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Submitted on 1 Jan 1982
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The ν3 band of PF5
M.L. Palma, J. Bordé, J. Dupré, C. Meyer
To cite this version:
M.L. Palma, J. Bordé, J. Dupré, C. Meyer. Theν3 band of PF5. Journal de Physique, 1982, 43 (6), pp.869-874. �10.1051/jphys:01982004306086900�. �jpa-00209464�
The 03BD3 band of PF5
M. L. Palma (*), J. Bordé (**), J. Dupré (***) and C. Meyer (***)
(*) Laboratoire de Spectroscopie Moléculaire (1), Université Pierre et Marie Curie, 4, place Jussieu, F 75230 Paris Cedex 05, France
(**) Laboratoire de Physique des Lasers, Université Paris-Nord, avenue J.-B. Clément, F 93430 Villetaneuse Cedex, France
(***) Laboratoire d’Infrarouge, Bâtiment 350, Campus d’Orsay, F 91405 Orsay Cedex, France (Reçu le 18 janvier 1982, accepti le 25 fevrier 1982) ’
Résumé. 2014 Nous avons analysé un spectre de PF5 situé dans la région de la bande 03BD3 et enregistré avec une réso-
lution de 0,014 cm-1. Les valeurs des constantes spectroscopiques 03BD0, B", B’-B", A’-A" et DJ de la bande 03BD3, et 03BD0,
B ", B’-B" de la bande 03BD3 + 03BD7 - 03BD7 ont été obtenues. Des spectres synthétiques sont présentés et comparés au spectre observé; nous donnons une liste de raies de PF5 en coincidence avec des raies du laser à gaz carbonique.
Abstract 2014 We have analysed a 0.014 cm-1 resolution spectrum of PF5 in the 03BD3 region. The values of the spectro- scopic constants 03BD0, B", B’-B", A’-A" and DJ for the 03BD3 band, and 03BD0, B", B’-B" for the 03BD3 + 03BD7 - 03BD7 band are given;
theoretical contours are shown and compared with the spectrum; lines in coincidence with CO2 laser lines are
listed.
Classification
Physics Abstracts
33.20E
1. Introduction. - The ultimate goal of our interest
in FFS is to observe the internal large amplitude
motion which exchanges axial and equatorial fluorine
nuclei (Berry pseudo-rotation [1]). We hope to resolve
the tunnelling induced splittings [2, 3] through a satura-
tion spectroscopy technique which has already
demonstrated the high density of PF5 lines in coinci- dence with CO2 laser lines [4] and which has since
improved its resolution to 1 kHz in the v3 band region.
Unfortunately, the exploitation of saturation spec- tra, which consist of separate 15 mK wide recordings
around the laser lines, requires first a fairly good knowledge of the vibration-rotation spectroscopic
constants in order to identify which vibration-rotation lines are observed. So a preliminary necessary work is to assign a less resolved but more continuous spectrum of the V3 band. Before this paper, a 60 mK resolution spectrum has been analysed [5] and yielded only an assignment in J which was not precise enough to
start saturation spectra interpretation. We have used
(1) Part of this work was supported by the Laboratoire de
Physique Moleculaire et d’Optique Atmospherique, C.N.R.S., Orsay, France.
a SISAM spectrometer and obtained a 14 mK reso-
lution spectrum which provided us with the values of the constants OCA 3 and a’ responsible for the K structure.
To do so we had to perform contour simulations since the K structure is still not clearly resolved and one
would really need Fourier transformed or diode laser spectra to give unambiguous assignments of
saturation spectra lines; we give at the end the V3 lines whose calculated positions are in coincidence with C02
laser lines.
2. ExperimentaL - The SISAM spectrometer has been extensively described elsewhere [6]. It is a double
pass interferometer fitted with 25 cm wide gratings.
All the optical path is evacuated to a 10- 4 torr vacuum.
A spectral range from 6 pm to 12 pm may be covered.
In our experiment a PbSnTe detector was used. The effective limit of resolution is 0.012 to 0.016 cm-’
according to the incident angle on the gratings.
The line calibration is obtained from the fringes of a
Michelson interferometer scanned by the gratings.
