Rotational population distribution of KH (v=0, 1, 2, and 3) in the reaction of K(52PJ, 6 2PJ, and 72PJ) with H2: Reaction mechanism and product energy disposal

Article abstract of DOI:10.1063/1.472746

Using a pump-probe method, we have systematically studied the rotational distribution of KH (v=0-3) produced in the reaction of K (5P, 6P, and 7P) with H₂. The resulting rotational states fit roughly a statistical distribution at the system temperature, while the vibrational populations are characterized by a Boltzmann vibrational temperature of 1800, 3000, and 3100 K for the 5p, 6P, and 7P states, respectively. These results provide evidence that the reaction follows a collinear collisional geometry. This work has successfully probed KH from the K(5P) reaction, and confirms that a nonadiabatical transition via formation of an ion-pair K⁺H₂^- intermediate should account for the reaction pathway. The available energy dissipation was measured to be (68±4)%, (26±2)%, and (6±3)% into the translation, vibration, and rotation of the KH product, respectively. The energy conversion into vibrational degree of freedom generally increases with the principal quantum number, indicating that the electron-jump distance elongates along the order of 5P<6P<7P. The result is different from the Cs(8P,9P)-H₂ case, in which the electron-jump distances were considered roughly the same. Furthermore, a relatively large distance is expected to account for highly vibrational excitation found in the KH product. According to the classical trajectory computation reported by Polanyi and co-workers, the strong instability of the H₂^- bond, inducing a large repulsion energy, appears to favor energy partitioning into the translation.

Full text of DOI:10.1063/1.472746

Rotational population distribution of KH (v=0, 1, 2, and 3) in the reaction of K(52 P J , 62
P J , and 72 P J ) with H2: Reaction mechanism and product energy disposal
DeanKuo Liu and KingChuen Lin
Citation: The Journal of Chemical Physics 105, 9121 (1996); doi: 10.1063/1.472746
View online: http://dx.doi.org/10.1063/1.472746
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Rotational population distribution of KH (v؍0, 1, 2, and 3) in the reaction
of K(5 2PJ , 6 2PJ , and 7 2PJ) with H2: Reaction mechanism
and product energy disposal
Dean-Kuo Liu and King-Chuen Lina)
Department of Chemistry, National Taiwan University, Taipei, Taiwan, Republic of China
and Institute of Atomic and Molecular Sciences, Acedemia Sinica, P.O. Box 23-166, Taipei 10764, Taiwan,
Republic of China
͑Received 10 June 1996; accepted 14 August 1996͒
Using a pump–probe method, we have systematically studied the rotational distribution of KH
͑ ϭ0–3͒ produced in the reaction of K ͑5P, 6P, and 7P͒ with H . The resulting rotational states
v
2
fit roughly a statistical distribution at the system temperature, while the vibrational populations are
characterized by a Boltzmann vibrational temperature of 1800, 3000, and 3100 K for the 5p, 6P,
and 7P states, respectively. These results provide evidence that the reaction follows a collinear
collisional geometry. This work has successfully probed KH from the K(5P) reaction, and confirms
that a nonadiabatical transition via formation of an ion-pair KϩH2Ϫ intermediate should account for
the reaction pathway. The available energy dissipation was measured to be ͑68Ϯ4͒%, ͑26Ϯ2͒%, and
͑6Ϯ3͒% into the translation, vibration, and rotation of the KH product, respectively. The energy
conversion into vibrational degree of freedom generally increases with the principal quantum
number, indicating that the electron-jump distance elongates along the order of 5PϽ6PϽ7P. The
result is different from the Cs(8P,9P)–H2 case, in which the electron-jump distances were
considered roughly the same. Furthermore, a relatively large distance is expected to account for
highly vibrational excitation found in the KH product. According to the classical trajectory
computation reported by Polanyi and co-workers, the strong instability of the HϪ2 bond, inducing a
large repulsion energy, appears to favor energy partitioning into the translation. © 1996 American
Institute of Physics. ͓S0021-9606͑96͒01443-2͔
tially proceed via an abstraction mechanism.9 Note that in
I. INTRODUCTION
some nonadiabatic reaction mechanisms, more complicated
parameters determine the isotope effect, such that the simple
indication may fail.4,11 Spectroscopic analysis of the rovibra-
tional state distribution of the product is also indicative of
the reaction mechanism. A bent-geometric insertion usually
leads to a product accompanied by hot rotation and cold
vibration, whereas a collinear abstraction reaction leads to a
product with cold rotation and hot vibration. For many com-
plicated systems, however, potential energy surface and tra-
jectory computation should be considered to gain full insight
into the reaction complexity.
The simplicity of a three-atom reaction scheme,
AϩH2→AHϩH,
͑1͒
is next to the case of HϩH2→HϩH2 and its isotopic vari-
ants. The information related to Eq. ͑1͒ may provide insight
into the dynamical behavior of more complicated systems.
