27 State-to-State Considerations in Reactions in Interstellar Clouds R. N. PORTER
Downloaded by AUBURN UNIV on March 1, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0056.ch027
Department of Chemistry, State University of New York, Stony Brook, NY 11794
In a symposium on "State-to-State Chemistry" in the late 1970's, i t seems appropriate to c a l l attention to a class of re actions for which such detailed knowledge is essential. These are the ion-molecule reactions that are presumed to occur at the extremely low temperatures and pressures of the i n t e r s t e l l a r clouds. Detailed analyses of i n t e r s t e l l a r chemistry have been given by Herbst and Klemperer (1,2) and by Watson (3). Since the temperatures range between ~10-50 K, only exothermic and thermoneutral reactions without activation energy can occur; and since molecular densities are of the order of 10 cm , molecules coupled to the radiation f i e l d w i l l have vibration-rotation temperatures close to the 2.7 Κ blackbody temperature. Since hydrogen is by far the most numerous species, the states of the molecules are generally widely spaced and many of the molecules have ortho-para species that do not interconvert r a d i a t i v e l y . Under these conditions one expects classical dynamics to give an inadequate picture. Furthermore, averages and sums over states of molecules with ortho-para modifications must treat nuclear spin s t a t i s t i c s properly. A central question is how to extrapolate thermal rates of the reactions, usually measured near room temperature, down to i n t e r s t e l l a r temperatures. An important exothermic reaction is 4
H + H 2
+ 2
-> H
+
+ H,
3
-3
(Rl)
the 40 kcal/mole being released into vibration and rotation of H as well as relative translation (4,5). The observation of the radiospectrum of HCO in several clouds (6) suggests that it may be formed by (1,2) +
3
+
H
+ 3
+
+ CO + HC0 + H . 2
(R2)
+
The observation of DCO in concentrations nearly as great as that of HCO (7) when the D/H atomic ratio is on the order of 10 (8) indicates isotope fractionation by (3,9) +
-5
236
In State-to-State Chemistry; Brooks, Philip R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
27.
PORTER
237
Reactions in Interstellar Clouds
H HD 3
+
+ H D + H 2
+
2
.
(R3)
The measured forward r a t e of t h i s r e a c t i o n i s 3 χ 1 0 cm s e c ' ( 1 0 ) , a f a c t o r of about 6 l e s s than the Langevin r a t e . This r e a c t i o n i s of p a r t i c u l a r i n t e r e s t , not only because of i t s p o s s i b l y key r o l e i n c o n c e n t r a t i n g deuterium i n i n t e r s t e l l a r m o l e c u l e s , but because the s t r u c t u r e and spectra of the t r i a t o m i c species are a t t h i s p o i n t known e x c l u s i v e l y from ab i n i t i o calculations (3,11-15). To use Eq. (R3) i n a s a t i s f a c t o r y model of i n t e r s t e l l a r chemistry, we need (a) i t s e q u i l i b r i u m constant Kp, from which we can c a l c u l a t e i t s backward r a t e , and (b) the value of i t s forward r a t e e x t r a p o l a t e d to i n t e r s t e l l a r temperatures. We have obtained (a) from sums over the r o t a t i o n s t a t e s of the r e a c t a n t and product molecules, t a k i n g due account of o r t h o para m o d i f i c a t i o n s . The r e a c t i o n has a ∆Ε/R * 134 Κ as measured from the ground v i b r a t i o n s t a t e s (12, 1 4 ) , but t h i s r e s u l t i s misleading since H has a z e r o - p o i n t r o t a t i o n a l energy of 91.7 Κ (13) and a combined nuclear s p i n - r o t a t i o n a l degeneracy of 6 i n the ground s t a t e . The extent to which the r e s u l t i n g entropy o f f s e t s the r o t a t i o n a l energy i s h i g h l y temperature-dependent, of course. The r e s u l t s f o r K of (R3) range from V I 0 a t 10 Κ to VI0 a t 50 Κ and depend upon assumptions about ortho/para r a t i o s . With H D h i g h l y favored a t low temperature, the observed i n t e n s i t i e s of DC0 formed by the deuterium analogue of (R2) are q u i t e reasonable ( 9 ) . Obtaining (b) may be a more formidable t a s k , s i n c e the c o l l i s i o n complex i s the s t a b l e ion H , one might expect the a c t i v a t i o n energy to be n e g l i g i b l e . Then why i s the r a t e only 1/6 the Langevin r a t e ? The c r i t i c a l r o t a t i o n a l b a r r i e r s are a t l l a and 7 . 