8 April 2002
Chemical Physics Letters 355 (2002) 509–516
www.elsevier.com/locate/cplett
Structures and stabilities of CaC3 isomers
A. Largo
b
a,*
, P. Redondo a, C. Barrientos a, L.M. Ziurys
b
a
Departamento de Quımica Fısica, Facultad de Ciencias, Universidad de Valladolid, ES-47005 Valladolid, Spain
Department of Chemistry, Department of Astronomy, and Steward Observatory, 933 N. Cherry Ave., University of Arizona,
Tucson, AZ 85721, USA
Received 29 November 2001; in final form 7 February 2002
Abstract
A theoretical study of CaC3 species has been carried out. As a general trend, triplet states are found to be more stable
than singlet ones for all isomers. The predicted global minimum is a rhomboidal species, 4tð3 B1 Þ, whereas another
rhomboidal four-membered ring, 3tð3 A1 Þ, is predicted to lie quite close in energy (about 8.2 kcal/mol higher in energy at
the G2(P) level). The corresponding singlet states, 3sð1 A1 Þ and 4sð1 A1 Þ, lie about 11.5 and 13 kcal/mol, respectively,
above the predicted global minimum. Therefore our calculations suggest that several species could be accessible to
experimental detection. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction
Several binary carbon compounds of the general formula XCn have been observed in space. So
far SiC2 [1], SiC3 [2], SiC4 [3], SC2 [4] and SC3 [5]
have been detected by radioastronomical observations, and it is expected that new molecules of
this type could be identified in interstellar and
circumstellar gas. In addition metal carbides corresponding to the same general formula are also
relevant in solid-state chemistry, since they correspond to the basic structural units of potentially
interesting new materials. As a consequence the
structure of binary carbides has received considerable attention in recent years. Non-linear ground
states have been found in many cases. For example
both laboratory [6,7] and theoretical [8,9] studies
*
Corresponding author. Fax: +34-983-423-013.
E-mail address: [email protected] (A. Largo).
have shown that SiC2 has a cyclic ground state,
whereas for SiC3 the ground state is a rhomboidal
isomer. Other theoretical works have studied the
structure of aluminum, magnesium, and sodium
carbides, such as AlC2 [10–15], AlC3 [16,17], MgC2
[14,18,19], MgC3 [20,21], and NaC3 [22], concluding that several isomers are quite close in energy
and might be accessible to experimental detection.
A theoretical study [23] of calcium dicarbide,
CaC2 , was carried out in order to provide predictions of its molecular parameters that could help in
its radioastronomical observation. In this Letter
we provide a theoretical study of the CaC3 system,
with the intention to stimulate experimental studies on binary calcium carbides.
2. Computational methods
We have employed the same methods used in
our previous studies on AlC3 [17], MgC3 [21], and
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 2 8 4 - 1
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A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
NaC3 [22]. The geometries and harmonic vibrational frequencies of the different CaC3 species
have been obtained at the second-order Møller–
Plesset level with the 6-311G(d) basis set [24], including all electrons in the calculation (MP2(full)/
6-311G(d)). We have also employed density functional theory (DFT), in particular the B3LYP exchange-correlation functional [25] with the 6311G(d) basis set.
The G1 and G2 [26] methods have been applied
in order to compute accurate relative energies.
Since spin-contamination might affect the reliability of these methods, approximate projected
MP values were used to compute electronic energies. These results will be denoted as G1(P) and
G2(P), respectively. In addition CCSD(T) calculations (coupled-cluster single and double excitation model augmented with a non-iterative triple
excitation correction) [27], with the 6-311G(2df)
basis set, have been carried out on the B3LYP
geometries. The reliability of single-referencebased methods has been tested through the socalled T1 diagnostic [28], as well as by
CASSCF(6,8) calculations (complete active space
SCF calculations, including six electrons in eight
orbitals) for some of the more stable CaC3 isomers. The results were very close to those obtained
with the MP2 method, thus confirming the reliability of our calculations.
