M. Dulick et al- Far- and Mid-Infrared Emission Spectroscopy of LiH and LiD

8/3/2019 M. Dulick et al- Far- and Mid-Infrared Emission Spectroscopy of LiH and LiD

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OURNAL OF MOLECULAR SPECTROSCOPY 188, 1426 (1998)

RTICLE NO. MS977430

Far- and Mid-Infrared Emission Spectroscopy of LiH and LiD

M. Dulick,* K.-Q. Zhang, B. Guo, and P. F. Bernath ,1

* National Solar Observatory, National Optical Astronomy Observatories, P.O. Box 26732, Tucson, Arizona 85726; and Centre for Molecular Beams

and Laser Chemistry, Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received May 16, 1997; in revised form August 14, 1997

High-resolution Fourier transform spectra of LiH and LiD were recorded in the far-infrared region, 100360cm01 , and the mid-infrared regions, 8001200 cm01 and 20003000 cm01 . A total of 261 pure rotational lines and678 rovibrational lines were measured for the isotopomers 6LiH( D) and 7LiH(D). Molecular constants for the X1S/

ground state in the form of mass-dependent Dunham Yij s and mass-independent Dunham Uij s were determinedfrom a data set of 1476 lines, consisting of our measured line positions and previously reported microwave, millimeter-wave, and infrared lines. An effective internuclear potential for the ground electronic state where the BornOppenhei-mer part is modeled as a parameterized modified-Morse function was also determined from a fit of the data. 1998Academic Press

I. INTRODUCTION tect interstellar LiH(D) submillimeter emission so far have

not been successful ( 17).

Prior to 1990, precise information about the properties ofLithium hydride, the simplest of the metal-bearing di-

theX1S/ ground electronic state was obtained either directlyatomic molecules, has long attracted the interest of spec-

from SCF calculations ( 1822 ) or indirectly from the analy-roscopists and theoreticians alike ( 1, 2 ). Ever since the

sis of electronic spectra ( 2, 23 ) (A 1S/ X1S/ and B 1Pnception of quantum chemistry, LiH has been the subject

X1S/). Only a handful of spectroscopic studies of limitedof numerous ab initio calculations, some of which served

scope were devoted exclusively to the X1S/ ground stateo validate various approximations used in calculating

The combined microwave studies by Pearson and Gordyproperties of electronic states of more complex diatomics

( 24 ) and Plummer et al. (25, 26) managed to measure only311 ). Because LiH is one of the lighter known hetero-

the lowest J 0 r 1 and J 1 r 2 transitions for the firstnuclear diatomics, it is also becoming an important candi-two vibrational states of the hydride and deuteride isotopom-

date in spectroscopic studies investigating the effects ofers. The low-resolution absorption infrared study by James

breakdown in the Born Oppenheimer approximationet al. (27) established the ratio of the first two terms in

1214 ) .the dipole moment expansion, while the diode laser spectra

Lithium hydride may also be of prospective interest torecorded by Yamada and Hirota (28 ) led to the refinement

astrophysicists as a means of monitoring the evolutionaryof the vibrational constants obtained from lower-resolution

ycle of the nucleosynthesis of light elements in stars orelectronic spectra. Since then, Bellini and co-workers ( 29,

determining the primordial deuterium to hydrogen cosmic30 ) extended the number of hydride and deuteride rotational

abundance ratio in interstellar clouds ( 15 ), an importanttransitions measured in the millimeter region to higher Jand

oncern to cosmologists in establishing whether the universe. In a similar fashion, Maki et al. ( 31 ) succeeded in measur-

s open or closed. According to Wharton et al. ( 16), LiH has

ing an extensive number of rotational absorption lines in botha large dipole moment of 5.882 D. As a result, submillimeter the far- and mid-infrared spectra with a Fourier transformmission should be easy to detect in interstellar space. Fur-

spectrometer.hermore, detecting submillimeter emission would not be

Maki et al. were unable to obtain a satisfactory fit of theirhindered by the great quantities of dust and gas that fre-

infrared data to the Dunham potential. Subsequent treatmentsquently surround galactic cores, which are opaque to the

by Coxon ( 13 ) and Ogilvie ( 14 ) attributed the failure toransmission of visible light used to monitor the atomic ab-

inadequate treatment of J-dependent Born Oppenheimerorption of lithium (the D lines). However, attempts to de-

breakdown. For instance, using a variable-b Morse function

to model the BornOppenheimer potential and power series

expansions to correct for J-independent and J-dependent1 Also Department of Chemistry, University of Arizona, Tucson, AZ5721. Born Oppenheimer breakdown, Coxon was able to success-

14022-2852/98 $25.00

opyright 1998 by Academic Press

ll rights of reproduction in any form reserved.


