Cheminl Physics 16 (1976) 109-116
D North-Hollmd Publishing Company
CROSSED-BEAM STUDY OF THE REACTIONS OF H; WITH D2 AND D; WITH Hz
J.R. KRENOS and K.K.
LEHMANN
ofOkrnistry,Douglass College, Rutgers - the State University, New Brunswick,
Department
h’ew Jersey 08903, USA
J.C. TULLY
Bell LaboraroriEs, Murray Hill, New Jersey 07974, USA
P.M. HIERL
Department of C7lemistry. University of Kansas, Lawrence, Kansas 66044, USA
and
G.P. SMITH
Depnrtmenr of C’hcmisfry, Columbia University, New York, New York 10027, USA
Received 8 April 1976
We have studied the reactions D: + Hz -+ D211* + H and HI + D 2 --c (HzD*, DzH+) + (D, H) using the crossed-beam a~paratus EVA. Sample contour velocity distributions of product ions have b+een obtained at relative kinetic energies between
0.4 and 5 cV. In addition potentid energy surfaces were constructed for Hq by the diatomics-in-molecules method and repre
scntative geometries were investigated. The expeiimental results are consi?ent with the predominant early downhill nature
of the grounti-state surface, in that a direct mechanism is observed at all energies studied. As the reactantsapproachone another, avoided surface crossings leading to charge transfer XICaccessibie.Because of the occurrence of reputed electron
jumps, tlic initial identity of the molecularion is largelyinconsequenliti and it is meanin@less
to label the mechanismas
atom or ion transfer
The reaction Ht t H, + Hi + H was one of the earion-molecule reactions studied [I]. Because of
iis apparent simplicity, it is a reaction of fundamental
interest to chemical dynamics. It plays a major role in
the chemistry of interstellar clouds [2,3] and planetary atmospheres [4].
The reaction rate constant has been determined by
single-source mass spectrometry [S] and ion cyclotron
resonance [6,7]. Cross sections and/or product velocity distributions have been obtained as a function of
collision energy by ion beam plus scattering gas measurements [8-121 andmerged.beammethods
[13-1.51.
The detailed dynamics of the reaction has not been
energy (<2 eV). There are also questions concerning
the behavior of the direct “stripping” process at higher
energies and the role of charge transfer in the reaction.
Although the techniques used in previous studies do
complement one another, they do not overlap sulkiciently in either the kinetic energy range studied or
the internal energy states of the reactants to allow an
unambiguous picture of the reaction dynamics to
emerge.
In this paper we report results of experimental and
theoretical studies which shed light on these unanswered questions. We have carried out the first crossedbeam investigation of this reaction system. Specifically,
we report kinematic measurements of reactions (1)
and (2) over the relative kinetic energy range 0.4-S
completely resolved,however. At issue is whether a
eV using the crossed-beamapparatus EVA [16].
1. Introduction
liest
long-lived collision complex exists at low collision
110
J.R. Krerros et
D;+Hz-,H,D++D
+D*H++H
al.fCro$sed-beam srudy olrire reactions of Hi with 02 and D; wiih Hz
(la)
(lb)
H+2+D2+H2D++D
@a)
GD,H++H
(2b)
Complete product velocity contour plots arc presented
for reactions (lb), (li): and (7b). Measurements of
reaction (la) are not reported because the product signal is obscured by the primary ion of equal mass. Our
results conlirm the direct “stripping” nature of the
reaction and suggest a possible explanation for the
discrepancy between the early single beam [IO,1 l]
and more recent merged-beam results [14j.
We have aIso calculated several low-lying potential
energy surfaces for Hi by the diatomics-inmolecules
(DIM) method [17-191. The ground-state surface
clearly shows the absence of a barrier to reaction and
the presence of early downhill character leading to a
predominantly direct reaction prcccss. The locations
of avoided surface crossings suggest that electron hops
occur repeatedly as reactants approach.
