Huet et al.: Near infrared spectroscopy of H2Oϩ
5646
II. EXPERIMENT
rotational motion and the electronic spin (Sϭ1/2) splits each
rotational level into two components F1(JϭNϩS) and
F2(JϭNϪS).
Our experimental apparatus has been recently described
in detail.11 Only the main characteristics are discussed here.
A titanium sapphire laser ͑model 899-29, Coherent, CA͒
pumped by an Innova 400, 15 W cw Arϩ laser was employed
to record a spectrum of H2Oϩ in the region between 12 000
and 13 450 cmϪ1. The H2Oϩ ions are produced in a water-
cooled glass cell ͑20 mm i.d., length 1 m͒ through an ac glow
discharge. The discharge is driven at 30 kHz with typical
sinusoidal current of 450 mA peak to peak. A gas mixture of
helium ͑99.999% purity͒ at a pressure of 10 Torr and of
water vapor at a pressure of a few tenths of a mTorr is
introduced at both ends of the cell, near the electrodes, and is
pumped through a central outlet by a rotary pump. This
chemistry favors the production of the water cation in the
ground electronic state through Penning ionization reaction.
The dynamical calculations carried out recently by Ishida on
the He/H2O system support this approach.12 No hot bands
have been observed, indicating that the discharge is vibra-
tionally cold, probably around room temperature.
The equilibrium structure of the first excited state was
calculated ab initio as being linear.6 The vibrational levels
lin
are therefore assigned as K(
,
, 3). The value of K is
v1 v2 v
denoted by the corresponding greek letter, i.e., ⌺,⌸,⌬,... for
Kϭ0,1,2,... . The rotational structure of the excited state ex-
periences the l-type doubling interaction which splits the lev-
els with K different from zero into two components. Also,
the relation linϭ2 bentϩKϩ1 is verified. In this paper, we
v2
v2
will follow the convention used by the experimentalists,
which consists of characterizing the rotational transitions
with the N, Ka , and Kc quantum numbers for the upper and
lower states.
The ⌺͑0,7,0͒–͑0,0,0͒, ⌬͑0,7,0͒–͑0,0,0͒, and ⌸͑0,6,0͒–
͑0,0,0͒ bands have been recorded and analyzed. The vibra-
tional assignment of the observed bands is based on the
variational calculations of Brommer et al.6
The rotational analysis was carried out using the combi-
nation differences technique. In the lowest vibrational level
of the ground state, the energy levels were calculated with
the molecular parameters obtained by Huet et al., for
The velocity-modulated detection technique13 and a
noise subtraction technique14 were used in order to eliminate
signals from neutral species and to reduce the noise fluctua-
tions from the laser and the discharge, respectively. For this
purpose, two counterpropagating laser beams are sent into
the cell and detected by two PIN photodiodes. The voltages
are subtracted, demodulated, and amplified by a lock-in am-
plifier ͑LIA͒, at the frequency of the discharge. Most spectra
were recorded with a time constant of 1 s and a sensitivity of
100 V, giving rise to a typical signal-to-noise ratio equal to
30. The main noise limitation was found to come from the
modulated emission background of the discharge. Also, in
order to reduce the noise from the laser beams two low fre-
quency RC filters were used in front of the LIA. All the lines
were measured with the Autoscan software, calibrated
against the well-known Ar lines.15 The absolute accuracy is
Nϭ0–10 and Kaϭ0–3.16 The A A1 –X B1 transition fol-
lows the c-type selection rules: ⌬Ka odd and ⌬Kc even.
Almost only the strongest lines following the ⌬Jϭ⌬Nϭ0,
Ϯ1 selection rules have been observed. Taking into account
the good precision of the present measurements, our assign-
ments were done using a rejection criteria of 0.02 cmϪ1 on
the observed minus calculated value for the combination dif-
ferences. Any assignment of an upper level is also confirmed
by at least three transitions when possible. This leaves al-
most no doubt on the rotational assignments presented in this
paper.
2
2
˜ ˜
The ⌺͑0,7,0͒–͑0,0,0͒ band (13 411 cmϪ1) was previ-
ously observed and partly assigned by Lew2 as the ⌺͑0,5,0͒–
͑0,0,0͒ band. The rotational transitions are presented in Table
I͑a͒. Forty-two lines have been assigned up to Nϭ7. A por-
tion of the spectrum displaying the structure of the Q branch
is shown in Fig. 1. The 3:1 intensity alternation, due to the
nuclear spin statistics, is clearly observed. The F2 –F2 lines
form a regular series. On the contrary, the rather erratic
structure of the F1 –F1 lines reflects a perturbation which has
a maximum at Jϭ3.5. Almost all the F1 –F1 transitions have
been reassigned. The upper level energies have been deter-
mined by making an average over all the observed transitions
involved in a set of combination differences, we called them
the observed values. They are presented in Table II͑a͒.
The ⌬͑0,7,0͒–͑0,0,0͒ band (13 331 cmϪ1) has been iden-
tified for the first time. Thirty-six lines have been assigned in
the region 13 000–13 325 cmϪ1. They are presented in the
Table I͑b͒. The energy of the upper levels of the transition
are presented in Table II͑b͒, in a similar way as for the
⌺͑0,7,0͒–͑0,0,0͒ band. Again the presence of a perturbation
for Nу4 is observed. Large splitting between the F1 –F1
estimated to be 0.007 cmϪ1
.
III. ANALYSIS
2
The electronic ground state of the H2Oϩ ion is a ⌸u
linear state. Its bending vibrational mode is doubly degener-
ate. The electronic ⌳ and the vibrational L angular momenta
combine to form a resultant angular momentum which is
called the vibronic angular momentum K. The corresponding
quantum number is given by Kϭ͉lϮ⌳͉. Consequently the
bending potential function splits into two components when
the molecule is bent, this is known as the Renner–Teller
effect. In H2Oϩ the vibronic splitting of the potential energy
2
˜
function produces the ground (X B1) and the first excited
2
˜
(A A1) states.
The equilibrium structure of the ground state has
been experimentally characterized by Huet et al. ͓re
ϭ0.9992(6) Å and ⌰eϭ109.30(10) deg͔.16 The rotational
motion is described with an asymmetric rotor Hamiltonian
and the levels are assigned with the N, Ka , and Kc quantum
numbers, with KϭKa . In addition, the coupling between the
and F2 –F2 transitions are observed. This is due to the value
so
v,K
of the spin–orbit constant of the upper state A
as dis-
cussed later.
J. Chem. Phys., Vol. 107, No. 15, 15 October 1997
Huet
