K photolysis is only a few percent of the H atoms produced. Therefore, the efficiency of H abstraction from C2HG during the photolysis at 77 K is very small as compared with that of the reaction of the detrapped H atoms a t 50 and 77 K. Decay Rate of H and D Atoms in X e Matrices. The decay rates of H end D atoms were compared by using the sample containing both HI and DI simultaneously. Shown in Figure 7 are the relative amounts of Haand D,,measured after the successive annealing at -50 K. Although the decay rate of ]It,is slightly lower, a good linear relation in Figure 7 indicates that the mass effect in the decay rate is very small as is the decay of hydrogen atoms in frozen ice reported by Kroh and Plonka.18 They have interpreted this in terms of the detrapping process which is induced by the collapse of'the cage wall. If this is the rate-determining step of the decay process, the mass effect on the decay rate may not be observed. The same interpretation may be applicable to our case. The temperature a t which the decay of H,, and the increase of C2H5 lbecome remarkable in the Xe matrices is considerably higher (50 K) than that (10-20 K) in the CH4 matrices containing 0.5 mol % of C2H6as reported in our previous paper.l These results suggest that the decay rate of H,, (doesnot directly reflect the rate of abstraction but the rate of detrapping. Photolytic Decomposition of C2Hb Very recently Pacansky and Confallg have reported that ethyl radicals in Ar matrices decompose into C2H4 and H with X < 2800 A although the quantum yield is not so high. This gives rise to the problem thlat the reaction of detrapped H atoms with photolytically produced CzH4 might give C2HP To
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The Journal of Physical Chemistry, Vol. 84, No. 25, 1980
eliminate this possibility, we have examined the photolytic decomposition of C2H5 in Xe matrices by our low-pressure mercury lamp. Firstly, C2H5 was produced in the Xe/C21& mixtures X-irradiated at 4.2 K by the energy transfer from Xe to CzHg." Then, the sample was exposed to 2537-A light for 4 min. However, an appreciable decrease of C2H5 was not observed. Secondly, we have carried out the photolysis of Xe/C2H6/HI mixtures by our high-pressure mercury lamp with X > 2800 A. If the photolytic decomposition of CZH5 with X < 2800 A is appreciable, the relative yield of CzH5 to H,, obtained with X > 2800 A may be higher than that with 2537 A. However, we have obtained essentially the same relative yield with X > 2800 A. Thirdly, the Xe/C2H6/HI mixture photolyzed with 2537 8, at 4.2 K was brought to 77 K to produce ample CzH5, and then the sample was reexposed to 2537-A light at 77 K. Since the CzH5 yield by 2537-A photolysis at 77 K is very small as described in the foregoing section, the decrease of C2H5 must be observed by the reexposure at 77 K if the photolytic decomposition of CzH5 is serious. However, the decrease of CzH5 was not so remarkable for the duration of the reexposure of 18 min. From these results it is suggested that the photochemical decomposition of C2H5 is not so significant in our system. Kr/C2H6/HIMixtures. To examine the matrix effect on the reaction of detrapped H atoms with C2H6, we have carried out similar experiments using Kr matrices. It was then confirmed that the samples frozen at 4.2 K gave essentially the same results obtained from the Xe matrices. The initial C2H5 yield relative to H, and the efficiency of the reaction of the detrapped H atoms with C2H6 are nearly the same as those in the Xe matrices. Although the reason is not clear, the I, signal could not be detected in the Kr matrices. One of the possibilities may be in the lower yield of H2-It, complexes in the Kr matrices. It is noteworthy that the signal of H, shows superhyperfine structures with s3Kr similar to those reported by Morton et aL21 So, H, is considered to be trapped in the interstitial site. However, after annealing at 30-45 K, the ESR spectra of H, change into the ones having no superhyperfine structures. This suggests that the detrapped H atoms are retrapped in the different sites in which the interaction of H,, with Kr is weaker than that in the interstitial site. Since the lattice constant of Kr is smaller than that of Xe, only the hot H atoms with an excess kinetic energy may be able to occupy a small interstitial site (1.65 A) while the detrapped H atoms having no extra kinetic energy may not be able to occupy the intersitital site again and they are supposed to be retrapped in the preexisting substitutional defect (3.99 A). The spectral change of Ht, in Kr matrices gives clear evidence of a detrap and retrap process of H, during the thermal annealing.
