JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 13
1 OCTOBER 1998
Microwave spectra of the Ne–N2 Van der Waals complex:
Experiment and theory
W. Jäger, Y. Xu, and G. Armstrong
Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2 Canada
M. C. L. Gerry
Department of Chemistry, University of B.C., Vancouver, B.C. V6T 1Z1 Canada
F. Y. Naumkin, F. Wang,a) and F. R. W. McCourt
Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
~Received 16 March 1998; accepted 25 June 1998!
High-resolution microwave spectra of the ground state 20Ne– 14N2, 20Ne– 15N2, 22Ne– 14N2, and
22
Ne– 15N2 Van der Waals complexes, involving rotational levels up to J54, are reported.
Interpretation and assignment of the observed transitions were made by combining results of
measurements and theoretical predictions of the MW line positions in terms of available empirical
potential energy surfaces and of a new high-level ab initio potential energy surface. The deviations
of the calculated MW spectra from those observed experimentally are more uniform for the ab initio
potential surface than they are for the empirical potential surfaces, allowing for reduction of the
deviations to within 0.07% for all isotopomers by a single-parameter scaling of the ab initio
potential energy surface. The scaled Ne–N2 interaction potential was used to predict the MW line
positions for the transitions J 8 -J 9 53-2, 4-3 for all species. A simple procedure is proposed to
improve the ab initio results for atom–diatom systems on the basis of atom–atom interaction
components. © 1998 American Institute of Physics. @S0021-9606~98!01437-8#
I. INTRODUCTION
was possible to resolve 14N nuclear quadrupole hyperfine
structure of the rotational transitions in these high-resolution
studies. The resulting nuclear quadrupole coupling constants
contain detailed information about the large amplitude bending motions within the complexes. It was found, for example, that the quadrupole coupling constants depend upon
the asymmetric top quantum number K a . The resulting average excursion from the equilibrium geometry as a function
of internal state is a delicate measure of the angular anisotropy of the potential energy surface. Hutson5 has recently
treated the effect of the large amplitude motions on nuclear
quadrupole coupling constants in complexes of rare gas atoms with linear molecules explicitly, and obtained expressions consistent with the experimentally observed
K-dependence of the quadrupole coupling constants. Consequently, an accurate value for the 14N2 monomer quadrupole
coupling constant could be obtained from the rotational spectra of the Ar–N2 and Kr–N2 complexes. As the Ne–N2 complex exhibits Van der Waals motions of even larger amplitude than do its heavier analogues, the effects of these
motions on the nuclear quadrupole interactions can be expected to be more severe. Experimental difficulties were
therefore anticipated in locating rotational transitions for this
complex because of its floppy nature, lower dissociation energy, and small induced dipole moment.
The present paper represents a unified experimental/
theoretical effort to determine the microwave spectra of several isotopomers of the Ne–N2 Van der Waals complex, and
to refine the Ne–N2 PES. Four previous potential surfaces6–9
for the Ne–N2 interaction, two of them fully empirical,6,9 the
other two semiempirical,7,8 are available for use in theoreti-
Investigation of weakly bound Van der Waals complexes formed by closed-shell molecules and atoms is a challenge for both experimentalists and theoreticians. The weak
binding makes it difficult to prepare these systems and retain
them intact for a sufficiently long time to obtain accurate
measurements. It also imposes stringent requirements upon
the quality of a potential energy surface ~PES! and upon the
accuracy of calculations predicting the properties of the complexes from it. Microwave ~MW! spectroscopy is one efficient way for probing such species, as the rotational energy
levels are quite sensitive to the nature of the atoms making
up the complex. Modern MW spectroscopic methods, such
as pulsed jet cavity Fourier transform ~FT! MW spectroscopy, allow for a sufficiently high resolution ~typically of the
order of a few kHz! of the recorded spectra. However, the
scanning of a wide spectral interval then becomes a very
time-consuming task. Theoretical studies enable us to evaluate directly the positions of the spectral lines, and can help to
narrow the experimental search range. Therefore, a combined experimental/theoretical approach appears to be an efficient way to proceed.
Rotational spectra of Ar–N2 ~Refs. 1, 2! and Kr–N2
~Ref. 3! were previously investigated using a FTMW spectrometer. The experimental spectra are in accord with Tshaped equilibrium structures for these complexes, confirming earlier results4 from infrared investigations on Ar–N2. It
a!
Present address: School of Chemistry, University of Melbourne, Parkville,
Victoria 3052, Australia.
0021-9606/98/109(13)/5420/13/$15.00
5420
© 1998 American Institute of Physics
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
cal simulations of the MW spectrum. However, previous
experience2 with the simulation of MW spectra for the analogous Ar–N2 system has shown that considerable differences
in the positions of the MW lines are possible even when the
simulations have been carried out for apparently quite similar potential surfaces. Indeed, two similar Ar–N2 potential
surfaces8,10 gave calculated spectra2 that differed significantly from the experimental spectrum ~well beyond the uncertainties in the measurements!. In order to bring the spectra
simulated with a particular PES into agreement with the
measured spectra, the PES could, in principle, be modified
by tuning one or more of its parameters:2 in practice, however, such a tuning was readily accomplished in only one
case. Moreover, the functional forms normally employed to
represent empirical potential surfaces have been found11 to
have a limited flexibility in the fitting of high-level ab initio
data obtained for the Ar–N2 interaction. In light of these
comments, the success achieved recently12 in the fitting of
high-level ab initio Ar–Cl2 potential data to the MW spectrum of the Ar–Cl2 complex, and the absence ~so far as we
are aware! of high-level ab initio results for the Ne–N2 interaction, we have generated new ab initio potential data.
The present simulations of the MW spectra of the Ne–N2
isotopomers have therefore employed both empirical
surfaces8,9 and this new high-level ab initio PES.
A previous ab initio study11 of Ar–N2 gave a potential
surface with a single minimum for the T-shaped geometry.
This study corroborated earlier empirical predictions8,13,10 of
the overall topology of the Ar–N2 PES. However, the difference between the binding energies for the T-shaped and linear configurations was found to be significantly less than that
obtained from the empirical surfaces. A similar relation between ab initio and empirical data has also been found by Hu
and Thakkar14 for the more weakly bound He–N2 complex.
The generally smaller binding energy associated with the
Ne–N2 complex can be expected to reduce the energy difference between the T-shaped and linear configurations relative
to that for Ar–N2, so that the role of large-amplitude bending
motions, and hence the effect of the bent configurations on
the MW spectra, may be more significant for the neon complex. One purpose of the present work is to investigate this
effect, and to compare the anisotropy of the ab initio and
empirical potential surfaces for the Ne–N2 complex.
It has also been shown recently11 that the effective interaction between a N atom within N2 and Ar is perturbed ~relative to the potential for isolated ArN! more strongly in the
direction perpendicular to the N–N axis than it is along the
axis; this is just the opposite to what would be anticipated
from consideration of the relevant s p-hybridization of the N
atoms within N2. The corresponding situation for the Ne–N
interaction is examined here.
The experimental and theoretical procedures are described in Secs. II and III, while the results, including both
the measured and simulated MW spectra, and the new PES,
are presented in Sec. IV. The conclusions to be drawn from
the present study are given in Sec. V.
5421
II. EXPERIMENT
Two pulsed jet cavity FTMW spectrometers of the
Balle-Flygare type15 were used to measure the pure rotational transitions of Ne–N2 Van der Waals molecules. The
instrument in Vancouver16 and that in Edmonton17 are of
similar design; both have an operating range of 4–26 GHz. A
brief description of the main features of the latter, and of the
Ne–N2 experiments done with it, follows.
