J . Phys. Chem. 1988, 92, 5123-5128
5123
Dissociation Dynamics of Energy-Selected Ion-Dipole Complexes. 2. Butyl Alcohol Ions Jian Dong Shao, Tomas Baer,* and David K. Lewist Chemistry Department, University of North Carolina, Chapel Hill, North Carolina 27599-3290 (Received: February 1 , 1988)
The thermochemistry and dissociation rates of energy-selected butanol ions have been determined by photoionization and photoelectron photoion coincidence spectroscopy. The appearance energies of m / z 56 from 1-butanol, m / z 44, 45, and 59 from 2-butanol, m / z 33, 42, 43, and 56 from isobutyl alcohol, and m / z 59 from tert-butyl alcohol have been determined from photoionization efficiency spectra. The dissociation rates of those channels have been examined, and those that involve the loss of the strongly dipolar water molecule have been found to be slow. These rates have been analyzed in terms of either single- or double-exponentialdecay. The slow rates are attributed to the long-range ion-dipole interaction potential, which is extremely anharmonic. The kinetic energy release of the methyl group loss of tert-butyl alcohol has been determined as a function of the ion internal energy. The average kinetic energy release was extrapolated to the dissociation limit from which new values of AHfoo(C3H70+) = 475 14 kJ/mol and AHf0298(C3H70+) = 453 f 14 kJ/mol were derived.
*
Introduction The conclusion derived from investigations of many gas-phase unimolecular reactions of energy-selected ions is that these reactions are by-and-large well accounted for by statistical theories,' such as the RRKM2 or the quasiequilibrium theory3 (QET). One reason for the statistical behavior is the strong coupling of the electronic states in radical cations, which aids the rapid internal conversion from any excited electronic state in which an ion is produced to the ground electronic state, thereby leaving the ion with all of its excess energy in the vibrational degrees of freedom. The agreement between the measured and calculated rates has been shown to be quantitative when reasonable vibrational frequencies for the ion and the transition state are chosen. Furthermore, it has been found that the simple harmonic oscillator approximation in calculating the density of vibrational states is sufficient for this purpose. Although most large ions dissociate statistically from the ground electronic state, there are a number of smaller ions, including CzF6+,4CH3C1+,Sand C2H5Br+,6that decay rapidly from the excited state prior to internal conversion to the ground electronic state. These are reactions to which the statistical theory cannot be applied because it does not involve vibrational predissociation. There is a class of dissociation reactions in which the ions dissociate from the ground state at a rate that is much slower than predicted with the usual statistical theory treatment. These are reactions in which the neutral fragment has a strong dipole moment. Examples are HCl loss from C2H5C1+,7HBr loss from 2-C4H9Br,*HzO loss from C3H70H+,9and H C N loss from CzH5CN+.Io In each case the activation energy is very small so that the predicted rates are higher than 1O'O s-l, while the measured rates are in the 1 0 6 d range. We have recently reportedg in detail the study of the H20 loss from C3H70H+and have suggested that the origin of the apparent "nonstatistical" dissociation rate lies in the long-range ion-dipole interaction potential, which is very anharmonic and thus supports an extremely large number of vibrational states. Under these circumstances the simple harmonic oscillator approach to calculating densities of states does not work. In addition, it was shown that the reaction can proceed only by coupling the internal energy into the rotation of the dipole such that the long-range 1/$ locked ion-dipole potential is averaged out. A detailed model for such reactions has not yet been advanced. We present here further evidence for the role of the ion-dipole interaction in the dissociation dynamics of ions involving the loss of a dipolar neutral fragment. To this end, the dissociation channels at low ion energies of four isomers of C 4 H 9 0 H +ions t Visiting Professor. Permanent address: Chemistry Department, Colgate University, Hamilton, NY 13346.
0022-3654/88/2092-5123!$01.50/0
(1-butanol, 2-butanol, isobutyl alcohol, and tert-butyl alcohol) are examined. Some of these ions are known to be metastable. The study includes the photoionization efficiency (PIE) curves for all the major low-energy fragment ions, the dissociation rates of the slow reactions as a function of the parent ion internal energy, and the measurement of the kinetic energy released in each dissociation. Our data will show that those dissociation processes involving the loss of the dipolar H 2 0 molecule are slow, even though the activation energy is very small.
