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High-resolution infrared spectrum of the fundamental band of LiCl at a temperature of 830°C
JOURNAL
OF MOLECULAR
SPECTROSCOPY
124, I30- 138 (1987)
High-Resolution Infrared Spectrum of the Fundamental Band of LiCl at a Temperature of 830°C G.
A. THOMPSON,’
A. G. MARI,
WM. B. OLSON, AND A. WEBER
Molecular SpectroscopyDivision,NationalBureau of Standards, Gaithersburg,Maryland 20899 High-resolution Fourier transform spectra of ‘jLic1 and ‘LiCl have been recorded at 830°C. A total of 2522 lines have been measured at 0.006 cm-’ resolution in the 500- to 730-cm-’ region. The data for all four isotopic species have been fit with a standard deviation of 0.00027 cm-’ using 19 isotopically invariant rovibrational constants including five Ai] correction terms to the usual Dunham Yij terms. Comparison is made with the constants derived from a direct fit of the observed transitions to a Dunham potential function with only 13 coefficients including four A correction terms. The gas phase band center for the n = 1-O transition of 7Li35C1is 634.0753(7) cm-‘. Q 1987 Academic Press, Inc. INTRODUCTION
Lithium chloride is a promising candidate for studying the finer details of the effects of nuclear mass on the internuclear potential curve. In addition to the ready availability of four different isotopic species (6Li35C1,6Li37C1,7Li35C1,and 7Li37C1)the presence of a light atom will make mass-dependent effects easier to observe. The combination of a strongly bound (DO zs 4.8 eV), electronically simple ground state, lx+, and the absence of low-lying electronic states will simplify the identification of mass-dependent shifts in the spectrum. Experimentally lithium chloride forms a stable equilibrium mixture of monomer, dimer, and possibly higher polymers in the gas phase and is relatively easy to work with, thus facilitating the measurement of effects that are expected to be small. Previously, the spectrum of this molecule has been studied by several workers. The extensive microwave measurements (1-3) determined, in addition to the usual highly accurate first-order rotational constant, YO,~5:Be, estimates of the higher-order spectroscopic constants Y,o, Y2,, Y, i, Y2i, Y02, and Y,, . These microwave data, which are also available in the reference tables of Lovas and Tiemann (4), have recently been reanalyzed by Lefloch and Rostas (5) in order to determine the isotopically invariant Dunham rovibrational constants. The only previous gas phase infrared study (6), to our knowledge, measured the bandhead positions without resolving individual rotational transitions within the bands and without observing the chlorine isotope splitting. That earlier low-resolution work determined YiOand Y2,,(w, and w,x,). We report here extensive rotationally resolved infrared spectra of each of the four stable LiCl isotopic species. At the high temperatures used for these experiments a ’ Present address Frequency Electronics, Inc., 55 Charles Lindbergh Blvd., Mitchel Field, Long Island, NY 11553. 0022-2852187 $3.00 Copvright 0 1987 by Academic All rights of reproduction
130 Press, Inc.
in any form reserved.
SPECTRUM OF LiCl
131
large number of rotational levels were observed for most of the nine observed vibrational levels. These new infrared transitions were combined with the published microwave transitions to determine both the Dunham potential coefficients and several different versions of the Dunham rovibrational constants. The data have been fit to the Dunham potential coefficients both separately for each isotopic species and in a single fit that combined all isotopic species together. EXPERIMENTAL
DETAILS
The infrared spectrum of gas phase lithium chloride was measured using a Bomem DA.002 Fourier transform interferometer.2 The interferometer was coupled to the high-temperature sample cell via evacuated transfer optics (7). The sample cell was a stainless-steel tube 135~cm long and 5 cm in diameter which was fitted with KBr windows and mounted in a 75-cm-long tube furnace. The windows were outside the oven and kept at room temperature. The spectra were recorded at a temperature of about 830°C as determined by a chromel-alumel thermocouple placed at the center of the oven. Argon buffer gas at a pressure of 15 Torr was used to prevent migration of the lithium chloride out of the hot zone of the sample cell. The absorption cell acted as a heat pipe and could be operated indefinitely without refilling. The ‘LiCl sample with natural isotopic abundance was obtained commercially and was used without further purification. The 6LiCl was prepared by reacting Lithium metal, enriched to -95% 6Li, with distilled water. The resulting solution of LiOH was then titrated with HCl to neutral pH and evaporated to dryness by heating to 80°C for several days. The spectra were recorded at 0.006-cm-’ resolution (after apodization with a Hamm function) and individual scans were coadded to obtain the desired signal-to-noise ratio. A HgCdTe detector was used. A small amount of CO2 was placed in the absorption path to provide an internal calibration for the spectra. The CO2 wavenumber values given by Kauppinen (8) were used to determine a linear correction to be applied to the frequency scale. We believe this procedure permits us to measure the line positions of LiCl to within 0.0007 cm-‘. DESCRIPTION
OF THE SPECTRA
A portion of the ‘LiCl spectrum is shown in Fig. 1. The entire spectrum spans the region from 500 to 730 cm-‘. This spectrum was recorded with a resolution of 0.006 cm-’ and represents a total of 4 hr of scan time. The spectrum was congested due to overlapping of the large number of vibrational-rotational states populated at 830°C. It was further congested by the presence of two chlorine isotopes (35Cl/37Cl - 3/l) and weaker features due to the 7.5% 6LiCl present in natural abundance. As demonstrated by the lower trace in Fig. 1, the resolution and signal-to-noise ratio were quite good. Figure 2 shows a portion of the spectrum of 95% 6LiCl recorded under the same experimental conditions as the spectrum of ‘LiCl. The portion of the spectrum chosen ’ Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
132
THOMPSON
ET AL.