The operating principle of this type of spectrometer is
based on the coherent excitation of a molecular ensemble
with a MW pulse and subsequent detection of the molecular
emission signal. The sample cell is a MW cavity that consists
of two spherical aluminum mirrors, 28 cm in diameter, each
with a radius of curvature of 38.4 cm. The MW cavity is
mounted in a vacuum chamber which is evacuated by a 12
in. diffusion pump. One mirror is fixed to a flange of the
vacuum chamber, while the other is adjustable. The mirror
separation is approximately 30 cm, and the cavity can be
fine-tuned into resonance with the MW excitation radiation
by a computer-controlled dc actuator. This feature allows
relatively large frequency regions to be scanned
automatically.18 The bandwidth of the cavity is ;0.5 MHz at
a frequency of 10 GHz. The step size in an automated search
is typically 200 kHz. The molecular signal is recorded as a
time domain signal and a Fast Fourier Transformation yields
the frequency spectrum. A time domain signal fitting procedure was used19 for the analyses of some narrow splittings in
the spectra of 20Ne– 15N2.
The sample gas mixtures consisted of 1% nitrogen in
neon at 3 atm. A sample was injected through a nozzle with
orifice diameter 0.8 mm into the MW cavity parallel to the
cavity axis.20 The repetition rate for the experiment was limited to approximately 5 Hz by the capacity of the diffusion
pump. The natural abundance of 22Ne was sufficient to observe spectra of complexes containing this isotope; it was
necessary, however, to use enriched 15N2 ~Cambridge Isotope Laboratories! in order to obtain sufficient signal intensity for the Ne– 15N2 complexes.
III. THEORETICAL DESCRIPTION
Microwave spectra can be predicted directly from energy differences between the rotational levels for a given
potential surface. The TRIATOM code of Tennyson et al.,21
which is based on the decomposition of the PES using basis
sets of 40 eigenfunctions of the Morse potential ~with optimized parameters D e 50.1 mhartree, b e 5231025 a.u., and
R e 512 bohr) for the radial coordinate and 25 Legendre
polynomials for the angular coordinate, has been employed
here for this purpose. Further extension of the basis set has
been found to affect the results negligibly. For instance, doubling the number of Legendre polynomials or increasing the
number of Morse eigenfunctions by 50% leads to a variation
of energy in the 7th decimal only, with the differences between the levels being even much less sensitive.
The calculations of the rovibrational energy levels in this
way requires a knowledge of the potential energy of the system as a function of its geometry. As it is intractable to
employ time-consuming high-level ab initio computations
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5422
Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
for many arbitrary geometries, a standard procedure is to
calculate several cuts of the PES, to introduce a representation of the interaction that is able to reproduce these limited
data accurately, and then to obtain points on the total surface
at arbitrary configurations by interpolation and extrapolation.
The traditional approach to atom–diatom interactions involves interpolation of the radial dependence for each cut by
an appropriate analytic function and then use of Legendre
polynomials for the angular dependence at a given radial
distance. However, a high-quality interpolation requires
rather extensive ab initio information, since it has been
shown11 for Ar–N2 that versions using only two cuts ~for the
linear and T-shaped geometries! or three cuts ~with the bent
geometry at 45° added! may be unreliable, even for the prediction of the overall surface topology. An alternative model
based on anisotropic atom–atom interactions has proven to
be more stable, and provides the correct topology, together
with spectroscopic accuracy of interpolation with only three
cuts.11 This method has been used for the present calculations.
The model employs a simple additive approximation for
the Ne–N2 potential surface in terms of NeN potentials,
namely
V Ne–N2~ R, u ! 5V NeN~ R 1 , u 1 ! 1V NeN~ R 2 , u 2 ! ,
~1!
with R and u being polar coordinates of the Ne atom relative
to the center of the N2 molecule or (R i and u i ) from one of
the N atoms. Each of the two V NeN potentials can be represented in terms of the model based on the symmetry of the
diatomic electronic wave functions corresponding to
sp-hybridization of the N atoms within the N2 molecule,11
i.e., by
V NeN~ R i , u i ! 5V i ~ R i ! cos2 u i 1V' ~ R i ! sin2 u i ,
i51,2,
~2!
in which V i and V' are the Ne–N interactions along and
perpendicular to the N–N axis. These effective atom–atom
potentials may be expected to differ from the potential for an
isolated NeN molecule because of the distortion of the electronic structure of N within N2.
By construction, V Ne–N2 at u 50° is determined by V i
only, so that V i can be obtained from the corresponding u
50° cut of the PES. The component V' can then be extracted from any other cut, such as that at 90°, to give a 2-cut
version of the model. Since for the Ar–N2 interaction it has
been found11 that minimally a third cut is required to describe the PES correctly at intermediate angles, we shall do
the same for the Ne–N2 interaction. Thus, if we use a cut at
angle u s to obtain a potential V's , we may then utilize a
switching function to give a final V' for u . u s of the form
V' 5V's 1 ~ V'90° 2V's ! sin2
F
G
90°
~u2us! .
90°2 u s
rected for basis set superposition error ~BSSE! using a standard counterpoise method.27 The N–N distance has been
fixed at the equilibrium value of 1.10 Å, obtained in preliminary calculations in good agreement with experimental
data28 for the ground electronic state, 1 S 1
g , of N2.
IV. RESULTS AND DISCUSSION
A. Observed spectra and spectral analyses
Following the measurements on Ar–N2 ~Refs. 1, 2! and
Kr–N2 ~Ref. 3!, we set out to search for rotational transitions
of Ne–N2. Much difficulty was encountered in the initial
search. The MW spectra of Ne–N2 were expected to be
weaker than those of Ar–N2 and Kr–N2, since the dipole
moment induced by the weak interaction between the rare
gas atom and the N2 subunit is smaller for Ne than for Ar or
Kr. Further, the complex is predicted to be much more flexible than its heavier counterparts, so that difficulties in predicting rotational line positions from an assumed equilibrium
structure were expected.
The first two rotational transitions were found initially
using the FTMW spectrometer in Vancouver.16 The intensities of these two transitions were about one to two orders of
magnitude lower than those of Ar–N2. The observed 14N
nuclear hyperfine splitting patterns were recognized to be
those of rotational transitions with K a 51. From their relative
intensities, they were tentatively identified as belonging to
20
Ne– 14N2 and to 22Ne– 14N2. However, extensive searches
for additional transitions were not successful, and a definite
assignment could not be achieved.
In the meantime, predictions of the rotational spectra of
20
Ne– 14N2 and 22Ne– 14N2 were performed based on the potential energy surfaces of Bowers et al.8 ~BTT! and of Beneventi et al.9 ~ESMSV!. These calculations enabled a tentative assignment of the two transitions initially observed
(J K a ,K c 52 1,2-1 1,1 of 20Ne– 14N2 and 2 1,1-1 1,0 of 22Ne– 14N2).
It was recognized, by using the nuclear quadrupole hyperfine
patterns as an identification aid, that the BTT potential predicts the isotopic shift and the K-splittings quite well, even
though the absolute frequencies differ significantly from the
~3!
Because no high-level ab initio data were previously
available for either the Ne–N or Ne–N2 interactions, calculations have been carried out at the comprehensive coupled
cluster CCSD-T level22,23 of theory with the extensive basis
sets24,25 aug-cc-pVTZ and aug-cc-pVQZ, using the MOLPRO
suite of ab initio programmes.26 The results have been cor-
FIG. 1. A composite spectrum of the J K a ,K c 52 0,2 – 1 0,1 rotational transition
of 20Ne– 14N2, showing complicated nuclear hyperfine structure due to the
14
N nuclei.
