High resolution infrared spectra of H2-Ar, HD-Ar, and D2-Ar van der Waals complexes between 160 and 8620 cm-1

Article abstract of DOI:10.1063/1.472158

Spectra of weakly bound hydrogen-argon complexes have been studied at high spectral resolution (0.04-0.10 cm^-1) using a long-path (154 m), low-temperature (77 K) absorption cell and a Fourier transform infrared spectrometer. The observations cover a wide spectral range from the far-infrared D₂-Ar S₀(0) band at 180 cm^-1 to the near-infrared H₂-Ar S₂(1) band at 8600 cm^-1. Compared to earlier studies, the new results have considerably improved resolution and accuracy. They also extend to new regions, namely the first overtone band of H₂ and the pure rotational band of H₂ and D₂, and they include weak transitions involving excitation of the van der Waals stretching motion. These data serve as a basis for determining a greatly improved three-dimensional intermolecular potential energy surface for the hydrogen-argon system in the following paper.

Full text of DOI:10.1063/1.472158

High resolution infrared spectra of H2–Ar, HD–Ar, and D2–Ar van der Waals complexes
between 160 and 8620 cm−1
A. R. W. McKellar
Citation: The Journal of Chemical Physics 105, 2628 (1996); doi: 10.1063/1.472158
View online: http://dx.doi.org/10.1063/1.472158
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/105/7?ver=pdfcov
Published by the AIP Publishing
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High resolution infrared spectra of H –Ar, HD–Ar, and D –Ar
2
2
؊
1
van der Waals complexes between 160 and 8620 cm
A. R. W. McKellar
Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario K1A 0R6,
Canada
͑
Received 17 January 1996; accepted 6 May 1996͒
Spectra of weakly bound hydrogen–argon complexes have been studied at high spectral resolution
Ϫ1
͑
0.04–0.10 cm ͒ using a long-path ͑154 m͒, low-temperature ͑77 K͒ absorption cell and a Fourier
transform infrared spectrometer. The observations cover a wide spectral range from the far-infrared
Ϫ1
Ϫ1
D –Ar S (0) band at 180 cm to the near-infrared H –Ar S (1) band at 8600 cm . Compared to
2
0
2
2
earlier studies, the new results have considerably improved resolution and accuracy. They also
extend to new regions, namely the first overtone band of H and the pure rotational band of H and
2
2
D , and they include weak transitions involving excitation of the van der Waals stretching motion.
2
These data serve as a basis for determining a greatly improved three-dimensional intermolecular
potential energy surface for the hydrogen–argon system in the following paper.
͓
S0021-9606͑96͒00231-0͔
͑8050–8620 cmϪ1͒, and excited van der Waals stretch (n
ϭ1) transitions of H –Ar and D –Ar. This extended cover-
age means that the hydrogen–argon potential energy surface
is more fully probed, especially in terms of its dependence
on the hydrogen stretching coordinate.
I. INTRODUCTION
The detection of rotational structure due to the H –Ar
2
2
2
Ϫ1
complex in the H -stretching region near 4500 cm ͑2.2
2
1
␮m͒ by Kudian et al. in 1966 was one of the very first
spectroscopic observations of a van der Waals molecule.
Since that time, there has been a series2 of refinements of
the original IR experiment, involving improved spectral
resolution, extended wavelength coverage, and the study of
In the present paper, these new hydrogen–argon IR
spectra are presented, discussed, and compared with theory.
In the following paper, the IR data are used, together with
other experimental input and appropriate theoretical con-
straints, to determine a definitive new potential surface. This
new exchange-coulomb ͑XC͒ surface fits the present data
–8
27
other hydrogen isotopes ͑HD, D ͒ and other rare gas atoms
2
͑
Ne, Kr, Xe͒. Radio frequency hyperfine spectra of
9
hydrogen–rare gas complexes have also been reported.
about 7 times better than the best previous empirical surface,
1
The original observation stimulated the first theoretical
14
TT of Le Roy and Hutson.
10
3
study of the H –Ar spectrum, which was made by Cashion
2
The hydrogen molecule ͑H , D , or HD͒ within a
2
2
in 1966. Subsequently, large scale analyses of the IR spectra
hydrogen–argon complex exhibits almost completely free
rotation and vibration, because its rotational and vibrational
level spacings are very much larger than any hindering terms
in the intermolecular potential. The consequences of this
freedom are that the hydrogen vibrational and rotational
11
have been made by Le Roy and Van Kranendonk, Dunker
1
2
13
and Gordon, Le Roy and Carley, and, most recently, by
Le Roy and Hutson.14 These workers determined anisotropic
intermolecular potential surfaces for hydrogen–rare gas sys-
tems by directly fitting the observed IR spectra, sometimes in
combination with other experimental data. In two cases, an
induced dipole moment surface was also derived for
quantum numbers ͑denoted here by v and j ͒ remain good
H
labels in the complex, and the spectra due to the complex
occur as rotational bands, each of which is approximately
centered around a hydrogen vibration–rotation transition.
These hydrogen transitions, and hence hydrogen–argon
1
2,15
H –Ar.
The hydrogen–argon system has become a popu-
2
16
lar benchmark for theory, especially for calculations of ro-
tational and vibrational predissociation effects.1
7–26
This
‘
‘bands,’’ are labeled here as S (0), Q (1), etc., where the
popularity can be ascribed to the fundamental nature of the
0 1
Q or S denotes ⌬j ϭ0 or 2, respectively, the subscript 0, 1,
H –Ar system, to the relatively weak anisotropy of the inter-
H
2
or 2 denotes vϭ0←0, 1←0, or 2←0, respectively, and the
molecular forces, and to the availability of high-quality ex-
perimentally based potential energy surfaces.
number 0 or 1 in parentheses denotes the initial value of j .
