Internal Energy of Product Ions
713
thracene is a more efficient electron scavenger ” than dienes and therefore the formation of diene anions is suppressed when anthracene is as an additive. The presence of anthracene anions in such samples has been confirmed by ESR measurements as well.4 No direct proof for the existence of diene cations can be given.
References and Notes (1) H. Katzer and H. Heusinger, Makromol. Chem., 163, 195 (1973). (2) A. v. Raven and H. Heusinger, J. folym. Sci., in press. (3) R. Kaufmann, Thesis, Technical Universtty Munich, 1974.
E: ~
~
~
~
~ yFf;06 , u
,
(1970), (6) H. C. Longuet-Higgins and J. A. Pople, Roc. fhys. Soc., 68, 591 (1955).
~
Internal Energy of Product Ions Formed in Mass Spectral Reactions. The Degrees of Freedom Effect‘ P. F. Bente, 111,28~b F. W.
McLafferty,’
D. J. McAdoo,2a,Cand C. Lifshitz2d
Department of Chemistry, Cornel1 University, Ithaca, New York 14850 (ReceivedJune 28, 1974; Revised Manuscript Received December 23, 1974)
The factors affecting the distribution of internal energy values, P(E),in secondary ions produced in the ion source of a mass spectrometer have been studied through experimental and theoretical investigations of the degrees of freedom (DOF) effect on the metastable to precursor intensity ratio for a common metastable transition (m*) in a homologous series of molecular ions (M.+). An experimental study of the C3HsO.’ and metastable intensities for the process M.+ C3Hs0.+ C2H30+ (m*) for 16 2-alkanones ranging from C6H120 to C31H620 showed a linear relationship between [m*(C3H~0.+ C2H30+ CHy)] and the reciprocal of the number of internal degres of freedom in Ma+. Theoretical calculations of the DOF effect used the 2-alkanone photoelectron spectra and the optical approximation of Meisels to obtain P(E)M.+. Rate constants for formation of C3HsO+, and other competing pathways as a function of molecular ion internal energy, k ( E ) ,were calculated using Rice-Ramsperger-Kassel-Marcus theory. The P(E)QH~O.+ functions were calculated by assuming statistical randomization of the excess internal energy between the C3H60-+ and the neutral fragment. The resulting calculated DOF plot was linear and had a slope in excellent agreement with the experimental results. The decreasing average internal energy of C3H60-+with increasing size of M.+ arises because increasingly large neutral fragments carry away a larger fraction of the M-+ internal energy. Offsetting this is an increasing abundance of tight complex fragmentations of Ma+ which compete with C3H60-+ formation a t low Ma+ internal energies, causing the average internal energy of those M.+ ions which fragment to give C3H60.+ to be higher for larger M.+ ions. The general factors which affect P ( E ) of product ion A+ are (1)P(E)M.+;(2) reactions competitive with A+ formation; and (3) the partitioning of excess energy between A+ and the neutral fragment.
-
Mass spectral ion abundances have been interpreted in terms of fragmentation rate constants as a function of ion internal energies, Iz(E), and the internal energy values of the precursor ions, P(E).3s4Calculations of K(E) using the Rice-Ramsperger-Kassel-Marcus theory5 have provided satisfactory agreement with e ~ p e r i m e n t . ~For - ~ molecular ions, M.+, useful approximations to P(E)M.+ can be derived from the photoelectron spectrum of the corresponding mole~ule.6,~ However, such methods will not yield information about P(E) of a primary product ion, such as A+; for the reaction sequence M.+ A+ D+, prediction of [D+] using ~ ( E ) A + + Dfrom + RRKM calculations requires a knowledge of P(E)A+.The following factors should be important in determining p @ ) ~ +(i) : P(E)M.+; (ii) k ( E ) for Ma+ A*+; (iii) the k ( E ) functions for competing decompositions of M.+ (M.+ B+, C+,. . .); and (iv) partitioning of excess energy between the A+ ion and the neutral lost.3,6v8*9 A qualitative assessment of these factors has been made;1° this paper presents quantitative calculations to test further these assumptions.
- -
-
-
-
-
+
A further reason for this study is to investigate the origin of the so-called “degrees-of-freedom effe~t”.~0-13 For the fragment ion A+ found in each of the mass spectra of a homologous series of molecules and the metastable decomposition of A+ forming the daughter ion D+ in a field-free region of the mass spectrometer, m*(A+ D+), the abundance ratio [m*(A+ D+)]/[A+] is found to decrease as the size of the molecule increases. In fact, for all of over 30 homologous series of a wide variety of compounds examined in this laboratory the logarithm of [m*(A+ D+)]/ [A+] is found (Figures 1 and 2) to give within experimental error a linear correlation with the reciprocal of the number of internal degrees of freedom of the molecule (DOF = 3n - 6, where n is the number of atoms in Ma+). This correlation is notable because of its generality, especially considering all of the competing factors which affect P(E)*+.1° Further, the linearity of the correlation predicts a finite value for [m*]/[A+] for an infinite molecular size, meaning that some A+ ions formed from such a molecular ion will still have sufficient internal energy to fragment at a rate of