The chemical nature of the bonding for the
different CaC3 species has been characterized
through a topological analysis of the electronic
charge density [29]. All calculations reported in
this work were carried out with the GA U S S I A N -98
program package [30].
3. Results and discussion
We have searched for possible minima on both
the singlet and triplet surfaces of CaC3 , and their
optimized MP2 and B3LYP geometries are shown
in Figs. 1 (linear chains), 2 (rhomboidal structures), and 3 (three-membered rings). In Table 1
the relative energies at different levels of theory are
given, whereas the corresponding harmonic vibrational frequencies and dipole moments are provided in Table 2.
It is observed that in general there are no severe
discrepancies between the geometrical parameters
obtained at the MP2 and B3LYP levels. The only
exceptions are 2s, where a very different Ca–C2
length is found at both levels of theory, and 3s
longer at the
where the C1 –C3 distance is 0.26 A
MP2 level. We will discuss the CaC3 species according to the different types of isomers.
3.1. Linear chains
1s is the lowest-lying open-chain singlet species,
and corresponds to the following electronic configuration:
fcoreg 11a02 12a02 13a02 14a02 15a02 3a002 16a02
ð1Þ
The reasons for the non-linearity of 1s are the
same than in the case of MgC3 [21], namely that its
dominant valence-bond description implies two C–
C double bonds, an electron lone-pair at C1 , and a
Ca–C r bond with a high dative character from
calcium toward carbon.
The lowest-lying open-chain structure on the
triplet surface, 1t, is linear corresponding to the
following electronic configuration:
Fig. 1. MP2/6-311G(d) and B3LYP/6-311G(d) (in parentheses) optimized geometries for the open-chain CaC3 species. Distances are
given in angstroms and angles in degrees.
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
511
Fig. 2. MP2/6-311G(d) and B3LYP/6-311G(d) (in parentheses) optimized geometries for the rhomboidal CaC3 species. Distances are
given in angstroms and angles in degrees.
Fig. 3. MP2/6-311G(d) and B3LYP/6-311G(d) (in parentheses) optimized geometries for the three-membered CaC3 rings. Distances
are given in angstroms and angles in degrees.
fcoreg 9r2 10r2 11r2 3p4 12r2 13r1 4p1
ð2Þ
This 3 P state is also quite similar to the lowestlying linear triplet state of the isovalent system
MgC3 . One of the unpaired electrons is located at
the calcium atom, whereas the second one is almost equally distributed between C1 and C3 .
Therefore we may propose two main valence-bond
structures for the description of this species:
Ca–C_ @C@C :$ Ca–CBC–C_ :
This description is also consistent with the linearity
of this molecule and with the fact that the C1 –C2
distance is shorter than the C2 –C3 one.
We also report in Fig. 1 the geometrical parameters of the linear species with the calcium
atom in a central position. As can be seen in Table
2, 2s has two imaginary frequencies at both MP2
and B3LYP levels, whereas 2t is a true minimum at
the MP2 level, but it has two imaginary frequencies when the B3LYP method is employed. We
have tried to obtain optimized structures for
76.1
136.8
145.3
6.6
0.1
1.0
6.3
93.6
5.0
2.7
2.2
2.8
4.6
)7.6
)5.6
0.0
7.3
9.8
9.9
8.1
0.0
0.0
0.0
0.0
7.0
)3.1
)1.4
3.4
31.5
18.4
18.9
23.3
16.9
6.8
7.9
14.6
60.6
139.6
)5.3
16.3
15.0
23.1
21.8
7.4
23.3
22.1
31.1
29.9
)5.3
5.6
5.4
10.3
10.1
0.0
0.0
0.0
0.0
0.0
)20.7
2.8
1.2
9.8
8.2
148.2
4.0
12.3
11.6
15.8
15.1
80.6
)10.9
5.1
3.7
12.9
11.5
0.3
5.2
5.1
13.0
12.9
4ð3 B1 Þ
4ð1 A1 Þ
3ð3 A1 Þ
3ð1 A1 Þ
2ð3 PÞ
2ð1 DÞ
1ð3 PÞ
non-linear geometries, but in all cases finally other
cyclic or rhombic structures were reached. Nevertheless it is evident in Table 1 that both singlet and
triplet C–Ca–C–C species are high-lying structures
and consequently of rather limited interest for
experimentalists.
