1769
INTERNAL ENERGY PARTITIONING UPON ION DECOMPOSITION
Degrees of Freedom Effect and Internal Energy Partitioning upon Ion Decomposition by Y. N. Lin and B. S. Rabinovitch Department of Chemistry, University of Washington,Seattle, Washington 98106
(Received October 81, 1969)
A random statistical theory has been applied to the internal energy partitioning that accompanies parent ion decomposition for a homologous series of primary alcohols from propanol to heptanol. The metastable ion abundances upon decomposition of the common product ion CzHbOf were calculated on this basis and found to be in reasonable agreement with the data of McLafferty and Pike which demonstrated the dependence of the metastable ion abundances on the number of internal degrees of freedom of the parent alcohol.
Introduction
then readily be seen whether the model reasonably encompasses observed behavior. For exothermic reactions, or for endothermic processes which involve a reorganization energy of the products relative to the activated complex, Le., EoME p > 0, where EOpris the zero point level of the products, it should be clear that RRK or RRKRI unimolecular reaction theories offer no generalization concerning the distribution of the reorganization energy among products of decomposition : the latter aspect depends on the details of the potential surface.
Fragmentation of vibrationally excited molecular ions has recently been examined from the point of view of energy partitioning among the fragments produced. McLafferty and Pike’ studied the fragmentation of homologous alcohol series. They found that the log of the relative abundance of the metastables produced from the intermediate CzHjO+ ion was inversely proportional to the number of vibrational degrees of freedom in the parent molecular alcohol ion. This experimental demonstration is novel and important. A degrees of freedom effect was also later examined by Reaction Scheme Cooks and Williams2in the study of the relative rates of The general alcohol decomposition scheme is fragmentation of benzoyl ions generated by electron impact upon different precursors. RC%HhOH+(R/I+)+ This phenomenon has not heretofore been the subject CzHrjO+(P+) R (a) of quantitative theoretical examination. By assuming I m*(8 0) the randomization of the excess energy of the molecule 4H30+(D+) C2H2 (b) (1) ion above the critical threshold for reaction, i.e., EtM m*’(18 7) = E M - EoM, among the active degrees of freedom of the activated complex of concern, as is appropriate where M + is the molecular ion produced by electron in the RRKIliI formulation, it should, in principle, be impact; the intermediate ion CZHbO+(P+)formed from a straightforward matter to calculate the distribution of M + can undergo (metastable) decomposition to daughexcess energy among the fragment species in the case ter ions D + and D’+, corresponding to m* = 8.0 and of endothermic reactions involving no reorganization m*’ = 18.7, respectively; R is an alkyl radical. energy of the products. This model is applicable whenModel for Energy Partitioning. The model for energy ever the initially formed electronic states relax quickly partitioning has the following features. (1) The total to the lowest level. excess energy of A I + is assumed available for energy In this paper the model has been applied to the calpartitioning and is completely randomized through all culation of the energy distribution in the fragmentation of normal primary alcohols which give rise to CzH50+ internal modes before decomposition. (2) For the homologous series, the excess energy of M + is assumed and alkyl radicals. As a practical matter, it is necesconstant, and the only variable parameter is the chain sary to introduce several assumptions concerning specif(3) During the decomposition, one stretchlength. ics of energetics, critical threshold, molecule-ion strucing mode disappears and becomes the relative translature, etc., which together may mean that the present tion, and the other five modes (if both fragments are results may not precisely represent the alcohol system. This is not too important, however, since we are pri(1) F. W. McLafferty and W. T. Pike, J . Amer. Chem. SOC.,89,5951 marily interested in exploring the expected behavior for (1967). what should be a typical illustrative system. It can (2) R. G. Cooks and D. H. Williams, Chem. Commun., 627 (1968).
