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The laser spectroscopy of highly excited vibrational states of HD16O
JOURNAL
OF MOLECULAR
SPECTROSCOPY
153, 197-207 ( 1992)
The Laser Spectroscopy of Highly Excited Vibrational States of HD160 A. D. BYKOV, V. A. KAPITANOV, 0. V. NAUMENKO, T. M. PETROVA, V. I. SERDYUKOV,AND L. N. SINITSA Institute of Atmospheric Optics, Siberian Branch Academy of Sciences of USSR, Tomsk 634055, USSR
Theabsorption spectra ofHD160wererecorded using a F$:LiF color center intracavity laser spectrometer in the 0.9~pm region and an optoacoustic dye laser spectrometer in the 0.59-pm spectral region. Energy levels and rotational and centrifugal distortion constants of the (003) and (005) states were determined. Improved sets of vibrational and vibration-rotation constants have been obtained by fitting all available data for the energy levels of HDO. o 1992 Academic press. IX. 1. INTRODUCTION
The investigation of high-resolution spectra of Hz0 and its major isotopomers is required for the interpretation of atmospheric spectra and calculations of the absorption due to minor atmospheric constituents in the atmospheric transmittance windows. Since the HD I60 molecule is an asymmetric isotopic modification of water, studying its spectrum will provide additional information needed for the determination of the intramolecular potential function of the water molecule. The absorption spectrum of H2160 has been very extensively studied; about 100 bands from 0 to 22 596 cm-’ have been included in databases (1, 2). However, for the HD I60 molecule only 13 bands have been observed so far. The first extensive study of the HDO in the infrared region using spectral resolution of 0.25 cm-’ was carried out by Benedict et al. (3)) where 10 vibration-rotation bands were found in the region 2400-8000 cm-‘. The high-resolution spectra of HD I60 were discussed in Refs. (d-14). Pure rotational lines were observed in the MW (4, 5) and the far-infrared FTS (6) experiments. Recently, Fourier transform spectra were recorded for the v2band ( 7) (in the spectrum of natural water vapor), for the zq and 2~~ bands (8, 9), for the u3, u1 + v2, and 3v2 bands (ZO), and for the ~2 + v3 band (II). The absorption spectra of the q + ~3and 2u2 + v3 bands have been recorded from 6380 to 6600 cm-’ by using single-mode distributed feedback semiconductor lasers ( 12) with an experimental accuracy of about 0.004 cm-‘. The highly excited vibrational states of the HDO molecule, (0 12 ), ( 12 1)) and ( 3 lo), were studied using highly sensitive intracavity laser spectrometers ( 13, 14) from 8000 to 9500 cm-‘. Accurate values for the rotational energy levels of the ground vibrational state and spectroscopic constants of the Watson-type reduced Hamiltonian have been reported by Johns and colleagues (6) and by Papineau et al. (8). A least-squares fit of rotational and resonance constants was carried out by Pert-in eta1.(15,16)inthecaseofthefirsttworesonancediads{(100)-(020)}and{(110)(030) >. The parameters of the Watson Hamiltonian for the well-isolated vibrational states (OOI), (01 l), and (012) have been reported in Refs. (II, Z4, 17). A model of the nonresonant vibrational state has been used and the values of rotational constants 197
0022-2852/92 $5.00 Copyright 0 1992 by Academic Press, Inc. AH rights of reproduction in any form reserved.
198
BYKOV
ET AL.
were obtained for the vibrational states (3 10) and ( 12 1) belonging to the resonance triad { ( 3 10) - ( 12 1) - (04 1) > in Ref. ( 13). The rotational and resonance constants of the (( lOl )-(021) > diad were reported in a recent publication (12). In this paper we report the first observations and analysis of the spectra of HD I60 in the 0.9- and 0.59-pm regions. 2. EXPERIMENTAL
DETAILS
The HDO vibrational bands in the short wavelength spectral range are very weak and consequently we used a highly sensitive laser spectrometer for the investigation. The absorption spectra were measured using a F::LiF color center intracavity laser spectrometer in the 0.9-pm region and an optoacoustic dye laser spectrometer in the 0.59~pm spectral region. The Intracavity Laser ~~ect~~rneter The method of intracavity laser (ICL) spectroscopy consists of quenching the laser emission at the absorption-line frequencies of the species placed in a broadband laser cavity. In ICL spectroscopy the laser itself is a nonlinear detector of weak absorption. The ICL spectrum in the vicinity of an absorption line can be described as J(v, 0 = J(v,
o)ew[-k(vW,ffl
LeR= GJLL,,
(1)
where J( Y, 0) represents the normalized spectrum formed at the initial time of generation, L, is the length of the absorbing layer, L, is the length of laser cavity, and c is the speed of light. To obtain a highly sensitive ICL spectrometer the laser should have a long pulse duration t . A F: :LiF laser operated at room temperature was used in a highly sensitive ICL spectrometer. A detailed description of the spectrometer was presented in Ref. (18). The pumping of the color center laser was performed with a quasi-c.w. ruby laser with a pulse duration of 900 PS in the longitudinal pump geometry. The pulse duration of the F2+:LiF laser was 400 I.LSand thus provided the EL spectrometer with a threshold absorption sensitivity of 3 X lo-* cm-’ . The spectral range per pulse was 100 cm-’ and the total tuning range of the spectrometer was 10 280-10 770 cm-‘. The ICL spectrum was recorded using a spectrograph with a spectral resolution of 0.05 cm-‘. An equilibrium mixture of HzO, D20, and HDO (its total pressure was 19 Torr and the tem~rature was 296-600 K) was used. The abso~tion lines of HZ0 present in the spectrum served as reference lines, relative to which the positions of the HDO lines were measured with an accuracy of 0.03 cm-‘.