Discussion Reaction of H Atoms during Photolysis. Although the main subject of this work is the reaction of detrapped H atoms with CzH6 and HI, information on the reactions of H atoms during photolysis at 4.2 K can also be extracted from the initial yield of H, and CzB5 as well as from their dependence on the C2H6 and HI concentrations. As shown in Figure 2, the rate of production of H,,and C2H5 decreases with illumination time. The measured spin concentration of the products indicates that the saturation is not due to the consumption of HI, Since the saturation of H, production with time is independent of the.HI concentration, the possibility of recombination loss (H + fi H2) of H atoms with increasing H-atom density is excluded. One of the possibilities is the increasing ab-
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Muto et al.
sorption of photons by the photolytic products such as I atoms. The saturation of C2H5 production with time is lower than that of H,, giving the increasing fractional CzH5 yield with time. This may be due to detrapping of H, to react with C2H6 during the prolonged illumination. Since the initial fractional yield of C2H5 is very small (0.14 or less), the increase of the fractional CZH5 yield during the prolonged illumination can result from the expense of only a minor part of Htr. The saturation of C2H5 production with time is dependent upon HI concentration and becomes larger with increasing HI, suggesting competition of HI and C2H6in the reaction of the detrapped H atoms. This is consistent with the reaction of detrapped H atoms at elevated temperature, as will be described in a later section. Now, H atoms produced by photolysis (2537 A) have initially an excess kinetic energy (at most 1.8 eV). If it is assumed that H atoms escaped from cage recombination in the photolysis site are thermalized and trapped after n collisions involving no CzH6 and HI and that the rest of the H atoms undergo hot abstraction forming CzH5 and I atoms, the probability of thermalization is (1- fin and that of forming C2H5is [1- (1- F)"]( f l F ) , where F is the total fraction of CzH6 and HI and f the fraction of C2Hs. Then, it is further assumed that the trapped H atoms react with neighboring CzH6 or HI if they are involved in the cage wall. Thus, the probability of forming H, becomes (1 - F)n+N and that of forming CzH6by thermal reactions is given by eq 3,8 where N is the number of neighbors N
(1 - F)n
c NC&l
i=l
-9N-i
(3)
surrounding H,, and it is assumed that H, reacts with HI exclusively when both CzH,and HI are involved in the cage wall. For small fractions of additives the fractional yield of C2H5, Yo,becomes YO= [C~HijI/([Htrl+ [C2H51) ( n + N)f (4) Therefore, Yoincreases linearly with C2H6 concentration. The experimental results shown in Figure 3a agree with this prediction. Equation 4 also suggests that the slope of this linear relation is independent of [HI] in agreement with the experimental results shown in Figure 3b. From the slope, n + N is estimated to be -14. Recently Miyazaki and his co-workers22have reported that H atoms photolytically produced from HI in Xe matrices are trapped in the substitutional site. Their results are based on the assumption that the superhyperfine couplings with Xe are isotropic. However, very recently Morton, Adrian, and their co-workers21have pointed out that the superhyperfine couplings are anisotropic, leading to the conclusion that H atoms are trapped in an octahedral interstitial site. On the other hand, C2H6 and HI are assumed to occupy the substitutional site because of their sizes. Thus, if Hh reacts only with the first neighbors, N = 6 , and, if €&reads with the second neighbors aa well, N = 14 for the face-centered cubic lattice of Xe. Since n is reasonably assumed to be a small number, the observed C2H5 fraction can be expected from the simple statistical model described above. Reactions of Detrapped H Atoms with c&3 and HI. As is discussed in the foregoing section, Ht, is supposed to be trapped in a site involving no C2H, and HI in the cage wall. Upon warming to 35-50 K, detrap and retrap of H atoms take place to encounter the additives. When H atoms are retrapped in a site involving c2H6 or HI in the cage wall, they abstract H, forming C2H5or I atoms, respectively. For small fractions of additives used throughout the experi-
Competitive H Abstraction from
CpH6and HI
ments, the probability of finding both c2H6 and HI in the cage wall is very small. Therefore, if the jumping rate from cage to cage is sufficiently slow, H atoms react with C2H6 or HI during their stay in a new cage giving the rate constant of diffusion control limit; that is, the k(HI)/k(C2H6) ratio is expected to be unity. As the jumping rate becomes faster at higher temperature, the probability of the reaction with c2H6 during a stay becomes lower than that with HI because of a large difference in activation energy. Thus, the k(HI)/k(C21-4)ratio increased with increasingjumping rate at higher temperature. The increase of the classical activated process in the abstraction reaction at higher temperature may also contribute to the increase of the rate-constant ratio. The lowering of the efficiency of the reaction with c2H6 with increasing HI. concentration in Figure 5a indicates that H atoms competitively react with HI and C2HG.If the reactions of H eitoms with other radicals and atoms are ignored, the efficiencyis given by eq 5. Neglecting a small
