Rate constants for the recombination reaction H + H + M→H2 + M are calculated within the framework of the resonance complex theory for a variety of third bodies (M=H, He, Ar, and H2). The stabilization cross sections for bimolecular collisions of M with the highly excited orbiting resonance states of H2 were computed from exact three‐dimensional classical trajectories. Calculations were carried out for several different reasonable potential surfaces in order to determine the effects of variations in the interaction potential upon the macroscopic rate constant. For example, the inclusion of long range attractive forces between the inert third body and each H atom in H2 leads to a systematic increase in the low temperature rate constant. Using a best estimate for the potential parameters, good agreement with experiment is found for all the third bodies investigated over the temperature range ∼77–300°K. For inert third bodies it is shown that the so‐called ``energy transfer'' mechanism is much more important than the ``chaperon'' mechanism. However, for the case M=H, both mechanisms play a significant role with the ``chaperon'' mechanism being the more important. Furthermore, H atoms are found to be more efficient than inert M in causing recombination to occur. Data for the nonequilibrium ortho/para product distribution are also presented.

1.
See, for example,
I.
Amdur
,
J. Am. Chem. Soc.
60
,
2347
(
1938
).
2.
D. O.
Ham
,
D. W.
Trainor
, and
F.
Kaufman
,
J. Chem. Phys.
53
,
4395
(
1970
).
3.
J. E.
Bennett
and
D. R.
Blackmore
,
Proc. R. Soc. A
305
,
553
(
1968
).
4.
F. S.
Larkin
,
Can. J. Chem.
46
,
1005
(
1968
).
5.
A.
Jones
and
J. L. J.
Rosenfeld
,
Proc. R. Soc. A
333
,
419
(
1973
).
6.
V. H.
Shui
,
J. Chem. Phys.
58
,
4868
(
1973
).
7.
P. A.
Whitlock
,
J. T.
Muckerman
, and
R. E.
Roberts
,
Chem. Phys. Lett.
16
,
460
(
1972
).
8.
R. T.
Pack
,
R. L.
Snow
, and
W. D.
Smith
,
J. Chem. Phys.
56
,
926
(
1972
).
9.
V. H.
Shui
and
J. P.
Appleton
,
J. Chem. Phys.
55
,
3126
(
1971
).
10.
R. E.
Roberts
,
R. B.
Bernstein
, and
C. F.
Curtiss
,
J. Chem. Phys.
50
,
5163
(
1969
).
11.
J. C.
Keck
,
J. Chem. Phys.
32
,
1035
(
1960
).
12.
D. L.
Bunker
,
J. Chem. Phys.
32
,
1001
(
1960
).
13.
See Ref. 6 for summary of high temperature measurements.
14.
D. W.
Trainor
,
D. O.
Ham
, and
F.
Kaufman
,
J. Chem. Phys.
58
,
4599
(
1973
).
15.
A. G.
Clarke
and
G.
Bums
,
J. Chem. Phys.
55
,
4717
(
1971
).
16.
T. G.
Waech
and
R. B.
Bernstein
,
J. Chem. Phys.
46
,
4905
(
1967
).
17.
R. J.
LeRoy
and
R. B.
Bernstein
,
J. Chem. Phys.
54
,
5114
(
1971
).
18.
W.
Kołos
and
L.
Wolniewicz
,
J. Chem. Phys.
43
,
2429
(
1965
).
19.
D. E.
Stogryn
and
J. O.
Hirschfelder
,
J. Chem. Phys.
31
,
1531
(
1959
).
20.
See, for example, the recent text by R. D. Levine, Quantum Mechanics of Molecular Rate Processes (Clarendon, Oxford, England, 1969).
21.
D. G.
Truhlar
,
A.
Kuppermann
, and
J. T.
Adams
,
J. Chem. Phys.
59
,
395
(
1973
).
22.
For a recent survey of the literature see H. F. Schaefer, The Electronic Structure of Atoms and Molecules: A Survey of Rigorous Quantum Mechanical Results (Addison‐Wesley, Reading, MA, 1972).
23.
F.
London
,
Z. Elektrochem.
35
,
552
(
1929
);
H.
Eyring
and
M.
Polanyi
,
Z. Physik. Chem. B
12
,
279
(
1931
);
and
S.
Sato
,
J. Chem. Phys.
23
,
592
,
2465
(
1955
).
24.
R. D.
Levine
,
B. R.
Johnson
,
J. T.
Muckerman
, and
R. B.
Bernstein
,
J. Chem. Phys.
49
,
56
(
1968
);
J. T.
Muckerman
,
J. Chem. Phys.
50
,
627
(
1969
); ,
J. Chem. Phys.
J. T.
Muckerman
and
R. B.
Bernstein
,
J. Chem. Phys.
52
,
606
(
1970
); ,
J. Chem. Phys.
and
J. T.
Muckerman
and
R. B.
Bernstein
,
Chem. Phys. Lett.
4
,
183
(
1969
).
25.
See, for example,
R. B.
Bernstein
and
J. T.
Muckerman
,
Adv. Chem. Phys.
12
,
389
(
1967
).
26.
H. L.
Kramer
and
D. R.
Herschbach
,
J. Chem. Phys.
53
,
2792
(
1970
).
27.
W. D.
Davison
,
Proc. Phys. Soc. Lond.