The distinction between the absorption spectra of H20, HDO, and DzO can effectively be made in the spectrometers based on narrowband lasers (Au < 0.001 cm-’ ) by recording the absorption due to the mixture and the absorption due to a single component simultaneously with a pair of optoacoustic detectors. The detection sensitivity of the optoacoustic (OA) spectrometers can be improved by 10 or 100 times by placing an OA detector in the laser cavity. However, setting the OA detector in the cavity of the single-mode tunable laser requires a considerable
HIGHLY
EXCITED
HDO STATES
199
(more than twofold) increase in the cavity length and, consequently, a decrease in the distance between the longitudinal cavity modes. This makes it difficult to select one longitudinal mode and to obtain a smooth tuning. In a linear dye laser, due to space-inhomogeneous saturation in a thin active medium (the jet thickness is 0.02 cm) the most stable and easily co&rolled is a two-frequency generation regime. The distance Au between the generated frequencies is a function of the distance L on the jet up to the cavity mirror Au = c/4L. In our case the lasermode difference was 1.8 GHz and remained constant in laser spectral tuning. Thus an optoacoustic spectrometer with a two-frequency dye laser with OA detectors inside the cavity scanned every absorption line twice and two absorption lines appeared in the spectrum instead of one. The distance between them is equal to the distance between generating modes. Since the distance is not changed during tuning one can easily take into account such doubling lines and can obtain a real absorption shape. The OA spectrometer with two detectors inside the cavity of a two-frequency dye laser is simpler in performance than the spectrometer with a one-frequency laser. Narrowing of the laser linewidth is achieved by means of two selecting elements, i.e., using a birefringent filter and a fine Fabry-Perot &talon with a relatively small reflection coefficient. The linewidth of the modes was determined by frequency fluctuations and was equal to lo-20 MHz. The signals of optoacoustic detectors are measured by the frequency modulation method (recording the first derivative). This completely excludes a frequency-independent background signal and increases the spectrometer resolution. The OA spectrometer has a threshold sensitivity of < 1O-’ cm-’ for a power of 1 W; its detailed description is presented in Ref. ( 19). In order to separate the absorption spectra of the isotopomers, the Hz0 vapor was placed in one of the OA detectors and a mixture of HDO, D20, and Hz0 was placed in the other. Moreover, the spectrum of Hz0 in the visible region has been fairly well studied (20) and Hz0 absorption lines were used as reference lines relative to which the line positions of HDO were measured with an accuracy of 0.005 cm-‘. 3. THEORETICAL
ANALYSIS
To interpret the spectra of HDO in the 0.9- and 0.59-pm regions where investigations of the HDO spectra have not been performed previously, estimations of the band origins and rotational constants are needed. The vibration-rotation constants czi, &, vibrational frequencies wi, anharmonic constants x,, and Fermi-resonance constant F were determined using a least-squares fitting to previously obtained (3, 7-17) band centers, and the A, B, and C rotational constants of 13 bands of HDO. These parameters were used to calculate the spectra of HDO in the 0.9- and 0.59-pm regions. The Line Assignments The band center calculations have provided us with the general structure of the absorption spectrum of HDG and D20 in the spectral regions under investigation. There are four absorption bands of HDO: 3v3, 2ul + ~2 + ~3, IJ~+ 31~2+ ~3, and 5~ + u3at 0.9 pm. The vibrational quantum numbers and energies of the upper vibrational states are presented in Table I. The 3~3band appears to be the strongest among others because of smaller changes in vibrational quantum numbers. The preliminary calculations have shown that in the region 16 746- 17 0 12 cm-’ the lines of the 5u3, 4ul + 22~ + v3, ul + 4v3, and 5~ + u3 bands may occur. The
200
BYKOV ET AL. TABLE I The Band Origins for Some Vibrational Bands of HD I60 (in cm-‘) 0.9 YY”
123
0.59
pm
E Y
051
10343
211 131 003
y*yzvJ
pm
E Y
501
16491
1039s
104
16525
10474
421
16684
10623
005
16899
estimations of the band origins are shown in Table I. It may be supposed that the strongest band in this region is 5v3 for the same reason as in the 313 case. Another strong band ZQ+ 4~~ with the same Au = 5 as for 5v3 is out of the spectral region under investigation. The other bands listed in Table I for the 0.59-pm region must be at least an order of magnitude weaker. For line assignment the calculations of positions and relative strengths of the lines in the spectral regions from 10 280 to 10 780 cm-’ and from 16 500 to 17 800 cm-’ have been carried out. The results of the calculations as well as combinational differences of the lower state were used to assign the lines with J = 1, 2, and 3. After dete~ination of the energy levels with J G 3 the rotational constants have been fitted and new values of constants were used for the line center calculations. The assignments of the lines with larger values of Jwere accomplished by refining spectroscopic constants at each new step. From 667 lines, found in the 0.9-pm spectrum, 317 lines have been assigned as transitions from the ground to the (003) vibrational state. In the 0.59-pm spectrum, 231 lines have been assigned as transitions from the ground to the (005) vibrational state among 2.51 lines previously attributed to HDO. The energy levels of the (003) vibrational state deduced from the spectrum are shown in Table II. We have found 97 energy levels of the (003) vibrational state up to J = 14 and iu, = 7. The analysis of the relative strength of the lines has shown that the 3v3 band is a “hybrid” band with nearly equal intensities for “a” and “b” type transitions. Eighty-six energy levels have been determined for the (005) vibrational states up to J = 11 and iu, = 7. These energy levels are also shown in Table II. It follows from the relative line-strength ~ompa~son that the 5~ band is an “a” type, and an intensity of “b” transitions is 10 times weaker than that of an “a” transition. The Rotational Constants Determination The energy levels determined are used to fit the rotational and centrifugal distortion constants for both the (003) and the (005 ) vibrational states. We have used the Watson A-reduced Hamiltonian for this dete~ination, + B” i- C” J2 + B” - C” Jz xy 2 2
TABLE II The Rotational Energy Levels for the ( 003 ) and (005 ) Vibrational States of HD I60 (in cm-‘) (003) JK
K a c
0 1
0 0
0 1
111 110 2 0 2 2 12 211 2 21 2 2 0 3 0 3 313 312 3 2 2 3 21 3 31 3 3 0 4 0 4 414 413 4 2 3 4 2 2 4 3 2 431 4 41 4 4 0 5 0 5 5 15 514 5 2 4 5 2 3 5 3 3 5 3 2 5 4 2 5 4 1
5 5 1
5 5 6 0 616 615
0 6
E exF.. 10631.68 10646.90 10658.17 10661.05 10676.63 10685.76 10694.42 10728.23 10726.74 10720.65 10726.80 10744.09 10773.93 10776.23 10837.35 10837.41 10777.36 10781.14 10809.56 10834.29 10840.87 10898.96 10899.36 10985.93 10985.93 10846.25 10848.31 10890.01 10903.27 10922.88 10976.09 10977.44 11062.84 11062.89 11173.38 11173.38 10927.14 10328.21 10984.63
(0051
Na 2 3 4 3 3 6 3 3 2 4 5 5 5 6 3 3 4 3 5 3 5 4 4 2
1 3 4 5 7 6 3 2 3 4 3 3 4 3 5
6; -4 -3 1 2 2 -1 0 0 -3 2 2 -1 -5 -1 -1 -2 -1 -4 -2 6 -1 2 -3 0 0 -1 0 7 1 0 2 4 3 2 -3 -3 0 1 0
E oxp.
6 6 6 6 6 6 6 6
a
K
2 2 3 3 4 4 5 51
c 5 4 4 3 3 2 2
6 6 1 6 6 0 7 0 7 7 17 716 7 2 6 7 2 5 7 3 5 7 3 4 7 4 4 7 4 3 7 5 3 7 5 2 7 6 2 7 6 1 7 7 i 7 7 0 8 0 8 818 81-I 8 2 7 8 3 6
E exp. 10998.32 11021.91 11068.63 11072.50 11155.39 11155.62 11265.42 11265.42 11398.65 11398.65 11020.10 11020.63 11091.99 11100.99 11137.34 11176.29 11184.94 11263.65 11264.33 11373.02 11373.02 11505.78 11505.78 11660.71 11660.71 11125.12 11125.34 11211.53 11216.89 11289.75
N
1 2 3 3 3 4 4 2 3 4 4 4 4 5
17123.364 17130.583 17173.647 17187.500 17203.558 17246.453 17248.523 17320.994 17321.069 17415.786 17415.766 17207.914 17208.482 17265.894
4 4 3 4 3 2
-3 4 0 -1 3 0 0 0 2 2 -2 -4 8 -3
E exp.