To overcome the endoergicity involved, the method of en-
ergy disposal in the atomic reactant with a tunable radiation
source is feasible and widely employed. The cases, which
have been under investigation, include nonmetal atoms such
as C,1 O,2 and F ͑Ref. 3͒ as well as metal atoms such as Na,4
K,5 Cs,6 Hg,7 Zn,8 and Cd.8 Among the courses of dynamical
complexity studied, the reaction pathway is an issue of com-
mon concern. To achieve this goal, measurements by crossed
molecular beams,3,6 isotope effects,9,10 and spectroscopic
methods1,2,8 are frequently adopted. In the crossed-beam ex-
periment, the scattering distribution of the product with re-
spect to the center of mass of the system is correlated with a
direct or indirect reaction mechanism. With the use of HD as
a reactant, information on the H/D ratio may imply interme-
diate geometry. If the ratio is larger than unity, an insertive
reaction is preferred. Otherwise, the reaction may preferen-
Although the collisions of excited alkali atoms with H2
have been investigated for decades, the related reaction dy-
namics is not well understood. For instance, the argument
was once focused on whether a single collision between
Cs(7P) and H2 could produce CsH.6,12–15 Sayer and co-
workers provided a model for the CsH formation via a sec-
ondary collision through either the vibrationally excited H2
or ͑CsH2͒ as a mediate step.12,13 In contrast, Vetter and
*
co-workers measured the CsH product with two crossed mo-
lecular beams, which ensured that the observation was under
a single-collision condition.6,14,15 They demonstrated that the
reaction cross section for Cs͑7P1/2͒ was larger than
Cs͑7P3/2͒, despite a larger energy disposal in the latter reac-
tant. They also expected that CsH was formed in a collinear
collision via an electron harpoon mechanism. Since the sys-
a͒
Author to whom correspondence should be addressed. Fax: 886-2-
3636359; e-mail: kclin@hp9k720.iams.sinica.edu.tw
J. Chem. Phys. 105 (20), 22 November 1996
0021-9606/96/105(20)/9121/9/$10.00
© 1996 American Institute of Physics
9121
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9122
D.-K. Liu and K.-C. Lin: The reaction of H2
tem energy is just over the reaction threshold, only the
ground vibrational state of CsH can be observed, but the
information on extra energy partitioning is not available. In a
very recent study with Cs 8P and 9P atoms as reactants,
Bersohn and co-workers reported that the vibrational state
ϭ1 of CsH could be observed, and about 90% available
v
energy was released as translation.16 A collinear geometric
collision was anticipated to cause the CsH product, but the
electron transfer occurred at a shorter distance between Cs
and H2 than the harpoon model predicted. Due to similarity
of the product rovibrational distributions between the
Cs(8P) and Cs(9P) reactants, their nonadiabatic surface
crossings were almost at the same region.
The nonreactive behavior of Na(3P)ϩH2 is well under-
stood, but the reaction behavior for the excited Na atom has
seldom been studied. In a recent study on the reaction of
Na(4P) with H2, Bililign and Kleiber11 found that ͑1͒ a
bimodal rotational distribution of NaH resulted with the mi-
nor component peaking at low J and the major component
peaking at high J; ͑2͒ there was no kinematic isotope effect
on the rotational distribution. Accordingly, the bimodal na-
ture was anticipated to originate from a side-on attack along
an attractive surface, which determined the microscopic
branching late in the exit channels. A similar model was
previously proposed by Breckenridge et al. to account for the
rotational bimodality found in the Mg͑1P1͒–H2 reaction.17
However, in measuring far-wing absorption profiles of the
NaH2 collision complex, the blue-wing detuning was found
to favor low rotational states of the NaH product, while the
red-wing detuning leaded preferentially to high rotational
states.4 This suggests that the reaction may also proceed via
a second pathway. That is, an impulsive end-on attack
mechanism along a repulsive surface probably results in
NaH, with low rotational excitation. On the other hand, the
theoretical work of Sevin and Chaquin indicates that the
Na(4P)–H2 reaction mechanism follows an attractive 3 2B2
surface, which evolves through a series of surface crossings
and finally joins to the reactive 1 2B2 surface, correlating
FIG. 1. Schematics of pump–probe apparatus.
was worthwhile to repeat this experiment, but using a more
sensitive pump–probe technique with a laser-induced fluo-
rescence ͑LIF͒ detection. In this manner, we found for the
first time the KH product, which resulted from the single
collision between K(5P) and H2. In addition, we systemati-
cally studied a series of K(nP) ͑nϭ5, 6, and 7͒ reaction with
H2 in attempt to clearly understand the reaction pathways
and the energy partitioning involved.