Experimental Procedure The photoelectron photoion coincidence (PEPICO) measurements have been described in detail previo~sly.~l-'~ Briefly, the ions were produced by dispersed vacuum UV light in a gas cell filled to a sample pressure of about 2 X Torr. In the applied electric field, electrons and ions were accelerated in opposite directions. The electrons passed through a steradiency analyzer that transmits only zero-energy e1e~trons.l~The electron arrival signal was used to start a time-to-pulse-height converter, while the ion signal served as a stop signal. The ion time-of-flight (TOF) distribution was then collected on a multichannel pulse height analyzer. Mass spectra at various photon energies were taken with a quadrupole mass filter located between the photoionization region and the detector. The mass resolution was about 110 at m/z 74. In addition, photoionization efficiency spectra were collected for parent and daughter ions of these alcohols between 9- and 13-eV (1) Forst, W. Theory of Unimolecular Reactions; Academic: New York, 1973. Robinson, P. J.; Holbrook, K. A. Uni-molecular Reactions; WileyInterscience: New York, 1972. (2) Marcus, R. A,; Rice, 0. K. J. Phys. Colloid Chem. 1951, 55, 894. (3) Rosenstock. H. M.; Wallenstein, M. B.; Wahrhaftia- A. L.; Eyrina, . - H. Proc.' Natl. Acad. Sci. U.S.A. 1952, 38, 667. (4) Simm. I. G.: Danbv. C. J.: Eland. J. H. D. Int. J . Mass Soectrom. Ion Phjs.' 1974, i4,285. (5) Eland, J. H. D.; Frey, R.; Kuestler, A,; Schulte, H.; Brem, B. Int. J . Mass Spectrom. Ion Phys. 1976, 22, 155. Dunbar, R. C.; Kramer, J. M. J . Chem. Phys. 1973, 58,1266. (6) Miller, B. E.; Baer, T. Chem. Phys. 1984, 85, 39. (7) Tsai, B. P.; Werner A. S.; Baer, T. J . Chem. Phys. 1975, 63, 4384. (8) Oliveria, M. C.; Baer, T.; Olesik, S.;Almoster-Ferreira, M. A. Int. J . Mass Spectrom. Ion Proc. 1988, 82, 299. (9) Shao, J. D.; Baer, T.; Morrow, J. C.; Fraser-Monteiro, M. L. J . Chem. Phys. 1987, 87, 5242. (IO) Shao, J. D.; Baer, T., unpublished results. (1 1) Baer, T. Adu. Chem. Phys. 1986, 64, 111. (12) Butler, J. J.; Baer, T. J . Am. Chem. SOC.1980, 102, 6764. (13) Fraser-Monteiro, M. L.; Fraser-Monteiro. L.; Butler, J. J.; Baer, T. J . Phys. Chem. 1982,86, 739. (14) Baer, T.; Peatman, W. B.; Schlag, E. W. Chem. Phys. Lett. 1969, 4, 243. , I
I
0 1988 American Chemical Society
Shao et al.
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
5124
,I CH,CH,CH2CH,0H
/ \
-
CH,CH,CH,CH,OH*
-
C,H,+ + H,O
1
I
10 19eV
1015eV
9.8
10.2
10.6
11.0
1200
1300
Figure 1. Photoionizationefficiency curve for I-butanol. The parent ion is m / z 74, while m / z 56 is the C4Hst ion.
TABLE 1: IE’s and Fragment Ion AE’s of the Alcohol Isomers IP or AE, eV m/ Z this work other values
n-Butyl Alcohol 74 56
9.99 f 0.05 10.18 i 0.05
74 59 45 44
9.88 f 0.03 10.14 f 0.02
14 00
TIME OF FLIGHT ( p e c )
PHOTON ENERGY (eV)
Figure 2. Coincidence TOF distributions for the C4Hst product ion at several ion internal energies. The tail toward the long TOF is a result of metastable ion decomposition
CH,CH,CH(OH)CH,
i
hA
10.09,“ 10.04b
2-Butanol
74 56 43 42 33
9.88c 10.24‘ 10.18‘
10.20 f 0.02 0.02
10.12‘
Isobutyl Alcohol 10.02 i 0.05
10.09‘
10.05 i
10.33 f 11.28 f 11.OO f 10.43 f
0.03 0.05 0.03 0.03
PHOTON ENERGY (eV)
Figure 3. Photoionization efficiency curves for 2-butanol. The parent ion is m / z 74, while the product ions are m / z 44 (CH2CHOH+),m / r 59 (CH3COHCHIt),and m / z 45 (CH,CHOHt).