2. Experimental
The crossed-beam apparatus EVA and the method
of analysis used in this study have been described previously [l&20]. $ or D: is formed by electron impact,
mass analyzed in a 1800&s spectrometer, and decelerated and focused into a beam of narrow angular
(full width at half maximum, fwhm, of about 2”) and
energy spread (fwhm of about 0.25 eV) by a system
of electrostatic lenses. In the collision region the ion
beam is intersected at 90” by a modulated, thermal
beam of H, or D, (temperature about 330 K). Ions
from the collision zone pass throu& a detection slit,
a stopping-potential energy analyzer, and a 60” sector
mass spectrometer before being detected by an electron
r-multiplier.Phase sensitive detection ofproduct ions is
employed to eliminatebackgroundproblems,and a
multichanne! analyzer is used to improve signal to
noise. Since the beam sources are mounted on the
rotatable lid of the collision chamber, both angular
and velocity distributions of the ionic products can be
obtained.
Contour velocity distributions are derived from
translational energy distributions measured at discrete
laboratory angles. The area normalized energy distributions are weighted according to the total product intensity measured at the corresponding angles. The distributions are then converted into velocity space in the
Cartesian coordinate system by application’bf the
proper nominal jacobian transformation [21]. The
resulting velocity distributions are plotted and contour values arc assigned relative to the highest point.
The contour points are transferred to a -most probable Newton diagram [22] and points of equal contour value arc connected by a smooth curve. The
relative probability of formation of product with
given center-of-mass velocity and angle can be cstimated directly from the diagram.
The total in-plane velocity space energetically accessible to products is in general not accessible experimentally. Two constraints limit our experimental
observations. Because of difficulties in detecting lowenergy ions, the absolute laboratory kinetic energy of
product must be greater than approximately 0.5 eV
[20]. The laboratory ang!c is constrained between
-15” and +55’. The energy restriction greatly limits
the measurement of backward scattered products in
the center-of-mass system.
The molecular reactant ions are formed by tilpact
with electrons accelerated to approximately I?-0 eV.
The predicted distributions [X3,24] of vibrational
states of @ and D?/ ions produced under these conditions (-F&&-C&don)
have broad peaks at v = 2
and v = 3, respectively, corresponding to approximately 0.3 eV internal energy. In the neutral beam, the
ground-state vibrational level is populated with cssentially unit probability.
3. Results
Contour diagrams for reactions (lb), (2a), and (Zb)
are given in figs.1 through 5. The position of the most
probable center of mass(c.o.m.) is indicated by an open
circ!e where the two center-of-mass reactant velocity
vectors meet. The forward region of velocity space is
defined by ~9= 0”, the backward by 0 = 180”, where
0 = 0’ is the direction of the center-of-mass velocity
vector of the reactant ion. E, is the most probable relative kinetic energy. The dashed straight lines are the
largest positive and negative laboratory andes at which
J.R. Krends
01 E, = 0.7 eV
b)Er=
er oL/Crosscd-beam
srlrdy
of rile rcacrions
\
1.4eV
Fig. 1. Velocity conto+urdiagrams obtained from cros2cd-beam
cx+pcriments for DzH produced by the reaction ofD2 with Hz.
D2 is initially incident from the Mt.
energy distributions were taken; thus, their intersection point is the origin of the laboratory coordinate
system. Circles with radii of II,,,, and urnin bound
areas energetically forbidden to products formed from
H; or D; in the most probable vibrationallevel. Because of energy (kinetic and internal) and angular spread
of the reactant beams, boundary transgressions can and
do occur. Products formed with laboratory kinetic
energy below 0.5 eV are difficult to measure reliably.
A dashedcircle with IaboratoIy radiuscorresponding
to 0.5 eV (Emin) is given where necessary.
Fig. 1 clearly shows that product ions from reaction
(lb) are formed predominantly in the forward hemisphere
near 0 = 0” at velocities somewhat larger than that pre-
dicted by a spectator stripping mechanism [IL%](spectator stripping velocities are given by closed circles in
the figures). The backward hemisphere is accessible experimentally, and little scattering is observed there. At
high energies (figs 1c and 1d), product dissociation can
o/H:
with D2 orrd b: wit/r H2
ill
occur and the contour distributions appear to bc “eaten
away” at low c.o.m. vclocitics. The values OFthe most
probable product velocity as a function of collision
energy are in excellent accord with the measurements
of Doverspike and Champion [ 1I]. An additional measurement at E, = 0.4 eV (not shown) also exhibits predominantly fonvard scattering.
