JOURNAL OF MOLECULAR
SPECTROSCOPY
Far-Infrared
62,326337
(1976)
Absorption Spectra of Water
and Isotopic Modifications
Vapor H,160
J. W. FLEMING AND M. J. GIBSON
Division
of Electrical Science, National Physical Laboratory,
Teddington, Middlesex TWll OLW, U. K.
Far-infrared absorption spectra of Ho160,H+80, H”OD, HIgOD, DzleO, Dz**Ohave been
observed between 10 and 40 cm-l at a resolution of 0.07 cm-l. Experimental and calculated
line positions agree within the accuracy of the experiment (f0.003 cm-l). The relative intensities of type a and type b transitions of H’*ODand HISODare used to estimate the ratio &M.
INTRODUCTION
The water molecule has for many years attracted much spectrometric attention.
In
recent years, with improved understanding
and treatment of centrifugal distortion (I),
detailed studies have been made of the rotational energy levels of virtually all its isotopic forms. Combined analyses of the microwave spectra, and combination differences
from rotation-vibration
spectra, have yielded precise knowledge of many of the rotation
and distortion constants.
Far-infrared
absorption
techniques have also made great
strides in recent years, in wavenumber
precision, resolution, and sensitivity.
In some
very long path length far-infrared experiments (such as those designed to detect trace
gases in the atmosphere), it is possible that strong lines of the isotopic forms of water
could be observed. It is therefore of some importance to have laboratory observations
of the more common isotopic forms. We report here far-infrared
absorption spectra
(1040 cm-l) of HPO, HPO, Hr60D, H180D, DPO, and DPO. Our experimental
data are compared with calculated spectra, based upon the most recent molecular
parameters supplied to us by Dr. G. Steenbeckeliers.
EXPERIMENTAL
METHODS
Spectra were observed with an NPL-Grubb
Parsons Cube interferometer,
equipped
with a liquid helium cooled Rollin-type InSb detector. Continuous spectra covering the
region W-40 cm-l were obtained at a resolution of 0.07 cm-‘. The spectra are true
transmission
spectra obtained by dividing specimen spectra by background
spectra
after the interferograms
had been Fourier transformed. The path length was 203 mm.
Four independent
spectra were recorded in each of the experiments described below.
Mean peak positions are listed in the tables; they are believed to be accurate to f0.003
cm-’ when lines of reasonable strength are observed free from overlapping effects (2).
326
Copyright @ 1976 by Academic Press. Inc.
All rights of reproduction in any form reserved.
WATER
VAPOR
FAR-INFRARED
327
Wavenumber
cm-’
FIG. 1. Natural
water
vapor.
Pressure,
18 Torr;
RESULTS
AND
path
length,
203 mm; resolution,
0.07 cm-l.
DISCUSSION
High-resolution
far-infrared
studies of the absorption
spectrum of normal water
have been reported by Hall and Dowling (3), and by Sanderson and Scott (4). Our
nssifpment
'lo532?I
14.74:
14.9437
'01
18.575
~~.5174
20.703
20.7043
25.004
25.os51
441
331
5z4c
431
*02+
111
303
'llC Ooo
18
o 321 + 31%
312 +. 221
321 + 312
&.od
5
330
422+
a
ref-
12.6820
* *02
312+
(Cm-‘)
12.603
%4* 321
423+
obeerved
l-he3
1'9.571
25.035
30.560
30.55;
32.366
32.365
32.953
32.X1
36.5¶iJ
3G.605
37.134
37.337
37.926
38.465
3C.465
3P.785"
38.792
_ rrecise location of centre impossible.
328
FLEMING
AND
Wavenumber
FIG. 2. I, 9.5% enriched
resolution, 0.07 cm-l.
experiment
DzO at 10 Torr;
GIBSON
(cm-‘)
II, 1: 1 mixture
HtO/DzO
at 14 Torr. Path
differs from theirs in that we measure a transmission
all instrumental
background
variations,
length,
203 mm;
spectrum corrected
and in that our experiment
for
is optimized for the
W-40 cm-’ spectral region. Figure 1 shows the observed spectrum, and the mean line
centers are given with assignments in Table I. The spectrum is useful in demonstrating
the high signal-to-noise ratio typical of our experiments. The sensitivity of the observations is indicated by the observation of the HJ80 321 t 312 transition at 37.916 cm-r;
180 has a natural abundance of 0.2%.