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LiH AND LiD IR SPECTRA 15

FIG. 2. An expanded portion of the LiH(D) FTS spectrum in the far-FIG. 1. An overview of the LiH(D) FTS spectrum in the far-infraredinfrared region.egion.

ully fit the data directly to the numerical eigenvalues of the pressions instead to approximate the eigenvalues of the rovi-

brational levels (similar to the treatment used by Dunham)adial Schrodinger equation to within experimental errors.

Ogilvie followed a different approach, using analytical ex- where both the BornOppenheimer potential and corrections

TABLE 16LiH Infrared Transitions (cm01) a

Copyright 1998 by Academic Press


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DULICK ET AL.6

TABLE 27LiH Infrared Transitions (cm01) a



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TABLE 2Continued

o the breakdown in the Born Oppenheimer approximation rovibrational transitions have now been extended up to

vibrational levels 5 for 7LiH and 6 for 7LiD. Inare represented by series expansions involving the expansion

addition, we report the first overtone (D /2 ) rotationalvariable z 2 (R 0 Re )/(R / Re ) .

lines of 7LiH, which were measured successfully for theThe purpose of this paper is to report new measurementsfirst time.of6LiH( D) and 7LiH( D) infrared transitions from Fourier

ransform spectra in the far- and mid-infrared regions that

were obtained by detecting emission rather than monitor- II. EXPERIMENTng absorption. Most of the rotational transitions measured

n the far-infrared spectra (278 lines) overlap with those The source for producing gas-phase lithium hydride con-

sisted of an evacuated 1.2-m-long mullite tube with water-measured by Maki et al. In the mid-infrared, D /1



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DULICK ET AL.8

TABLE 36LiD Infrared Transitions (cm01) a

ooled end windows made of either polyethylene for de-7

LiH(D) lines are given in Tables 15. The precision forthe sharpest and most intense rotational lines listed in theseecting far-infrared emission or KBr for detecting mid-infra-

ed emission. The cell was heated by enclosing the central tables (approximately 65%) is estimated to be 0.0005 cm01

In Table 5, pure rotational lines in the wavenumber rangeportion in a CM Rapid Temp tube furnace. Lithium hydride

or deuteride) was produced by reacting molten lithium, 100 130 cm01 were measured to a precision no better than

0.005 cm01 . A problem with the phase correction in trans-maintained at a temperature of 1050C, with 20 Torr of

hydrogen (or deuterium) gas. High-resolution spectra were forming the one-sided interferogram in this wavenumber

range reduced the precision of the measured line positionsecorded by detecting LiH(D) emission with a Bruker IFS

20 HR Fourier transform spectrometer that utilized a 3.5-

mm Mylar beamsplitter and liquid helium-cooled bolometerIII. ANALYSISdetector in the far-infrared region, 100 360 cm01 , and a

KBr beamsplitter and a HgCdTe detector (8001200 cm01 )

or an InSb detector (20003000 cm01 ) in the mid-infrared To determine the most precise empirical molecular con-

stants for the X1S/ ground state required supplementingegion. The resolution of the spectrometer was set to 0.01

m01 . Spectra were obtained by transforming interferograms our set of infrared measurements with the Plummer et al.

microwave lines, the Bellini et al. millimeter-wave linesonstructed from 100 coadded scans for the far-infrared and

50 coadded scans for the mid-infrared. Two far-infrared and the Maki et al. Fourier transform infrared lines, bringing

the total number of lines in the dataset to 1476. Owing topectra are displayed in Figs. 1 and 2.

Rotational line positions were measured using Braults the generally lower precision and redundancy with lines in

the infrared Fourier transform spectra, the Yamada and Hir-omputer program PC-DECOMP and calibrated to absolute

wavenumbers by impurity H2O absorption lines present in ota and the Maki et al. lines from diode laser spectra were

excluded. The Pearson and Gordy microwave lines were alsoall three spectra. Complete lists of measured 6LiH(D) and



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TABLE 47LiD Infrared Transitions (cm01) a



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DULICK ET AL.20

TABLE 5

Lithium Hydride and Deuteride Jr J / 1 Pure Rotational Transitions (cm01) a

xcluded, in this case, being superseded by the more accurate lines, 65% of the 939 lines measured, were assigned a

weighting factor of 0.0005 cm01 . For the remainder ofmeasurements of Plummer et al.