H
For a given H state ͑v and j ͒ the energy levels of a
A new and much more complete set of experimental IR
spectra of the hydrogen–argon complex has now been ob-
tained. These data, which were obtained using a cooled ͑77
K͒ long-path absorption cell and a Fourier transform spec-
trometer, exhibit significantly improved resolution and wave
number accuracy compared to the best previous results.7
Equally important is that they extend the coverage of the
2
H
complex may be characterized by an end-over-end rotational
quantum number, l, and a van der Waals stretching quantum
number, n. The total angular momentum of the complex, J,
is the vector sum of jH and l. The rovibrational energy of the
complex is then given, to a first approximation, by the inter-
nal rovibrational energy of its constituent hydrogen minus
the complex binding energy ͑which is a function of n͒ plus
its end-over-end rotational energy, Bcomplexl(lϩ1). Values of
spectra to include far-IR pure rotational transitions of H and
2
Ϫ1
D ͑160–610 cm ͒, vibrational overtone transitions of H2
2
2628
J. Chem. Phys. 105 (7), 15 August 1996
0021-9606/96/105(7)/2628/11/$10.00
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A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2629
2
2
TABLE I. Experimental conditions for the present measurements. In all
a
cases, the absorption path was 154 m and the temperature was 77 K.
H /HD/D2
2
Region
Resolution pressure Ar pressure
Ϫ1
Ϫ1
Transition
͑cm
͒
͑cm
͒
͑Torr͒
͑Torr͒
H –Ar S (0)
350
590
0.06
56
72
22
44
70
20
2
0
H –Ar S (1)
0.10
0.04
0.04
0.10
0.15
0.10
0.05
0.07
0.08
2
0
H –Ar Q (0)/S (0) 4160/4500
2
1
1
H –Ar Q (1)/S (1) 4150/4710
30
30
2
1
1
H –Ar S (0)
8400
208
208
80
49
73
195
195
80
62
77
2
2
H –Ar Q (1)/S (1) 8070/8600
2
2
2
D –Ar S (0)
180
2
0
D –Ar Q (0)/S (0) 2990/3170
2
1
1
D –Ar Q (1)
2990
2
1
HD–Ar Q (0)/S (0) 3630/3890
59
79
1
1
a
Additionally, weak Q (0) nϭ1 features were studied with total pressures
1
of 260 Torr for H –Ar ͑as used for Fig. 2͒ and 223 Torr for D –Ar.
2
2
FIG. 1. Approximate radial potential energy curve for hydrogen–argon,
showing the locations of the ground (nϭ0) and excited (nϭ1) van der
Waals stretching states for the lϭ0 levels of H –Ar and D –Ar. Note the
large zero-point energy, and the wide radial extent of the states, especially
nϭ1.
2
2
The spectra were recorded with a Bomem DA3.02 Fou-
rier transform spectrometer at spectral resolutions varying
Ϫ1
from 0.04 to 0.10 cm . Modulated IR radiation was passed
by transfer optics from the spectrometer to the cell and then
to an IR detector, such that the entire IR radiation path out-
the rotational constant, B
, are about 0.57, 0.39, and
complex
Ϫ1
side of the cell was evacuated. For the mid-IR spectra,
0
.31 cm for H –Ar, HD–Ar, and D –Ar, respectively.
2 2
Ϫ1
2
900–8620 cm , a CaF beamsplitter, quartz–halogen tung-
On closer examination, each l level is split by the anisot-
ropy of the intermolecular potential into 2j ϩ1 sublevels
2
sten filament source, and fused silica cell windows were
used. The liquid nitrogen cooled photovoltaic detector was
H
with different values of J ͑or 2lϩ1 sublevels for lϽjH͒.
Transitions involving the ground intermolecular stretch lev-
els (nϭ0) predominate in the observed spectra of
Ϫ1
Ϫ1
InSb ͑2900–5000 cm ͒ or Ge ͑8050–8620 cm ͒. For the
Ϫ1
far-IR spectra, 160–610 cm , a mylar beamsplitter, ceramic
hydrogen–rare gas complexes. As noted previously,5,10 this
glower source, and CsI cell windows were used. The liquid
Ϫ1
helium cooled detector was a Si bolometer ͑160–190 cm
͒
is because the induced dipole moment depends very strongly
on intermolecular separation, being weaker for larger sepa-
rations, and levels with higher n-values have larger separa-
tions due to the considerable anharmonicity of the potential.
Weak transitions involving nϭ1 levels are reported for the
first time in the present paper.
Figure 1 shows an approximate radial potential energy
curve for hydrogen–argon, based on TT3.14 The actual TT3
potential is, of course, angle dependent and also changes
slightly depending on the hydrogen isotope and the value of
v. Also indicated in Fig. 1 are the positions of the nϭ0 and
Ϫ1
or a Ge:Cu photoconductor ͑340–610 cm ͒. Data acquisi-
tion times were typically 5–15 h per spectrum. Details of the
various spectral resolutions and gas pressures used are sum-
marized in Table I.
The low temperature equilibrium species, para-hydrogen
and ortho-deuterium, were produced in the conventional
manner by liquefying H or D for about 15 min in the pres-
2
2
ence of a chrome–alumina catalyst. Each H –Ar run was
2
performed using either para-H , which is virtually all in the
2
j ϭ0 rotational state at 77 K, or with normal H , composed
H
2
of 25% j ϭ0 and 75% j ϭ1. In the case of low temperature
1
van der Waals stretching states for both H –Ar and D –Ar.