C02 superradiant lines are used for calibration (10 P34
to 10 P2).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004306086900
870
A White multipath cell is used. Optical path up to 32 m may be achieved with a good signal to noise ratio
in the 10 gm spectral range. This cell may be cooled down to 180 K by flowing liquid nitrogen. A high speed
turbomolecular pump with heating system gives a high
vacuum and good elimination of impurities.
The experimental conditions are : optical path
3.35 m, temperature 238 K, pressure 0.1 torr.
3. Description of the spectrum. - We give in the
upper parts of figures 1-5 characteristic sections of the observed spectrum. It is important to note the rather symmetric shape of the V3 Q branch (Fig. 5) and the
series of bumps on the low frequency side. The
V3 + v7 - V7 band has a Q branch whose intensity is
about 70 % of the V3 Q branch intensity and its
maximum is located at 946.903 cm-1; it is very similar in shape and contributes substantially to features of the V3 Q branch : for instance, the two bumps at
946.507 cm-’ and at 946.620 cm-’ on figure 5 are
caused by lines of this hot band Q branch. Reproducing
these features of the Q branch (bumps and symmetric shape) was very helpful to bracket the parameter cx A
this was done through contour analysis because of the very large number of lines in this interval : if we neglect
lines weaker than 1 % of the most intense one, there are
about 460 lines between 946.308 cm-’ 1 and 946.460 em - 1 among which 170 belong to v3 + v - V7.
All through this paper we shall call a line the sum of all transitions with the same J, K, AJ and with AK = 0 and we shall label them Q(J, K), P(J, K) or R(J, K);
because of our resolution we shall neglect all further
splittings. Because of their resolution, Schatz and Reichman [5] did not consider the quantum number K and fitted only P(J) and R(J) peaks; figures 1-4 show
that these peaks have indeed a very complex structure
Fig. 1. - Observed (top) and theoretical (bottom) spectra of
a section of the P branch. The hot band K = 4 lines are
assigned to the left shoulder of the J-peaks and the bumps on
the right are assigned to the K structure of the fundamental.
In figures 1-4, the assignments refer to data used in the least- squares fit; V3 + V7 - V7 lines are specified by ".
due to a large number of underlying lines (around
75 lines for V3 and V3 + v7 - V7 altogether between
955.060 cm-1 and 955.210 cm-’). However, we shall still speak of J-peaks since, even with 14 mK resolution, the P and R branches look like a succession of peaks
due to lines with low K. These peaks include both v3 and V3 + v7 - V7 which is more or less in phase with
the fundamental : in a section of the R branch (Fig. 3)
the hot band is completely hidden; in the P branch (Figs. 1, 2), it is responsible for more bumps in the peak
Fig. 2. - Observed (top) and theoretical (bottom) spectra of a section of the P branch where the hot band K = 4 lines
are assigned to the right of the fundamental K = 3 lines.
Fig. 3. - Observed (top) and theoretical (bottom) spectra of the section of the R branch where the hot band is exactly
hidden by the v3 branch.
shape due to a shift between the two K structures. The
intensity of the spectrum is not zero between J-peaks firstly because there are other hot bands and secondly
because the K structures of one peak extend over
several of the following J-peaks. All these reasons make
it difficult to assign a precise frequency to the bumps
of each J-peak (especially for the hot band); again we
have relied upon contour analysis to check the agree- ment between our assignments and the observed spectrum.
4. Line assignment and data reduction. - First we
have verified that the maxima of P(J) or R(J) peaks
could reasonably be assigned to K = 3 lines for V3 and
to K = 4 lines for V3 + v7 - V7. This has been done
using a 14 mK linewidth and the Boltzmann factor at 238 K and depends mainly on the statistical weights of (v, J, K) levels (Table I) which have been derived from the symmetry species of the rovibrational wave
functions in D3h [7] but we have also varied the para- meters responsible for the K structure to check their effects.
Table I. - Statistical weights / (2 J + 1).
So most of the maxima of P(J) and R(J) peaks have
been assigned to K = 3 lines of the fundamental; this provided us with 84 data. These data have been correct- ed to give K = 0 line frequencies which we have least- squares fitted by a formula in J only introducing vo,
B", CXB and D J (the variations of D J with vibration will be neglected). The correction from K = 3 to K = 0
was made with the constants of [5] as a first approxima-
tion but its effect is merely to shift vo.