-
-
-
The Journal of Physical Chemisrry, Vol. 79, No. 7, 7975
~
P. F. Bente, F. W.
71 4
McLafferty, D. J. McAdoo, and C. Lifshitz
P ( E ) c ~ H ~ ois. +probed experimentally by comparing the abundance of metastable A+ ions having the narrow range of internal energies required for methyl loss in the fieldfree drift region to the abundance of the lower energy C3HsO-+ ions which reach the detector undecomposed [m*(C3HsO.+ CzH30 + CHy)]/[C3H,@.+]. This system is well suited for experimental study and the quasiequilibrium theory calculations for several reasons. The C3H&+ ions, which are of high abundance in all these 2-alkanones, are formed by y-hydrogen rearrangement involving a sixmembered ring transition state which has been shown to be highly specific for several lower molecular weight 2-alkanones.6 A substantial body of experimental data exists for the 2-alkanones including studies by photoionization and charge exchange, and for the product CSH6O-+ ion including studies of its structure and decomposition.6*9J~-'7 The energy requirement for the reaction C3H60-+ C2H30+ CHY has a relatively high value of 1.2 eV,17J8 so that the CzH30+)] value provides a measure of the [m*(C&O.+ abundance of C3HsO.+ ions formed with this relatively high internal energy. To recheck the linearity of the DOF effect, data for 16 homologous 2-alkanones were measured in one time period using a reverse-geometry double-focusing mass spectrometer under computer control (Figure 2). +
-+
L
I
I
I
1
0
I
2 IO?DOF(M?)
3
4
-
Figure 1. The degree-of-freedom (DOF)effect in 1-alkanols: (a) experimental results of ref 11; (b,c)calculated results of ref 14 assuming Eo(C2H50+ H30+) = 3.4 and 3.7 eV, respectively.
\
0
5
-
+
-+
Experimental Section
/
/ 0
m"
C,H,O+CJI
CJH,0+-C2H30' 52
6'
2
I
IOO/DOF
(M')
Figure 2. The DOF effect for 2-alkanones: 0, experimental values; 0, calculated values (see text), using calculation II for c6. C7, and Cg,and calculation I for the remaining compounds.
-IO6 sec-l in the metastable drift region. Although it is perhaps a moot question whether an infinitely large molecular ion will indeed fragment to give any A+ ions, the existence of a finite interceptll could imply that the excess internal energy of the fragmenting M-+ ion is not randomized between the very large neutral fragment and the A+ ion, contrary to the assumptions of the quasiequilibrium theory (vide infra).3 In a calculation of the DOF effect for C2H50+ ions formed from 1-alkanols, Lin and Rabinovitch14 predicted a nonlinear DOF effect in which log [m*]/[A+] approaches -00 as 1/DOF approaches zero (Figure 1). The model used assumed statistical partitioning (randomization) of the excess energy of M.+ between the CzH50+ ion and the alkyl neutral fragment, and the disagreement of the calculated results with experiment (Figure 1) at high DOF values could be due to the failure of this assumption. The disagreement could also arise from their assumption that P(E)M.+is independent of the size of Me+; apparently no study comparing P(E)M.+functions for a homologous series of molecules has been reported previously. We present here experimental and theoretical studies on P ( E ) of the primary product C3HsO-+ions formed from 2alkanones ranging in size from CBHIZO to C31H620. The Journal of Physical Chemistry, Vol. 79, No. 7, 7975
Mass spectra, metastable ion (MI) spectra, and collisional activation (CA) spectra were obtained on a modified Hitachi RMU-7 double-focusing mass spectrometer in which the magnetic sector precedes the electrostatic analyzer.19 Operating conditions were: 70-eV electron energy, 100-pA total emission, 3.9-kV ion accelerating potential, 1.25-1.5kV multiplier voltage, 1-2 X Torr source pressure, and an ion source temperature of 225'. Abundances of C3H6O.+, C2H3O+, C3H70+, and C,H,+ (signifying all ions containing only C and H) ions in the normal mass spectra are shown in Figures 3 and 4; an AEI MS-902 was used where necessary to resolve isobaric ions. For the MI data the pressure in the field-free drift region between the magnet and the electrostatic analyzer was less than 3 X Torr so contributions from collision-induced metastables were negligible. The mass spectrometer was interfaced with a Digital Equipment Corp. PDP-8 computer to give automated data acquisition and computer control of the electrostatic analyzer (ESA) potential.20 The relative intensities of m*(58-+ 43+) and m/e 58-+ for the DOF plot were determined by scanning the ESA potential alternately over the metastable and precursor ion regions, changing the gain of the dc amplifier manually be a factor of 625 between regions. Ten scans were computer summed to give composite peaks, and the ratio [m*(58.+ 4 43+)]/ [%e+] was calculated from the maximum intensities and the known gain of the dc amplifier. The shape and peak width of the metastable transition were identical for all the 2-alkanones examined, indicating that the peak heights adequately represent the relative peak intensities.21 The experimental ratios (Figure 2) were found to be reproducible to within -5%. MI and CA spectraz2 were obtained for the molecular ions and other high mass oxygen-containing ions as described previ0usly.19,~~ The MI spectrum of 2-dodecanone is shown in Figure 5 ; other spectra are included in ref 2a.
