We   have  been  able  to  measure  the  threshold 

energy Eo for  the reaction D+H_2→DH+H. The 

value  obtained was  (0.33±0.02)  eV.  Apparently,  this 

is  the first  direct  determination  of  a  threshold  energy 

for  a reaction involving the formation  and breaking of 

covalent bond

Kuppermann, Aron

White, John M.

English

Caltech Authors - Main

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4352 LETTERS TO THE EDITOR 
?IJeV 
25 
ION INTENSITY DISTANCE FROM SUAFACE IN ANGST!lOMS 
I 
I 
I 
I 
I 
I 
I 
FIG. 1. Plot of surface-potential configuration on the right and 
observed ion energy distribution on the left for H2 molecules 
with an applied field of approximately 2.5 V /A. The ion distribu-
tion is shifted from !1E (the energy deficit from surface potential) 
by I, the ionization potential, so that the features are aligned with 
the pertinent level. The potential distribution with an atom (of 
I= 15.6 e V) present is drawn in dashed lines. Extrapolation of 
the potential energy (not including the atomic field) to the surface 
defines Eo. Locations of the first five stationary states of the infinite 
triangular well are also shown. The scale in the center is in electron 
volts and applies to both sides. 
the surface states depend on the field rather than 
the crystal lattice. 
The conventional model of a surface, with an atom 
near that surface, in an electric field is shown in Fig. 1. 
Low-energy electrons tunneling into the roughly tri-
angular well outlined in the figure have a certain 
probability of being reflected by the metal surface.2 
That such reflectivity exists can be empirically demon-
strated by the familiar difficulty of collecting low-
energy electrons; special means such as a Faraday 
cage must be used for quantitative collection. If the 
reflectivity is unity and tunneling back to the atom is 
unlikely, well-defined energy levels will exist within 
the well. Lower reflectivities will result in short-lived 
states and consequent level broadening. 
Alternately, the problem may be described in terms 
of the matching of wavefunctions at the boundaries of 
the three regions of interest: the atom, the triangular 
well, and the surface. The probability amplitudes in the 
region of linearly increasing potential are given in terms 
of Airy functions3 and are initially unspecified in am-
plitude and phase. These two parameters are fixed by 
equating logarithmic derivatives at the boundaries and 
result in small amplitudes in the well except at energies 
near the eigenvalues of the simple infinitely high tri-
angular well. Consequently, low tunneling rates are 
expected for atomic levels not aligned with the well 
levels. The presence of the atomic potential and asso-
ciated image force acts as a small perturbation on the 
well levels. A calculation using square potentials verifies 
this picture; a square well open on one side to a higher-
energy continuum demonstrates resonances at energies 
very near to the closed-well eigenvalues. 
Eigenvalues E,. of the infinite triangular well are 
given by the relation 
- (2mjfi}e2F2 )iEn=an, 
where m is the electronic mass, e the electronic charge, 
F the field, and a,. the nth root of the particular Airy 
function which is finite for all real values of its argu-
ment. To complete a rough correspondence with our 
picture, we must add to En a quantity Eo given by the 
difference between the Fermi energy and the energy 
at which the extrapolated field curve intersects the 
surface. Results of this calculation and an observed dis-
tribution are compared in Fig. 1. Good agreement is 
not expected for the first level because of the influence 
of the image potential which is not included in the above 
calculation and because of the sensitivity of this level 
to the assumed surface configuration. The calculated 
variation of peak spacings with electric field agrees 
closely with experimental values and, over the energy 
range observable, is very nearly indistinguishable from 
a first-power field dependence. 
In addition to the main structure explained above, 
the experiments show further detail in peak structures 
indicative of the nature of the surface and surface 
reactions. It is expected that this type of analysis will 
be useful in surface studies. For example, it is to be 
noted that a pure surface reaction such as H3+ forma-