tert-Butyl Alcohol 59
9.90 f 0.03
“Cocksey et aLi5 bWatanabe et and Sorokin.’*
9.87d all6
CHolmeset al.” dPotapov
TABLE 11: Dissociation Rates (us-’) of 1-Butanol Ions
H 2 0 loss ion energy. eV
k,
B
k-
10.15 10.19 10.25 10.28 10.35
>5 >5
0.085 0.085 0.058 0.053 0.018
0.33 0.38 0.45 0.55 0.70
>5 >5 >5
photon energies, with a photon energy resolution of about 17 meV at 1200 A. Since a gas cell was used in this experiment, the internal thermal energy distribution has an influence on the PIE and coincidence spectra. In particular, for metastable ions the kinetic shift and internal thermal energy distribution have opposite effects on the observed daughter ion onsets or appearance energies (AE). The kinetic shift tends to give higher apparent onsets because of the slow rate of dissociation near the dissociation limit, while the internal thermal energy distribution lowers the apparent onset due to the population of the higher energy states. Results and Data Analysis I-Butanol. As shown in the PIE plot of Figure 1, the only dissociation channel of the 1-butanol ion below 11.2 eV is the loss of HzO. The onset for this reaction lies just 0.19 eV above the ionization potential (IP) at 9.99 & 0.05 eV. As a result, the parent ion signal is extremely weak and ceases to rise above 10.2 eV. The onsets, as determined from the extrapolation of the straight line
portion of the PIE scans, are shown in Table I. Although the activation energy for the HzO loss channel is very small, the reaction is slow near the dissociation limit. A number of fragment ion time of flight distributions near the dissociation limit are shown in Figure 2. The asymmetry extending toward the long-TOF side is a result of the slow dissociation rate. However, we also note that the distribution cannot be fitted with a single-exponential decay, which is an indication of a complex reaction mechanism. The experimental T O F distributions were analyzed in terms of a two-component decay scheme of the parent ion signal, P ( t ) , given by p ( t ) = e-k+t + Be-k-1
(1)
in which k+ and k- are the fast and slow reaction rates, respectively, and B is a coefficient that determines the relative contributions of the two components. The fast rate constant was faster than we could measure (Le., > 5 X lo6 s-’) at all 1-butanol ion internal energies. However, the slow rate constant varied from 0.33 X lo6 to 0.70 X lo6 s-l. The mechanism for this two-component rate is discussed in more detail in the next section. 2-Butanol. Figure 3 shows the PIE curves for 2-butanol ion between the IP at 9.88 and 10.9 eV. Three major fragmentation (15) Cocksey, B. J.; Eland, J. H. D.; Danby, C. J. J . Chem. SOC.B 1971, 790. (16) Watanabe, K.; Nakayama, T.; Mottl, J. J . Quant. Spectrosc. Radial.
Transfer 1962, 2, 369. (17) Holmes, J. L.; Burgers, P. C.; Mollah, Y . A. Org. Mass Spectrom. 1982, 17, 127. (18) Potapov, V. K.; Sorokin, V. V. Dokl. Akad. Nauk SSSR 1970,195. 616; (Engl. Transl. 1970, 195, 848).
Butyl Alcohol Ions
-I
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5125
-(CHJ,CHCH,OH*
&=33
(CH,),CHCH,OH
/ CH30H2'
'
'IH,
C,HB+ + H,O
10.68 eV
1
p,kL9
10
PHOTON ENERGY (eV)
paths are observed in this energy range, which are, in order of increasing onset energy
-
14
13
Figure 5. Coincidence TOF distributions of product ions from isobutyl alcohol at several ion internal energies. The asymmetric TOF distributions are a result of metastable ion decompositions. I
CH2CHOH' ( m / z 44) + C2H6 CH3COHCH3+( m / z 59) CH3CHOH+ ( m / z 45)
+ CH3
+ C2H5
In addition, near 10.1 eV, the loss of CH4 is a very minor channel, with a maximum intensity of only 10% that of the C H 3 loss channel. At higher energy it disappears entirely. The onsets for the various dissociation channels are listed in Table I. All dissociation reactions were found to be fast for the 2-butanol ion; no dissociation rates could be derived. It is thus curious that McAdoo and Hudsonlg have recently reported metastable ion decompositions for this ion to m / z 44, 45,and 49. In addition, they reported the loss of H 2 0 , a product that is totally absent in our investigations. Since neither the normal mass spectrurn2Oof 2-butanol nor the electron impact studies of Holmes et al." show any H 2 0 loss, we can only conclude that the observations of McAdca are a result of either collision-induced processes or sample impurities. In this connection, we have found it important to keep the sample temperature low to prevent sample decomposition in the inlet system. Isobutyl Alcohol. The PIE curves in Figure 4 show that there are a total of four major fragmentation channels below 12.4 eV for the isobutyl alcohol ion. The reactions are, again in order of increasing threshold energy (CH3)2CHCH2OH+
12
11
TIME OF FLIGHT ( p e c )
Figure 4. Photoionization efficiency curves for isobutyl alcohol. The parent ion is m / z 74, while the product ions are m / z 56 (C4Hs+),m / z 33 (CH30H2+),m / z 42 (C3H6+),and m / z 43 (C3H7+).
