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Infrared diode laser spectroscopy of NaCl
JOURNAL
OF MOLECULAR
SPECTROSCOPY
(1989)
l&$98-105
Infrared Diode Laser Spectroscopy of NaCl HIROMICHI UEHARA, KOUI HORIAI, KUNIAKI NAKAGAWA, AND TOSHIYUKI FUJIMOTO’ Departmentof Chemistry,Faculty of Science, Josai University,Keyakidai, Sakxdo, Saitama 350-02. Japan The infrared spectra of the Au = I bands of Na% and Na”‘CI at about 900°C have been observed in a frequency range between 365 and 390 cm-’ with a tunable diode laser spectrometer. Transitions of the 1-0,2-I, 3-2,4-3, and 5-4 bands of Na% were analyzed in a single leastsquares fit to a set of seven Dunham coefficients Y-,. Yioand Y, for Na3’CI were determined to be 364.687 1(32) and - 1.7763( 2 I) cm-‘, respectively, with the standard errors in parentheses. From the Y,, constants the Dunham potential constants were determined. A least-squares fit of the observed transitions in the I-O, 2-1, and 3-2 bands of Na”‘C1 has yielded three Dunham vibrationalconstants, which confirmed that the set of Y, values obtained for Na3’Cl was masonable. Q 1989 Academic Press. Inc. INTRODUCTION
Prior to the present work ( 1 ), no high-resolution vibration-rotation spectrum has been reported for NaCl, which is a chemical substance of fundamental importance. The NaCl bond is almost completely ionic. So far, the only infrared spectroscopic study of monomeric NaCl, a high-temperature molecule (2), in the gaseous phase is that of Rice and Klemperer in 1957 (3). They observed the absorption spectrum under a rather high sample pressure and calculated the value of w, using the observed u = 1-O bandhead position and the previous microwave results of the rotational constants (4). Although their value of w, = 366.1(40) cm -’ was good within the experimental error, a much more accurate value of W,is desirable. Among the extensive microwave studies of NaCl (4, 5)) the millimeter-wave molecular-beam spectroscopy by Clouser and Gordy (5) has revealed extremely accurate molecular constants. They also reported accurate values of w, and w,x, which were predicted by applying Dunham’s theory to their results. However, for that case, the validity of the application of Dunham’s theory should be examined by determining o, and o,xe experimentally with the more direct and accurate method of vibrationrotation spectroscopy. Using an infrared diode laser spectrometer, we have observed the Av = 1 vibrationrotation spectra of monomeric NaCl (I). A newly acquired laser diode allowed us more extensive measurements of the Av = 1 spectral lines from II = 1-O to 5-4 bands for Na3’Cl and from 11= 1-O to 3-2 bands for Na3’Cl. The present paper reports an extensive observation of the An = 1 diode laser spectra of Na35C1and Na3’Cl and the molecular constants obtained from the analysis. ’ Present address: Research Institute for Catalysis, Hokkaido University, Kita-ku, Sapporo 060, Japan. 0022-2852189 $3.00 Copyright 8 I989 by Academic Press, Inc. All rights of reproduction in any form reserved.
98
LASER
SPECTROSCOPY
OF NaCl
99
A total of 132 vibrational rotational lines of Na35Cl were analyzed by using the Dunham’s solution to yield the YUconstants. A similar procedure was separately applied to 41 spectral lines of Na3’Cl. The present values of w, and w,x, have disclosed the remarkable accuracy of the corresponding values calculated by Clouser and Gordy by use of the Dunham theory. Infrared diode laser spectroscopy of the high-temperature species has been made by Maki and Lovas (6). Recently, diode laser spectroscopy of NaF was reported by Douay et al. ( 7). EXPERIMENTAL
DETAILS
Since the experimental details were described previously ( I ) , only a brief description is given here with complementary details for some experimental procedures. A commercial diode laser spectrometer, Spectra Physics SP5000, was successfully operated down to 350 cm-‘. It was equipped with two copperdoped germanium photoconductive detectors mounted on a closed cycle He refrigerator. KRS-5 windows were used for the laser source, the detector, a sample cell, and a beam splitter. We used an air-spaced cadmium telluride Ctalon with a free spectral range of about 0.0300 cm-’ . The signals with 1 kHz laser source modulation were 2f-detected with a phasesensitive detector and then recorded. A single-pass heat-pipe high-temperature cell was incorporated into an optical system of the spectrometer. The heat-pipe cell, which is similar in design to that used by Maki et al. (8), was made of an alumina tube of 30-mm diameter. Inside of the tube, granulated alumina which acted as the “wick” was uniformly inserted and 10 g of NaCl was placed at the center portion of the tube on the granulated alumina. The total length of the cell was 80 cm. A buffer gas of 6 Torr of argon was introduced into the cell. The cell was heated to about 900°C. The spectra were calibrated by use of the wavenumbers of the spectral lines for the v2 bands of CS2 reported by Jolma and Kauppinen (9). The CdTe &talon was used to measure the frequency difference between the CS2 reference line and the NaCl absorption line. A composite of errors in the relative calibration system and those in the reference wavenumbers was estimated to be *0.003 cm-‘. The present procedure for the measurement of the spectral lines consisted of a set of three successive recordings for NaCl, CSZ, and the etaIon. Five minutes were required for each recording. Although this procedure introduced additional errors for the determination of the spectral wavenumbers, simultaneous recording of signals by use of the two divided laser beams was not successful in most of the spectral range due to a lack of beam intensity at the detector elements. This partly resulted from the large reflection losses of the beam intensity due to the KRS5 windows inevitably inserted into the radiation paths. Moreover, the quality of the laser diode may be lower in the longer wavelength region in which we are working. We carefully examined the possible errors introduced by the present procedure of the measurements. After about 3 hr warm-up under “rough” temperature setting of the laser diode, the recorded spectral position was stabilized enough to yield a spectral shift well within the spectral linewidth for the time interval of about 10 min. Thus, we always started measurements after we confirmed the stabilization of the recorded spectral positions. The total sum of errors due to the measurement procedure, the
100
UEHARA
ET AL.