change in the concentration of HI by photolysis, we have plotted C H - ~against [HI]/[C2H6]to estimate the k(HI)/ k(CZH6) ratio. The experimental data lie on a straight line giving the rate-constant ratio of -2 at 50 K as shown in Figure 5b. The ratio close to unity indicates that the reaction of H[ atomci at 50 K in the Xe matrices is strongly diffusion controlled. The dotted line in Figure 5b corresponds to the reaction of the diffusion-controlledlimit with the unit ratio. The reaction at 35 K is very close to this limit, while the reaction at 77 K gives a ratio of 6, which might be the lowest limit, though, because of the reason mentioned before. The temperature change of the k(HI)/k(C2H,J ratio suggests that the jumping rate increases with increasing temperature in agreement with the prediction from the simple model given above. Since the concentrations of radicals and atoms are very much lower than those of additives, the reactions of H atoms with other radicals and atommi are less probable in such diffusioncontrolled reactions. The low C2H6 yield in the 77 K photolysis may be due to a higher k(HI)/rk(CzH6)ratio at 77 K resulting in the domination of the reaction with HI, although an increasing contribution from the recombination reactions with other radicals and atoms may not be disregarded. The k(HI)/ k(C2H6) ratio in the reaction of H atoms photolytically produced at 77 K may be considerably higher than that of the detrapped H atoms at 77 K after the 4.2 K photolysis, because the considerable amount of the detrapped H atoms is supposed to react with additives before the thermal equilibrium is achieved at 77 K. The initial CzH6 yield in the 77 K plhotolysis is of the order which is expected from hot restctions with a small value of n in eq 3. Thus, most of the H atoms produced are thermalized and are supposed to be scavenged by HI at 77 K. Miyazaki et al.23have reported that C4H9radicals are selectively formed when Xe/i-C4Hlo/HIare photolyzed at 77 K. It is, however, unlikely that H atoms produced by HI photolysis in Xe matrices selectively react with i-C4H10 without reacting with HI at 77 K. They have further assumed a long-range migration of hot H atoms to react with i-C4H10.22*23 However, judging from the spectra shown in Figure 2 of ref 22,,the C4H9radicals trapped during the 77 K photolysis seem to be only a few percent of the amount of H,,obtained from the 4 K photolysis. This is similar to our results obtained from the Xe/C2H6/HI mixtures at 77 K. A low yield of C4HBradicals in the 77
The Journal of Physical Chemistry, Vol. 84, No, 25, 1980 3407
K photolysis suggests that the assumption of an unusually long-range migr(ationof hot H atoms is not always needed. They have further studied 4 K photolysis of the same mixture and have examined the annealing effect of the sample at 77 H: to compare with their previous results obtained from the 77 K photolysis.22 Since a decrease of the C4H9radicalls was observed with the decay of H,, they have concluded that thermal H atoms do not react with i-C4H10 and rather disappear by recombination with other H atoms and radicals. Their results differ from those obtained by us ffrom the Xe/C&/HI mixtures, in which we have observed a clear increase of c2H6 by the annealing even at 77 K. We presume that in their experiments C4Hg radicals were once formed by the reaction of detrapped H atoms and then decayed out during the transfer of the sample, as is described in the foregoing section. We have also reexamined the Xe/i-C4Hlo/HI mixtures and have observed a clear increase of C4H9with the decrease of Htr.24926 On the basis of our preliminary results,l Willard and his co-workers= have recently interpreted the decay behavior of H, in 3-methiylpentane-d14and other glasses below 50 K in terms of tunneling abstraction by H, from the matrix molecules. In contrast to our case, the matrix molecules are reactive with1 H, in their case so that H, directly reacts with the surrounding molecules without being required to detrap. Therefore, the decay rate is independent of HI concentration in their case. Finally, it is concluded that the reaction of thermal hydrogen atoms in the rare-gas matrices at temperatures below 77 K is strongly diffusion controlled, giving an extremely smaller k(HI)/k(C2He)ratio than that expected from the rate-constant ratio in the gas- and liquid-phase reactions at ordinary temperature. This is consistent with our recent conclusion derived from the deuterium kinetic isotope effect in the hydrogen abstraction from C2H6 and C2D6 by thermal H atoms in Xe matrices.26 Acknowledgment. We thank Dr. K. Toriyama for her helpful cooperation and valuable discussions throughout the course of this study. We are also indebted to Dr. T. Kawamura of Kyoto University for a computer simulation of ESR spectra of randomly oriented iodine atoms.