-+
+
10.39 eV
1
CH3CH2CHOHCH3'
10.43 eV
-
--
+ H2O CH30H2' ( m / z 33) + C3H5 C3H6' ( m / z 42) + H3COH C3H7+( m / z 43) + H2COH
C4Hs' ( m / z 56)
The H 2 0 loss channel is extremely weak and important only very near threshold. It is quickly overtaken by the rearrangement reaction which results in the loss of C3H5. This is rather unusual because it is generally the direct cleavage reactions with high entropies of activation that are capable of overtaking a lower activation energy process. This is well illustrated in the case of the fragment ions m/z 42 and 43. The lower energy path involves a rearrangement to form the C3H6+( m / z 42) ion, while the higher energy channel that overtakes this process is the direct C - C bond cleavage reaction to produce the C3H7+ion. The onsets for the four reactions are shown in Table I. (19) McAdoo, D. J.; Hudson, C. E. Org. Mass Spectrosc. 1987, 22, 615. (20) Selected Mass Spectral Data (Standard), Thermochemical Research Center Hydrocarbon Project; Thermodynamics Research Center, Texas Engineering Experimental Station, The Texas A&M University System, College Station, TX 77843, 1983.
9.8
10.2
11.0
10.6
PHOTON ENERGY (eV)
Figure 6. Photoionization efficiency curve for tert-butyl alcohol. The only ion observed in this energy range was the fragment ion, CH3COHCH3+,corresponding to the loss of the CH3 radical. rABLE I11 Dissociation Rates (d) of Isobutyl Alcohol Ions CpH5 IOSS ion energy, eV H,O loss k k, B k10.39 10.43 10.50 10.55 10.68
0.12 0.20 0.33 0.48 1.10
>5 >5 >5 >5 >5
0.09 0.06 0.05
0.04
0.6 0.5 0.6 0.6
The first two reaction channels involve slow dissociations. Some examples of ion TOF distributions at several ion internal energies are shown in Figure 5. They show that the H 2 0 loss channel can be very well represented by a single-exponential decay. On the other hand, the loss of C3H5proceeds via a nonexponential decay, similar to the water loss channel from 1-butanol. As before, the data were fit with a two-component decay rate given by eq 1. The fast rates were faster than we could measure, while the slow rates varied in a normal manner. It is evident from the last column in Table I11 that the slow rate component in the CH30H2+ formation from isobutyl alcohol does not vary with ion energy. This rather odd effect is a result of the broad thermal energy distribution in the precursor molecule. This will be discussed further in the following section. tert-Butyl Alcohol. The parent ion of tert-butyl alcohol is not stable, so that only daughter ions are observed. The only fragment ion at energies below 12 eV is m/z 59, which corresponds to CH3 loss. The onset for ionization/dissociation is difficult to determine because of the gentle rise in the PIE spectrum (Figure 6). The upper limit for the adiabatic IP is given as 9.9 eV in Table I. This onset is clearly limited by the vanishing Franck-Condon factors
Shao et al.
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
5126
a 13.50
13.00
12.50
9WeV
w >OH
TIME OF FLIGHT (psec)
Figure 7. Coincidence TOF distributions of the product ion from fertbutyl alcohol at several parent ion internal energies. The symmetric broadening of the peaks is a result of kinetic energy release in the dissociation.