LiCl
625.0 ‘jl’;rii’“”
640.0
631.0 WAVENUMBER
(cm-‘)
FIG. 1. A portion of the absorption spectrum of gas phase lithium chloride at a temperature of 830°C.
for this figure shows the R branchheads for each chlorine isotope of the first few vibrational subbands. By measuring the spectrum at high temperature where these higher states have significant population a wide range of rovibrational levels can be measured permitting the determination of higher-order spectroscopic constants. Table I summarizes the total number of transitions observed and the extent of the rotational levels observed for each vibrational subband of LiCl. sLi35CI, V=4-3 6Li37CI, V=3-2 6Li35CI, V=3-2 r
sLi37CI, V=2-
1
eLi35CI, V=2-
1
eLi37Cl, V= 1-O
!
700.0
:
:
;
i
:,
:
!
:
I
WAVENUMBER
:
:,
::
:
!
740.0
720.0 (cm-9
FIG. 2. A portion of the absorption spectrum of 6LiCI at 830°C. The bandheads are formed at J = 70.
133
SPECTRUM OF LiCl TABLE I Extent of Observed Transitions for LiCl Vib. No. of TlYUlS. Transitions 1-o 2-1 3-2 4-3 5-4 6-5 7-6 8-7
Anin
P-Branch .I max
R-Branch Jmax
73 70 66 62 54 53 66 31
79 79 72 71 58 52 45 44
519 506 461 407 308 200 91 30
total transitions:
2522
transitions for 7Li35C1: 'Li3'C1: 6Li35Cl: 6Li37C1:
740 496 736 550
To obtain the initial assignments for the u = 1-O and 2-l transitions the observed spectrum was compared to a spectrum calculated by using the constants given in Ref. (2). Initially only a few low J transitions for II = 1-O were combined with the microwave data in several trial fits in which the infrared J values were systematically changed. The correct J assignment was immediately apparent because changing the infrared rotational assignment by just one unit dramatically changed the rms deviation of the fit. The number of infrared measurements included in the fit was gradually increased while closely monitoring the rms deviation of the residuals. As higher rotational and vibrational levels were added it was of course necessary to add higher terms in the potential function. Once we were sure of the assignment of about 80 transitions for one isotopic species, an automatic assignment program was used to assign the remaining transitions, not all at once but in gradual steps. ANALYSIS OF THE MEASUREMENTS
The measurements were fit to several different functions but in all cases a leastsquares fitting procedure was used in which the data were weighted by the inverse square of the estimated uncertainty in the data. The uncertainties in the microwave data were taken from Ref. (4) and the infrared data were all given an uncertainty of 0.0003 cm-’ (chosen to agree with the rms deviation of the infrared measurements). In Table II we give the coefficients determined by fitting the infrared and microwave data to the usual Watson expression (9) for the isotopically invariant Dunham rovibrational coefficients using the equations Kj = Uij[ 1 + (Me/Ma)Ayj + (M,lMb)Abj]/Cl’if2”‘2, G(V,J)= 2 Yij(U+ $)‘[J(J+ l)]’ ,
(1) (2)
and l&=G-G”,
(3)
where LJij, ATj, and A:’ are isotopically invariant coefficients, A4, is the mass of the
134
THOMPSON
ET AL.
TABLE II Isotopically Invariant Rovibrational Constants’ for LiCl UlO AlO AlO(Cl] u20 u30 u40 u50 UO1
bol(Li)
AOl(CL] u11 AlI u21 "31
1554.26185(113]b 0.0247(37) -0.440(40) -26.15071(52) 0.293997(353) -0.2113(107)x10-2 -0.163(117)x10-4 4.1285767(102) 0.3497(105) -1.052(154) -0.11315142(179) 1.227(151) 0.137242(59)x10-2 -0.5673(101)x10-5
uo2 u12 u22 '32 uo3 u13 "23 "33 uo4 u14 '24 %5 u15 '06
-0.1165087(34)x10-3 O.166O39(195)x1O-5 0.1741(44)x10“ [-0.5113x10-91c O.8935(32)x1O-g 0.4101(134~x10-'0 [-0.192x10-~ ] [0.936x10-13] [-0.132x10-l3] [-0.407x10-15] [0.119x10-15] [0.801x10-183 I-O.9O6x1O-2o] [-0.676~10-~~]
a) The u.. constants are given in units 0f ,-l~(-)(i+2j)/2 &i A constants are dimensionless. b) The uncertainty (20) in the last digits is given in parentheses after each value. c) The constants enclosed in square brackets were held fixed.
