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The far infrared spectrum of H2O2 observed and calculated rotational levels of the torsional states : (n, τ)
= (0, 1), (0, 3) and (1, 1)
F. Masset, L. Lechuga-Fossat, J.-M. Flaud, C. Camy-Peyret, J.W.C. Johns, B.
Carli, M. Carlotti, L. Fusina, A. Trombetti
To cite this version:
F. Masset, L. Lechuga-Fossat, J.-M. Flaud, C. Camy-Peyret, J.W.C. Johns, et al.. The far infrared spectrum of H2O2 observed and calculated rotational levels of the torsional states : (n, τ) = (0, 1), (0, 3) and (1, 1). Journal de Physique, 1988, 49 (11), pp.1901-1910.
�10.1051/jphys:0198800490110190100�. �jpa-00210870�
1901
The far infrared spectrum of H2O2 observed and calculated rotational levels of the torsional states : (n, 03C4) = (0, 1), (0, 3) and (1, 1)
F. Masset (1), L. Lechuga-Fossat (1), J.-M. Flaud (1), C. Camy-Peyret (1), J. W. C. Johns (2),
B. Carli (3), M. Carlotti (4), L. Fusina (4) and A. Trombetti (4)
(1) Laboratoire de Physique Moldculaire et Atmosphdrique, Université Pierre et Marie Curie et CNRS, 4 place Jussieu, Tour 13, 75252 Paris Cedex 05, France
(2) Herzberg Institute of Astrophysics, NRC, Ottawa, Ont., Canada K1A 0R6
(3) IROE-CNR, via Panciatichi, 64-50127 Firenze, Italy
(4) Istituto di Chimica Fisica e Spettroscopia, viale Risorgimento, 4-40136 Bologna, Italy (Reçu le 3 juin 1988, accepté le 19 juillet 1988)
Résumé. 2014 Des spectres par transformée de Fourier à haute résolution enregistrés entre 30 et 460 cm-1 ont
été utilisés pour une analyse systématique des bandes de torsion-rotation (n, 03C4) = (0, 3) ~ (n’, 03C4’) = (0,1), (0,1) ~ (0, 3) et (1, 1) ~ (0, 3) de H2O2. L’utilisation d’un hamiltonien qui traite explicitement la forte
interaction de type |0394Ka| = 2 entre les niveaux rotationnels des états de torsion (n, 03C4) = (0, 1) et (1,1) ainsi
que l’interaction en |0394Ka| = 2 entre les niveaux de (n, 03C4) = (1,1) et (2, 1), a permis de reproduire de façon
très satisfaisante les niveaux observés des états de torsion (n, 03C4) = (0,1) et (1,1) tout en foumissant un
ensemble précis d’énergies de torsion et de constantes rotationnelles et de couplage. De la même façon pour
reproduire les niveaux observés de (n, 03C4)= (0, 3) a été utilisé un hamiltonien qui tient compte de l’interaction
en |0394Ka| = 2 entre les niveaux rotationnels des états de torsion (n, 03C4) = (0, 3) et (1, 3) et des énergies de
torsion et des constantes rotationnelles et de couplage précises ont été ainsi déterminées pour ces états.
Abstract. 2014 High resolution Fourier transform spectra, recorded between 30 and 460 cm-1, have been used for an extensive analysis of the (n, 03C4) = (0, 3) ~ (n’, 03C4’) = (0, 1), (0,1) ~ (0, 3) and (1, 1) ~ (0, 3) torsion-
rotation bands of H2O2. Then, using a Hamiltonian which takes explicitly into account the strong
| 0394Ka| = 2 interaction between the rotational levels of the (n, 03C4) = (0,1) and (1,1) torsional states, as well as
the |0394Ka| = 2 interaction between the (n, 03C4) = (1, 1) and (2, 1) rotational levels, it has been possible to reproduce very satisfactorily the experimental rotational levels of the (n, 03C4) = (0, 1) and (1,1) torsional states
and a precise set of torsional energies and rotational and coupling constants has been derived. In the same way, to fit the (n, 03C4) = (0, 3) experimental energy levels we have used a Hamiltonian taking into account the
|0394Ka| = 2 interaction between the rotational levels of the (n, 03C4) = (0, 3) and (1, 3) torsional states, and this calculation has also provided a precise set of torsional energies, rotational and coupling constants for the (n, 03C4) = (0, 3) and (1, 3) torsional states.