3.2. Rhomboidal structures
Isomer 3 corresponds to a rhombic structure
where the calcium atom is bonded to the side of a
cyclic C3 unit. The electronic configuration of the
singlet 3s species is the following:
fcoreg 8a21 4b22 9a21 3b21 10a21 5b22 11a21
B3LYP/6-311G(d) geometry
B3LYP/6-311G(d)
20.3
CCSD(T)/6-311G(d)
2.0
CCSD(T)/6-311+G(d)
3.2
CCSD(T)/6-311G(2df)
9.8
ð3Þ
which is similar to that of the predicted MgC3 [21]
global minimum. The triplet state, 3t, results upon
11a1 ! 12a1 excitation, with one of the unpaired
electrons located at the calcium atom and the
other one distributed around the C3 unit (mainly
at C2 ). In the case of 3t the transannular C–C
distance suggests the possibility of a transannular
bonding. However the topological analysis of the
charge density shows that there is no transannular
C1 –C3 bond, and therefore that 3t should be described as a truly four-membered ring. In the case
of 3s the topological analysis reveals that, whereas
at the MP2 level a four-membered ring is obtained,
when the B3LYP density is employed there is a
transannular C1 –C3 bond which confers to the
molecule a bicyclic character.
Structure 4 may be viewed as the result of the
side interaction of a calcium atom with a quasilinear C3 unit. The lowest-lying singlet state of
isomer 4 corresponds to the following electronic
configuration:
fcoreg 8a21 4b22 9a21 10a21 5b22 3b21 6b22
MP2(full)/6-311G(d) geometry
MP2(full)/6-311G(d)
1.5
G1*
8.0
G2*
7.8
G1(P)*
15.8
G2(P)*
15.6
1ð1 A0 Þ
Table 1
Relative energies (kcal mol1 ) of the CaC3 species at different levels of theory, including ZPVE corrections
4ð3 B2 Þ
5ð1 A1 Þ
5ð3 B2 Þ
6ð3 A2 Þ
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
6ð1 A1 Þ
512
ð4Þ
The 3b1 orbital represents a p orbital delocalized
almost completely over the C3 unit, resulting in
relatively strong peripheral C–C bonding. According to the analysis of the electronic charge
density 4s is in fact a four-membered ring, since
there is no formal Ca–C2 bond even though this
transannular distance is slightly shorter than the
peripheral Ca–C1 and Ca–C3 bond distances.