TABLE I Observed Infrared Transitions for Na”Cl
1-o 1-o 1-O
1-O 1-o 1-o 1-o 1-o 1-O 1-O 1-O 1-o 1-o 1-O 1-O 1-O 1-o 1-o 1-o 1-o 1-O 1-o 1-O 1-O 1-O 1-o 1-o 1-o 1-O 1-o 1-o 1-O 1-o 1-o 2-1 2-l 2-1 2-l 2-1 2-l 2-1 2-1 2-1 2-1 2-l 2-1 2-1 2-l 2-l 2-l 2-l 2-l 2-l 2-1 2-1 2-l 2-l 2-1 2-1 2-l 2-l 2-l 2-1 2-1 2-1 2-1
*
Lines
R(24l RI251 Ri26l ~(27) R(2t3) R(29) R(30) R(32) R(33) R(44) R(45) R(46) R(47) Rl65) R(66) R(67) Rl68) R169) Rl70) R171) R(72l R(74l Rt75l R(76l R(87) R(91) R192) R(931 R(94) R(97) R(98) R(99) R(100) R,l01) RI341 R(35) R(37) Rl38) R(39) R140) R141) RI421 R(43l R144) Rt45l R(58l R(59) R(61) R(621 R187) R1881 R(89) R(90l R(91) R(92) R(93) R(94) R(95) Rl96) R197, Rissj Rl99) R(100) R(101) RIlO2) R1103)
excluded
370.9460
371.2954 371.6398 371.9823 372.3180 372.6605 372.9847 373.6369 373.9563 377.2511 377.5334 377.8031 378.0785 382.3482 382.5484 382.7465 382.9413 383.1322 383.3199 383.5037 383.6847 384.0319 384.2026 384.3684 385.9368 386.3934 386.4983 386.5951 386.6944 386.9589 387.0406 387.1200 387.1928 387.2619 370.6750 370.9849 371.5975 371.8986 372.1969 372.4959 372.7788 373.0664 373.3483 373.6295 373.9060 377.1717 377.4001 377.8371 378.0562 382.2402 382.3590 382.4714 382.5819 382.6887 382.7922 382.8918 382.9872 383.0799 383.1673 383.2505 383.3308 383.4064 383.4795 383.5491 383.6136 383.6745
from
the
-0.0011 0.0002 -0.0002 0.0010 -0.0011 0.0070* 0.0002 0.0008 -0.0004 -0.0014 0.0024 -0.0028 0.0012 0.0032 0.0010 0.0004 0.0001 -0.0003 -0.0002 -0.0004 0.0005 -0.0015 0.0002 0.0008 0.0007 0.0011 0.0016 -0.0022 0.0003 -0.0022 -0.0017 0.0003 -0.0004 -0.0009 0.0009 -0.0004 0.0002 0.0005 0.0015 0.0067* -0.0007 0.0001 -0.0013 0.0002 0.0004 -0.0011 0.0011 -0.0034 0.0004 0.0026 0.0028 0.0005 0.0001 -0.0002 0.0000 0.0001 -0.0001 0.0008 0.0003 -0.0006 -0.0005 -0.0013 -0.0007 0.0003 0.0000 0.0000
fit.
2-l 2-1 2-l 2-1 2-1 2-l 2-l 2-l 2-1 2-l 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4
R(104) R(lO9) R(110) Rtlll) RI1121 RI1131 Rl114) Rt1151 R(116) R(117) R(47) R(49) Rl50) R(51) R(52) R(53) R(55) R(57) R(58) Rl59) R(60) R(77) R(78) R(79) Rl82) R183) RI631 RI641 RI651 R(66l R(671 R(68) R(69) ROO) R(71) R(72) R(73) R(74) R(75) R(76) R(77) R179) RI801 R(82) R(83) R(84) R(85) Rl86) Rl87) RI881 RI891 RI911 RI931 R(94l RI951 RI961 Rt97l R(98l RI1001 R(101) R(102l R(103) Rl104) R(105) R(106) R(109)
383.7326 383.9554 383.9903 384.0202 384.0461 384.0685 384.0867 384.1006 384.1104 384.1172 370.8488 371.3730 371.6303 371.8872 372.1392 372.3788 372.8631 373.3291 373.5573 373.7775 374.0032 377.1923 377.3513 377.5041 377.9296 378.0686 371.0525 371.2593 371.4540 371.6554 371.8484 372.0410 372.2236 372.4072 372.5931 372.7603 372.9335 373.0993 373.2670 373.4260 373.5840 373.8863 374.0347 370.7325 370.8675 370.9928 371.1179 371.2440 371.3557 371.4709 371.5858 371.7968 371.9947 372.0875 372.1730 372.2578 372.3393 372.4221 372.5668 372.6314 372.6897 372.7457 372.8015 372.8510 372.8987 373.0174
0.0012 -0.0023 -0.0010 -0.0006 -0.0004 0.0003 0.0008 0.0009 0.0008 O.OOlt3 -0.0051* -0.0037 -0.0028 0.0012 0.0039 -0.0023 0.0012 0.0006 0.0009 -0.0032 0.0018 -0.0036 0.0006 0.0024 -0.0029 -0.0001 0.0006 0.0029 -0.0032 0.0010 0.0003 0.0030 -0.0008 0.0001 0.0070* -0.0013 0.0002 -0.0021 0.0012 -0.0005 0.0005 -0.0002 0.0022 0.0026 0.0041 -0.0004 -0.0014 0.0023 -0.0046 -0.0043 -0.0006 -0.0007 0.0010 0.0014 -0.0017 -0.0018 -0.0014 0.0041 0.0056' 0.0042 0.0004 -0.0018 -0.0005 -0.0016 -0.0007 0.0006
101
LASER SPECTROSCOPY OF NaCl TABLE II Observed Infrared Transitions for Na3’C1
1-o 1-O l-0 1-O 1-O
1-o 1-o 1-o 1-o 1-o 1-O 1-O 1-o 1-o 1-O 1-o 1-o 2-1 2-l 2-l 2-l
*
R(38) R(401 R(43i R(45) R(46) R(47) R(93) R(94) R(97) R(98) R(100) R(103) R(104) R(105) R(106) R(110) R(112) R(49) R(50) R(52) R(53)
Lines
excluded
371.3730 371.9614 372.8154 373.3663 373.6369 373.9060 382.3757 382.4714 382.7465 382.8284 382.9872 383.1892 383.2505 383.3054 383.3602 383.5369 383.6023 370.8781 371.1277 371.6303 371.8740
from
2-l 2-l 2-l 2-l 2-l 2-l 2-1 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2
-0.0037* -0.0013 -O.OOOE* -0.0018 -0.0020* -0.0002* 0.0029 0.0001* 0.0021* 0.0004 0.0034* -0.0001 0.0003* -0.0020 -0.0005 0.0008 0.0015 0.0029 -0.0024 0.0007* -0.0001
the
fit.