-8 -4 0 -2 -6 0 1 -13 2 11 2 12 1 -2 1 0 3 5 3 1 3 4
N
62
17274.861 17302.046 17338.058 17343.644 17412.926 17413.290 17507.254 17507.254 17621.634 17621.634 17298.268 17298.519 17370.159 17375.397
1 3 2 3 2 2 2 2 2 2 3 4 4 3
11 0 -5 7 2 3 -5 4 -4 -3 -S -7 13 3
17456.523 17520.408 17521.658 17614.191 17614.235 17728.092 17728.092
1 2 3 1 2 1 1
-10 -7 6 -6 3 0 0
17400.465 17400.564 17485.857 17488.657 17565.124
3 4 3 2 1
-4 3 13 2 3
1 1 5 -1 1 1 3 -4 -4 2 2 0 3 2 -3 1
a The number of observed lines arriving at the corresponding level.
b S, = (I&. - Ed,)
1 2 3 2 5 2 3 3 3
2 7 2 -2 0 1 -a 3 3 3 -5 0 2 0 -4 0 -3 -3 0 -10 2 -4 0
(005) 6,
2 4 7 2 5 2 3 3 1 1 4 3 4 4 2 2 4 3 3 3 3 1 1 1 1 4 3 3 5 3
6;
16920.023 16935.073 16944.542 16847.571 16964.563 16971.620 16980.691 17008.985 17009.600 17007.382 17011.877 17029.907 17054.108 17057.025 17108.866 17108.941 17062.494 17064.965 17094.561 17113.763 17121.669 17169.992 17170.533
(003) JK
N
lo* cm-‘.
c& = (Eotn.Ed,.)IO3cm-‘. 201
BYKOV
202
ET AL.
TABLE &--Continued
.(005)
(003) JK
a
K G
8 8 8 8 8 8 8 8 8 9 S 9 9 Q s
3 4 4 5 5 6 6 7 7 0 1 1 2 2 3
5 5 4 4 3 3 2 2 1 9 9 8 8 7 7
9 9 9 9 9 10 10 101 102 102 103 103 104 105 106 11 11 12 12 121 122 130 13 13 14 14
4 6 5 7 7 0 1
6 5 4 3 2 10 10 9 9 8 8 7 7 6 4 11 11 12 12 11 11 13 13 12 14 14
J2 = J;+
0
1 0 1
1 2 0 1
J;+
E cnp.
N
61
11387.49 11389.42 11496.25 11496.35
2 3 2 2
11628.25 11628.25 11782.69 11782.69 11242.33 11242.45 11342.68 11345.63
1 1 1 1 3 2 2 2
2 7 0 0 1 1 -1 -1 -1 -2 1 3
11435.58
2
-1
11371.72 11371.72 11485.44 11487.06
11513.22 11513.22 11666.85 11666.85 11806.40 11806.85 11832.60 11832.60 11984.94 12010.49 12010.49
J:,
2 2 2 1
2 2 2 2 1 1 1 1 1 1 1
E erp.
Ii
*2
17586 990 17643.335 17646.794
2 2
17736.897 17849.917 17849.917
2
17514.538 17614.594
1 1
9 -2
17SR5.972 17699.622
1 1
-4 -17
17781.437 17874.751 17875.463 18119.438 18119.438
1 2 2 1
0 -8 -4 0 0
17839.058 17847.346 17897.256 17934.441 18028.375 ~8140,000 17778.435 17778.435
1 i 1 1 2 1 1
0 -5 -3 11 4 0 -7 0
1 1 1
I
3 -6 7 -10 -2 4
-3 2 3 -1
-1 1 2 3 2 -3 4 4 2 -1 0
1
J$ = J; - J;>, (A, B} = AB -I- BA
The results of the fit are shown in Table III. The quoted errors are in the last digits (one standard deviation) and are given in parentheses. The values without errors were fixed during the fit. It may be seen that the mean deviations of calculated energy levels from experimental ones are comparable with mean experimental errors for both the (003) and the (005) vibrational states. A statistical analysis of differences 6 = I Ebbs.- Ecalc.1 shows a satisfactory agreement between the observed and calculated energies. For 97 rotational levels of the (003) vibrational state used in the least-squares fit,
HIGHLY EXCITED HDO STATES
203
TABLE III The Rotationa Constants of the (003) and (005) Vibrational States of HD160 (in cm-‘)a (003)
E
1005)
10631.6366s,(831
Y
16920.0248e(23~
20.381464G!1)
18.513179(72)
9.06731,_w91
9.044389(22)
6. 1703028(22)
6.01198s(223
o.9319a(11)
0.81659(63)
0.64437(65)
0.037s(121
3.5998s(821
4.324s(36)
1.50733c42)
1.531811il
1.23STsf41f
1.50646(76)
3.3s8*c19)
2.SSo(15)
-14.043(13)
-9. 26Sb
2.4b
3. 1438(85)
3.sb
J hk
10’
1.8b
h
IO8
l.Ob
,* h. , L*
lo*
2. lb
107
-2. 51zb
L
do* lk lo7
P
* rms J/K
lo=
16. 30(20) 1.9818C45)
-2. 512b
8.6b -l.sb 0.58331)
3.453(21)
0.028
0.006
14/7
1117
* The quoted errors (one standard deviation f in the last digits are in parentheses. b Constants were fixed to (000) values during the fit.
S G 0.02 cm-’
65.9% (of the levels)
0.02 < 6 G 0.04
26.9%
0.04 < 6 < 0.06
4.1%
0.06 < 6 =G0.08
3.1%.
Of all energy levels, 92.8% are reproduced by the fit with errors not exceeding 0.04 cm-‘. A statistical analysis of 86 values of 6 = I Eobs.- Eca~c. I of the (005) vibrational state leads to the following results: 6 G 0.005 cm-’
72% (of the levels)
0.005 < 6 G 0.010
19%
0.010 < 6 =S0.018
9%.
It may be noted that errors of calculation are not greater than 0.0 1 cm-’ for 9 1% of the levels.
204
BYKOV ET AL.
The Vibration Energy Levels of HD160 The new band centers and those known from earlier studies (3, 7-14) have been used to derive the vibrational constants of HD 160. The usual vibrational Hamiltonian with matrix elements (VlHI
Xo(L’;
V) = C w~(V, + l/Z!) + 2 i
+
l/Z)(Vj
+
l/2)
isj +
C
Yijk(vi
i
+
l/z)(vj
(~1 v2 vx/HIvI + 1 v2 - 2 vj) = Fi(v,
+
l/2)(%
+
l/2),
+ l)v2(v2 - 1)/4,
(3) (4)
where V = ~1~2~3 have been used. Among the anharmonic resonances only the Fermi resonance was taken into account. The harmonic frequencies, the anharmonic xv and some of the ytik constants, and the resonance constant F have been determined from least-squares fitting to 14 band centers. The parameters obtained are shown in Table IV. The vibrational frequencies
TABLE IV The Harmonic Frequencies and Anharmonic, Fermi-Resonance, and Vibration-Rotation Constants of HD I60 (cm-‘) ul= 2823.946'
2624.3b
02=
1443.723"
1440.2b
03= 3893.40saf0.67
3889.8b
x1,= -43.648,8+0.085 x
= -5.9235f0.17 12
x
= -13.4589+0.26 13
x = -12.0262+o.16 22 xz3= -24.81 f0.37 10
-43.4b -8.6' -13.1b -1l.P
YzZz=-0.697,0f0.052
-20.1b
Y223=1.6477+0.14
xz3= -84.3796+0.24
-82.gb
Y333=0.4686~+0.027
F
= -9.2619*f0.057
-9.37c
A
=
23.3f?lo8+0.113
=
0.449,0'0.097
e
aIr
PI,,= 0.068s2f0.025
a = -1.2711t0.10 2*
P 22*= o.4196*+o.024
a 3* =
o.890~2+o.025
P23*=-o.19622+o.031
B e
9.127821'0.0080 C
=
e
= 6.545662+0.0032
= 0.172120+0.0030 OLIB
a,c= o.1101~2+o.oo12
=-o.13402*+o.oo29
azc= 0.085981+0.0011
= 0.0115,,'0.0020
azc= 0.0791672'0.00079
"ze %
a Calculated with isotopic rules, Ref. ( 21) bFrom Ref. (3). ’ From Refs. (15, 16).