For the least-squares fits discussed below, our best weaker and blended lines, the next two larger classes



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TABLE 5Continued



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DULICK ET AL.22

TABLE 6

Mass-Dependent Dunham Constants (cm01)

which constituted 21 and 11% of the total number of lines The normalized standard deviations were 1.0882 for the6

LiDmeasured, were assigned weighting factors of 0.001 and fit, 0.9762 for the 7LiD fit, 0.8193 for the 6LiH fit, and 0.75200.002 cm01 , respectively. As for the Maki et al. data, the for the 7LiH fit. The second set of molecular constants, the

ar-infrared lines, with the exception of 22 lines, were mass-independent Dunham Uij s given in Table 7, were de-assigned a weighting factor of 0.0006 cm01 and 82% of termined from a global fit of the data tohe mid-infrared lines a weighting factor of 0.0008 cm01 .

A weighting factor of 0.000003 cm01 (90 kHz) was as-E(, J)

i , j

m0( i/2 j ) / 2 Uij [1 / (me/MA )DAij

[2]igned for all but two of the microwave lines (three times

he estimated uncertainty of 30 kHz quoted in Ref. ( 25 ) ) ,

with the exceptions being the 7LiD 0 and 6LiD 1 / ( me/MB )DBij ] / 1

2

i

[J(J / 1 )] j ,J 0 r 1 lines where weights of 0.000006 cm01 (180

kHz) were used. Quoted uncertainties of the line positions

rom Ref. ( 30 ) for the most part served as weighting fac- where Dij are empirical RossWatson parameters that correctors for the millimeter-wave lines. In the fits each datum for Born Oppenheimer breakdown on the lithium (A) and

was weighted with the square of the reciprocal of the hydrogen (B) centers ( 3335), m is the reduced mass, MA andstimated uncertainty. MB are the lithium and hydrogen atomic masses, and me is the

The first set of molecular constants, the mass-dependent electron mass. Unlike the Dunham Yij fits, the only adjustableDunham Yij s listed in Table 6, were determined by fitting parameters were the Ui 0s and Ui 1s while the remainder ofhe lines of each individual isotopomer to ( 32 ) Uijs were calculated from analytical relationships (36) that

functionally depend on the Ui 0s and Ui 1s. The normalized

E(, J) i , j

Yij / 12

i

[J(J / 1)] j . [1] standard deviation for this fit was 0.8697. Residuals of our

measured line positions are given in Tables 1 5. To save space



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TABLE 7

Mass-Independent Dunham Constants (cm01)

esiduals corresponding to the microwave, millimeter-wave, is the Born Oppenheimer potential modeled as a modified-Morse function (hereafter referred to as simply MMP),and Maki et al. infrared lines are not listed here. Atomic masses

rom Ref. (37) were used for all of the computations.

In the final stage of the analysis an internuclear poten- b(R ) zi0

bizi , [5]

ial was determined from a fit of the observed data to

he numerical eigenvalues of the radial Schrodingerandquation,

z (R 0 Re )/(R / Re ) . [6] 2

2m

d2

dR 20 Ueff(R ) / E(, J)

Born Oppenheimer breakdown on the lithium and hydrogen

centers is taken into account by the inclusion of J-indepen-0

2

2m[1/

q (R )]J(J/

1)/R2

c( r;

, J)

0, dent terms,

using the form UC (R ) M01A i1

u Ai (R 0 Re )i

/ M01B i1

u Bi (R 0 Re )i , [7 ]

Ueff(R ) UBO (R) / UC (R ) , [3] and J-dependent terms,

q (R ) M01A i0

q Ai (R 0 Re )i

/ M01B i0

q Bi (R 0 Re )i . [8]where

UBO De {1 0 exp[ 0b(R)]}2/{1 0 exp[ 0b()]} 2 [4] The radial Schrodinger fit gave a normalized standard



