Isotope Effects in Gas-Phase Chemistry - American Chemical Society

Chapter 13

Isotope Effects in the Reactions of Atomic Ions with H , D , and HD 2

2

Peter B . Armentrout

Downloaded by GEORGETOWN UNIV on August 22, 2015 | http://pubs.acs.org Publication Date: September 8, 1992 | doi: 10.1021/bk-1992-0502.ch013

Department of Chemistry, University of Utah, Salt Lake City, UT 84112

Reactions of various atomic ions with H , D , and HD have been studied as a function of kinetic energy by using guided ion beam mass spectrometry. For exothermic reactions, the dependence on translational and rotational energy and the effect of angular momentum conservation are illustrated. For endothermic reactions, the observed behavior falls into several distinct groups (statistical, direct and impulsive) that can be used to characterize the potential energy surfaces for the reactions. The characteristic behavior of each of these groups is illustrated and then used to understand more complex reaction systems. 2

2

Of a l l the systems where isotope e f f e c t s might be observed, the simplest i s that of atomic species with H , D , and HD, reactions 1-4. 2

A* + Ho A

+

+ D,

A

+

+ HD

2

+

+ H

(D

+

+ D

(2)

r- AH + D

(3)

AH AD

+

— +

AD

+ H

(4)

In our laboratory, such reactions for the atomic ions of 44 d i f f e r e n t elements have now been studied (2). A wide v a r i e t y of d i f f e r e n t types of r e a c t i v i t y are displayed by these systems, but several unifying themes are found. Among these are the observation that the intermolecular and intramolecular isotope e f f e c t s f a l l into several d i s t i n c t categories. Here, we i l l u s t r a t e such behavior and review i t s o r i g i n s . A unique aspect of these studies i s that the reactions are studied over a broad range of k i n e t i c energies. The k i n e t i c energy dependence provides a more complete evaluation of the origins of the isotope e f f e c t s observed. I t also allows the characterization of isotope e f f e c t s for endothermic reactions, processes that have not been studied i n as much d e t a i l as reactions accessible at thermal energies. 0097-6156/92/0502-0194S06.00/0 © 1992 American Chemical Society

In Isotope Effects in Gas-Phase Chemistry; Kaye, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

13.

ARMENTROUT

Reactions of Atomic Ions with H , D , & HD 2

2

195

We do not discuss charge transfer or d i s s o c i a t i v e charge transfer reactions of A with H , D , or HD, processes that can compete d i r e c t l y with reactions 1-4. For most elements, however, these reactions occur only at high energies (since the i o n i z a t i o n energy of H exceeds that of A) and consequently are not i n f l u e n t i a l i n the reaction dynamics of reactions 1-4. This i s also true i n borderline cases such as A - Ar and Ν where we have studied these charge transfer channels (2,3). In only a few systems (A = He, Ne, and F) are the charge transfer processes strongly exothermic. In these cases, a complete understanding of the interactions of A with dihydrogen should include a consideration of the charge transfer processes (4). +

2

2

2

+


Experimental Method The experimental technique used i n our laboratory to examine the reactions of atomic ions with hydrogen i s guided ion beam tandem mass spectrometry, as detailed elsewhere (2). In this instrument, ions are formed i n one of several available sources that enable the populations of d i f f e r e n t e l e c t r o n i c states of the atomic ion to be manipulated. In a l l cases, the results discussed below correspond to a single e l e c t r o n i c state, usually the ground state, of the atomic ion. These ions are extracted from the source and focused into a 60° magnetic sector for mass analysis. The mass-selected beam i s decelerated to a k i n e t i c energy that can vary from -0.05 eV to over 500 eV and i s focused into an r f octopole ion beam guide (5) that passes through a c o l l i s i o n c e l l containing the neutral reactant. The c o l l i s i o n zone i s designed so that reactions occur over a well-defined path length and at a pressure low enough that a l l products are the r e s u l t of single ionneutral encounters, as v e r i f i e d by pressure dependence studies. The octopole helps ensure e f f i c i e n t c o l l e c t i o n of both product and reactant ions by containing them u n t i l they are extracted and focused into a quadrupole mass f i l t e r . After mass analysis, ions are detected by using a secondary electron s c i n t i l l a t i o n ion detector (6) and counted by using standard pulse counting e l e c t r o n i c s . The absolute i n t e n s i t i e s of the reactant and product ions as a function of the ion k i n e t i c energy i n the laboratory frame are converted to absolute reaction cross sections as a function of the k i n e t i c energy i n the center-of-mass frame, σ(Ε), as described previously (2) . Conversion of the laboratory ion energy to the centerof-mass frame energy involves a simple mass factor (except at very low energies where truncation of the ion beam must be accounted for) (2). The absolute zero of energy i s determined by a retarding p o t e n t i a l analysis that i s f a c i l i t a t e d by the use of the octopole beam guide. Exothermic Reactions Intennolecular Isotope E f f e c t s . For most atomic ions, we f i n d that the t o t a l cross sections for reactions 1, 2 and the sum of reactions 3 and 4 are very s i m i l a r , although small differences can be observed. For instance, when A - 0 ( S) , the cross section for reaction 1 i s 19% larger than that for reaction 2 and 12% larger than that for the sum of reactions 3 and 4 (7). While these differences do f a l l within our absolute experimental error of ±20%, they are reproducible and f a l l outside of our estimated r e l a t i v e error of ±5%. Such intermolecular isotope e f f e c t s have not been explained. +