In this work, we present a detailed nascent rotational
distribution of KH resulting from K(nP) ͑nϭ5, 6, and 7͒.
The obtained KH spectra extend to a more complete wave-
length range than ever before.5 The resulting rotational states
suitably fit a statistical thermal distribution, while the vibra-
tional population was highly excited to at least ϭ3. Accord-
v
ingly, we confirmed that KH was produced by a collinear
H-abstraction reaction via a harpoon mechanism. The avail-
able energy dissipation was measured to be 68%, 26%, and
6% into translation, vibration, and rotation of the KH prod-
uct, respectively. Most available energy was released as
translation; the case is similar to the recently reported CsH
product. A detailed interpretation on the reaction pathway
and energy partitioning will be discussed.
2
with the lowest P state of Na.18
We have studied the reaction of K(7S) and H2, observ-
ing the resultant nascent KH product with low rotational and
high vibrational states.5 The reaction mechanism was antici-
pated to follow a collinear geometry via an electron harpoon
process, by analogy with the Cs case. In addition, KH can be
state-selectively produced by K(7S) but not by K(5D), de-
spite a similar energeticity shown by these two states. The
symmetry correlation between the reactants and the products
was considered to appropriately account for the reactivity
discrepancy. So far, K(7S) state has been the only state stud-
ied that successfully produces KH. Lin, Schilowitz, and Wie-
senfeld previously studied collisional deactivation of K(5P)
by H2, but failed to observe any KH product.19 This system
is exothermic by 9 kcal/mol. The lack of KH detection was
ascribed to an adiabatic transition, in which the K(5P)ϩH2
II. EXPERIMENT
A pump–probe technique, as depicted in Fig. 1, has been
illustrated elsewhere,5,11,17 so only a brief description is
stated below. One Nd:YAG laser-pumped dye laser was used
as the pump source. The 5P state of the K vapor was excited
at 404.4 nm with the mixed laser dyes of LD 390 and stil-
bene 420 in a volume ratio of 4:1. The 6P and 7P states
were prepared with LDS 698 and DCM, respectively. But the
output wavelength from the dye laser needed to be
frequency-doubled through a KDP crystal emitting at 344.6
and 321.7 nm for excitation of 6P and 7P state, respec-
tively. The unfocused beam was collimated through a pin-
hole of ϳ0.3 cm2 cross section with energy output less than
100 ␮J, small enough to avoid occurrence of optical satura-
tion or multiphoton absorption process.
1
ϩ
*
reactants is correlated with the KH ͑A ⌺ ͒ϩH products, and
the states are energetically inaccessible. In the light of the
K(7S)–H2 reaction,5 however, the proposed mechanism for
the K(5P)–H2 collision seems questionable. We decided it
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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D.-K. Liu and K.-C. Lin: The reaction of H2
9123
The second dye laser pumped by the other Nd:YAG la-
ser was used to probe the LIF spectra of the KH product in
the A1⌺ϩ –X1⌺ϩ transition. The time delay between pump
and probe laser, controlled by a delay generator, was ad-
justed to be about 10 ns. The delay time was short enough to
ensure that the product distribution could be considered in a
nascent state. The unfocused probe beam was collimated
through a pinhole of ϳ0.3 cm2 cross section, propagating
opposite with respect to the pump beam. The output energy
was kept less than 100 ␮J to prevent the obtained LIF spectra
from optical saturation.
respectively, at 404.4, 344.6, and 321.7 nm. The obtained
LIF spectra are under the nascent conditions. For evidence of
this fact, we measured the H2 pressure dependence of KH
͑7,0͒P9, P10, R10, and R11 rotational branch lines at time
delay of 20 ns between pump and probe lasers. The results
show a linear relationship, which indicates that the reaction
under the appropriate H2 pressure and delay time can be free
from interference of rotational cooling. One example for R11
branch line is given in Fig. 3. Assuming the collisional cross
section of 10 Å2 and the averaged relative speed of 2.4ϫ103
m/s, the estimated probability for KH to encounter a second-
ary collision is less than 0.26 for the condition of 5 Torr H2
pressure and 10 ns delay time. Thus the resulting distribution
was partially disturbed by a secondary collision. In the mea-
surement of the delay time dependence, the relative intensi-
ties of overall signals in the varied distributions resembled
each other within 20 ns, but the related signal to noise ratio
for a brief delay time was poor. This fact indicated that the
rotational relaxation was negligible, and the obtained rota-
tional distribution can be reasonably considered to be in a
nascent state.