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
TABLE I. Observed frequencies of the
14
N hyperfine structure of Ne– 14N2 isotopomers.
22
20
Ne– 14N2
J K8 8 K 8 – J K9 9 K 9
a c
a c
1 01 – 0 00
2 02 – 1 01
3 03 – 2 02
2 12 – 1 11
3 13 – 2 12
2 11 – 1 10
3 12 – 2 11
F 8I 8 – F 9I 9
1
1
3
1
1
2
0
2
2
1
1
3
4
2
2
0
2
3
1
2
4
5
3
3
1
2
4
1
2
3
2
1
2
3
4
2
3
2
2
1
3
1
2
3
4
2–2
2–0
2–2
0–2
0–0
2–2
2–1
0–2
0–1
2–2
2–1
2–2
2–3
2–2
2–1
2–1
0–1
2–3
2–1
2–3
2–3
2–4
2–2
0–2
2–0
2–1
2–4
1–1
1–1
1–2
1–2
1–0
1–2
1–2
1–3
1–1
1–3
1–2
1–1
1–0
1–2
1–1
1–1
1–2
1–3
2
0
2
2
0
2
0
2
0
2
0
2
2
2
0
2
2
2
2
2
2
2
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5423
Ne– 14N2
n obs
~MHz!
D n HFS
~kHz!
n obs
~MHz!
D n HFS
~kHz!
6506.4536
6505.6829
6506.3363
6506.8125
6506.8125
6506.8651
13 003.5747
13 002.7816
13 002.8350
13 002.8724
13 002.9245
13 003.4954
13 003.5269
13 003.6695
13 003.7217
20.1
20.1
0.3
0.0
0.0
20.1
20.5
0.1
0.8
0.0
20.6
0.2
0.7
0.3
20.1
13 003.9647
13 004.0236
13 004.0535
1.0
20.8
21.1
19 481.9210
19 481.8967
19 481.9496
19 481.9751
19 482.0461
19 482.0988
20.2
0.1
20.1
22.0
0.8
1.4
6178.8096
6178.0346
6178.6916
6179.1699
6179.1699
6179.2243
12 349.2612
12 348.4643
12 348.5146
12 348.5557
12 348.6053
12 349.1817
12 349.2127
12 349.3575
12 349.4089
12 349.4524
12 349.6525
12 349.7147
12 349.7430
12 349.8885
18 502.9025
18 502.8792
18 502.9320
0.4
0.4
0.4
20.9
20.9
0.6
20.6
1.4
21.3
1.3
22.1
0.2
0.4
0.9
20.6
1.1
0.0
0.7
21.0
20.6
22.1
1.4
0.2
12 274.3233
12 273.9472
12 274.3373
12 275.2565
12 275.8184
18 385.2159
18 385.1217
18 385.2156
18 385.4405
18 386.0424
13 303.8086
13 303.4335
13 303.5251
13 303.9723
13 305.5310
19 933.6511
21.4
0.4
2.4
0.3
21.8
21.4
22.6
4.6
2.6
23.2
0.0
0.1
20.1
0.1
0.0
0.5
18 503.0282
18 503.0781
18 503.3589
11 706.1714
11 705.7943
11 706.1854
11 707.1016
11 707.6650
0.9
21.9
1.5
20.9
0.7
1.7
20.9
21.8
17 534.9490
17 534.9463
17 535.1706
21.9
1.7
0.1
19 933.7310
0.3
12 628.8732
12 628.4974
12 628.5902
12 629.0370
12 630.5968
18 923.6401
18 923.5464
18 923.7194
0.2
0.0
20.4
20.1
0.2
2.5
22.0
20.6
experimental observations. These characteristics can be approximately attributed to a realistic angular anisotropy of the
BTT PES and to an equilibrium separation that is slightly too
large. Additional transitions of 20Ne–N2 and 22Ne–N2 were
then predicted by assuming the frequency differences from
the BTT potential relative to the tentatively assigned transitions. Detection of additional transitions relatively close to
the predictions confirmed the assignment. These further measurements and the final assignment were done at the University of Alberta. An example rotational transition of 20Ne–N2
showing its nuclear hyperfine structure is given in Fig. 1.
Altogether, seven a-type transitions with J quantum
number ranging from 0 to 3, and K a quantum number from 0
to 1, were measured for 20Ne– 14N2 and for 22Ne– 14N2. The
assignments were further confirmed by the nuclear quadrupole hyperfine structures observed for these two 14N2 isotopomers. The measured frequencies and quantum number assignments for 20Ne– 14N2 and for 22Ne– 14N2 are listed in
Table I. The assigned quantum numbers correspond to the
coupling scheme I5I1 1I2 and F5I1J, with I1 and I2 being the nuclear spins of the two 14N nuclei and J the overall
rotational angular momentum of the complex. The line positions corresponding to the centers-of-gravity of the quadrupolar hyperfine multiplets for the Ne– 14N2 isotopomers, designated by n center , are listed in Table II together with their
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5424
Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
TABLE II. Microwave center frequencies for Ne– 14N2 isotopomers.
20
22
14
Ne– N2
14
Ne– N2
J K8 8 K 8 – J K9 9 K 9
n center
~MHz!
D n center
~kHz!
n center
~MHz!
D n center
~MHz!
1 01 – 0 00
2 02 – 1 01
3 03 – 2 02
2 12 – 1 11
3 13 – 2 12
2 11 – 1 10
3 12 – 2 11
6505.6829
13 002.6339
19 481.8742
12 272.4929
18 383.9840
13 302.6130
19 933.5179
4.3
23.5
0.9
0.0
0.0
0.0
0.0
6178.0346
12 348.3141
18 502.8537
11 704.3465
17 534.8550
12 627.6770
18 923.5092
5.1
24.1
1.0
0.0
0.0
0.0
0.0
a c
a c
TABLE III. Observed frequencies of the
ture of 20Ne– 15N2.
J K8 8 K 8 – J K9 9 K 9
a c
a c
2 12 – 1 11
2 11 – 1 10
1–0
1–1
1–2
1–2
1–0
1–1
1–2
1–2
1
1
1
1
1
1
1
1
N spin-rotation hyperfine struc-
n center
~MHz!
n obs
~MHz!
D n HFS
~kHz!
11 973.2707
11 973.2615
11 973.2634
11 973.2717
11 973.2861
12 964.2197
12 964.2249
12 964.2347
12 964.2428
0.9
20.5
22.3
2.0
20.7
1.1
0.8
21.2
F 8I 8 – F 9I 9
1
2
3
2
1
2
3
2
15
12 964.2305
TABLE IV. Rotational transition frequencies for 20Ne– 15N2 and 22Ne– 15N2.
22
20
Ne– 15N2
J K8 8 K 8 – J K9 9 K 9
n ~MHz!
Dn ~kHz!
n ~MHz!
Dn ~kHz!
1 01 – 0 00
2 02 – 1 01
2 12 – 1 11
2 11 – 1 10
3 03 – 2 02
3 13 – 2 12
3 12 – 2 11
4 04 – 3 03
4 14 – 3 13
4 13 – 3 12
6343.3425
12 677.9315
11 973.2707a
12 964.2305a
18 994.9171
17 935.5755
19 425.5347
25 285.2489
23 868.4412
25 861.6110
20.8
0.7
20.4
0.4
20.3
0.4
20.5
0.0
20.1
0.1
6014.8171
12 021.8218
11 401.8835
12 287.4295
18 013.1168
17 080.3709
18 412.6450
23 980.6324
22 731.6848
24 515.4554
20.5
0.6
1.9
22.0
20.3
22.2
2.3
0.1
0.7
20.7
a c
a
Ne– 15N2
a c
Frequencies obtained from an analysis of the
components in Table III.