Gordy and co-workers have made great progress in extending
microwave
techniques
into the submillimeter region. De Lucia el al. (5) have reported the spectrum of HP0
up to 25 cm-’ using a submillimeter microwave spectrometer.
The accuracy of this
technique is at least fl
MHz (3 X 1W cm-‘), so their measurements provide a useful
check on our absolute accuracy. From the five lines measured in common, the rms
deviation between our data and those of De Lucia et al. is f0.0016
cm-‘. Several extra
WATER
arui&mmt
VAPOR FAR-INFRARED
oberved
(or?)
calculated
(09-l)
329
sawl
lO.%Y
10.5673
2
*11* 202
13.4592
13.4614
9
312- 221
15.2947
15.2950
0.6
202‘ '11
15.61?7
1SlYO
4
312+ 303
1n.:255
18.5238
0
%+
532
19.0733
19m37
0.5
111+ oco
20.25c7
2Q.2590
‘10* '01
92a- 835
21.44l3
21.4353
11
0.2
I21.4565
0.3
PI.6672
21.G670
0.5
23.01(77
23dWYi
26
23.so2
23.2?02
11
7?&- ‘?.3
23.815a
23.8194
1
L,C
24.1OG7
24.1057
I
2200c 2,,
24.m42
24.8026
16
523' 5,4
25.o::e
25.0542
14
413+ 4@4
26.OYZ
26.1004
23
303'%2
25.37435.
26.3782
15
c
c G15
.24
23.693:
29.7002
2s
I7
I
%4"53
'35*‘42
422. 413
321 + 312
4,2
*12+ '01
29.9479
29.9???
73.$CG4>
.
30.:810
30.1763
1
413+ 322
31.0:3)
31.0529
11
?45 + :::.3
31.3760
31.36a
3l.CO60
31.co71
9
31.7305
?l.iS%
0.7
a- 725
.3.l
?A?!+3
34.797r
13
322+ 3,)
?5.rG"il
35.5272
30
35$?17
20
221. 212
PjG+ 743
s3,+ 8%
,
35.PT
514+ 505I
‘33C ‘24
" '60
2
3c.:7:7
0.6
I 35.GYYo
32
36.1212
35
33013
945-Q
36.933
36.9755
725c 716
37.2137
37.21%
0.4
I4
1P
313* 202 =2 O
33.iop
33.1016
313+ 202
38.6X?
35.6262
70
532- 523
39.0138
39.0179
21
39.6!07
39.6297
1
33.':w
39.8541
14
945-Q
9.36
* 927
0.14
lines were observed with the microwave technique; these lines all have line strengths
10% or lower than that of the weakest lines observed in common, or else are obscured
by the wings of strong neighbors.
330
FLEMING
AND GIBSON
b. H160D, DPO
These molecules have been extensively studied by several groups of workers in the
microwave spectrum. Steenbeckeliers and Bellet (6) reported microwave transitions of
DQ60 up to 20 cm-‘, together with an extensive tabulation
of calculated’rotational
energy levels. Benedict et al. (7) have calculated ground vibrational
state rotational
transitions of DPO up to 30 cm-l, using mainly microwave transitions observed up to
10 cm-I. Lafferty, Bellet, and Steenbeckeliers
(8) have studied the H160D molecule;
TAME III
‘-
H”OD
ooo
33of
423
msitiona
and a8simments
obssorved (m-1)
*sSi&tlW”t
lo1 +
line
a
CalouIJted
(Cm-‘)
s1pl
i 5.509
rg.:os
0.14
16.04
lC.010
0.05
0.6
202+
l,,
16.3613
16.364
'lo*
'01
16.9873
- t6.989
:,,c
?o_
20.0105
20.012
3.4
2o.760
X.164
0.1
7% * C33
2
5s: + 5,4 D20
-..
:,,c
zoo-iI,O
1
-
I_
4,,c A,< il
'3::\
11,
27.535
I
27.913
27.9533
0.