H
H
2
2
D , the normal species is 67% j ϭ0 and 33% j ϭ1; most
These serve to indicate which regions are sampled by tran-
sitions involving these states, and to emphasize the much
wider probing of the potential afforded by nϭ1. Note that
the zero-point energy is more than half the well depth for
H –Ar, and almost half for D –Ar. Figure 1 applies to lϭ0
2
H
H
experiments were performed with ortho-D ͑j ϭ0͒, and only
2
H
one, to examine the Q (1) transition, with normal D ͑see
1
2
Table I͒. For HD, with its inequivalent nuclei, there is no
possibility of separating states of different j , and only the
H
2
2
HD–Ar bands with an initial value of j ϭ0 could be probed
levels; those with larger values of l tend to probe larger
values of the intermolecular separation.
H
at 77 K.
III. RESULTS
II. EXPERIMENTAL DETAILS
A. The H –Ar spectrum
2
The 5.5 m long-path cell used here has been described
7
,28
previously. It is vacuum insulated and was cooled to 77 K
by means of liquid nitrogen contained in a concentric jacket
surrounding the inner sample tube, which has a diameter of
2 cm. The total absorption path was 154 m, obtained with
8 traversals of the cell.
The overall appearance of the H –Ar absorption over a
2
Ϫ1
wide range of 670 cm in the region of the fundamental
band of H (vϭ1←0) is illustrated in Fig. 2. This result was
2
1
2
obtained using a mixture of para-H and Ar at a total pres-
2
sure of 260 Torr, and it shows two H –Ar bands, corre-
2
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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2630
A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2 2
FIG. 2. An overview of the absorption induced by argon ͑120 Torr͒ in
para-hydrogen ͑140 Torr͒ at 77 K in the region of the H fundamental band.
2
Ϫ1
The path was 154 m and the spectral resolution was 0.10 cm . Note the
broad lines due to collision-induced absorption with superimposed sharp
structure due to H –Ar complexes. The inset shows the simple P- and
2
R-branch structure of the Q (0) band of H –Ar.
1
2
FIG. 4. Expanded views of the central portions of the S (0) and S (0)
0
1
bands of the H –Ar complex. Experimental conditions are given in Table I.
2
Ϫ1
sponding to the transitions Q (0) near 4161 cm
and
1
Ϫ1
S1(0)near 4498 cm . Each band, consisting of a number of
sharp lines arising from bound H –Ar complexes, sits on top
2
Ϫ1
of a much broader ͑Ϸ100 cm ͒ continuous absorption fea-
ture which is due to collision-induced absorption29 ͑CIA͒
arising from transient H –Ar collision events. Figure 2 helps
2
to illustrate a close connection between the CIA and complex
spectra in this system.30 These two parts of the spectrum are
aspects of the same absorption process, governed by the
same induced dipole moment and intermolecular potential
surface, but distinguished from each other mainly by the du-
ration of the relevant molecular interaction.
The simplest H –Ar band is Q (0), as shown in the
2
1
inset of Fig. 2. Since the H is in its spherically symmetric
2
jHϭ0 level for both the initial and final states of this transi-
tion, the end-over-end rotational levels of the complex have
lϭJ and only P(l) and R(l) transitions (⌬lϭϯ1) are pos-
sible. Note that transitions higher than R(6) and P(7) are
not present, indicating that only levels with lϽ8 are bound.
The S (0) band, for which j ϭ2←0, is considerably
1
H
more complicated than Q (0), as shown in the central trace
1
of Fig. 3. The angular dependence of the induced dipole
moment of the complex results in strong N(l) and T(l) (⌬l
ϭϯ3) transitions, and there are also splittings and shifts of
the P(l) and R(l) transitions. Also shown in Fig. 3 are the
FIG. 3. The S(0) bands of the H –Ar complex accompanying the pure
rotational band ͑top trace͒, the fundamental band ͑middle trace͒, and the first
2
Ϫ1
Ϫ1
overtone band ͑lower trace͒ of H . Experimental conditions are given in
2
bands S (0) near 350 cm and S (0) near 8410 cm ;
0
2
Table I. The structure of the three bands is very similar ͑apart from effects
due to the different pressures used͒, but the slight differences between them
directly probe the dependence of the intermolecular potential on the H2
stretching state, v.
these have very similar structures to S (0), differing only
1
because of effects due to the dependence of the H –Ar po-
2
tential on the H vibrational state ͑or, equivalently, on the H2
2
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2631
2
2
FIG. 6. The S(1) bands of the H –Ar complex accompanying the pure
rotational band ͑top trace͒, the fundamental band ͑middle trace͒, and the first
2
FIG. 5. The Q(1) bands of H –Ar accompanying the fundamental band
2
͑
center trace͒ and first overtone band ͑lower trace͒ of H . Also shown in the
2
overtone band ͑lower trace͒ of H . Experimental conditions are given in
2
short upper trace is the Q (0) band ͑measured using pure para-H ͒, the lines
1
2
Table I.
of which are also present in the Q (1) spectrum ͑measured using normal
1
H2͒.
weaker than S (0), requiring higher sample pressures and
1
bond length͒. Figure 4 shows the central portions of S (0)
hence showing larger pressure broadening effects.
0
and S (0) in detail.
The strong lines near the center of S (0) and S (0)
which go off the scale in Fig. 3 are not part of the spectrum
Using normal H , the Q(1) ͑j ϭ1←1͒ and S(1)
1
2
H
͑j ϭ3←1͒ bands of H –Ar were observed, as shown in Fig.
1
2
H
2
5 ͓Q (1) and Q (1)͔ and Fig. 6 ͓S (1), S (1), and S (1)͔.