15
N spin-rotation hyperfine
~experimental! uncertainties d n center . These are the primary
quantities which are compared with the calculations from the
potential surfaces. Tables III and IV give the corresponding
information for the spin-rotation hyperfine multiplets and
line centers for the Ne– 15N2 isotopomers.
A first-order nuclear quadrupole coupling program,
which includes the spin-rotation interaction, was used to fit
nuclear quadrupole coupling constants, a spin-rotation constant, and hypothetical unsplit center frequencies to the observed hyperfine frequencies. It was found, however, that a
simultaneous fit including all observed hyperfine components led to an unacceptably large standard deviation of the
fit ~44 kHz!, far outside the experimental measurement uncertainty. Instead, three individual hyperfine fits were performed, one for the energy level stack with K a 50, and one
each for the upper and lower K a 51 stacks. The standard
deviation decreased to about 1 to 3 kHz. Similar behavior
was found previously in the rotational spectra of Ar–N2
~Ref. 1! and Kr–N2 ~Ref. 3!. It was noted that the fit for the
lower K a 51 stack was slightly worse than for the others, as
was also observed for Ar–N2 and Kr–N2.
The hypothetical unsplit center frequencies were used as
input for a fitting procedure to obtain rotational and centrifugal distortion constants. The Watson A-reduction Hamiltonian in its I r representation29 was used in this procedure.
Since only a-type transitions were measured, and the complex is a near symmetric top, it was not possible to determine
the A rotational constant and the quartic distortion constants
D K and d K . An approximate value for the A rotational constant of Ne–N2 was obtained from the results of the nuclear
hyperfine structure analysis as outlined below. The resulting
rotational and distortion constants are listed in Table V and
the nuclear hyperfine structure constants are given in Table
VI.
The search for isotopomers with 15N2 followed the procedure described previously2 for Ar– 15N2. The frequencies
of the K a 50 transitions were predicted by extrapolation
from Ne– 14N2 using a pseudo-diatomic approach, and the
K a 51 transitions were predicted by superimposing the separations between the K a 50 and K a 51 transitions calculated
from the BTT PES. Transitions of isotopomers containing
15
N2 were stronger than those of 14N2 isotopomers, mainly
because of the absence of nuclear quadrupole hyperfine
structure, and were readily found. For the 20Ne– 15N2 isoto-
TABLE V. Rotational and centrifugal distortion constants ~in MHz! of Ne–N2 complexes.
Constant
Aa
B
C
DJ
D JK
d1
HJ
H JK
s ~kHz!b
20
Ne– 14N2
Ne– 14N2
22
69 778.
3510.5628~31!
2996.9450~31!
0.26374~10!
53.5173~20!
0.035 152~88!
69 676.
3319.9564~6!
2859.8446~6!
0.248 006~19!
45.290 08~39!
0.038 720~17!
20.107 52(13)
4.1
20.093 224(26)
0.8
20
Ne– 15N2
65 212.
3419.406~16!
2924.871~16!
0.2389~11!
52.1846~9 3!
0.02949~22!
20.000 026(34)
20.106 14(36)
30.0
22
Ne– 15N2
65 112.
3228.705~12!
2786.996~12!
0.225 21~86!
44.1514~74!
0.033 17~17!
20.000 031(27)
20.091 06(29)
23.8
Fixed at the values determined from the hyperfine structure analysis ~see text!.
Standard deviation of the fit.
a
b
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
5425
TABLE VI. Nuclear quadrupole coupling constants and spin-rotation constants ~in MHz! of Ne–N2 complexes.
Complex
20
14
Ne– N2
22
Ne– 14N2
20
Ne– 15N2
Constant
K a 50
x aa
x bb
x cc
M aa
x aa
x bb
x cc
M aa
M aa
1.1760~4!
22.072(59)
0.8969~59!
–
1.1834~6!
22.188(90)
1.005~90!
–
–
pomer, narrow spin-rotation splittings were detected for low
J transitions (J52-1) with K a 51, while no splittings were
observed for higher J transitions. An example transition of
20
Ne– 15N2 is depicted in Fig. 2, showing the narrow spinrotation hyperfine structure. The transition intensities of
22
Ne– 15N2 were too low to allow such narrow spin-rotation
splittings to be resolved. Since the observed linewidths are of
the order of 7 kHz and the narrow splittings are of the order
of 5 to 15 kHz, direct time domain data analyses19 were
performed in order to obtain the frequency information. The
frequencies of the hyperfine components thus obtained are
listed in Table III, together with the corresponding quantum
number assignments. The resulting spin-rotation constant
M aa is given in Table VI. Altogether, ten transitions were
measured for both 20Ne– 15N2 and 22Ne– 15N2, with J ranging
from 0 to 4, and K a having values of 0 and 1. For the
Ne– 15N2 isotopomers, the rotational frequencies are listed in
Table IV, and the resultant rotational and distortion constants
are listed in Table V.
B. Discussion of the experimental results
Both Ne– 14N2 and Ne– 15N2 spectra are consistent with
those of two equivalent nitrogen atoms in the complexes.
The intensities for the K a 51 transitions in both cases were
observed to be similar to those of the corresponding K a 50
transitions, despite the fact that the K a 51 rotational levels
are about 2 cm21 higher in energy than the K a 50 levels.
FIG. 2. A composite spectrum of the J K a ,K c 52 1,1 – 1 1,0 rotational transition
of 20Ne– 15N2, showing spin-rotation hyperfine structure due to the 15N nuclei.
Lower K a 51
Upper K a 51
1.5296~64!
1.5209~14!
24.4203(53)
24.2076(12)
2.8907~53!
2.6867~12!
0.0175~36!
0.0150~7!
1.5317~47!
1.5237~45!
24.4118(40)
24.2104(38)
2.8801~40!
2.6867~38!
0.0153~23!
0.0152~22!
20.0202(13)
This observation can be attributed to the effects of spin statistics, as has been argued previously.3 Since spin conversion
is not allowed in a molecular beam expansion, rotational
levels with even and odd K a cool individually, with the consequence that both the K a 50 and K a 51 stacks are populated in the cold molecular expansion (T rot,1K).
Nuclear quadrupole coupling constants of rare gas
atom–linear molecule complexes have in the past often been
interpreted in terms of projections of the quadrupole coupling constants of the linear monomer onto the principal inertial axes of the complexes. The underlying assumption is
that the complex formation causes only negligible perturbation of the electronic structure at the site of the quadrupolar
nucleus. Such a relationship is described by x gg
5 21 x mon^ 3 cos2 ug21&, with g5a, b, c; the x gg are the coupling constants of the complex, x mon is the coupling constant
of the monomer, and u g is the angle between the axis of the
linear molecule and the g principal axis of the complex.