There are two lowlying triplet states resulting,
respectively, from electronic configuration (4)
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
513
Table 2
MP2(full)/6-311G(d) and B3LYP/6-311G(d) (in parentheses) vibrational frequencies (in cm1 ), ZPV energies (in kcal mol1 ), and
dipole moments (in debye) for the different CaC3 species
1ð1 A0 Þ
1ð3 PÞ
2ð1 DÞ
2ð3 PÞ
3ð1 A1 Þ
3ð3 A1 Þ
4ð1 A1 Þ
m1 ða1 ; a0 ; rÞ
m2 ða1 ; a0 ; rÞ
m3 ða1 ; a0 ; rÞ
m4 ðb2 ; a0 ; pÞ
1859(1929)
1213(1225)
450(407)
328(293)
1854(1758)
525(504)
353(346)
1854(176)
84(89)
42(7i)
38(36i)
1581(1627)
876(877)
362(365)
1245(1195)
1183(1202)
703(692)
462(462)
1449(1342)
86(97)
1741(1873)
710(474)
258(352)
104(130)
95(109)
252i(31i)
262i(39i)
1855(1384)
918(1063)
311(520)
1434(973)
m5 ðb2 ; a0 ; pÞ
2396(1878)
1234(1238)
319(330)
1498(410)
450(278)
98(89)
44(87)
308(408)
302(284)
318(286)
m6 ðb1 ; a00 ; pÞ
ZPVE
l
263(231)
6.00(5.98)
6.580(7.287)
8.63(6.16)
7.174(7.393)
4.15(4.20)
12.044(5.865)
6.79(4.11)
2.517(2.980)
279(222)
7.30(6.53)
9.303(13.062)
222(223)
6.56(6.53)
2.213(2.644)
251(225)
6.24(6.02)
12.572(10.788)
4ð3 B1 Þ
4ð3 B2 Þ
5ð1 A1 Þ
5ð3 B2 Þ
6ð1 A1 Þ
6ð3 A2 Þ
1289(1223)
671(613)
495(490)
1156(1410)
335(321)
502(456)
6.36(6.45)
11.772(10.134)
1266(1230)
522(474)
310(306)
1701(1759)
188(176)
215(167)
6.01(5.88)
2.688(3.006)
1601(1484)
789(647)
286(289)
935(422i)
170(163)
214(195)
5.71(3.97)
11.045(10.518)
1603(1604)
1247(1236)
310(312)
98(146)
1133i(454i)
160(170)
4.89(4.96)
6.216(6.129)
1572(1732)
485(467)
250(320)
1052(373)
399(65)
106(94)
5.52(4.36)
11.806(5.303)
1771(1834)
524(508)
370(356)7
281(240)
60(36)
54(25)
4.37(4.29)
0.725(0.151)
m1 ða1 ; a0 ; rÞ
m2 ða1 ; a0 ; rÞ
m3 ða1 ; a0 ; rÞ
m4 ðb2 ; a0 ; pÞ
m5 ðb2 ; a0 ; pÞ
m6 ðb1 ; a00 ; pÞ
ZPVE
l
upon 6b2 ! 1a2 promotion (4tð1Þ; 3 B1 state), and
6b2 ! 11a1 excitation (4tð2Þ; 3 B2 state). In the case
of 4t(1) the two unpaired electrons are mainly located at C1 and C3 , whereas in the case of 4t(2) one
of the electrons is also distributed among C1 and
C3 and the other one is located at calcium. The
topological analysis shows that for 4t(2) there is
only Ca–C2 bond and no peripheral Ca–C bonding, and therefore this species is in fact a T-shape
structure. The same description is provided by the
MP2 level for 4t(1), whereas at the B3LYP level
this species is found to be a truly four-membered
ring with peripheral Ca–C bonding.
3.3. Three-membered rings
5s and 5t were found when searching for isomers containing a C3 ring and an exocyclic calcium
atom. 5s has the following electronic configuration:
fcoreg 8a21 4b22 9a21 10a21 3b21 11a21 5b22
ð5Þ
and is only a true minimum at the MP2 level, since
at the B3LYP level has an imaginary frequency.
All our attempts to obtain a true minimum at the
B3LYP level in Cs symmetry finally collapsed into
the rhomboidal structure 3s. The most interesting
feature of the geometrical parameters of 5s is the
relatively long C2 –C3 distance at both MP2 and
B3LYP levels. In fact a topological analysis of the
electronic charge density reveals that there is no
C2 –C3 bonding, and therefore that 5s should not
be classified as a cyclic species.
The lowest-lying triplet state corresponding to
structure 5 results from 5b2 ! 12a1 excitation and
has an imaginary frequency (b2 symmetry) at both
MP2 and B3LYP levels of theory. Consequently,
this structure should be in fact considered as the
transition state for the degenerate rearrangement
of 3t. A much shorter C2 –C3 distance is found for
5t than for 5s, suggesting that 5t should be a truly
three-membered ring, a fact that is confirmed by
the topological analysis.