We observed mass = 4 product in the reaction of
H; with D,. This undoubtedly is H,D+, not D: for
the following rcnsons. Dr fw-mcd by charge t&sfcr
should appear nt labor;lov
wlocitics not much difi
fercnt than lhe original tht:ma; D, v:llucs. The backward peaking ofchargc transi;‘r products is well estabIishcd cxperimcntally [ 161 and theoretically [20,27 j
for several reaction systl:ms, and has recently been successfully measured by crcdscd-htiam te+niqucs [28].
In our apparatus, this corresponds to an inaccessible
region (EL < 0.5 eV and O,> 60”). Furthermore, the
mass = 4 product in reaction (2) behaves !ike DzH+ product in reaction (1). ltscross section is large,attains its
maximum value at the lowest energy studied, and dccsys
rapidly as reactant translational energy increases. At all
energies (see figs. 2 and 3), mass = 4 product peaks
strongly in the same direction as incoming Ht reactant
and close to the spectator stripping position [25] calculated for H,D’. Since the backward region is not
experimentally accessible, the reaction mechanism for
reaction (2a) cannot be established from our results.
If a direct mechanism prevails, then reaction (2b)
should be similar to reaction (la), which was studied
partially by Doverspike and Champion [ 111. This is
indeed the case. At lligh energies (see fig. S), product
is formed in the backward hemisphere in conformity
with a direct reaction process. There is a small amount
of forward scattering which peaks near 0 = 0” at the
points marked with an X, but at contour values less
than I. The shape of the distribution is extremely distorted, since it lies on the boundary of the experimentally inaccessible region. It is likely that the observed
distribution is only a remnant of the true one, which
probably peaks at a larger value of the c.o.m. velocity;
i.e., one closer to the spectator stripping value.
The results at lower collisionenergiesare givenin
fig. 4. As the energy drops, the backward peak falls
into the inaccessible region and eventually disappears,
leaving only a small forward-scattered component
(fig. 4a). Thus, below 2 eV it is impossible to determine the mechanism of reaction (2b) from our results.
J.R. Krenos er al/Crossed-beam
il2
corn
\
* 1 ooev
alE,
L---
\
+
H2(
--
\
_/-
wefl
t,
__*------_-_
study o/the reactions of Hi wirh D2 and D; with Hz
e*--
A--,=
_/
02
&$$I
97
3
_‘x+____y5_&_-_,-I
biE,=335eV
I
\
cl Er : 2 15eV
Fig 2. Velccity contour diagrams obtained from crossed-beam
cxpcrimentsfor HzD*producedby the reactionolH: with D2.
4. Reaction dynamics
Our results demonstrate conclusively that the reaction mechanism is predominantly “direct” for reaction (1 b) for energies above 0.4 eV and for reaction
(2b) for energies above 2.0 eV. T!te symmetric forward-backward scattenng characteristic of a longlived complex is defiiitely absent.
The direct mecharism picture is supported by theory. We have performed calculations of the ground state
and several excited potential energy surfaces of Hi
using the approximate diatomics-in-molecules (DIM)
method [I7-191. The procedure is described briefly
in the appendix. We find that the energy decreases
monotonically as one proceeds from Hl -H, reactants to H; -H products along the ground state surface. There is no potential well except for a very shallow dip of about 0.05 eV in the Hi -H product re@on. This feature is insignificant when compared to
the reaction exoergicity af 1.8 eV. Ab initio calcula-
FOE.3. Same as fig. 2, but at hi&Jierrelative kinetic cncrgies.
tions of Poshusta and Zetik [29] are in agreement with
our semiempirical results; they obtain a product region
well depth of 0.07 eV. .These results strongly suggest
that reactions (1) and (2) and all isotopic variants proceed by a direct “stripping-type” mechanism at all collision energies E, even as E + 0.
Exammation of the computed Hi potential energy
surfaces provides additional information of interest
about the reaction mechanism. Equal energy contours
for the ground state surface, as computed by DIM, are
plotted in rig. 6 for.trapezoidal Hi geometries.RAB
and R, are the internuclear separations of the two
diatomic fragments AB and CD whose centers of mass
are separated by a fmed distance r. At large r, AB and
CD refer to Hz and Hi, respectively. The potential
minimum, marked with a cross, corresponds to H, and
PI; at their respective eqiriliirium internuclear distances. The surfaces are symmetric about the 45’ diago-.