?,,3
+ ?,2 D.,C
,_ I
'I, - 000
.'oz+ lo1
26.502
27.5Y35
II
..,_+ 7.
q i
.I
2,;+
5.4
26.5~70
‘1,:+ $2
‘hi +
25.105
I
d
3...f :o:
n
524 * .ly "2"
28.3510
l
0.1
O.?
0.M
27.935
0.1
29. jl9
0.7
I 2G.3792
29.8135
^~.~ayl
4
30.6655
30.i65
1
32.372
'
32.3d
413 + 404
32.8270
32.825
2oz+
I,, "20
32.9558
b
32.953
303'
212
33.2008
33.204
5
'IO
33.63i5
33.6?2
1
3G.6015
36.co5b
I,, * ooo ,120
37.13co
37.137’
3,2+
221
38.4675
38.46;
523+
514
211*
312:
=
303 'so
,,,o
3~%759
38.7783
321 + 312
4x-
413
514-
5,5
38.i92
31
b
Ii,0
39.36Yo
abslxwd
positionsref
3.
c
6
b
3.552
3
3?.?i2
0.14
WATER
VAPOR
FAR-INFRARED
331
Benedict and Clough (9) have prepared a table of the H160D ground vibrational state
rotational energy levels. De Lucia et al. have measured the microwave spectrum up to
25 cm-l (10). Apart from a grating spectrometer study of Dz160 by Slone (11), no
high-resolution
far-infrared studies of these molecules have been reported.
Figure 2 shows (spectrum I) an experimental spectrum of DJ60 at 10 Torr pressure.
To distinguish lines of DJBO from H160D and H$jO, spectra of a 1: 1 mixture of HJfiO
and DJ60 were also run. A typical result is shown as spectrum II in Fig. 2. It is a
simple matter to identify the particular absorptions due to each isotopic form. All the
observed absorption lines in Fig. 2 can be assigned with no difficulty. The DJ”O and
H160D observed lines have been separately listed in Tables II and III, even though
many of the lines occur in both spectra. Assignments have been made by calculating all
the allowed transition wavenumbers and relative intensities from appropriate rotational
energy-level schemes. For DPO, energy levels to J = 13 from Steenbeckeliers
and
Bellet (6) were used, while for H160D, energy levels to J = 9 due to Benedict and
Clough (9) were used. The relative intensities help considerably in making assignments;
we define a relative intensity Srel by
Srel = (expC:-&/AT]
- exp[-Ei/kT])~iiSzjgi,
(1)
where EL, Ej are the lower- and upper-state energies, respectively, ~ii is the transition
wavenumber,
Sij is the transition strength (12), and gi is the lower-state statistical
weight. .Srel is tabulated for T = 300 K, and it is related to the absolute line strength by
So (cnr” atnl-’
at 300 9) = 10.18 I*$&.J@,
(2)
where ,.&nis the dipole moment in Debye, and Q the partition function for the molecule.
While observed peak absorptions are not directly proportional
to Srel, this quantity
serves to make useful comparisons.
Observed and calculated positions agree well within experimental
uncertainty
for
D2160 (Table II). The peak at 25.057% cm-’ is probably a blend of three transitions
D2160 5z3 +- 5,, at 25.0542 cm-‘, H160D 312+- 303 at 25.131 cm-‘, and H2160 211c 2oz
at 25.085 CI+. Similarly, the 28.3748 cm-’ peak is a blend of 28.3782 303+- 212 Dz160
and the type u H160D transition 2126 1x1 at 28.3180 cm-‘. In the same way as with
HPO, the exFerimenta1 sensitivity is sufficient to detect the DJ80 transition 313c 202
at 38.105 cnl-l (calculated at 38.1016 cm-‘). This transition is, by a factor of 2, the
strongest DJYO transition below 40 cm-‘.
Good agreement is also found between the observed lines due to H160D and the
transitions calculated from the energy levels of Benedict and Clough, as shown by the
comparison in Table III. The inertial axes of H160D are rotated away from the position
they assume in the HP0 molecule. Therefore, while the CzU isotopic forms of water
have only a pb component, the semideuterated forms have both a pa and a pb component.
We can clearly identify five type a H160D transitions;
they are listed in Table III.