205
HIGHLY EXCITED HDO STATES
marked with an “a” were calculated by means of isotopic rules (21) and were fixed during the fit. The a~ment between caIculated and experimental vibrational energies is satisfactory (the rms is 0.20 cm-‘). The parameters from Table IV are in agreement with those obtained by Benedict et al. (3). The value of the resonance parameter F is almost the same as that obtained by Pen-in et al. (15, 16) from the analysis of the first and second diads of interacting vibrational states of I-DO. The first set of vibrational parameters used to predict spectra in the 0.9- and 0.59pm regions had errors of about 8 cm-’ for the band center of 3v3 and 20 cm-’ for 5~. We believe that the new set of parameters which was obtained using the (003) and (005) states showed marked improvement in the predictions. The new values of vibrational constants were used to calculate bands origins up to 13 000 cm-‘. The results are presented in Table V, We have found the vibration-rotation constants (Y; , & from least-squares fitting to rotational constants of 14 vibrational states. The following formulas have been used, X(V) = Xe - C CXi\.(Ui + l/2) + x Bij_x(Vi+ 1/2)(Vj + i/2), i
(5)
isj
where X ( =A, B, or C) is the rotational constant in the vibrational state V and X, is the equilibrium values. The constants obtained are presented in Table IV. A comparison of the experimental A, B, and C constants of the (005) state with predicted ones shows that errors of prediction are about 0.01 cm-’ . 4. CONCLUSIONS
The highly excited vibrational states (003) and (005~ of HID I60 have been investigated for the first time. Line assignments and energy levels were determined and the rotational constants of the Watson A-reduced Hamiltonian were obtained. TABLE V The Vibmtion~ Energy Levds of HDi60 up to 13 000 cm-’
0 1 0 10 0 0 2 0 0 0 1 0 3 0 1 1 0 0 11 2 0 0 0 4 0 12 0 1 0 1 0 2 1 0 s 0 2 10 13 0 0 0 2 0 3 1 1 1 1 3 0 0 2 2 0 1 4 0 0 12 2 0 1 0 4 1 12 1 3 1 0
1403.68 2723.83 2781.80 3707.45 4099.99 4145.53 5089.62 5363.60 6414.04 5508.64 6415.41 6451.93 6677.43 6749.08 6851.63 7250.37 7759.83 7810.97 7916.43 8087.72 8177.15 8611.02 9041.90 9058.46 9161.83 9292.84
0.19 0.15 -0.20 -0.01 0.04 0.06 0.08 0.01
-0.05 0.03
-0.07
-0.03
1 2 0 1 0 4 2 1 0 3 2 0 1 3 1 4 2 3 0 0 2 1 5 3 1 0
5 0 3 0 2 2 0 2 5 1 0 0 1 i 3 1 0 3 2 0 4 0 3 2 12 0 1 4 1 1 0 2 1 3 0 1 3 4 2 0 2 2 2 0 0 1 1 5 1 0 5
9367.82 9494.68 9936.89 9963.10 10310.99 10391.53 10405.33 10493.02 10631.56 10650.71 10735.82 11252.14 11314.85 11583.05 11722.96 11756.24 11610.83 11943.79 11970.70 12532.69 12560.67 12651.24 12759.36 12335.43 12991.30 16920.02
-0.12
0.002
206
BYKOV ET AL.
FIG. 1. The ug dependence of the rotational A (a) and centrifugal Ak (b) constants of HDO (0, (0011~) states; X, ( 0 1vj ) states).
The energy level calculations of the vibration-rotation states (003 ) and (005 ) of the HDO molecule appear to be reliable without taking into account accidental resonances. This is contrary to our experience with the highly excited energy level calculations for light asymmetric top molecules (such as HzO, HIS) where it was necessary to include the effects of a large number of resonances (see, for instance, Ref. (22)). The vibrational states (00~) of HDO may be considered isolated ones because the Darling-Dennison or Coriolis type resonances are not significant due to the large difference between the v1, 2vz, and v3 vibrations. The resonances between considered vibrational states and others nearby are negligible because of large changes in vibrational quantum numbers. Indeed, the energy difference between the (003) state and its nearest vibrational state (320) is only 19 cm-‘, but nondiagonal matrix elements of the Hamiltonian are small, at least for small values of quantum number J. Hence, in the first approximation we can neglect the accidental resonances in energy level calculations. The situation is the same in the case of the (005) vibrational state. It is useful to compare the parameters of the (003 ) and (005 ) states with the parameters of the (00~~) and (0 103) type vibrational states. The dependence of rotational constants on u3 is shown in Fig. 1. It may be seen that there is a systematic trend in the rotational and centrifugal distortion constants with an increase in the quantum number 03. The rotational constants show a near linear dependence on the number of OH-stretching vibration quanta. The same behavior of rotational constants occurs in the case of the (0 1213)set of vibrational states of HD I60 (14, 17). This shows that the nonresonant Hamiltonian ( 1) is a realistic one for the (003) and (005) states despite the high-energy excitation. The redetermination of the spectroscopic constants of HDO appears to make possible a more accurate calculation of the rotational constants for the bands in the short wavelength range. ACKNOWLEDGMENTS The authors express their gratitude to Dr. A. Karablev and Dr. S. Kobtsev, who gave them the opportunity to record the spectrum
RECEIVED:
at Novosibirsk
December 9, 1991
State University.