electron, M, and Mb are the atomic masses of atom a and atom b, respectively, p = M&&/(M, + Mb) is the reduced mass, and B and Jare the vibrational and rotational quantum numbers of a given energy level. Equation (2) has been derived by Dunham (10) from a simple potential function. To fit the observed transitions to Eqs. (l)-(3) we have used an iterative nonlinear least-squares fitting program. The results are in excellent agreement with those of Lefloch and Rostas (5) although the present data allow us to determine many more constants. To determine these constants we have used the following masses (II, 12): M, = 5.4858026 X 1O-4 u, A4(6Li) = 6.015 1232 u, M(‘Li) = 7.01600450 u, M(35C1) = 34.968852729 u, and M(37C1) = 36.965902624 u. The mass-reduced constants given in Table II were used to calculate the Dunham Yi, constants for ‘Li3%Z1given in the first column of Table III. In fitting the data to a function in the form of Eq. (2) it is necessary to truncate the summation when the uncertainty in the value of Yij becomes too large. Such a truncation affects the values of all the determined Yij terms. To minimize this truncation effect, we have used the Dunham equations to estimate the values of the undetermined Yij terms and included those terms as fixed constants in the least-squares fits. This procedure does not affect the standard deviation of the fit and primarily affects those Yij constants that are least well determined, We have also fit the same data to a model in which the A terms were all fixed at
135
SPECTRUM OF LiCl TABLE III Dunham Rovibrational Constants (in cm-‘) for Lithium Chloride
I
From Constants of
Table
From Constants
I
642.95821(14)a
YlO Y20 Y30x10 Y40x104
7Li37C1
‘Li35Cl 642.95813(10)
-4.475132(89)
-4.475085(57)
0.208166(250) -0.6243(312)
values
(20)
enclosed
in in
683.34148(11) -5.054900(65)
0.205262(129)
0.252786(160)
0.249787(158)
-0.7948(184) -0.3056(837) 0.804443020(86)
-0.7822(181) -0.2996(820) 0.798065315(99)
-0.8010889(31)
-0.7902663(31)
-0.9732726(38) 0.520456(145)
-0.9617213(38)
0.394247(110) -0.6405(102) -0.33511850(17)
-0.9064(144) -0.44239865(19)
0.200860(22)
0.196358(22)
0.277860(31)
0.272385(30)
0.10558(98)
0.10275(95)
0.15585(145)
0.15217(141)
-0.1027(215)
-0.1670(350)
0.461963(12)
0.449565(11)
0.681893(17)
0.87425(168) -0.1650(37)
0.84695(163)
1.37692(266)
0.512236(143) -0.8885(141) -0.43541169(21)
-0.1624(340) 0.665803(17) 1.33909(259)
-0.1591(36)
-0.2773(62)
0.319(58) -0.109001(39)
0.596(108)
0.575(104)
-0.113027(41)
-0.189945(69)
-0.183994(67)
-0.1444(64)
-0.1386(62) 0.167(30)
-0.2589(115) 0.335(60)
-0.2498(111)
0.175(31) 0.11755(17)
0.11234(17)
-0.55(17) -0.1698(45) uncertainty
-5.095296(65)
-0.6020( 140) -0.2160(591) 0.700145721(94)
0.332(60)
The
686.06649(11)
640.04956(10)
bLi37Cl
0.208072(131)
-0.1060(222)
The
IV
-0.6131(142) -0.2209(604) 0.706523485(90)
-0.6552(104) -0.3417X63(16)
b)
Table
6Li35Cl
-4.434689(56)
0.401462(112)
a)
of
II
7Li35Cl
the square
last
digits
brackets
0.22493(33)
-0.2686(60)
0.322(57) 0.21616(32)
-0.52(16)
-1.13(34)
-1.08(33)
-0.1608(43)
-0.3699(98)
-0.3527(93)
is were
given
in
parentheses.
fixed.
zero. The rms deviation of the infrared measurements only increased from 0.00027 to 0.00032 cm-‘, but the deviations were more systematic than before. On the other hand the microwave transitions had deviations that were much larger than the expected errors and the overall standard deviation of the fit increased by 73%. Now we shall describe an alternative way in which the data were fit. In recent papers from this laboratory (13-15) we have advocated fitting spectroscopic data on diatom& directly to the potential function coefficients because that forces the resulting rovibrational constants to conform to a physically meaningful model and gives more reliable extrapolations beyond the range of the input data. This has been done by means of a nonlinear least-squares program that fits the observed transitions directly to the potential coefficients (B,, w,, al, a2, etc.) given in Dunham’s paper (10). This program relates the potential coefficients to the Dunham Yij rovibrational terms through the equations given by Dunham (ZO), WoolIey (16), Bouanich (17), Ogilvie and Bouanich (18), and Ogilvie and Tipping (19). The program also incorporates some unpublished higher-order terms provided by Tipping (20). The equations relating the Y;j constants to the potential coefficients include terms in Be and we that have a mass dependence of ~-(~+*j)‘~and higher-order terms that have an additional B$uz factor that gives an additional mass dependence of cc-’ similar to the A terms in Eq. (1). Because of this one might expect this fit to be better than the fit to Eqs. (l)-(3) with the A fixed at zero; but it actually is worse. If the potential coefficients are considered to be isotopically invariant, the rms deviation of the fit of the infrared measurements to the potential coefficients is 0.00037 cm-‘, the overall
136
THOMPSON
ET AL.
standard deviation is 84% larger than the best fit, and the deviations are quite systematic. This means that, at least for LiCl, Watson’s A terms have little contribution from the higher-order terms in the Dunham Ylj expressions (which are included in our work). Instead, the Watson A terms are predominantly due to effects not included in the Dunham treatment, such as breakdown in the Born-Oppenheimer approximation. These effects will most likely take the form of effective potential coefficients that are not isotopically invariant. As indicated in an earlier paper on LiF (15), terms similar to Watson’s A terms for YO,and Yi, could be introduced for Be and w,: & = UB[1+ U&.IMJ& + bK/~~)Abll~
(4)
w, = U,[ 1 + &&/&)A”, + (MJM,)A:]/j?‘2.