MI, which also defines the location of an avoided intersection with the first excited Hi energy surface.
Thus the 45” diagonal represents a boundary line for
J.R. Krenos et al./Crossed-beam
study of the reactions of Hi rvirh D2 and D: with Hz
H;+D?-
Fig. 4. Velocity contour diagrams obtained from crossed-beam
experiments for DzH+produced by the reaction of Hl with Dz.
possible charge transfer; i-e., if the molecu!es possess
sufficient vibrational energy to traverse this region,
charge transfer becomes likely.
For r +- the two surfaces actually intersect; i.e.,
are degenerate along the 4.5” line. Thus diabatic behavior
prevails and charge transfer cannot occur at very large
separations r. As the reactants approach, the intersection becomes increasingly more %oided” and the adiabatic path corresponding to charge transfer becomes important. This is illustrated in fig. 7 which shows slices
through the potential surfaces of fig. 6 along the minimum energy path denoted by a dashed line in fig. 6a.
The well bottoms are normalized to the same energy,
so they do not reflect the rapid decrease in absolute
energy as reactants approach. For Hz and H, in their
pound vibrational states (u” = 0, Y= 0) the 4S” line
can almost be reached at r = 8 uo. By r= 6 a,-,, the barrier is washed out considerably, and even in their
ground vibrational states, reactants can easily traverse
the 45” boundary. We conclude from these results that
113
D2 H++H
Fig. 5. Same as tig. 4, but at higher rcIativc kinetic energies.
charge transfer can occur readily at fairly large separations as the reactants approach. Charge transfer is even
more probable for vibrationally excited reactants. Jhis
conclusion is supported by the recent impact parameter calculations of Flannery and co-worker; [3031].
Through consideration ofexperimental and theoretical results, the following picture of the reaction
mechanism emerges: As the Hi and H, reactants approach, electrdn hops occur repeatedly prior to the
hard collision. Atomic rearrangement to form products
then occurs by a direct impulsive process. Because of
the multiple electron jumps, it is meaningless to describe the reaction process as atom or ion transfer.
Contrary to statements in the literature [32-341,
this picture of the reaction mechanism is consistent
with essentially all experimental studies of the Hi-H,
reaction and its isotopic variants. The results of Doverspike and Champion [II] on reaction (la) and our
results on reaction (2b) are similar in that the backward peaks are of relatively low intensity and are
shifted toward rhe c.o.m. from the position expected
J.R. Krcnos er al.fCrosscd-beam
114
sfudy of /Irereacriom
of Hf wifh D2 and Df with Hz
Championsuffer from similarproblems, and that the
merged-beam results are more reliable for this feature
of the reaction.
Merged-beam experiments 114,353 have produced
nearly symmetric forward-backward scattering patterns in some cases, but only for symmetric systems;
i.e., reactions (3) and (4). This need not signify a long
lived complex.
H; + H, --f H; + H ,
(3)
D; + D, -+ D; + D .
(4)
Rather, it is much more likely that it arises from mul-
Fig. 6. Equal cncrgy contour maps for trapezoidal II: geomclrics cxllcul~tcdby the DIM metllod.
”
-06
-04
DISTiNCE
-02
ALOX
0
@2
94
06
MINIMUM ENERGY PATH loo)
Fig. 7. Slices througl~the patcntial surfrxcs of 6g. 6 along the
minimum cncrgy path.
for a stripping-like process. This is in disagreement
with a merged-beam
study of these reactions
[I41
showing large intensity backward stripping peaks. The
discrepancy in our results can be accounted for by the
low-encra product ion discrimination problem described in the previous section (see figs. 4 2nd 5). It is
very likely that the measurements of Doverspike and
tiple electron hops between the approaching reactants
which, if they occur frequently, would eliminate any
distinction between the two reactant species. This interpretation is consistent with the merged-beam studies
of Douglass et al. [I 51 who observe that the product
distributions of the reaction of HD+ with D, exactly
mirror those of the reaction of D; with HD. Note that
in the merged-beam experiments, both the neutral and
ionic reactants are vibrationally excited, thus enhancing
the probability of electron jumps.