HIGHLY
EXCITED HDO STATES
207
REFERENCES 1. M. HLJ~~ON, B. BONNET,N. A. Scan, AND A. CHEDIN,The “GEISA” data bank 1991 version, Laboratoire de Meteoroiogie Dynamique du CNRS, unpublished. 2. L. S. ROTHMAN,Appl. Opt., to be published. 3. W. S. BENEDICT, N. GAILAR,AND E. K. PLYLER,J. Chem. Phys. 24,1139-l 165 ( 1956). 4. J. K. MESSER,F. C. DE LUCIA,AND P. HELMINGER, J. Mol. Spectrosc. 105, 139-155 ( 1984). 5. F. C. DE LIJ~IA,R. L. COOK,P. HELMINGER, ANDW. G~RDY, J. Chem. Phys. 55,5334-5339 ( 1971 f. 6. J. W. C. JOHNS,J. Opt. Sot. Am. B 2, 1340-1354 (1985). 7. G. GUELACHVILI, J. Opt. Sot. Am. 73, 137-150 (f983). 8. N. PAPINEAU, C. CAMY-PEYRET,J.-M. FLAUD,AND G. GLJELACHVILI, J. Mol. Spectrosc. 92,45 l-468 (1982). 9. R. A. Tow, V. D. GUPTA,AND J. W. BRALJLT, Appl. Opt. 21,3337-3347 ( 1982). IO. R. A. TOTHANDJ. W. BRAULT,Appl. Opt. 22,908-926 ( 1983). II. A. D. BYKOV, 0. V. ZOTOV, V. S. MAKAROV,AND 0. V. NAUMENKO,to be published. 12. T. OHSHIMAAND H. SASADA,J. Moi. Spectrosc. 136,250-263 ( 1989). 13. A. D. BYKOV, V. P. L~PASOV,Yu. S. MAKUSHKIN,L. N. SINITSA,0. N. ULENIKOV,ANDV. E, ZUEV, J. Mol. Spectrosc. 94, l-l 7 ( 1982). 14. A. D. BYKOV, Yu. S. MAKUSHKIN,V. I. SERDYUKOV,L. N. SINITSA,0. N. ULENIKOV,AND G. A. USHAKOVA,J. Mol. Spectrosc. 105, 397-409 ( 1984). IS. A. PERRIN,J.-M. FLAUD,AND C. CAMY-PEYRET,J. Mol. Spectrosc. 112, 153-162 (198.5). 16. A. PERRIN,C. CAMY-PEYRET,AND J.-M. FLAUD,Can. J. Phys. 64,736-742 ( 1986). 17. A. D. BYKOV,V. S. MAKAROV,N. 1. MOSKALENKO, 0. V. NAUMENKO,0. N. ULENIKOV.AND 0. V. ZOTOV, J. Mol. Specirosc. 123, 126-134 ( 1987). 18. V. P. KOCHANOV,V. I. SERDYUKOV,AND L. N. SINITSA,Opt. Actu 32, 1273-1280 ( 1985). 19. B. V. BONDAREV,V. A. KAPITANOV,S. M. KOBTSEV,AND Yu. N. PONOMAREV, Opt. Atmos. l( lo), 18-24 (1988). 20. C. CAMY-PEYRET,J.-M. FLAUD,J.-Y. MANDIN,J.-P. CHEVILLARD, J. BRAULT,D. A. RAMSAY,AND M. VERVLOET,J. Mol. Spectrose. 113,208-228 ( 1985). 21. A. D. BYKOV, Yu. S. MAKUSH~N, AND 0. N. ULENIKOV,f. Mol. Spectrosc. 85,462-479 ( 1981). 22. Yu. S. MAKUSHKIN,0. N. ULENIKOV,ANDI. V. LEVASHKIN,J. Mol. Spectrosc. 144, l-17 ( 1990).
OF MOLECULAR
SPECTROSCOPY
153, 197-207 ( 1992)
The Laser Spectroscopy of Highly Excited Vibrational States of HD160 A. D. BYKOV, V. A. KAPITANOV, 0. V. NAUMENKO, T. M. PETROVA, V. I. SERDYUKOV,AND L. N. SINITSA Institute of Atmospheric Optics, Siberian Branch Academy of Sciences of USSR, Tomsk 634055, USSR
Theabsorption spectra ofHD160wererecorded using a F$:LiF color center intracavity laser spectrometer in the 0.9~pm region and an optoacoustic dye laser spectrometer in the 0.59-pm spectral region. Energy levels and rotational and centrifugal distortion constants of the (003) and (005) states were determined. Improved sets of vibrational and vibration-rotation constants have been obtained by fitting all available data for the energy levels of HDO. o 1992 Academic press. IX. 1. INTRODUCTION
The investigation of high-resolution spectra of Hz0 and its major isotopomers is required for the interpretation of atmospheric spectra and calculations of the absorption due to minor atmospheric constituents in the atmospheric transmittance windows. Since the HD I60 molecule is an asymmetric isotopic modification of water, studying its spectrum will provide additional information needed for the determination of the intramolecular potential function of the water molecule. The absorption spectrum of H2160 has been very extensively studied; about 100 bands from 0 to 22 596 cm-’ have been included in databases (1, 2). However, for the HD I60 molecule only 13 bands have been observed so far. The first extensive study of the HDO in the infrared region using spectral resolution of 0.25 cm-’ was carried out by Benedict et al. (3)) where 10 vibration-rotation bands were found in the region 2400-8000 cm-‘. The high-resolution spectra of HD I60 were discussed in Refs. (d-14). Pure rotational lines were observed in the MW (4, 5) and the far-infrared FTS (6) experiments. Recently, Fourier transform spectra were recorded for the v2band ( 7) (in the spectrum of natural water vapor), for the zq and 2~~ bands (8, 9), for the u3, u1 + v2, and 3v2 bands (ZO), and for the ~2 + v3 band (II). The absorption spectra of the q + ~3and 2u2 + v3 bands have been recorded from 6380 to 6600 cm-’ by using single-mode distributed feedback semiconductor lasers ( 12) with an experimental accuracy of about 0.004 cm-‘. The highly excited vibrational states of the HDO molecule, (0 12 ), ( 12 1)) and ( 3 lo), were studied using highly sensitive intracavity laser spectrometers ( 13, 14) from 8000 to 9500 cm-‘. Accurate values for the rotational energy levels of the ground vibrational state and spectroscopic constants of the Watson-type reduced Hamiltonian have been reported by Johns and colleagues (6) and by Papineau et al. (8). A least-squares fit of rotational and resonance constants was carried out by Pert-in eta1.(15,16)inthecaseofthefirsttworesonancediads{(100)-(020)}and{(110)(030) >. The parameters of the Watson Hamiltonian for the well-isolated vibrational states (OOI), (01 l), and (012) have been reported in Refs. (II, Z4, 17). A model of the nonresonant vibrational state has been used and the values of rotational constants 197
0022-2852/92 $5.00 Copyright 0 1992 by Academic Press, Inc. AH rights of reproduction in any form reserved.
198
BYKOV
ET AL.
were obtained for the vibrational states (3 10) and ( 12 1) belonging to the resonance triad { ( 3 10) - ( 12 1) - (04 1) > in Ref. ( 13). The rotational and resonance constants of the (( lOl )-(021) > diad were reported in a recent publication (12). In this paper we report the first observations and analysis of the spectra of HD I60 in the 0.9- and 0.59-pm regions. 2. EXPERIMENTAL
DETAILS
The HDO vibrational bands in the short wavelength spectral range are very weak and consequently we used a highly sensitive laser spectrometer for the investigation. The absorption spectra were measured using a F::LiF color center intracavity laser spectrometer in the 0.9-pm region and an optoacoustic dye laser spectrometer in the 0.59~pm spectral region. The Intracavity Laser ~~ect~~rneter The method of intracavity laser (ICL) spectroscopy consists of quenching the laser emission at the absorption-line frequencies of the species placed in a broadband laser cavity. In ICL spectroscopy the laser itself is a nonlinear detector of weak absorption. The ICL spectrum in the vicinity of an absorption line can be described as J(v, 0 = J(v,
o)ew[-k(vW,ffl
LeR= GJLL,,
(1)
where J( Y, 0) represents the normalized spectrum formed at the initial time of generation, L, is the length of the absorbing layer, L, is the length of laser cavity, and c is the speed of light. To obtain a highly sensitive ICL spectrometer the laser should have a long pulse duration t . A F: :LiF laser operated at room temperature was used in a highly sensitive ICL spectrometer. A detailed description of the spectrometer was presented in Ref. (18). The pumping of the color center laser was performed with a quasi-c.w. ruby laser with a pulse duration of 900 PS in the longitudinal pump geometry. The pulse duration of the F2+:LiF laser was 400 I.LSand thus provided the EL spectrometer with a threshold absorption sensitivity of 3 X lo-* cm-’ . The spectral range per pulse was 100 cm-’ and the total tuning range of the spectrometer was 10 280-10 770 cm-‘. The ICL spectrum was recorded using a spectrograph with a spectral resolution of 0.05 cm-‘. An equilibrium mixture of HzO, D20, and HDO (its total pressure was 19 Torr and the tem~rature was 296-600 K) was used. The abso~tion lines of HZ0 present in the spectrum served as reference lines, relative to which the positions of the HDO lines were measured with an accuracy of 0.03 cm-‘.