V4e can estimate
the ratio ~,/PI, by comparing the intensities of type a and type b
absorption lines. Depending upon whether the lines are observed in the linear or square
root region of the curve of growth, the equivalent widths are proportional
to Sfl or
(.S”)g, respectively [.Y is the line strength Eq. (2)]. If we
. are careful to compare lines
with similar equivalent widths, it is of lesser importance whether linear or square root
behavior is followed, so long as both lines are behaving similarly. Furthermore,
the
332
Lorentzian half-widths
ratio of the equivalent
FLEMING
AND
GIBSON
of type a and type b lines will not be too disparate,
widths (EW), and (EW)a is given simply by
(El+%/ (EW)
b ‘v
where we have assumed strong region behavior.
s,o/sbQ =
(p2/Pb2)
(&“/sbo)’
so that the
The ratio of the line strengths
’ (faeaSija/fblbSijb),
(3)
7
is
(4)
where f, 8, .Sij are the Boltzmann factor, the wavenumber, and the transition strength
of a given transition j + i. Two well-isolated lines of similar equivalent width are type
a 2rr+- 110at 33.688 cm-’ and type b 413+-- 322 at 27.595 cm-‘; these give (EW),/(EW)b
= 1.0046. From Eq. 4, we find pa/,.&b = 0.380 assuming strong region behavior, this
figure changing to 0.379 if weak region behavior is followed. The probable error we
estimate to be f3%,, so that this comparison gives ,&/,.‘b = 0.38 f 0.01. This is in
complete agreement with the ratio obtained from the microwave measurements
of
Clough et al. (13), who obtained po. = 0.6567D, pb = 1.731813, pa/,.&b = 0.379. The
relative intensities of the type a lines in Table III have been weighted by (,.&a/,.&b)2
in
order to make them directly comparable with the .!&I values of the type b lines.
c. H2180>H’*OD 9 D21sO
Our spectra of 90% enriched H2180 were recorded after the deuterated experiments
in the same absorption cell. A typical spectrum is shown in Fig. 3 ; very many more
absorption lines were observed than were expected from an H2160/HJ80 mixture. It
is apparent that a considerable amount of deuterium (in a bound form) had remained
on the walls of the absorption cell after evacuation, and that exchange occurred between
this and the H2160/H21s0. Over 50 absorption peaks were observed reproducibly
in
our ‘Qenriched
spectra; they can all be assigned to transitions of the six possible forms
of water formed from the H, D, 160, la0 isotopes, with the exception of one weak line
at 38.323 cm-‘; this is the Hz”0 32r+- 312 transition.
Toth and Margolis (14) have reported a study of the HJ80 spectrum around 3000
cm-’ from which they derived a set of ground-state
rotational energy levels. The submillimeter-microwave
spectrum of H2180 up to 25 cm-’ has been measured and analyzed
by De Lucia et al. (15). We base our assignments on a table of energy levels calculated
by Steenbeckeliers
(16) ; this is based on 12 observed microwave transitions and many
more infrared combination
differences. Similar tables supplied by Steenbeckeliers
(16)
for H180D and D&*0 were used in our assignments. Microwave measurements on DJ80
have been reported up to 400 GHz (13 cm-l) (17). Relative intensities for all isotopic
forms were calculated according to Eq. 1; an isolated line for each species was chosen
on which to base an estimate of the abundance of the different species. These abundances
were used to weight the calculated relative intensities. Table IV gives the assignments
and weighted relative intensities of all the lines observed in the 180-enriched spectra.
All the observed lines, down to the very weakest showing barely 2y0 absorption, have
been assigned satisfactorily.
Peak positions of some weak lines close to strong lines
are effected by the side lobes characteristic of unapodized Fourier transform spectrometry. The possible presence of Hz”0 absorption lines was tested for by calculating the
WATER
FIG. 3. 90y0 Enriched H&80 (deuterium
mm; resolution, 0.07 cm-l.
VAPOR
333
FAR-INFRARED
also present;
see text).
Pressure,
16 Torr;
path
length,
203
transitions
from the energy levels of De Lucia et al. (18). The two strongest transitions
are 312+ 303 at 36.573 cm-l and 32r+ 3r2 at 38.325 cm-r. The former position is obscured by a strong H2r60 line, but a small absorption peak is seen at 38.323 cm-‘. None
of the other isotopic forms of water considered here has a transition at this wavenumber.