-
Synthesis of Compounds The 2-alkanones C14H280, C15H300, C17H340, Cz1H420,
715
Internal Energy of Product Ions
-
0.4r
gies, Eo, were calculated using RRKM t h e ~ r y . For ~ - ~reactions with Eo < Eo(M.+ C3H60.+), k ( E ) were estimated using the available experimental information from metastable ion spectra, collisional activation spectra, and low electron-energy mass spectra. The probability that a molecular ion of any particular internal energy E will fragment to form a C3H60.+ ion was then calculated from the corresponding k(M.+ C3H6OS+)and the rate constants at that energy for the competing fragmentations. The internal energy of the C3H60.+ from an Ma+ of a particular energy was calculated assuming that the excess internal energy in Me+ is randomized between the C3H60.+ ion and the 1-alkene neutral fragment in porportion to the density of states in each. These results weighted according to P(E)M.+ gave P(E)QH~O.+. For the ratio [m*(C3HsO-+ C2H3o+)]/[C3H60.+] the value of [C3H&.+] was derived from the area of P(E)c~H~o.+ below the appearance potential for CzH3O+ formation, A(C2H30+), and the value of [rn*(C3H&.+ + CzH30+)] from the area of the "metastable window" of energies a t A(C2H30+). Rate constants and energy partitioning were a t 0.lO-eV intervals; a sample calculation for 2-hexanone a t 0.05-eV intervals showed no significant differences in the calculated [rn*]/[C3H&.+] ratio. Details of these steps are given below. Complete calculations were carried out for C~HIZO,C7H140, C ~ H I ~ O , CgH180, C11H220, C17H340, C31H620; results for all but C7H140 and C9H180 are shown in Figures 4-8.24 Calculation o ~ P ( E ) M .Photoelectron +. spectra at 21.2 eV were obtained for acetone, 2-butanone, 2-pentanone, and 2-hexan0ne~~ and for 2-hexanone, 2-heptanone, 2-octanone, and 2 - u n d e ~ a n o n e(Figure ~~ 6a-8a).24 The spectra show a transition a t low energy, assigned to ionization from a nonbonding orbital on oxygen, and an unresolved group of transitions a t higher energies assumed to arise principally from orbitals belonging to the alkyl chain. The energy difference in onset of the alkyl and carbonyl peaks was found to correlate with the size of the 2-alkanone (Figure Ila); data from the two sets of spectra gave linear correlations with the same slope when the ratio of the areas of these peaks was plotted against the number of carbon atoms in the 2-alkanone (Figure l l b ) . Photoelectron spectra for the other 2-alkanones (Figures 9a and were obtained by interpolation and extrapolation of the correlations of Figure 11. Following the treatment of Meisels,7 the energy deposition function D(E)was obtained from the photoelectron spectrum and the electron energy loss function F(E,) using the relationship
-
T 0.6r
0
0.4
O
0
I-
0
I
- 0 . 0
d
.
2
+
1001DOF (M)
Figure 3. Abundances of C3H60.+ and C*H30+ ions relative to the total ion abundance, in the normal mass spectra of 2-alkanones as a function of the, number of molecular degrees of freedom: 0 , experimental values: 0, calculated values; 0,calculated for only the direct process, M-+ C*H3O+.
-
0 4-
0O 0'
II
L2
IOO/DOF(M)
Figure 4. Abundances of CsH70+ and C,H,+ (species containing only C and H) ions relative to the total ion abundance, in the normal mass spectra of 2-alkanonss as a function of the number of molecular degrees of freedom: 0 , experimental values; 0, calculated values.
C23H460, C26H520, and C31H620 were synthesized from the corresponding straight chain carboxylic acids by refluxing the acid with CH3Li in t e t r a h y d r ~ f u r a nwith , ~ ~ purification by vacuum sublimation. The remaining 2-alkanones were obtained from commercial sources, with purity checked by gas chromatography and mass spectrometry.
-
Calculations The ratio [m*(C3H60-+ C~H30+)]/[C3H60+]was determined from P(E)QH~O.+ based on the factors outlined previously.8J0 Calculation I considered the effects of dissociations of both low and-high energy M.+ ions in competition with the formation of C3M6O-+,while calculation I1 assumed that only high energy pathways were of importance competitively. The energy deposition function for electron impact ionization was obtained from the photoelectron spectrum of the 2-alkanone, using the optical approximation of M e i ~ e l sthis ; ~ was convoluted with the thermal energy of the molecule before ionization to obtain P(E)M.+. Rate constants as a function of ion internal energy, k(E), for unimolecular decompositions of Ma+ to C3H60.+ ions and to form product ions requiring higher activation ener-
D(E)=
s"""
x(En, E ) P ( E n )dEn
I(M)
where I(M) is the ionization potential of the molecule M and E,,, is the energy of the ionizing electrons. x(E,,E ) , the probability that an electron which loses energy E , will deposit internal energy E in the molecular ion during the ionization process, was obtained from the photoelectron spectrum of M. For E,, less than E H ~the ~ energy , of the helium I resonance line at 21.2 eV, x(E,, E ) was set equal to the photoelectron spectrum truncated a t E = E, and normalized to unit area. For E, > E H ~x(E,, ~ , E ) was set equal to the He1 photoelectron spectrum normalized to unit area. In calculating the energy loss function from the relation
the relative photoionization cross section, a@,), for the 2alkanones was assumed to be equal to that obtained experiThe Journal of Physical Chemistry, Vol. 79, No. 7, 1975
716
P. F .
Bente, F. W . McLafferty, D. J. McAdoo, and C. Lifshitz
1/
2-dodecanone m/e 184 ( M t ) Unimolecular Metastable Spectrum
1
md
Figure 5. The metastable ion decompositions (MI spectrum)of the molecular ion ( d e 184) of 2-dodecanone. mentally for n-butane.27 Theoretical calculations2* and the limited experimental data available indicate that the general shape of u@) is the same for most organic molecules. D(E)was convoluted with the thermal energy distribution in the molecules before ionization to obtain the distribution of internal energy in the molecular ion, P ( E ) ~ + , 4 - 7 9 ~ 4 Figures 6b-lob. Reaction Mechanisms. The C3H60.+ and CzH3O+ ions were assumed to be formed from the 2-alkanone molecular ions as shown in reactions 1 and 2,6J7 with assumed free 0+‘
1’
0
2
4
6
1 0 1 2 1 4
8
E(eV)
Figure 6. Data and results of calculations for C6HI2O: (a)photoelectron spectrum of the molecule (experimental data): (b) calculated functions for p(&.+ and p(E)M.+-~H~o.+;(c) calculated HE) functions for (i) M.+ c~H~o.+; (ii) M-$ c ~ H ~ o -(iii)+ ;M.+ c,H,,,*+; (d) calculated value of ~ ( E ) c ~ H ~ functions. o.+ The vertical line at 1.2 e V represents the “metastable window” for C3H60*+ C2H30+.