The distinction between the absorption spectra of H20, HDO, and DzO can effectively be made in the spectrometers based on narrowband lasers (Au < 0.001 cm-’ ) by recording the absorption due to the mixture and the absorption due to a single component simultaneously with a pair of optoacoustic detectors. The detection sensitivity of the optoacoustic (OA) spectrometers can be improved by 10 or 100 times by placing an OA detector in the laser cavity. However, setting the OA detector in the cavity of the single-mode tunable laser requires a considerable
HIGHLY
EXCITED
HDO STATES
199
(more than twofold) increase in the cavity length and, consequently, a decrease in the distance between the longitudinal cavity modes. This makes it difficult to select one longitudinal mode and to obtain a smooth tuning. In a linear dye laser, due to space-inhomogeneous saturation in a thin active medium (the jet thickness is 0.02 cm) the most stable and easily co&rolled is a two-frequency generation regime. The distance Au between the generated frequencies is a function of the distance L on the jet up to the cavity mirror Au = c/4L. In our case the lasermode difference was 1.8 GHz and remained constant in laser spectral tuning. Thus an optoacoustic spectrometer with a two-frequency dye laser with OA detectors inside the cavity scanned every absorption line twice and two absorption lines appeared in the spectrum instead of one. The distance between them is equal to the distance between generating modes. Since the distance is not changed during tuning one can easily take into account such doubling lines and can obtain a real absorption shape. The OA spectrometer with two detectors inside the cavity of a two-frequency dye laser is simpler in performance than the spectrometer with a one-frequency laser. Narrowing of the laser linewidth is achieved by means of two selecting elements, i.e., using a birefringent filter and a fine Fabry-Perot &talon with a relatively small reflection coefficient. The linewidth of the modes was determined by frequency fluctuations and was equal to lo-20 MHz. The signals of optoacoustic detectors are measured by the frequency modulation method (recording the first derivative). This completely excludes a frequency-independent background signal and increases the spectrometer resolution. The OA spectrometer has a threshold sensitivity of < 1O-’ cm-’ for a power of 1 W; its detailed description is presented in Ref. ( 19). In order to separate the absorption spectra of the isotopomers, the Hz0 vapor was placed in one of the OA detectors and a mixture of HDO, D20, and Hz0 was placed in the other. Moreover, the spectrum of Hz0 in the visible region has been fairly well studied (20) and Hz0 absorption lines were used as reference lines relative to which the line positions of HDO were measured with an accuracy of 0.005 cm-‘. 3. THEORETICAL
ANALYSIS
To interpret the spectra of HDO in the 0.9- and 0.59-pm regions where investigations of the HDO spectra have not been performed previously, estimations of the band origins and rotational constants are needed. The vibration-rotation constants czi, &, vibrational frequencies wi, anharmonic constants x,, and Fermi-resonance constant F were determined using a least-squares fitting to previously obtained (3, 7-17) band centers, and the A, B, and C rotational constants of 13 bands of HDO. These parameters were used to calculate the spectra of HDO in the 0.9- and 0.59-pm regions. The Line Assignments The band center calculations have provided us with the general structure of the absorption spectrum of HDG and D20 in the spectral regions under investigation. There are four absorption bands of HDO: 3v3, 2ul + ~2 + ~3, IJ~+ 31~2+ ~3, and 5~ + u3at 0.9 pm. The vibrational quantum numbers and energies of the upper vibrational states are presented in Table I. The 3~3band appears to be the strongest among others because of smaller changes in vibrational quantum numbers. The preliminary calculations have shown that in the region 16 746- 17 0 12 cm-’ the lines of the 5u3, 4ul + 22~ + v3, ul + 4v3, and 5~ + u3 bands may occur. The
200
BYKOV ET AL. TABLE I The Band Origins for Some Vibrational Bands of HD I60 (in cm-‘) 0.9 YY”
123
0.59
pm
E Y
051
10343
211 131 003
y*yzvJ
pm
E Y
501
16491
1039s
104
16525
10474
421
16684
10623
005
16899
estimations of the band origins are shown in Table I. It may be supposed that the strongest band in this region is 5v3 for the same reason as in the 313 case. Another strong band ZQ+ 4~~ with the same Au = 5 as for 5v3 is out of the spectral region under investigation. The other bands listed in Table I for the 0.59-pm region must be at least an order of magnitude weaker. For line assignment the calculations of positions and relative strengths of the lines in the spectral regions from 10 280 to 10 780 cm-’ and from 16 500 to 17 800 cm-’ have been carried out. The results of the calculations as well as combinational differences of the lower state were used to assign the lines with J = 1, 2, and 3. After dete~ination of the energy levels with J G 3 the rotational constants have been fitted and new values of constants were used for the line center calculations. The assignments of the lines with larger values of Jwere accomplished by refining spectroscopic constants at each new step. From 667 lines, found in the 0.9-pm spectrum, 317 lines have been assigned as transitions from the ground to the (003) vibrational state. In the 0.59-pm spectrum, 231 lines have been assigned as transitions from the ground to the (005) vibrational state among 2.51 lines previously attributed to HDO. The energy levels of the (003) vibrational state deduced from the spectrum are shown in Table II. We have found 97 energy levels of the (003) vibrational state up to J = 14 and iu, = 7. The analysis of the relative strength of the lines has shown that the 3v3 band is a “hybrid” band with nearly equal intensities for “a” and “b” type transitions. Eighty-six energy levels have been determined for the (005) vibrational states up to J = 11 and iu, = 7. These energy levels are also shown in Table II. It follows from the relative line-strength ~ompa~son that the 5~ band is an “a” type, and an intensity of “b” transitions is 10 times weaker than that of an “a” transition. The Rotational Constants Determination The energy levels determined are used to fit the rotational and centrifugal distortion constants for both the (003) and the (005 ) vibrational states. We have used the Watson A-reduced Hamiltonian for this dete~ination, + B” i- C” J2 + B” - C” Jz xy 2 2
TABLE II The Rotational Energy Levels for the ( 003 ) and (005 ) Vibrational States of HD I60 (in cm-‘) (003) JK
K a c
0 1
0 0
0 1
111 110 2 0 2 2 12 211 2 21 2 2 0 3 0 3 313 312 3 2 2 3 21 3 31 3 3 0 4 0 4 414 413 4 2 3 4 2 2 4 3 2 431 4 41 4 4 0 5 0 5 5 15 514 5 2 4 5 2 3 5 3 3 5 3 2 5 4 2 5 4 1
5 5 1
5 5 6 0 616 615
0 6
E exF.. 10631.68 10646.90 10658.17 10661.05 10676.63 10685.76 10694.42 10728.23 10726.74 10720.65 10726.80 10744.09 10773.93 10776.23 10837.35 10837.41 10777.36 10781.14 10809.56 10834.29 10840.87 10898.96 10899.36 10985.93 10985.93 10846.25 10848.31 10890.01 10903.27 10922.88 10976.09 10977.44 11062.84 11062.89 11173.38 11173.38 10927.14 10328.21 10984.63
(0051
Na 2 3 4 3 3 6 3 3 2 4 5 5 5 6 3 3 4 3 5 3 5 4 4 2
1 3 4 5 7 6 3 2 3 4 3 3 4 3 5
6; -4 -3 1 2 2 -1 0 0 -3 2 2 -1 -5 -1 -1 -2 -1 -4 -2 6 -1 2 -3 0 0 -1 0 7 1 0 2 4 3 2 -3 -3 0 1 0
E oxp.