J. Phys. France 49 (1988) 1901-1910 NOVEMBRE 1988,
Classification Physics Abstracts
33.20E - 35.20J - 35.20P
1. Introduction.
The study of hydrogen peroxide is of interest for two main reasons :
- first, this molecule is one of the simple
molecules exhibiting a large amplitude motion : 0-H torsion around the 0-0 bond.
- second, H202 is an atmospheric constituent
playing an important role in the stratospheric HO. chemistry affecting the ozone layer.
Different methods can be used to measure the concentration of hydrogen peroxide in the atmos- phere and, among them, one possibility is optical
remote sensing in the far infrared but this method necessitates an accurate knowledge of the spectro- scopic parameters of this molecule.
The far-infrared spectrum of H202 below 700 cm- 1 has been previously studied by Hunt et al. [1]
at medium resolution (0.3 cm- 1) allowing the deter-
mination of the six lowest torsional states of this
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198800490110190100
molecule and of the height of the trans-barrier (Fig.
1). At the same time the authors pointed out the
existence of a strong resonance between the
I (n, r) = (0, 1) J, Ka = 8) and the I (n, T) = (1,1) ; J, Ka = 6 levels, but, because of the modest resolution attained in their spectra, it was possible to
treat this resonance using perturbation theory. More recently, the microwave spectrum of H202 has been
recorded between 80 and 700 GHz by Helmin- ger et al. [2, 3] who reported about 180 lines
belonging to the two rotation-torsion bands
(n, T) = (0, 3) H (0, 1). These lines were reproduced using the A-reduced Watson type Hamiltonians in the If representation both for the (n, r) = (0, 1) and (0, 3) torsional states [2, 3, 4]. No resonance effects
were observed because the microwave lines do not include sufficiently high Ka values. ,
Finally, Olson et al. [5], through the study of the (V2 + V6, V5) bands, were able to generate combi- nation differences for the ground state with suffi-
ciently high values of Ka so that the resonance
between the (n, T) = (0, 1) and (1, 1) rotational
levels could be seen clearly.
We report in this work new Fourier transform measurements and more complete and precise ana- lyses of the 3 torsion-rotation bands : (n, T ) _
(0, 3 ) , (0,1 ), (0, 1) +- (0, 3), and (1, 1) +- (0, 3)
which has allowed us to derive experimental levels
up to high J and Ka values (respectively 35 and 11).
These levels were then reproduced taking into
account the appropriate interactions between the
(0,1 ) and (1,1 ) rotational levels and between the
(1,1 ) and (2,1 ) levels, as well as between the
(0, 3 ) and (1, 3 ) levels, leading to a precise set of
torsional energies and rotational and coupling con-
stants.
2. Experimental details.
Two different spectra were used covering the region :
30-460 cm-1 :
- the first spectrum (denoted in the following as spectrum 1) has been recorded with a BOMEM Fourier transform spectrometer at N.R.C. (Ottawa, Canada) and, in order to get the best signal to noise ratio, it has been divided into 4 spectral regions (see
Tab. I) ;
- the second spectrum (referred in the following
as spectrum 2) has been recorded between 30 and 206 cm-1 1 with the Fourier transform spectrometer
[6] at I.R.O.E. (CNR, Firenze, Italy) and its carac-
teristics are given in table I.
For. spectrum 1 the wavenumber calibration was
achieved by using the H20 lines measured by Johns [7]. For spectrum 2, the wavenumber calibration was
made using 9 HCI lines [8] measured immediately
before and after the H202 measurements. Moreover,
Fig. 1. - Sketch of the torsional potential function for H202 together with the lowest (n, T) torsional states.
1903
Table I. - Characteristics of the different spectra.
Spectrum 1 : Recorded at Ottawa (see text).
Spectrum 2 : Recorded at Florence (see text).
in order to check the consistency between the different spectra, a relative calibration was per- formed by comparing the positions of well-isolated lines absorbing in the common spectral intervals.
Finally, uncertainties in the positions of well-isolated lines are estimated to vary between 0.15 and 0.30 x 10- 3 cm-1 1 according to the resolution of the spectra.