+

A


196

ISOTOPE EFFECTS IN GAS-PHASE CHEMISTRY

A much more severe and i n t e r e s t i n g exception to the norm i s the case where A - K r ( P ) (8). Here, the cross section for reaction 1 i s 43% larger than that for reaction 2 and 50% smaller than that for the sum of reactions 3 and 4. The o r i g i n s of t h i s unusual r e s u l t are not well characterized although we speculate on several p o s s i b i l i t i e s elsewhere (8). +

+

2

3/2

Intramolecular Isotope E f f e c t s . E f f e c t of T r a n s l a t i o n a l Energy. When reactions 3 and 4 are exothermic, the competition between them usually shows a f a i r l y strong dependence on t r a n s l a t i o n a l energy. At low k i n e t i c energies, the systems y i e l d about 50 ± 10% of the AH product which then gradually increases with energy. The r e s u l t s for A - 0 ( S) shown i n Figure 1 are t y p i c a l (7). At higher energies, the behavior can be understood i n terms of the models developed f o r endothermic reactions, as described below. As discussed i n d e t a i l previously (7,9-12), the explanation f o r the intramolecular isotope e f f e c t observed at low energy l i e s i n the f a c t that the a t t r a c t i v e ion-induced dipole i n t e r a c t i o n exerts a torque on the HD molecule since the center of p o l a r i z a b i l i t y (which i s at the center of the molecule) i s displaced from the center of mass (which i s nearer the D atom). This force rotates the H atom toward the incoming 0 ion, and thus H i s more l i k e l y to be abstracted i n the reaction. Detailed calculations by Dateo and Clary (12) v e r i f y t h i s , as can be seen i n Figure 1 by the good agreement between t h e i r t h e o r e t i c a l and our experimental r e s u l t s . (Any deviations are within the experimental error i n the energy scale.) Their r e s u l t s show that as the k i n e t i c energy increases, the maximum impact parameter that can lead to a reactive c o l l i s i o n decreases; and as the impact parameter decreases, the torque exerted on the HD molecule increases, thereby enhancing the p r o b a b i l i t y that hydrogen i s abstracted. +


+

+

4

+

O r b i t a l Angular Momentum Conservation. Above about 0.3 eV, the t h e o r e t i c a l predictions no longer describe the experimental work, Figure 1. In addition, at about this same energy, the reaction cross sections f o r reactions 1-4 cease to follow the predictions of the Langevin-Gioumousis-Stevenson (LGS) model f o r ion-molecule reactions (13), namely a - πβ(2α/£) , where e i s the charge on the electron, α i s the p o l a r i z a b i l i t y of the neutral reactant, and Ε i s the k i n e t i c energy of the reactants. We have shown that these deviations can be explained i n terms of the conservation of o r b i t a l angular momentum (which couples the entrance and e x i t channels) (7). Such an e x i t channel e f f e c t was not included i n the t h e o r e t i c a l c a l c u l a t i o n s . To see the o r i g i n s of this e f f e c t , we consider the general case where reactants with r e l a t i v e v e l o c i t y ν and reduced mass μ evolve to products with s i m i l a r quantities denoted by primes. The o r b i t a l angular momentum of the reactants i s L - μvb - (2μΕ) & and that for the products i s L' - (2μ'Ε') ά', where b i s the impact parameter. For hyperthermal k i n e t i c energies, the r o t a t i o n a l angular momentum of the reactants, J , i s small compared with L. As a f i r s t approximation, we further assume that the r o t a t i o n a l angular momentum of the products, J ' , i s also small, and consequently, angular momentum conservation requires that L « L'. This leads to the r e l a t i o n s h i p that b ~ b ' (μ'£'/>£) , and thus to an expression f o r the reaction cross section, σ - π 5 « & ' ( μ Έ ' / μ Ε ) , or upon applying the LGS c r i t e r i o n for reaction i n the e x i t channel, σ πβ(2α'/Ε') (μ'Ε'/μΕ). 1/2

L G S

1/2

1/2

1/2

2

χ

2

π

1,2

χ


ARMENTROUT

2

ENERGY


197

Reactions of Atomic Ions with H , D , & HD

(QV.