The early results of Durup and Durup [IO] have
been cited [32,33] as support for a long-lived collision
complex mechanism for reaction (4). Unfortunately,
this has resulted from an incomplete reading of their
original paper [IO]. The results were modified by an
overlooked statement added in proof, which reverses
the conclusions expressed in the main text. The corrected results of Dump and Durup are in accord with
those of Doverspike and Champion [I l] for reaction
(4). It is likely that the measurements of both Doverspike and Champion and Dump and Durup suffer from
discrimination effects associated with the determina.
tion of low laboratory energy product ions.
Finally, Chupka et al. [36] have observed that at
low collision energy the Hi -Hz reaction cross section
decreases as the reactant H’; vibrational state is increased. This has also been cited as evidence for a longlived complex mechanism [34]. It is, however, also
consistent with the view that there exists a competition between reactive and non-reactive events associated with the charge transfer process. If the reactants
are in low vibrational states, the Hi system should be
adequately described by the adiabatic, ground-state
potential surface. As the vibrational energy of the reactants increases, the probability of the system under-
J.R. Kro7os et al.fCrossed-beam
smd_v oj‘the reacliorrs of ff: wirh D2 uud 0; wit/r Hz
going a transition to the first excited surface of Hqf
(see fig. 7) should also increase. The first excited Hi
potential energy surface computed by DIM exhibits a
high barrier to reaction, so that transitions to this SW
face would almost certainly reduce the reaction probability. The results of Chupka et al. [36] are thereby in
qualitative agreement with the direct mechanism nature of the Hf f H, reaction.
Acknowledgement
We appreciate the assistance and guidance of Dr.
Zdenek Herman in the early stages of this work. In addition, WCwish to thank Dr. Donald McClure and Dr.
James T. Muckerman for helpful discussions. The ex-
perimental work was initiated under the direction of
the late Dr. Richard Wolfgang at the University of
Colorado and Yale University and was supported by
the National Aeronautics and Space Administration
through contract NCL 07004043. The theoretical
studies were supported in part by the Research Council and the Center for Computer and Information Services of Rutgers University.
Appendix: DIM calculation of ‘l-l; potential energy
surfaces
Hi potential energy surfaces have been computed
by the approximate DIM method [ 17,191. The calculations were carried out using the same procedure as
Pfeiffer et al. [I 81, with overlap between functions on
different centers neglected. States of doublet symmetry.were investigated, and the energy levels given by
the roots of an 8 X S matrix. H2 and HY$diatomic imput data employed has been published previous [37,
381 and found to provide a quantitatively accurate description of the two lowest singlet states of Hf [20,39].
While we cannot demonstrate that the Hi surfaces
computed here are of equally high accuracy, comparison with ab initio results [29] on the ground state surface are encouraging. It is almost certainly true that
qualitative features such as the downhill nature of the
ground state, the absence of a deep potential well and
the behavior in the reactant region related to charge
exchange are described correctly by DIM.
II.5
References
[11 H.D. Smyth, Phys. Rev. 25 (1925) 452.
[I] E. Herbst and W. Klcmpcrcr,Ap. J. 185 (1973) 505.
(31 W.D. Watson, Ap. J. 183 (1973) L17.
[4] S-S. Prasad and A. Tan, Gcophys. Res. Letters I (1974)
337.
151 D.P. S!cvcnson and D.O. Schisslcr, J. Chcm. Phys. 23
(1955) 1353.
[6] h1.T. Bowers, D.D. Ellcman, and J. King. Jr., J. Chcm.
Phys. 50 (1969) 4787.
[7] R.P. Claw and J.H. Futrcll, Int. J. 3lnss Spcctrom.Jon
Phys. 8 (1977) 119.
18) C-I’. Cicsc and W.B. 5lnicr II, J. Chcm. Phys. 39 (1963)
739.
T.L. Bailey,J. Chcnr.Phys.44 (1966)
486.
[IO] J. Durup and bl. Durup, J. Chim. Phys. 64 (1967) 386.
[9] D.W. Vance and
[I I] L.D. Dovcrspikc and R.L. Champion, J. Chcm. Phys. 46
(1967) 4718.