1 2 0 1 2
of the H –Ar complex, but rather are the quadrupole transi-
At the top of Fig. 5 is a high-resolution trace of Q (0), to
2
1
tions of the H monomer. There is also a S (0) quadrupole
illustrate that some of the weaker lines in the Q (1) spec-
2
0
1
transition located at the position indicated by the arrow in the
top trace of Fig. 3, but it is too weak to be observed due to
the frequency cubed dependence of the quadrupole absorp-
tion strength. Note that in Fig. 3, and elsewhere in this paper,
trum are due to Q (0) lines since there is 25% para-H in
1
2
normal H . Interestingly, it was not possible to detect any
2
trace of a Q (0) band for H –Ar. This failure is consistent
2
2
31
with the previously observed absence of Q (0) in CIA
2
arrows connected to the band labels ͓like S (0)͔ indicate the
positions of the unperturbed hydrogen transition frequencies.
This position corresponds to a quadrupole line except for the
spectra of hydrogen, ascribed to the weakness of the ‘‘over-
lap induced’’ component of the transition dipole moment for
the vϭ2←0 overtone band. The S(1) bands ͑Fig. 6͒ are the
most complicated of those studied here. Not only P(l) and
R(l), but also N(l) and T(l) lines, are split into a number of
components by anisotropic intermolecular interactions. This
1
far IR, where they are too weak, and for Q (0), where a
1
quadrupole transition is forbidden. Any shift between the
arrow and the apparent center of the complex band is a re-
flection of the small vibrational ͑and, to a lesser extent, ro-
tational͒ frequency shift induced in the hydrogen by the pres-
ence of the nearby argon.
larger number of individual transitions means that the S (1)
0
and, especially, S (1) bands are only partially resolved in
2
Fig. 6.
S1(0) is the best resolved of the three S(0) bands in Fig.
The measured positions of the observed H –Ar lines are
2
3
. In comparison, the S (0) band is inherently stronger, but
listed in Tables II–V, together with estimates of their uncer-
tainties and comparisons with the new calculations27 based
on the XC͑fit͒ potential surface ͑see below͒. In the case of
0
this advantage is outweighed by reduced experimental sensi-
tivity in the far-IR ͑350 cm ͒ region compared to the
mid-IR ͑4500 cm ͒. And the S (0) band is inherently much
Ϫ1
Ϫ1
Q (0), some weak lines due to transitions with nϭ1←0
2
1
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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2632
A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2
2
a
TABLE II. Observed transitions in the Q (0) band of H –Ar.
1
2
Observedb
Obs–calc
XC ͑cm ͒
Obs–calc
Ϫ1
c
Ϫ1
TT3 ͑cmϪ1͒
d
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
5
4
3
2
1
0
1
2
3
4
5
6
1
0
5
4
3
2
1
0
1
2
3
4
5
6
1
0
6
5
4
3
2
1
0
1
2
3
4
5
2
1
6
5
4
3
2
1
0
1
2
3
4
5
2
1
4153.926͑4͒
4154.762͑4͒
4155.734͑4͒
4156.778͑4͒
4157.869͑4͒
4158.985͑7͒
4161.220͑7͒
4162.317͑4͒
4163.384͑4͒
4164.407͑4͒
4165.362͑4͒
4166.211͑4͒
4179.550͑20͒
0.003
0.001
Ϫ0.005
Ϫ0.010
Ϫ0.014
Ϫ0.019
Ϫ0.021
Ϫ0.019
Ϫ0.019
Ϫ0.019
Ϫ0.018
Ϫ0.015
Ϫ0.013
Ϫ0.012
Ϫ0.174
Ϫ0.167
Ϫ0.001
Ϫ0.004
Ϫ0.004
Ϫ0.001
Ϫ0.002
Ϫ0.002
Ϫ0.002
0.000
0.001
0.003
Ϫ0.043
Ϫ0.048
e
4181.400͑20͒e
a
In all cases, vϭ1←0 and j ϭ0←0. Unless otherwise indicated, nϭ0←0.
H
b
c
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
d
Calculation ͑Ref. 33͒ based on the TT potential surface of Le Roy and Hutson ͑Ref. 14͒.
3
e
For these two weak transitions, nϭ1←0.
were observed, two of which are reported in Table II. Such
ones. Measured positions for uniquely assigned lines of
transitions were relatively more prominent in the D –Ar
Q (0) and Q (1) are given in Tables VI and VII. Overviews
2
1
1
spectrum, as discussed below. Most of the transitions in-
cluded in Tables II–V are ‘‘uniquely assigned’’ ones which
are reasonably sharp and unblended, and therefore suitable
for direct comparison with theoretical line positions.
of the S (0) and S (0) bands are shown in Fig. 8, and more
0 1
detailed views of their crowded central portions are shown in
Fig. 9. The line positions for these bands are given in Table
VIII. The S(1) bands and the D overtone ͑␯ϭ2←0͒ region
2
were not studied.
B. The D –Ar spectrum
By using a higher sample-pressure, it was possible to
observe some weak transitions involving the excited inter-
2
Due to its greater reduced mass, the D –Ar complex has
more bound states than H –Ar ͑up to about lϭ11 as com-
pared to lϭ7͒, and it therefore exhibits more extensive rota-
2
molecular stretching state, nϭ1, in the regions of Q (0) and
1
2
S1(0). These are illustrated in Fig. 10. The top and center
traces of Fig. 10 show structure just below and above the
tional structure. Figure 7 illustrates the Q region near 3000
1
Ϫ1
main region of the Q (0) band which can be assigned to
cm for mixtures of argon with ortho-D ͑upper trace͒ and
1
2
normal D ͑lower trace͒. Since the ortho-D concentration
combination bands with ⌬nϭϪ1 and ϩ1. Measured posi-
tions for the more well-defined transitions in these subbands
are given in Table VI. In addition to these lines, there is also
2
2
was actually somewhat less than 100%, some Q (1) lines
1
are visible in the upper trace along with the expected Q (0)
1
a
TABLE III. Observed transitions in the Q (1) and Q (1) bands of H – Ar.
