JOURNAL OF CHEMICAL PHYSICS
VOLUME 120, NUMBER 6
8 FEBRUARY 2004
Reaction pathway and potential barrier for the CaH product in the reaction
of Ca„4 s 4 p 1 P 1 …¿H2 \CaH„ X 2 ⌺ ¿ …¿H
Yu-Wen Song, Jye-Jong Chen, Ming-Kai Hsiao, and King-Chuen Lina)
Department of Chemistry, National Taiwan University, Taipei, and Institute of Atomic and Molecular
Sciences, Taipei, Taiwan 106, Republic of China
Yu-Ming Hung
Department of Chemistry and Institute of Applied Chemistry, Chinese Culture University, Taipei,
Taiwan 111, Republic of China
共Received 5 September 2003; accepted 10 November 2003兲
The nascent CaH product in the reaction Ca(4s4 p 1 P 1 )⫹H2 →CaH(X 2 ⌺ ⫹ )⫹H is obtained using
a pump–probe technique. The CaH( v ⫽0,1) distributions, with a population ratio of CaH( v
⫽0)/CaH( v ⫽1)⫽2.7⫾0.2, may be characterized by low Boltzmann rotational temperature.
According to Arrhenius theory, the temperature dependence measurement yields a potential barrier
of 3820⫾480 cm⫺1 for the current reaction. As a result of the potential energy surfaces 共PES兲
calculations, the reaction pathway favors a Ca insertion into the H2 bond along a 共near兲 C 2 v
geometric approach. As the H2 bond is elongated, the configurational mixing between the orbital
components of the 4p and nearby low-lying 3d state with the same symmetry makes significant the
nonadiabatic transition between the 5A ⬘ and 2A ⬘ surface in the repulsive limbs. Therefore, the
collision species are anticipated to track along the 5A ⬘ surface, then undergo nonadiabatic transition
to the inner limb of the 2A ⬘ surface, and finally cross to the reactive 1A ⬘ surface. The observed
energy barrier probably accounts for the energy requirement to surmount the repulsive hill in the
entrance. The findings of the nascent CaH product distributions may be reasonably interpreted from
the nature of the intermediate structure and lifetime after the 2A ⬘ – 1A ⬘ surface transition. The
distinct product distributions between the Ca(4 1 P 1 ) and Mg(3 1 P 1 ) reactions with H2 may also be
realized with the aid of the PES calculations. © 2004 American Institute of Physics.
关DOI: 10.1063/1.1637588兴
I. INTRODUCTION
less, the Ca(4 1 P 1 ) state, as electronically excited with a
tunable laser at 422.7 nm, may cause the reaction with exothermicity of 1267 cm⫺1. Although the Ca and Mg elements
are in the same group IIA, their chemical properties exhibit
marked difference. In contrast to the bimodal nature of rotation distribution given by Mg(3 1 P 1 ), the nascent product
CaH in the reaction of Ca(4 1 P 1 ) with H2 has been found to
show a single-peaked distribution, as characterized by low
Boltzmann rotational and high vibrational temperature.13 The
former reaction proceeds predominantly via a Mg-insertion
mechanism, while the latter still deserves further study to
confirm the mechanism. Thus, this work aims to understand
the detailed reaction pathway for the Ca(4 1 P 1 ) with H2 reaction and then make comparison to the Mg(3 1 P 1 ) case.