Isomer 6 is the analogue of 5, but with the
calcium atom in central position. The singlet state
has the same electronic configuration than 5s, but
the lowest-lying triplet isomer is a 3 A2 state resulting from 5b2 ! 4b1 promotion. Although both
species are true minima since all their vibrational
frequencies are real, they lie quite high in energy
514
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
and therefore of limited interest from the practical
point of view.
3.4. Stability order
It can be seen in Table 1 that, as in our previous
studies on other similar systems [21,22], the
B3LYP level is found to perform much better than
MP2, since in most cases predicts the same relative
stability order than the more expensive G2 or
CCSD(T) levels. This suggests that the B3LYP
results should be more reliable than the MP2 ones
for predicting relative energies.
It is interesting to note that for all CaC3 isomers, as in the case of MgC3 [21], triplet states are
in general predicted to lie lower in energy than
singlet states. As expected isomers 2 and 6, with
calcium in a central position, lie much higher in
energy at both MP2 and B3LYP levels, and
therefore no higher-level calculations have been
performed in both cases. However all other isomers lie relatively close in energy. In this sense the
CaC3 system is quite similar with the isovalent
system MgC3 , even though in the case of MgC3
[21] isomer 3 is predicted to be the most stable
species, whereas for CaC3 a triplet state of isomer
4 seems to be the predicted global minimum. Although with the largest basis set, 6-311G(2df), 3t
and 4t(1) are virtually isoenergetic at the CCSD(T)
level of theory, it seems that both inclusion of
diffuse and additional polarization functions favour the latter one. Furthermore at the G1 and G2
levels, 4t(1) is predicted to lie lower in energy, and
the energy difference is increased when projected
MP energies are employed. Nevertheless both
isomers should be quite close in energy and
probably both could be accessible to experimental
detection, since isomerization between them is
symmetry-forbidden. The next isomer in stability
order is the open-chain isomer 1, followed by
isomer 5. The relative energy ordering at the G2(P)
level of theory is the following: 4tð3 B1 Þ <
3tð3 A1 Þ < 4t ð3 B2 Þ < 3sð1 A1 Þ < 4s ð1 A1 Þ < 1tð3 PÞ
< 1sð1 A0 Þ < 5tð3 B2 Þ < 5sð1 A1 Þ: At the CCSD(T)
level the ordering of 4tð3 B2 Þ and 3sð1 A1 Þ is reversed, as well as that of 4sð1 A1 Þ and 1tð3 PÞ. We
consider the G2(P) results more reliable since they
include calculations with rather large basis sets
(the G2 method makes additivity assumptions but
computes the electronic energy effectively at the
QCISD(T)/6-311+G(3df,2p) level), and inclusion
of diffuse and polarization functions seem very
important in this case as suggested by the
CCSD(T) results.
3.5. Spectroscopic data
In order to aid in their possible experimental
detection we provide the corresponding rotational
constants at the MP2 and B3LYP levels (in parentheses) for the two predicted lowest-lying CaC3
species:
4tð3 B1 Þ
A ¼ 13:016 ð13:103Þ GHz;
B ¼ 6:223 ð6:279Þ GHz;
C ¼ 4:210 ð4:245Þ GHz:
3tð3 A1 Þ A ¼ 36:098 ð36:978Þ GHz;
B ¼ 3:367 ð3:434Þ GHz;
C ¼ 3:079 ð3:142Þ GHz:
Although the MP2 and B3LYP predictions for
the two lowest-lying CaC3 species are in reasonable agreement, a brief discussion on the reliability of these methods is perhaps in order to
guide an experimental search. Although recognizing that the reliability of DFT methods in
predicting molecular properties for open-shell
systems is still a matter of debate, in principle we
consider that in this case the B3LYP predictions
should be more reliable. There are mainly three
reasons supporting this consideration: (i) as
mentioned earlier, spin contamination may affect
the MP calculations (for example hS2 i values of
the HF reference wavefunctions for 3t and 4t(1)
are 2.022 and 2.355, respectively); (ii) the rather
good performance of DFT methods in predicting
molecular properties (structures and vibrational
frequencies in excellent agreement with coupled
cluster calculations and with experiments) for
small carbon clusters [31]; (iii) the work of other
authors [32–35] in the field, as well as our previous experience [17,21,22], suggests that B3LYP
calculations perform better than MP2 ones for
small open-shell Cn X compounds. Therefore we
suggest that in this case the B3LYP predictions
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
should be the preferred set for an experimental
search.