1
+
+
Volume 7 4 , Number 8 April 16, 1970
1770
Y. N. LIN AND B. S. RABINOVITCH
polyatomic) go to the rotations and perpendicular relative translations; these are termed the transition modes. (4) The probability of the energy, AE, being found in P+ is proportional to the product of the degeneracy, D ,of the internal degrees of freedom of P+, at energy AE, and the sum of the degeneracies of all permitted energy eigenstates of the active degrees of freedom of the rest of the molecule ion, i.e., (alkyl radical plus transition modes) at energy Et" - AE. The probability of AE in C2HSO+is
[
Pr (AE)p +
=
Et-0
I
-
0.3
*
0
u
0.2
ai
0
Eta4- AE
[D(AWp+I
"4
1.0
P(l%st]
t
(2)
The total specific rate of decomposition of M + is (with neglect of centrifugal effects) EtM
where Z P(Bt") is the sum of the degeneracies of all permitted energy eigenstates of the activated complex of nil+, N*(E") is the density of eigenstates of the active degrees of freedom of M + at energy E , and C is a constant. No restrictions were placed on the small fraction of complexions which placed an energy greater than a bond dissociation energy in stretching modes. This ostensibly resulted in a slight overcount of states but helps to compensate for neglect of anharmonicity effects on the density of vibrational level^;^ no consideration need be given these complications here.
Calculated Energy Distribution of CzH50+ Energy Distribution of M+. It was assumed that the internal energy of M + has a "conventional" parabolic distribution4 (Figure 1) which ranges from 0 t o 13 eV (0-299 lical mol-l). If the critical threshold energy EO" for alcohol ion decomposition is somewhere in the region of a C-C bond energy, say 69 kcal (3 eV),5 the excess energy of )I+ ions which decompose is 0 to 230 kcal mol-' (0 to 10 eV), with a truncated parabolic distribution. No account was taken of alteration of
ENERGY l e v )
Figure 1. Internal energy distribution assumed for parent ions. The vertical line is at EoM and the area to the right represents the excess energy distribution. The Journal of Physical Chemistry
E CtH50+
(IO'CM*')
Figure 2. Curves showing random statistical distribution of excess energy of M + in CtHnO product. Illustrative values of Et)' are 1, 5, and 9 eV. +
this shape due t o competitive processes and their change in relative importance with energy. Vibrational Models of the Molecular Ion and Activated Complex. Two vibrational models were considered for the activated complex for >I+ decomposition, a rigid model and a loose model. These correspond roughly t o preexponential factors of -1013-14 and -1016-17 sec-l, respectively, in the Arrhenius equation. In the former model, the complex retains the frequencies of the par(3) F. TV. Schneider and B. S. Rabinovitch, J . Amer. Chem. Soc., 8 4 , 4215 (1982). (4) (a) I. Howe and D. H. Williams, ibid., 90, 5461 (1988); (b) R. G. Cooks, R. S. Ward, I. Howe, and D. H. Williams, Chem. Com-
(1968). (5) A referee suggests that 1 e\' is a better estimate; little change would result in the calculations and virtually none if the energy distribution of 1LI. assumed ranges from 0 to 11 eV. mun., 837
+
INTERNAL ENERGY PARTITIONING UPON ION DECOMPOSITION Table 11: The Standard Deviation and Coefficient of Dispersion for the Energy Distribution of P +
Table I : Some Energy Quantities for CzH60+ EtM, eV Compd
1
ca C4
c5
C6 Ci.
3
ca
C4
c5 c 5
5
Ci. Ca c 4 c 5
7
9
C6 C7 Ca C4 C6 C6 C? Ca c 4
C, C6
c7 a
1771
Fraction
Emp,
(E),
koa1 (eV)
kea1 (eV)
(E)/EtM
of DFn
13.7 (0.60) 9.60(0.42) 7.20 (0.31) 5.40 (0.23) 4.40 (0.19) 39.0(1.70) 30.4(1.32) 23.3 (1.01) 19.0 (0.83) 16.1 (0.70) 69.4(3.02) 52.2 (2.27) 3 9 . 3 (1.71) 33.6 (1.46) 27.8(1.21) 98.1 (4.26) 72.5 (3.15) 5 8 . 1 (2.52) 48.1 (2.09) 39.6 (1.72) 126.0(5.48) 94.2 (4.10) 75.5 (3.28) 61.3 (2.67) 52.2 (2.27)
12.9 (0.56) 9.68 (0.42) 7.68 (0.33) 6.23 (0.27) 5.32 (0.23) 39.2 (1.70) 29.4 (1.28) 23.4 (1$02) 19.2 (0.84) 16.4(0.71) 67.0 (2.91) 50.6 (2.20) 40.5(1.76) 33.5 (1.46) 28.6 (1.24) 94.5 (4.11) 72.0 (3.13) 57.8 (2.51) 48.0 (2.09) 41.2 (1.79) 122.0 (5.31) 93.3 (4.06) 75.1 (3.26) 62.7(2.72) 53.9 (2.34)
0.56 0.42 0.33 0.27 0.23 0.57 0.43 0.34 0.28 0.24 0.58 0.44 0.35 0.29 0.25 0.59 0.45 0.36 0.30 0.26 0.59 0.45 0.36 0.30 0.26
0.60 0.46 0.38 0.32 0.27
DF (degrees of freedom) in CpH,O+:DF in M+.