We have followed a similar procedure for the hot band but, this time, the K = 4 lines were chosen as another intense bump in the R(J) or P(J) peaks; in
Fig. 4. - Observed (top) and theoretical (bottom) spectra of a section of the R branch. The two bands which cannot be
distinguished at the left split apart progressively as J increa-
ses. A single J-peak includes over 75 lines of the two bands.
some regions, it was impossible to decide between the
K-structure of the fundamental and the K = 4 hot band lines. Because of that blend, we had only 46 data
and used only three adjustable parameters, vo, B" and
aB, in the least-squares fit (Dj was held fixed to its V3
value).
Once we obtained a satisfactory fit which established this partial assignment, we tried to interpret remaining bumps as stemming from the K structure. We used first
the shape of the Q branch; to our approximation the Q
lines positions are given by
and the coefficients of J(J + 1) and K2 must be
different to obtain a symmetric shape; so we varied the
value of A’-A" and, in addition to the symmetric shape, bumps arose towards the P branch as observed in figure 5. These contour simulations gave us a first estimate of A’-A" with which we performed synthetic spectra of P and R branches. The comparison of these spectra with experimental ones helped us to assign
some bumps to lines of V3 with K 0 3 : we assigned
K = 9 lines in the P(20), P(21), P(22), P(40), P(41), P(42), P(43), P(44), P(46), P(47) and P(48) manifolds
and K = 12 lines in P(41), P(42), P(43), P(44), P(46), P(47) and P(48). These data were added to the K = 3 data (102 data altogether between P(15) and P(48) and
between R(15) and R(73)) and we introduced five parameters in a least squares fit which involved both J and K. The standard deviation is 4.8 mK and all observed minus calculated frequencies are less than
10 mK with the values given in table II for the para-
Fig. 5. - Observed (top) and theoretical (bottom) spectra of the Q branch of the V3 band. The bumps cannot be assigned
to definite lines but’are due to clusters of lines with different J and K. The great number of lines around vo saturated the detection and four different intensity scales were used in the sections A, B, C, D, of the theoretical spectrum.
872
Table II. - Spectroscopic constants of the V3 and V3 + V7 - V7 bands in wavenumbers. Standard devia- tions in parentheses, are in units of the last decimal
place given.
meters. Table II also gives the values of the hot band parameters; we have not been able to assign bumps to
the K structure of V3 + v7 - V7 and we have done
only the J dependent fit mentioned earlier; however,
in the synthetic spectra shown in figures 1-5, DJ and LX3’
with their v3 values were introduced to calculate the hot lines positions.
Also there is no fit in the theoretical spectrum of the Q branch shown in figure 5 : this is a direct calculation
performed with the parameters of table II deduced from P and R branches. A last detail concerning the
theoretical spectrum should be pointed out : the frequency is not a linear function of the paper length
on the observed spectrum and, for each figure, we had
to obtain an interpolation polynomia to match the
observed and theoretical frequency scales.
5. Discussion. - Figures 1 to 5 show a fairly repre- sentative sample of the agreement between the observ- ed and calculated spectra; in regions where it was impossible to assign V3 + V7 - V7 lines (mainly
between 937.5 cm-1 and 939.5 cm-’), differences are more pronounced and show how critical is the fit of this hot band to obtain a good reproduction of the V3-K structure. We have had several opportunities to
see how sensitive the contour is to the hot band : for
instance, on figure 2, we did check that if the hot line "P(24,4) is calculated at its observed frequency, the bump assigned to P(22,9) would show up on the theore- tical spectrum. Also many of the discrepancies surely
come from hot bands whose intensities are not negli- gible : at the experiment temperature, we estimated that V3 +2V7 -2V7, v3 + Vs - Vs, V3 + V6 - V6, V3 + V4 - V4 and V3 + v2 - V2 have intensities res-
pectively 36 %, 9 %, 8 %, 3 % and 2 % of the V3
intensity. We did see more than two Q branches on the spectrum; the observed maxima of these other Q
branches are located at 943.374 cm-’, 943.818 cm-1,
944.344 cm-1, 947.401 cm-1 and 947.565 cm- 1; the
last two are by far the most intense and can be assigned
to the two Q branches associated with the two compo- nents of V3 +2V7 -2V7(1171 I = 2 and h = 0) ;
their average location is consistent with the value 0.56 cm-1 for X37 deduced from vo(v3) -
VO(V3 + V7 - V7). I
We could also in principle obtain tentative values for Ct.7 and Y7 from the variation of B" and aB between
V3 and V3 + v7 - V7 but the uncertainties would be too large. The main reason is that we trust our results
for V3 but are much less confident in the hot band fit;
if we compare our results to [5], we see that the agree- ment is good for V3 but much poorer for V3 + v7 - V7
(except for vo, hence a good agreement also on x37).