500
1
2
I
1
1
3
,
/
tert-butyl alcohol ion. TABLE IV: Heats of Formation of the Alcohols and Their Products species m/z AHf0298 AHf0d
EXCESS ENERGY (eV) 0
REACTION COORDINATE
Figure 9. Diagram of the dissociative potential energy surface of the
1-butanol 2-butanol isobutyl alcohol H20 CH, C3H5 CH30H2+
B
C2H6
CH2CHOHt (CH3)2COH+ CH3-c-C,H5+ 2-C4H8+
9
10
11
12
I
13
PHOTON ENERGY (eV)
Figure 8. Measured average kinetic energy release (points) as a function of the tert-butyl alcohol ion internal energy. The solid line is a statistical theory (Klots) calculation, while the dashed line is a straight line through the data points.
for producing the ion at the adiabatic ionization energy. The dissociation rate for CH, loss is rapid, which leads to symmetric T O F distributions. However, we noted that these distributions were broadened by kinetic energy release. Figure 7 shows how their width increases with increasing ion internal energy. Since the observed TOF distribution is Gaussian, we conclude that the kinetic energy release is described by a Maxwellian distribution. Under these conditions, the average kinetic energy release can be derived from the full width at half-maximum (fwhm) by2' M 3 (qt(fwhm))z - n1(3RT) M-m 2 ( E ) = m ( M - m) 15 In 2
(2)
where M and m are the parent and daughter ion masses respectively, q is the electron charge, and t is the electric field in the ionization region. The second term in eq 2 is a correction term that subtracts the effect of the parent molecule thermal translational energy. The results of this analysis are plotted (squares) in Figure 8. The plot of the kinetic energy release as a function of the ion internal energy in Figure 8 is a straight line over more than 2 eV of ion internal energy. This means that the fraction of the available energy channeled into translation remains constant over this energy range. This fact suggests a simple method for determining the true dissociation limit. If we can assume that the fraction of the (21) Stockbauer, R. I n t . J. Mass Spectrom. Ion Ph,ys. 1977, 25. 8 9
74 74 74 18
15 41 33
30 44 59 56 56
-274.4" -292.9' -283.8" -241.8" 142.3" 17O.Oc
552.9d -84.7" 751.3' 453 f 16 937.0h 87 1 .O"
-246.0a -260.1 -252.3 -238.9' 145.6" 180.9 567.9 -69.1' 767.6 415/524.6g 960.1 894.3
'Rosenstock et aLZ2 bPedley et cBenson.26 dReference 27. 'Holmes et a1.28'Present result from the dissociation of tert-butyl alcohol ions. gPotapog and Sorokin.'* L o ~ s i n g .'Except ~~ where noted, the conversions from 28 to 0 K are calculated with the frequencies listed in Table V. available energy going into translation remains constant down to the adiabatic dissociation limit, an extrapolation of the apparent straight line through the points to zero translational energy should identify the true dissociation limit. This intercept lies a t 9.35 f 0.10 eV, which is considerably below the measured IP of 9.9 eV. The low dissociation onset is a measure of the large displacement of the ionic potential energy surface from the neutral tert-butyl alcohol surface. A diagram of this is shown in Figure 9. From the appearance energy of 9.35 eV, we can determine the heat of formation of the ionic product, C3H70+,to be AHfoo= 475 f 14 kJ/mol. The previously reported heat of formation of this ion of 525 kJ/mol had been determinedzz from only the measured A E of 9.87 eV from tert-butyl alcohol,I8 a value that was clearly too high. The nature of the geometry change shown in Figure 9 is most likely the variation in the bond angles, which increase from the 1 0 9 O (tetrahedral) in the tert-butyl alcohol molecule to 120' (trigonal planar) in the (CH3)zCOH+ion. The statistically expected average kinetic energy release is also plotted in Figure 8. This average energy is determined from Klots'*j equation, which has been discussed in a variety of publ i c a t i o n ~ . " ~it~is~ evident that the measured kinetic energy greatly exceeds the calculated one. This is further evidence for a repulsive ionic potential energy surface as shown in Figure 9. Discussion Dissociation Energetics. Table IV lists the heats of formation at both 0 and 298 K for the molecules, ions, and fragments relevant (22) Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J. Phys. Chem. Rex Data, Suppl. 1977, 6, I . ( 2 3 ) Klots. C . E. J. Chem. Phys. 1973, 58, 5364. (24) Brand. W . A . ; Baer, T.; Klots, C. E. Chem. Phys. 1983, 7 6 . 1 1 1
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5127
Butyl Alcohol Ions 62 a n-C,H,OH* k h
7.6
"1
lb
S 5
CH,CHO"
> 74 W
5
5
g
70
CH,CHCHCH,'
CH,CH(OH)CH,+
-___
+ CH,
4
66
62
REACTION COORDINATE
Figure 10. Potential energy profiles of the dissociation reactions for the three stable butanol ions. The energy scale is the absolute heat of formation based on 0 K.