2

Lab)

ENERGY (eV. CM) +

+

Figure 1. Fraction of 0H formed i n reactions 3 and 4 (f(OH ) σ(3)/[σ(3) + σ(4)]) with A - 0 ( S) as a function of k i n e t i c energy i n the lab frame (upper axis) and center-of-mass frame (lower axis) f o r HD temperatures of 305 Κ (open c i r c l e s ) and 105 Κ (closed squares). The dashed lines are calculated values from r e f . 12 and the s o l i d l i n e s are the calculated values convoluted over the experimental energy d i s t r i b u t i o n . Reproduced with permission from ref. 16. Copyright 1990. E l s e v i e r Science Publishers +

+

4


198


We now need to address whether the reaction cross section i s l i m i t e d by σ or by a . Comparison of these two expressions shows that

-

XeH

g 0.10 G

"S* 0.00 0.0

-L

5.0

10.0

15.0

ENERGY (eV. CM) +

+

Figure 5. Cross sections f o r reactions 2-4 with A - Xe as a function of the ion k i n e t i c energy i n the center-of-mass frame. The r e a c t i v i t y shown i s due primarily to X e ( P ) . Arrows indicate the thresholds and d i s s o c i a t i o n energies predicted by the pairwise model f o r a l l three reactions, see text. Adapted from r e f . 30. +

2

3/2


13. ARMENTROUT

Reactions of Atomic Ions with H , D , & HD 2

2

207

occuring v i a a non-impulsive pathway (30). while the absolute energy predictions of the impulsive model do not correspond d i r e c t l y with observation, the pairwise scheme r e a d i l y explains the r e l a t i v e s h i f t s i n the thresholds and d i s s o c i a t i o n energies observed for the H , HD and D systems, and suggests that the enhanced production of AD i n process 4 i s due the much lower threshold for this reaction compared to that for reaction 3. The pairwise energy frame may be f a m i l i a r to some as the spectator s t r i p p i n g model (SSM) (31). The SSM i s a highly s p e c i f i c example of a model which incorporates the pairwise energy concept. The difference i s that the SSM assumes there i s no momentum transfer to the product atom C, while the more general pairwise model allows such transfer. As a consequence, the SSM makes very s p e c i f i c predictions about the v e l o c i t y and internal energy of the products, while the pairwise model allows f o r d i s t r i b u t i o n s of these quantities. The l a t t e r , not s u r p r i s i n g l y , corresponds more c l o s e l y to observation. As shown above, the extremely useful concept of a pairwise energy scale can e a s i l y be derived without the severe assumption made i n the SSM. 2

+


2

Mixed Behavior. While the reactions of many atomic ions f a l l n i c e l y into the categories described above, we have observed a number of systems that exhibit mixtures of these behaviors, Table I. An example that we have recently studied i s the reactions of S ( S) (32) . This species i s isovalent with 0 ( S) , but now reaction 1 i s endothermic by 0.92 eV. As shown i n Figure 6, the cross section for reaction 2 has two features (as does that for reaction 1). The f i r s t begins promptly at the thermodynamic threshold. When HD i s the reactant, the f i r s t feature does not s h i f t i n energy and exhibits a s t a t i s t i c a l branching r a t i o between SH and SD . The second, higher energy feature, however, does s h i f t i n energy and c l e a r l y favors formation of SD , results that correspond to an impulsive mechanism. The threshold and d i s s o c i a t i o n energies predicted by the impulsive model (calculated as for the Xe example above) are indicated i n Figure 6. I t can be seen that the predictions match the s h i f t s observed i n the experimental cross sections reasonably well. These results indicate that the reaction must pass through a stable SH intermediate at low energy. However, this species has a B ground state and therefore i t s formation from S ( S) + H ( Z ) i s spinforbidden. This explains the r e l a t i v e i n e f f i c i e n c y of this pathway. The second feature i n the cross section can then be assigned to reaction proceeding along a spin-allowed but r e l a t i v e l y repulsive p o t e n t i a l energy surface. Ab i n i t i o calculations on this system confirm these q u a l i t a t i v e ideas concerning the p o t e n t i a l energy surfaces (32). +

+

+

4

4

+

+

+

+

2

2

X

+

A

1

2

+

g


208


1

' I

I ' I

1

I

1

1

I

I

1

I

1

I

1

I

1

1

I

1

1.0

I Ν


to

I

0.5

CO

1

Co

1

+

/""•ν-^*

:

