Volume 24, number
1
CHEMICAL
PHYSICS
1 January
LETTERS
1974
COLLINEAR
QUANTUM
MECHANICAL
CALCULATlONS
OF THE He + Hz PROTON TRANSFER REACTlOw
Donald J. KOURIT
Dcporrr,lol t of Clre~nical Physics. The IVeizt~mtrr~
Imtitrrrc of Scierrc~.
Rehowt.
Israel
and
Michael BAER
Applied Optics Deporrrtler~t. Sorcq Ndear Researcl~ Center, Yartle. Israel
and Departntelrt of Chemical Physics, The Weizrnann lnstirrrre of Science,
Rehmor.
Israel
Received 20 July 1973
Revised manuscript
received 11 October
1973
Exact quantum
mechanical results for callincar Hr + Hi - 21 + HeH+reac:ive
collisions arc prescnled Ior rhe
(total) energy range of 0.93 CV to I .4 eV. The Hz initial vibrational
states include u = 0 through u = 5. The diaromicsin-molecules
semi-empirical
surface of Kuntz is used in the compurntions.
Excep\Tor a short range orcncrgics, [he
calculated reaction probabilities for Hi (u = 0) are laker than those of excited Hz.
1. Introduction
A major objective of chemical dynamics studies
is the understanding of how potential energy surface
details affect the course of chemical reactions [I-3].
In particular, because of the potential importance of
reactions
involving
population inversions, considerable
effort is being expended in dynamical studies focusing
on the roIe of vibrational energy in chemical reactions
[4-g]. The present study is focused on the reaction
He+H;+H+HeH*,
(1)
an example of a proton transfer reaction. Experimental studies of this system have been reported by Chupka and Russell [IO] and by Chupka et al. [I l] in
which enhancement of the reaction cross section was
* This rcscuch
was supported
in part by the Volkswagenwerk
Stiftung.
t Alfred P. Sloan Fellow 1972-74;
currently on leave from
the Departments
of Chemistry and Physics, University of
H&ton,
Houston, Texas 77004, USA.
found for vibrationally hot Ht molecules. In addition
to these studies, Brown and Hayes [ 121 have reported
ab-initio potential surface calculations. Their results
suggest this system to be especially promising because
the correlation energy appears to vary relatively little
with nuclear configuration [12] _Thus, a reasonably
accurate ab-initio surface has been obtained for this
system. Furthermore, Kuntz [13] has recently reported a diatomics-in-molecules
procedure which
yields an empirical surface in semiquantitative
agreement with the ab-initio surface of Brown and Hayes.
This surface is in a form convenient for applications
to collisional dynamics studies (fig. 1). We have performed fully quantum mechanical calculations, in
the collinear approximation, for this reaction. Results for various initial .tibrational states are given
and a preliminary comparison against the experimental results of Chupka et, al. is made. The method employed is that due to Kuppermann [14], &modified
by Baer and Kuppermann [15], and is described_.
elsewhere [S; 151.
.
Volume 24. r.umbcr 1
CHEMICAL PHYSICS LETTERS
2. Results and discussion
to this is the range of energies around E = 1 .O eV).
seems to be in striking contrast with experiment
[IO, 1 l] , and with ideas regarding the effect of late
barriers on the influence of vibrational energy in a
reaction. Thus, one might expect vibrational excitation to be particularly effective in promoting reaction for such a surface as the present one (fig. 1) since
the system must overcome the large barrier (endoergicity) in the exit channel (fig. 1). Although the
present calculations seem to violate this picture
(which was used in discussing the experimental cross
section [ 10,111) that still does not necessarily mean
that the present resuIts contradict the experimental
fmdings. First, the collinear calculations yield transition probabilities only and not cross sections so that
even relative magnitudes cannot be directly compared
without additional assumptions. The second reason
has to do with the high endoergicity of the system
(0.8 eV). Consequently a relatively large quantity
of kinetic energy is concentrated in the (Hz, He)
channel, before passing the reaction zone, which distorts the “collinear picture”.
This
In fig. 2 are represented
the various transition
prob-
abilities, i.e.,
He+HS(u)+H+HeH+(u=O,l),
u=O,l,2,3.
(13)
Ca!culations have been made for total energies ranging
iiom 0.93 eV up to 1.40 eV. At the low energies (less
than 1 .O ev) one has u = 0 through u = 3 as open channels in the Ht + He arrangement and only u =O in the
HeH+ arrangement whereas at the high energies (larger
than ! .3 eV) one has u = 0 through u = 5 as open
states for the Hi molecule and u =O, 1 for the HeH+
(table I). As many as 17 basis functions were employed in most of the calculations. Flux conservation was satisfied in general within 2 percent.
