JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 18
8 NOVEMBER 1999
Spectroscopic and theoretical characterization of linear
centrosymmetric NwN––Hⴙ ––NwN
Dorinel Verdes, Harold Linnartz,a) and John P. Maier
Institute for Physical Chemistry, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
Peter Botschwina and Rainer Oswald
Institut für Physikalische Chemie, Tammannstrasse 6, D-37077 Göttingen, Germany
Pavel Rosmus
Theoretical Chemistry Group, Université de Marne-la-Vallée, F-77454 Champs sur Marne, France
Peter J. Knowles
School of Chemistry, University of Birmingham, Birmingham, B15 2TT, United Kingdom
共Received 24 May 1999; accepted 18 August 1999兲
The first high resolution infrared spectrum of the ionic complex N2 ••H⫹ ••N2 and its deuterated
derivative is reported. The spectra were obtained in direct absorption in a supersonic slit nozzle
plasma. The observed rovibrational transitions were assigned to the ␯ 3 antisymmetric NN stretching
vibration and the spectrum is consistent with a linear centrosymmetric equilibrium structure. The
band origin is found at 2352.2364共6兲 cm⫺1 and the ground state rotational constant is determined
as B ⬙ ⫽0.081 809(14) cm⫺1 . The assignment is supported by ab initio calculations including
electron correlation effects. The best estimate for the equilibrium structure is R e 共NN兲⫽1.095 Å and
r e 共N••H兲⫽1.277 Å. The transition moment of the ␯ 3 band of N2 ••H⫹ ••N2 is predicted to be 0.21
D, an order of magnitude larger than for the NN stretching vibration of HN⫹
2 . The equilibrium
is
calculated
to
be ⬃5900 cm⫺1 .
dissociation energy D e for fragmentation into N2 and HN⫹
2
© 1999 American Institute of Physics. 关S0021-9606共99兲01342-2兴
INTRODUCTION
assignment of the observed spectra and provide additional
information currently not accessible to experiment, like predictions of the equilibrium bond lengths, the transition moment of the ␯ 3 band, the harmonic wave number of the lowest bending vibration and the equilibrium dissociation
energy.
Proton bound complexes are involved in a variety
of chemical processes, but high resolution spectra of such
species are still scarce. Only for Ar•••H⫹
3 共Ref. 1兲 and
Ar•••HCO⫹ 共Ref. 2兲 detailed submillimeter and microwave
studies have been reported. While lower resolution predissociation infrared spectra could be obtained for a variety of
ionic complexes,3 IR spectra with a resolution better than
0.002 cm⫺1 are currently available only for Ar•••HN⫹
2
共Ref. 4兲 and Ar•••HCO⫹ . 5 These were investigated by
direct absorption techniques in a supersonic slit nozzle
plasma. Such an approach meets the principal conditions required for the formation and detection of relatively weakly
bound ionic complexes and is used here for the investigation
of the protonated molecular nitrogen dimer, (N2 ) 2 H⫹ . This
proton bound complex was found earlier in a mass spectrometric investigation of the equilibrium reaction N2 H⫹ ⫹N2
0
6
(N2 ) 2 H⫹ (⌬H298
K⫽⫺16.0 kcal/mol). It may be considered as a prototype of cluster ions of the form
Mol⫺H⫹ ⫺Mol, of which H2 O⫺H⫹ ⫺OH2 is a particularly
important one.
Early ab initio calculations predicted a linear equilibrium structure for N2 ••H⫹ ••N2 , but could not conclude
whether the structure is centrosymmetric or not.6–8 This
problem has been solved by carrying out state-of-the-art ab
initio calculations that are reported here. These confirm the
METHODS
The details of the experimental set-up have been described previously.9 The spectrometer consists of a commercial tunable diode laser system sampling a supersonic plasma
that is generated by electron impact ionization of an Ar:
N2 :H2 (D2 ) expansion 共90:5:5 mixing ratio at a stagnation
pressure of 800 mbar兲 through a 32 mm⫻50 ␮ m slit. The
production is optimized by monitoring the plasma with a
quadrupole mass spectrometer. A Perry multi-pass arrangement increases the total absorption length to ⬃50 cm. The
laser radiation is focused onto an InSb detector and is phasesensitively detected by production modulation, typically at
10 kHz. An additional 5% band pass filter in front of the
detector is used to suppress background radiation of the
plasma. The spectra are calibrated by simultaneously recording marker etalons and CO2 reference gas spectra. The absolute accuracy is estimated to be ⬃0.004 cm⫺1 , which is
about a factor two less than achieved usually with the set-up.