The vibrational frequencies, shown in Table 2,
may also be useful in a possible experimental observation. In general there is a reasonable agreement in the MP2 and B3LYP vibrational
frequencies. Although for the sake of space the IR
intensities are not shown, we may briefly comment
that for both 4t(1) and 3t isomers both MP2 and
B3LYP levels agree in that the IR spectrum should
be clearly dominated by the m3 (a1 symmetry) frequency.
It is also worth mentioning that in general the
CaC3 species are characterized by high dipole
moments, as a consequence of the high ionic
character of the Ca–C bond, with the calcium
atom bearing in most cases a relatively high positive charge. This would make their possible detection in astronomical sources more likely. In fact
for the predicted global minimum, 4t(1), a very
high dipole moment around 10–11.7 debye is
found. On the other hand the second lowest-lying
isomer, 3t, is predicted to have only a moderate
dipole moment around 2.2–2.6 debye. The main
reason for the very different dipole moment mainly
resides in the positive charge supported by calcium
in each case, namely about +0.97e for the former
and +0.6e for the latter.
4. Conclusions
A theoretical study of the low-lying CaC3 species has been carried out, showing that there are
several species lying quite close in energy which
could be accessible to experimental detection. It
has been observed that for all isomers triplet states
are found to be more stable than singlet ones. The
higher levels of theory employed in our study
predict a rhomboidal species, 4tð3 B1 Þ, as the global
minimum, although another rhomboidal fourmembered ring, 3tð3 A1 Þ, is predicted to lie quite
close in energy (about 8.2 kcal/mol higher in energy at the G2(P) level). Both rhomboidal isomers
could be accessible to experimental detection, since
isomerization between them is symmetry-forbidden. There is also another T-shape structure,
4tð3 B2 Þ, lying only about 10 kcal/mol higher in
515
energy than the predicted global minimum, followed by the corresponding singlet states of isomers 3 and 4, lying about 11.5 and 13 kcal/mol,
respectively, above 4tð3 B1 Þ at the G2(P) level of
theory. The open-chain triplet and singlet species
lie even higher in energy.
The CaC3 system therefore is similar to the
isovalent MgC3 system, since there are several lowlying species which could be possible experimental
targets. Another similar characteristic is that for
both systems theoretical calculations predict a cyclic global minimum. However, an essential difference remains in that for MgC3 a singlet rhombic
isomer (similar to 3s) is predicted to be the ground
state, whereas in the case of CaC3 a triplet state is
found to be the most stable one.
Spectroscopic parameters for the low-lying
isomers have been provided to aid in their possible
experimental observation. Particularly interesting
is the very high dipole moment (more than 10D)
predicted for the lowest-lying species, which undoubtedly should help in its possible radioastronomical detection.
Acknowledgements
This research has been supported by the Ministerio de Educacion y Cultura of Spain (DGICYT, Grant PB97-0399-C03-01) and by the Junta
de Castilla y Leon (Grant VA18/00B).
References
[1] P. Thaddeus, S.E. Cummins, R.A. Linke, Astrophys. J.
Lett. 283 (1984) L25.
[2] A.J. Apponi, M.C. McCarthy, C.A. Gottlieb, P. Thaddeus,
M. Guelin, Astrophys. J. 516 (1999) L103.
[3] M. Ohishi, N. Kaifu, K. Kawaguchi, A. Murakami, S.
Saito, S. Yamamoto, S. Ishikawa, Y. Fujita, Y. Shiratori,
W.M. Irvine, Astrophys. J. Lett. 345 (1989) L83.