-
rotations indicated by the circular arrows (vide infra). Collisional activation spectra, as well as metastable ion spectra, of a variety of odd-electron ions in the mass spectra of higher 2-alkanones gave no evidence for the formation of C3H&.+ ions from fragment ions. Substantial evidence has been offered that reaction 1 proceeds through a stepwise m e c h a n i ~ m .At ~ ,lowest ~ ~ ion energies transfer of the y hydrogen has been shown to be substantially faster than the subsequent ,B cleavage for butanoic a ~ i d ; a~ t9higher internal energies, it would be expected that the tighter-complex rearrangement would be less favored relative to the simple cleavage of this second step. We have assumed that the hydrogen rearrangement is nearly complete in the transition state and that the /3 bond is partially cleaved; however, the relative results are not changed appreciakly if the ,B bond is assumed to be normal in the activated complex. The most important properties (besides the Eo values) of the activatThe Journal of Physical Chemistry, Vol. 79, No. 7, 7975
-
-
-
ed complexes for the competing M-+ dissociations are the relative number of free rotors in each, as an additional free rotor causes the sum of energy states to rise more rapidly with increasing energy. All hydrocarbon ions were assumed to originate by direct cleavage of a carbon-carbon bond in the alkyl chain with retention of the charge on the alkyl fragment to form the CnHan+l+ ion series (for example, reaction 3), and with subsequent loss of Hz or CH4 t o form the CnH2n-l+ ion series. Activation Energies, Eo. For reaction 1, Eo was chosen as 0.6 eV in order to give kl(E) N lo6 sec-l for E = 0.9 eV, in agreement with the difference between the extrapolated 0°K photoionization appearance potential ( A ) of C3H60.+ and the adiabatic ionization potential ( I ) of 2-hexanone.15 The onset of CzH30+ production from 2-hexanone is not clearly defined in measuring A, so that the value of A = 1.7 eV is an upper limit on Eo(CsH120.+ C2H3O+) and includes the effects of a kinetic shift and a competitive shift.5
-
717
Internal Energy of Product Ions
I/
\ d'
L4 I ,IC1
0
2
0
E (eV)
Figure 7. Data and results of calculations for C8H160:(a)photoelectron spectrum of the molecule (experimental data); (b) calculated functions for q&.+ and q&.+-.C H 6 ~ . + ; (c) calculated HE) functions for (i) M.+ C3H80"; (ii) M-S C2H30"; (iii) M.+ c,H,++; (d) calculated value of qE)c3Hso.+ functions. The vertical line at 1.2 eV represents the "metastable window" for C3H&-+ +
-
-
-
C2H3O+.
I
4
I
I
I
6
I
B
I
,
I
I
1 0 1 2
,
,
14
E (eW
Figure 9. Data and results of calculation for C17H340: (a)photoelectron spectrum of the molecule (extrapolated data): (b) calculated functions for q&.+ and P(&.++c H~o.+; (c) calculated YE) functions for (i) M.+ C3H60.+; (ii) M.$ ~ 2 ~ 3 0 . f ;(iii) M.+ c,H,,,-+; (d) calculated value of ~ . € ) C ~ H ~ O functions. .+ The vertical line at 1.2 eV represents the "metastable window" for C3H60-+ C~H~O+.
-
-
-
+
E(eW
Figure 8. Data and results of calculations for CllH220: (a) photoelectron spectrum of the molecule (experimentaldata); (b) calculated functions for S 4 M . t and ~E)M.+-.c nee.+; (c) calculated N€j functions for (i) M.+ C3HeO.'; (ii) M.$ C2H30"; (iii) M.+ C,,H,.+; (d) calculated value of SE)C3He0.+ functions.The vertical line at 1.2 eV represents the "metastable window" for CSH~O-+ C#30+.
Figure 10.~Data and results of calculations for C31H620: (a) photoelectron spectrum of the molecule (extrapolated data); (b) calculated functions for PI&.+ and q€)~.+-cH ~ O . + ;(c) calculated HE) functions for (i) M.+ c ~ H ~ o - +(ii); M-S c ~ H ~ o * +(iii) ; M.+ c,H,-+; (d) calculeted value of q & H & . t functions. The vertical line at 1.2 eV represents the "metastable window" for C3H80-+
Eo = 1.0 eV was chosen to give agreement with the above
curves for these three processes are shown ip Figures 6c1oc. The competition from processes with activation energies lower than 0.6 eV but with activated complexes which are tighter than that for C3HcOv+ formation is important for the larger 2-alkanones. The unimolecular metastable spec-
-
-+
-
-+
results and with the competition between C3H60.+ and C&@+ formation as measured by charge exchange.I6 Eo = 1.1 eV was chosen for reactions of type 3 to give agreement with the observed intensity of hydrocarbon ions in the normal mass spectrum of 2-hexanone. The calculated rate
-
-
-+
-+
c~H~o+.
The Journal of Physical Chemistry, Vol. 79, No. 7, 1975
P. F. Bente, F. W. McLafferty,D. J. McAdoo, and C. Lifshitz
2 .o
r
-
E (eV)
*
e
LOL
28L ,I-
!
j
24
jlij
20
/
12
1
1
n
Figure 11. Photoelectron spectra of 2-alkanones: (a) the difference
in onset energies (eV)for the alkyl and carbonyl peaks as a function of the number of carbon atoms: (b) the ratio of areas of the alkyl and carbonyl peaks as a function of the number of carbon atoms for spectra from two different sources (see text).