TABLE V Vibrational Frequencies (cm-')
2-C4HgOH" i-C4HgOHb CHIOHZ' CH2CHOHd CH3-c-C,HSC 2-C4H$
3500 926 3500 955 2961 250 3500 995 3006 847 2964 978
(1) (2) (1) (6) (5) (1) (1) (2) (7) (4) (8) (2)
2921 (9) 766 (2) 2926 (10) 797 (1) 1470 (3)
1384 (12) 421 (2) 1468 (6) 415 (1) 1345 (2)
1195 (4) 234 (1) 1360 (6) 382 (2) 1165 (2)
1024 (3) 149 (3) 1174 (3) 115 (3) 1000 (1)
3032 (3) 923 (2) 1451 (4) 739 (1) 1661 (1) 846 (2)
1653 575 1366 500 1428 430
1420 (1) 428 (1) 1173 (4) 383 (1) 1282 (1) 383 (1)
1299 (2) 200 (1) 1054 (5) 193 (1) 1066 (4) 195 (2)
(1) (1) (1) (1) (7) (2)
Constructed from n-C4H9Ffrequencies.,' bSchrader and PacanConstructed from CHIOH freq~encies.~~ dConstructed from CH,CHCH, frequencie~.'~ Constructed from cyclo-C3H6frequencies.), /Constructed from 2-methylpropene frequencies. sky.'*
to this study. The conversion from AHfo298to AHf', was accomplished in the usual mannerI3 by calculating the integral over the heat capacity by using the known or assumed vibrational frequencies shown in Table V. These energetics are graphically illustrated in Figure 10. The common feature in the dissociation of all of the ions is the low activation energy and the considerable reverse activation energy for each dissociation. That is, the product energies are as low as, or lower than, that of the initial molecular ion. It is evident from the variety of products that the mechanism for dissociation is different in each ion. Furthermore, there are dynamical rather than thermochemical constraints that are determining the open product channels. The thermochemically most stable dissociation path is to the trans-2-butene ion plus water, a reaction clearly driven by the great stability of the water molecule. This may be one of the paths in the dissociation of 1-butanol, but it is certainly not the only one. As will be discussed in the following section, there is evidence that some of the reaction results in the formation of methylcyclopropane ions. Dissociation Rates. Role of the Ion-Dipole Complex. Two of the four butyl alcohol ion isomers, 1-butanol and isobutyl alcohol, are metastable, that is, they have a slow dissociation rate. This is remarkable when one considers the low activation energy, E,, involved in both cases. According to the statistical theory (RRKM/QET) the dissociation rate for an ion with internal energy E is given by U W ( E - E,) k(E) = (3) hP(E) where u is the path degeneracy, W ( E - Eo) the sum of states from 0 to E - Eo in the transition state, and p(E) the density of states of the precursor molecular ion. The minimum rate at E = Eo is given simply by u/hp(E,) because at this energy there is only one accessible state in the transition state. The density of states is a strongly increasing function of the ion energy and
the number of vibrational degrees of freedom in the ion. The potential energy diagrams of Figure 10 show in both 1butanol and isobutyl alcohol that at the dissociation threshold, the ion internal energy is already 0.2 eV above the dissociation limit to C4H8+ H 2 0 (if we assume the methylcyclopropane structure for the product ion). We do not know the energy of the ion-dipole complex. However, we can assume that it is not much different from the c-C3H6+.-OH2complex, which was foundg to be between 0.6 and 0.4 eV more stable than the dissociation products. With these assumptions, the minimum calculated rate is lo8 s-I for a very tight activated complex and lo9 s-' for a more reasonably loose complex. These rates are 2-3 orders of magnitude greater than is experimentally observed. It is instructive to compare the C2H6 loss from the 2-butanol ion with the H 2 0 loss discussed in the previous paragraph. The C2H6 loss proceeds with rates in excess of 1 0 ' s ~even ~ though its activation energy is very similar to the activation energy for H 2 0 loss from 1-butanol and isobutyl alcohol (see Figure 10). We see then that the slow reactions involve the loss of the strongly dipolar H 2 0 . These considerations point again to the unique features of the ion-dipole interaction in determining the dissociation rates. As pointed out previously? a part of the problem in reconciling the measured slow rates for H20loss with the calculated fast rates may lie in the assumption of harmonic oscillators in calculating densities of states. However, simple first-order corrections to the harmonic potential, such as in the Morse potential, are not sufficient to resolve this problem because the ion-dipole potential is far more anharmonic than a Morse potential. In fact, Case35 has shown that a l / r 2 potential, which describes the locked iondipole interaction, supports an infinite number of vibrational states. From this fact, one draws the absurd conclusion that the io11 will never dissociate. The resolution of this dilemma may be found in the symmetric wag motion of the ion-dipole complex, which turns into a free rotation as the ion-dipole distance i n c r e a ~ e s . ~