In this work, a pump–probe technique is employed to
obtain a nascent rotational population distribution of the CaH
product ( v ⫽0 and 1兲 in the current reaction. The resultant
single-peaked rotational distributions of product are consistent with those reported.13 A temperature dependence measurement is carried out to yield a reaction barrier of 3820
⫾480 cm⫺1 , in contrast to the Mg(3 1 P 1 ) reaction which
shows no reaction barrier is encountered.1,2,4,10 Finally, ab
initio potential energy surfaces 共PES兲 calculations for the
collision species in approach of either collinear or bent configuration are performed. With the aid of PES calculations,
Among reactions of alkaline earth metals with H2 , the
Mg atom is the only one that has been well investigated for
its reaction mechanism.1–10 The feature of large endothermic
energy blocks the reaction initiated by the ground-state atoms of alkaline earth metals. The advent of the tunable laser
makes it feasible to deposit excitation energies in various
atomic states, which are large enough to overcome the energy requirements of endothermic reactions. In the
Mg(3 1 P 1 ) with H2 reaction, the nascent product MgH( v ,N)
in the v ⫽0 and 1 levels shows both a bimodal rotational
distribution with a major large N component and a minor low
N component.1,2,5–9 The Mg(3 1 P 1 ) – H2 reaction is dominated by an insertion process tracking along the attractive
1
B 2 (C 2 v symmetry兲 or 1 A ⬘ (C s symmetry兲 surface, which
crosses the ground-state surface.1,7,9–12 After the colliding
species undergo the nonadiabatic transition, the decomposition occurs on the anisotropic ground-state surface. If a collinear approach is followed, a substantial potential barrier as
high as 30– 41 kcal/mol will impede the reaction.4,10
As for Ca, to our knowledge, only a handful of reports
are related to the reaction dynamics.13,14 The scheme
Ca(4 1 S)⫹H2 →CaH(X 2 ⌺ ⫹ )⫹H is endothermic by 22 390
cm⫺1, which blocks the reaction from occurring. Neverthea兲
Electronic mail: [email protected]
0021-9606/2004/120(6)/2774/6/$22.00
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© 2004 American Institute of Physics
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J. Chem. Phys., Vol. 120, No. 6, 8 February 2004
the reaction mechanism is suggested and the experimental
observation may be reasonably interpreted.
II. EXPERIMENT
A pump–probe technique employed similarly as in this
work has been reported elsewhere.13,15,16 The radiation
sources contained two tunable dye lasers, which were
pumped, respectively, by a frequency-doubled and a
frequency-tripled Nd:YAG laser operating at 10 Hz with
pulse duration of 5– 8 ns. The pump laser, operated with
stilbene 420 emitting at the wavelength of 422.7 nm, was
used to prepare the Ca atom in the 4 1 P 1 state. After a brief
time delay, the probe laser beam, with spectral resolution
better than 0.1 cm⫺1, was guided in the opposite direction to
excite the laser-induced fluorescence 共LIF兲 of CaH in the
B 2 ⌺ ⫹ – X 2 ⌺ ⫹ transition in the wavelength range of 620–
640 nm.13 The unfocused pump and probe beams were collimated via an individual pinhole of ⬃0.3 cm2 cross section,
with the output energies less than 100 ␮J for both beams.
The probe beam was delayed by ⬃10 ns. The zero delay time
was defined as the maximum temporal overlap between
pump and probe pulses. Adjustment of a brief delay time
could avoid occurrence of two-color multiphoton excitation
processes. To ensure that the obtained rotational distributions
are in the nascent states, free from interference of rotational
cooling and secondary reaction processes, a rotational line
CaH(0,0)R2 5 was selected for the measurements of H2 pressure and pump–probe delay time dependence. The H2 pressure was adjusted from 2 to 10 Torr with a delay time fixed
at 10 ns, and the delay time from 2 to 25 ns with a H2
pressure at 10 Torr. The corresponding rotational line intensities were found to be in linear dependence.
A six-armed heat-pipe oven was used to deposit the Ca
metal, which was heated to 930⫾1 K. 13,16 Temperature was
monitored with a thermocouple intruding through the top
arm near the reactive region. The H2 gas, at about 8 Torr
monitored by an MKS capacitance pressure gauge, flowed
slowly through the chamber. The obtained LIF signal of CaH
was transmitted through a monochromator and detected by a
photomultiplier tube 共PMT兲 enclosed in a cooler at ⫺20 °C.
The monochromator functioned as a filter to reduce interference of scattered light.
For the measurement of temperature dependence, an additional PMT was attached on the opposite side of the reactor, relative to the other detector, for recording simultaneously the atomic Ca emission in the 4 1 P 1 →4 1 S
transition from the reactive region. The LIF signal of a rotational line CaH(0,0)R2 5, as selected for the temperature dependence measurements, was normalized to the atomic emission intensity to keep the factor of the Ca density unchanged
throughout the experiments. In this manner, the normalized
rotational peak area was treated as a function of temperature
in the range 930–980 K to determine the reaction barrier
based on the Arrhenius theory.16,17 Such a normalization
treatment is necessitated, otherwise the reactant concentration may increase with temperature.