see
R(541 Ri55i R(56) R(57) RL59) R(60) R162) Ri65i R(66l R(671 R(68) R(70) R(71l R(74) R(75l R(76) R(77) R(79) RL801 R(82)
372.1180 372.3520 372.5808 372.8154 373.2670 373.4882 373.9182 370.9849 371.1836 371.3730 371.5619 371.9356 372.1180 372.6314 372.7960 372.9596 373.1185 373.4260 373.5705 373.8545
0.0028 -0.0008 -0.0061* -0.0021 -0.0013* -0.0003 "."""" 0.0011* 0.0025 -0.0019* -0.0032 0.0006 0.0034* -0.0006* -0.0013 0.0005 0.0012* 0.0032* 0.0003 0.0003
text.
relative calibration system, and the reference wavenumbers was estimated to be M.OO~ - +0.005 cm-‘. OBSERVED SPECTRA AND ANALYSIS
Spectral lines ranging between 390 and 365 cm-’ were observed and assigned by use of three laser diodes. Spectral lines in the wavenumber range lower than 365 cm-’ were also observed but could not be assigned due to lack of an appropriate reference spectrum. Overlapping of spectral lines of (probably monomeric and polymeric ( 10)) NaOH as well as those of many hot bands of NaCl resulted in a congested spectrum. Under the high temperature, NaOH was generated in the sample cell by a reaction of NaCl with Hz0 which could not be removed from the sample. Spectral lines for the authentic sample of NaOH were independently measured and they were subtracted from the spectral lines obtained from the NaCl gas. The spectrum of monomeric NaCl was much weaker than that of NaOH. In Tables I and II, the measured spectral lines for the u = 1-0,2-l, 3-2,4-3, and 5-4 bands of Na3’Cl and the 11= l-0, 2-1, and 3-2 bands of Na3’C1 are listed, respectively. The quality of the determined line positions can be seen in a LoomisWood diagram shown in Fig. 1. The diagram was plotted with the abscissa axis referred to the calculated wavenumbers for the u = 1-O transition. Spectral lines of Na35Cl were analyzed in a single least-squares fit’ to the transition frequency v given by the usual Dunham formula, * The least-squaresprogram system SALS was used: T. Nakagawa and Y. Oyanagi, “Program System for Statistical Analysis with Least-Squares Fitting, SALS (Version II),” The University of Tokyo Computer Center, Tokyo, 1979.
102
UEHARA ET AL.
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FIG. 1. Loomis-Wood diagram showing the quality of the determined line positions. The diagram was plotted with the abscissa axis referred to the calculated wavenumbers for the u = 1-O transition of Na”Cl. The line positions for the I) = 1-O band of Na3%I are indicated with dots slightly larger than those for other bands.
,, = F’ _ F”
(1)
and
F = Z YU(v + 1/2)‘[J(J+ Li
l)]‘,
(2)
where YiOz we, Y,, E - w,x,, etc. The exact relations between YGand the usual spectroscopic constants are given in Refs. ( II, 12). The Dunham Y, coefficients retained as adjustable parameters were Y,o, y20, y30, y40, YII, Y21, and Y12. Since only the R-branch lines were observed Yo, ,Yo2, and Yo3were constrained to those determined by millimeter-wave spectroscopy ( 5). Although the diode laser spectrometer has quite a high resolving power, many of the weaker spectral lines of Na3’C1 were overlapping with other stronger lines almost all of which were those of the Na3%1 bands. Some of the overlapping lines of Na3’C1 were included in Table II but were excluded from the least-squares fit. They am marked by an asterisk. The spectral lines of Na”C1 were analyzed separately from Na3’C1 in the leastsquares fit to the transition frequency Y.Since the number of the spectral lines assigned for Na3’C1 is rather small, only three vibrational Dunham coefficients, Ylo, Yzo, and Y30,were retained as parameters. Values for seven other coefficients, YM, Yo, , Y, , ,
LASER SPECTROSCOPY OF NaCl
103
TABLE III Dunham Coefficients for Na3’Cl Coefficients
This
Work
Other
Sources
Calculated Potential
(cm-lj Ref.
5
Ref.