4 a i n the r e a c t a n t and product channels, r e s p e c t i v e l y , so l a r g e as to i n d i c a t e a p p l i c a b i l i t y of L i g h t ' s s t a t i s t i c a l theory ( 1 7 , 1 8 ) . One must of course use the quantum-mechanical form, as i n the c a l c u l a t i o n of K . The hope then i s t h a t the f a c t o r 1/6 might f i n d i t s explanation i n the d e t a i l e d s t a t i s t i c s of the P a u l i - p r i n c i p l e dominated r o t a t i o n s t a t e s of these molecules (14,15). Since the number of a c c e s s i b l e s t a t e s i s manageable, the c a l c u l a t i o n i s e a s i l y done, g i v i n g the r e s u l t s 502A , 286A , and 234A f o r the r e a c t i o n cross s e c t i o n s a t ε/k = 10 Κ, 30K, and 50 K, r e s p e c t i v e l y . The percent o - H i n the product p r e d i c t e d by the theory i s 18, 37, and 57 at the three r e s p e c t i v e e n e r g i e s , and the percent o - H D i s p r e d i c t e d to be 64, 50, and 68, respectively. The r o t a t i o n a l temperatures of nascent H D as determined by the r e l a t i v e populations of the two l o w e s t - l y i n g para s t a t e s (v = 1361 GHz) are p r e d i c t e d to be 29 K, 173 K, and 571 Κ a t the three e n e r g i e s . These temperatures are expected to r e l a x r a d i a t i v e l y to about 2.7 Κ before a c o l l i s i o n o c c u r s . U n f o r t u n a t e l y , the t o t a l r e a c t i o n cross s e c t i o n s are w i t h i n a few percent of the Langevin v a l u e s . Simple reasoning about
Downloaded by AUBURN UNIV on March 1, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0056.ch027
1 0
3
1
+
9
p
2
3
+
+
5
+
0
0
p
2
2
2
2
2
+
2
In State-to-State Chemistry; Brooks, Philip R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
+
238
STATE-TO-STATE CHEMISTRY
tunneling through r o t a t i o n a l b a r r i e r s does not appear to provide the f a c t o r 1/6, although s t e r i c arguments help e l u c i d a t e d i s t i n c t i o n s between "reactive" and "nonreactive" r o t a t i o n s t a t e s . At present i t appears that beam-spectroscopy measurements, coupled with a f u l l quantum-dynamical a n a l y s i s , may be required f o r a s a t i s f a c t o r y s o l u t i o n to problem (b) f o r use i n models of i n t e r s t e l l a r chemistry — a challenge the papers at t h i s symposium i n d i c a t e we may soon be able to accept!
Downloaded by AUBURN UNIV on March 1, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0056.ch027
Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
Herbst, E. and Klemperer, W., Astrophys. J. (1973) 185, 505. Herbst, E. and Klemperer, W., Physics Today (1976) 29, 32. Watson, W. D., Rev. Mod. Phys. (1976) 48, 513. Carney, G. D., and Porter, R. Ν., J. Chem. Phys. (1974) 60, 4251. Stine, J. R. and Muckerman, J. T . , J. Chem. Phys. (1976) 65, 3975 and private communications. Hollis, J. M., Snyder, L. E., Lovas, F. J. and Buhl, D., Astrophys. J. (1975) 200, 584. Hollis, J. M., Snyder, L. E., Lovas, F. J. and Buhl, D., Astrophys. J. (1976) 207, 663. McKellar, A. R. W., Goetz, W. and Ramsay, D. Α., Astrophys. J. (1976) 207, 663. Solomon, P. M., Porter, R. N. and Jura, M., unpublished results. Huntress, W. T. and Anicich, V. G., Astrophys. J. (1976) 208, 237. Salmon, L. and Poshusta, R. D., J. Chem. Phys. (1973) 59, 3497. Carney, G. D., and Porter, R. N., J. Chem. Phys. (1976) 65, 3547. Carney, G. D., and Porter, R. N., J. Chem. Phys. (1977) 66, 2756. Carney, G. D., and Porter, R. Ν., "Ab initio prediction of the vibration spectra of the deuterated species of H ," Chem. Phys. Lett, (in press). Carney, G. D., and Porter, R. Ν., "Rotation states of H and its isotopes," unpublished. Porter, R. Ν., details to be published elsewhere. Pechukas, P. and Light, J. C., J. Chem. Phys. (1965) 42, 3281. Pechukas, P., in "Dynamics of Molecular C o l l i s i o n s , Part B , " Ed. by Miller, W. H., Ch. 6, p269, (Plenum, Ν. Y., 1976). +
3
(15) (16) (17) (18)
+
3
In State-to-State Chemistry; Brooks, Philip R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.