We adopted the molecular constants reported by
Stwalley and co-workers for the spectrum assignment.21
Since the rotational lines from varied vibrational states hap-
pen in the same LIF spectra region, spectra identification
becomes complicated. To confirm the assignment’s reliabil-
ity, a relaxed spectra under high pressure H2Ͼ60 Torr and
delay time of 300 ns was taken. As reported previously,5 the
resulting excited vibrational states were quenched, and thus
the rotational spectra became ready to be identified. Alterna-
tively, by choosing an appropriate combination of excitation
and emission bands, one may reduce the spectral complica-
tion to the minimum extent and facilitate identification of a
particular vibrational state. For instance, for monitoring the
For achieving a better spectral resolution and signal to
noise ratio, appropriate pairs of excitation and emission
bands were selected for the various vibrational states. In this
work, we selected the pairs of ͓͑ Ј, Љ͒ϭ͑7,0͒,͑7,1͔͒, ͓͑7,1͒,
v v
͑7,0͔͒, ͓͑5,2͒, ͑5,0͔͒, and ͓͑6,3͒, ͑6,1͔͒, respectively, for prob-
ing population at ϭ0, 1, 2, and 3. Coumarin 480, coumarin
v
500, rodamine 575, and a mixture of rodamine 590 and
rodamine 610 in a volume ratio of 1:1 were the dyes used for
the corresponding vibrational states. The obtained LIF signal
of KH was transmitted through a monochromator and de-
tected by a photomultiplier tube enclosed in a cooler at
Ϫ20 °C. The monochromator with dispersion of 18 Å/mm
allowed for spectral transmittance of 14.4 nm. The mono-
chromator functioned as a filter to reduce interference of
scattered light. The detected signal was fed into a boxcar
integrator for signal improvement. By adjusting the delay
time appropriately, one could reduce the atomic emission
interference to the minimum extent, such that the signal to
noise ratio for the LIF spectra may be enhanced. Note that
each LIF spectra was recorded over a wavelength range of 15
nm to cover complete rotational states populated. Thus the
grating setting in the monochromator had to change positions
to record such long wavelengths. The segment of spectra
obtained in a respective fixed grating position overlapped
each other for more than 5 nm, and then normalized to the
identical condition of detection system.
A six-armed heat pipe was used to deposit the K metal,
allowing for spectral observation at 90° with respect to the
incident laser beam axis.20 A thermocouple was intruded in
the vicinity of the reactive regime to monitor the system
temperature within an accuracy of Ϯ1 K. The K metal in the
oven was heated to 500 K, yielding a vapor pressure of about
100 mTorr. The chamber was evacuated to 10Ϫ5 Torr prior to
introduction of H2. The H2 gas, regulated at a constant pres-
sure of less than 5 Torr which was monitored by a MKS
capacitance gauge, flowed slowly through the chamber.
Since occurrence of ‘‘laser snow’’ ͑the KH product͒ will
gradually reduce H2 pressure, a closed static system may
otherwise cause significant error. Also, the chamber needs to
be cleaned frequently to prevent a great amount of KH ac-
cumulation.
ϭ3 state, we selected the ͑6,3͒ and ͑6,1͒ band as the exci-
v
tation and emission band, respectively. In this combined
spectral detection, as shown in Fig. 2͑a͒, only high J levels
of ϭ0, 1, and 2 may appear simultaneously in the same
v
wavelength region, but their intensities are weak. In this
manner, we could record the rotational levels, Jϭ0–19, for
vibrational states of 0 and 1, and rotational levels up to 14
for ϭ2 and 3. The assigned rotational line deviates from its
v
theoretical counterpart within 1 cmϪ1. K2 spectral interfer-
ence with a relatively small rotational constant is free from
the spectral region studied. Although population at ϭ4 was
v
not probed, we anticipate that some unassigned rotational
lines in the ͑6,3͒ band might result from this state, especially
for the K(6P) atom.
¨
By taking into account Franck–Condon and Honl–
London factors, the rotational quantum state distributions of
KH ͑ ϭ0, 1, 2, and 3͒ for the K 5P, 6P, and 7P states are
v
displayed in Figs. 4–6. The Franck–Condon factors are
adopted from the results by Pardo et al.,22 which exhibit
agreement with the data we conducted using the INTENSITY
program developed by Stwalley and co-workers.23 For evi-
dence of a reliable nascent rotational distribution, the R
branch lines of ͑5,0͒ and ͑7,0͒ bands were monitored and
III. RESULTS
A portion of excitation spectra of KH ͑7,0͒, ͑7,1͒, and
͑6,3͒ bands in the A1⌺ϩ –X1⌺ϩ transition are shown in Fig.