[4] S. Saito, K. Kawaguchi, S. Yamamoto, M. Ohishi, H.
Suzuki, N. Kaifu, Astrophys. J. 317 (1987) L115.
[5] S. Yamamoto, S. Saito, K. Kawaguchi, N. Kaifu, H.
Suzuki, M. Ohishi, Astrophys. J. 317 (1987) L119.
[6] D.L. Michalopoulos, M.E. Geusic, P.R.R. LangridgeSmith, R.E. Smalley, J. Chem. Phys. 80 (1984) 3556.
[7] M.C. McCarthy, A.J. Apponi, P. Thaddeus, J. Chem.
Phys. 110 (1999) 10645.
516
A. Largo et al. / Chemical Physics Letters 355 (2002) 509–516
[8] R.S. Grev, H.F. Schaefer III, J. Chem. Phys. 80 (1984)
3551.
[9] I.L. Alberts, R.S. Grev, H.F. Schaefer III, J. Chem. Phys.
93 (1990) 5046.
[10] J.R. Flores, A. Largo, Chem. Phys. 140 (1990) 19.
[11] L.B. Knight, S.T. Cobranchi, J.O. Herlong, C.A. Arrington, J. Chem. Phys. 92 (1990) 5856.
[12] G.V. Chertihin, L. Andrews, P.R. Taylor, J. Am. Chem.
Soc. 116 (1994) 3513.
[13] B. Ma, Y. Yamaguchi, H.F. Schaefer, Mol. Phys. 86 (1995)
1331.
[14] H.L. Yang, K. Tanaka, M. Ahinada, J. Mol. Struct.
(Theochem) 422 (1998) 159.
[15] D.V. Lanzisera, L. Andrews, J. Phys. Chem. A 101 (1997)
9660.
[16] X. Zheng, Z. Wang, A. Tang, J. Phys. Chem. A 103 (1999)
9275.
[17] C. Barrientos, P. Redondo, A. Largo, Chem. Phys. Lett.
320 (2000) 481.
[18] S. Green, Chem. Phys. Lett. 112 (1984) 29.
[19] D.E. Woon, Astrophys. J. 456 (1996) 602.
[20] X.E. Zheng, Z.Z. Wang, A.C. Tang, J. Mol. Struct.
(Theochem) 492 (1999) 79.
[21] P. Redondo, C. Barrientos, A. Largo, Chem. Phys. Lett.
335 (2001) 64.
[22] C. Barrientos, P. Redondo, A. Largo, Chem. Phys. Lett.
343 (2001) 563.
[23] P. Redondo, Y. Ellinger, G. Berthier, R. Cimiraglia,
Astron. Astrophys. 247 (1991) L1.
[24] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem.
Phys. 72 (1980) 650.
[25] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.
[26] L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople,
J. Chem. Phys. 94 (1991) 7221.
[27] K. Raghavachari, G.W. Trucks, J.A. Pople, M. HeadGordon, Chem. Phys. Lett. 157 (1989) 479.
[28] T.J. Lee, P.R. Taylor, Int. J. Quantum Chem. Symp. 23
(1989) 199.
[29] R.F.W. Bader, Atoms in Molecules. A Quantum Theory,
Clarendon Press, Oxford, 1990.
[30] M.J. Frisch et al., GA U S S I A N 98, Gaussian Inc., Pittsburgh, PA, 1998.
[31] A. van Orden, R. Saykally, Chem. Rev. 98 (1998) 2313,
and references therein.
[32] J. El-Yazal, J.M.L. Martin, J.P. Francßois, J. Phys. Chem.
A 101 (1997) 8319.
[33] S. Lee, Chem. Phys. Lett. 268 (1997) 69.
[34] G. Pascoli, H. Lavendy, J. Phys. Chem. A 103 (1999) 3518.
[35] J.M.L. Martin, J. El-Yazal, J.P. Francßois, Chem. Phys.
Lett. 242 (1995) 570.