The predominant feature of the results as shown
in fig. 2 is the fact that q (u = 0) + He reaction
probabilities are in general larger than those for
$ (u = 2) + He and Hz (u = 3) + He (an exception
38
Volume
24, number
1
CHEMlCAL
1 January
PHYSICS LETTERS
Eigenslates
1974
Table 1
of tls and Hell’
HUH+b)
ground s~atc
lsr cscired slate
2nd excited state
3rd esciwd srntc
4111 cscitcd state
5th cscitcd rtntc
a)
0.135
0.396
0.642
0.816
1.095
1.301
0.929
I .287
1.605
1.882
2.121
2.352
In units of cV.
b) hleasurcd
from
rhc bottom
of 11; hlorsc potential
well.
the scnsc that all three of them, namely, reactions
(3), (4) and (5) have the same exoergicity. Now asthat the experimental
results of Mnylotte et
al. would approximately
apply to reaction (5) as well,
we realize that in this respect the collinear picture
suming
A
L
r)9
IO
I
Fig. 2. The transition
.ey. Lower part: -
II
I
II
12
Tot01 Energy
+He-
hns much more relevance, i.e., 3 relatively small population
inversion
[which is equivalent to a weak vibra-
0
I
probnbilily
13
14
tional enhancement
of the transition probability
of
reaction (l)] , and consequently
the calculations
seem to be at least qualitatively,
in reasonable agree-
of total cner-
ment with the experimental
IeVl
as a function
H;(O) + HeHHe+(O,l)+ Ft. Upperpmt:
I
H;(l)+
He-+
HHe’(0. I)+ H; - - - H;(3) + He - HHe+(O,l) + H. Arrows A
nnd B show the opcninp of the ground state and the fust excited state of HHe+.
References
111hl. Karplus,
Some support
to the present
results
can be found
from recent experiments done by Maylotte et al. [14] _
They studied the exothermic reactions:
Cl + HI+ HCl + I,
-AJ$=
Br+HI+HBr+I,
-MO
Cl + HBr + HCI + Br,-N!i
0
31.7 kcal mole-‘;
(2)
= 162 kcal mole-’
; (3)
= 15.5 kcal mole-l
(4)
and noticed a large difference between reaction (2) and
reactions (3) and (4) with regard to the final vibrational distribution. They found that the most populated vibration due to reaction (2) was u = 3 whereas
the most populated level in reaction (3) is v = 2 and
in reaction (4) u = 1 (they cannot measure the relative population of u = 0). Considering now the backward (exothermic) reaction
HHe+ + H --f I~; + He,-mi
ones.
HHe+(O.l)+ II;---H:(2)
= 18 kcal mole-‘,
R.N. Porter and R.D. Sharma, J. Chem.
Phys. 43 (1965) 3259.
121P.K. Kuntz,
E.hl. ,Memcth, S.D. Rosncr and J.C. Polnnyi.
J. Chem. Phys. 44 (1966) 1168.
131 R.N. Porter, L.B. Sims, D.L. Thompson and L.M. Raff.
3. Chem. Phys. 58 (1973) 2855.
[41 CC. Rankin and J.C. L&ht, J. Chem. Phys. 51 (1969)
1701;
G. Miller and J.C. Light, J. Chem. Phys. 54 (1971) 1643.
1 D.C. Truhlx and A. Kuppermann, J. Chem. Phys. 56
(1972) 2232.
‘I S.F.Wu and R.D. Levine, Mol. Phys. 22 (1971) 881;
S.1:. Wu, B.R. Johnson and R.D. Levine, hlol. Phys. 2.5
(1973) 609.
I.
1 G.C. Schatz, J.M. Bowman and A. Kuppcrmann.
Chcm.
Phys. 58 (1973)
4023:
181 XI. Baer, to bc published.
PI A. Perski and hi. Bacr, to be published.
to1 W.A. Chupka and h1.E. Russell, J. Chcm. Phys. 49
(1968)
5426.
and b1.E. RUSSCII, Sixth
International
Conference
on Atomic and Electronic
Collisions (M.I.T., Cambridge. hfaswchusetts.
1969)
p. 71;
111 W.A. Chupka, J. Berkowitz
(5)
we notice that it is similar to reactions (3) and (4) in
39’
Volume 24, nurni~er 1
CHEMICAL
R.H. Neynaber and C.D. h~~~nuson, J. Chem. Phys.
59 (1973) 82.5.
[I21 P.J. Brown and E.F. Hayes, J. Chem. Phys. 55 (1971)
932.
1131 P.J. Kuntz, Chem. Phys. Letters 16 f1972) 581.
[ 14 1 A. Ruppwnann,
VIIth International
Conference
on
PlfYSICS
LE-iTERS
[IS]
(161
I January
1974
the Physks of Electronic and Atomic Collisions, Abstmcts of Papers, Amsterdam
(1971).
M. Lkter and A. Kuppermann.
to be published.
D.ff. Maylotte, J.C. Polanyi nnd K.B. Woodsll, J. Chem.
Phys. 57 (1972) 1547.