The reaction of Ca⫹H2 →CaH⫹H
2775
III. POTENTIAL ENERGY SURFACE CALCULATIONS
The basis sets for Ca and H, comprising 5s5p5d1 f
Gaussian-type orbitals 共GTOs兲 and 7s3p2d GTOs, respectively, were adopted from the work by Kim et al.14 Allelectron restricted Hartree–Fock 共RHF兲 calculations and
complete active self-consistent field 共CASSCF兲 were performed with MOLPRO 96 program. A number of six A ⬘ molecular orbitals were optimized by considering 14a ⬘ and 3a ⬙
active spaces in the CASSCF calculations. As the H2 bond
was fixed at 0.75 Å, the 1A ⬘ – 6A ⬘ PES calculations in 共near兲
C ⬁ v and C 2 v collision configurations with the CASSCF
method have been found to be consistent with those by Kim
et al. with the MRCI method.14 Furthermore, as the H2 bond
was stretched to 0.9 Å, the current CASSCF PESs calculations involving enlarged active spaces were also found to be
consistent with those in the C 2 v symmetry by the MRCI
method, with the same basis sets and active spaces
(7a 1 ,2b 1 ,2b 2 ,1a 2 ) as those given by Kim et al. As compared
to the calculations at collinear and perpendicular geometries,
the advantage to using a C s symmetry in the PES calculations lies in the feasibility to change the CaHH angle for
comparison. In particular, for nonadiabatic processes like the
current reaction, the energy surfaces calculated in C s symmetry allow one to examine the possibility for surface crossing.
For the current CASSCF calculations, inclusion of only
8a ⬘ 共including 4s, 4p y , 4p z , 3d z2 , 3d yz , 3d x2⫺y2 on Ca
and two 1s orbitals on H兲 and 3a ⬙ 共including 4p x , 3d xy ,
and 3d xz ) may be enough. Nevertheless, when the active
spaces are enlarged, the resultant composition of wave function involves more terms and becomes more flexible, thus
leading to a more accurate calculation of potential energy.
For instance, the potential energies of the Ca 3 1 D and 4 1 P
states were calculated in this work to yield 22 252 and 23 710
cm⫺1, respectively, in comparison with the corresponding
experimental values of 21 850 and 23 652 cm⫺1 and the
CASSCF results of 41 847 and 28 744 cm⫺1 with smaller
active spaces. An enlarged active space should apparently
improve the accuracy of energy calculation.
IV. RESULTS AND DISCUSSION
A. Reaction barrier determination
The LIF spectrum of nascent CaH ( v ⫽0 and 1兲 product
is shown in Fig. 1. The 共0,0兲 and 共1,1兲 bands were excited in
the B 2 ⌺ ⫹ – X 2 ⌺ ⫹ transition, while the 共0,1兲 and 共1,2兲 emission bands were monitored. As compared to the spectroscopic data,18 the accuracy of assignments for each rotational
line is within ⬍1 cm⫺1 deviation. The rotational lines N
⫽0 – 23 and N⫽0 – 20 of the R branches in the 共0,0兲 and
共1,1兲 bands, respectively, may be spectrally resolved to better
than a resolution of 0.1 cm⫺1. Given the Hönl–London factor, the rotational line intensities for the v ⫽0 and 1 levels
can thus be determined simultaneously from the same spectrum. A plot of line intensity against N(N⫹1) yields a slope
corresponding to Boltzmann rotational temperature. The obtained rotational temperatures are 951⫾71 K( v ⫽0) and
947⫾80 K( v ⫽1), consistent with our previous work yielding 929 K( v ⫽0) and 900 K( v ⫽1). 13 Furthermore, by sum-
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2776
J. Chem. Phys., Vol. 120, No. 6, 8 February 2004
Song et al.
FIG. 1. LIF spectra of CaH ( v ⫽0 and
1兲 in the B 2 ⌺ ⫹ – X 2 ⌺ ⫹ transition.