References anld Notes Iwasakl, M.; Ttxlyama, K.; Muto, H.; Nunome, K. Chem. Phys. Lett. 1978, 56, 494. Toriyama, K.; Iwasakl, M.; Nunome, K. J. Chem. Phys. 1979, 71, 1698. Sulllvan, J. H. J. Chem. Phys. 1959, 30, 1292; 1962, 36, 1925. Le Roy, R. J.; Sprague, E. D.; Williams, F. J . Phys. Chem. 1972, 76,546. Hadam, R. L.; Shiotani, M.; Williams, F. Chem. Phys. Lett. 1977, 48, 193 and references clted therein. Toriyama, K.;IUunome. K.; Iwasaki, M. J. Am. Chem. Soc.1977, 99, 5823. Toriyama, K.; Iwasaki, M. J. Phys. Chem. 1978, 82, 2050. Iwasekl, M.; MI&, H.; Todyama, K.; Fukaya, M.; Nunome, K. J. Phys. Chem. 1979, 83, 1590. Iwasakl, M.; Torlyama, K. J . Phys. Chem. 1979, 83, 1596. Iwasakl, M.; Tcrlyama, K.; Muto, H. J. Chem. Phys. 1979, 77, 2853. Iwasaki, M.; Tloriyama, K.; Muto, H.; Nunome, K. J . Chem. Phys. 1976, 65, 596. Chem. Phys. Lett. 1976, 39, 90. Iwasaki, M.; Torlyama, K.; Nunome, K.; Fukaya, M.;Muto, H. J. phys. Chem. 1977, 81, 1410. Foner, S. N.; Cochran, E. L.; Bowers, V. A,; Jen, C. K. J. Chem. Phys. 1960, 32, 983. Jen, C. K.; Fonier, S. N.; Cochran, E. L.; Bowers, V. A. Phys. Rev. 1958, 172, 1169. The annealing temperaturesgben in our preliminaryreport' for the results obtalned from Xe/C,He/HI mlxtures are lower by 10-15 K as compared with those in the present work. The detrapplngtern perature of I-&seems to depend upon the conditions of the sample preparation. Ilowever, we have never experlenced such a low detrapplng tempratwe as 26 K for Xe matrices slnce thls prelkninary experiment. The Involvement of the accidental errors in measuring the annealing lnmperature might be more probable. Toriyama, K.; Iwasaki, M., unpublished work.
3408
J. Phys. Chem. 1980, 84, 3408-3411
(16) Freed, J. H. J. Chem. Phys.1985, 43, 1710. (17) For example, see McDowell, C. A.; Raghunathan, P.; Shlmokoshl, K. J . Chem. Phys. 1973, 58, 114. (18) Kroh, J.; Plonka, A. J. Phys. Chem. 1975, 79, 2600. (19) Pacansky, J.; Coufal, H. J. Chem. Phys. 1979, 77, 2811. (20) Bouldin, W. V.; Gordy, W. Phys. Rev. 1964, 135, A806. (21) Morton, J. R.; Preston, K. F.; Strach, S. J.; Adrian, F. J.; Jette, A. N. J. Chem. Phys. 1979, 70, 2889. (22) Kinugawa, K.; Miyazaki, T.; Hase, H. J. Phys. Chem. 1978, 8 2 ,
1697. (23) Miyazakl, K.; Kasugai,J.; Wada, M.; Kinugawa, K. Buii. Chem. Soc. Jpn. 1978, 51, 1676. (24) TOriyama, K.; Iwasaki, M.; Nunome, K. Int. Congr. Radtat. Res. 6th, 1979, Abstract p 176. (25) Adltya, S.; WIky, D. D.; Wang, H. Y.; Willard, J. E. J. Phys. Chem. 1979, 83, 599. Wang, H. Y.; Willard, J. E. IbM. 1979, 83, 258. (26) Torlyama, K.; Nunome, K.; Iwasakl, M. J. Phys. Chem. 1980, 84, 2374.