+
(25) Pedley, J. C.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: New York, 1986. (26) Benson, S. W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1976. (27) The value is calculated on the basis of the heats of formation of methanol (from ref, 25) and H+ (from ref 24) and the proton affinity of methanol (from Aue, D. H.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M. T.,Ed.; Academic: London, 1979; Vol. 2, p 18). (28) Holmes, J . L.;Terlouw, J . K.; Lossing, F. P.J . Phys. Chem. 1976, 80, 2860. (29) Lossing, F. P. Can, J . Chem. 1972, 50, 3973. (30) Baer, T.; Brand, W. A,; Bunn, T. L.; Butler, J. J. Faraday Discuss. Chem. Soc. 1983, 75, 45. (31) Crowder, G. A,; Mao, H. K. J . Mol. Struci. 1974, 23, 161. (32) Schrader, B.; Pacansky, J.; Pfeiffer, U. J . Phys. Chem. 1984,88,4069. (33) Shirnanouchi, T. Tables of Molecular Vibrational Frequencies; NSRDS-NBS 39, 1972; consolidated Vol. I . (34) Tupitsyn, I. F.; Kane, A. A. Zh. Strukt. Khim. 1979, 20 987. (Engl. Transl. 1979, 20, 844). (35) Case, K. M . Phys. Reu. 1950, 80, 797.
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The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
Once the dipole rotates, the interaction is no longer that of a locked ion-dipole but rather a rotating dipole that behaves similarly to an ion-induced dipole potential. The 1 /r4 dependence leads to a finite number of vibrational levels and thus a finite dissociation time. The dynamical treatment of this problem is clearly not trivial and is not yet available. We can thus not analyze these slow rates in any quantitative manner. 1-Butanol. It is evident from the energetics in Figure 10a that there are three different dissociation channels open for the loss of water when the 1-butanol ion absolute energy is on the order of 7.7 eV. In fact, there is one more C4Hx+ion not shown in the figure. It is the cis-2-butene, which is 50 meV less stable than trans-2-butene ion. On the basis of the results for the 1-propanol ion reaction, we conclude that the slow reaction does not produce the most stable C4Hx+product, the 2-butene ion. Rather it forms a higher energy product ion, probably the methylcyclopropane ion. This is supported by energetic considerations. The energy barrier is so far above the dissociation limit to the 2-butene ion that the reaction rate for the production of that ion would be extremely rapid. The choice between the methylcyclopropane and 1-butene ions is less obvious as both are probably consistent with a slow reaction, although the cyclic ion formation should result in a much slower reaction than the 1-butene ion production. Since we have no means for calculating these rates at this time, we cannot rule out one of these isomers by comparing experimental and theoretical rates. However, on the basis of the 1-propanol reaction, for which collisional activation studies have shown that the cyclopropane ion is produced, we tend to favor the methylcyclopropane ion as the product for 1-butanol as well. The T O F distributions in Figure 2 show that 1-butanol dissociates via a fast component in addition to the slow component. We propose that the fast component may involve a rearrangement from the 1-butanol ion to an ion-dipole complex between water and the 2-butene ion. Thus the overall mechanism could be written as
P
C H 3 - c - C3H5'
OH2
3 C H 3 - c - C3H5' +
H20
Such a mechanism gives rise to a two-component decay rate in which the slow rate in eq 1 is given approximately by k3,the fast rate by kg,and the ratio of slow to fast components by B = k l / k 2 . The variation of the three constants in Table I1 indicates that the rearrangement of the 1-butanol ion to the 2-butene ion-water complex dominates at high energies so that slow complex dissociation takes place only near the dissociation threshold. Isobutyl Alcohol. The dissociation of isobutyl alcohol is clearly more complex than that of n-butyl alcohol. First of all, there are two slow dissociation channels. Second, the C3H5loss path is characterized by a two-component decay, whereas the H z O loss is one-component. Finally, the