(5)
and Since YiO= w, + small correction terms
(6)
Yol = Be + small correction terms
(7)
and and evaluation of the correction terms (for LiCl) in Eqs. (6) and (7) shows that they are smaller than the Watson A terms, then Alo
= A,(Li),
Furthermore,
Ar,(Cl) = AJCl),
Aor
= AB(Li), and
&,(Cl) = AdCl).
since Y, , = 6(B&,)(
1 + a,) + small correction terms,
(8)
then, if ai is isotopically invariant, one can show that A, i(Li) = 2A8(Li) - A,(Li).
(9)
With Eqs. (4) and (5) added to the potential function, the rms deviation for the infrared transitions drops to 0.00028 cm-’ and the constants given in Table IV are determined. The constants given in Table IV were used to calculate the rovibrational constants given in columns 2-5 of Table III. DISCUSSION
In comparing column 1 of Table III with column 2 it is gratifying to note that fitting the transitions directly to the Ys gives values that are nearly identical to those obtained by fitting the transitions to the potential coefficients, and then calculating the Y’s. The constants all agree within 3a with the exception of the Yo2, Yes, and Yr3 constants which disagree respectively by 7a, Sa, and 3.6~. We believe that the strong correlation (a correlation coefficient of -0.96) between Y02and Yn in the fit to the Y’s is responsible for this large discrepancy. This is supported by the observation that the deviation in YO,tends to cancel the effect of the deviation in YOU. The correlation coefficient between these two constants is only -0.26 in the fit to the potential coefficients. This reduction in the correlation among certain constants is another advantage of fitting directly to the potential function.
SPECTRUM
OF LiCl
137
TABLE IV Dunham Potential Constantsa for LiCl UB AB(Li) AB(C1) % A,(Li) A,,,(U) a1 a2 a3 =4 a5 a6 a7
4.1285800(108Jb 0.3374006) -1.069(163) 1554.26352(109) 0.0670(27) -0.485(42) -2.71972583(665) 5.0234585(508) -7.419211(536) 8.96342(299) -8.4130(189) 5.2588(669) -2.251(389)
a) The U and A constants are defined to be mass invariant constants g:V,, by Eqs. UB is in un~:s of cm units of cm x (amu)t. a's are dimensionless. b) The uncertainty (20) in the last digits is given in parentheses after each value.
In comparing Table II with Table IV one Sees that, as expected, &r x As and A i0 = A, although Alo is not so large as A,(Li). On the other hand, A, ,(Li) is too large, according to Eqs. (8) and (9); this seems to indicate that ai should not be treated as isotopically invariant. This is not surprising since al is apparently determined with so many significant figures that a discrepancy of one part in 1O5should be discernible. The constants given in the second and third columns of Table III give u = 1-O band centers of 634.07528 -I-0.00002 and 63 1.24659 + 0.00002 cm-’ for ‘Li3%l and 7Li37C1, respectively. Because of possible systematic errors in the calibration, the absolute uncertainties in these band centers should be more like -+0.0007 cm-‘. If the most recently published (21) wavenumbers for the CO2 calibration lines are correct, then the band centers given here are too high by about 0.0003 cm-‘. RECEIVED:
December 12, 1986 REFERENCES
1. D. R. LIDE, P. CAHILL, AND L. P. GOLD, J. Chem. Phys. 40, 156-159 (1964). PEARSON AND W. GORDY, Phys. Rev. 177,52-58 (1969). 3. T. L. STORY, PH.D. thesis, University of California, Lawrence Radiation Lab., Berkeley, CA, 1968. 4. F. J. LOVAS AND E. TIEMANN,J. Phys. Chem. Ref Data 3,609-769 (1974). 5. A. C. LE~L(XH ANDJ. ROSTAS,J. Mol. Spectrosc. 92,276-28 I (1982). 6. W. KLEMPERER, W. G. NORRIS, A. BOCHLER, AND A. G. EMSLIE, J. Chem. Phys. 33, 1534-1540 (1960). 7. WM. B. OLSON, to be published. 8. J. KAUPPINEN,University of Turku, Turku, Finland, private communication. 9. J. K. G. WATSON,J. Mol. Spectrosc. 80,411-421 (1980). 10. J. L. DUNHAM,Phys. Rev. 41,721-731 (1932).
2. E. F.
138 II.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
THOMPSON
ET AL.
E. R. COHEN AND B. N. TAYLOR, J. Phys. Chem. Ref: Data 2,663-134 (1973). H. S. PEISER,Pure Appf. Chem. S&695-768 (1984). A. G. MAKEAND F. J. LOVAS, J. Mol. Spectrosc. 95, 80-9 I (1982). A. G. MAKI AND F. J. LOVAS, J. Mol. Spectrosc. 98, 146-153 (1983). A. G. MAKI, J. Mol. Specfrosc. 102, 361-367 (1983). H. W. WOOLLEY,J. Chem. Phys. 37, 1307-1316 (1962); 56, 1792 (1972). J. P. BOUANICH,J. Quant. Spectrosc. Radiat. Transfer 19, 381-386 (1978). J. F. OCILVIEAND J. P. BOUANICH,J. Quant. Spectrosc. Radiat. Transfer 27,481-482 (1982). J. F. OGILVIEAND R. H. TIPPING,Int. Rev. Phys. Chem. 3, 3-38 (1983). R. H. TIPPING,University of Alabama, private communication. G. GUELACHVILI AND K. NARAHAR~RAO, “Handbook of Infrared Standards,” Academic Press. Orlando, Florida, 1986; this includes more recent measurements by Kauppinen.