The wavenumbers used in the analysis were taken
either from spectrum 1 or from spectrum 2 depend- ing on the quality of the line in the spectra. We present in figure 2 a portion of spectra 1 and 2 near 130 cm- 1 showing the excellent’’ signal to noise ratio of the two spectra. -Moreover it cafi be noticed that
because of its higher resolution spectrum 2 shows
features which are not completely resolved in spec- trum 1. Figure 3 presents a portion of spectrum 1
near 360 cm- 1 and again the excellent quality of this spectrum can be noticed.
3. Analysis.
As a starting point of the analysis, we have used
the rotational constants of Hillman [4] for the (n, T ) = (0,1 ) and (0, 3) torsional states to compute
the spectrum of the two bands (0, 3) - (0, 1) and (0, 1) +- (0,3) ; in this way, we were able to identify
in our far infrared spectra about 400 lines belonging
to these two bands with Jrnax = 22 and (Ka)max = 5 ;
we then extended the assignment tracing up series of lines with higher J and Ka values (H202 is a near prolate rotor) and obtaining about 700 lines with
J.ax = 24 and (Ka)max = 7. The corresponding
rotational levels (belonging to the (0, 1) and (0, 3)
torsional states) were introduced in a least squares fit using single Watson type Hamiltonians and im-
proved constants for the (n, T) = (0, 1) and (0, 3)
torsional states were obtained. In this way we obtained good agreement between experimental and
calculated values for all the rotational levels of
(n, r (0, 3 and for the rotational levels of
(n, T (0,1 ) up to Ka = 6. At this stage of the analysis it became clear that the calculated energy
Fig. 2. - Portion of the H202 spectrum around 130 cm-’.
Spectra 1 recorded at NRC (Ottawa) and 2 recorded at IROE (Firenze) exhibit an excellent signal to noise ratio.
The rQb branch of (0, 3 )- (0, 1) is prominent but because of its higher resolution, spectrum 2 shows lower J lines not
completely resolved in spectrum 1.
levels of the torsional state (n, T) = (0, 1) disagreed significantly with the experimental values (for Ka = 7 the disagreement was of the order of 40 to 100 X 10- 3 em-I). This is because of the strong
AKa = 2 interaction between the Ka = 8 rotational
levels of (n, T) = (0, 1) and the Ka = 6 rotational
levels of (n, T) = (1, 1) which was first pointed out by Hunt [1]. Because of the high accuracy achieved in this work, this interaction is already evident for Ka = 7. We therefore decided to analyse the (1, 1) +- (0,3) torsion-rotation band in order to determine rotational levels of the (n, -r) = (1, 1)
torsional state. To start the analysis of this latter band we used the rotational levels determined by
Olson et al. [5] for the (n, T) = (1, 1) torsional state,
and the rotational levels (n, T) = (0, 3) derived from
our previous analysis of the (0, 3) «- (0, 1) and
Fig. 3. - H202 absorption around 360 cm-1. The series fQ6(J) of the (1, 1) +- (0, 3) torsion rotation band is clearly
visible.
(0, 1) +- (0, 3) bands. The derived ,levels were then
introduced in a least squares fit taking into account the resonance previously mentioned allowing a reli-
able extrapolation and hence new assignments ; the
process was iterated until it was not possible to identify new lines of the three bands we were
studying, i.e. (0, 3)«-(0, 1), (0, 1) - (0,3) and (1,1) - (0, 3). Finally, about 3 200 rotation-torsion lines were assigned from which, using the method extensively described in [9], a large set of precise experimental rotational levels (presented in Tab. II)
for the 3 torsional states (0, 1), (0, 3) and (1,1) were
derived. More precisely, 1650 experimental
rotational levels were obtained as follows : 588 for (n, T ) = (0,1 )
4. Energy level calculations.
We used the A-reduced Hamiltonians in the I r
representation because as found by Hillman [4], it gives the best convergence.
1. (n, T)=(0, 1) and (1, 1) torsional states.
In the first stages of the calculations, we used a
Hamiltonian which takes into account explicitly the
strong interaction between the rotational levels of the (n, T) = (0, 1) and (1, 1) torsional states. This
leads to the following form for the Hamiltonian matrix :
where H," is a Watson A-reduced Hamiltonian for a
single state.
and with
and
1905
Table II. - Experimental rotational levels for the (n, T) = (0, 1), (0, 3) and (1, 1) torsional states.
J, Ka, K, : Rotational quantum numbers. When d appears in place of the usual K,, quantum number the two
components of the nearly degenerate asymmetry doublet are split by less than 0.0001 cm-1, E : Energy of the level in
cm-1; SE : Uncertainty in 10-3 cm- 1. Calc in this column means that the level was not observed in our experimental
conditions.