364.6871(32)a
5.82(55)x10-3
5.84x10-3
-6.9(490)x10-6
-12.9x10-6 0.21806309(20)
standard
the value d) -wexe.
error.
with of
the
2.0640
I"
-1.7736
0.21806309
-1.62482(30)n10-3
al One
of Table
364.6869
-1.7763(21)
c) Calculated
3
From Constants
-1.62551x10-3
5.14(27)~10-~
5.363x1o-6
-3.1202(17)x10-'
-3.1187xlo-7
8.3(17)x10-1~
6.97x10-1'
-3.402133)~10-~~
-3.468~10-~~
bl we. Dunham equations. -1 cm for raexe.
Pekeris's
theory
(Morse potential)
has
lead
to
e) Fixed.
YzI, Yo2, Ylz, and YOU,werefixed to those calculated with the approximate isotopic relation, y, = (p~/p)(i+*iWy;,
(3)
where p is the reduced mass of the molecule and the prime denotes Na3’Cl isotopic species. RESULTS AND DISCUSSION
The Dunham coefficients for Na3’Cl obtained by the least-squares fit are listed in column 2 of Table III along with those reported by Clouser and Gordy (5) and Rice and Klemperer (3). The fit is good judged from the obs - talc values listed in Table I and the value of the standard deviation, 0.0017 cm-‘. Potential constants, al-as, Be, and we, were obtained by a least-squares fit to the values of 10 Dunham coefficients given in column 2 of Table III by using the relations in Ref. ( I I ) . The results are listed in Table IV. In column 5 of Table III Y, values calculated from the constants of Table IV are listed. Judging from the calculated values, a reasonable set of Yij coefficients has been determined for Na3’Cl as shown in column 2 of Table III. The Dunham’s correction applied to YO,has led to the Be value in Table IV. However, other corrections due to the inadequacy of the Born-Oppenheimer approximation (12) could not be adopted since the experimental data required for the corrections have not been obtained. The Dunham coefficients for Na3’Cl obtained by the least-squares fit are listed in column 2 of Table V. The Y0values listed in column 3 of Table V are those calculated from the values of Yii for Na3SC1 listed in column 2 of Table III with the use of the
104
UEHARA ET AL. TABLE IV Dunham Potential Constants for Na3’CI hl-lt
Li’e
364.6880(33ta
(CIU-')
Be
0.21806295(20~ -3.07776(35)
al
6.4184(60)
=2
-10.539(48)
=3
a)
=4
13.19(Sl)
a5
-9.491550)
one
standard
error.
mass dependence relation ( 3). The difference between the observed values of YiJ (Na37C1) and the calculated values are 0.5~ for Yio, 1.8~ for YZO,and 2.0~ for the higher-order coefficient Y30. Since the agreement is satisfactory, the Y,, coefficients obtained for Na37CI also confirm that the set of the Y$values of Na “Cl given in Table III is reasonable. There may be a small deviation from the approximation, Eq. (3). However, the deviation was not evident because the uncertainty in the measurements of spectral lines for Na37C1 is larger. A striking result is the excellent agreement between the present values of Y,,, and YzOfor Na3’C1 and the corresponding values which Clouser and Gordy (5) obtained by applying the Dunham theory to their results of millimeter-wave spectroscopy. Along with the Dunham theory, they also calculated the w,xe value using the Pekeris formula which is based upon the Morse potential function. Since the value of oexe by the Pekeris formula gave better agreement with the infrared result given by Rice and Klemperer (3), they pointed out that a possible discrepancy within the Dunham theory
TABLE V Dunham Coefficients for Na”CI
360.7578(15l=
360.75848
-1.73673(86)
-1.73824
5.35(14)x10-3
5.634x10-3
-6.61x10-6b
al
One
-6.61x10-6
0.213390192b
0.213390192
-1.573793x10-3b
-1.573793x10-3
5.1356~10-~~
5.1356x10-6
-2.98790x10-7b
-2.98790x10-7
7.095x10-1Ob
7.095~10-~0
-3.1B79x10-14b
-3.1879x10-14
standard
error.
b) Fixed.
LASER SPECTROSCOPY OF NaCl
105
existed for the anharmonicity constant Y20. However, from the present result of the high-resolution infrared study, it is definitely concluded that the vibrational constants of Clouser and Gordy by use of the Dunham theory are in excellent agreement with those given by infrared spectroscopy. RECEIVED:
September 21, 1988 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12.
K. HORIAI, T. FIJJIMOTO,K. NAKAGAWA, AND H. UEHARA, Chem. Phys. Left. 147,133-136 (1988). M. SP~LITI, private communication (1979). S. A. RICE AND W. KLEMPERER, J. Chem. Phys. 27,573-579 (1957). A. HONIG, M. MANDEL, M. L. STITCH, AND C. H. TOWNES, Phys. Rev. %,629-642 (1954). P. L. CLOUSER AND W. G~RDY, Phys. Rev. 134, A863-870 (1964). For example, A. G. MAKI AND F. J. L~VAS, J. Mol. Specrrosc.85, 368-374 (198 1). M. C. D~UAY, A. M. R. P. BOPEGEDERA,C. R. BRAZIER, AND P. F. BERNATH, Chem. Phys. Left. 148, l-5 (1988). For example, G. THOMPSON, A. G. MAKI, AND A. WEBER, J. Mol. Specfrosc. 118.540-543 (1986). K. JOLMA AND J. KAUPPINEN, J. Mol. Specfrosc. 82,214-219 (1980). N. ACQUISTA AND S. ABRAMOWITZ, J. Chem. Phys. 51,2911-2914 (1969). J. L. DUNHAM, Phys. Rev. 41,721-731 (1932). W. G~RDY AND R. L. COOK, “Microwave Molecular Spectra,” 3rd ed., Wiley, New York, 1984.
