On the Stability of Noble-Gas Molecules
Tsung-Hui Li, Tai-Yen Yeh, Ya-Lin Liu, Jen-Jie Lin, and Wei-Ping Hu*
Department of Chemistry and Biochemistry, National Chung Cheng University
Chia-Yi, Taiwan 621
RECEIVED DATE (automatically inserted by publisher); E-mail: chewph@ccu.edu.tw
The interest in studying the noble-gas molecules seem to have
been revived after the discovery that the noble gas can act as
ligands to transition metals and the discovery of the first neutral
argon-containing molecules.1-5 Most of the noble-gas molecules
studied to date are metastable species, and were observed only at
cryogenic conditions in noble-gas matrixes.6 Theoretical
calculation plays a very important role in studying simple noblegas molecules because the fingerprint IR peaks can be readily
calculated and compared with experimental data. Furthermore, the
stability of the observed noble-gas molecules can be justified by
high-level electronic structure calculation. More importantly, new
stable noble-gas molecules can be predicted theoretically, and
thus the computational work can guide future synthesis effort.
Recently, a few new noble-gas molecules or ions have been
predicted to be metastable, and some of them have been
confirmed experimentally. 7-16 In this communication we wish to
address the issues regarding (1) the appropriate theoretical
methods and (2) the energetic criteria for predicting the stability
of noble-gas molecules. For the first issue, we tested the MP2 and
CCSD(T) theory with 6-311++G(2d,2p) and aug-cc-pVnZ (n =
D, T, Q) basis sets on the reaction energies and barrier heights of
the two dissociation channels (a) XNgY  X + Ng + Y, and (b)
XNgY  Ng + XY where X and Y are atoms or functional
groups, and Ng is the noble gas atom Ar or Kr. We wish to
demonstrate that while the MP2 method is quite successful for
studying channel (b), it systematically overestimates the bond
energies of XNgF molecules and is thus unreliable for studying
channel (a). For the second issue, we obtained the theoretical halflives of HArF and FArCCH as a function of temperature and
energy barriers by calculating the unimolecular thermal rate
constants of the two dissociation channels. The HArF and
FArCCH were chosen to model systems in which the tunneling
effects are important and not important, respectively. Since
channel (b) is highly exoergic, the XNgY molecules can only be
metastable at best. From the experimental point of view the
stability of these XNgY molecules in the noble-gas matrixes is not
only determined by the unimolecular dissociation rates, but also
on the cage effects and the presence of other reactive species in
the matrixes.3,4,17 It has been speculated that some of the noblegas molecules can also exist in the gas-phase6,17 where many
more interesting chemical studies can be performed. Here we wish
to quantitatively define the “meta-stability” of the XNgY
molecules in the gas phase in terms of the energy barriers and
temperature.
Table 1 lists the calculated energies of reaction and barrier
heights for the two dissociation channels. As shown in the table,
the calculated energies are very different from the MP2 and
CCSD(T) theory for the first channel. The MP2 theory predicts
significantly higher XNg and NgY bond energies than the
CCSD(T) theory, as shown in the calculated energy of reaction of
the first channel; and the differences are much more significant in
Table 1. Calculated Energiesa of Reactions and Barrier Heights
(kcal/mol)
XNgY X + Ng +Y
Barrier
Erxn
XNgY  Ng + XY
Barrier
Erxn
HArF
6311dpb
13.7 (34.0)
2.1 (1.1)
24.9 (23.7)
aug-cc-pVDZ 13.4 (22.8)
2.1 (0.7)
23.1 (21.8)
aug-cc-pVTZ 18.1 (38.5)
5.4 (9.7)
23.7 (23.0)
aug-cc-pVQZ 19.5 (33.0)
7.4 (12.5)
24.4 (23.9)
OBArF
6311dp
7.7 (35.5)
3.4 (1.1)
20.0 (18.9)
aug-cc-pVDZ
6.2 (12.3)
6.8 (0.8)
18.2 (17.0)
aug-cc-pVTZ 14.7 (39.5)
0.8 (9.8)
18.3 (17.5)
aug-cc-pVQZ 16.2 (40.9)
3.0 (12.8)
18.7 (18.1)
FArCCH
6311dp
7.5 (25.8)
3.5 (15.7)
37.5 (36.8)
aug-cc-pVDZ
9.5 (23.1)
4.8 (15.2)
35.3 (33.8)
aug-cc-pVTZ 14.4 (30.0)
5.0 (24.4)
33.8 (33.7)
HArC4H
6311dp
13.1 (40.9)
4.3 (10.1) 27.9 (26.2)
aug-cc-pVDZ
3.7 (31.8)
1.6 (11.5) 25.1 (23.2)
aug-cc-pVTZ
5.4 (38.9)
0.4 (15.9) 26.2 (25.2)
HKrCCH
6311dp
8.8 (27.5)
5.1 (11.7)
35.9 (38.8)
aug-cc-pVDZ 11.2 (28.7)
3.6 (12.8)
38.6 (37.4)
aug-cc-pVTZ 13.6 (32.5)
9.6 (22.3)
39.3 (41.7)
aThe molecular structures used are listed in the Supporting
CCSD(T) and MP2 (in parentheses) energies.
bAbbreviation for 6-311++G(2d,2p) basis set.