EtM, eV
1 3 5 7 9
koa1 (eV)-----
-----u,
----Ku----
c 3
c7
c3
c7
4.29(0.19) 9.63(0.42) 14.3 (0.62) 18.6 (0.81) 22.6 (0.98)
3.11 (0.14) 7.19 (0.31) 10.4(0.45) 13.3(0.58) 16.3 (0.71)
0.327 0.238 0.209 0.194 0.193
0.507 0.404 0.348 0.315 0.294
Because of the fluctuations about the average value,' the minimum value of Et" required in order to produce a (small percentage of) daughter ion P+ with sufficient energy to decompose further is simply the critical threshold value for the latter process. The standard deviation u of the energy distribution in P + produced from various ROH+ precursors has been calculated at five values of Et". The coefficient of dispersion is defined as K , = u / a j where a is the arithmetic mean. Illustrative calculational results are given in Table 11. It is evident that u increases as the molecular ion energy increases and decreases as the molecular ion size increases. The coefficient of dispersion decreases as the molecular ion energy increases and increases as the molecular ion size increases.
Relative Abundances of Parent C2H50 + and Metastable Ions ent ion except for a C-C bond stretch assigned as the reaction coordinate. In the loose model, several freThermochemistry and Structure of C2H.50+. Several quencies are reduced relative to the parent. The asisomers of CzH50+ have been proposed;s heats of formasignments are given in the Appendix. H2C-CH2 CHsCH=OH+ CHsCHzOf Computational Results. Calculations were made at \/ integral values of Et" for primary alcohols from C3 to O+ Cy. The two models for the activated complex gave H similar distribution curves, the loose complex being I I1 I11 shifted a little to lower energies; only the behavior for one of these models need be described in detail in the 172 (7.5j9 145 (6.3)1p10 211 (9.2)"~'~ remainder of this paper. HOCHzCH2+ CH3O +=CH2 Some illustrative distributions of the internal energy IV V of the C2HjO+ion for the rigid complex case are shown (211) (9.2)" in Figure 2 a t three values of Et". The distribution 170 (7.4)'O curves at other energies may be readily inferred; detion are listed under the structure number in kcal mol-' tails of the distributions for all other energy states and (eV) . From deuterium labeling and energetic studies of for both complex models can be found in ref 6. It is reaction l b in 2-alkanols) Van Raalte and HarrisonI2 seen that for a given value of Et", the maximum probproposed that the fragmenting ions had structure I ability shifts to lower energies with increase of molecular size. The separation of the maxima of the dis(6) Y. N. Lin, Ph.D. Thesis, University of Washington, 1970. tribution curves also increases somewhat as Et" in(7) H. M. Rosenstock and M. Krauss, "Mass Spectrometry of Organic Ions,'' F. W. McLafferty, Ed., Academic Press, New York, creases. N. Y., Chapter 1. Table I gives the most probable and the average A. G. Harrison and B. G. Keyes, J . Amer. Chem. Soc., 90, 6046 energies of P+ at some representative values of E + ~ . (8) (1968). The fractions of the average energy carried by P+ rela(9) J. L. Beauchamp and R. C. Dunbar, ibid., 92, 1477 (1970). (IO) A. G. Harrison, A. Ivko, and D. Van Raalte, Can. J . Chem., 44 tive to the total excess energy are also given. As Et" 1625 (1966). increases, the fraction of the average energy carried by (11) F. W. McLafferty, private communication. P + approaches the fraction of the total degrees of (12) D. Van Raalte and A. G. Harrison, Can. J . Chem., 41, 3118 internal freedom of M + associated with P+. (1963). Volume 74, Number 8
April 1 6 , 1970
Y. N. LIN AND B. S. RABINOVITCH
1772
c
2 "
(3.1 -4.1)
001
+ Figure 3. Schematic reaction path energy diagram.