OF MOLECULAR
SPECTROSCOPY
124, I30- 138 (1987)
High-Resolution Infrared Spectrum of the Fundamental Band of LiCl at a Temperature of 830°C G.
A. THOMPSON,’
A. G. MARI,
WM. B. OLSON, AND A. WEBER
Molecular SpectroscopyDivision,NationalBureau of Standards, Gaithersburg,Maryland 20899 High-resolution Fourier transform spectra of ‘jLic1 and ‘LiCl have been recorded at 830°C. A total of 2522 lines have been measured at 0.006 cm-’ resolution in the 500- to 730-cm-’ region. The data for all four isotopic species have been fit with a standard deviation of 0.00027 cm-’ using 19 isotopically invariant rovibrational constants including five Ai] correction terms to the usual Dunham Yij terms. Comparison is made with the constants derived from a direct fit of the observed transitions to a Dunham potential function with only 13 coefficients including four A correction terms. The gas phase band center for the n = 1-O transition of 7Li35C1is 634.0753(7) cm-‘. Q 1987 Academic Press, Inc. INTRODUCTION
Lithium chloride is a promising candidate for studying the finer details of the effects of nuclear mass on the internuclear potential curve. In addition to the ready availability of four different isotopic species (6Li35C1,6Li37C1,7Li35C1,and 7Li37C1)the presence of a light atom will make mass-dependent effects easier to observe. The combination of a strongly bound (DO zs 4.8 eV), electronically simple ground state, lx+, and the absence of low-lying electronic states will simplify the identification of mass-dependent shifts in the spectrum. Experimentally lithium chloride forms a stable equilibrium mixture of monomer, dimer, and possibly higher polymers in the gas phase and is relatively easy to work with, thus facilitating the measurement of effects that are expected to be small. Previously, the spectrum of this molecule has been studied by several workers. The extensive microwave measurements (1-3) determined, in addition to the usual highly accurate first-order rotational constant, YO,~5:Be, estimates of the higher-order spectroscopic constants Y,o, Y2,, Y, i, Y2i, Y02, and Y,, . These microwave data, which are also available in the reference tables of Lovas and Tiemann (4), have recently been reanalyzed by Lefloch and Rostas (5) in order to determine the isotopically invariant Dunham rovibrational constants. The only previous gas phase infrared study (6), to our knowledge, measured the bandhead positions without resolving individual rotational transitions within the bands and without observing the chlorine isotope splitting. That earlier low-resolution work determined YiOand Y2,,(w, and w,x,). We report here extensive rotationally resolved infrared spectra of each of the four stable LiCl isotopic species. At the high temperatures used for these experiments a ’ Present address Frequency Electronics, Inc., 55 Charles Lindbergh Blvd., Mitchel Field, Long Island, NY 11553. 0022-2852187 $3.00 Copvright 0 1987 by Academic All rights of reproduction
130 Press, Inc.
in any form reserved.
SPECTRUM OF LiCl
131
large number of rotational levels were observed for most of the nine observed vibrational levels. These new infrared transitions were combined with the published microwave transitions to determine both the Dunham potential coefficients and several different versions of the Dunham rovibrational constants. The data have been fit to the Dunham potential coefficients both separately for each isotopic species and in a single fit that combined all isotopic species together. EXPERIMENTAL
DETAILS
The infrared spectrum of gas phase lithium chloride was measured using a Bomem DA.002 Fourier transform interferometer.2 The interferometer was coupled to the high-temperature sample cell via evacuated transfer optics (7). The sample cell was a stainless-steel tube 135~cm long and 5 cm in diameter which was fitted with KBr windows and mounted in a 75-cm-long tube furnace. The windows were outside the oven and kept at room temperature. The spectra were recorded at a temperature of about 830°C as determined by a chromel-alumel thermocouple placed at the center of the oven. Argon buffer gas at a pressure of 15 Torr was used to prevent migration of the lithium chloride out of the hot zone of the sample cell. The absorption cell acted as a heat pipe and could be operated indefinitely without refilling. The ‘LiCl sample with natural isotopic abundance was obtained commercially and was used without further purification. The 6LiCl was prepared by reacting Lithium metal, enriched to -95% 6Li, with distilled water. The resulting solution of LiOH was then titrated with HCl to neutral pH and evaporated to dryness by heating to 80°C for several days. The spectra were recorded at 0.006-cm-’ resolution (after apodization with a Hamm function) and individual scans were coadded to obtain the desired signal-to-noise ratio. A HgCdTe detector was used. A small amount of CO2 was placed in the absorption path to provide an internal calibration for the spectra. The CO2 wavenumber values given by Kauppinen (8) were used to determine a linear correction to be applied to the frequency scale. We believe this procedure permits us to measure the line positions of LiCl to within 0.0007 cm-‘. DESCRIPTION
OF THE SPECTRA
A portion of the ‘LiCl spectrum is shown in Fig. 1. The entire spectrum spans the region from 500 to 730 cm-‘. This spectrum was recorded with a resolution of 0.006 cm-’ and represents a total of 4 hr of scan time. The spectrum was congested due to overlapping of the large number of vibrational-rotational states populated at 830°C. It was further congested by the presence of two chlorine isotopes (35Cl/37Cl - 3/l) and weaker features due to the 7.5% 6LiCl present in natural abundance. As demonstrated by the lower trace in Fig. 1, the resolution and signal-to-noise ratio were quite good. Figure 2 shows a portion of the spectrum of 95% 6LiCl recorded under the same experimental conditions as the spectrum of ‘LiCl. The portion of the spectrum chosen ’ Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
132
THOMPSON
ET AL.