slow rate of C3H5loss appears to undermine the ultimate importance of ion-dipole interactions in reducing the dissociation rates. A possible mechanism that explains all of these features is illustrated by the double-well model30 in Figure 1Oc. If k , , k2 >> k3, k4, the slow component rate for both H,O and C I H q losses can be approximated by k- = k l + k, - k2k3/(k, + k;),"in which the ratei'are those shown in Figure 1oc. The model depicted in Figure 1Oc connects the slow rate of C3H5 loss with the H 2 0 loss channel because of the partial equilibration between the isobutyl alcohol and the ion-dipole complex structures. This model also predicts that the slow rates for the two reaction channels are the same. Yet, the rates listed
Shao et al. in Table I11 are not the same except at high ion internal energies. It is also significant that the slow rates for the C3H5loss channel do not vary with ion internal energy. We believe that this behavior results from the slightly lower dissociation threshold for H 2 0 loss and the broad thermal energy distribution of the isobutyl alcohol, which extends over 120 meV. Under these circumstances, the C3H5loss channel contributes to the signal even when the nominal photon energy is below its onset. It is only the high-energy tail of the internal energy distribution that contributes to this decay channel. Thus, the average internal energy of the ions that lose C3H5is not the same as the average energy of the ions that lose H 2 0 . Furthermore, because the tail of the internal energy distribution is approximately exponential, the average energy of the ions that lose C3H5remains about constant until the photon energy actually exceeds the C3H5loss threshold. At this energy, the parent ions that decay via the two paths have the same average internal energy and decay via the same rate, as found experimentally. There are two energetically possible channels for the formation of the ion-water complex. These are the isobutene ion-water complex and the methylcyclopropane-water complex. The dissociation limit to the isobutene ion lies 0.91 eV below the threshold energy. This would certainly imply a fast dissociation. The fact that there is no fast component in the H 2 0loss rate indicates that the isobutene ion is not produced. Rather, we suggest that the reaction proceeds exclusively to the methylcyclopropane ion-water complex for which the dissociation limit is only 0.2 eV below the experimental dissociation threshold.
Conclusions This study of the dissociation dynamics of the butyl alcohol ions has shown that no common mechanism accounts for the products of all four ions. Rather, a variety of transition states leading to different products have slightly different energies and are dominant to different extents in these ions. The loss of HzO occurs in two of the ions, 1-butanol and isobutyl alcohol. Both of these ions are metastable. From this we conclude that the ionic product produced from the slow reaction is not the lowest energy butene or isobutene ion. Rather, it probably has the methylcyclopropane structure, similar to the cyclopropane ion ~ loss of H 2 0 product in the H 2 0 loss reaction of l - p r ~ p a n o l .The must involve an ion-dipole complex which calculations have shown is on the order of 0.5 eV more stable than the dissociation products t h e m s e l ~ e s .However, ~ as in the case of 1-propanol, the normal application of the statistical theory RRKM/QET cannot account for the slow dissociation rates. The predicted rates are 2-4 orders of magnitude higher than the experimentally measured rates. Thus, the water loss channel from the butanol ions is another example of the decisive role apparently played by the ion-dipole interaction in rendering this reaction slow. According to the recently proposed model,9 the long-range, extremely anharmonic potential associated with the ion-dipole interaction makes the calculation of the vibrational density of states very complicated. In addition, there may exist certain dynamical constraints associated with the transfer of vibrational to rotational energy that inhibit this reaction. Further theoretical work is required to understand this problem more completely. Acknowledgment. We thank the National Science Foundation for financial support of this work. D.K.L. also thanks the UNC-CH Chemistry Department for a Visiting Professorship, January-June 1987. Registry No. CH3(CH2)30H, 71-36-3; CH3CH2CH(OH)CH, 7892-2: (CH,),CHCH,OH, 78-83-1; (CH,)gOH, 75-65-0; (CH3)*COH+, 17 104-38-0.