OF MOLECULAR
SPECTROSCOPY
(1989)
l&$98-105
Infrared Diode Laser Spectroscopy of NaCl HIROMICHI UEHARA, KOUI HORIAI, KUNIAKI NAKAGAWA, AND TOSHIYUKI FUJIMOTO’ Departmentof Chemistry,Faculty of Science, Josai University,Keyakidai, Sakxdo, Saitama 350-02. Japan The infrared spectra of the Au = I bands of Na% and Na”‘CI at about 900°C have been observed in a frequency range between 365 and 390 cm-’ with a tunable diode laser spectrometer. Transitions of the 1-0,2-I, 3-2,4-3, and 5-4 bands of Na% were analyzed in a single leastsquares fit to a set of seven Dunham coefficients Y-,. Yioand Y, for Na3’CI were determined to be 364.687 1(32) and - 1.7763( 2 I) cm-‘, respectively, with the standard errors in parentheses. From the Y,, constants the Dunham potential constants were determined. A least-squares fit of the observed transitions in the I-O, 2-1, and 3-2 bands of Na”‘C1 has yielded three Dunham vibrationalconstants, which confirmed that the set of Y, values obtained for Na3’Cl was masonable. Q 1989 Academic Press. Inc. INTRODUCTION
Prior to the present work ( 1 ), no high-resolution vibration-rotation spectrum has been reported for NaCl, which is a chemical substance of fundamental importance. The NaCl bond is almost completely ionic. So far, the only infrared spectroscopic study of monomeric NaCl, a high-temperature molecule (2), in the gaseous phase is that of Rice and Klemperer in 1957 (3). They observed the absorption spectrum under a rather high sample pressure and calculated the value of w, using the observed u = 1-O bandhead position and the previous microwave results of the rotational constants (4). Although their value of w, = 366.1(40) cm -’ was good within the experimental error, a much more accurate value of W,is desirable. Among the extensive microwave studies of NaCl (4, 5)) the millimeter-wave molecular-beam spectroscopy by Clouser and Gordy (5) has revealed extremely accurate molecular constants. They also reported accurate values of w, and w,x, which were predicted by applying Dunham’s theory to their results. However, for that case, the validity of the application of Dunham’s theory should be examined by determining o, and o,xe experimentally with the more direct and accurate method of vibrationrotation spectroscopy. Using an infrared diode laser spectrometer, we have observed the Av = 1 vibrationrotation spectra of monomeric NaCl (I). A newly acquired laser diode allowed us more extensive measurements of the Av = 1 spectral lines from II = 1-O to 5-4 bands for Na3’Cl and from 11= 1-O to 3-2 bands for Na3’Cl. The present paper reports an extensive observation of the An = 1 diode laser spectra of Na35C1and Na3’Cl and the molecular constants obtained from the analysis. ’ Present address: Research Institute for Catalysis, Hokkaido University, Kita-ku, Sapporo 060, Japan. 0022-2852189 $3.00 Copyright 8 I989 by Academic Press, Inc. All rights of reproduction in any form reserved.
98
LASER
SPECTROSCOPY
OF NaCl
99
A total of 132 vibrational rotational lines of Na35Cl were analyzed by using the Dunham’s solution to yield the YUconstants. A similar procedure was separately applied to 41 spectral lines of Na3’Cl. The present values of w, and w,x, have disclosed the remarkable accuracy of the corresponding values calculated by Clouser and Gordy by use of the Dunham theory. Infrared diode laser spectroscopy of the high-temperature species has been made by Maki and Lovas (6). Recently, diode laser spectroscopy of NaF was reported by Douay et al. ( 7). EXPERIMENTAL
DETAILS
Since the experimental details were described previously ( I ) , only a brief description is given here with complementary details for some experimental procedures. A commercial diode laser spectrometer, Spectra Physics SP5000, was successfully operated down to 350 cm-‘. It was equipped with two copperdoped germanium photoconductive detectors mounted on a closed cycle He refrigerator. KRS-5 windows were used for the laser source, the detector, a sample cell, and a beam splitter. We used an air-spaced cadmium telluride Ctalon with a free spectral range of about 0.0300 cm-’ . The signals with 1 kHz laser source modulation were 2f-detected with a phasesensitive detector and then recorded. A single-pass heat-pipe high-temperature cell was incorporated into an optical system of the spectrometer. The heat-pipe cell, which is similar in design to that used by Maki et al. (8), was made of an alumina tube of 30-mm diameter. Inside of the tube, granulated alumina which acted as the “wick” was uniformly inserted and 10 g of NaCl was placed at the center portion of the tube on the granulated alumina. The total length of the cell was 80 cm. A buffer gas of 6 Torr of argon was introduced into the cell. The cell was heated to about 900°C. The spectra were calibrated by use of the wavenumbers of the spectral lines for the v2 bands of CS2 reported by Jolma and Kauppinen (9). The CdTe &talon was used to measure the frequency difference between the CS2 reference line and the NaCl absorption line. A composite of errors in the relative calibration system and those in the reference wavenumbers was estimated to be *0.003 cm-‘. The present procedure for the measurement of the spectral lines consisted of a set of three successive recordings for NaCl, CSZ, and the etaIon. Five minutes were required for each recording. Although this procedure introduced additional errors for the determination of the spectral wavenumbers, simultaneous recording of signals by use of the two divided laser beams was not successful in most of the spectral range due to a lack of beam intensity at the detector elements. This partly resulted from the large reflection losses of the beam intensity due to the KRS5 windows inevitably inserted into the radiation paths. Moreover, the quality of the laser diode may be lower in the longer wavelength region in which we are working. We carefully examined the possible errors introduced by the present procedure of the measurements. After about 3 hr warm-up under “rough” temperature setting of the laser diode, the recorded spectral position was stabilized enough to yield a spectral shift well within the spectral linewidth for the time interval of about 10 min. Thus, we always started measurements after we confirmed the stabilization of the recorded spectral positions. The total sum of errors due to the measurement procedure, the
100
UEHARA
ET AL.