LiCl
625.0 ‘jl’;rii’“”
640.0
631.0 WAVENUMBER
(cm-‘)
FIG. 1. A portion of the absorption spectrum of gas phase lithium chloride at a temperature of 830°C.
for this figure shows the R branchheads for each chlorine isotope of the first few vibrational subbands. By measuring the spectrum at high temperature where these higher states have significant population a wide range of rovibrational levels can be measured permitting the determination of higher-order spectroscopic constants. Table I summarizes the total number of transitions observed and the extent of the rotational levels observed for each vibrational subband of LiCl. sLi35CI, V=4-3 6Li37CI, V=3-2 6Li35CI, V=3-2 r
sLi37CI, V=2-
1
eLi35CI, V=2-
1
eLi37Cl, V= 1-O
!
700.0
:
:
;
i
:,
:
!
:
I
WAVENUMBER
:
:,
::
:
!
740.0
720.0 (cm-9
FIG. 2. A portion of the absorption spectrum of 6LiCI at 830°C. The bandheads are formed at J = 70.
133
SPECTRUM OF LiCl TABLE I Extent of Observed Transitions for LiCl Vib. No. of TlYUlS. Transitions 1-o 2-1 3-2 4-3 5-4 6-5 7-6 8-7
Anin
P-Branch .I max
R-Branch Jmax
73 70 66 62 54 53 66 31
79 79 72 71 58 52 45 44
519 506 461 407 308 200 91 30
total transitions:
2522
transitions for 7Li35C1: 'Li3'C1: 6Li35Cl: 6Li37C1:
740 496 736 550
To obtain the initial assignments for the u = 1-O and 2-l transitions the observed spectrum was compared to a spectrum calculated by using the constants given in Ref. (2). Initially only a few low J transitions for II = 1-O were combined with the microwave data in several trial fits in which the infrared J values were systematically changed. The correct J assignment was immediately apparent because changing the infrared rotational assignment by just one unit dramatically changed the rms deviation of the fit. The number of infrared measurements included in the fit was gradually increased while closely monitoring the rms deviation of the residuals. As higher rotational and vibrational levels were added it was of course necessary to add higher terms in the potential function. Once we were sure of the assignment of about 80 transitions for one isotopic species, an automatic assignment program was used to assign the remaining transitions, not all at once but in gradual steps. ANALYSIS OF THE MEASUREMENTS
The measurements were fit to several different functions but in all cases a leastsquares fitting procedure was used in which the data were weighted by the inverse square of the estimated uncertainty in the data. The uncertainties in the microwave data were taken from Ref. (4) and the infrared data were all given an uncertainty of 0.0003 cm-’ (chosen to agree with the rms deviation of the infrared measurements). In Table II we give the coefficients determined by fitting the infrared and microwave data to the usual Watson expression (9) for the isotopically invariant Dunham rovibrational coefficients using the equations Kj = Uij[ 1 + (Me/Ma)Ayj + (M,lMb)Abj]/Cl’if2”‘2, G(V,J)= 2 Yij(U+ $)‘[J(J+ l)]’ ,
(1) (2)
and l&=G-G”,
(3)
where LJij, ATj, and A:’ are isotopically invariant coefficients, A4, is the mass of the
134
THOMPSON
ET AL.
TABLE II Isotopically Invariant Rovibrational Constants’ for LiCl UlO AlO AlO(Cl] u20 u30 u40 u50 UO1
bol(Li)
AOl(CL] u11 AlI u21 "31
1554.26185(113]b 0.0247(37) -0.440(40) -26.15071(52) 0.293997(353) -0.2113(107)x10-2 -0.163(117)x10-4 4.1285767(102) 0.3497(105) -1.052(154) -0.11315142(179) 1.227(151) 0.137242(59)x10-2 -0.5673(101)x10-5
uo2 u12 u22 '32 uo3 u13 "23 "33 uo4 u14 '24 %5 u15 '06
-0.1165087(34)x10-3 O.166O39(195)x1O-5 0.1741(44)x10“ [-0.5113x10-91c O.8935(32)x1O-g 0.4101(134~x10-'0 [-0.192x10-~ ] [0.936x10-13] [-0.132x10-l3] [-0.407x10-15] [0.119x10-15] [0.801x10-183 I-O.9O6x1O-2o] [-0.676~10-~~]
a) The u.. constants are given in units 0f ,-l~(-)(i+2j)/2 &i A constants are dimensionless. b) The uncertainty (20) in the last digits is given in parentheses after each value. c) The constants enclosed in square brackets were held fixed.