1
2
2
Q (1)
Q (1)
2
1
Observedb
Obs–calc
XC ͑cm
Observedb
Obs–Calc
XC ͑cm ͒
Ϫ1
c
Ϫ1
Ϫ1
c
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
͒
͑cm
͒
4
3
2
1
0
3
4
5
6
7
8
5
4
3
2
1
2
3
4
5
5
6
7
6
5
4
3
0
1
2
3
4
5
6
5
4
3
2
1
2
3
4
5
4
4135.969͑10͒
4138.319͑4͒
4141.175͑4͒
4144.270͑4͒
4147.500͑7͒
4160.778͑7͒
4163.998͑4͒
4167.076͑4͒
4169.932͑4͒
4172.354͑8͒
0.019
0.000
0.000
0.001
0.000
Ϫ0.004
0.000
0.002
0.004
Ϫ0.007
8054.910͑40͒
8057.330͑20͒
8060.195͑20͒
8063.295͑20͒
Ϫ0.015
0.015
0.006
0.000
8082.998͑20͒
8086.065͑20͒
8088.917͑20͒
8091.395͑20͒
8093.38͑20͒
0.008
0.019
0.020
0.012
0.030
a
In all cases, j ϭ1←1 and nϭ0←0. For Q (1), vϭ1←0; and for Q (1), vϭ2←0.
H
1
2
b
c
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2633
2
2
a
TABLE IV. Observed transitions in the S (0), S (0), and S (0) bands of H –Ar.
0
1
2
2
S0(0)
S1(0)
S2(0)
b
Observedb
Observedb
Observed
Obs–calc
XC ͑cm
Obs–calc
XC ͑cm
Obs–calc
XC ͑cm ͒
Ϫ1
c
Ϫ1
Ϫ1
c
Ϫ1
Ϫ1
c
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
͒
͑cm
͒
͒
͑cm
͒
4
6
5
4
3
2
2
1
1
2
2
3
3
3
4
4
5
6
1
2
3
4
5
6
7
6
5
4
3
2
1
2
2
3
2
3
4
3
4
5
5
0
1
2
3
4
5
7
6
5
4
3
2
1
2
2
3
2
3
4
3
4
5
5
0
1
2
3
4
5
335.812͑8͒
338.135͑3͒
340.993͑3͒
344.118͑3͒
347.454͑5͒
352.689͑8͒
356.033͑8͒
0.011
0.001
0.003
0.000
0.001
4478.108͑10͒
4480.476͑3͒
4483.349͑3͒
4486.489͑3͒
4489.832͑5͒
4495.126͑7͒
4498.376͑5͒
4499.130͑7͒
4499.857͑5͒
4500.258͑7͒
4500.463͑6͒
4500.999͑5͒
4501.265͑7͒
4501.507͑5͒
4502.025͑7͒
4502.907͑5͒
4503.312͑5͒
4502.476͑7͒
4505.791͑3͒
4508.916͑3͒
4511.810͑3͒
4514.289͑4͒
Ϫ0.020
Ϫ0.002
Ϫ0.002
Ϫ0.004
Ϫ0.003
Ϫ0.011
Ϫ0.003
Ϫ0.001
Ϫ0.003
0.001
Ϫ0.006
Ϫ0.007
Ϫ0.003
Ϫ0.005
0.002
8385.560͑30͒
8387.960͑20͒
8390.859͑20͒
8394.008͑20͒
Ϫ0.028
Ϫ0.003
0.002
3
2
1
0
1
2
3
3
4
3
4
5
4
5
6
6
3
4
5
6
7
8
Ϫ0.005
Ϫ0.007
0.000
357.483͑8͒
358.635͑8͒
Ϫ0.004
Ϫ0.002
359.661͑8͒
360.521͑8͒
360.877͑10͒
0.004
0.000
0.003
0.000
0.006
Ϫ0.004
Ϫ0.003
Ϫ0.003
Ϫ0.001
Ϫ0.005
363.484͑3͒
366.618͑3͒
369.501͑3͒
371.884͑6͒
Ϫ0.002
Ϫ0.004
Ϫ0.004
Ϫ0.024
8413.240͑20͒
8416.350͑20͒
8419.235͑20͒
8421.760͑20͒
8423.80͑10͒
Ϫ0.005
0.001
0.003
0.000
0.049
a
In all cases, j ϭ2←0 and nϭ0←0. For S (0), vϭ0←0; for S (0), vϭ1←0; and for S (0), vϭ2←0.
H
0
1
2
b
c
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
some structure, indicated on Fig. 10, due to CH impurity in
Fig. 10 and listed in Table VIII; although some ⌬nϭϪ1
structure was also noted at lower wave numbers, below
S1(0), it was too weak to be reliably measured.
4
the gas sample. Another weak structure is due to D –Ar
2
Q (1) transitions, though the ortho-D purity is better here
1
2
than in Fig. 7. Still other structure may be due to the Q (2)
band, which can arise from the equilibrium population of D2
1
C. The HD–Ar spectrum
͑
15%͒ in the j ϭ2 state at 77 K. Some lines due to S (0)
The Q (0) and S (0) bands of the HD–Ar complex are
H
1
1
1
transitions with ⌬nϭϩ1 are shown in the lower trace of
shown in Fig. 11. The Q (0) band appears rather similar to
1
a
TABLE V. Observed transitions in the S (1), S (1), and S (1) bands of H –Ar.