2, as the 5P, 6P, and 7P states of the K atom are excited,
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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9124
D.-K. Liu and K.-C. Lin: The reaction of H2
FIG. 2. Portions of LIF spectra of KH in the A1⌺ϩ –X1⌺ϩ transition. ͑a͒ Excitation of ͑6,3͒ band for K(5P); ͑b͒ excitation of ͑7,1͒ band for K(6P);
͑c͒ excitation of ͑7,0͒ band for K(7P).
resulted in a consistent distribution for ϭ0 state. Analo-
gously, the R branch lines of ͑7,1͒ and ͑8,1͒ bands were
able, since the signal was buried in the atomic spectral inter-
ference from the pump laser. For ease of comparison, all the
rotational distributions are represented with the R branch
v
probed together to give rise to the KH ͑ ϭ1͒ population
v
distribution. The population in ϭ3 for K(7P) is not avail-
lines. The distributions thus obtained for ϭ0, 1, 2, and 3
v
v
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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D.-K. Liu and K.-C. Lin: The reaction of H2
9125
FIG. 3. H2 pressure dependence of the KH ͑7,0͒R11 rotational branch line at
time delay of 20 ns between the pump and probe lasers.
FIG. 5. Rotational quantum state distribution of KH ͑ ϭ0, 1, 2, and 3͒
v
produced in the reaction of K͑6 2PJ͒ with H2 .
states appear to be monomodal, peaking in Jϭ7–8. The ro-
tational population profile is roughly consistent with a statis-
tical distribution at the system temperature. A plot of line
intensity against J(Jϩ1) yields a slope corresponding to a
rotational temperature of 585Ϯ65 K, as shown in Fig. 7. The
rotational temperature was close to the system temperature,
but the fraction of total available energy into the rotation was
far from a prior rotational distribution of 2/7. For this reason,
a cold rotation is sometimes called from the point of view of
the energy disposal, which will be discussed in the next sec-
tion. The sum of each integrated rotational line equals the
population of the corresponding vibrational state. The vibra-
tional populations were characterized by a Boltzmann vibra-
tional temperature of 1712Ϯ55, 3010Ϯ124, and 3127Ϯ138
K for the 5P, 6P, and 7P states, respectively. The results
are shown in Fig. 8. The total available energy for dissipa-
tion is 10.84, 23.73, and 29.59 kcal/mol for the 5P, 6P, and
7P states. Note that the values are estimated by adding a
term 5/2kT to the exothermic energy. The fraction of the
energy release as rotation, vibration, and translation are
listed in Table I.
In this work, we only studied the reaction of the K P3/2
state and neglected the spin–orbit effect, which had no evi-
dence showing any difference in the product rotational dis-
tributions in the Na(4P) and Cs͑8P and 9P͒ reactions. In
fact, the cross section of fine-structure mixing induced by H2
for the K 5 2PJ doublets has been measured to be 134 Å2 for
the transition 5 2P3/2←5 2P1/2 and 72 Å2 for its reverse
FIG. 4. Rotational quantum state distribution of KH ͑ ϭ0, 1, 2, and 3͒
FIG. 6. Rotational quantum state distribution of KH ͑ ϭ0, 1, and 2͒ pro-
v
v
produced in the reaction of K͑5 2PJ͒ with H2 .
duced in the reaction of K͑7 2PJ͒ with H2 .
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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9126
D.-K. Liu and K.-C. Lin: The reaction of H2
FIG. 8. Plot of ln(Iv) as a function of vibrational energy Gv for the reaction
of K5P, 6P, and 7P with H2 , respectively. The slopes are characterized by
the Boltzmann vibrational temperature.
form an intermediate ion pair of KϩHϪH was suggested.
Since the rotational spectra covered an incomplete wave-
length range of only 63 cmϪ1, the previous report fell short
of information on the precise rotational population distribu-
tions of KH for various vibrational states. The present work
provides further evidence that a collinear reaction is more
plausible for the K case.
The reaction of K(5P) with the H2 state was previously
investigated,19 using a photolysis laser to produce K(5P)
following KI photodissociation at 193 nm, in which the K
fragment was predominantly partitioned to the 5 2PJ
state.19,25 Upon photolysis, the atomic resonance absorption
spectra of population relaxation from this state were mea-
sured with and without the H2 mixture. The subsequent spec-
tra appeared to be identical, suggesting that the channel of
chemical reaction was negligible. The lack of KH detection
was ascribed to an adiabatic transition. The present pump–
probe measurement using LIF detection proved to be more
sensitive than that adopted previously. In addition, our work
demonstrates that KH should be produced through a nona-
diabatic transition, in which the harpoon mechanism forming
a KϩHϪH ion-pair intermediate is anticipated.
FIG. 7. Plot of ln[Ij/(2Jϩ1)] as a function of J(Jϩ1) for the reactions of
K5P ͑a͒, 6P ͑b͒, and 7P ͑c͒ with H2 , respectively. The slopes of the graphs
are characterized by the Boltzmann rotational temperature.
process.24 Such large mixing cross sections may have caused
the distributions of overall signals being in the statistical 2:1
ratio.