The fact is that Schatz and Reichman’s hot band constants correspond to a different assignment in
which the hot band does not cross the fundamental in the P branch (see Figs. 1, 2) but always stays on the high frequency side; we did try this assignment which
allows a good least-squares fit but leads to a hot band
D J of opposite sign; however, in this case, the bumps
that we assign to the hot band, on the low frequency
side of fundamental peaks (e.g. "P(47,4) on Fig. 1)
would be left unassigned and it is more likely that
Schatz and Reichman assigned to the hot band shoulders due in fact to the K structure of V3. We must say that the section of the P branch where v3 + v - V7
crosses V3, between P(37) and P(44), is poorly repro-
duced ; this is understandable for two reasons : on one
hand we have no data in the crossing section since the hot band is hidden by the fundamental; on the other hand, the way the data we have on the edges of this
section are fitted makes us think of a local rotational
resonance (lobs - calc I rapidly increasing with opposite signs on each side of the section). According
to the Wi’S we know [8], indeed the vibrational states
V6 = V4 = 1 ; V4 = vs- = 1; V4 = 1, V7 = 3 and V4 = 2
are close enough (around 20 cm- 1) to create a vibra-
tional or rotational resonance with the V3 = 1, V7 = I state. We have also looked for a vibrational
resonance which would explain why B’-B" of the hot band is so different from B’-B" of V3; to do so we
have let Dj vary in V3 = V7 = 1 but the least squares fit did not improve significantly; fitting separately
the lower levels and the upper levels, through combi-
nation relations, did not lead either to significant
results because we had too few data. Thus we finally
decided to present a fit with 3 parameters only and 46
data whose standard deviation is 12.6 mK (if we take
off 4 data on the edges of the resoning section, this
standard deviation diminishes to 8 mK but neither the parameters nor the contours are strongly changed) ;
for all these reasons, we think there still might be a large uncertainty about the hot band constants.
6. Coincidences with C02 laser lines. - Waveguide
lasers now allow to study 15 mK intervals centred on
the laser lines; since we estimate that the uncertainty
on calculated frequencies can reach 9 mK for v3
(20 mK for V3 + v7 - V7), we have chosen to list
(Table III) PFS lines which are detuned up to + 15 mK
Table III. - PF5 lines in coincidence with C02 laser lines.
I" = line Of V3 + V7 - V7-
874
from the laser lines. We have discarded some CO2
laser lines : P(14) and P(12) are in regions with unassigned lines (probably due to other hot bands);
around P(16) and P(20), there is no strong line of V3
or V3 + V7 - V7 (but there are certainly plenty of lines
of other hot bands) ; P(4) and P(2) are in high J values regions. We have retained P(26) and P(18) although
around the former the hot band is badly reproduced
and the latter is located on the low frequency side of the
V3 Q branch, where the shift between theoretical and
experimental bumps becomes noticeable (see Fig. 5);
also we have limited the list of table III to PFS lines
with J" 5 70 and whose intensities are greater than 1 % of the most intense line of each branch.
References
[1] BERRY, R. S., J. Chem. Phys. 32 (1960) 933.
[2] DALTON, B. J., J. Chem. Phys. 54 (1971) 4745.
[3] CHÉRON, M., BORDÉ, J., J. Physique 35 (1974) 641.
[4] BORDÉ, C., C.R. Hebd. Séan. Acad. Sci. 271 (1970) 371.
[5] SCHATZ, J., REICHMAN, S., J. Chem. Phys. 57 (1972)
4571.
[6] PINSON, P., Appl. Opt. 13 (1974) 1618.
[7] TARRAGO, G., Thesis, Paris (1965).
[8] GRIFFITHS, J. E., CARTER, R. P., HOLMES, R. R., J.
Chem. Phys. 41 (1964) 863.