TABLE I Observed Infrared Transitions for Na”Cl
1-o 1-o 1-O
1-O 1-o 1-o 1-o 1-o 1-O 1-O 1-O 1-o 1-o 1-O 1-O 1-O 1-o 1-o 1-o 1-o 1-O 1-o 1-O 1-O 1-O 1-o 1-o 1-o 1-O 1-o 1-o 1-O 1-o 1-o 2-1 2-l 2-1 2-l 2-1 2-l 2-1 2-1 2-1 2-1 2-l 2-1 2-1 2-l 2-l 2-l 2-l 2-l 2-l 2-1 2-1 2-l 2-l 2-1 2-1 2-l 2-l 2-l 2-1 2-1 2-1 2-1
*
Lines
R(24l RI251 Ri26l ~(27) R(2t3) R(29) R(30) R(32) R(33) R(44) R(45) R(46) R(47) Rl65) R(66) R(67) Rl68) R169) Rl70) R171) R(72l R(74l Rt75l R(76l R(87) R(91) R192) R(931 R(94) R(97) R(98) R(99) R(100) R,l01) RI341 R(35) R(37) Rl38) R(39) R140) R141) RI421 R(43l R144) Rt45l R(58l R(59) R(61) R(621 R187) R1881 R(89) R(90l R(91) R(92) R(93) R(94) R(95) Rl96) R197, Rissj Rl99) R(100) R(101) RIlO2) R1103)
excluded
370.9460
371.2954 371.6398 371.9823 372.3180 372.6605 372.9847 373.6369 373.9563 377.2511 377.5334 377.8031 378.0785 382.3482 382.5484 382.7465 382.9413 383.1322 383.3199 383.5037 383.6847 384.0319 384.2026 384.3684 385.9368 386.3934 386.4983 386.5951 386.6944 386.9589 387.0406 387.1200 387.1928 387.2619 370.6750 370.9849 371.5975 371.8986 372.1969 372.4959 372.7788 373.0664 373.3483 373.6295 373.9060 377.1717 377.4001 377.8371 378.0562 382.2402 382.3590 382.4714 382.5819 382.6887 382.7922 382.8918 382.9872 383.0799 383.1673 383.2505 383.3308 383.4064 383.4795 383.5491 383.6136 383.6745
from
the
-0.0011 0.0002 -0.0002 0.0010 -0.0011 0.0070* 0.0002 0.0008 -0.0004 -0.0014 0.0024 -0.0028 0.0012 0.0032 0.0010 0.0004 0.0001 -0.0003 -0.0002 -0.0004 0.0005 -0.0015 0.0002 0.0008 0.0007 0.0011 0.0016 -0.0022 0.0003 -0.0022 -0.0017 0.0003 -0.0004 -0.0009 0.0009 -0.0004 0.0002 0.0005 0.0015 0.0067* -0.0007 0.0001 -0.0013 0.0002 0.0004 -0.0011 0.0011 -0.0034 0.0004 0.0026 0.0028 0.0005 0.0001 -0.0002 0.0000 0.0001 -0.0001 0.0008 0.0003 -0.0006 -0.0005 -0.0013 -0.0007 0.0003 0.0000 0.0000
fit.
2-l 2-1 2-l 2-1 2-1 2-l 2-l 2-l 2-1 2-l 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4 5-4
R(104) R(lO9) R(110) Rtlll) RI1121 RI1131 Rl114) Rt1151 R(116) R(117) R(47) R(49) Rl50) R(51) R(52) R(53) R(55) R(57) R(58) Rl59) R(60) R(77) R(78) R(79) Rl82) R183) RI631 RI641 RI651 R(66l R(671 R(68) R(69) ROO) R(71) R(72) R(73) R(74) R(75) R(76) R(77) R179) RI801 R(82) R(83) R(84) R(85) Rl86) Rl87) RI881 RI891 RI911 RI931 R(94l RI951 RI961 Rt97l R(98l RI1001 R(101) R(102l R(103) Rl104) R(105) R(106) R(109)
383.7326 383.9554 383.9903 384.0202 384.0461 384.0685 384.0867 384.1006 384.1104 384.1172 370.8488 371.3730 371.6303 371.8872 372.1392 372.3788 372.8631 373.3291 373.5573 373.7775 374.0032 377.1923 377.3513 377.5041 377.9296 378.0686 371.0525 371.2593 371.4540 371.6554 371.8484 372.0410 372.2236 372.4072 372.5931 372.7603 372.9335 373.0993 373.2670 373.4260 373.5840 373.8863 374.0347 370.7325 370.8675 370.9928 371.1179 371.2440 371.3557 371.4709 371.5858 371.7968 371.9947 372.0875 372.1730 372.2578 372.3393 372.4221 372.5668 372.6314 372.6897 372.7457 372.8015 372.8510 372.8987 373.0174
0.0012 -0.0023 -0.0010 -0.0006 -0.0004 0.0003 0.0008 0.0009 0.0008 O.OOlt3 -0.0051* -0.0037 -0.0028 0.0012 0.0039 -0.0023 0.0012 0.0006 0.0009 -0.0032 0.0018 -0.0036 0.0006 0.0024 -0.0029 -0.0001 0.0006 0.0029 -0.0032 0.0010 0.0003 0.0030 -0.0008 0.0001 0.0070* -0.0013 0.0002 -0.0021 0.0012 -0.0005 0.0005 -0.0002 0.0022 0.0026 0.0041 -0.0004 -0.0014 0.0023 -0.0046 -0.0043 -0.0006 -0.0007 0.0010 0.0014 -0.0017 -0.0018 -0.0014 0.0041 0.0056' 0.0042 0.0004 -0.0018 -0.0005 -0.0016 -0.0007 0.0006
101
LASER SPECTROSCOPY OF NaCl TABLE II Observed Infrared Transitions for Na3’C1
1-o 1-O l-0 1-O 1-O
1-o 1-o 1-o 1-o 1-o 1-O 1-O 1-o 1-o 1-O 1-o 1-o 2-1 2-l 2-l 2-l
*
R(38) R(401 R(43i R(45) R(46) R(47) R(93) R(94) R(97) R(98) R(100) R(103) R(104) R(105) R(106) R(110) R(112) R(49) R(50) R(52) R(53)
Lines
excluded
371.3730 371.9614 372.8154 373.3663 373.6369 373.9060 382.3757 382.4714 382.7465 382.8284 382.9872 383.1892 383.2505 383.3054 383.3602 383.5369 383.6023 370.8781 371.1277 371.6303 371.8740
from
2-l 2-l 2-l 2-l 2-l 2-l 2-1 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2 3-2
-0.0037* -0.0013 -O.OOOE* -0.0018 -0.0020* -0.0002* 0.0029 0.0001* 0.0021* 0.0004 0.0034* -0.0001 0.0003* -0.0020 -0.0005 0.0008 0.0015 0.0029 -0.0024 0.0007* -0.0001
the
fit.