tra of the 2-alkanone molecular ions show many transitions, increasing in number as the 2-alkanone becomes larger (Figure 5);many of the ions resulting from these low energy reactions are of negligible abundance in the normal mass spectrum, as noted p r e v i o ~ s l y . For ~ ~ , 2-alkanones ~~ larger than CSHI~O, there is no observable metastable transition of the molecular ion to give C3H60.+ despite the fact that this “tight complex” reaction gives a favored product in the normal spectrum. On the other hand, the ions present in the metastable ion spectrum of these M.+ are not common in the normal mass spectrum, indicating that these processes have tighter activated complexes as well as Eo < 0.6 eV. These processes should cause a competitive shift in A(C3H&.+); for this in calculation I, it was required that the rate constant for formation of C3H&b+ reach -107 sec-l before the process can be observed. A sharp onset in P(E)M.+-+c~H~o.+ a t this internal energy, E,, was assumed as shown in Figures 6b-lob. This low energy competition is not important for the lower 2-alkanones; the effect of this assumption was checked in calculation I1 by assuming a minimum rate constant of 106 sec-l. Calculation I11 neglects competition from both low and high energy processes, and assumes the energy deposition function in producing M-+to be approximately parabolic, ranging in energy from 0 to 8 eV, similar to the assumptions of Lin and Rabinovitch;l4 however, in contrast, in calculation 111, this function is convoluted with the thermal energy calculated for each 2-alkanone. Eo for C3H60+ C2H3O+ was estimated to be C1.2 eV from heat of formation data;ls calculations were made with values of 0.8, 1.0, and 1.2 eV to test the effect of this assumption. Calculation of k ( E ) .Rate constants for decomposition of the molecular ion via the nth pathway were calculated as a function of internal energy from RRKM theory using the relation
-
where G i ( E - EO)is the sum of states up to energy E - EO in the activated complex, N*(E) is the density of states of the molecular ion at energy E, h is Planck’s constant, and Lt is the reaction path degenera~y.~ The ratio of the partition functions for the adiabatic rotations of the activated complex and the molecular ion, Qnt/Qn*, was assumed equal to unity. Vibrational frequencies for the 2-alkanone molecular ions, assumed to be equivalent to those for the corresponding molecules, were obtained by combining the frequencies characteristic ,of the CH3COCH2- group with those of the appropriate alkyl group, CH3(CH&-. The latter were obtained from the frequencies of the n-alkane CH3(CH2)n-1CH3 by removing three frequencies associated with a C-H bond in the CH3 group and changing the other CH3 to the corresponding CH2 f r e q ~ e n c i e s .The ~~ frequencies for the CH3COCHp group were obtained from those of acetone in a similar fashion. In addition six new frequencies were added which correspond to the six modes associated with the new C-C bond. In a similar way the frequencies for the 1-alkene molecules were calculated from the frequencies for the n-alkanes and propene.24 Three free internal rotations were included in the energized M.+, and reduced moments of inertia were calculated from standard bond angles and distances according to the method of Hershbach.32 For the activated complex configuration of reaction 1, the three free internal rotations of M-+ were substituted by low frequency torsional modes; earlier studies have shown that the change, not the absolute number of free rotors, is the principal factor in determining k (E).6CH2 deformation frequencies for methylene groups in the ring were increased by a factor of 2, the CH stretching and CH bending frequencies for the hydrogen transferred to the oxygen were reduced by a factor of 2, and the reaction coordinate was taken to be a C-C stretch a t 1050 cm-l. The symmetry factor was equal to 2 for this reaction. Reaction 2 was assumed to proceed by a “loose” complex in which the C-C bonds involved in ring formation in reaction 1 were taken as free rotations and a C-C stretch a t 1200 cm-l as the reaction coordinate. Other frequencies were assumed to be the same as in the molecule ion, and the symmetry factor was set equal to 1. Reaction 3 was assumed to proceed by a “loose” complex equivalent to that for reaction 2. To account for the fact that alkyl fragment ions, or their further decomposition products, are produced by cleavage of any C-C bond in the alkyl chain of the 2-alkanone molecular ion, the symmetry factor L was varied linearly with increasing size of the alkyl chain. L was set equal to 2 for 2hexanone in order to give agreement with the experimentally observed abundance of hydrocarbon ions in its mass spectrum. This gives a range of L from 2 for C6H12O-+to 27 for C31H620.+.Sums and densities of states for the active molecule-ion and the activated complexes, respectively, were evaluated using the approximations of Whitten and Rabinovit~h.j,~4>3~ Energy Partitioning. The excess energy of the molecular ion was assumed to be partitioned statistically between C3H60.+ and the 1-alkene neutral fragment according to the formula given by V e ~ t a l : ~ r
where W ( E ,e) de is the probability of finding energy e to ( t The Journal of Physical Chemistry, Vol. 79, No. 7, 1975
719
Internal Energy of.Product Ions
+
de) in the C3H60.+ ion when there is energy E in Ma+, and N1 and Nz are the densities of states5~24~32 for the C3H60.+ ion and the neutral fragment, respectively. As noted by Lin and Rabinovitch,14 the general results of energy partitioning are not sensitive to the details of the vibrational frequencies, and uncertainties in these parameters are outweighed by the uncertainties in P ( E ) M +and
P(E)M.+-C3HeO.+P ( E ) c ~ H ~ oThe . + . internal energy distribution function for the C3H60.+ ion was calculated by integrating W ( E , e) de over all values of E weighted by P(E)M.+--c~H~o.+ as follows:
These distributions are shown in Figures 6d-10d. The intensities of the C3H60-+, m*(C&O*+ .+ C&@+), and the CzH3O+ formed from C3H60.+ were calculated from P ( E ) c ~ H ~ ousing . + the approximation that ions with internal energy less than Eo remain as undecomposed C3&0.+ ions while ions with internal energy greater than Eo will decompose to form CzH3O+ ions in the source. Those ions in a narrow energy range (-0.01 eV) about Eo will appear as metastables; the width of this “metastable window” was arbitrarily chosen so that the calculated and experimental ratios of [m*(C3H60.+ CzH30+)]/[C3H60-+] would be equal for 2 - h e ~ a n o n e . 1 ~The 3 ~ ~use of such a “metastable window” in place of a more complicated calculation of the metastable intensity based on the contribution from precursor ions with a range of rate constants for decomposition over the time interval the precursor ion spends in the field free drift region has been shown to be reasonable by Lin and Rabinovitch.14 Figure 12 shows the relative probabilities that a molecular ion with internal energy E will decompose to give nondecomposing C3H60.+ ions, to give C3H60.+ ions undergoing metastable decomposition, or to give C3H60.+ ions with sufficient energy to produce C2H30+ ions, using calculation I with Eo(C3H@+ CzH30+) = 1.0 eV. These data combined with P(E)M.+give the predicted values of [C3H60.+] in the normal mass spectra shown in Figure 3; the calculated values of [CzH30+] combine the production from C3Hs0.+ and directly from M.+. The value for the total hydrocarbon ions [C,H,+] represents the combined products for high energy reactions, and [C3H,0+] signifies the total abundance of the doubly-rearranged product plus other low Eo, tight complex reactions as predicted by calculation I.