0
1
2
2
S0(1)
S1(1)
Observedb
S2(1)
Observedb
Obs–calc
Obs–calc
Observedb
Ϫ1
c
Ϫ1
Ϫ1
c
Ϫ1
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
XC ͑cm
͒
͑cm
͒
XC ͑cm
͒
͑cm ͒
4
3
3
2
2
1
0
4
5
5
6
6
7
7
7
6
6
5
5
4
3
1
2
2
3
3
4
4
568.633͑9͒
571.015͑6͒
4693.365͑10͒
4695.635͑10͒
4695.764͑8͒
4698.529͑10͒
4698.666͑8͒
4701.829͑8͒
4705.212͑10͒
4720.321͑8͒
4723.524͑8͒
4724.147͑8͒
4726.456͑8͒
4727.047͑8͒
4728.944͑12͒
4729.542͑8͒
8583.640͑30͒
8586.060͑20͒
573.899͑6͒
577.050͑6͒
580.432͑8͒
595.593͑10͒
598.793͑8͒
599.457͑8͒
601.706͑8͒
602.347͑8͒
604.103͑12͒
604.767͑8͒
8588.970͑20͒
8592.170͑20͒
8595.570͑50͒
2
3
2
4
3
5
4
1
2
1
3
2
4
3
0.006
0.005
0.001
0.000
0.000
0.001
0.003
Ϫ0.002
0.001
0.000
Ϫ0.004
Ϫ0.006
Ϫ0.011
Ϫ0.005
a
In all cases, j ϭ3←1 and nϭ0←0. For S (1), vϭ0←0; for S (1), vϭ1←0; and for S (1), vϭ2←0.
H
0
1
2
b
c
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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2634
A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2 2
D –Ar would be at a similar pressure. The excess linewidth
2
for S (0) is due to relatively rapid predissociation of the
1
upper state ͑vϭ1, j ϭ2͒ levels. Predissociation effects are
H
more prominent here because of the lower symmetry of HD,
which results in a much greater effective anisotropy of the
intermolecular potential for HD–Ar. The vϭ1, j ϭ2 upper
H
state of the HD–Ar S (0) band is able to predissociate to
1
vϭ1, j ϭ1, unlike in H –Ar and D –Ar where the allowed
H
2
2
predissociation channels are strictly limited by the selection
rule ⌬j ϭ2. The HD–Ar Q (0) band remains relatively
H
1
sharp because it can only predissociate by ⌬vϭ1 processes,
which are much slower than the ⌬vϭ0 processes open for
S (0). The measured line positions for HD–Ar Q (0) are
1
1
listed in Table IX, which includes some weak ⌬nϭ1 transi-
tions not shown in Fig. 11. New measurements are not given
FIG. 7. The Q (0) and Q (1) bands of the D –Ar complex, measured
1
1
2
here for S (0) since the width of the lines in this band means
1
using ortho-D ͑upper trace͒ and normal D ͑lower trace͒. There are residual
2
2
7
that the previously reported positions cannot be significantly
Q (1) lines in the upper trace because the ortho conversion of the D2
1
sample used was not complete. Experimental conditions are given in Table
I.
improved upon.
A number of detailed calculations19,22,24,26 of HD–Ar
S (0) predissociation linewidths were made for comparison
1
7
with the earlier observation of this band. In view of this
those of H –Ar and D –Ar, showing sharp lines and an in-
2
2
termediate number of bound levels ͑l values up to about 9͒,
as expected. However, as noted previously,6 the lines of the
S (0) band are much broader than those of H –Ar and
interest, an effort was made here to obtain more accurate
experimental widths from the present spectrum. A nonlinear
least-squares fit was made in the regions of the unblended N-
,7
1
2
a
TABLE VI. Observed transitions in the Q (0) band of D –Ar.
1
2
Observedb
Obs–calc
XC ͑cm ͒
Obs–calc
Ϫ1
c
Ϫ1
TT3 ͑cmϪ1͒
d
lЈ
JЈ
←
lЉ
JЉ
nЈ
←
nЉ
͑cm
͒
3
3
4
5
6
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
10
5
4
3
2
1
5
2
2
3
4
5
10
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
6
5
4
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2971.347͑30͒
2972.723͑15͒
2974.351͑15͒
2976.220͑15͒
2987.050͑7͒
2987.483͑4͒
2987.975͑4͒
2988.513͑4͒
2989.078͑7͒
2989.674͑4͒
2990.286͑4͒
2990.906͑4͒
2991.527͑7͒
2994.025͑7͒
2994.636͑4͒
2995.239͑4͒
2995.818͑4͒
2996.389͑4͒
2996.934͑4͒
2997.451͑4͒
2997.927͑4͒
2998.353͑7͒
3009.696͑20͒
3011.683͑10͒
3013.326͑10͒
3014.670͑10͒
3015.755͑10͒
3016.473͑20͒
Ϫ0.021
0.010
0.003
0.158
Ϫ0.001
0.009
0.004
0.001
Ϫ0.006
Ϫ0.004
0.000
0.485
0.530
0.547
0.434
0.025
0.036
0.031
0.028
4
5
6
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
0
5
4
3
2
1
5
3
4
5
10
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
6
5
4
3
2
4
0.021
0.024
0.024
0.019
0.017
0.017
0.020
0.014
0.018
0.018
0.018
0.014
0.014
Ϫ0.126
Ϫ0.074
Ϫ0.033
Ϫ0.020
Ϫ0.022
Ϫ0.089
0.002
Ϫ0.002
Ϫ0.001
0.000
0.004
Ϫ0.002
0.003
0.004
0.005
0.004
0.008
Ϫ0.016
Ϫ0.011
0.012
0.015
0.009
1
0.025
a
In all cases, vϭ1←0 and j ϭ0←0.
H
b
c
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
Calculation ͑Ref. 33͒ based on the TT potential surface of Le Roy and Hutson ͑Ref. 14͒.
d
3
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2635
2
2
a
TABLE VII. Observed transitions in the Q (1) band of D –Ar.