Ernesti and Hutson30,31 have recently emphasized the importance of the correct choice of axis system in interpreting and
relating spectroscopic parameters. They pointed out, in particular, that the nuclear quadrupole coupling constants depend upon an angle u g between the monomer axis and the g
internal axis of the Eckart axis system ~which effects a separation of the rotational and vibrational motion!.32 The following values for ^ cos2 ua& ~corresponding to ^ cos2 bEck& in
Ref. 31! were obtained using the above relation: 0.1869
~K a 50 stack!, 0.1436 ~lower K a 51 stack!, and 0.1446 ~upper K a 51 stack!. In calculating these values from the quadrupole coupling constants, the best value for x cc , namely
2.6867 MHz from the upper K a 51 fit, was taken in each
case ~see discussion below!. Values for the rotational constants A in Table V were calculated using Eq. ~9! and the
lower Eq. ~12! in Ref. 31, and the relevant approximations,
together with the corresponding B 0 rotational constant of the
14
N2 (B 0 559 645.93 MHz) or 15N2 (B 0 555 691.76 MHz!33
monomer. The ^ cos2 ua& values from the upper K a 51 stack
were used in the calculations. The A constants were fixed at
the calculated values during the rotational fitting procedures.
The K a -dependence of the nuclear quadrupole coupling
constants of Van der Waals molecules has recently been investigated theoretically by Hutson,5 who calculated the
nuclear quadrupole coupling constants by including explicitly the dependence of the electric field gradient tensor upon
the large-amplitude Van der Waals motions. It was established that x aa is indeed K a -dependent, which supports the
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5426
Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
TABLE VII. Ab initio Ne–N2 and NeN potential energies ~in m E h ).
R/Å
u 50°
22.5°
45°
67.5°
90°
V NeN
V NeNa
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
5.00
5.50
6.00
8.00
10.00
36 923.3
13 160.0
4369.4
1253.8
221.9
274.4
2129.4
2115.5
289.1
247.4
225.3
214.3
22.3
20.6
27991.9
9922.9
3220.1
860.3
97.3
2107.3
2133.7
13 726.7
4654.3
1345.9
230.9
291.3
2149.2
2131.8
6085.7
1830.3
366.1
273.9
2164.4
2151.4
2117.2
4154.3
1133.6
137.3
2135.5
2171.8
2144.7
2109.0
2724.0
753.1
107.6
270.9
298.4
284.5
264.3
2554.8
668.3
61.0
299.3
2116.5
296.2
271.5
284.8
244.8
273.8
238.6
262.0
232.5
257.1
230.5
233.9
217.8
236.7
219.1
213.5
22.1
20.7
212.0
21.9
20.5
210.4
21.9
20.5
29.9
21.7
20.5
25.6
20.8
20.0
26.1
21.0
20.1
a
With aug-cc-pVQZ basis set.
use of different values in evaluations of experimental data.
For energy levels with K a 50, xaa was also found to be
slightly J-dependent, proportional to J(J11). In the present
experimental analyses, however, the J-dependence was sufficiently weak that it could be neglected. An even stronger
J-dependence, not simply linear in J(J11), of the quadrupole coupling constants was found for energy levels with
K a 51. The necessity of using separate fits for upper and
lower K a 51 stacks is a result of this peculiar J-dependence.
In the present work, it was possible to use a combined fit for
all observed K a 51 hyperfine components by including centrifugal distortion terms for the nuclear quadrupole coupling
constants that are proportional to J(J11) and to J 2 (J
11) 2 . However, it is then not clear how the resulting constants can be interpreted in terms of physical properties of
the complexes. Instead, the procedure of determining three
individual fits was retained. As was pointed out in Ref. 5, the
J K a ,K c 51 1,0 level depends only upon x cc , and has the largest hyperfine splittings within the upper K a 51 stack. The
value of x cc resulting from the upper K a 51 fit was therefore
taken to be the value least influenced by centrifugal distortion effects. Since x cc is expected to be independent of the
large-amplitude motions, it is determined by x cc 52 21 x mon ,
in which x mon is the nuclear quadrupole coupling constant of
free N2. The procedure is validated by the corresponding
values of x cc from the MW spectra of Ar–N2 and Kr–N2
that agree, within mutual error limits, with the values found
here. Averaging of all available data yields a N2 monomer
coupling constant x mon525.372~2! MHz.
The standard deviation of the rotational fit for the
20
Ne– 14N2 isotopomer is about 4.1 kHz, considerably larger
than the accuracy of the experimental frequencies. Even
larger standard deviations ~see Table V! were obtained for
isotopomers containing 15N2, for which three additional
higher J transitions could be measured. The introduction of
additional distortion constants caused very high correlations
(.0.999) between some of the constants. This reflects the
rather floppy nature of the complex and a possible breakdown of the semi-rigid rotor model employed here to fit the
data.
C. Potential energy surfaces
The Ne–N2 potential energy surface has been calculated
at 12–14 separations between 2.5 and 10 Å for 5 angles
between 0° and 90° ~see Table VII! using the aug-cc-pVTZ
basis set. Fixed-angle cuts of the PES are plotted in Fig. 3.
Prior to taking the BSSE into account, the PES has two distinct wells, one corresponding to C 2 v geometry, the other
corresponding to linear geometry. The shallower well for the
linear geometry is removed on making the BSSE correction,
leaving only the minimum for the T-shaped geometry. The
behavior for Ne–N2 is similar to that found earlier11 for
Ar–N2. Thus, the ab initio results confirm the PES topology
obtained previously by both empirical6,9 and semiempirical7,8
methods. However, the dissociation energy D e for the equilibrium T-shaped configuration is smaller by 30%–50% in
comparison with earlier values ~see Table VIII!, and the
equilibrium distance R e is 2%–12% longer. At the saddle
point occurring for the linear configuration, both D e and R e
lie between the values obtained previously. The calculated
difference DD e between the two stationary points is 2–5
FIG. 3. Cuts of the Ne–N2 ground state potential energy surface at different
polar angles ~from 0° to 90° with a step size of 22.5° from right to left! for
the Ne atom relative to the center of N2: ab initio data ~symbols! and
predictions of the model ~curves! using the effective NeN potentials determined from cuts at 0°, 90°, and 45°.
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
5427
TABLE VIII. Binding parameters of the Ne–N2 potential at the stationary points.
C ` v (0°)
Reference
C 2 v (90°)
D e /meV
R e /Å
D e /meV
R e /Å
3.53
4.07
4.02
3.97
4.72
5.41
3.45
3.42
3.56
4.23
4.14
4.12
2.60
4.84
2.60
3.97
3.93
3.98
3.87
4.12
3.90
4.15
5.37
6.46
5.76
6.70
7.30
6.20
6.70
3.43
3.38
3.40
3.27
3.26
3.38
3.06
Present ab initio:
• with aug-cc-pVTZ basis set
• with aug-cc-pVQZ basis set
Model using ab initio NeN potentials:
• with aug-cc-pVTZ basis set
• with aug-cc-pVQZ basis set
Model using corrected NeN potentials
Ling, Mehrvarz, Rigbya
McCourt et al.b
BTTc
ESMSVd
a
Reference 6.
Reference 7.
c
Reference 8.
d
Reference 9.
b
times smaller than the previous results, while DR e varies
from having nearly the same value to having a value twice as
large as previous results. Thus, as for the Ar–N2 system, the
ab initio PES has a smaller anisotropy. The Ne–N2 binding
is about twice as weak as that for the argon complex, with,
accordingly, about 2.5 times smaller DD e , while the equilibrium distance is about 0.3–0.4 Å shorter, and DR e is
nearly the same as for Ar–N2. Similar relations between the
D e , R e , and DR e values for the neon and argon complexes
are also obtained for the earlier potential surfaces; the DD e
values, however, vary from a slightly larger relative value7
for Ne–N2 to a nearly fourfold larger relative value8 for
Ar–N2. These trends are in line with the recent ab initio
results14 for He–N2, which has an even smaller value of
DD e , but nearly the same value of DR e .
