J . Phys. Chem. 1986, 90, 41 14-41 18
4114
t = 0 in the upper limit of the integrals on the right-hand side of (2.16a) or (2.16b). The solution of the linear diffusion equation (2.13) subject to (2.16a) or (2.16b) can often be obtained with Laplace transforms. In passing we note that the solution of the steady-state diffusion reaction-equation (cf. (1.4) with & / a t = 0) can alwavs be reduced to a auadrature. ' The referie has asked us to iompare our early-time (t < 1) solution to a perturbation solution of eq (3.1 1) based on using the reaction term c2 as a perturbation.' A necessary (but not sufficient) condition that the perturbation represent the solution
in (0,Z) is that the dimensionless parameter (cf. eq 1.2)
ib - < I, 22
i =
(L2?o)-'
Our solution is not limited by such a parameter condition. Acknowledgment. We are indebted to the Army Office of Research and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work.
Heat of Formatlon for the I-Methylallyl Cation by Photoionlzatlon Mass Spectrometry John C. Traeger Department of Chemistry, La Trobe University, Bundoora, Victoria 3083, Australia (Received: December 26, 1985)
The ionization energies and C4H7+appearance energies for a series of organic compounds have been measured by dissociative photoionization mass spectrometry. A 298 K heat of formation of 870.0 & 0.5 kJ mol-', based on the stationary electron convention, is derived for the I-methylallyl cation in the gas phase which results in an absolute proton affinity for trans1,3-butadiene of 770.0 & 1.4 kJ mol-'. An ab initio molecular orbital calculation of the radical and cationic vibrational frequencies is used in conjunction with the radical adiabatic ionization energy to derive a 298 K heat of formation of 148.3 & 2.4 kJ mol-' for the I-methylallyl radical. From a consideration of the thermochemistry associated with competing fragmentation processes, a self-consistent set of heats of formation for nine C4H8and CSHloisomers is obtained.
Introduction The C4H7+cation is known to have a number of stable isomeric structures.] Lossing2 used monoenergetic electron impact mass spectrometry to measure ionization energies ( I E s ) for the 1methylallyl and 2-methylallyl radicals. The appearance energies (AEs) for C4H7+fragment ions from five C4Hsand eight C5H10 isomers were also measured, and, from the derived C4H7+heats of formation (862 f 8 kJ mol-'), it was concluded that, despite extensive skeletal rearrangements, there was a common threshold structure which corresponded to the more stable 1-methylally1 cation (854 f 13 kJ mol-'). From a recent photoelectron spectroscopic study of isomeric C4H7radicals, Beauchamp and co-workers3 were able to directly observe the photoelectron spectra for 1-methylallyl, 2-methylallyl, and cyclobutyl radicals. The vibrational fine structure present in each of the first bands was interpreted as being consistent with local minima on the C4H7+potential surface for each of the corresponding cations. In agreement with theoretical calculations,' the most stable of these ions was shown to be the 1-methylallyl cation. Although there was no direct evidence for either the cis or trans isomer, the adiabatic IE of 7.49 eV was demonstrated to be consistent with that expected for the trans- 1-methylallyl structure. The cationic heat of formation (850 f 6 kJ mol-') calculated from the observed adiabatic IE was based on a recommended value for the 1-methylallyl radical: which in turn was derived from a kinetic study of the iodine-catalyzed positional isomerization of butene;s this value was also used by However, it has recently been proposed6 that such radical heats
of formation could be in error by some 10-20 kJ mol-'. In a study of the dissociation dynamics of energy-selected C5Hio' ions, Brand and Baer7 measured the C4H7+fragment ion AE's for three CsHloisomers by photoionization mass spectrometry (PIMS). On the basis of their data for cyclopentane, they derived a 298 K heat of formation of 876 kJ mol-' for C4H7+which is 13 kJ mol-' higher than the recommended 863 kJ mol-' listed in Rosenstock's compilation.* However, this latter value, which was based on Losing's measurements,* did not make any correction for the thermal energy of the dissociation fragments: which would consequently underestimate the cationic heat of formation. The proton affinity (PA) for trans-1,3-butadiene has recently been evaluatedI0 as 807.5 kJ mol-'. This is based on unpublished experimental data of Aue and Bowers'' and leads to a C4H7+heat of formation of 832.5 kJ mol-', considerably lower than all of the above measurements. The present investigation was initiated in an attempt to resolve these discrepancies and to firmly establish an absolute heat of formation for the I-methylallyl cation in the gas phase.
Experimental Section The threshold photoionization efficiency curves obtained in this study were measured with a high-sensitivity photoionization mass spectrometer which has been described in detail e l s e ~ h e r e . ' ~ J ~ The photon source used in the present experiments was the hydrogen pseudocontinuum with the band-pass of the Seya-Namioka monochromator set at 0.125 nm. The absolute photon energy scale (7) Brand, W. A.; Baer, T. J. Am. Chem.Soc. 1984, 106, 3154-3160.