IV. DISCUSSION
A. Collinear geometry
The nascent rovibrational distributions of KH produced
by K 5P, 6P, and 7P states with H2 collision were investi-
gated systematically for the first time in this work. The rota-
tional distributions of KH for various vibrational states are
similar, giving rise to a low rotational temperature equivalent
to the system temperature. In contrast, the vibrational popu-
lations are markedly excited. The observation of hot vibra-
tion ͑temperature of 1700–3100 K͒ and low rotation ͑tem-
perature of 585 K͒ suggests that the reaction follows
preferentially a collinear geometric collision.
TABLE I. Disposal of available energy in reactions of K(nl) with H2 .
K(nl)
5 2PJ
6 2PJ
7 2PJ
a
EAVL ͑kcal/mol͒
10.84
3.01
0.93
0.27
0.09
0.64
23.73
5.65
1.04
0.24
0.04
0.72
29.59
8.14
0.97
0.28
0.03
0.69
E
E
f
͑kcal/mol͒
͑kcal/mol͒
͗
͗
͗
͗
͗
͘
͘
͘
V
R
b
v
f
f
͘
͘
R
T
c
Using a similar pump–probe method, a previous work
on K(7S) with H2 reaction, which is exothermic by 26 kcal/
mol, also led to KH under a single collision condition.5
Analogous to the case of Cs(7P),6 a collinear approach to
aEAVLϭϪ⌬Hϩ5/2kT.
b
f
f
ϭ E /E
;
f
ϭ E /E
.
͗
͗
͘
͘
͗
͘
͗
͘
͗
͘
v
v
AVL
R
R
AVL
c
ϭ1Ϫ f Ϫ f .
͘ ͗ ͘
R
͗
T
v
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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D.-K. Liu and K.-C. Lin: The reaction of H2
9127
TABLE II. Symmetry correlation among reactants, ion-pair intermediates,
and products for varied geometric approaches.
In the case of Na(4P) with the H2 reaction, the rota-
tional distribution of NaH exhibits bimodality.4,11 Bililign
and Kleiber suggested that the major reaction pathway pro-
ceeds via a bent collisional geometry with Na-insertion into
the H2 bond, leading to the branching of low J and high J
components late in the exit channel. The bent NaH2 interme-
diate may be partially stabilized through the electron dona-
tion between the metal and the unfilled antibonding of H2.
Similar interpretation was adopted in the Mg(3P)–H2 reac-
tion for the MgH2 stabilization.17 In contrast, in the case of K
or Cs, the center HϪ of the ion-pair intermediate functions
analogously as a divalent element, such as Be. According to
the valence shell electron pair repulsion ͑VSEPR͒ model, a
linear geometry might be the best structure to reduce the
repulsive interaction between the metal and the end H atom
to the minimum extent. Alternatively, Bersohn and co-
workers suggested that the atomic size might determine the
collisional geometry.16 K and Cs, which have a larger size
than Li and Na may encounter a repulsive force in an inser-
tive approach, and thus a collinear reaction is preferentially
obeyed. In their study on the Cs 8P and 9P state, Bersohn
and co-workers concluded that a collinear reaction between
the reactants is preferred as a result of cold rotation found in
CsH. The result confirms the mechanism proposed by Vetter
and co-workers in a crossed-beam experiment of Cs(7P)
and H2.6 Some theoretical results also lend support to such a
collinear reaction mechanism. For instance, the theoretical
work by Gadea et al. predicted that the Cs(7P)–H2 reaction
proceeds via a collinear ion-pair intermediate with the 7P
electron jumping on the H2 system at a harpoon distance of 6
bohr.26,27
Symmetry
System
Cϱv
Cs
C2v
ϩ
K(n2S)ϩH2(X1⌺ϩg
)
)
⌺
⌺
A
3A
2A
A1
2A1
A2
B1
B2
A1
B1
B2
A1
A1
Ј
Ј
Љ
ϩ
K(n2D)ϩH2(X1⌺ϩg
2⌸
2⌬
ϩ
K(n2P)ϩH2(X1⌺ϩg
Kϩ͑1S͒ϩHϪ2 ͑2⌺ϩu ͒
)
⌺
2A
A
Ј
Љ
2⌸
ϩ
⌺
⌺
A
A
Ј
Ј
ϩ
KH(X1⌺ϩ)ϩH(1s2S)
the total deactivation processes. For evidence of this, in the
nonreactive measurement of the K 7S state by H2, the total
deactivation cross section was dominated by the 7S–5D
state-to-state transition.28 Analogously, the total deactivation
process of the K 5P state by H2 was dominated by the 5P-
(3D,5S) state-to-state exit channel.19 Although the reaction
cross section has not been measured yet, the corresponding
value should be relatively small because of the measurement
for the state-to-state deactivation cross section. A known re-
action cross section may be found in the Cs(7P)–H2
collision,6,32 yielding an expectably small value. The fact
was interpreted as arising from at least five states in between
interacting with the ionic curve competes with the reaction
channel.