Table II (continued).
1907
Table II (continued).
where VOl, 11 has matrix elements in AK = ± 2 and
appropriately describes the effect of the resonance
which links levels with I AKa I = 2.
The net result of this calculation was in good agreement for all the (n, T) = (0, 1) energy levels and for the (n, T) = (1, 1) energy levels with Ka :s: 8, but we observed discrepancies for the (n, T)
= (1, 1) levels with Ka :::. 8. This is because these latter levels resonate with the (n, T) = (2, 1) levels :
we then also took into account the interaction between the rotational levels of these last two torsional states. Consequently, the final Hamiltonian matrix used to fit the experimental energies of the (n, T) = (0, 1) and (1, 1) levels was :
where the interaction operator V 11, 21 has the same
form as V 01, ".
The torsional energies as well as the rotational and coupling constants of the three interacting states
Table III. - Torsional energies, rotational and coupling constants for the (n, T) = (0, 1), (1, 1) et (2, 1)
torsional states (*).
Coupling constants
Statistical analysis : Standard deviation
1909
Table IV. - Torsional energies, rotational and coupling constants for the (n, T) = (0, 3) and (1, 3) torsional
states (*).
Coupling constant :
Statistical analysis :
(*) All the results are in cm-1 and the errors are one standard deviation. Constants without errors were held fixed
during the fit.
(n, T ) = (o,1 ), (1, 1) and (2, 1) resulting from the
fit of the experimental energy levels appear in table III and it can be seen from the statistical analysis quoted also in this table that the agreement between the experimental and calculated energy levels is excellent.
It is interesting to make two remarks :
i) Although we did not observe any (n, T) = (2, 1)
torsion-rotational levels, it should be noted that the
resonance between the (n, T) = (1, 1) and (2, 1)
states is strong enough to allow the constants E, A,
B and C of (n, T) = (2, 1) to be determined, showing clearly that it is essential to take this last interaction into account.
ii) The rotational and coupling constants deter-
mined for the torsional (n, T) = (0, 1) and (1, 1)
states depend, in some way, on the fixed constants
(4K) of the (n, T) = (2, 1) torsional state and further
work is needed to obtain experimental values for the rotational levels of the (2, 1) torsional state.
2. (n, T) = (0, 3) torsional state.
The first calculation performed for the (n, r) (o, 3 ) energy levels showed that it was legitimate as
a start to treat this state as an isolated one. However,
as soon as we observed high Ka levels, it became
clear that this assumption was no longer correct.
Therefore, we decided to fit the (n, T) = (0, 3) experimental energies with a Hamiltonian taking explicitly into account the resonance between the levels of the (n, r) = (0, 3) torsional state and those
of the (n, T) = (1, 3) state. The corresponding
Hamiltonian matrix has the following form :
where HWT is a A-1 r Watson Hamiltonian and the interaction operator is :
The torsional energies, as well as the rotational
and coupling constants of the two interacting states (n, ’T) = (0, 3) and (1, 3), resulting from the fit of the
experimental energy levels of the (n, T) = (0, 3)
torsional state, appear in table IV and, as in the
previous case ((n, T) = (0, 1) and (1, 1)) the
statistical analysis quoted in this table shows the
excellent agreement between the observed and the calculated energies. It can be noticed that, without knowing any (n, T) = (1, 3) rotational level it has been possible to determine the A, B and C constants
of this torsional state. This shows again, that it is
essential to take this I AKa I = 2 interaction into account. These theoretical predictions for (n, T) = (1, 3) will help to locate the transitions involving this
state in the spectra. Also, as for the (n, T) = (0, 1), (1, 1) torsional states, the rotational constants of the
(0, 3) state depend in some way on the assumed values of the constants of the (1, 3) state.
5. Conclusion.
High resolution Fourier transform spectra of H202,
recorded between 30 and 460 cm- 1 have been used to determine a very extensive and precise set of experimental rotational levels for the (n, T) = (0, 1), (1, 1) and (0, 3) torsional states of this molecule.
These rotational levels were reproduced using a
Hamiltonian which takes explicitly into account the
interactions affecting the levels. As a consequence, the levels were fitted very satisfactorily and an
extended set of precise torsional energies and
rotational and coupling constants has been derived for the torsional states studied in this work.
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