6 6 6 6 6 6 6 6
a
K
2 2 3 3 4 4 5 51
c 5 4 4 3 3 2 2
6 6 1 6 6 0 7 0 7 7 17 716 7 2 6 7 2 5 7 3 5 7 3 4 7 4 4 7 4 3 7 5 3 7 5 2 7 6 2 7 6 1 7 7 i 7 7 0 8 0 8 818 81-I 8 2 7 8 3 6
E exp. 10998.32 11021.91 11068.63 11072.50 11155.39 11155.62 11265.42 11265.42 11398.65 11398.65 11020.10 11020.63 11091.99 11100.99 11137.34 11176.29 11184.94 11263.65 11264.33 11373.02 11373.02 11505.78 11505.78 11660.71 11660.71 11125.12 11125.34 11211.53 11216.89 11289.75
N
1 2 3 3 3 4 4 2 3 4 4 4 4 5
17123.364 17130.583 17173.647 17187.500 17203.558 17246.453 17248.523 17320.994 17321.069 17415.786 17415.766 17207.914 17208.482 17265.894
4 4 3 4 3 2
-3 4 0 -1 3 0 0 0 2 2 -2 -4 8 -3
E exp.
-8 -4 0 -2 -6 0 1 -13 2 11 2 12 1 -2 1 0 3 5 3 1 3 4
N
62
17274.861 17302.046 17338.058 17343.644 17412.926 17413.290 17507.254 17507.254 17621.634 17621.634 17298.268 17298.519 17370.159 17375.397
1 3 2 3 2 2 2 2 2 2 3 4 4 3
11 0 -5 7 2 3 -5 4 -4 -3 -S -7 13 3
17456.523 17520.408 17521.658 17614.191 17614.235 17728.092 17728.092
1 2 3 1 2 1 1
-10 -7 6 -6 3 0 0
17400.465 17400.564 17485.857 17488.657 17565.124
3 4 3 2 1
-4 3 13 2 3
1 1 5 -1 1 1 3 -4 -4 2 2 0 3 2 -3 1
a The number of observed lines arriving at the corresponding level.
b S, = (I&. - Ed,)
1 2 3 2 5 2 3 3 3
2 7 2 -2 0 1 -a 3 3 3 -5 0 2 0 -4 0 -3 -3 0 -10 2 -4 0
(005) 6,
2 4 7 2 5 2 3 3 1 1 4 3 4 4 2 2 4 3 3 3 3 1 1 1 1 4 3 3 5 3
6;
16920.023 16935.073 16944.542 16847.571 16964.563 16971.620 16980.691 17008.985 17009.600 17007.382 17011.877 17029.907 17054.108 17057.025 17108.866 17108.941 17062.494 17064.965 17094.561 17113.763 17121.669 17169.992 17170.533
(003) JK
N
lo* cm-‘.
c& = (Eotn.Ed,.)IO3cm-‘. 201
BYKOV
202
ET AL.
TABLE &--Continued
.(005)
(003) JK
a
K G
8 8 8 8 8 8 8 8 8 9 S 9 9 Q s
3 4 4 5 5 6 6 7 7 0 1 1 2 2 3
5 5 4 4 3 3 2 2 1 9 9 8 8 7 7
9 9 9 9 9 10 10 101 102 102 103 103 104 105 106 11 11 12 12 121 122 130 13 13 14 14
4 6 5 7 7 0 1
6 5 4 3 2 10 10 9 9 8 8 7 7 6 4 11 11 12 12 11 11 13 13 12 14 14
J2 = J;+
0
1 0 1
1 2 0 1
J;+
E cnp.
N
61
11387.49 11389.42 11496.25 11496.35
2 3 2 2
11628.25 11628.25 11782.69 11782.69 11242.33 11242.45 11342.68 11345.63
1 1 1 1 3 2 2 2
2 7 0 0 1 1 -1 -1 -1 -2 1 3
11435.58
2
-1
11371.72 11371.72 11485.44 11487.06
11513.22 11513.22 11666.85 11666.85 11806.40 11806.85 11832.60 11832.60 11984.94 12010.49 12010.49
J:,
2 2 2 1
2 2 2 2 1 1 1 1 1 1 1
E erp.
Ii
*2
17586 990 17643.335 17646.794
2 2
17736.897 17849.917 17849.917
2
17514.538 17614.594
1 1
9 -2
17SR5.972 17699.622
1 1
-4 -17
17781.437 17874.751 17875.463 18119.438 18119.438
1 2 2 1
0 -8 -4 0 0
17839.058 17847.346 17897.256 17934.441 18028.375 ~8140,000 17778.435 17778.435
1 i 1 1 2 1 1
0 -5 -3 11 4 0 -7 0
1 1 1
I
3 -6 7 -10 -2 4
-3 2 3 -1
-1 1 2 3 2 -3 4 4 2 -1 0
1
J$ = J; - J;>, (A, B} = AB -I- BA
The results of the fit are shown in Table III. The quoted errors are in the last digits (one standard deviation) and are given in parentheses. The values without errors were fixed during the fit. It may be seen that the mean deviations of calculated energy levels from experimental ones are comparable with mean experimental errors for both the (003) and the (005) vibrational states. A statistical analysis of differences 6 = I Ebbs.- Ecalc.1 shows a satisfactory agreement between the observed and calculated energies. For 97 rotational levels of the (003) vibrational state used in the least-squares fit,
HIGHLY EXCITED HDO STATES
203
TABLE III The Rotationa Constants of the (003) and (005) Vibrational States of HD160 (in cm-‘)a (003)
E
1005)
10631.6366s,(831
Y
16920.0248e(23~
20.381464G!1)
18.513179(72)
9.06731,_w91
9.044389(22)
6. 1703028(22)
6.01198s(223
o.9319a(11)
0.81659(63)
0.64437(65)
0.037s(121
3.5998s(821
4.324s(36)
1.50733c42)
1.531811il
1.23STsf41f
1.50646(76)
3.3s8*c19)
2.SSo(15)
-14.043(13)
-9. 26Sb
2.4b
3. 1438(85)
3.sb
J hk
10’
1.8b
h
IO8
l.Ob
,* h. , L*
lo*
2. lb
107
-2. 51zb
L
do* lk lo7
P
* rms J/K
lo=
16. 30(20) 1.9818C45)
-2. 512b
8.6b -l.sb 0.58331)
3.453(21)
0.028
0.006
14/7
1117
* The quoted errors (one standard deviation f in the last digits are in parentheses. b Constants were fixed to (000) values during the fit.
S G 0.02 cm-’
65.9% (of the levels)
0.02 < 6 G 0.04
26.9%
0.04 < 6 < 0.06
4.1%
0.06 < 6 =G0.08
3.1%.
Of all energy levels, 92.8% are reproduced by the fit with errors not exceeding 0.04 cm-‘. A statistical analysis of 86 values of 6 = I Eobs.- Eca~c. I of the (005) vibrational state leads to the following results: 6 G 0.005 cm-’
72% (of the levels)
0.005 < 6 G 0.010
19%
0.010 < 6 =S0.018
9%.
It may be noted that errors of calculation are not greater than 0.0 1 cm-’ for 9 1% of the levels.
204
BYKOV ET AL.