This is due to strong atmospheric CO2 absorptions in the
2320 to 2380 cm⫺1 region,10 even when the path of the infrared beam is purged by nitrogen gas.
a兲
Author to whom correspondence should be addressed. Electronic mail:
linnartz@ubaclu.unibas.ch
0021-9606/99/111(18)/8400/4/$15.00
8400
© 1999 American Institute of Physics
Linear centrosymmetric NwN••H⫹••NwN
J. Chem. Phys., Vol. 111, No. 18, 8 November 1999
8401
The theoretical part of this work deals with the results of
high-level ab initio calculations which were mainly carried
out by the coupled cluster variants CCSD-T11 and
CCSD共T兲.12 They include the effects of connected triple substitutions in an economical noniterative way following a
converged coupled cluster calculation with single and double
excitation operators, CCSD.13 Large basis sets of 250 and
419 contracted Gaussian-type orbitals 共cGTOs兲 were employed. These correspond to Dunning’s cc-pVQZ and
cc-pV5Z sets,14 respectively. Since core–valence correlation
effects are not very important in N2 and HN⫹
2 , only the 20
valence electrons were correlated. Throughout, the MOLPRO
suite of programs15 was used in the calculations.
RESULTS AND DISCUSSION
In total 39 vibration–rotation lines around 2352.2 cm⫺1
were observed that are assigned to the ␯ 3 antisymmetric NN
stretch of N2 ••H⫹ ••N2 . The spectrum shows the ordered
structure of a ⌺ –⌺ transition of a linear molecule, with P
and R branches and a band gap of approximately 4B. In
Fig. 1 a typical spectrum of adjacent R-branch transitions is
shown. The line positions and rotational assignments are
given in Table I. The accurate determination of some transitions was hampered by strong laboratory CO2 absorptions
and these line positions are not included in the Table. For the
FIG. 1. Adjacent R-branch transitions of the ␯ 3 band of N2 ••H⫹ ••N2 observed in a continuous slit nozzle plasma. The lines indicated by * are most
likely due to hot band transitions.
TABLE I. Observed frequencies 共in cm⫺1 ) of rotational transitions involving the ␯ 3 NN antisymmetric stretch of N2 ••H⫹ ••N2 and N2 ••D⫹ ••N2 and the
derived spectroscopic constants 共1␴ deviations in brackets兲.
N2 ••H⫹ ••N2
J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
P-branch
o – ca
(10⫺4 )
2352.0699
2351.9039
2351.7407
2351.5745
⫺29
⫺45
⫺27
⫺31
2351.2412
2351.0768
2350.9065
2350.7391
2350.5703
2350.3969
R-branch
o – ca
(10⫺4 )
2352.3966
2352.5586
2352.7207
⫺27
⫺29
⫺22
⫺26
10
⫺6
15
29
4
2353.2013
2353.3628
2353.5224
2350.6783
2353.8356
2353.9918
2354.1455
⫺15
14
33
21
31
37
25
2350.0542
2349.8812
2349.7086
2349.5349
2349.3581
2349.1808
2349.0027
2348.8259
2348.6468
17
18
30
38
23
10
⫺4
3
⫺6
2354.7554
2354.9064
2355.0571
2355.2069
2355.3536
2355.5020
2355.6517
2
0
2
2
⫺22
⫺21
1
2348.2855
2348.1075
2347.9260
⫺34
⫺10
⫺14
␯0
B⬙
B⬘
a
N2 ••D⫹ ••N2
Observed–calculated.