The 共0,0兲 and 共1,1兲 bands are excited,
while the 共0,1兲 and 共1,2兲 emission
bands are monitored simultaneously.
ming up the rotational lines for each level and taking into
account the Franck–Condon factor,19 the corresponding vibrational population may be estimated. The population ratio
of CaH( v ⫽0)/CaH( v ⫽1) yields 2.7⫾0.2, consistent with a
previous report of 3.1⫾0.5.13 Since only two levels are
found, vibrational temperature may not be informative. As
reported,13 however, the fraction for the available energy partitioned into vibrational levels is larger than the prior prediction. This work shows a difference from the previous one by
acquiring data with a better spectral resolution. Our previous
LIF spectra were obtained with a low spectral resolution
such that the CaH v ⫽0 and 1 levels may not be resolved
completely. Thus, the minor CaH( v ⫽1) population had to
be determined by monitoring the 共1,0兲 emission band to
avoid the CaH( v ⫽0) interference.13
For the temperature dependence measurements, a representative line (0,0)R2 5 is selected. Its peak area was first
normalized to the atomic peak area of the Ca(4 1 P 1 →4 1 S)
emission, as described in Sec. II, and then plotted against the
reciprocal of temperature on a semilogarithmic scale.16,17 According to Arrhenius theory, the slope shown in Fig. 2 yields
a potential barrier of 3820⫾480 cm⫺1 . In contrast to the
FIG. 2. Arrhenius plot for the normalized peak area of the rotational line
(0,0)R2 5 against the reciprocal of
temperature on a semilogarithmic
scale in the range from 930 to 980 K.
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J. Chem. Phys., Vol. 120, No. 6, 8 February 2004
FIG. 3. 共a兲 Potential energies calculated for the 1A ⬘ – 6A ⬘ surfaces, correlating with the Ca 4 S, 3 D, and 4 P states, as a function of the distance
between Ca and the center of H2 in 共near兲 C ⬁ v symmetry 共the angle⫽1°).
The H2 bond is fixed at 0.75 Å. 共b兲 Potential energies calculated similarly as
in 共a兲, but the H2 bond is stretched to 0.9 Å. The dashed curves denote the
5A ⬘ surface.
Ca(4 1 P 1 ) reaction, the reactive collisions of Mg(3 1 P 1 ) and
H2 have been found to follow an attractive surface without
suffering from any potential barrier.1,2,4,10 Note that in the
normalization of CaH rotational line, all the time-resolved
atomic spectra were integrated from a lower bound at about
10–15 ns. The exclusion of the early portion should minimize the error caused by the neglect of deconvolution treatment and the scattering light. In spite of retainment in a low
temperature range, radiation trapping, which prolonged the
Ca fluorescence decay up to 250–350 ns, probably may
cause systematic error for the reaction barrier determination.
A better improvement is to employ an additional laser to
probe the Ca(4 1 P 1 ) population. Nevertheless, different
sources of error will be introduced in the complicated system.
B. Understanding reaction pathway
with aid of PES calculations
Figures 3共a兲 and 共b兲 show the PES calculations when
Ca(4 1 P 1 ) approaches H2 in 共near兲 C ⬁ v symmetry with the
H–H bond fixed either at 0.75 Å or at 0.9 Å. The potential
energies for all six A ⬘ surfaces change slightly in the early
portion and then increase monotonically as the distance de-
The reaction of Ca⫹H2 →CaH⫹H
2777
FIG. 4. 共a兲 Potential energies calculated for the 1A ⬘ – 6A ⬘ surfaces as a
function of the distance between Ca and the center of H2 in 共near兲 C 2 v
symmetry 共the angle⫽89°). The H2 bond is fixed at 0.75 Å. 共b兲 Potential
energies calculated similarly as in 共a兲, but the H2 bond is stretched to 0.9 Å.
The dashed curves denote the 5A ⬘ surface.
creases. The dashed curves in the figures indicate the 5A ⬘
surface in C s symmetry, which the colliding species are expected to follow as the entrance channel. However, the lowest excited state surface 2A ⬘ , correlating with the Ca 3 1 D
state, is separated too far to allow for nonadiabatic transition
to the ground-state surface 1A ⬘ with which the products are
correlated. Similar results are found for the cases where the
H–H bond is stretched from 0.75 to 1.0 Å. Therefore, the
observation of the nascent CaH product is unlikely to be
caused by the collinear H abstraction.