tion exhibits no secondary structure.I 
The model described here is simplified and lacking 
in detail but is believed to be essentially correct. A more 
thorough analysis and presentation of data will be 
submitted at a later date. 
* Work supported in part by the National Science Foundation 
and in part by the Advanced Research Projects Agency. 
1 A. J. Jason, R. P. Burns, and M. G. Inghram, J. Chern. Phys. 
43,3762 (1965). 
2 For example, I. Gimpel and 0. Richardson, Proc. Roy. Soc. 
(London) A182, 17 (1943). 
3 L. D. Landau and E. M. Lifshitz, Quantum Mechanics 
(Addison-Wesley Pub!. Co., Inc., Reading, Mass., 1958), p. 70. 
Energy Threshold forD +H2---?DH +H 
Reaction* 
ARON KUPPERMANN AND JOHN M. WHITEt 
Gates and Crellin Laboratories of Chemistry, t 
California Institute of Technology, Pasadena, California 
(Received 3 March 1966) 
WE have been able to measure the threshold energy Eo for the reaction D+HrDH+H. The 
value obtained was (0.33±0.02) eV. Apparently, this 
is the first direct determination of a threshold energy 
for a reaction involving the formation and breaking of 
covalent bonds. 
The method used consists of photolyzing a mixture 
of DI or DBr plus H2 with monochromatic light and 
determining the wavelength dependence of the resulting 
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LETTERS TO THE EDITOR 4353 
[DH]/[D2] concentration ratio. The photodissociation 
of DI produces translationally hot D atoms1- 4 capable 
of reacting with H2 at room temperature. Light in the 
wavelength interval 3660 to 3030 A excites DI from 
its ground electronic state 1~+ to the repulsive state 
arr1 from which it dissociates into ground state 2 p!o 
iodine and 2S1 deuterium atoms.5 The minimum energy 
needed to product excited 2 P!0 iodine atoms6 correspon~s 
to a wavelength of 3130 A. However, even at 3030 A, 
the contribution of this state is probably unimportant. 
Therefore, in the wavelength region mentioned, the pho-
ton energy in excess of the DI bond dissociation energy 
(D0°=3.098 eV) appears as translational energy of the 
fragments, most of it (98.5%) in the D atoms. It is 
thus possible to produce essentially monoenergetic D 
atoms with translational energies relative to the H2 i~ 
the range of 0.14 to 0.48 eV. Photolyzing DBr at 2537 A 
extends this range to 0.53 eV since the dipole strength 
for transitions from ground-state DBr to excited states 
which dissociate into excited 2P1/ bromine atoms is 
quite low.5 The hot D atoms produced can, if suffi-
ciently energetic, react with H2 to form DH and H. 
The D atoms that escape this reaction react with DI 
to form D2. 
The experimental equipment consisted of a mercury 
lamp, a monochromator, a Teflon-lined photolysis 
vessel, and a thermopile. Mixtures of DI or DBr and 
H2 of different concentration ratios were photolyzed at 
room temperature or at 196°K. The [D2]/[DH] ratio 
was then determined with a special double-collector 
hydrogen isotope-ratio mass spectrometer.7 Plots of 
[D2]/[DH] versus [DI]/[H2] were linear, and. the 
nonvanishing nature of their intercepts was attnbu-
ted3.4 to the hot D-atom reaction with H2. Similar 
experiments with DI or DBr and He mixtures also 
furnished straight lines of [D2]/[DH] versus 
[DI]/[He] due to the presence of a small amount 
(2% to 4%) of HI or HBr impurity. 
In Fig. 1 we have plotted, as a function of the average 
initial energy E; of the D atoms relative to the 
H2 molecules, the difference Ll= ([DH]/[D2])oH2-
([DH];[D2])0H•, where the ([DH]/[D2])ox refer to 
the reciprocals of the linear intercepts mentioned above. 
The values of E; include small thermal contributions 
(of about 0.03 eV). Consideration of thermal rate 
constants shows unequivocally that the D atoms that 
escape the hot reaction with H2 and become thermal-
ized do not form DH since they react exclusively with 
DI to form D2 even at the lowest [DI]j[H2J ratios 
used in our experiments. This conclusion is confirmed 
by the equality of the results at 196°K and room tem-
perature. Therefore, Ll is a measure of the DH formed 
by this hot reaction plus that formed by reaction of 
the resultant H atoms with Dl.8 Consequently, when 
E; equals the threshold energy, Ll vanishes. From Fi~. 1 
we thus obtain Eo= (0.33±0.02) eV.9 The error ts a 
rough estimate based on the bandpass of the mono-
chromator and the accuracy of the analyses. 