The effective V i and V' potentials obtained by applying
the model of Sec. III to the ab initio PES are shown in Fig.
4, where they are also compared with the ab initio NeN
potential calculated at the same level of theory. The Ne–N
interaction along the N–N axis deviates from that for isolated NeN rather weakly, being slightly more attractive at
intermediate distances and more repulsive at short distances.
The latter feature corresponds to what would be expected
from sp-hybridization of the N atom, accompanied by extension of the electron density along the axis, although it differs
from the argon counterpart,11 in that the associated change of
D e is very small ~see Table IX!. The Ne–N interaction in the
perpendicular direction becomes significantly less attractive
at intermediate distances, but almost preserves the value of
R e ; this is similar to the behavior of the ArN interaction.
These relations are reflected in the model Ne–N2 potential
surface obtained with the ab initio NeN potential: the major
deviation from the ab initio Ne–N2 data is an overestimation
of the binding for the T-shaped geometry ~see Table VIII!.
Using the model with the effective V i and V' potentials
results in an underestimation of the binding at intermediate
angles, with the strongest deviation occurring at 45°. This
means that the effective Ne–N interaction in this direction is
different from that supplied by the model. Using a 3-cut
version of the model, with switching angle u s 545°, a new
V'45° is obtained. It closely resembles the unperturbed NeN
potential, with only slightly reduced repulsion at short and
intermediate distances ~see Fig. 4!. The situation for the
Ar–N interaction is basically similar,11 though the ~also
small! deviations for the new potential are of the opposite
sign. When the 3-cut version of the model is employed, the
remaining cuts of the Ne–N2 PES at 22.5° and 67.5° are
reproduced sufficiently accurately ~see Fig. 3! that further
improvements are unnecessary.
Two of the available Ne–N2 PES7,9 have smaller values
TABLE IX. Equilibrium parameters of NeN.
Vi
Reference
FIG. 4. Comparison of the ab initio NeN potential ~symbols! with the effective Ne–N interactions determined from cuts of the Ne–N2 PES at 0°
~solid curves!, 90° ~dot-dashed!, and 45° ~dashed!.
ab initio:
• with aug-cc-pVTZ basis set
• with aug-cc-pVQZ basis set
Derived from NeN2:
• with aug-cc-pVTZ basis set
• Correcteda
a
V'
D e /meV
R e /Å
2.69
3.23
3.47
3.42
2.70
3.19
3.53
3.48
D e /meV
R e /Å
2.35
2.87
3.49
3.44
Equation ~4!.
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5428
Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
of D e and larger values of R e for the linear geometry than
have been obtained from the ab initio calculations ~see Table
VIII!. Because a further increase in the accuracy of the calculations can be expected to make D e larger and R e smaller
at any angle, these two potential surfaces are likely inaccurate. The other two available potential surfaces6,8 are consistent with this expected trend, and their equilibrium parameters for both stationary points are in better agreement with
the present ab initio results.
Limited calculations have been carried out with a more
extensive, aug-cc-pVQZ, basis set in order to verify the
above expectations. Both the NeN potential and cuts of the
Ne–N2 PES for the linear and T-shaped geometries so obtained show increased binding energies and shortened equilibrium distances, with the values for Ne–N2 approaching
the preferred empirical/semiempirical data6,8 ~see Table VIII!
even more closely. The DR e value remains almost unchanged, while the DD e value increases significantly ~because D e for the T-shaped configuration is approximately
double that for NeN!, now nearly coinciding with the semiempirical BTT8 values. An analogous result has been
obtained14 for the He–N2 system. Such a modification is
similar to that for the Ar–N2 system,11 but with a DD e value
significantly smaller than that obtained from the empirical
PES. The calculated value of D e for the linear configuration
of Ar–N2 exceeds the empirical value. Although the new ab
initio Ne–N2 PES correlates well to the BTT potential surface, it is worth noting that more accurate calculations can be
expected to increase DD e , possibly giving rise to an anisotropy exceeding that for the BTT PES. The empirical PES of
Ref. 6 has a larger value of DD e , but has a value of D e for
the linear configuration that nearly coincides with the present
ab initio value; this value can be expected to be exceeded
when still higher-level calculations are employed.
It is desirable to evaluate the full Ne–N2 PES at the
higher accuracy achieved for the two cuts. One means of
accomplishing this has been utilized12 for the Ar–Cl2 PES by
transferring the influence of the electronic structure distortions of the Cl atoms within the Cl2 molecule, evaluated ab
initio, to the empirical ArCl potentials. This procedure allowed for nearly exact agreement with the available experimental data for the total system. An analogous correction can
be applied to the purely ab initio data, by using the correspondence
new
V new
i ,' 'V NeN1 ~ V i ,' 2V NeN ! ,
FIG. 5. Comparison ~in the linear and T-shaped geometries! of the ab initio
results for Ne–N2 obtained using the larger basis set ~symbols! with predictions made in terms of ab initio NeN data calculated at a similar level of
accuracy, and then corrected for the distortions of N within N2 as evaluated
using the smaller basis set.
the more extensive basis set is employed. This can be seen
explicitly by comparing the model predictions using the
more accurate ab initio NeN potential to the corresponding
ab initio results for Ne–N2 ~see Table VIII!. Because the
Ne–N ~and hence Ne–N2) binding energy for the T-shaped
geometry is reduced by this perturbation, it can be overestimated when it is evaluated with a smaller basis set. Nevertheless, as a further increase of accuracy should provide
stronger binding, the above deviations can be accepted, thus
allowing expensive additional higher accuracy computations
for many geometries to be avoided. The topologies of the
four model PES, shown in Fig. 6, illustrate the transfer of
modifications from the lower level to the higher-level results.
D. Simulated microwave spectra
The final ~corrected! version of the ab initio Ne–N2 PES
has been used to calculate the rotational levels up to J54 of
the complex in its ground vibrational state ( v 50) and to
~4!
new
in which V NeN
means the NeN ab initio potential of higher
accuracy. This formula assumes that the influence of the perturbation of the electronic structure of N within N2 is similar
for both basis sets employed. The results of applying this
modification to the Ne–N2 PES are compared in Fig. 5 with
direct ab initio calculations for the two geometries. It can be
seen that the more accurate atom–diatom data are reproduced with sufficient accuracy, with the remaining deviations being a slight overestimate of the binding energy
~mostly for the T-shaped geometry! and an underestimate of
the equilibrium distance ~see Table VIII!. These small differences can be explained in terms of the larger effect of the
perturbation of N within N2 on the Ne–N2 interaction when
FIG. 6. Comparison of the topologies of the Ne–N2 PES predicted by the
model using: the ab initio NeN potential obtained with the smaller ~lower
left! and the larger basis set ~lower right!; the effective Ne–N interactions
determined from calculations with the smaller basis set for Ne–N2 at 3 cuts
~upper left!; the ab initio NeN potential obtained with the larger basis set
and corrected for the intramolecular perturbations of N within N2 obtained
with the smaller basis set ~upper right!.
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
5429
TABLE X. Ne–N2 ( v 50) microwave spectra ~frequencies in MHz! for different potentials.