rather than 11; support was advanced by Shannon and M ~ l a f f e r t y . ' ~Recently, Harrison and Keyess reported studies of 2-propanol-2-13C; 13C retention in CHO+ (reaction IC) indicates that 64% (using 20-eV electrons) or 52% (using 70-eV electrons) of the C2H60+ ions are structure I ; support for I1 has been given recently. g Since I apparently contributes most among isomers giving rise to the metastable decomposition, we have assumed for simplicity that we may specialize our considerations to the symmetrical oxirane ion structure for P+. It is plausible that in the 1-alkanol decomposition, CzH6O+ is formed with structure IV13and rearranges to I (and other isomers). Figure 3 is an energy diagram for reaction scheme 1. The constant increment 39 kcal (Le., 211-172) is to be superimposed on the distribution of P+in Figure 2. Model for CzH60+ Decomposition. I n order to calculate the mass spectrometric ion abundances, the critical threshold EoPfor C2Hs0+ decomposition and vibrational models for the precursor and the activated complexes are required. No literature value for EoP is available and the consequences of several assumed values were examined, namely, 71, 78, 87, and 109 kcal mol-l(3.08,3.39, 3.78, and 4.74 eV), called cases a, b, c, and d, respectively. McLafferty, et aZ.,I have noted that the activation energies for the two paths in scheme 1 are closely the same, and that the specific rates differ by a factor of 1.8-2.8,13*14 with m* (8.0) being larger. The activated complexes for the two decomposition paths were chosen to account for these facts (Appendix). The exact choice of frequencies is in no way crucial for our purpose here. Relative Abundances. Rletastables are observed in the conventional mass spectrometer if the rate constant k ( E p ) for decomposition is 105-106 sec-': for k ( E P )> 106 sec-l, daughter ions are mainly observed and for k(EP) < l o 6 sec-1, most P+ ions reach the collector. To find the yields of m" (8.0) and P + once EoPwas assigned, the total energy EP of I required to give a specific rate of decomposition of 3.3 X lo5 sec-l was computed. For the four EoP values of 71, 78, 87, and 109 kcal, EP (3.3 x 106) is 76.2, 84.7, 96.2, and 124.8 kcal mol-' (3.31, 3.68, 4.18, and 5.42 eV), reThe Journal of Physical Chemistry
a z E 0 0
c
U
0.001
-0 C
J
a
a
0.0001
1
I
I
I
1
I
2
3
4
I/D.F, ' M
(id)
Figure 4. Illustration of variation of relative abundance of m* (8.0) us. inverse degrees of freedom of M + for several assumed values of EO?ranging from 71 (case a ) to 109 (case d ) kcal mol-'.
spectively. By defining a practical energy width for metastable ion detection, the abundance can be found. An energy width was arbitrarily assigned to k(EP) values corresponding to one-tenth of the range from lo5 to lo0 sec-'.l5 This range of k(EP)corresponds to 5.56 kcal (0.24 eV) for Eop = 71 kcal mol-' (3.08 eV) and 6.86 kcal (0.30 eV) for EoP = 109 kcal mol-' (4.74 eV), for the m* = 8.0 process. For simplicity, 5.71 kcal (0.25 eV) was taken for all cases in the calculation of the metastable ion abundances. This procedure is justified in the Appendix. The relative abundance of the metastable and the parent ion was calculated for the energy distributions of P+ (Figure 2)) each evaluated a t integral energy increment between 0 and 10 eV for EtM, The parabolic weighting of Figure 1 was applied to each energy state of the molecular ion. Table 111 gives the details of the calculational results. (13) T. W. Shannon and F. W. McLafferty, J . Amer. Chem. SOC.,
5021 (1966). (14) F. W. McLafferty and H. D. R. Schuddemage, ibid., 91, 1866
88,
(1969).
(15) W. A. Chupka, private communication.