“i 1, 3 c31 H63°
, , , , ,
-
0.2 ‘ 0
2
4
6
8
EW)
IO
12
14
16
-
Figure 12. Calculated probabilities as a function of internal ener y that M a + wilt decompose to give C3H60*+, me(C3H6O.+ C2H309), and C2H30+ from the decomposition of C3H60-+.
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from 4-alkanonesp indicating that the change in [m*(A+ D’)]/[A+] does reflect the change in P(E)A+. Ion Abundances. In general, the abundance values for the major ions in the normal mass spectra (Figures 3 and 4) agree well with those predicted. The error in predicting C3H60.+ abundances for the smaller 2-alkanones may result from errors in the P(E)M.+distribution, since C3H60-+ is produced from a region of P(E)M.+which shows a valley for these compounds. The proportion of Ma+ ions of these energies could be much greater than that assumed (Figures 6a, 7a) due to autoionization or optically forbidden transitions which occur with finite cross section under electron impact. The calculated values for [C3H6O.+] and [CzH30+] would agree with experiment more closely if Eo(C3H6O.+ C2H30+) > 1.2 eV, but there is no particular justification for this change. The values of [C3H6O.+]/[C2H30+] observed in charge exchange experiments16 on 2-hexanone Discussion (Table I) are consistent with those calculated here in view of the sensitivity of the latter to the value chosen for Eo A number of alternative explanations for the DOF effect were first considered and discarded.2aIt was shown experi(M.+ C3H60-+). Charge exchange experiments16 on 2hexanone-l,1,1,3,3-d5 indicate that direct cleavage (Ma+ .+ mentally that the linearity of the DOF correlation is largely independent of molecular ion internal energy and half-life CzD3O+) predominates at these low energies over indirect by varying the ionizing electron energy, thermal energy, ion acetyl ion formation (as indicated by [CzHD20+]); abunsource residence time, and time required to reach the field dances of these ions in the normal mass spectrum of this lafree drift region.zaJOThe intensities of M-+, m*(M.+ beled compound are also consistent with the values calculated here.24 Also, ionization efficiency studies using 2-hexA+), and A+ relative to the total ion current were plotted as a function of the size of M-+ for a number of homologous anone-l,l,l,3,3-d5 indicate that the energy threshold for series; no consistent trends were observed for any of these. CzHD20+ formation (indirect pathway) occurs approximately 0.7 eV higher than that for CzD3O+ ions, which preHowever, all of these series give linear DOF correlations for sumably are produced by the direct process at thresh0ld.~4 [m*(A+ D+)]/[A+], and this is also true for certain secondary daughter ions in normal spectra. For example, a The comparisons for the trends in ion intensities with inreasonably linear correlation with 1/DOF is found for the creasing size of the 2-alkanone and the more detailed comlogarithm of [H30+]/[C2H50+]from 2-alkanols, [CzH502+]/ parisons possible for 2-hexanone indicate that the calcula[ C ~ H ~ O Zfrom + ] ethyl esters, and [C~H~O-+]/[C$I~OO-+] tions adequately predict the competition between the path-
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The Journal of Physical Chemistry, Vol. 79,No. 7,1975
720
P. F.
Bente, F. W . McLafferty,D. J. McAdoo, and C. Lifshitz
TABLE I: Decomposition of 2-Hexanone Ions Formed with Specific Internal Energies by Charge Exchange [~,H,O*+l/[C2H,O+I E,
6 12
O.+,eV 1.0
2.1
Obsd 23 5.8 Calcd, Eo(M*+ -+ C,H,O*+) 1.1 eV -lo3 81 2.3 1.0 eVa 99 8.6 0.61 0.9 eV a Value actually used for other reported results.