Isotopomer
J K8 8 K 8 – J K9 9 K 9
Experimental
Ab initio
Adjusteda
BTTb
ESMSVc
1 01 – 0 00
6506.454
2 02 – 1 01
13 003.574
3 03 – 2 02
19 481.921
6362.699
(22.21%)
12 715.780
(22.21%)
19 049.500
(22.20%)
4 04 – 3 03
2 12 – 1 11
12 274.323
3 13 – 2 12
18 385.217
4 14 – 3 13
2 11 – 1 10
13 303.809
3 12 – 2 11
19 933.651
4 13 – 3 12
1 01 – 0 00
6178.810
2 02 – 1 01
12 349.261
3 03 – 2 02
18 502.903
4 04 – 3 03
2 12 – 1 11
11 706.171
3 13 – 2 12
17 534.949
4 14 – 3 13
2 11 – 1 10
12 628.873
3 12 – 2 11
18 923.640
6506.009
(20.007%)
13 001.835
(20.013%)
19 477.160
(20.024%)
25 921.392
12 268.628
(20.046%)
18 375.060
(20.055%)
24 447.725
13 304.194
(10.003%)
19 932.117
(20.008%)
26 530.691
6179.260
(10.007%)
12 349.411
(10.001%)
18 501.229
(20.009%)
24 625.258
11 702.738
(20.029%)
17 528.349
(20.038%)
23 322.776
12 630.925
(10.016%)
18 924.854
(10.006%)
25 192.661
6486.384
(20.31%)
12 963.294
(20.31%)
19 421.137
(20.31%)
25 850.079
12 240.024
(20.28%)
18 332.685
(20.29%)
24 392.289
13 268.717
(20.28%)
19 880.760
(20.27%)
26 465.730
6160.184
(20.30%)
12 311.882
(20.30%)
18 446.508
(20.30%)
24 555.272
11 674.648
(20.27%)
17 468.703
(20.38%)
23 268.210
12 596.599
(20.26%)
18 875.008
(20.26%)
25 129.304
6331.014
(22.7%)
12 654.265
(22.7%)
18 961.921
(22.7%)
25 246.002
12 258.856
(20.13%)
18 369.726
(20.094%)
24 458.078
12 867.205
(23.3%)
19 281.616
(23.3%)
25 672.779
6012.654
(22.7%)
12 018.393
(22.7%)
18 010.241
(22.7%)
23 981.098
11 666.483
(20.34%)
17 483.049
(20.30%)
23 279.396
12 213.176
(23.3%)
18 302.663
(23.3%)
24 371.446
a c
Ne14N2
20
22
Ne14N2
a c
12 006.320
(22.18%)
17 983.177
(22.19%)
13 006.929
(22.23%)
19 487.563
(22.24%)
6042.796
(22.20%)
12 076.987
(22.21%)
18 093.864
(22.21%)
11 451.321
(22.18%)
17 152.678
(22.18%)
12 348.128
(22.22%)
18 501.854
(22.23%)
4 13 – 3 12
For the modified ab initio potential ~radially compressed by 1.2%!.
Reference 8.
c
Reference 9.
a
b
obtain the associated MW spectra of 20Ne– 14N2, 20Ne– 15N2,
22
Ne– 14N2, and 22Ne– 15N2. For all isotopomers the predicted line positions underestimate the measured values uniformly by about 2.2% ~see Table X for 14N2, with results for
15
N2 being very similar!. To eliminate this discrepancy, the
V i ,' components of the the potential surface have been radially compressed by about 1.2% to fit the J 8 -J 9 51-0 and 2-1
transitions. The experimental information, including the
available J 8 -J 9 53-2 transition frequencies not used in the
fit, is reproduced within 60.05%, or within at most
65 MHz by the modified PES. In turn, predictions for the
4-3 transitions have been used to identify the experimentally
detected higher frequency MW lines, which have been located within 0.07%, or at most 10 MHz, of their predicted
positions.
The dissociation energy for the 20Ne– 14N2( v 50) complex is calculated to be D 0 53.55 meV (28.6 cm21), resulting in the zero point energy E 0 5D e 2D 0 52.21 meV
(17.8 cm21). As this value exceeds the energy difference
DD e 51.62 meV (13.1 cm21) between the bottom of the potential well in the T-shaped configuration and the saddle
point in the linear configuration, it appears that the Ne atom
can also revolve rather freely in the plane of the N2 mol-
ecule. Nonetheless, the pattern of the MW spectrum ~triplets
of closely spaced lines! remains typical of a T-shaped triatomic, which thus suggests a sensitivity of the rovibrational
wavefunction of the complex to the topology of the PES.
This is confirmed by the concentration of the calculated
probability density distribution around the T-shaped Ne–N2
configuration ~see Fig. 7!. An analogous result has been
obtained34 for the ArC2 complex, which has a preferred linear configuration and a ~predicted! MW spectrum consisting
of doublets of closely spaced lines. The same behavior is
found for the other three isotopomers, 22Ne– 14N2,
20
Ne– 15N2, and 22Ne– 15N2, with D 0 values 3.59, 3.58, 3.62
meV, and E 0 values 2.17, 2.18, 2.14 meV, respectively.
MW spectra have been calculated also for the BTT8 and
ESMSV9 potential surfaces. While the BTT surface gives
relatively uniform deviations between the predicted and measured MW line positions, the ESMSV surface gives rather
irregular behavior with respect to different groups of lines
~see Table X!. It has not been found possible to adjust the
ESMSV PES by a simple radial change, although it might be
possible to adjust the BTT PES in this way. As has been
mentioned earlier, calculations made with the BTT surface
were initially used to identify the experimentally observed
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5430
Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
FIG. 7. Contour diagram of the normalized probability density u C u 2 ~with C
being the ground state rovibrational wave function! for Ne–N2. Contours
are given for a step size of 0.1.
MW lines up to J 8 53. The variation in the deviations from
the measured line positions is about twice as large for the
BTT PES as it is for the ~unscaled! ab initio PES, and therefore at least the same ratio could be expected after adjustment. The result for the ESMSV PES suggests a possible
inadequacy in its representation of the Ne–N2 interaction.
The D 0 and E 0 values calculated for these two empirical
potential surfaces are similar to those for the ab initio PES
insofar as the localization of the Ne atom is concerned. For
the BTT PES, E 0 exceeds DD e , while for the ESMSV PES
they are nearly equal, presumably because of an overestimation of the anisotropy. The heavier isotopomers are found to
behave analogously to 20Ne– 14N2.
It is instructive to compare not only the MW line positions calculated from the potential surfaces with experiment,
but also the corresponding spectroscopic parameters. For this
purpose, rotational and centrifugal distortion constants were
derived by using the calculated line frequencies in fitting
procedures, analogous to those used for the experimental
data. The resulting constants for the 20Ne– 14N2 complex are
compiled in Table XI; the experimental results have been
repeated for ease of comparison. The complex can be approximated as a ~linear! pseudo-diatomic rotor and its spec-
trum can be described using the linear combination (B
1C)/2 and the centrifugal distortion constant D J . The quantity (B1C)/2 corresponds to an effective pseudo-diatomic
separation, while D J provides a measure of the anisotropy of
the PES. For the full Ne–N2 PES D J is determined primarily
by the radial anisotropy. The values of D J in Table XI indicate that all the potential surfaces have radial anisotropies
that are comparable and in accord with the experimental MW
spectrum. A major effect of the scaling procedure for the ab
initio potential is a reduction of the equilibrium separation,
as reflected in the improved value for (B1C)/2.
In this simple picture the linear combination B2C and
the distortion constant D JK are determined by the deviation
from linearity of the complex, i.e., by the extent of the largeamplitude bending motion. The best agreement for B2C and
D JK is found for the adjusted ab initio surface, indicating a
realistic angular anisotropy of this surface. However, the
BTT surface also does remarkably well in this respect. It was
in fact this feature of the BTT PES that made the initial
assignment of the Ne–N2 rotational spectrum possible. The
ESMSV surface produces values for B2C and D JK that are
too small by up to 57%, indicating that it has too great an
anisotropy in the angular coordinate. It is remarkable that
two further distortion constants, i.e., d 1 and the sextic constant H JK , are quite well reproduced by the ab initio and the
BTT surfaces, whereas there is poor agreement for the
ESMSV surface.