1
2
b
Observed
Obs–calc
XC ͑cm ͒
Ϫ1
c
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
8
9
8
7
6
5
4
3
5
6
7
8
9
10
11
10
9
8
7
6
5
3
4
5
6
7
8
10
9
8
7
6
5
4
4
5
6
7
8
9
2973.596͑4͒
2974.784͑4͒
2976.221͑4͒
2977.795͑4͒
2979.443͑4͒
2981.159͑4͒
2982.903͑7͒
3000.062͑4͒
3001.746͑4͒
3003.380͑4͒
3004.926͑4͒
3006.356͑4͒
3007.573͑4͒
0.005
Ϫ0.003
Ϫ0.001
0.004
Ϫ0.003
0.002
7
6
5
4
3
2
6
7
8
9
0
1
0.007
Ϫ0.004
Ϫ0.005
0.000
0.000
0.007
1
1
0.008
a
In all cases, vϭ1←0, j ϭ1←1, and nϭ0←0.
H
b
Estimated line position uncertainties in units of the last quoted digit are
given in parentheses.
c
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref.
7͒.
2
FIG. 9. Expanded views of the central portions of the S (0) and S (0)
0
1
bands of the D –Ar complex. Experimental conditions are given in Table I.
2
and T-branch lines, using a sum of Lorentzian lines having
adjustable widths, positions, and strengths. The measured
widths resulting from the fit are compared with theory in
Table X. The agreement is generally satisfactory, especially
considering that these calculations were based on the now-
tions, which is quite evident in the spectrum ͑Fig. 11͒, is well
reproduced by all three calculations.
Figure 11 illustrates another distinctive feature of HD:
the presence of a HD electric dipole transition, R (2), in
1
13
obsolete BC ͑6,8͒ potential. In particular, the observed de-
3
crease in width with increasing l for the T(2)–T(6) transi-
FIG. 8. The S(0) bands of the D –Ar complex accompanying the pure
FIG. 10. Spectra showing weak transitions of the D –Ar complex involving
2
2
rotational band ͑top trace͒ and the fundamental band ͑lower trace͒ of D2 .
Arrows mark the positions of the rotation–vibration transitions of free D2 ,
and, for S (0), the D quadrupole line is visible at this position. Experimen-
the excited van der Waals stretching mode: ⌬nϭϪ1 lines of Q (0) ͑upper
1
trace͒, ⌬nϭϩ1 lines of Q (0) ͑middle trace͒, and ⌬nϭϩ1 lines of S (0)
1
1
͑lower trace͒. Some of the features in the Q (0) region are due to CH
1
2
1
4
tal conditions are given in Table I.
impurity in the gas sample, as indicated.
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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2636
A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2 2
a
TABLE VIII. Observed transitions in the S (0) and S (0) bands of D –Ar.
0
1
2
S0(0)
S1(0)
Observedb
Obs–calc
XC ͑cm
Observedb
Obs–Calc
XC ͑cm ͒
Ϫ1
c
Ϫ1
Ϫ1
c
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
͑cm
͒
͒
͑cm
͒
8
7
6
5
4
3
2
1
0
4
5
6
7
8
9
0
1
1
0
3
4
5
10
9
8
7
6
5
4
3
2
2
3
4
5
6
7
8
9
3
2
1
2
3
11
10
9
8
7
6
5
4
3
1
2
3
4
5
6
7
8
4
3
0
1
2
11
10
9
8
7
6
5
4
3
1
2
3
4
5
6
7
8
4
3
0
1
2
161.719͑20͒
162.895͑15͒
164.326͑15͒
165.900͑15͒
167.589͑15͒
169.323͑15͒
171.140͑15͒
172.995͑25͒
0.003
0.004
0.002
Ϫ0.003
0.009
Ϫ0.008
Ϫ0.001
Ϫ0.005
3148.060͑6͒
3149.252͑3͒
3150.702͑3͒
3152.297͑3͒
3153.990͑3͒
3155.752͑3͒
3157.575͑3͒
3159.442͑8͒
3161.320͑10͒
3170.274͑10͒
3172.150͑8͒
3173.950͑3͒
3175.690͑3͒
3177.361͑3͒
3178.939͑3͒
3180.395͑3͒
3181.655͑3͒
3183.997͑20͒d
3186.149͑20͒d
Ϫ0.003
Ϫ0.001
0.000
0.001
0.002
0.000
0.005
0.007
Ϫ0.031
Ϫ0.006
0.003
0.001
0.001
0.003
0.002
0.001
0.004
187.560͑15͒
189.331͑15͒
191.004͑15͒
192.598͑15͒
194.055͑15͒
195.257͑20͒
Ϫ0.012
0.003
Ϫ0.007
Ϫ0.003
Ϫ0.002
Ϫ0.025
1
1
Ϫ0.001
0.025
0.020
Ϫ0.039
Ϫ0.056
d
3191.988͑20͒
3192.820͑20͒d
3193.287͑20͒d
a
b
c
In all cases, j ϭ2←0. For S (0), vϭ0←0; and for S (0), vϭ1←0. Unless otherwise indicated, nϭ0←0.
H
0
1
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
Calculation based on the XC͑fit͒ potential surface of Bissonette et al. ͑Ref. 27͒.
For these weak transitions, nϭ1←0.
d
addition to the Q (1) and S (0) quadrupole lines. Some
due to the unresolved P(l) and R(l) branches of the HD–Ar
1
1
weaker sharp lines in the region of the S (0) spectrum are
Q (1) band, though this is not obvious from the portion
1
1
due to CH impurity. The somewhat wavy background un-
shown here ͑about 35% of the HD molecules are in the j ϭ1
4
H
derlying the Q (0) band in the top trace of Fig. 11 is partly
state at 77 K͒.