General Formulas for the Evaluation of the Valence Orbital Ionization Potentials for the K(2)L(8)3sm3p" Atoms and for the Lower Excited Configuratlons of the Flrst- and Second-Row Atoms Yoshlko Sakal and Toslnobu Anno" College of General Education, Kyushu lJnivers& Ropponmatsu, Fukuoka, 810 Japan (Received: March 26, 1980; In Final Form: July 21, 1980)
Formulas with which the 2s,2p, 3s, 3p, and 3d VOIP of any atom in any configuration of the type ls22sm2p"Xr (x = 3s, 3p or 3d; r = 0 or 1) (type 111) and the 3s, 3p, 3d, 48, and 4p VOIP of any atom in any configuration of the type K(2)L(8)3sm3pnx'(x = 3d, 4s, or 4p; r = 0 or 1)(type IV) may be calculated are obtained. The procedure adopted is a least-squaresfitting of all of the empirical data available on VOIP of atoms and ions with these configurations to quadratic functions of m,n, r, and the atomic number, in much the same way as was adopted in a previous work. The resulting formulas should be useful in predicting VOIPs of these atoms and ions for which direct evaluation is impossible for lack of experimental data. The formulas should thus facilitate the parametrization of the semiempirical molecular orbital theory and should be useful in locating the average energy of a configuration for which direct experimental values are unknown for lack of the experimental spectroscopic data.
I. Introduction
perimental spectroscropic data. Since the energy difference between a spectroscopicterm and the average energy In previous p a p e r ~ , l -we ~ have made an empirical of a configuration may be expressed in terms of the Slaanalysis of the 3d, 4s, or 4p VOIP (valence orbital ioniter-Condon parameters,13which may be calculated easily zation potential) of atoms4with the electron configurations if suitable forms of the atomic orbitals are assumed, this of the type K(2)L(8)3s23p63da4s@4py (type I) and the 2s means that the VOIP formulas should be useful even in or 2p VOIP of those with the ls22sm2pn(type 11) configlocating the spectroscopic terms unknown as yet experiurations and have derived general formulas for such VOIPs mentally and should facilitate the analyses of atomic of these atoms. In the present paper, the results of a spectra. similar attempt for the 3s and 3p VOIP of the K(2)L(8)Technical details of the present work will be described 3sm3pnatoms as well as for the VOIPs corresponding to in a supplementary report to be published elsewhere,14 the removal of an electron from various orbitals of the firstwhere some insight into the electronic structure of atoms and second-row atoms in their lower excited configurations and ions will also be discussed on the basis of various will be given. The formulas should be useful because the information on VOIP, all of which can be obtained from VOW is an important quantity in the semiempirical theory of molecular electronic structure, as was stressed b e f ~ r e . ~ ~our ~ VOIP formulas. It is true that the nonempirical methods for the molecular 11. Procedure electronic structure have progressed very much in recent The electron configurations of atoms and ions to be years6 and that general interests have waned in some of covered in the present work can be summarized either as the semiempirical methods such as the extended Hiicke17 ls22sm2pnxr(x = 3s, 3p or 3d; m = 0, 1, or 2; n = 0, 1, ..., and the Pariser-Parr-Pople methods: but semiempirical 6; r = 0 or 1) (type 111) or as K(2)L(8)3sm3pnxr(x = 3d, methods such as CNDO? IND0:O and MINDOll still have 4s, or 4p; m, n, and r range as above) (type IV). In the to be used especially in calculating large molecules of present work, formulas for the 2s,2p, 3s, 3p, and 3d VOIP chemical interest.12 The valence-state ionization potential of the type I11 atoms as well as those for the 3s, 3p, 3d, (VSIP) is one of the fundamental empirical data in the 4.9, and 4p VOIP of the type IV atoms are to be given. parametrization in some versions of the above-mentioned The form of the formulas to be obtained is expected to semiempirical theories,lZand the VSIP can easily be obbe of the following type tained from VOIP, as was described b e f ~ r e .Therefore, ~ the VOIP still remains an important quantity in eluciVOIP = B1 + Bzm + B3n + B4m2+ B5mn + B6n2 + dating the molecular electronic structure. (B, + Barn + B9n)Z' + B I J a + (Bll + Blzm + B13n + The VOIP is by definition a difference in average energy, Bl4r + B15Z?r (1) referred to the same energy reference, between a pair of configurations, so that the VOIP formulas may be used in from Slater's simple theory15 for the total energy of an locating the average energy of a configuration for which atom with the idea of a screening effect due to inner direct empirical values are unknown for lack of the exelectrons, in just the same way as was adopted previous1y.l2 0022-3654/a012084-3408~0 I ,001o
0 1980 American Chemical Society