INTERNAL ENERGY PARTITIONING UPON ION DECOMPOSITION
EtM,
eV
__--
C-
7 -
m*
P+
0 0.0 1.o 1 0.0 1.o 2 0.0101 0.930 3 0.0220 0.354 4 0,0090 0.075 5 0.0021 0.020 6 0.0006 0.003 7 0.0002 0.001 8 0.0 0.0 9 0.0 0.0 10 0 .o 0 .o Tot abund 0.0896 5.39 m* (8.O)/P+ 0.017 D +/P + 1.95
m*
0.0 0.0 0.0
1.o 1.0 2 1.0 3 1.o 4 0.0003 0.998 5 0.0187 0.885 6 0.0134 0.578 7 0.0106 0.291 8 0.0059 0.123 9 0.0030 0.056 10 0.0015 0.020 Tot abund 0.088 12.30 m* (8.0)/P+ 0.0072 D +/P + 0.290
0.0 0.0 0.0 0.0
C --E-
-C 6
P+
Case b: EoP= 78 kcal (3.39 eV) 0.0 1.o 1.o 0.0 1.o 1.o 0.0 1.o 1.o 0.993 0.941 0.0012 0.0054 0.880 0.657 0.0089 0.0170 0.0158 0.632 0.0156 0.326 0.383 0.137 0.0159 0.0092 0.211 0.049 0.0114 0.0044 0.101 0.022 0.0070 0.0020 0.009 0.0040 0.043 0.0008 0.020 0.003 0.0020 0.0003 11.01 8.99 0.111 0.106 0.012 0.010 0.760 G .432
0.0 1.o 1 0.0 1.o 2 0.0 1.0 3 0.0042 0.965 4 0.0182 0.573 5 0.0120 0.213 6 0.0050 0.061 7 0.0018 0.023 8 0.0006 0.006 9 0.0002 0.0005 10 0.0001 0.0 Tot abund 0.085 8.22 m* (8.0)/P+ 0.010 D +/P + 0,908
0 1
m*
Case a : EoP = 71 kcal (3.08 eV) 1.o 1.o 0.0 0.0 1.o '1.0 1.o 0.994 0.0 0.0011 0.923 0.744 0.0074 0.0176 0.665 0.366 0.0184 0.0196 0.368 0.138 0.0182 0.0106 0.165 0.050 0.0121 0.0047 0.0068 0.078 0.0019 0.015 0.036 0.006 0.0034 0.0007 0.014 0.002 0.0017 0.0003 0.0008 0.005 0,0001 0.0001 0.130 9.16 0.116 7.33 0.016 0,014 1.15 0.735
0.0 0.0 0.0
0
7 -
P+
0.0 0.0
0.0 1.o 1 0.0 1.o 2 0.0 1.0 3 0.0174 0.685 4 0.0150 0.236 5 0.0053 0.060 6 0.0018 0.015 7 0.0005 0.004 8 0.0 0.0 9 0.0 0.0 10 0.0 0.0 Tot abund 0.088 6.68 m* (8.0)/P+ 0.013 D +/P + 1.38
0
c4-
1773
Case c: EoP = 87 kcal (3.78 eV) 1.o 1.o 0.0 1.o 1.0 0.0 0 .o 1.o 1.o 0.0002 0.995 0.0 1.o 0.985 0.916 0.0015 0.0068 0.648 0.0072 0.893 0.0146 0.0141 0.364 0.0132 0.690 0.176 0.0093 0.0142 0.460 0.0052 0.081 0.0117 0.280 0.0026 0.030 0.0084 0.155 0.0012 0.007 0.0050 0.071 0.093 10.98 0.085 13.02 0,0085 0.0065 0,443 0.221 Case d : Eop= 109 kcal (4.74 eV) 0.0 1.0 0.0 1.0 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.0 0.0 1.o 0.0017 0.985 0 .o 1.0 0.0044 0.924 0.0008 0.990 0.0096 0.765 0.0032 0.955 0.0116 0.533 0.0070 0.836 0.0101 0.338 0.0097 0.682 0.0050 0.170 0,0110 0.500 0.048 14.57 0.024 15.78 0.0033 0,0015 0.103 0,0319
7
m*
P+
c7-
7 -
m*
P+
1.o 1.0 1.o 0.985 0.0066 0.921 0.0140 0.765 0.0176 0.538 0.0172 0.374 0.0132 0.225 0.0092 0.138 0.0050 0.070 0.126 12.00 0.010 0,298
0.0 1.o 0.0 1.o 0.0 1.o 0.0023 0.978 0.0119 0.836 0.0178 0.602 0.0177 0.374 0.0129 0.208 0.0084 0.108 0.0049 0.056 0.0020 0.027 0.132 10.83 0.012 0.447
0.0 0.0 0.0 0.0011
0.0 0.0 0.0
1.o 1.0 1.0 0.0001 0.998 0.0036 0.963 0.0103 0.831 0.0153 0.633 0.0157 0.426 0.0126 0.247 0.0089 0.140 0.0050 0.070 0.103 12.42 0.0083 0.255
0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0012 0.990 0.0055 0.930 0.0113 0.783 0.0154 0.622 0.0152 0.447 0.0131 0.294 0.0110 0.160 0.088 13.84 0.0064 0.148
0.0 0.0 0 .o 0.0
1.0 1.0 1.o 1.o 0.0003 0.998 0.0026 0.973 0.0075 0.882 0.0180 0.707 0.0140 0.525 0.0124 0.360 0.0110 0.200 0.075 14.42 0.0052 0.107
0.0 1 .o 0.0 1.o 0.0 1.o 0.0 1.0 0.0 1.0 0.0008 0,990 0.0037 0.945 0.0076 0.875 0.0112 0.718 0.0132 0.565 0.0130 0.410 0.048 15.23 0.0032 0.057