The abundance of I70 in our specimen is not known, but the process of enriching with
I80 also enriches the natural I70 content.
Four type a transitions
in H’*OD are observed. We can compare the equivalent
widths of type a and type b lines as for Hr60D to find the ratio ,.L,/P~. None of the lines
of interest in H”OD is particularly well isolated; but the best pair with similar equivalent
width is the type a 212+- 111at 28.138 cm-’ and the type b 4r3 +-- 322 at 27.996 cm-‘. The
ratio of the two equivalent widths is (EW),/(EW)b
= 0.8224, which gives&pb
= 0.374
if strong region behavior is assumed, or ,u,/P~ = 0.41 if weak region behavior is followed.
The associated statistical error is f30/,, but it is clear that for H180D, we can only set
upper and lower limits on the ratio pJr(lb. The result p,/j~, = 0.39 f 0.02 is certainly
very reasonable from our knowledge of the Hr60D system.
FLEMING
D
AND GIBSON
WATER VAPOR FAR-INFRARED
.:
I
I
I
I
1i
I
I
I I
335
336
FLEMING
AND
GIBSON
TABLE IV-CmtimerE
CONCLUSION
The far-infrared
spectra of HJ60, D2160, H160D, H180D, H2180, and Dar80 have
been observed between 10 and 40 cm-’ at a resolution of 0.07 cm-l. Tables of energy
levels calculated for these molecules using recent centrifugal distortion theory results
have been used to assign all observed transitions. Theory and experiment agree within
the accuracy (f0.003 cm-l) of this experiment. Line positions and intensities measured
here are of importance to a full understanding
of very long path observations on the
earth’s atmosphere.
ACKNOWLEDGMENT
The authors are especially grateful to Dr. G. Steenbeckeliers
for these molecules, and for his useful comments.
RECEIVED: April 1,1976
for supplying his energy-level calculations
WATER
VAPOR
FAR-INFRARED
337
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
If.
12.
J. IL G. WATSON, J. Chem. Phys. 45, 1360 (1966).
J. W. FLEMING, IEEE Trans. MTT-22, 1023 (1974).
R. T. HALL AND J. M. DOWLING, J. Chem. Phys. 47, 2454 (1967).
R. B. SANDERSONAND H. E. SCOTT, Appl. Opt. 10, 1097 (1971).
F. C. DE LUCIA, P. HELWNGER, R. L. COOK, AND W. GORDY,Phys. Rev. A 5,487 (1972).
G. STEENBECKELIERS
AND J. BELLET, J. Mol. Spedrosc. 45, 10 (1973).
W. S. BENEDICT, S. A. CLOUGH,L. FRENKEL, AND T. E. SULLIVAN,J. Gem. Phys. 53, 2565 (1970).
W. J. LAFFERTY, J. BELLET, AND G. STEENBECKELIEKS,C. R. Acad. Sci. Paris 273,388 (1971).
W. S. BENEDICTAND S. A. CLOUGH,private communication from Dr. G. Steenbeckeliers.
F. C. DELUCIA, R. L. COOK, P. HELMINGER,AND W. GORDY, J. Chem. Phys. 55, 5334 (1971).
H. J. SLONE, Ph.D. thesis, Ohio State University, 1964.
C. H. TOWNESAND A. L. SCHAWLOW,“Microwave Spectroscopy,” App. V, McGraw-Hill, New York,
195.5.
13. S. A. CLOUGH,Y. BEERS, G. P. KLEIN, AND L. S. ROTHMAN,J. Chem. Phys. 59,2254
(1973).
13. R. A. TOTH AND J. S. MARGOLIS, J. Mol. Spectrosc. 57, 236 (1975).
15. F. C. DELUCIA, P. HELMINGER,R. 1,. COOK, AND W. GORDY, Phys. Rev. A. 6, 1324 (1972).
16. G. STEENBECKELIERS
AND Dr. J. BELLET, private communication.
17. J. BELLET, W. J. LAFFERTY, AND G. STEENBECKELIERS,
J. Mol. Speclrosc. 47, 388 (1973).
I,?. I:. C. DE LUCIA AND P. HELMINGER,J. Mol. Spectrosc. 56, 138 (1975).