According to the harpoon model, the crossing region be-
tween the ionic potential surface and the covalent potential
surface should be located in the long-range attractive portion.
In previous work on the K(7S) atom, the crossing location
corresponded to 4.1–4.8 Å, and the activation energy of the
reaction was determined to be 2–3 kT.5 This small potential
barrier fits the conditions required for the harpoon mecha-
nism. The term energies for the nP states studied are com-
parable to the K(7S) state; therefore, we expect that the
surface crossing is analogously located in a long-range re-
gion, and the reaction should encounter the least activation
barrier.
B. Harpoon mechanism
The reactions of K and Cs with H2 favor a nonadiabatic
transition through an ion-pair intermediate, although Bersohn
and co-workers16 suggest that the electron transfer occurs
within a shorter distance than predicted by the harpoon
model. Alternative evidence for the fit of the harpoon mecha-
nism to our case is provided elsewhere.28–30 In the measure-
ment of total cross section of collisional deactivation for
K͑n2S, nϭ7–11͒ by H2, the resulting value increases abnor-
mally with principal quantum number.29 The cross section of
7S, 8S, and 9S, for instance, were measured to be 150Ϯ2,
167Ϯ5, and 189Ϯ9 Å2.29 The obtained values are much
larger than those predicted by the hard sphere model. In con-
trast, K-rare gas collisions yield values of 32Ϯ4, 35Ϯ2, and
56Ϯ3 Å2 for the corresponding state as quenched by Ar.30 H2
and rare gas are regarded as the inefficient quencher towards
In the harpoon mechanism, a linear ion-pair KϩHϪH in-
termediate may symmetrically correlate with the K͑2P͒ and
H2͑1⌺ϩg ͒ reactants and with the KH͑1⌺ϩ͒ and H͑2S͒ products
through the ⌺ϩ symmetry. The symmetry correlations asso-
ciated with reactant, intermediate, and product for different
angular quantum states are listed in Table II. In the Cϱ␯
symmetry, a fraction, which is associated with the covalent
surface effectively undergoing a nonadiabatic transition, is 1,
1/3, and 1/5 for the S, P, and D orbital, respectively. In other
words, the feasibility of producing KH from different atomic
orbital follows the order of DϽPϽS, assuming similar term
energies are involved. The trend is consistent with the pre-
diction by Bersohn and co-workers,16 adopting the concept
of electronic wave function for the high-lying atomic state.
They interpreted that the extent of wave function penetration
near the atomic nuclear core is along the order of DϽPϽS,
the lower excited alkali atoms, for their lowest unoccupied
31
*
molecular orbitals belonging to ␴ symmetry. The abnor-
mal quenching behavior reflected in the H2 collision of a
highly excited K atom is caused by a long-range electron
transfer. The collision complex hops to the ionic surface,
which crosses several lower K–H2 covalent surfaces as the
exit channels. The probability for the nonadiabatic curve
crossing may be estimated by the Landau–Zener theory. The
exit into the physical quenching channel seems to dominate
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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9128
D.-K. Liu and K.-C. Lin: The reaction of H2
and the feasibility of electron transfer depends on the mutual
wave function overlap. Accordingly, the probability for sur-
face hopping follows the same trend.
approach, the new bond LH tends to be formed before the
HH repulsion completely dissipates. In contrast, for the
HϩLL type, the bond forming and breaking occur simulta-
neously. That is, during the energy release of LL bond break-
ing, the new bond HL is still forming. Accordingly, when the
halogen molecules are replaced by the hydrogen molecule,
the fraction Evib/Etot is expected to increase, if all other con-
ditions remain the same.33 Observations of the K–Br2 and
K–H2 cases seem to go against the mass effect prediction.
The discrepancy might be interpreted as arising from the
difference between the repulsion of BrϪ2 and H2Ϫ, which is
estimated by the bond dissociation energy to be 1.15 eV and
4.78 eV.36 ͑The electron affinity of H2 is not taken into ac-
count.͒ According to classical trajectory computations,33 the
Evib/Etot tends to decrease with increasing the repulsion of
XϪ2 . In the cases of K or Cs, the strong instability of the H2Ϫ
bond apparently favors the energy partitioning into the trans-
lation. Alternatively, due to the large electron affinity of Br2
relative to H2, a larger electron-jump distance in the K–Br2
reaction may also partially enhance vibrational excitation.