When the Ca–H2 approach is turned to a C 2 v 共or C s )
configuration, the potential surfaces corresponding to the
3 1 D and 4 1 P states are split into the 2 – 4A ⬘ and 5 – 6A ⬘
surfaces, respectively. Among these surfaces, as shown in
Fig. 4共a兲, the 3 – 6A ⬘ surfaces are weakly affected as the
Ca–H2 distance is shortened; only the 2A ⬘ surface becomes
strongly attractive and has much chance to cross the 1A ⬘
surface. Although Fig. 4 shows only the A ⬘ surfaces, the
CASSCF calculations have considered the interaction among
the molecular orbitals. Unless Coriolis interaction becomes
important, there might be no need to display the A ⬙ surfaces.
For occurrence of the current reaction, the 5A ⬘ 共the dashed
curve兲–4A ⬘ surface transition should first take place. There
are several pathways for this to happen: First, the colliding
species along the 5A ⬘ surface may cross nonadiabatically to
the 4A ⬘ surface at a distance 3– 4 Å 关‘‘A’’ in Fig. 4共a兲兴 be-
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2778
J. Chem. Phys., Vol. 120, No. 6, 8 February 2004
tween Ca and the center of H2 . Nevertheless, according to
the Landau–Zener theory, the surface transition probability
should be small since these two surfaces are almost parallel
to each other, in spite of only a ⬃0.13 eV energy splitting.
Such inefficiency of the collisional deactivation from the Ca
4 1 P to 3 1 D state has been reported by Breckenridge and
Merrow using inert gases as quenchers.20 If the probability of
surface crossing in this region can be enhanced, probably by
the involvement of Ca⫹ H⫺
2 ion-pair character, then the nonadiabatic transition between the 2A ⬘ – 1A ⬘ surfaces may occur
at crossing region ⬃1.5 Å without any energy barrier encountered 关Fig. 4共a兲兴. This result goes against our experimental findings.
Second, the 5A ⬘ – 4A ⬘ surface transition probably may
happen in a shorter Ca–H2 distance, about 2 Å 关‘‘B’’ in Fig.
4共a兲兴, but a potential repulsion of ⬃1.5 eV is too large for the
colliding species to surmount. Radiative cascade from the Ca
4 1 P to 3 1 D state is another alternative channel to reach the
2A ⬘ – 1A ⬘ surface crossing at ⬃1.5 Å without any energy
barrier encountered. The reaction of Ca(3 1 D) with H2 is
endothermic by ⬃535 cm⫺1. The observed energy barrier
3820 cm⫺1 is unlikely to account for such endoergicity. On
the other hand, as the pump–probe delay time is increased,
the relaxed amount of Ca(3 1 D) is increased proportionally
to make a quadratic dependence for the CaH product yield.
The observed linear dependence for the CaH product as a
function of the pump–probe delay time is also indicative of
insignificant contribution from this pathway via the IR radiative cascade.
When the H2 molecule is fixed at the equilibrium bond
distance, the reaction pathways proposed above apparently
fail to meet the experimental findings. From theoretical point
of view, Kim et al. also expected that the current reaction
may not occur in a single collision event, as considering the
energy surfaces with H2 fixed at 0.75 Å.14 Nevertheless,
when the H2 molecule is stretched to 0.9 Å, the corresponding energy surfaces exhibit a distinct difference from those
discussed above. As shown in Fig. 4共b兲, the resulting potential energies for the 5A ⬘ – 4A ⬘ surface crossing 共at the ‘‘B’’
region兲 and the 2A ⬘ – 1A ⬘ surface crossing are lowered substantially. As similarly explained in Fig. 4共a兲, it would be
difficult for the 5A ⬘ – 4A ⬘ surface transition in the ‘‘A’’ region to take place. If it does, the result is against the observation of a potential barrier. The IR radiative cascading process may not dominate either, as is explained above.
Nevertheless, the 5A ⬘ – 4A ⬘ surface transition probably
may occur in the ‘‘B’’ region. As H2 is stretched, the potential repulsion in this region becomes lowered to ⬃0.6 eV
共4840 cm⫺1兲, which is slightly larger than the determined
energy barrier. Accordingly, upon surmounting the potential
repulsion, as shown in Fig. 4共b兲, the colliding species along
the 5A ⬘ surface may join the 2A ⬘ surface, and then the reactive 1A ⬘ surface around 1.7–1.9 Å. The observed energy
barrier probably accounts for the energy requirement to surmount the potential repulsion in the ‘‘B’’ region. One should
assume that the effective collisions take place only when
H2 ( v ⫽0) stretches to its outer turning point, which is close
to the value 0.9 Å. If the energy may first be deposited in the
H2 v ⫽1 level, enlargement of the H2 bond distance may
Song et al.