., 
%~ 
e. e. 
..._,_.. 
N %T :I: N 
oo ~~
..._,_.. 
H 
<I 
0.30 
0.20 
0.10 
I 
I 
I 
I 
I 
t 
I 
I 
I 
I 
I 
I~ 
I 
I 
1' 
I 
I 
I Jl 0 ~o---oT.I-- o~.2---o~.~31~'o.-4---o.'5---or.6--~ 
El./eV 
FIG. 1. Effect of average relative initial kinetic energy of reac-
tants of D+H2-->DH+H reaction. Open circles: photolysis of 
DI mixtures at 3660, 3340,3130 and 3030 A, in order of increasing 
energies. Full circle: photolysis of DBr at 2537 A.• 
Using the method of classical trajectory calculations, 10 
and a semiempirical potential-energy surface, 11 Karplus 
et al. 12 recently obtained a value of 0.26 eV for the 
rotationally averaged E0 •9 Micha,l3 using an approxi-
mate quantum-mechanical method and a different 
potential-energy surface, obtained a value of Eo=0.23 
e V for the J = 0 to J' = 0 reaction. 
We are presently performing additional experiments 
of higher accuracy. We are also attempting to extract 
the energy dependence of the rotationally averaged9 
reaction cross section from the data. Using assumed 
but reasonable elastic and reactive cross sections, we 
have obtained preliminary numerical solutions of a 
Boltzmann equation pertinent to our experimental 
conditions. They furnished theoretical [DH]/[D2] 
ratios which are of the right order of magnitude and 
sensitive to the assumed cross sections. 
*Work supported in part by the U.S. Atomic Energy Commis-
sion and the Petroleum Research Fund. 
t Work performed while in residence at the California Institute 
of Technology in partial fulfillment of the requirements for the 
Ph.D. degree in chemistry from the University of Illinois, Urbana, 
Ill. Present address: Department of Chemistry, University of 
Texas, Austin, Tex. 
t Contribution No. 3035. 
1 R. A. Ogg, Jr., and R. R. Williams, Jr., J. Chern. Phys. 13, 
586 (1945). 
2 H. H. Schwarz, W. H. Hamill, and R. R. Williams, Jr., 
J. Am. Chern. Soc. 74, 6007 (1952). 
a R. J. Carter, W. H. Hamill, and R. R. Williams, Jr., J. Am. 
Chern. Soc. 77, 6457 (1955). 
4 (a) R. M. Martin and J. E. Willard, J. Chern. Phys. 40, 
2999 (1964); (b) p. 3007. 
6 (a) R. S. Mulliken, Phys. Rev. 51, 310 (1937); (b) J. Chern. 
Phys. 8, 382 (1940). 
s C. E. Moore, Atomic Energy Levels (U.S. Department of 
Commerce, National Bureau of Standards, Washington, D.C., 
1958), Vol. 3, p. 106. 
7 C. R. McKinney, J. M. McRea, S. Epstein, H. A. Allen, and 
H. C. Urey, Rev. Sci. Instr. 21, 724 (1950). We are extremely 
grateful to Professor Sa~mel. Epste~n for permitting us to use 
his instrument at the Cahforma Institute of Technology. 
Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
4354 LETTERS TO THE EDITOR 
8 The point obtained using DBr and 2537-A light should not 
be included in Fig. 1 without a correction which takes into account 
the presently unknown differences in the thermal rate constant 
ratio of the reactions H+DX->HD+X and H+DX->HX+D 
for X=I and X=Br. This correction would slightly lower or 
raise the curve of Fig. 1 around £;=0.55 eV, but would not affect 
Eo. 
9 At room temperature practically only the ground vibrational 
state of H 2 is populated, but several of its rotational states con-
tribute to the reaction. Therefore, the reaction cross section 
and threshold energy corresponding to these experiments refer 
to a rotational average at this temperature. 
10 M. Karplus, R. N. Porter, and R. D. Sharma, J. Chern. 
Phys. 42, 1105 ( 1965) and references therein. 
11 M. Karplus and R. N. Porter, J. Chern. Phys. 40, 1105 
(1964). 
12 M. Karplus, R. N. Porter, and R. D. Sharma (private com-
munication). 
13 (a) D. A. Micha, Arkiv Fysik 20, 411 (1965); (b) p. 425; 
(c) p. 437. 
Phosphorescence of KaCo(CN)6 
MAURIZIO MrNGARDI AND GERALD B. PORTER 
Department of Chemistry, University of British Columbia, Vancouver 
British Columbia, Canada 
(Received 14 March 1966) 
THE complex ions of only a few of the transition metals have been found to luminesce/ with most 
of the data referring to the phosphorescence of d3 ions, 
particularly of chromium(III).2 •3 We report here our 
observation of the emission spectrum of potassium 
hexacyanocobalta te (III). 
One other example of luminescence of d6 complexes, 
the tris(dipyridyl) and tris(phenanthroline) ruthen-
ium(II) salts, is known,4 and has been characterized as 
fluorescence.5 On the basis of the lifetime of the emission, 
"-'10 p.sec, and of the position of the emission bands, 