electron, M, and Mb are the atomic masses of atom a and atom b, respectively, p = M&&/(M, + Mb) is the reduced mass, and B and Jare the vibrational and rotational quantum numbers of a given energy level. Equation (2) has been derived by Dunham (10) from a simple potential function. To fit the observed transitions to Eqs. (l)-(3) we have used an iterative nonlinear least-squares fitting program. The results are in excellent agreement with those of Lefloch and Rostas (5) although the present data allow us to determine many more constants. To determine these constants we have used the following masses (II, 12): M, = 5.4858026 X 1O-4 u, A4(6Li) = 6.015 1232 u, M(‘Li) = 7.01600450 u, M(35C1) = 34.968852729 u, and M(37C1) = 36.965902624 u. The mass-reduced constants given in Table II were used to calculate the Dunham Yi, constants for ‘Li3%Z1given in the first column of Table III. In fitting the data to a function in the form of Eq. (2) it is necessary to truncate the summation when the uncertainty in the value of Yij becomes too large. Such a truncation affects the values of all the determined Yij terms. To minimize this truncation effect, we have used the Dunham equations to estimate the values of the undetermined Yij terms and included those terms as fixed constants in the least-squares fits. This procedure does not affect the standard deviation of the fit and primarily affects those Yij constants that are least well determined, We have also fit the same data to a model in which the A terms were all fixed at
135
SPECTRUM OF LiCl TABLE III Dunham Rovibrational Constants (in cm-‘) for Lithium Chloride
I
From Constants of
Table
From Constants
I
642.95821(14)a
YlO Y20 Y30x10 Y40x104
7Li37C1
‘Li35Cl 642.95813(10)
-4.475132(89)
-4.475085(57)
0.208166(250) -0.6243(312)
values
(20)
enclosed
in in
683.34148(11) -5.054900(65)
0.205262(129)
0.252786(160)
0.249787(158)
-0.7948(184) -0.3056(837) 0.804443020(86)
-0.7822(181) -0.2996(820) 0.798065315(99)
-0.8010889(31)
-0.7902663(31)
-0.9732726(38) 0.520456(145)
-0.9617213(38)
0.394247(110) -0.6405(102) -0.33511850(17)
-0.9064(144) -0.44239865(19)
0.200860(22)
0.196358(22)
0.277860(31)
0.272385(30)
0.10558(98)
0.10275(95)
0.15585(145)
0.15217(141)
-0.1027(215)
-0.1670(350)
0.461963(12)
0.449565(11)
0.681893(17)
0.87425(168) -0.1650(37)
0.84695(163)
1.37692(266)
0.512236(143) -0.8885(141) -0.43541169(21)
-0.1624(340) 0.665803(17) 1.33909(259)
-0.1591(36)
-0.2773(62)
0.319(58) -0.109001(39)
0.596(108)
0.575(104)
-0.113027(41)
-0.189945(69)
-0.183994(67)
-0.1444(64)
-0.1386(62) 0.167(30)
-0.2589(115) 0.335(60)
-0.2498(111)
0.175(31) 0.11755(17)
0.11234(17)
-0.55(17) -0.1698(45) uncertainty
-5.095296(65)
-0.6020( 140) -0.2160(591) 0.700145721(94)
0.332(60)
The
686.06649(11)
640.04956(10)
bLi37Cl
0.208072(131)
-0.1060(222)
The
IV
-0.6131(142) -0.2209(604) 0.706523485(90)
-0.6552(104) -0.3417X63(16)
b)
Table
6Li35Cl
-4.434689(56)
0.401462(112)
a)
of
II
7Li35Cl
the square
last
digits
brackets
0.22493(33)
-0.2686(60)
0.322(57) 0.21616(32)
-0.52(16)
-1.13(34)
-1.08(33)
-0.1608(43)
-0.3699(98)
-0.3527(93)
is were
given
in
parentheses.
fixed.
zero. The rms deviation of the infrared measurements only increased from 0.00027 to 0.00032 cm-‘, but the deviations were more systematic than before. On the other hand the microwave transitions had deviations that were much larger than the expected errors and the overall standard deviation of the fit increased by 73%. Now we shall describe an alternative way in which the data were fit. In recent papers from this laboratory (13-15) we have advocated fitting spectroscopic data on diatom& directly to the potential function coefficients because that forces the resulting rovibrational constants to conform to a physically meaningful model and gives more reliable extrapolations beyond the range of the input data. This has been done by means of a nonlinear least-squares program that fits the observed transitions directly to the potential coefficients (B,, w,, al, a2, etc.) given in Dunham’s paper (10). This program relates the potential coefficients to the Dunham Yij rovibrational terms through the equations given by Dunham (ZO), WoolIey (16), Bouanich (17), Ogilvie and Bouanich (18), and Ogilvie and Tipping (19). The program also incorporates some unpublished higher-order terms provided by Tipping (20). The equations relating the Y;j constants to the potential coefficients include terms in Be and we that have a mass dependence of ~-(~+*j)‘~and higher-order terms that have an additional B$uz factor that gives an additional mass dependence of cc-’ similar to the A terms in Eq. (1). Because of this one might expect this fit to be better than the fit to Eqs. (l)-(3) with the A fixed at zero; but it actually is worse. If the potential coefficients are considered to be isotopically invariant, the rms deviation of the fit of the infrared measurements to the potential coefficients is 0.00037 cm-‘, the overall
136
THOMPSON
ET AL.
standard deviation is 84% larger than the best fit, and the deviations are quite systematic. This means that, at least for LiCl, Watson’s A terms have little contribution from the higher-order terms in the Dunham Ylj expressions (which are included in our work). Instead, the Watson A terms are predominantly due to effects not included in the Dunham treatment, such as breakdown in the Born-Oppenheimer approximation. These effects will most likely take the form of effective potential coefficients that are not isotopically invariant. As indicated in an earlier paper on LiF (15), terms similar to Watson’s A terms for YO,and Yi, could be introduced for Be and w,: & = UB[1+ U&.IMJ& + bK/~~)Abll~
(4)
w, = U,[ 1 + &&/&)A”, + (MJM,)A:]/j?‘2.