(1) (a) Schleyer, P. v. R.;Dill, J. D.; Pople, J. A,; Hehre, W. J. Tetrahedron 1977,33,2497-2501. (b) Mayr, H.; Foerner, W.; Schleyer, P. v. R. J . Am. Chem. SOC.1979, 101,6032-6040. (c) Lien, M. H.; Hopkinson, A. C. J. Phys. Chem. 1984,88, 1513-1517. (2) Lossing, F. P. Can. J . Chem. 1972, 50, 3973-3981. (3) Schultz, J. C.; Houle, F. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106, 7336-7347. (4) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493-532. ( 5 ) Golden, D. M.; Benson, S. W. Chem. Reu. 1969, 69, 125-134. (6) Tsang, W. J. Am. Chem. SOC.1985, 107, 2872-2880.
0022-3654/86/2090-4114$01.50/0
(8) Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J . Phys. Chem. Re$ Data Suppl. 1 1977, 6. (9) Traeger, J. C.; McLoughlin, R. G. J. Am. Chem. SOC.1981, 103, 3647-3652. (10) Lias, S. G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. Re$ Data 1984, 13, 695-808. (1 1) Aue, D. H.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 11, Chapter 9. (12) Traeger, J. C.; McLoughlin, R. G. Int. J . Mass Spectrom. Ion Phys. 1978, 27, 319-333. (13) Traeger, J. C. Int. J. Mass Spectrom. Ion Processes 1984, 58, 259-271.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 4115
Heat of Formation for the 1-Methylallyl Cation TABLE I: Calculated‘ Vibrational Frequencies (cm-I) (a) trans-1-Methylallyl Cation 847 848 1012 508 558 98 183 298 1101 1128 1157 1251 1287 1343 1395 1442 1498 1549 2835 2870 2974 2981 2989 3042 113 993 1486
201 1031 1499
(b) trans-1-Methylallyl Radical 283 489 507 694 748 1064 1129 1225 1326 1416 2853 2887 2920 2963 2970
828 1446 2977
TABLE II: Thermochemistry for the Gas-Phase Reaction at 298 K, C,H,X hv C,H,+ + X e-
+
1027 1456 3071 937 1475 3051
“See text.
was calibrated with known atomic emission lines and found to be accurate to better than 0.003 eV. All compounds used were of research grade purity which showed no impurities of significance in their mass spectra. The photoionization experiments were performed at ambient temperature (297 K) with sample pressures Pa in the ion source region. of
Results and Discussion We have previously shown9 that the calculation of 298 K heats of formation can be made from the AE for the process AB + hv A+ B + eby means of the thermochemical expression
-.
+
1-butene 2-methylpropene cis-2-butene trans-2butene cyclopentane 2-methyl-lbutene 2-methyl-2butene cis-2-pentene I-pentene
H H
9.57 11.13 9.19 11.26
16.4 16.4
-0.4 -16.9
218.0 218.0
871.9 867.9
H H
9.13 11.19 9.09 11.24
16.4 16.4
-7.8 -12.2
218.0 218.0
870.3 870.7
CH3 10.35 11.08 CH3 9.10 10.66
20.6 20.6
-78.4 -35.6
143.9 143.9
867.4 869.7
CH3
8.69 10.80
20.6
-42.1
143.9
876.7
CH3 CH3
9.02 10.62 9.50 10.50
20.6 20.6
-29.1 -21.9
143.9 143.9
872.3 867.9
‘From the linear extrapolation of Figures 1-9; values reproducible to fO.O1 eV. bCalculated from eq 2; HoZg8- Hoo(C4H7+)calculated by using 3-21G vibrational frequencies from this work; HOZg8- HOo(B) from ref 14. cReference 19. dReference 9. eCalculated from eq 1 and 1 eV = 96.487 kJ mol-’.