+

s

+ D — SD 2

+D

î

>

0.0

I . I . I ι I . I ι I ι I

1.0

3.0

5.0

7.0

9.0

11.0

13.0

ENERGY (eV, CM) 1

2.0

1

I

S

I

1

I

1

I

1

+ HD —

I

1

I

1

I

1

I 1

1

I

II

I

I

I

I

I

I

I

I

V

to I

Ο

.· SD

I··

CO CO

1

i 0.0 1.0

I . I . I • I . I • I . 1 . 1 . I 3.0

5.0

7.0

9.0

11.0

13.0

ENERGY (eV. CM) +

+

Figure 6. Cross sections f o r reactions 2-4 with A - S (*S) as a function of the ion k i n e t i c energy i n the center-of-mass frame. Arrows indicate the thermodynamic thresholds at -0.9 eV, and the thresholds and d i s s o c i a t i o n energies predicted by the pairwise model f o r a l l three reactions, see text. Adapted from r e f . 32.


13. ARMENTROUT Reactions of Atomic Ions with H , D , & HD 2

2

209

Acknowledgments. This work i s supported by the National Science Foundation. I also thank my research collaborators f o r t h e i r contributions to the work discussed here.

Literature Cited


1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

Armentrout, P. B. Int. Rev. Phys. Chem. 1990, 9, 115. Ervin, Κ. M.; Armentrout, P. B. J. Chem. Phys. 1985, 83, 166. Ervin, Κ. M.; Armentrout, P. B. J. Chem. Phys. 1987, 86, 2659. See for example, Jones, E. G.; Wu, R. L. C.; Hughes, Β. M.; Tiernan, T. O.; Hopper, D. G. J. Chem. Phys. 1980, 73, 5631. Teloy, E.; Gerlich, D. Chem. Phys. 1974, 4, 417. Daly, N. R. Rev. Sci. Instrum. 1959, 31, 264. Burley, J . D.; Ervin, Κ. M.; Armentrout, P. B. Int. J. Mass Spectrom. Ion Processes 1987, 80, 153. Ervin, Κ. M.; Armentrout, P. B. J. Chem. Phys. 1986, 85, 6380. Light, J . C.; Chan, S. J. Chem. Phys. 1969, 51, 1008. George, T. F.; Suplinskas, R. J . J. Chem. Phys. 1971, 54, 1046. Hierl, P. M. J. Chem. Phys. 1977, 67, 4665. Dateo, C. E.; Clary, D. C. J. Chem. Soc. Faraday Trans 2, 1989, 85, 1685. Gioumousis G.; Stevenson, D. P. J. Chem. Phys. 1958, 29, 292. Miller, T. M.; Bederson, B. Adv. Atomic Molec. Phys. 1977, 13, 1. Rothe, E. R.; Bernstein, R. B. J. Chem. Phys. 1959, 31, 1619. Sunderlin, L. S.; Armentrout, P. B. Chem. Phys. Lett. 1990, 167, 188. Marquette, J . B.; Rebrion, C.; Rowe, B. R. J. Chem. Phys. 1988, 89, 2041. Gerlich, D. J. Chem. Phys. 1989, 90, 3574. Elkind, J . L.; Armentrout, P. B. J. Phys. Chem. 1984, 88, 5454. Ervin, Κ. M.; Armentrout, P. B. J. Chem. Phys. 1986, 84, 6750. Ervin, Κ. M.; Armentrout, P. B. J. Chem. Phys. 1986, 84, 6738. Mahan, B. H.; Sloane, T. M. J. Chem. Phys. 1973, 59, 5661. Boo, Β. H.; Armentrout, P. B. J. Am. Chem. Soc. 1987, 109, 3549. Elkind, J. L.; Ervin, Κ. M.; Armentrout, P. B. unpublished work. Georgiadis, R.; Armentrout, P. B. J. Phys. Chem. 1988, 92, 7060. Schilling, J. B.; Goddard, W. Α.; Beauchamp, J. L. J. Phys. Chem. 1987, 91, 5616. Elkind, J . L.; Armentrout, P. B. J. Phys. Chem. 1985, 89, 5626. Aristov, N.; Armentrout, P. B. J. Am. Chem. Soc. 1986, 108, 1806. Sunderlin, L.; Aristov, N.; Armentrout, P. B. J. Am. Chem. Soc. 1987, 109, 78. Ervin, Κ. M.; Armentrout; P. B. J. Chem. Phys. 1989, 90, 118. Henglein, A. In Ion-Molecule Reactions in the Gas Phase; Ausloos, P. J., Ed.; ACS: Washington, D.C., 1966; p 63. Stowe, G. F.; Schultz, R. H.; Wight, C. Α.; Armentrout, P. B. Int. J. Mass Spectrom. Ion Processes 1990, 100, 177.

RECEIVED October 3, 1991


Isotope Effects in Gas-Phase Chemistry - American Chemical Society

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