87
,
133
(
1966
).
28.
G.
Das
and
A. C.
Wahl
,
Phys. Rev. A
4
,
825
(
1971
).
29.
G.
Das
and
S.
Ray
,
Phys. Rev. Lett.
24
,
1391
(
1970
).
30.
A.
Dalgarno
,
R. J. W.
Henry
, and
C. S.
Roberts
,
Proc. Phys. Soc. Lond.
88
,
611
(
1966
).
31.
G.
Wolken
,
W. H.
Miller
, and
M.
Karplus
,
J. Chem. Phys.
56
,
4930
(
1972
);
K. T.
Tang
,
Phys. Rev.
187
,
122
(
1969
).
32.
M. A. D.
Fluendy
,
R. M.
Martin
,
E. E.
Muschlitz
,Jr.
, and
D. R.
Herschbach
,
J. Chem. Phys.
46
,
2172
(
1967
);
W. C.
Stwalley
,
A.
Niehaus
, and
D. R.
Herschbach
,
J. Chem. Phys.
51
,
2287
(
1969
).,
J. Chem. Phys.
33.
R. R. Luise, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1970.
34.
R. N.
Porter
and
M.
Karplus
,
J. Chem. Phys.
40
,
1105
(
1964
).
35.
M.
Karplus
,
R. N.
Porter
, and
R. D.
Sharma
,
J. Chem. Phys.
43
,
3259
(
1965
).
36.
These workers used the term “quasiclassical” to indicate the choice of initial diatomic molecule states from only those which are quantum mechanically allowed.
37.
For recent review articles on classical trajectory methods see (a)
D. L.
Bunker
,
Methods Comput. Phys.
10
,
287
(
1971
);
(b) M. Karplus, in Molecular Beams and Reaction Kinetics, edited by C. Schlier (Academic, New York, 1970).
38.
See, for example, (a)
L. M.
Raff
,
L. B.
Sims
,
D. L.
Thompson
, and
R. N.
Porter
,
J. Chem. Phys.
53
,
1606
(
1970
);
(b)
B. H.
Mok
and
J. C.
Polanyi
,
J. Chem. Phys.
53
,
4588
(
1970
); ,
J. Chem. Phys.
(c)
R. N.
Porter
,
L. B.
Sims
,
D. L.
Thompson
, and
L. M.
Raff
,
J. Chem. Phys.
58
,
2855
(
1973
) and references therein. ,
J. Chem. Phys.
L. Jaffe and J. B. Anderson, J. Chem. Phys. 54, 2224.
39.
(a)
J. T.
Muckerman
,
J. Chem. Phys.
54
,
1155
(
1971
);
J. T.
Muckerman
, (b)
56
,
2997
(
1972
); ,
J. Chem. Phys.
J. T.
Muckerman
, (c)
57
,
3388
(
1972
); ,
J. Chem. Phys.
and (d) J. T. Muckerman (unpublished data). Several similar studies are (e) R. (1971);
(f)
R. L.
Wilkins
,
J. Chem. Phys.
57
,
912
(
1972
);
and (g)
N. C.
Blais
and
D. G.
Truhlar
,
J. Chem. Phys.
58
,
1090
(
1973
).
40.
See, for example,
A. G.
Clark
and
G.
Burns
,
J. Chem. Phys.
56
,
4636
(
1972
) and Ref. 7.
41.
This argument was proposed in Ref. 35. For a further discussion, see Ref. 37.
42.
A.
Gelb
,
R.
Kapral
, and
G.
Burns
,
J. Chem. Phys.
56
,
4631
(
1972
).
43.
These results have been reported as a preliminary calculation in Ref. 7.
44.
This is clearly not the most efficient method for averaging over vibrational phase angles for these van der Waals molecules. Since our preliminary results indicated that a large number of such calculations would not be required, it was simpler not to modify our computational procedure.
45.
The data have been smoothed by the use of linear filters. For a discussion of the technique see R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw‐Hill, New York, 1962).
46.
Using Eqs. (5) and (10), we find [see M. M. Gradshteyn and M. M. Ryzhik, Table of Integrals, Series, and Products, (Academic, New York, 1965), p. 341] that the thermally averaged cross section is given by
. The rate constant is obtained trivially using Eq. (4).
47.
R. E.
Roberts
,
J. Chem. Phys.
54
,
1422
(
1971
).
48.
P. S. T.
Lee
and
F. S.
Rowland
,
Chem. Phys. Lett.
18
,
96
(
1973
).
49.
W. H.
Miller
,
J. Chem. Phys.
53
,
1949
,
3578
(
1970
);
W. H.
Miller
,
Chem. Phys. Lett.
7
,
431
(
1970
).
50.
R. A.
Marcus
,
J. Chem. Phys.
54
,
3965
(
1971
);
J. N. L.
Connor
and
R. A.
Marcus
,
J. Chem. Phys.
54
,
5636
(
1971
); ,
J. Chem. Phys.
R. A.
Marcus
,
J. Chem. Phys.
56
,
311
(
1972
).,
J. Chem. Phys.
51.
A. F.
Wagner
,
G.
Das
, and
A. C.
Wahl
,
J. Chem. Phys.
60
,
1885
(
1974
).
This content is only available via PDF.
You do not currently have access to this content.