1
ufo298([Al+) = AE298
+
+
1-BUTENE m/z
55
+ Mf0298(AB) - Mf0298(B) + M ~ m ( l )
AE298is the experimental appearance energy based on a threshold linear extrapolation of the PIE curve, and the thermal energy correction term, AH,,, is given by where M 0 2 9 8 represents H029s - Hoo and the stationary electron convention for cationic heats of formation (Le., AH0298(e-)= 0) has been a d ~ p t e d . ~ The thermal energy correction term, which is derived from statistical mechanical calculation^,^^ is a major source of error in obtaining absolute cationic heats of formation from dissociative PIMS measurements. An accurate value for AHrnrdepends on a knowledge of the vibrational frequencies for the photoionization products. Although this information is usually available for most common neutral products, it is rarely the case for the fragment ion and, as a result, data for similar neutral species must be used as an estimate. Because no experimental data is available for the C4H7+cation, an a b initio molecular orbital calculation was carried out by using the GAuSSiAN 82 suite of programs.” This included a geometry optimization and a subsequent determination of the vibrational frequencies. Separate calculations were performed for trans-lmethylallyl radical, trans- 1-methylally1 cation, and 1-butene by using both the STO-3G and 3-21G basis sets. The 1-butene data were used for comparison with available experimental data.16 At the STO-3G level it was found that the calculated vibrational frequencies were overestimated by 21.9 f 0.476, whereas at the 3-21G level this was reduced to 11.4 f 0.3%. This is in agreement with Pople et al.” who observed that, for a range of molecules in which 486 vibrational frequencies were examined, the average overestimation for 3-21G calculations was 12.3%. Because there is no significant advantage in performing vibrational frequency calculations at the 6-31G* level,” only 3-21G data were used in this work. The 3-21G vibrational frequencies which have been used here for the trans-1-methylallyl cation and radical are listed in Table I; these have already been adjusted by 11.4%. (14) Stull, D. R.; Prophet, H. Natl. Stand. Ref DataSer. (US., Narl. Bur. Stand.) 1971, No. 37. (15) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E.M.; Po&, J. A. Carnegie-Mellon University, Pittsburgh,-PA, 15213. (16) Durig, J. A.; Compton, D. A. C. J . Phys. Chem. 1980,84,773-781. (17) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J. Quantum Chem. Quantum Chem. Symp. 1981, IS, 269-278.
11.13
0
e
10.8
10.9
11.0
11.1
11.2
11.3
11.4
PHOTON ENERGY /eV Figure 1. Threshold photoionization efficiency curve for C4H7+fragment ions produced from 1-butene.
I
2-METHYL PROPENE
PHOTON ENERGY / 4 V Figure 2. Threshold photoionization efficiency curve for C4H7*fragment ions produced from 2-methylpropene.
The adiabatic ionization energies measured in this work and listed in Table I1 were obtained by taking the first maximum of the first differential PIE curves. These are all in good agreement with other photoionization measurements.l* The PIE curves for (18) Levin, R. D.; Lias, S.G. Natl. Stand. Ref Data Ser. (US.Natl. Bur. Stand.) 1982, No. 71.
4116
The Journal of Physical Chemistry, Vol. 90, No, 17, 1986
Traeger
CIS-2-BUTENE >-
m/z
U
2
2-METHYL-1-BUTENE
55
..
w W
z
2-
m/z
U
z
.'
55
!2 U H
LL LL
LL LL
W
W
..
z
6
E
H
I-
I-
U
U
E z Ef 0
tl z
11.19
10.66
E: 0
I-
k-
I
I .
0
I
0
n.
e
................. 11.0
11.1
11.2
11.3
11.4
11.5
10,s
10.4
r 10.7
10.6
10.8
11.0
10.9
PHOTON ENERGY /eV Figure 3. Threshold photoionization efficiency curve for C4H7+fragment
PHOTON ENERGY /eV Figure 6. Threshold photoionization efficiency curve for C4H7+fragment
ions produced from cis-2-butene.
ions produced from 2-methyl- 1-butene.
TRQNS-2-BUTENE >-
m/z
U
z
2-METHYL-2-BUTENE >-
55
z
2 U
2 LL
L LL
LL W
W
z
z
0
z
H
I-
U
E
H
z
11.24
'/
0
z
0
I
H
0 I-
0
1
e
..............
u-
11.1
11.0
11.2
11.3
0 I-
O
r e
11.4
11.5
Figure 4. Threshold photoionization efficiency curve for C4H7+fragment ions produced from trans-2-butene.
10.5
10.9
11.0
11.1
Figure 7. Threshold photoionization efficiency curve for C4H7+fragment ions produced from 2-methyl-2-butene.
2-
m/z
U
.'
z
55
..
!2
U
:
H
LL
LL W
LL L W
z
0
z
H
E
I-
5
k
N
U
3
z
10.8
CIS-2-PENTENE
55
W c
0
10.7
10.6
PHOTON ENERGY /eV
CYCLOPENTRNE m/z
I .......*-/
H
PHOTON ENERGY /eV
z
/
I-
U
N
U
55
!2
H
>-
m/z
U
11.08
H
N
/I
H
z
10.62
E: 0 + 0
0 I-
O
r
a.
..
I
r
e
............. PHOTON ENERGY /eV
Figure 5. Threshold photoionization efficiency curve for C4H7+fragment
ions produced from cyclopentane.