3.1 1.28 2.1 0.85 0.33
ways considered, and that the P(E)M.+functions are valid approximations. Degrees of Freedom Effect. Figure 2 compares the exi perimental values of [m*(C3H@-+ CZH~O+)]/[C~H~O.+] with those calculated using a threshold value of k(M-+ I I C3H6O.+) = IO6 sec-l (calculation 11) for C6H120, C7HI4O, U I 2 and CsH160, and lo7 sec-l (calculation I) for the other 2alkanones, and using Eo(C3H60.+ CzH3O+) = 1.2 eV. Figure 13. Comparison of results for different models used to calcuThe calculated DOF effect shows a remarkably good agreelate the DOF effect. Curves labeled according to type of calculation (I, 11, or 111, see text) and activation energy (in eV) assumed for the ment with the experimental results, duplicating the curvareaction C ~ H ~ O . + C ~ H ~ O +CH3.. ture observed for the smaller members of the series and the linearity in the region from CgH180 to C31H620, with a slope equal to that observed experimentally. All of these energy M-+ fragmentations competitive with the formation calculations, like those of Lin and Rabinovitch14for the 1of C3H&.+ ions have been included. The proportion of M-+ alkanol system, correctly predict the general decrease in which should decompose by such processes increases with [m*]/[A] with increasing molecular ion size. The increasing increasing molecular weight as can be seen from the very amount of internal energy carried off by the neutral fragslow rise with M.+ internal energy of the calculated h ( E ) ment lowers the average internal energy of A+, which gencurves for larger species (Figures 9c, 1Oc); the increasing erally lowers [m*]/[A+] (Figures 6-10). An exception can size of the molecular ion magnifies the effect of the differoccur for the smallest homolog; if the energy requirement ences in activation energy for two competing reactions. for m*(A+ D+) is less than the energy a t which P(E)A+ is This is also shown by the effect of increasing molecular size a maximum (these energies are equal in Figure 6d), the on the relative abundances of the C3H60.+ and direct area of P ( E ) A t corresponding to the metastable window CzH3O+ ions (Figure 3). will actually increase with increasing molecular ion size. This aiso causes the kinetic shift for C3H60-+formation Note (Figure 13) that reducing &(C3H@+ CzH30') to to increase with the size of M.+; the calculated values show 0.8 ev, a value less than the maximum in P ( E ) c ~ H ~ odoes .+ an approximately linear increase. The experimental ( A c ~ H ~ o .-+ ZM.+) values for 2-C6Hl2O and 2-C17H340 difcause [m*(C3H60.+ CzH30+)]/[C3H60-+]to increase in fer by approximately 1.0 eV;24from Figures 6c and 9c this going from CsHlzO to C7H140; the area corresponding to would correspond to k < lo6 sec-l for the onset for C3undissociating C3H60.+ does not increase as much as the area corresponding to m*(C3HeO.+ HsO.+ formation. The minimum rate constant for domiCzH30') with innant C3H60.+ formation would of course be substantially creasing size of the neutral fragment.24 higher, but calculation of this value would require informaThe calculations of Lin and Rabinovitch assume that tion on the k ( E ) functions for the competing low energy P(E)M.+is the same for all members of the series; these calM.+ decompositions. The slopes of these functions must be culations predict a correlation in which log ([m*]/[A+])apeven more shallow than that for M.+ C3H60.+;this preproaches --oo as 1/DOF approaches zero. This occurs bedicts that the increase of [C3H&-+]/[low energy products] cause an increasingly large neutral fragment removes a with increasing M-+ energy for higher 2-alkanones will be greater proportion of the internal energy of the molecular even more gradual than the increase of [C&!of]/[C3H6ion, resulting in a P(E)*+which is peaked more and more Om+] with M - + energy shown in Figures 9c and 1Oc. sharply at lower internal energy, so that the area correA low energy Ma+ decomposition of particular note is the sponding to [m*] approaches zero faster than does that corformation of C3H70+ (mle 59).34 This is an increasingly responding to [A+]. The results of calculation I11 generally important process for homologs larger than 2-heptanone duplicate this behavior; addition of the thermal energy disand becomes the most intense peak in the mass spectra of tribution to the assumed constant energy deposition func2-alkanones larger than 2-nonadecanone. However, unimotion produces a P ( E ) M . t - C 3 H s 0 . + which is weighted slightly lecular metastable transitions to form m/e 59 are observed to higher internal energies for larger molecules, but still only for C7H140.+, CsH16O.+, and C g H 1 ~ 0 - + . ~ ~ predicts a curved DOF effect in contrast to the experimenCollisional activation spectra of the major oxygen-contally observed linearity. Calculation 11, in which the change taining ions produced by alkyl fragment loss from the highin the energy deposition function has been approximated er 2-alkanones show no detectable formation of mle 59 as from photoelectron spectra, shows an improved, but still well m/e 58 ions, indicating that these ions are formed curved, DOF effect. mainly from the molecular The linearity of the DOF Linearity is nearly achieved in calculation I, in which low
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The Journal of Physical Chemistry, Vol. 79, No. 7, 1975
Internal Energy of Product lons
721
effect for the 2-alkanones can thus be explained without invoking nonrandomization of energy in the molecular ion fragmentation process. It also appears logical that the linear DOF effects observed for the other systems studied can arise through the same general causes. Lengthening of an alkyl chain for most types of molecular ions should increase the probability of low activation energy, tight complex reactions, which would provide increasing competition to the fragmentation pathway measured for the DOF study. Calculation I (Figure 13) indicates that a change in &(A+ D+) from 0.8 to 1.2 eV does not affect the essential linearity of the DOF plot. However, it is obvious that all systems will not necessarily give linear DOF plots, and that this relationship must fail a t sufficiently high molecular weights, as both [A+]and [m*(A+ D+)] must go to zero. Factors Affecting P(E)A+.The agreement of the calculated and experimental results support the previous postulate, based on the quasiequilibrium t h e ~ r yconcerning ,~ the factors which affect the internal energy distribution of A+ ions produced from Ma+. The effects of structure (peaks, valleys, general shape) in P(E)M.+are discernible in P(E)A+ for smaller molecules such as 2-hexanone, although the partitioning of energy between A+ and the neutral lost substantially smooths the distribution. For larger molecules the thermal energy distribution tends to smear out any structure in the photoelectron spectrum, and any remaining structure in P(E)M.+is completely removed by the effect of energy partitioning, giving P(E)A+ distributions which are sharply peaked at low energies. The calculations confirm that competition from reactions with higher activation energies and looser complexes will reduce the higher energy portion of P(E)A+,as expected. The increasing number of reaction pathways operative in the larger molecules (C,H,+ formation) approximately compensates for their slower rise of lz ( E ) ,so that the effect of high energy competition on P(E)M.+-.A+does not vary greatly over the series. The thermal energy distribution in the larger molecules shifts P(E)M.+-A. to higher internal energies. The dramatic effect of low energy competition has been discussed above. Because the rate constants, k ( E ) ,are very sensitive to changes in activation energy, variations in these parameters will be reflected in variations in the competition between different pathways and can cause substantial changes in P(E)M.+-A+. Energy partitioning between the ion and the neutral determines how P(E)A+is obtained from P(E)M.++A+.The calculations confirm that increasing the size of the neutral lost can produce a dramatic shift of P(E)A+to lower energies with a corresponding sharpening of the energy distribution. The energy partitioning is sensitive to the relative sizes of the neutral fragment and the A+ ion, but not to the details of the models chosen to represent them.