0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1 .o 0.0 1.o 0.0 1.0 0.0007 0.990 0.0025 0.963 0.0054 0.875 0.0100 0.760 0.010 16.19 0.00062 0.00970
0.0 1.0 0.0 1.o 0.0 1.0 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0 1.o 0.0007 0.990 0.0023 0.960 0.0046 0.870 0.004 16.32 0.00025 0.00328
a Weighted by the parabolic function y = ax2 and weights 0.72, 1.81, 2.04, 2.12, 2.12, 2-04, 1.81, 1.54, 1.17, 0.74, 0.20 a t the excess energy values EtM of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 eV, respectively. b The abundance of m*' (18.7) is one-half that for m* (8.0) and no further description is necessary.
Volume 74?Number 8 April 16,1970
1774
Y. N. LIN AND B. S. RABINOVITCH
Table IV : Comparison of Methods of Calculating Metastable Abundances
C8
c7
E?", eV
1
2
3
4
5
6
7
8
9
Practical Correct Practical Correct
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0194 0.0210 0.0 0.0001
0.0150 0.0141 0.0012 0.0018
0.0053 0,0048 0.0055 0.0069
0.0018 0.0015 0.0113 0.0126
0.0005 0.0003 0.0154 0.0161
0.0 0.0 0.0152 0.0155
0.0 0.0 0.0131 0.0129
Some trends may be noted. The relative abundance of P+ is appropriately higher at lower energies. The metastable abundance is a maximum at lower energy for CS,moving to higher energy as n increases. For a given EOP,m* (S.O)/P+ decreases from CBto C7. The reason for this decrease is, of course, the fact that as R increases in size, the curves in Figure 2 which give the energy distribution of P+ ions formed from R f + shift to lower energies. Thus, for example, if an abscissa mark is placed on the 5 eV diagram of Figure 2 at 24,800 cm-l, corresponding to Eop = 71 kcal mol-', a larger fraction of the distribution for C7 lies to the left of this mark, and corresponds to P+ product, than is the case for the distribution for Ci; the decomposition of P+ to yield detectable metastable arises mainly from a narrow region to the right of this abscissa mark; and most of the area to the right of this narrow region corresponds to production of daughter ions. The log of the relative abundances of the metastables are plotted in Figure 4 against the reciprocal of the degrees of freedom of the molecular ion. The parameter m* (8.0)/P+ ranges from 0.017 for C3 precursor to 0.010 for C7 precursor in case a, and 0.013 to 0.0064 in case b and in case d, the corresponding values are reduced to 0.0072 for C3 precursor and 0.00025 for C7 precursor. Experimentally, Mc1,afferty and Pike' found the value of the quantity m*/P+ to be 0.0032 for C3 precursor and 0.0014 for C7 precursor, with a ratio of roughly 2, for the m* (8.0) process. Cases a and b in our calculation give the correct ratios but have larger absolute abundances for m*/P+; however, the experimental absolute abundance is instrumentally dependent, and is frequently less than the theoretical prediction; hence cases a and b may be considered to be good representations of the n-primary alcohol molecule ion decomposition. Other systems with much greater spread in m*/P+ than the alcohols were also observed by McLafferty and Pike.' The calculations show that one way this can be realized is by going to higher values of EoP.