1
IV. CONCLUSIONS
All of the bands observed here may be subject to predis-
sociation, not just S (0) of HD–Ar, since the upper states
1
have much greater energy than is required to break the com-
7
13,17,18,20,23,32
plex apart. However, calculations
indicate that
the relevant predissociation line broadening is generally ex-
Ϫ1
pected to be of the order of 0.05 cm or less ͑much less in
some cases͒. Thus predissociation broadening is masked in
the current results by the combined effects of pressure broad-
ening and instrumental resolution.
The calculations27 represented here, based on the new
exchange-Coulomb ͑XC͑fit͔͒ potential surface, do an excel-
lent job of reproducing the present experimental results in
Tables II–VIII. In many regions, the smoothness of the
agreement between experiment and theory suggests that the
actual experimental uncertainties might be somewhat smaller
than is given in Tables II–VIII. This is partly a reflection of
the fact that the relative wave number accuracy ͑precision͒ of
the Fourier transform IR measurements is better than its ab-
solute accuracy. There are also a few data for which the
difference between observed and calculated values is larger
FIG. 11. The Q (0) and S (0) bands of the HD–Ar complex. Note the
1
1
presence of the R (2) electric dipole transition of the HD monomer, in
1
addition to the Q (1) and S (0) quadrupole transitions also present in H
1
1
2
and D . The stick spectrum above the S (0) trace indicates some weak lines
2
1
due to CH impurity in the gas sample. Experimental conditions are given in
4
Table I.
J. Chem. Phys., Vol. 105, No. 7, 15 August 1996
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A. R. W. McKellar: Infrared spectra of H –Ar, HD–Ar, and D –Ar
2637
2
2
TABLE IX. Observed transitions in the Q (0) band of HD–Ar.a
1
Observedb
Ϫ1
lЈ
JЈ
←
lЉ
JЉ
nЈ
←
nЉ
͑cm ͒
3
4
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
3
2
1
3
3
4
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
3
2
1
3
2
3
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
4
3
2
2
2
3
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
4
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3611.414͑20͒
3613.466͑20͒
3624.997͑8͒
3625.375͑5͒
3625.958͑5͒
3626.622͑5͒
3627.338͑5͒
3628.090͑5͒
3628.867͑5͒
3629.651͑6͒
3630.458͑8͒
3632.041͑8͒
3632.817͑6͒
3633.589͑5͒
3634.334͑5͒
3635.050͑5͒
3635.740͑5͒
3636.375͑5͒
3636.947͑5͒
3637.380͑8͒
3649.712͑15͒
3651.694͑15͒
3653.222͑15͒
3655.222͑20͒
a
In all cases, vϭ1←0 and j ϭ0←0.
H
b
Estimated line position uncertainties in units of the last quoted digit are given in parentheses.
than the quoted uncertainty. These are mostly broad, weak,
or overlapped lines whose measurement was more difficult.
The present data may also be compared with
stretching states, nϭ1, of H –Ar and D –Ar. Clearly, the
2 2
nϭ1 level positions contain important information on the
shape of the potential, especially for larger intermolecular
separations ͑see Fig. 1͒. This point is discussed further in the
3
3
calculations based on the TT potential of Le Roy and
3
1
4
27
Hutson. As an example, we show this comparison here for
following paper.
the H –Ar and D –Ar Q (0) bands in Tables II and VI. In
The results of the present and following27 research rees-
tablish hydrogen–argon as having the best known intermo-
lecular potential surface among weakly bound triatomic sys-
tems. In particular, extensive information on the hydrogen
stretching dependence of the potential comes from newly
2
2
1
some regions, the TT surface gives a good fit to the experi-
3
mental values, but in other regions there are fairly large sys-
tematic deviations. Overall, the dimensionless rms deviation
between the present IR data and theory is 5.6 for TT , as
3
compared to 0.7 for XC͑fit͒. It is interesting that some of the
observed bands involving H in its vϭ0 and 2 vibrational
2
largest discrepancies with the TT -based calculations occur
states, as well as D in vϭ0. And new information on the
3
2
for the transitions involving the excited van der Waals
shape of the potential comes from the observation of weak
transitions involving the excited van der Waals stretching
state, nϭ1.
TABLE X. Widths of transitions in the S (0) band of HD–Ar ͑in cmϪ1͒.
1
Calculated width
Observed widtha
ACKNOWLEDGMENTS
Transition
lЈ,JЈ
͑this work͒
Ref. 19
Ref. 22
Ref. 24
I am grateful to R. J. Le Roy and C. Bissonnette for
many helpful discussions over the course of this work, and
for providing the calculated results for comparison with ex-
periment. I also wish to thank my NRC colleagues J. W. C.
Johns, J. Sebesta, W. S. Neil, and M. N o¨ el for their valuable
N(9)
N(8)
N(7)
N(6)
N(5)
T(2)
T(3)
T(4)
T(5)
T(6)
T(7)
6,8
5,7
4,6
3,5
2,4
5,3
6,4
7,5
8,6
9,7
0.59͑7͒
0.73͑7͒
0.74͑7͒
0.78͑8͒
0.87͑10͒
0.84͑10͒
0.68͑6͒
0.56͑4͒
0.47͑3͒
0.38͑3͒
1.33͑19͒
0.663
0.723
0.769
0.795
0.801
0.758
0.643
0.535
0.425
0.329
0.726
0.74
0.73
0.70
0.66
0.61
0.79
0.69
0.50
0.42
0.34
0.76
0.78
0.70
0.71
0.60
0.54
0.40
0.33
0.76
assistance in obtaining these results.
1
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