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Acknowledgment. The authors are indebted to the Na-
tional Institutes of Health (Grant GM-16609) for generous financial support.
References and Notes (1) Metastable Ion Characteristics, XXXII. Part XXXI, F. W. McLafferty and J. Winkler, J. Amer. Chem. SOC., 96, 5182 (1974). (2) (a) Taken from the Ph.D. theses of PFB, 1974, and DJM, 1971. Cornell University. (b) E. I. du Pont de Nemours and Co., Wilmington, Del. 19898. (c) Marine Biomedical Institute. University of Texas Medical Center, Galveston. Tex. 77550. (d) Vising scientist from the Department of Physical Chemistry, The Hebrew University, Jerusalem. (3) H. M. Rosenstock, M. 8. Wallenstein, A. L. Wahrhaflig. and H. Eyring. Proc. Nati. Acad. Sci. U.S., 38, 667 (1952). (4) M. L. Vestal in ”Fundamental Processes in Radiation Chemistry”, P. Ausloos, Ed., Wiley-lnterscience, New York, N.Y., 1968. (5) P. J. Robinson and K. A. Holbrook, “Unimolecular Reactions”, Wiley-lnterscience, New York, N.Y., 1972. (6) F. W. McLafferty. T. Wachs, C. Lifshitz, G. Innorta, and P. Irving,-J. Am. Chem. Soc., 92, 6867 (1970); F. W. McLafferty, ”Interpretation of Mass Spectra”, 2nd ed, Benymin-Addison-Wesley, Reading, Mass., 1973, Chapter 8. (7) G. G. Meisels, C. T. Chen, B. G. Giessner, and R. H. Emmel. J. Chern. Phys., 56, 793 (1972), and references cited therein. (8) A. KroDf, E. M. Eyring, . - A. L. Wahrhaflig, and H. Eyring. J. Chem. Phys., 32, 149 (1960). (9) M. L. Vestal, J. Chem. Phys., 43, 1356 (1965). (10) D. J. McAdoo, P. F. Bente, 111, M. L. Gross, and F. W. McLafferty, Org. Mass Spectrom., 9, 525 (1974). (11) F. W. McLafferty and W. T. Pike, J. Am. Chem. Soc., 89, 5951 (1967). (12) F. W. McLafferty, T. Wachs, and W. T. Pike, Adv. Mass Spectrom., 4, 153 (1968). (13) R. G. Cooks, J. H. Beynon, R. M. Caprioli, and G. R. Lester, “Metastable Ions”, Elsevier, Amsterdam, 1973. (14) Y. N. Lin and B. S. Rabinovitch, J. Phys. Chem., 74, 1769 (1970). (15) E. Murad and M. G. Inghram, J. Chem. Phys., 40,3263 (1964). (16) T. 0. Tiernan and C. Lifshitz, J. Chem. Phys., 57, 1515 (1972). (17) F. W. McLafferty, D. J. McAdoo, J. S. Smith, and R. Kornfeld, J. Am. Chem. Soc., 93, 3720 (1971). (18) J. L. Franklin, J. G. Dillard. H. M. Rosenstock, J. T. Herron, K. Draxl, and F. H. Field, Nafl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 26 (1969). (19) T. Wachs, P: F. Bente, 111, and F. W. McLafferty, ht. J. Mass Spectrom. /on Phys., 9, 12 (1972). (20) T. Wachs and F. W. McLafferty, to be submitted for publication. (21) M. A. Baldwin and F. W. McLafferty, int. J. Mass Spectrom. /on Phys., 12, 86 (1973). (22) F. W. McLafferty, P. F. Bente, Ill, R. Kornfeld, S. -C. Tsai, and I. Howe, J. Am. Chem. Soc., 95, 2120 (1973); F. W. McLafferty, R. Kornfeld, W. F. Haddon, K. Levsen, I. Sakai, P. F. Bente, Ill, S. -C. Tsai, and H. D. R. Schuddemage, ibid., 95, 3886 (1973). (23) C. Tegner, Acta Chim. Scand., 6, 782 (1952). (24) For further details see the thesis of PFB.2a (25) We are indebted to Dr. Neil Ridyard, Perkin-Elmer, Ltd., for these spectra. (26) We are indebted to Professor R. E. Kirby, Queens College, CUNY, for these spectra. (27) R. I. Schoen, J. Chem. Phys., 37,2032 (1962). (28) L. I. Lohr and M. B. Robin, J. Am. Chem. SOC., 92, 7241 (1970). (29) J. S. Smith and F. W. McLafferty, Org. Mass. Spectrum., 5, 483 (1971). (30) F. W. McLafferty, D. J. McAdoo, and J. S. Smith, J. Am. Chem. SOC.91, 5400 (1969). (31) K. R. Jennings in “Mass Spectrometry: Techniques and Applications”, G. W. A Milne, Ed., Wiley-Interscience, New York, N.Y., 1971, p 419. (32) D. R. Hershbach, H. R. Johnston, K. S. Pitzer, and R. E. Powell, J. Chem. Phys., 25, 736 (1956). (33) G. E. Whitten and B. S. Rabinovitch, J. Chem. Phys., 41, 1883 (1965); D. C. Tardy, B. S. Rabinovbh, and G. Z. Whitten, ibid., 48, 1427 (1968); W. Forst, Chem. Rev.. 71, 339 (1971). (34) M. Kraft and G. Spiteller, Jusfus Liebigs Ann. Chem., 712, 28 (1968). (35) In a number of previous cases increasing the alkyl chain length has also been noted to increase the ratio of peaks from double- vs. single-hydrogen rearrangement; a recent detailed study36 of the reasons for this phenomenon did not consider, however, the effects of increasing molecular size on p ( € ) ~ . +and lower energy processes. (36) M. A. Winnik, C. K. Lee, and P. T. Y. Kwong, J. Am. Chem. Soc., 96, 2901 (1974).
The Journal of Physical Chemistry, Vol. 79, No. 7, 7975