(5)
and Since YiO= w, + small correction terms
(6)
Yol = Be + small correction terms
(7)
and and evaluation of the correction terms (for LiCl) in Eqs. (6) and (7) shows that they are smaller than the Watson A terms, then Alo
= A,(Li),
Furthermore,
Ar,(Cl) = AJCl),
Aor
= AB(Li), and
&,(Cl) = AdCl).
since Y, , = 6(B&,)(
1 + a,) + small correction terms,
(8)
then, if ai is isotopically invariant, one can show that A, i(Li) = 2A8(Li) - A,(Li).
(9)
With Eqs. (4) and (5) added to the potential function, the rms deviation for the infrared transitions drops to 0.00028 cm-’ and the constants given in Table IV are determined. The constants given in Table IV were used to calculate the rovibrational constants given in columns 2-5 of Table III. DISCUSSION
In comparing column 1 of Table III with column 2 it is gratifying to note that fitting the transitions directly to the Ys gives values that are nearly identical to those obtained by fitting the transitions to the potential coefficients, and then calculating the Y’s. The constants all agree within 3a with the exception of the Yo2, Yes, and Yr3 constants which disagree respectively by 7a, Sa, and 3.6~. We believe that the strong correlation (a correlation coefficient of -0.96) between Y02and Yn in the fit to the Y’s is responsible for this large discrepancy. This is supported by the observation that the deviation in YO,tends to cancel the effect of the deviation in YOU. The correlation coefficient between these two constants is only -0.26 in the fit to the potential coefficients. This reduction in the correlation among certain constants is another advantage of fitting directly to the potential function.
SPECTRUM
OF LiCl
137
TABLE IV Dunham Potential Constantsa for LiCl UB AB(Li) AB(C1) % A,(Li) A,,,(U) a1 a2 a3 =4 a5 a6 a7
4.1285800(108Jb 0.3374006) -1.069(163) 1554.26352(109) 0.0670(27) -0.485(42) -2.71972583(665) 5.0234585(508) -7.419211(536) 8.96342(299) -8.4130(189) 5.2588(669) -2.251(389)
a) The U and A constants are defined to be mass invariant constants g:V,, by Eqs. UB is in un~:s of cm units of cm x (amu)t. a's are dimensionless. b) The uncertainty (20) in the last digits is given in parentheses after each value.
In comparing Table II with Table IV one Sees that, as expected, &r x As and A i0 = A, although Alo is not so large as A,(Li). On the other hand, A, ,(Li) is too large, according to Eqs. (8) and (9); this seems to indicate that ai should not be treated as isotopically invariant. This is not surprising since al is apparently determined with so many significant figures that a discrepancy of one part in 1O5should be discernible. The constants given in the second and third columns of Table III give u = 1-O band centers of 634.07528 -I-0.00002 and 63 1.24659 + 0.00002 cm-’ for ‘Li3%l and 7Li37C1, respectively. Because of possible systematic errors in the calibration, the absolute uncertainties in these band centers should be more like -+0.0007 cm-‘. If the most recently published (21) wavenumbers for the CO2 calibration lines are correct, then the band centers given here are too high by about 0.0003 cm-‘. RECEIVED:
December 12, 1986 REFERENCES
1. D. R. LIDE, P. CAHILL, AND L. P. GOLD, J. Chem. Phys. 40, 156-159 (1964). PEARSON AND W. GORDY, Phys. Rev. 177,52-58 (1969). 3. T. L. STORY, PH.D. thesis, University of California, Lawrence Radiation Lab., Berkeley, CA, 1968. 4. F. J. LOVAS AND E. TIEMANN,J. Phys. Chem. Ref Data 3,609-769 (1974). 5. A. C. LE~L(XH ANDJ. ROSTAS,J. Mol. Spectrosc. 92,276-28 I (1982). 6. W. KLEMPERER, W. G. NORRIS, A. BOCHLER, AND A. G. EMSLIE, J. Chem. Phys. 33, 1534-1540 (1960). 7. WM. B. OLSON, to be published. 8. J. KAUPPINEN,University of Turku, Turku, Finland, private communication. 9. J. K. G. WATSON,J. Mol. Spectrosc. 80,411-421 (1980). 10. J. L. DUNHAM,Phys. Rev. 41,721-731 (1932).
2. E. F.
138 II.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
THOMPSON
ET AL.
E. R. COHEN AND B. N. TAYLOR, J. Phys. Chem. Ref: Data 2,663-134 (1973). H. S. PEISER,Pure Appf. Chem. S&695-768 (1984). A. G. MAKEAND F. J. LOVAS, J. Mol. Spectrosc. 95, 80-9 I (1982). A. G. MAKI AND F. J. LOVAS, J. Mol. Spectrosc. 98, 146-153 (1983). A. G. MAKI, J. Mol. Specfrosc. 102, 361-367 (1983). H. W. WOOLLEY,J. Chem. Phys. 37, 1307-1316 (1962); 56, 1792 (1972). J. P. BOUANICH,J. Quant. Spectrosc. Radiat. Transfer 19, 381-386 (1978). J. F. OCILVIEAND J. P. BOUANICH,J. Quant. Spectrosc. Radiat. Transfer 27,481-482 (1982). J. F. OGILVIEAND R. H. TIPPING,Int. Rev. Phys. Chem. 3, 3-38 (1983). R. H. TIPPING,University of Alabama, private communication. G. GUELACHVILI AND K. NARAHAR~RAO, “Handbook of Infrared Standards,” Academic Press. Orlando, Florida, 1986; this includes more recent measurements by Kauppinen.