We now attempt to interpret the difference of transla-
tional energy partitioning between K–H2 and Cs–H2. If the
electron-jump distance is kept constant, the fraction Evib/Etot
is anticipated to increase as the mass of attacking atom
increases.33 However, the experimental data disagree with
the prediction. The contradictory observation implies that the
Cs–H2 should have a shorter electron-jump distance, so that
the vibrational energy partitioning will be reduced. This con-
sideration is supported by the findings of vibrational states
up to only one for the Cs(8P,9P)–H2 reaction, but up to at
least three for the K(5P,6P,7P) case. Such prediction for
the Cs case is consistent with the report by Bersohn and
co-workers.
C. Energy partition
Among the reactions of K 5P, 6P, and 7P states with
H2, the determined values of energy partitioning into trans-
lation, vibration, and rotation of KH are roughly the same,
giving results of 0.68Ϯ0.04, 0.26Ϯ0.02, and 0.06Ϯ0.03, re-
spectively. However, when considering individual vibra-
tional degrees of freedom, one may find that the 5P, 6P, and
7P state has an energy disposal of 3.01, 5.65, and 8.14 kcal/
mol, respectively. This fact suggests that the surface crossing
region gradually increases with increase of the principal
quantum number, which agrees with the harpoon model. On
the other hand, the rotational energy conversion extent is
almost the same, irrespective of the varied P states, suggest-
ing that a collinear reaction can be effectively applied to all
the P states studied. In contrast, the total available energies
dissipated into the CsH vibration were roughly the same in
both Cs 8P and 9P states. Electron transfer at an almost
equal distance between the Cs atom and H2 was thus
suggested.16
By analogy with the Cs (8P,9P) and H2 system, most
available energy, of about 70% in the K–H2 collision, was
dissipated into translation. Therefore, one may expect that
the ion-pair formed in the electron transfer has no time to
adjust the HϪ2 bond distance prior to dissociation. The insta-
bility of HϪ2 , which is restricted to a H2 bond distance of 0.74
Å, breaks the bond abruptly, and the impulsive energy re-
leased is thus mostly changed to translation. Due to a short
lifetime compared to the rotational period, the dissociation of
ion-pair intermediate cannot lead to an isotropic product dis-
tribution, as has been revealed in a crossed-beam experiment
by Vetter and co-workers.14 They found that CsH scattered
in a forward direction relative to the incident Cs atom. We
expect a similar phenomena will be observed in our case.
In an electron-harpoon reaction MϩX2→MϩX2Ϫ
→MXϩX, the product energy distribution among various
degrees of freedom is closely related to the electron-jump
distance, the repulsive force for breaking the XϪ2 bond, the
incident collision angle, the initial kinetic energy, and the
mass effect. Polanyi and co-workers have thoroughly inves-
tigated such a reaction using a classical trajectory method on
an appropriate ionic potential energy hypersurface of
MϩXϪ2 .33,34 Based on their computations, we have attempted
to compare the behavior of energy distributions among the
V. CONCLUSION
We have systematically studied the rotational distribu-
tion of KH ͑ ϭ0–3͒ in the reaction of K͑5P, 6P, and 7P͒
v
with H2. The spectroscopic analysis indicates that the rota-
tional populations are in the statistically thermal distribution,
irrespective of varied vibrational and electronic states. These
results provide further evidence that the reaction follows a
collinear collisional geometry. This work has successfully
probed KH produced in the K (5P) reaction, and confirms
that a nonadiabatical transition via formation of an ion-pair
KϩHϪ2 intermediate should account for the reaction pathway.
The fraction of product energy partitioning yields 68%, 26%,
and 6% for translation, vibration, and rotation. The energy
conversion into vibration generally increases with the princi-
pal quantum number, indicating that the electron-jump dis-
tance elongates along the order of 5PϽ6PϽ7P. The sub-
ject reaction can be regarded as the type HϩLL ͑L, light
atom; H, heavy atom͒, in which the HL is still forming dur-
ing the energy release of LL bond breaking. The case differs
from the type of LϩHH, in which most energy is deposited
in the vibration. In the K–H2 reaction, the strong instability
of the HϪ2 bond favors the energy partitioning into the trans-
lation. As compared to the Cs–H2 case, relatively large
three cases KϩBr2,35 K ϩH2, and Cs ϩH2.16 The products
of these reactions are commonly characterized by a collinear
approach through an ion-pair intermediate. However, the
product energy partitioning into various degrees of freedom
is remarkably different, especially for vibration and transla-
tion. For instance, the fraction Evib/Etot was measured to be
Ͼ60%, 25%, and 10% for K–Br2, K–H2, and Cs–H2. Evib
and Etot denote the vibrational energy and the total available
energy. In the reaction of LϩHH ͑L, light atom; H, heavy
atom͒, when the attacking atom is light along a collinear
*
*
J. Chem. Phys., Vol. 105, No. 20, 22 November 1996
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D.-K. Liu and K.-C. Lin: The reaction of H2
9129
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The authors wish to thank Professor Bersohn for his
helpful discussion. This work is financially supported by the
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