2352.2364共6兲
0.081 809共14兲
0.081 444共13兲
P-branch
o – ca
(10⫺4 )
2357.0585
2357.8857
2356.7202
2356.5523
2356.3838
2356.2150
48
⫺17
1
5
14
30
2355.5236
2355.3470
2355.1667
2354.9862
2354.8100
35
24
⫺13
⫺42
⫺18
2353.9365
2353.7646
2353.5866
2353.4035
2353.2162
•••
•••
•••
•••
•••
R-branch
o – ca
(10⫺4 )
2357.7045
2357.8682
2358.0285
2358.1888
2358.3466
2358.5056
⫺40
⫺14
⫺13
0
⫺3
17
2359.1176
2359.2709
2359.4219
2359.5750
2359.7300
⫺41
⫺26
⫺25
8
70
2360.3146
¯
2360.5920
2360.7447
2360.8759
2361.0143
¯
¯
¯
¯
2357.3832共10兲
0.082110共35兲
0.081596共35兲
8402
Verdes et al.
J. Chem. Phys., Vol. 111, No. 18, 8 November 1999
TABLE II. Calculated equilibrium structures, total energies, equilibrium dissociation energies and rotational constants for NwN••H⫹ ••NwN.
a
Method
Basis
R e 共NN兲共Å兲
r e 共N••H兲共Å兲
V e (E h )
D e (cm⫺1 ) a
B e (cm⫺1 )
SCF
MP2
MP2
CCSD
CCSD
CCSD-T
CCSD-T
CCSD共T兲
CCSD共T兲
cc-pVQZ
cc-pVQZ
cc-pV5Z
cc-pVQZ
cc-pV5Z
cc-pVQZ
cc-pV5Z
cc-pVQZ
cc-pV5Z
1.0596/1.0633
1.1078
1.1071
1.0899
1.0890
1.0971
1.0963
1.0974
1.0966
1.0896/1.5896
1.2738
1.2747
1.2742
1.2749
1.2757
1.2765
1.2757
1.2765
⫺218.201968
⫺219.004511
⫺219.026979
⫺218.991647
⫺219.008745
⫺219.032796
⫺219.050972
⫺219.033638
⫺219.051797
4166
6445
6321
5643
5534
6027
5911
6028
5911
0.07960
0.08251
0.08248
0.08345
0.08344
0.08294
0.08291
0.08292
0.08290
With respect to N2 H⫹ and N2 in the equilibrium configurations of the individual methods.
same reason absolute intensities were not obtained, prohibiting the observation of an intensity alternation due to spin
statistics. The results have been analyzed assuming a conventional linear molecule energy level expression for the
ground and excited states, with the rotational energy levels
expressed as an expansion in J(J⫹1). The resulting parameter set is listed in Table I. The overall rms error of the fit is
better than 0.002 cm⫺1 . The band origin is found at
2352.2364共6兲 cm⫺1 and the ground state rotational constant
is 0.081 809共14兲 cm⫺1 . Upon ␯ 3 vibrational excitation this
value decreases by ⬃0.5%. Inclusion of centrifugal distortion constants does not appreciably improve the fit and yields
rather inaccurate values for D ⬙ and D ⬘ .
In the vicinity of the ␯ 3 band origin a second, ⬃5 – 10
times weaker, band system appears 共see Fig. 1兲. In total nine
transitions were observed that exhibit similar chemical behavior and have similar spacings between adjacent lines as
the main band system.16 It is unlikely that the lines are due to
multi-mode conditions of the laser because the etalon pattern
was regular. As vibrational temperatures in the jet expansion
are estimated from T rot (⬇15 K17兲 to be of the order 150–
200 K and the harmonic wave number of the lowest bending
vibration is calculated to be 141 cm⫺1 关CCSD共T兲/cc-pVQZ兴,
these transitions may be due to a hot band.