The Vibration Energy Levels of HD160 The new band centers and those known from earlier studies (3, 7-14) have been used to derive the vibrational constants of HD 160. The usual vibrational Hamiltonian with matrix elements (VlHI
Xo(L’;
V) = C w~(V, + l/Z!) + 2 i
+
l/Z)(Vj
+
l/2)
isj +
C
Yijk(vi
i
+
l/z)(vj
(~1 v2 vx/HIvI + 1 v2 - 2 vj) = Fi(v,
+
l/2)(%
+
l/2),
+ l)v2(v2 - 1)/4,
(3) (4)
where V = ~1~2~3 have been used. Among the anharmonic resonances only the Fermi resonance was taken into account. The harmonic frequencies, the anharmonic xv and some of the ytik constants, and the resonance constant F have been determined from least-squares fitting to 14 band centers. The parameters obtained are shown in Table IV. The vibrational frequencies
TABLE IV The Harmonic Frequencies and Anharmonic, Fermi-Resonance, and Vibration-Rotation Constants of HD I60 (cm-‘) ul= 2823.946'
2624.3b
02=
1443.723"
1440.2b
03= 3893.40saf0.67
3889.8b
x1,= -43.648,8+0.085 x
= -5.9235f0.17 12
x
= -13.4589+0.26 13
x = -12.0262+o.16 22 xz3= -24.81 f0.37 10
-43.4b -8.6' -13.1b -1l.P
YzZz=-0.697,0f0.052
-20.1b
Y223=1.6477+0.14
xz3= -84.3796+0.24
-82.gb
Y333=0.4686~+0.027
F
= -9.2619*f0.057
-9.37c
A
=
23.3f?lo8+0.113
=
0.449,0'0.097
e
aIr
PI,,= 0.068s2f0.025
a = -1.2711t0.10 2*
P 22*= o.4196*+o.024
a 3* =
o.890~2+o.025
P23*=-o.19622+o.031
B e
9.127821'0.0080 C
=
e
= 6.545662+0.0032
= 0.172120+0.0030 OLIB
a,c= o.1101~2+o.oo12
=-o.13402*+o.oo29
azc= 0.085981+0.0011
= 0.0115,,'0.0020
azc= 0.0791672'0.00079
"ze %
a Calculated with isotopic rules, Ref. ( 21) bFrom Ref. (3). ’ From Refs. (15, 16).
205
HIGHLY EXCITED HDO STATES
marked with an “a” were calculated by means of isotopic rules (21) and were fixed during the fit. The a~ment between caIculated and experimental vibrational energies is satisfactory (the rms is 0.20 cm-‘). The parameters from Table IV are in agreement with those obtained by Benedict et al. (3). The value of the resonance parameter F is almost the same as that obtained by Pen-in et al. (15, 16) from the analysis of the first and second diads of interacting vibrational states of I-DO. The first set of vibrational parameters used to predict spectra in the 0.9- and 0.59pm regions had errors of about 8 cm-’ for the band center of 3v3 and 20 cm-’ for 5~. We believe that the new set of parameters which was obtained using the (003) and (005) states showed marked improvement in the predictions. The new values of vibrational constants were used to calculate bands origins up to 13 000 cm-‘. The results are presented in Table V, We have found the vibration-rotation constants (Y; , & from least-squares fitting to rotational constants of 14 vibrational states. The following formulas have been used, X(V) = Xe - C CXi\.(Ui + l/2) + x Bij_x(Vi+ 1/2)(Vj + i/2), i
(5)
isj
where X ( =A, B, or C) is the rotational constant in the vibrational state V and X, is the equilibrium values. The constants obtained are presented in Table IV. A comparison of the experimental A, B, and C constants of the (005) state with predicted ones shows that errors of prediction are about 0.01 cm-’ . 4. CONCLUSIONS
The highly excited vibrational states (003) and (005~ of HID I60 have been investigated for the first time. Line assignments and energy levels were determined and the rotational constants of the Watson A-reduced Hamiltonian were obtained. TABLE V The Vibmtion~ Energy Levds of HDi60 up to 13 000 cm-’
0 1 0 10 0 0 2 0 0 0 1 0 3 0 1 1 0 0 11 2 0 0 0 4 0 12 0 1 0 1 0 2 1 0 s 0 2 10 13 0 0 0 2 0 3 1 1 1 1 3 0 0 2 2 0 1 4 0 0 12 2 0 1 0 4 1 12 1 3 1 0
1403.68 2723.83 2781.80 3707.45 4099.99 4145.53 5089.62 5363.60 6414.04 5508.64 6415.41 6451.93 6677.43 6749.08 6851.63 7250.37 7759.83 7810.97 7916.43 8087.72 8177.15 8611.02 9041.90 9058.46 9161.83 9292.84
0.19 0.15 -0.20 -0.01 0.04 0.06 0.08 0.01
-0.05 0.03
-0.07
-0.03
1 2 0 1 0 4 2 1 0 3 2 0 1 3 1 4 2 3 0 0 2 1 5 3 1 0
5 0 3 0 2 2 0 2 5 1 0 0 1 i 3 1 0 3 2 0 4 0 3 2 12 0 1 4 1 1 0 2 1 3 0 1 3 4 2 0 2 2 2 0 0 1 1 5 1 0 5
9367.82 9494.68 9936.89 9963.10 10310.99 10391.53 10405.33 10493.02 10631.56 10650.71 10735.82 11252.14 11314.85 11583.05 11722.96 11756.24 11610.83 11943.79 11970.70 12532.69 12560.67 12651.24 12759.36 12335.43 12991.30 16920.02
-0.12
0.002
206
BYKOV ET AL.
FIG. 1. The ug dependence of the rotational A (a) and centrifugal Ak (b) constants of HDO (0, (0011~) states; X, ( 0 1vj ) states).
The energy level calculations of the vibration-rotation states (003 ) and (005 ) of the HDO molecule appear to be reliable without taking into account accidental resonances. This is contrary to our experience with the highly excited energy level calculations for light asymmetric top molecules (such as HzO, HIS) where it was necessary to include the effects of a large number of resonances (see, for instance, Ref. (22)). The vibrational states (00~) of HDO may be considered isolated ones because the Darling-Dennison or Coriolis type resonances are not significant due to the large difference between the v1, 2vz, and v3 vibrations. The resonances between considered vibrational states and others nearby are negligible because of large changes in vibrational quantum numbers. Indeed, the energy difference between the (003) state and its nearest vibrational state (320) is only 19 cm-‘, but nondiagonal matrix elements of the Hamiltonian are small, at least for small values of quantum number J. Hence, in the first approximation we can neglect the accidental resonances in energy level calculations. The situation is the same in the case of the (005) vibrational state. It is useful to compare the parameters of the (003 ) and (005 ) states with the parameters of the (00~~) and (0 103) type vibrational states. The dependence of rotational constants on u3 is shown in Fig. 1. It may be seen that there is a systematic trend in the rotational and centrifugal distortion constants with an increase in the quantum number 03. The rotational constants show a near linear dependence on the number of OH-stretching vibration quanta. The same behavior of rotational constants occurs in the case of the (0 1213)set of vibrational states of HD I60 (14, 17). This shows that the nonresonant Hamiltonian ( 1) is a realistic one for the (003) and (005) states despite the high-energy excitation. The redetermination of the spectroscopic constants of HDO appears to make possible a more accurate calculation of the rotational constants for the bands in the short wavelength range. ACKNOWLEDGMENTS The authors express their gratitude to Dr. A. Karablev and Dr. S. Kobtsev, who gave them the opportunity to record the spectrum
RECEIVED:
at Novosibirsk
December 9, 1991
State University.
HIGHLY
EXCITED HDO STATES
207
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