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DULICK ET AL.24

atomic Hamiltonian for a S/ state (35), UC (R ) corrects

for both adiabatic and nonadiabatic effects. We have also

included in Fig. 4 for comparison the correction functions

determined from a variety of different sources: the ab initio

calculation by Bishop and Cheung (38 ), the analysis of

optical A X data by Chan et al. ( 39 ), the analysis of micro-

wave and infrared data by Coxon ( 13 ), and the most recent

analysis reported by Ogilvie (14 ), which in addition to mi-

crowave and infrared data also included the millimeter-wavelines of Bellini et al. (30 ). The experimentally determined

curves agree with each other reasonably well in the range

of our data. The most noticeable discrepancies occur past

the outer end of the spectral range where our correction

function in particular is no longer expected to provide reli-

able values. Since the theoretical curve furnishes information

only on the adiabatic correction term, comparing it directlyFIG. 3. Comparison of our experimentally determined MMP form ofhe BornOppenheimer potential with the Partridge and Langhoff ICSCF with the curves determined from experimental data indicatesheoretical potential curve. The solid circles denote the theoretical values. a substantial nonadiabatic contribution over much of the

range of internuclear separation, as previously noted by Chan

deviation of 0.8056. Determined potential parameters alongwith their uncertainties are displayed in Table 8, where the

TABLE 8dissociation energy De was held fixed to the value used byDerived Parameter Values for MMPCoxon ( 13 ) and the listed atomic masses were taken from

Ref. ( 37). The Schrodinger equation was numerically inte-

grated in the range 0.5 R 3.5 A, with a grid spacing

of 0.001 A.

Reliable information about the radial dependence of the

Born Oppenheimer potential of the X1S/ state has been

amassed through numerous theoretical investigations. The

omparison in Fig. 3 therefore is intended to show that

MMP, a quantum-mechanical potential, is consistent withheoretical calculations. Of the more recent ab initio calcula-

ions reported on the X1S/ state of LiH, the Partridge and

Langhoff ICSCF potential curve (21 ) is selected for this

purpose because it is one of a few that were extensively

abulated over a wide range of internuclear separation and,

moreover, served as a benchmark to gauge the results from

more elaborate calculations. Because the ICSCF 1S/ poten-

ial curve was reported in terms of total energy, to convert

t to the energy scale of Fig. 3 required referencing it relative

o its minimum at 3.0 au followed by scaling it so that the

nergy at 40 au coincided with De

20 286.0 cm01 (2.5151

V), which is slightly more (2%) than the calculated disso-

iation energy of 19 972 cm01 reported in Ref. (20 ). It is

lear from Fig. 3 that the shapes of the potential curves are

n excellent agreement in the range of the observed spectrum,

.2 R 2.5 A, and that this agreement is maintained well

out to the dissociation limit.

Shown in Fig. 4 is the plot of the radial function UC (R )

Eq. [8]), the correction to breakdown in the BornOppen-

heimer approximation on both atomic centers. Because our

model is based on Watsons treatment of an effective di-



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FIG. 4. A summary of reported adiabatic / nonadiabatic corrections FIG. 5. The adiabatic / nonadiabatic corrections to the BornOppen-o the Born Oppenheimer potential for LiH. Note that the Bishop and heimer potential obtained from the semiclassical inversion of the Dunham

Cheung theoretical curve only takes adiabatic corrections into account. The energy levels. For comparison the corrections that correspond to the MMPange of observed spectrum corresponds to our data set. form of the BornOppenheimer potential are also shown.

t al. ( 39 ). In the case of Ogilvies curve the nonadiabaticACKNOWLEDGMENTS

ontribution is only significant for R Re .

The empirical RossWatson delta parameters determined This work was supported in part by the Natural Sciences and Engineeringrom the Dunham fit provide yet another means of indepen- Research Council of Canada (NSERC), the Petroleum Research Fund

administered by the American Chemical Society, and the NASA Laboratorydently confirming the results obtained from the radial Schrod-Astrophysics Program.nger fit. Using Watsons inversion formula (Eq. [49] in

Ref. ( 35 )) and the parameters in Table 7 gave the radialREFERENCESxpansion parameters listed in Table 9. Plots of the correc-

ion function for 7LiH and 7LiD using the u s in Table 9 1. H. Hosoya, S. Yamabe, K. Morokuma, and K. Ohno, J. Mol. Structare shown in Fig. 5. In comparing these curves with those 289, 1 100 (1993).

2. W. C. Stwalley and W. T. Zemke, J. Phys. Chem. Ref. Data 22, 87associated with MMP the agreement is excellent over 75%112 (1993).of the spectral range except at the outer end, starting at R

3. A. M. Karo and A. R. Olson, J. Chem. Phys. 30, 1232 1240 (1959)2 A, where a much steeper rise is indicated by the correction

4. F. E. Harris, J. Chem. Phys. 32, 318 (1960).unctions associated with the delta parameters. 5. W. H. Adams, Phys. Rev. 127, 1650 1658 ( 1962).