help facilitate the reaction and increase the subsequent product yield. To further support the reaction pathway proposed,
an experiment has been conducted for the Ca(4 1 P) plus
H2 ( v ⫽1) reaction. The H2 v ⫽1 level was excited using
stimulated Raman pumping, while the fraction of vibrational
population in this level was determined by using coherent
anti-Stokes Raman spectroscopy.21 The resultant nascent
CaH( v ⫽0 and 1兲 rotational distributions appeared to be
similar to those with H2 ( v ⫽0) reaction, but the CaH product
yield 共or the reaction cross section兲 was enhanced by an order of magnitude under otherwise identical conditions.22 The
population in the higher levels ( v ⭓2) of CaH was not
found. Apart from enhancement of the reaction rate, the vibrational excitation may not change the effective colliding
configuration to open up an additional reaction pathway.
For the plausible pathway considered above, one point
needs to be addressed on how the 5A ⬘ and 2A ⬘ surface coupling occurs. One speculation is that the collision complex,
after the 5A ⬘ – 4A ⬘ surface transition in the ‘‘B’’ region, can
track along the repulsive 4A ⬘ surface and then join the 2A ⬘
surface at long range around 4 –5 Å. In fact, the collision
complex along the repulsive 4A ⬘ surface may readily decompose to Ca(3 1 D) and H2 , unless H2 is transiently excited to slow down the breaking apart. The induced barrier is
likely to bring the collision complex back to the 2A ⬘ – 1A ⬘
surface transition. This mechanism seems to be less efficient.
The second one is to consider the configurational mixing
between the 5A ⬘ , 4A ⬘ , 3A ⬘ , and 2A ⬘ states. Because of the
presence of a nearby low-lying 3d state, the two singly occupied orbitals of the 4p state on the triatomic plane 共yz
plane兲 have a great chance to mix with those three orbitals of
the 3d state with the same symmetry.23 When the H2 bond is
stretched, the electron back-donation from either singly occupied 4p y or 3d yz orbital of the Ca atom to the antibonding
␴ * of the molecular hydrogen becomes more efficient, and
the involvement of partial Ca⫹ H⫺
2 ion-pair character may
energetically stabilize the corresponding 2 1 B 2 共or 5A ⬘ ) and
1 1 B 2 共or 2 2 A ⬘ ) surfaces at short range. Furthermore, the H2
bond elongation makes the repulsive limbs of these surfaces
close to each other. The efficiency of the configurational
mixing becomes significant at short range, and thus the 5A ⬘
surface may undergo nonadiabatic transition to the repulsive
2A ⬘ surface. For instance, from the PESs calculations in C 2 v
symmetry using the MRCI method, we found that the 2 1 B 2
state has mingled with 30% of 1 1 B 2 character at the Ca–H2
distance 1.9 Å, in comparison to 0.002%, an insignificant
value at the asymptotes. Accordingly, upon surmounting the
energy barrier, the collision complex CaH2 , along the inner
limb of the 2A ⬘ surface, may feasibly cross to the reactive
1A ⬘ surface. This plausible reaction pathway seems to reasonably interpret the experimental findings.
C. Comparison between CaH and MgH distributions
The findings of the rotational and vibrational distributions of CaH may be interpreted with the aid of PES calculations. As shown in Fig. 4共b兲, when the H–H bond distance
is stretched to 0.9–1.0 Å, the CaH2 intermediate right after
the 2A ⬘ – 1A ⬘ surface transition has a structure with Ca–H
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The reaction of Ca⫹H2 →CaH⫹H
J. Chem. Phys., Vol. 120, No. 6, 8 February 2004
distance 1.76 –1.96 Å and the ⬔HCaH angle 28 –30°. If the
impulsive model is applicable and the collision complex is
short-lived enough to decompose rapidly, then a large fraction of the available energy should be partitioned into the
CaH rotation due to a large torque produced. Nevertheless,
after the 2A ⬘ – 1A ⬘ surface transition, the CaH2 intermediate,
with an energy state lying below the asymptote products,
may be energetically stabilized. Although the intermediate
lifetime cannot be estimated 共⬃ps兲 precisely, it should be
long enough for the energy randomization to be efficient.