Crosby et al. make the assignment of this transition 
to 1Tr-t1A,. 
The emission spectrum of crystalline K3Co ( CN )6 
was measured with a Jarrell-Ash 0.5-m J/6.3 grating 
spectrograph (20 A/mm in first order) on Kodak 1N 
plates. Excitation was front surface with ultraviolet 
radiation from a mercury arc. A broad band with a 
maximum at 14 400 cm-1 and a half-width of about 
2000 cm-1 was observed with the crystal at 4.2° and 
at 77°K. The luminescence is distinctly visible as a red 
glow; in fact, it can be seen even with the crystal at 
room temperature, although it is then quite weak. This 
band seems to be devoid of structure; however, because 
of the uneven spectral sensitivity of 1N plates in the 
red, this point is uncertain. Qualitative observations 
of the lifetime by the phosphoroscope technique indicate 
a value of about 10-a sec. 
In solution, there are three principal bands found in 
the absorption spectrum.6 At 50 000 em-', there is a 
very intense band, with Emax= 1.6X 104• Two weaker 
bands appear at 32 100 cm-1 (Emax= 180) and at 
38 600 cm-1 (Emax= 160). We have found, in addition, 
a weak band centered at about 18 500 cm-1, which 
could be seen only with a crystal, because it is masked 
by the tail of the more intense ultraviolet band in solu-
tion. The extinction coefficient at the band maxrmum 
is approximately 0.01. 
According to the calculations of Tanabe and Sugano,7 
the low-lying electronic states in a d6, low-spin octa-
hedral complex are, in order of increasing energy: 
1Atu(t296 ), the ground state, 3T,9 (t295eu'), 3T29 (t296eu'), 
'T,9 (t295e91), and 1 T29 (~96eu'). The two bands of the 
absorption spectrum which lie in the near ultraviolet 
can reasonably be assigned to the transitions 1T29- 1At9 
(38600cm-1) and 1Tt9- 1A19 (32100cm-1). They have 
about the expected extinction coefficients and the cor-
rect relative energies for this assignment. 
The weak absorption band probably represents the 
lowest energy transition: 3T19- 1A 19 (18 500 cm-1 ), 
although its intensity is somewhat low. From the band-
width and extinction coefficient, the natural lifetime 
of the 3 Tru state should be of the order of 0.1 sec. 
The mirror-image relationship of the observed emission 
band together with the long lifetime of the luminescence 
makes this assignment reasonable. Hence, the emission 
arises from the same transition, 3 T19~1A 19, and, since 
it is spin forbidden, is phosphorescence. 
A more detailed analysis of these band systems will 
be published in the near future. 
The authors wish to thank the North Atlantic Treaty 
Organization for support of this work. 
1 See G. B. Porter and H. L. Schlii.fer, Z. Elektrochern. 68, 
316 (1964), for references. 
2 G. B. Porter and H. L. SchUifer, Z. Physik. Chern. (Frankfurt) 
40, 280 (1964). 
3 L. E. Forster and K. DeArmond, Spectrochirn. Acta 19, 1403, 
1687 (1963). 
4 J. P. Paris and W. W. Brandt, J. Am. Chern. Soc. 81, 5001 
(1959). 
6 G. A. Crosby, W. G. Perkins, and D. M. Klassen, J. Chern. 
Phys. 43, 1498 (1965). 
6 A. Kiss and M. Czegledy, Z. Anorg. Chern. 235, 407 (1938). 
7 Y. Tanabe and S. Sugano, J. Phys. Soc. Japan 9, 753 (1954). 
Muonium Chemistry* 
R. M. MOBLEY, J. M. BAILEY,t w. E. CLELAND,t 
V. W. HUGHES, AND]. E. ROTHBERG 
Gibbs Laboratory, Yale University, New Haven, Connecticut 
(Received 17 March 1966) 
MUONIUM (M) is the atom consisting of a posi-tive muon and an electron, and it will behave as a 
light isotope of hydrogen with regard to its atomic 
interactions and chemical reactions since the muon 
mass is 207 times the electron mass and since the muon 
mean lifetime of 2.2 p.sec is long compared to electron 
atomic orbital times. The present Letter reports on two 
methods for studying muonium chemistry and on 
initial results for the interactions of muonium with a 
number of molecules.' 
The methods utilize the powerful techniques of 
elementary particle physics and rely upon parity non-
conservation in the weak interactions responsible for 
the production and decay of the muon. From the decay 
of positive pions, polarized positive muons are pro-
duced, and in the decay of positive muons into positrons 


Energy Threshold for D+H_2→DH+H Reaction

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Energy Threshold for D+H_2→DH+H Reaction

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