The good quality of the ab initio PES in terms of its
angular anisotropy is also apparent when comparing the expectation values ^ cos2 ua& obtained from this surface, 0.1803
(J K a ,K c 50 0,0), 0.1362 (J K a ,K c 51 1,1), and 0.1363 (J K a ,K c
51 1,0), with the values ~0.1869, 0.1436, and 0.1446, respectively! derived from the experimental quadrupole coupling
constants ~see Sec. IV B!. The deviations are at most about
6%. Averaging has been carried out with the ground state
rovibrational wave function ~obtained using the TRIATOM
code! and the relation
cos2 u a 5
1
112 d sin u 1 d 2
cos2 u ,
~5!
which can be deduced, within the formalism of Ref. 30, for a
TABLE XI. Rotational and centrifugal distortion constants ~in MHz! of
various potentials.
20
Ne– 14N2 from experiment and from
Constant
Experiment
Ab initio
Adjusteda
BTTb
ESMSVc
Ad
B
C
(B1C)/2
B2C
DJ
D JK
d1
H JK
69778.
3510.563
2996.945
3253.754
513.618
0.2637
53.517
0.0352
20.1075
69778.
3431.605
2932.229
3181.917
499.376
0.2831
52.223
0.0290
20.0966
69778.
3511.997
2995.206
3253.602
516.791
0.2981
53.783
0.0310
20.1039
69778.
3500.231
2987.231
3243.731
513.001
0.2699
52.079
0.0421
20.1126
69778.
3318.244
3013.901
3166.072
304.343
0.2808
22.885
20.0053
20.0229
For the modified ab initio potential ~radially compressed by 1.2%!.
Reference 8.
c
Reference 9.
d
Fixed at a value determined from the hyperfine structure analysis ~see text!.
a
b
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Jäger et al.
J. Chem. Phys., Vol. 109, No. 13, 1 October 1998
system having a T-shaped equilibrium configuration. The
quantity d is given in terms of the moments-of-inertia by
d (R)5I N2 / AI Ne–N2(R)I Ne–N2(R e ). Thus, in the present calculations we have determined ^ cos2 ua& directly by averaging
Eq. ~5!. For small-amplitude motions, for which d ' d 0
5I N2 /I Ne–N2(R e ), and accordingly sin u'1, relation ~5! reproduces the approximate formula30 ^ cos2 ua&'@1/(1
1 d 0 ) 2 # ^ cos2 u&. For (J K a ,K c 50 0,0) this approximation gives
the value ^ cos2 ua&50.1749; the approximate relation thus
gives a deviation from the experimental value twice as large
as that found when the full expression is used. The reason for
such a considerable difference between the two calculated
values is that the Ne atom is significantly delocalized, so that
the probability density for the linear configuration has about
40% of its value for the T-shaped configuration ~see Fig. 7!:
this invalidates the small-amplitude approximation. The corresponding values 0.1616 and 0.1135 of ^ cos2 ua& for the
BTT and ESMSV PES, respectively, show even larger deviations from the experimental value.
V. CONCLUSIONS
Rotational spectra of four isotopomers of Ne–N2 were
measured using a FTMW spectrometer. The initial assignment and the detection of further rotational transitions were
made possible by comparison with theoretical MW spectra,
calculated from potential surfaces. Nuclear quadrupole hyperfine splittings and spin-rotation splittings have been observed for isotopomers containing both 14N2 and 15N2. The
spectra are in accord with a T-shaped equilibrium configuration of the complex with two equivalent nitrogen atoms. The
results from the nuclear quadrupole hyperfine structure
analyses and the large number of quartic and sextic centrifugal distortion constants needed in the rotational analyses indicate that the complex exhibits large-amplitude vibrational
motions.
A high-level ab initio PES of the Ne–N2 complex has
been calculated for the first time, and compared with existing
empirical and semiempirical potential surfaces.6–9 The single
minimum occurring for the T-shaped configuration for each
of these potential surfaces has been confirmed by the ab
initio results. A secondary minimum for the linear configuration is removed by the basis set superposition error correction. Direct comparison with the present ab initio results allows a preliminary selection to be made of the empirical PES
with energies no higher than the ab initio data. In particular,
the ESMSV9 PES is too shallow for the linear geometry, and
it thereby provides too strong an anisotropy for the binding
energy. The BTT8 PES appears to be quite reliable in this
respect, providing an anisotropy in the binding energy that is
close to that obtained from the present ab initio PES. It
should be noted, however, that an increase in the accuracy of
the ab initio calculations may result in a further increase in
the anisotropy. Such an increase in the anisotropy could possibly reduce the agreement between the calculated and experimental MW line positions.
The effective potential describing the interaction of a Ne
atom with a N atom within the N2 molecule, and corresponding to the ab initio Ne–N2 PES, is found to differ from the
5431
diatomic ab initio NeN potential, the deviation being stronger in the direction perpendicular to the N–N axis than along
it, as has been found11 also for Ar–N2. Such a behavior can,
in general, be associated with an electron density redistribution due to sp-hybridization of the N atom. The generally
smaller deviations ~by comparison to those for the argon
system! can be assigned to a weaker interaction. On the basis
of these perturbed NeN potentials, a simple correction is proposed for improving the accuracy of the ab initio data for an
atom–diatom system, with higher-level results required only
for the ~one-dimensional! atom–atom components of the interaction. This procedure allows the construction of a more
accurate PES for the total system without additional
resource-consuming calculations.
An ab initio PES obtained in the manner described
above has been used to simulate the microwave spectra of
several Ne–N2 isotopomers, and to compare them with both
experimentally observed MW spectra and MW spectra predicted from two previous potential surfaces. This more detailed comparison confirms the preliminary selection made
on the basis of direct comparison of the surfaces. The ab
initio PES predicts MW line positions which deviate from
the experimental values in the most uniform manner among
the potential surfaces studied. The deviations can therefore
be reduced to within 0.05% by a simple single-parameter
scaling. The ESMSV PES shows rather irregular deviations
for different groups of the MW lines, so that no simple transformation can be expected to bring the predicted MW spectra
into comparable agreement with experiment. The situation is
more favorable for the BTT PES, which also exhibits fairly
uniform differences between the predicted and measured
MW line positions. The variation of the deviations for the
BTT surface is, however, nearly twice that for the ab initio
PES. The new adjusted PES, fitted to the lower frequency
transitions J 8 -J 9 51-0, 2-1 of the 20Ne– 14N2 complex, has
then been used to predict other transitions, including those
for other isotopomers.
The zero vibrational level is calculated to lie at an energy that is sufficiently high to allow essentially free rotation
of the Ne atom around the N2 molecule in the whole 3dimensional space. The rotational spectrum nonetheless corresponds to that typical of a T-shaped molecule, in accord
with the analogous behavior of the rovibrational wave function, even though it is relatively delocalized.
ACKNOWLEDGMENTS
This work has been supported by the Natural Sciences
and Engineering Research Council of Canada ~NSERC!
through grants-in-aid of research to W.J., M.C.L.G., and
F.R.W.M. F.N. thanks Professor R. J. Le Roy for partial
financial support. Y.X. thanks NSERC for a postdoctoral fellowship and the Izaak Walton Killam Trust for an honorary
postdoctoral fellowship.
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