see
R(541 Ri55i R(56) R(57) RL59) R(60) R162) Ri65i R(66l R(671 R(68) R(70) R(71l R(74) R(75l R(76) R(77) R(79) RL801 R(82)
372.1180 372.3520 372.5808 372.8154 373.2670 373.4882 373.9182 370.9849 371.1836 371.3730 371.5619 371.9356 372.1180 372.6314 372.7960 372.9596 373.1185 373.4260 373.5705 373.8545
0.0028 -0.0008 -0.0061* -0.0021 -0.0013* -0.0003 "."""" 0.0011* 0.0025 -0.0019* -0.0032 0.0006 0.0034* -0.0006* -0.0013 0.0005 0.0012* 0.0032* 0.0003 0.0003
text.
relative calibration system, and the reference wavenumbers was estimated to be M.OO~ - +0.005 cm-‘. OBSERVED SPECTRA AND ANALYSIS
Spectral lines ranging between 390 and 365 cm-’ were observed and assigned by use of three laser diodes. Spectral lines in the wavenumber range lower than 365 cm-’ were also observed but could not be assigned due to lack of an appropriate reference spectrum. Overlapping of spectral lines of (probably monomeric and polymeric ( 10)) NaOH as well as those of many hot bands of NaCl resulted in a congested spectrum. Under the high temperature, NaOH was generated in the sample cell by a reaction of NaCl with Hz0 which could not be removed from the sample. Spectral lines for the authentic sample of NaOH were independently measured and they were subtracted from the spectral lines obtained from the NaCl gas. The spectrum of monomeric NaCl was much weaker than that of NaOH. In Tables I and II, the measured spectral lines for the u = 1-0,2-l, 3-2,4-3, and 5-4 bands of Na3’Cl and the 11= l-0, 2-1, and 3-2 bands of Na3’C1 are listed, respectively. The quality of the determined line positions can be seen in a LoomisWood diagram shown in Fig. 1. The diagram was plotted with the abscissa axis referred to the calculated wavenumbers for the u = 1-O transition. Spectral lines of Na35Cl were analyzed in a single least-squares fit’ to the transition frequency v given by the usual Dunham formula, * The least-squaresprogram system SALS was used: T. Nakagawa and Y. Oyanagi, “Program System for Statistical Analysis with Least-Squares Fitting, SALS (Version II),” The University of Tokyo Computer Center, Tokyo, 1979.
102
UEHARA ET AL.
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FIG. 1. Loomis-Wood diagram showing the quality of the determined line positions. The diagram was plotted with the abscissa axis referred to the calculated wavenumbers for the u = 1-O transition of Na”Cl. The line positions for the I) = 1-O band of Na3%I are indicated with dots slightly larger than those for other bands.
,, = F’ _ F”
(1)
and
F = Z YU(v + 1/2)‘[J(J+ Li
l)]‘,
(2)
where YiOz we, Y,, E - w,x,, etc. The exact relations between YGand the usual spectroscopic constants are given in Refs. ( II, 12). The Dunham Y, coefficients retained as adjustable parameters were Y,o, y20, y30, y40, YII, Y21, and Y12. Since only the R-branch lines were observed Yo, ,Yo2, and Yo3were constrained to those determined by millimeter-wave spectroscopy ( 5). Although the diode laser spectrometer has quite a high resolving power, many of the weaker spectral lines of Na3’C1 were overlapping with other stronger lines almost all of which were those of the Na3%1 bands. Some of the overlapping lines of Na3’C1 were included in Table II but were excluded from the least-squares fit. They am marked by an asterisk. The spectral lines of Na”C1 were analyzed separately from Na3’C1 in the leastsquares fit to the transition frequency Y.Since the number of the spectral lines assigned for Na3’C1 is rather small, only three vibrational Dunham coefficients, Ylo, Yzo, and Y30,were retained as parameters. Values for seven other coefficients, YM, Yo, , Y, , ,
LASER SPECTROSCOPY OF NaCl
103
TABLE III Dunham Coefficients for Na3’Cl Coefficients
This
Work
Other
Sources
Calculated Potential
(cm-lj Ref.
5
Ref.