Discussion The quasi-linearity of the plot of log m*/P+ US. (DF)-I observed by RIcLafferty and Pike was not explained by them. From our calculational result, a slight curvature was found for this relationship. The agreement with the experimental data is quite satisfactory. Since there is an equilibrium between structure 1 and others,s the energetics used for the metastable The Journal of Physical Chemistry
0.01
I I
2
3
I / D.F. M' ( I O - * ) Figure 5 . Variation of relative abundance of D + us. DF M + for cases a, b, c, and d.
decomposition (39 kcal released by IV + I as used above to calculate the total excess energy of I) are somewhat arbitrary. Nevertheless, the calculated characteristic properties are still valid. The quantity of the energy released will only affect the choice of the C2HbO+energy in counting the abundance of m*. The Abundance of the Daughter Ion. A complete mass spectrum for 1-alkanols with 70-eV electrons at 250" was reported by Friedel, Shultz, and Sharkey.l6 By assigning m/e 19 as uniquely from H30+, the ratios of the abundances of m/e 19 to m/e 45 ((22H50+)for 1-alcohols are 0.60, 0.50, 0.36, 0.27, and 0.27 for C3, C4, CS,Ce, and C'I alcohols, respectively. Cases a and b in our calculation give ratios of D+/P+ of the (16) R. A. Friedel, J . L. Shultz, and A . G. Sharkey, Jr., J . Anal. Chem., 28, 926 (1956).
INTERNAL ENERGY PARTITIONING UPON ION DECOMPOSITION correct order of magnitude but larger variation with n in the series (Table 111). The log D+/P+ us. the reciprocal of the DF in the molecular ion is plotted in Figure 5 .
1775
CzHsO+ part of the complex was reduced to 0.167, i.e., 270 -t 45 cm-l. C. CzH60 + Metastable Decomposition. The frequen-
Appendix
cies of oxirane ion were obtained by adding three frequencies for one extra H + to the assignment for ethylene oxide;ls these three frequencies were estimated from the known frequencies for H20+ vis d vis HzO. The grouped frequencies are 3040 ( 5 ) , 1450 (4), 1170 ( 5 ) , 837 (4). The frequencies of the activated complex depend on the reaction path. The specific rate for the m* = 8.0 process is twice that for m*' = 18.7.1b The frequency factor for the thermal decomposition of ethylene oxide is 10i4.'3.'9 From these considerations, the grouped frequencies of the activated complex were taken as follows: (a) m* = 8.0: 3040 (3) 1523 (4) 1170 (3) 837 (4) 582 (2) 363; (b) m* = 18.7: 3040 (3) 1466 (3) 1203 (4) 837 (4) 725 (2) 567.
Frequency Assignments
Calculation of Metastable Abundances
A . ROH and the Rigid Model for M + Decomposition. The alcohol frequencies (cm-') were assigned by combining the frequencies of the n-alkanes17&with those of the alcohol function17b: six new modes (O-H stretch 3685, C-O-H bend 1390, C-0 stretch 1066, C-C-0 bend 898, C-C-0 bend 470, O-H twist 280) were added to, and three modes (C-H stretch 2965, H-C-H bend 1460 (2)) were removed from the alkane assignment. The reaction coordinate was a C-C stretch at -1020 cm-'. The frequencies of CzHsO+ combined the six new modes described above with C-H stretch 2966 (2), 2882 (2); C-H bend 1388 (2), 1305 (2); C-C stretch 1046; C-C bend 1279; C-C rock 903; C-C torsion 270. The alkyl radical frequencies and the transitional modes were those that remained after the CzH60+ frequencies were removed from the original alcohol. These assignments are very approximate, but are adequate for the present purpose. B. The Loose Model for M + Decomposition. The reductions in frequencies were arbitrary. In the loose model for propanol ion decomposition, three C-H bendings and one C-C bend were reduced to 0.1 of their values, and two torsions were reduced to 0.167. For butanol ion and the rest of the series, two C-C bendings and two C-H bendings were reduced to 0.1 of their values and three torsions mere reduced to 0.167 of their original values. One torsional mode in the
This method of calculating metastable ion abundances is "quick and dirty" and neglects the fact that k ( E P ) is a relaxation time and that the lifetime of excited molecules is not a &function distribution, C ? ~ , ~ ~ - I . The correct method of counting the metastable ion events should sum all the contributions for all k(EP)values. For each ,%(Ep) value, there is a decay curve obeying the relation nJno = exp (-k(EP)t). The metastables are observed in a one-microsecond interval taken at t = (3.3 X lo5)-' = 3 X sec. The fraction of P+ ions observed as the metastable so obtained is