The vibrational assignment to the ␯ 3 antisymmetric
stretch is supported by the present ab initio calculations. Ad-
FIG. 2. CCSD共T兲/cc-pVQZ potentials for antisymmetric proton stretching
motion at a different N⫺⫺N separation 共0 corresponds to equilibrium兲,
with R e 共NwN兲 kept fixed at its equilibrium value.
ditional evidence comes from the rather small vibrational
shift observed for the deuterium substituted derivative. In
total 32 transitions were observed for N2 ••D⫹ ••N2 . Due to
laboratory CO2 absorptions some transitions could not be
detected, including the band origin region. As a consequence
the rotational assignment may be off by ⫾1 J. The resulting
fit is rather inaccurate when transitions with J⬎19 are included. Perturbations in the vibrationally excited state may
thus be involved. However, due to the excessive consumption of D2 in the continuous jet expansion a more accurate
characterization was not possible. Therefore a reduced data
set, excluding the higher J-levels, was used for the fit. This
results in the constants listed in Table I. The isotopic shift of
5.14 cm⫺1 to higher energy appears to be somewhat peculiar
and must be the result of vibrational anharmonicity. However, such effects are not uncommon in hydrogen bonded
ions.18,19
Calculated equilibrium structures obtained by five different methods and two basis sets are listed in Table II. An
asymmetric linear equilibrium structure is obtained at the
Hartree–Fock level, just as for ClHCl⫺ . 19 The centrosymmetric structure with R e ⫽1.061 Å and r e ⫽1.274 Å corresponds to a saddle point on the potential energy surface and
lies higher in energy than the equivalent asymmetric minima
by 354 cm⫺1 共cc-pVQZ basis兲. Upon inclusion of electron
correlation the equilibrium structure becomes centrosymmetric. As expected, CCSD-T and CCSD共T兲 yield almost identical results. Compared with analogous calculations for the
nitrogen molecule, the NN distances are only slightly shortened by 0.0028 Å 关CCSD共T兲/cc-pV5Z兴. Consequently, a
similar error in the calculations as for N2 is expected, resulting in R e ⫽1.0949(2) Å for N2 ••H⫹ ••N2 , where an estimate of the uncertainty is given in parentheses. Compared to
HN⫹
2 , the NH equilibrium separation is elongated by as
much as 0.243 Å 关CCSD共T兲/cc-pV5Z兴. All methods accounting for electron correlation yield very similar values for the
NH distance.
The equilibrium dissociation energy D e for dissociation
⫺1
into the fragments N2 and HN⫹
2 is predicted to be 5911 cm
关CCSD共T兲/cc-pV5Z兴. This value is expected to have an uncertainty of less than 100 cm⫺1 . The same value is obtained
by CCSD-T. The inclusion of connected triple substitutions
increases D e by 377 cm⫺1 . MP2 overestimates the electron
correlation effects by about 400 cm⫺1 . Due to the strongly
anharmonic nature of the potential energy surface with re-
Linear centrosymmetric NwN••H⫹••NwN
J. Chem. Phys., Vol. 111, No. 18, 8 November 1999
8403
familiar double-harmonic approximation should work well in
the prediction of the vibrational transition moment ␮ 3 .
CCSD共T兲 calculations with the cc-pVQZ basis predict
␮ 3 ⫽0.21 D. This is much larger than a value of 0.016 D
obtained for the NN stretching vibration of HN⫹
2 from analogous calculations.
ACKNOWLEDGMENTS
This work has been supported by the Swiss National
Science Foundation, Project No. 20-55285.98, by the EEC as
part of the TMR network ‘‘Potential energy surfaces for
spectroscopy and dynamics,’’ Contract No. FMRX-CT96088 共DG12-BIUO兲, and by the French Embassy in Bern
共CH兲. P. B. thanks the Deutsche Forschungsgemeinschaft
共through Schwerpunkt ‘‘Molekulare Cluster’’兲 and the Fonds
der chemischen Industrie for financial support.
S. Bailleux, M. Bogey, H. Bolvin et al., J. Mol. Spectrosc. 190, 85 共1997兲.
Y. Ohshima, Y. Sumiyoshi, and Y. Endo, J. Chem. Phys. 106, 2977
共1997兲.
3
E. J. Bieske and J. P. Maier, Chem. Rev. 93, 2603 共1993兲, and references
therein.
4
T. Speck, H. Linnartz, and J. P. Maier, J. Chem. Phys. 107, 8706 共1997兲.
5
H. Linnartz, T. Speck, and J. P. Maier, Chem. Phys. Lett. 288, 504 共1998兲.
6
P. Kebarle, Annu. Rev. Phys. Chem. 28, 445 共1977兲; K. Hiraoka, P. P. S.
Saluja, and P. Kebarle, Can. J. Chem. 57, 2159 共1979兲.