138.8 (139.9)
136.5 (137.8)
133.9 (134.0)
133.5 (133.0)
152.5 (163.3)
156.2 (157.0)
158.8 (158.1)
158.6 (157.1)
127.9 (127.6)
127.2 (127.3)
126.9 (124.8)
148.3 (151.4)
148.1 (151.5)
147.2 (148.7)
132.8 (135.2)
130.2 (133.2)
129.1 (127.5)
Information,
larger systems. For example, at the CCSD(T)/aug-cc-pVTZ level
the differences are 5 and 10 kcal/mol for HArF and OBArF,
respectively, and are 19, 16, and 13 kcal/mol for FArCCH,
HArC4H, and HKrCCH, respectively. Since the energy of reaction
of the first channel is often used to judge the stability of the
XNgY molecules, the results obtained by the MP2 theory should
be taken with caution. That is, the MP2 theory seems to
overestimate the bond energies in this type of molecules. Of
course, the kinetic stability is determined by the energy barrier
instead of the energy of reaction which is only the lower limit for
the barrier height of an endoergic reaction. The barrier heights for
the first channel are more difficult to determine accurately due to
the open-shell characters of the reactions. Nonetheless, the
CCSD(T)/aug-cc-pVTZ calculation shows that the barrier heights
are 413 kcal/mol higher than the energies of reactions. The MP2
values are significantly higher due to severe spin-contamination
and are thus unreliable. Table 1 also shows that the size of the
basis sets has important effects on the energies of the first
channel, especially for systems containing fluorine. For example,
in FArCCH system, the energy of reaction and barrier height are
raised by 10 and 5 kcal/mol, respectively, from CCSD(T)/aug-ccpVDZ to CCSD(T)/aug-cc-pVTZ levels. From the CCSD(T)/aug-
30
300 K
250 K
200 K
20
100 K
100 K
5
-10
(5)
(6)
(7)
(8)
(9)
(17)
-6
-4
-2
0
2
4
6
8
10
12
14
16
log (t1/2)
Figure 1. The calculated half-lives as a function of barrier heights and
temperature for HArF  H + Ar + F (solid lines) and HArF  Ar + HF
(dashed lines) reactions.
-2
0
2
4
6
8
10
Supporting Information available: Tables of calculated
geometry, relative energies, and methods for dynamics calculations.
This material is available free of charge via the Internet at
http://pubs.acs.org.
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-8
-4
Acknowledgment. This work is supported by the National
Science Council of Taiwan; grant number NSC 94-2113-M-194010. We are grateful to the National Center for High-Performance
Computing (NCHC) of Taiwan for providing part of the
computational resources.
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-10
-6
Figure 2. The calculated half-lives as a function of barrier heights and
temperature for FArCCH  F + Ar + CCH (solid lines) and FArCCH 
Ar + FCCH (dashed lines) reactions.
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5
-8
log (t1/2)
(13)
10
150 K
15
10
(10)
(11)
(12)
15
250 K
200 K
(4)
150 K
300 K
20
(1)
(2)
(3)
25
barrier height (kcal/mol)
25
barrier height (kcal/mol)
cc-pVQZ calculation on HArF and OBArF systems the
convergence of the calculated energies by CCSD(T)/aug-cc-pVTZ
is probably less than 3 kcal/mol for the first channel. Table 1 also
shows that all the energies for the second channel are well
predicted by the MP2 method, and the size of the basis sets has
much smaller effects. In all cases, the results using 6311++G(2d,2p) and aug-cc-pVDZ basis sets are very similar.
The discussion above demonstrated high-level electron
correlation need to be included to predict the meta-stability of
noble-gas containing molecules. However, what are the
quantitative criteria for the meta-stability? More specifically, what
are the minimum barrier heights for the noble-gas containing
molecule to be stable in the gas phase? To answer this question,
we made transition state theory calculation18,19 on the
unimolecular rate constants on the HArF and FArCCH systems
for the two dissociation channels. The tunneling effects were
considered for the former system since it involves significant
hydrogen motions. The classical barrier heights were input as
parameters. The calculated half-lives, t1/2 = ln 2 / k(T), where k(T)
is the calculated rate constant at temperature T, are plotted as a
function of barrier heights and temperature in Figures 1 and 2 for
HArF and FArCCH systems, respectively. The two channels were
plotted on two types of lines. For example, Figure 1 shows that
for an HNgY system, in order to have ~100 s half-life for
spectroscopic study in the gas phase at 100 K, 200 K, and 300 K,
the first channel must have barriers of 12, 18, and 26 kcal/mol,
respectively; and the second channel must have 8, 16, and 23
kcal/mol, respectively. Similarly, Figure 2 shows that for an
XNgY system (X, Y are not hydrogen), the first channel must
have barriers of 5, 10, and 15 kcal/mol, respectively, and the
second channel must have 6, 11, and 17 kcal/mol, respectively. As
seen in Table 1, the HArC4H has a barrier of only ~5 kcal/mol for
the first channel. If we define the“metastability” as having halflife longer than 100 s, then HArC4H is probably not metastable
even at 100 K. All other molecules listed in Table 1 seem to be
metastable up to ~200 K in the gas phase.
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TS2
V2 TS1
V1
XNgY
t 1/2 = ln 2 / k(T)
Energetics and Dynamics of XNgY
(1) X + Ng + Y
Erxn1
Erxn2
(2) Ng + XY
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