[ 121 L. Xlalus, 1. Opauszky, D. Hyatt, A.J. Masson, K. Birkinshaw and M.J. IIcnchman, Disc. Faraday Sot. 44 (1967)
146.
[ 131 R.H. Neynabcr and S.hl. Trujillo, Phys. Rev. 167 (1968)
63.
[14] A.B. Lees and P.K. Rol, J. Chcm. Phys. 61 (1974) 4444.
[1.5] C.H. Douglass, D.J. SIc-Clurc, D.J. Trcvor, ;IndW.R.Centry,
in: Electronic and AtomicCollisions,
cds. J.S. Risicy and
R. Ccballc (Univcrsily ol’Wxhin~ton Press, Suattlc, 1975)
p. 584.
[ 161 2. Herman. J.D. Kcrstctrcr, T.L. Rose, and R. Woltgng,
Rev. Sci. Instrum. 40 (lS69) 538.
[17] F.0. ELlison. J. Am. Chcm. Sot. 85 (1963) 3540.
[181 G.V. Pfciffcr, N.T. FIuff, E.M. Grcenaw& and F.0.
Ellison, J. Chcm. Phys. 46 (1967) 821.
[I91 J.C. Tully. in: Blodcrn Thcorctical Chemistry: Approximate met!lods, cd. G. Scgal (Plenum Press, New York,
1976) in press.
[20] J.R. Krcnos, R.K. Preston, R. Wolfgang and J.C. Tully,
J. Chcm. Phys. 60 (1974) 1634.
[ZI] R. Wolfgang and R.J. Cross, Jr., J. Phys. Chcm. 73 (1969)
743.
[22] D.R. Hcrschbach, Disc. Faraday Sot. 33 (1962) 149.
[23] G.H. Dunn, J. Chcm. Phys. 44 (1966) 2592.
[24] E-14’.McDaniel, V. Ccrmak. A. Dalguno, E.L. Fcrgson,
and L. Friedman, in: Ion-XIolcculc Reactions OVileyIntcrsciencc, New York, 1970) p. 292.
[25] A. Henglcin, hlolccular Bexns and Reaction Kinetics,
lntcrnationrd School of Physics “Enrico Fermi,” XLIV
Course, 1968 (Acndcmic Press. NW York, 1970).
[26 1 T.L. Budzynski and T.L. Bnilcy, Int. J. Mass Spectrom.
lon Phys. 18 (1975) 317.
[27j S. Chapman and R.K. Preston, J. Chem. Phys. 60 (1974)
650.
[IS] K. Birkinshaw, V. Pncnk, and 2. Herman, in: Internrtions
between Ions and hloleculcs,cd. P. AUS~OOS
(Plenum
Press, New York, 1975) p. 103.
116
J.R. Krenos CTal./Crossed-beam
study of the reactions of H; with D2 and Dg with Hz
1291 RD. Poshhustaand D-F. Zctik, I. Chem. Phys. 58 (1973)
11%
(301 T.F. Moran, M.R. Flanncry, and D.L. .4lbritton. J. Chem.
Phys. 62 (1975) 2869.
[31] M.R. Flnnncry, J.V. Hornstcin, and T.F. Moran, C’hem.
Phys. Letters 32 (1975) 455.
(321 E.E. Ferguson, Advances in Electronics and Electron
Physics 24 (1968) 14.
[33] Rclcrencc [24], pp. 131-2.
[34] W.A. Chupka, in: Ion-Molecule Reactions, ed. J.L.
Franklin (Plenum Press, New York, i972) Vol. 1, pp.
69-70.
[35] W.R. Gentry, D.J. McClure, and C.H. Douglass, Rev. sci.
Instrum. 46 (1975) 367.
[361 W.A. Chupka, M.E. Russell, and K. Refaey, J. Chem.‘Phys-
48 (1968) 1518.
I371 R.K. Preston and J.C. TuUy, J. Chcm. Phyr;. 55 (1971)
4297.
I381 J.C. Tully, J. Chem. Phys. 58 (1973) 1396.
1391J.C. Tully and R-K. Preston, J. Chcm. Phyr 55 (1971)
562.