6. J. C. Browne and F. A. Matsen, Phys. Rev. A 135, 1227 1232 ( 1964)

7. W. A. Goddard, III, Phys. Rev. 157, 7380 ( 1967).

8. J. A. Keefer, J. K. Su Fu, and R. L. Belford, J. Chem. Phys. 50, 160TABLE 9173 (1969).

Radial Expansion Parameters Derived from the9. P. E. Cade and W. M. Huo, J. Chem. Phys. 47, 614 648, 649 672

RossWatson Delta Parameters(1969).

10. C. F. Bender and E. R. Davidson, Phys. Rev. 183, 2330 ( 1969).

11. N. G. Mukherjee and R. McWeeny, Int. J. Quantum Chem. 4, 97107

(1970).

12. C. R. Vidal and W. C. Stwalley, J. Chem. Phys. 77, 883898 (1982)

13. J. A. Coxon, J. Mol. Spectrosc. 152, 274282 (1992).

14. J. F. Ogilvie, J. Mol. Spectrosc. 180, 193195 (1996).

15. N. Prantzos, E. Vangioni-Flam, and M. Casse (Eds.), Origin and

Evolution of the Elements, Cambridge Univ. Press, Cambridge, UK

1993.

16. L. Wharton, L. P. Gold, and W. Klemperer, J. Chem. Phys. 52, 2804

(1970).

17. P. de Bernardis, V. Dubrovich, P. Encrenaz, R. Maoli, S. Masi, G

Mastrantonio, B. Melchiorri, F. Melchiorri, M. Signore, and P. E. Tan-

zilli, Astron. Astrophys. 269, 16 (1993).

18. K. K. Docken and J. Hinze, J. Chem. Phys. 57, 4936 4952 ( 1972).

19. W. Meyer and P. Rosmus, J. Chem. Phys. 63, 2356 2375 ( 1975).



13/13

DULICK ET AL.26

0. B. Jonsson, B. O. Roos, P. R. Taylor, and P. E. M. Siegbahn, J. Chem. 30. M. Bellini, P. DeNatale, M. Inguscio, T. D. Varberg, and J. M. Brown

Phys. Rev. A 52, 1954 1960 ( 1995).Phys. 74, 4566 4575 (1981).

1. H. Partridge and S. R. Langhoff, J. Chem. Phys. 74, 23612371 31. A. G. Maki, W. B. Olson, and G. Thompson, J. Mol. Spectrosc. 144

257268 (1990).(1981).

2. B. O. Roos and A. J. Sadlej, J. Chem. Phys. 76, 54445451 ( 1982) . 32. J. L. Dunham, Phys. Rev. 41, 721731 (1932).

33. A. H. M. Ross, R. S. Eng, and H. Kildal, Opt. Commun. 12, 433 (1974)3. K. P. Huber and G. Herzberg, Constants of Diatomic Molecules,

Van NostrandReinhold, New York, 1979. 34. J. K. G. Watson, J. Mol. Spectrosc. 45, 99113 (1973).

35. J. K. G. Watson, J. Mol. Spectrosc. 80, 411421 (1980).4. E. F. Pearson and W. Gordy, Phys. Rev. 177, 5961 ( 1969).

5. G. M. Plummer, E. Herbst, and F. C. DeLucia, J. Chem. Phys. 81, 36. J. Ogilvie, Comput. Phys. Commun. 30, 101 105 (1983) ; private com-

munication.4893 4897 (1984).

6. G. M. Plummer, E. Herbst, and F. C. DeLucia, Astrophys. J. 282, 37. I. Mills, T. Cvitas, K. Homann, N. Kallay, and K. Kuchitsu, Quanti-ties, Units, and Symbols in Physical Chemistry, Blackwell, OxfordL113L114 ( 1984).

7. T. C. James, W. G. Norris, and W. Klemperer, J. Chem. Phys. 32, UK, 1988.

38. D. M. Bishop and L. M. Cheung, J. Chem. Phys. 79, 29452950728734 (1960).

8. C. Yamada and E. Hirota, J. Chem. Phys. 88, 6702 6706 ( 1988 ) . ( 1983 ) .

39. Y. C. Chan, D. R. Harding, and W. C. Stwalley, J. Chem. Phys. 859. M. Bellini, P. DeNatale, M. Inguscio, E. Fink, D. Galli, and F. Palla,

Astrophys. J. 429, 507 ( 1994) . 24362444 (1986) .


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M. Dulick et al- Far- and Mid-Infrared Emission Spectroscopy of LiH and LiD