364.6871(32)a
5.82(55)x10-3
5.84x10-3
-6.9(490)x10-6
-12.9x10-6 0.21806309(20)
standard
the value d) -wexe.
error.
with of
the
2.0640
I"
-1.7736
0.21806309
-1.62482(30)n10-3
al One
of Table
364.6869
-1.7763(21)
c) Calculated
3
From Constants
-1.62551x10-3
5.14(27)~10-~
5.363x1o-6
-3.1202(17)x10-'
-3.1187xlo-7
8.3(17)x10-1~
6.97x10-1'
-3.402133)~10-~~
-3.468~10-~~
bl we. Dunham equations. -1 cm for raexe.
Pekeris's
theory
(Morse potential)
has
lead
to
e) Fixed.
YzI, Yo2, Ylz, and YOU,werefixed to those calculated with the approximate isotopic relation, y, = (p~/p)(i+*iWy;,
(3)
where p is the reduced mass of the molecule and the prime denotes Na3’Cl isotopic species. RESULTS AND DISCUSSION
The Dunham coefficients for Na3’Cl obtained by the least-squares fit are listed in column 2 of Table III along with those reported by Clouser and Gordy (5) and Rice and Klemperer (3). The fit is good judged from the obs - talc values listed in Table I and the value of the standard deviation, 0.0017 cm-‘. Potential constants, al-as, Be, and we, were obtained by a least-squares fit to the values of 10 Dunham coefficients given in column 2 of Table III by using the relations in Ref. ( I I ) . The results are listed in Table IV. In column 5 of Table III Y, values calculated from the constants of Table IV are listed. Judging from the calculated values, a reasonable set of Yij coefficients has been determined for Na3’Cl as shown in column 2 of Table III. The Dunham’s correction applied to YO,has led to the Be value in Table IV. However, other corrections due to the inadequacy of the Born-Oppenheimer approximation (12) could not be adopted since the experimental data required for the corrections have not been obtained. The Dunham coefficients for Na3’Cl obtained by the least-squares fit are listed in column 2 of Table V. The Y0values listed in column 3 of Table V are those calculated from the values of Yii for Na3SC1 listed in column 2 of Table III with the use of the
104
UEHARA ET AL. TABLE IV Dunham Potential Constants for Na3’CI hl-lt
Li’e
364.6880(33ta
(CIU-')
Be
0.21806295(20~ -3.07776(35)
al
6.4184(60)
=2
-10.539(48)
=3
a)
=4
13.19(Sl)
a5
-9.491550)
one
standard
error.
mass dependence relation ( 3). The difference between the observed values of YiJ (Na37C1) and the calculated values are 0.5~ for Yio, 1.8~ for YZO,and 2.0~ for the higher-order coefficient Y30. Since the agreement is satisfactory, the Y,, coefficients obtained for Na37CI also confirm that the set of the Y$values of Na “Cl given in Table III is reasonable. There may be a small deviation from the approximation, Eq. (3). However, the deviation was not evident because the uncertainty in the measurements of spectral lines for Na37C1 is larger. A striking result is the excellent agreement between the present values of Y,,, and YzOfor Na3’C1 and the corresponding values which Clouser and Gordy (5) obtained by applying the Dunham theory to their results of millimeter-wave spectroscopy. Along with the Dunham theory, they also calculated the w,xe value using the Pekeris formula which is based upon the Morse potential function. Since the value of oexe by the Pekeris formula gave better agreement with the infrared result given by Rice and Klemperer (3), they pointed out that a possible discrepancy within the Dunham theory
TABLE V Dunham Coefficients for Na”CI
360.7578(15l=
360.75848
-1.73673(86)
-1.73824
5.35(14)x10-3
5.634x10-3
-6.61x10-6b
al
One
-6.61x10-6
0.213390192b
0.213390192
-1.573793x10-3b
-1.573793x10-3
5.1356~10-~~
5.1356x10-6
-2.98790x10-7b
-2.98790x10-7
7.095x10-1Ob
7.095~10-~0
-3.1B79x10-14b
-3.1879x10-14
standard
error.
b) Fixed.
LASER SPECTROSCOPY OF NaCl
105
existed for the anharmonicity constant Y20. However, from the present result of the high-resolution infrared study, it is definitely concluded that the vibrational constants of Clouser and Gordy by use of the Dunham theory are in excellent agreement with those given by infrared spectroscopy. RECEIVED:
September 21, 1988 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12.
K. HORIAI, T. FIJJIMOTO,K. NAKAGAWA, AND H. UEHARA, Chem. Phys. Left. 147,133-136 (1988). M. SP~LITI, private communication (1979). S. A. RICE AND W. KLEMPERER, J. Chem. Phys. 27,573-579 (1957). A. HONIG, M. MANDEL, M. L. STITCH, AND C. H. TOWNES, Phys. Rev. %,629-642 (1954). P. L. CLOUSER AND W. G~RDY, Phys. Rev. 134, A863-870 (1964). For example, A. G. MAKI AND F. J. L~VAS, J. Mol. Specrrosc.85, 368-374 (198 1). M. C. D~UAY, A. M. R. P. BOPEGEDERA,C. R. BRAZIER, AND P. F. BERNATH, Chem. Phys. Left. 148, l-5 (1988). For example, G. THOMPSON, A. G. MAKI, AND A. WEBER, J. Mol. Specfrosc. 118.540-543 (1986). K. JOLMA AND J. KAUPPINEN, J. Mol. Specfrosc. 82,214-219 (1980). N. ACQUISTA AND S. ABRAMOWITZ, J. Chem. Phys. 51,2911-2914 (1969). J. L. DUNHAM, Phys. Rev. 41,721-731 (1932). W. G~RDY AND R. L. COOK, “Microwave Molecular Spectra,” 3rd ed., Wiley, New York, 1984.