7
S. Yamabe and K. Hirao, J. Am. Chem. Soc. 103, 2176 共1981兲.
8
S. Ikuta, Chem. Phys. Lett. 77, 369 共1981兲; J. Comput. Chem. 6, 116
共1985兲.
9
T. Ruchti, A. Rohrbacher, T. Speck, J. P. Connelly, E. J. Bieske, and J. P.
Maier, Chem. Phys. 209, 169 共1996兲.
10
G. Guelachvili and K. N. Rao, Handbook of Infrared Standards 共Academic, New York, 1986兲.
11
M. J. O. Deegan and P. J. Knowles, Chem. Phys. Lett. 227, 321 共1994兲.
12
K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem.
Phys. Lett. 157, 479 共1989兲.
13
G. D. Purvis and R. J. Bartlett, J. Chem. Phys. 76, 1910 共1982兲.
14
T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 共1989兲.
15
MOLPRO is a package of ab initio programs written by H.-J. Werner and
P. J. Knowles, with contributions from R. D. Amos, A. Berning, D. L.
Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, C. Hampel, T.
Leininger, R. Lindh, A. W. Lloyd, W. Meyer, M. E. Mura, A. Nicklass,
P. Palmieri, K. Peterson, R. Pitzer, R. Pulay, G. Rauhut, M. Schütz, H.
Stoll, A. J. Stone, and T. Thorsteinsson.
16
A list with frequencies is available on request.
17
T. Speck, T. Ruchti, H. Linnartz, and J. P. Maier, J. Mol. Spectrosc. 185,
425 共1997兲.
18
P. Botschwina, in Proceedings of the NATO Advanced Study Institute on
Structure/Reactivity and Thermochemistry of Ions 共Kluwer, Dordrecht,
1986兲, pp. 261–270.
19
P. Botschwina, P. Sebald, and R. Burmeister, J. Chem. Phys. 88, 5246
共1988兲.
20
K. P. Huber and G. Herzberg, Constants of Diatomic Molecules 共Van
Nostrand Reinhold, New York, 1979兲.
21
S. Schmatz and M. Mladenovic, Ber. Bunsenges. Phys. Chem. 101, 372
共1997兲.
1
2
FIG. 3. Variation of the electric dipole moment 关CCSD共T兲/cc-pVQZ兴 with
the NN and NH antisymmetric stretching coordinates.
spect to proton motion 共Fig. 2兲, an accurate calculation of the
corresponding D 0 value is a demanding task, which is outside the scope of the present work.
The antisymmetric NN stretching vibration is only
loosely coupled to the remaining vibrations and is quite well
described in the harmonic approximation. CCSD共T兲 calculations with the cc-pVQZ basis set yield ␻ 3 ⫽2383 cm⫺1 .
Analogous calculations for the nitrogen molecule overestimate ␻ e by 3 cm⫺1 and a similar error is expected for the
ionic complex. This gives a value of 2386 cm⫺1 for ␻ 3 . The
difference ␻ e ⫺ ␯ for N2 is known from experiment to be 29
cm⫺1 . 20 The corresponding anharmonicity contribution to
the NN stretching vibrational wave number of HN⫹
2 has been
calculated to be 37 cm⫺1 . 21 It is not unreasonable to expect
an anharmonicity contribution of comparable size for the
symmetric and antisymmetric NN stretching vibrations in the
complex N2 ••H⫹ ••N2 . Indeed, the difference between the
calculated ␻ 3 value and the experimental ␯ 3 band origin
from this work is 34 cm⫺1 , intermediate between the values
for N2 and HN⫹
2 . The present calculations thus confirm the
assignment of the observed infrared transitions to the ␯ 3 antisymmetric NN stretching vibration of N2 ••H⫹ ••N2 .
As is shown in Fig. 3, the variation of the electric dipole
moment with the antisymmetric NN stretching coordinate is
almost linear over a considerable range. Consequently, the