During the energy randomization, the relaxation rate of rotational energy is anticipated to be faster than that of vibrational energy. That is why the resultant CaH product is populated in low rotation and hot vibration, if Boltzmann
distribution is assumed. On the other hand, the short H–H
distance 0.9–1.0 Å of the CaH2 complex following the
2A ⬘ – 1A ⬘ surface transition may induce a strong coupling
between CaH and H to cause the excess internal energy of
CaH to dissipate rapidly. In addition, during the prolonged
lifetime of the collision complex, the moieties also probably
undergo multiple collisions between CaH and H prior to
breaking apart.
In contrast to the Ca–H2 PES results, the reported
Mg–H2 PES calculations show that the H–H distance for the
bent intermediate MgH2 around the surface transition is
about 1.47 Å.10,12 The coupling between MgH and H is weak
such that the moieties may readily break apart in a brief
vibrational period.9 In addition, as compared to CaH2 , the
MgH2 intermediate carries a large excess energy ⬃26 kcal/
mol relative to the asymptote products.10 According to the
quasiclassical trajectory calculation, the MgH2 collision
complex lasts about 0.5– 2.0⫻10⫺13 s. 12 The relatively
short-lived MgH2 causes the energy transfer to be inefficient.
The resultant rotational bimodality of MgH is subject to the
anisotropic interaction of the exit-channel potential
surface.7,9,10,12 In spite of a common insertion mechanism,
the Mg(3 1 P 1 ) and Ca(4 1 P 1 ) reactions with H2 exhibit distinct rotational distributions for the products. It is difficult to
gain insight into the reaction pathway and the product distributions without assistance of PES calculations.
In a 共near兲 C 2 v symmetry, the Mg(3 1 P 1 ) – H2 and
Ca(4 1 P 1 ,3 1 D) – H2 PESs both can be energetically stabilized at short distance due to involvement of partial ion-pair
character, which is caused by the metal electron backdonation. Such stabilization for the Ca(4 1 P 1 ,3 1 D) – H2 surfaces is enhanced as a result of enlargement of the H2 bond
distance. Nevertheless, as with the Mg(3 1 P 1 ) case,1,4,7,9,12,24
the Ca(4 1 P 1 ) plus H2 reaction may not proceed via an electron harpoon mechanism in the entrance channel, since they
both possess similar ionization potentials, 3.30 eV for
Mg(3 1 P 1 ) and 3.18 eV for Ca(4 1 P 1 ). The higher the state
is excited, the more feasible it is that the corresponding reaction follows a harpoon mechanism. For instance, the Mg
4 1 S 0 and 3 1 D 2 states are 1.1 and 1.4 eV above the 3 1 P 1
state, respectively. They become more ready to eject an electron forming an ion-pair complex Mg⫹ H⫺
2 before MgH is
produced.24
2779
V. CONCLUSION
The Ca(4 1 P 1 ) with H2 reaction is expected to favor
insertion mechanism with a reaction barrier encountered
prior to a series of surface crossing. The collision species
track along the 5A ⬘ surface in the entrance channel, which
corresponds to the Ca (4 1 P 1 )⫹H2 asymptotes. As the H2
bond is enlarged, the configurational mixing between the orbital components of the 4p and nearby 3d states with the
same symmetry makes significant the nonadiabatic transition
between the 5A ⬘ and 2A ⬘ surface in the repulsive limbs.
Therefore, the collision complex CaH2 , along the inner limb
of the 2A ⬘ surface, may feasibly cross to the reactive 1A ⬘
surface. The observed energy barrier probably accounts for
the energy requirement to surmount the repulsive hill in the
entrance. Alternative pathways are also discussed and each
one faces some problems.
With the aid of the PESs calculations, comparing the
intermediate structures and lifetimes between CaH2 and
MgH2 allows one to qualitatively realize the distinct product
distributions between the Ca(4 1 P 1 ) and Mg(3 1 P 1 ) reactions. A strong coupling exerted on the CaH and H moieties
of the CaH2 intermediate in the exit channel leads to efficient
energy randomization prior to breaking apart. This consideration may reasonably interpret the experimental findings of
CaH product distributions.
ACKNOWLEDGMENT
This work is supported by National Science Council,
Republic of China, under the Contract 90-2113-M-001-032.
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