10.4
10.5
10.6
I
10.7
10.8
10.9
11.0
PHOTON ENERGY /PV Figure 8. Threshold photoionization efficiency curve for C4H7+fragment
ions produced from cis-2-pentene.
C4H7+ produced from the corresponding C4Hs and C=,Hloisomers are shown in Figures 1-9. In order to obtain satisfactory signal-to-noise ratios in the threshold regions of these curves it was necessary to collect the experimental data for each curve over periods of several days. The extrapolated sections of the PIE curves, as indicated in Figures 1-9, all give prethreshold tailing that is consistent with the extent of hot band structure observed for each corresponding molecular ion. The 298 K AEs measured on this basis have been summarized in Table 11. For cyclopentane
and 1-pentene, the AEs reported here are significantly lower (0.07 and 0.13 eV, respectively) than the equivalent photoionization measurements of Brand and Baer.' No experimental PIE curves were published in that work, so it is difficult to critically compare the present results. However, because the photoionization efficiency near threshold for these fragment ions is extremely low, the most likely reason for such a discrepancy is a difference in the relative sensitivities of the two instruments.
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 4117
Heat of Formation for the I-Methylallyl Cation
2-METHYL-1-BUTENE
1-PENTENE >-
>-
m/z 55
U
z
m/z 4 2
U
2
2
E U
!A LL
c-(
LL IL W
LL W
z
z
EI + a E
El t-
.'
z
U
E Z
10.66
I
w
0 t0
0 IO
I
IO. 50
0
0
r a.
r 0-
-.... *._' 10.2
10.9
10.6
10.5
10.4
10.7
10.8
CYCLOPENTRNE
* U
10.7
10.9
10.8
11.0
frag-
2-METHYL-2-BUTENE m/z 4 2
2
E
10.6
PHOTON ENERGY /eV Figure 11. Threshold photoionization efficiency curve for C&'+ ment ions produced from 2-methyl-1-butene.
* U
m/z 4 2
2
10.5
10.4
PHOTON ENERGY /PV Figure 9. Threshold photoionization efficiency curve for C4H7+fragment ions produced from 1-pentene.
E !A
z
LL LL W
LL
LL W
z
z 0
El
w
I-
I-
a
a
E
N w
z
z
11.08
El 0
2 0
1
I
+ 0
10.80
I/
+ 0
e
L
10.8
10.9
11.1
11.0
11.9
11.2
11.4
TABLE 111: Thermochemistry for the Gas-Phase Reaction at 298 AB bv A+ B + e -
+
+
+
AB
A
B
AE, eV
A+c
1-butene 2-methylpropene cis-2-butene 1runs-2-butene cyclopentane 2-methyl-1-butene 2-methyl-2-butene cis-2-pentene 1-pentene
C3H5 C3H5 C3H5 C3H5 C3H6 C3H6 C3H6 C3H6 C3H6
CH3 CH3 CH3 CH3 C2H4 C2H4 C2H4 C2H4 C2H4
11.20' 11.33' 11.25' 11.30' 11.08' 10.66b 10.80' 10.62' 10.51'
951.9 947.9 949.3 949.7 955.4 957.7 964.7 960.3 956.9
10.6
10.5
PHOTON ENERGY /eV Figure 10. Threshold photoionization efficiency curve for C3H6'+ fragment ions produced from cyclopentane.
K,
10.8
10.9
11.0
11.1
PHOTON ENERGY /eV Figure 12. Threshold photoionization efficiency curve for C3H6" fragment ions produced from 2-methyl-2-butene.
CIS-2-PENTENE m/z 4 2
kJ/mol ABmdd C4H7+#
mf0298,
-2.7 -15.2 -7.5 -12.3 -75.6 -35.1 -48.6 -31.2 -20.6
10.7
869.6 869.6 870.6 870.6 870.2 870.2 870.2 870.2 869.2
.'
'
'Reference 13. From the linear extrapolations of Figures 10-14; values reproducible to fO.O1 eV. CCalculated from eq 1 with 1 eV = 96.487 kJ mol-l and auxiliary thermochemical data from ref 19, 22, and 23. dSee text. CCalculated as in Table 11, but using AZffo(AB)md.
In order to use this data in conjunction with eq 1 to extract a reliable cationic heat of formation it is essential that both the AE's and the auxiliary thermochemical data are accurately known. For internal consistency, the heats of formation for all precursor molecules were obtained from the Sussex-N.P.L. compilation of Pedley and Rylance;I9 the radical heats of formation were the recommended values used for previous thermochemical studies in this laboratory? On this basis the calculated heat of formation
10.4
10.5
10.6
10.7
10.8
10.9
11.0
PHOTON ENERGY /eV Figure 13. Threshold photoionization efficiency curve for C3H
