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The LiHg X2Σ+→22II32 transition: excitation spectrum and rotational analysis of the v″ = 0−v′ = 1 band
i
13 December 1996
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 263 (1996) 463-470
The LiHg X2X ÷ 22II3/2 transition: excitation spectrum and rotational analysis of the v" = 0-v' = 1 band X. Li ', P. Pircher, D. Gruber, L. Windholz Institut ffir Experimentalphysik, Technische Unioersit~t Graz, Petersgasse 16, A-8010 Graz, Austria Received 3 July 1996; in final form 3 October 1996
Abstract
We report the rotationally-resolved excitation spectrum of the LiHg X 2~ + ~ 22I~3/2 transition, the first case among Ia(Li, Na, K, Cs)-IIb(Zn, Cd, Hg) intermetallic molecules. Different vibronic transitions are assigned. A rotational analysis is made for the o" = 0 ~ v' = 1 band, and rotational constants have been obtained.
1. Introduction
Although spectra of Ia(Li, Na, K, Rb, Cs)-IIb(Zn, Cd, Hg) intermetallic molecules [1] were observed by Barrat [2] in 1920s, high resolution spectroscopy on these molecules remains reclusive. The reasons are manifold: because of the nature of their potentials, and of the increased bonding and decreased internuclear separation in the upper states, only the lowest o' levels of the excited states emit into the bound levels of the ground states, only the lowest v' levels of the excited states emit into the bound levels of the ground state. The Franck-Condon factors for the higher v' levels favor bound-free emission onto the repulsive part of the ground state potential. The high temperature emission spectra exhibit therefore mainly continuous emission from the high v' levels, and no vibrational or rotational structure is observed. In addition, because of the weak bonding in their
'Present address: Max-Planck-lnstitut fiir Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching bei Miinchen, Germany.
ground states, the equilibrium concentrations of the heteronuclear molecules are much smaller than those of their homonuclear alkali dimer counterparts. These facts make the investigation of the rotational structure of the Ia-IIb intermetallic molecules difficult. Using theoretical potential energy curves, Li et al. [3] gave the first theoretical interpretation on the emission spectra of the Ia-IIb molecules produced through photochemical reaction processes [1]. It was shown that the bound-bound transitions play an important role for the lowest vibrational levels of the excited states. The Franck-Condon factors of the bound-bound transitions decrease with increasing vibrational quantum number, whereas those of the bound-free transitions decrease with increasing vibrational quantum number, whereas those of the bound-free transitions behave otherwise. They further pointed out the possibility of direct excitation of these molecules through bound-bound transitions [3]. Subsequently, Gruber and Li [4] and Gruber et al. [5] successfully observed bound-bound transitions of the LiHg blue-green band. However, the rotational structure remained unresolved due to the
000%2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0009-261 4(96)01 222-5
464
X. Li et al. / Chemical Physics Letters 263 (1996) 463-470
ences among LiH, Li 2 and LiHg molecules, it is possible to distinguish transitions from different molecules by determining the Doppler width of the spectral lines whenever the spectral lines are well isolated. In this Letter we present the excitation spectrum of the LiHg X 2 X + ~ 221-I3/2 transition. The spectrum is vibrationally identified and a rotational analysis is made for the 0 ~ 1 vibronic transition. Rotational constants have been obtained for the first time.
small resolution of the monochromator, the limited set of observed transitions and the strong Li 2 B - X and LiH (A-X) transitions. Although the LiHg X 2 X + ~ 22II3/2 transition falls into the blue absorption wing of the Li 2 X IX~B IHu transition, the absorption and emission of the Li 2 (B-X) band is still about two or three orders of magnitude stronger than that of the LiHg. The major difference between these two molecular transitions is that the LiHg 22II3/2 ~ X 2 E + emission concentrates in the 430-450 nm spectral range, whereas the emission of the Li 2 (B-X) emission in the 430-450 nm region is rather weak. This enables us to obtain a relatively clean excitation spectrum of the LiHg X22~+~ 22I]3/2 transition by detecting fluorescence in the 430-450 nm spectral region. Emission from the LiH (A-X) transition (LiH is present as impurities in lithium) could also be attenuated with this method, due to the large vibrational spacing of the LiH molecule ( ~ 1400 cm -1) [6]. In addition, because of the relatively large mass differ-
2. E x p e r i m e n t a l
In Fig. 1 we present the experimental apparatus. The lithium-mercury vapor mixture, both of natural isotopic compositions (6Li: 7.5%, 7Li: 92.5%; 196Hg: 0.2%, 19SHg: 10.1%, ]99Hg: 16.9%, 2°°Hg: 23.1%, 2°lHg: 13.2%, 2°2Hg: 29.7%, 2°4Hg: 6.8%), was generated in a crossed heat-pipe oven. Argon was used as buffer gas. A modified ring dye laser (Coher-
{ Marker Etalon
I-(
)7
"Me'er
I
Hea P,peOven
Ar ++ laser I
I
i
"'
I
'
'
Chopper
' ' ~
/
'
±
J i_
~ ---' i i
i i i
IRM
tJ it
RS 232C IEEE488
1Loc-,:o,,,er)_
I'
onocrom.or ~
PMT
Fig. 1. Experimental apparatus. PD: photodiode; PMT: photomulitplier tube; IRM: image rotating mirros; OSMA: optical spectrometric multichannel analyzer.
X. Li et al./ Chemical Physics Letters 263 (1996) 463-470
465
ixm, whereas the exit slit in front of the photomultiplier was set to about 2.5 mm. Combined with the 150 grooves/mm grating, this gives a band pass from 430 to 450 nm when the central wavelength is set to approximately 440 nm. Throughout the scans the spectra were monitored by the OSMA in order to identify the source of molecular transitions. Each scan of the exciting laser was about 30 GHz long and about 1600 individual scans were taken in order to obtain the whole excitation spectrum. The signal from the photomultiplier was processed by an E G & G 5210 lock-in amplifier. The analog intensity signal from the marker &alon was digitized by one of the A / D ports of the Lock-in amplifier, which in turn was connected to a PC 486 through an IEEE-488 interface. An RS 232C interface was used to collect the signal from the lambdameter. The refresh rate of the lambdameter and the A / D conversion speed of the lock-amplifier set the time limit of each scan to about 30 s in order to achieve a reasonable spectral resolution. Each individual scan file contains the information on the readings of the lambdameter, intensity signals from the photomultiplier and the marker &alon. A computer program reads these data files and effectively 'glues' the individual scans into a complete
ent CR699-21) operated with Stilbene 3, and tunable in single mode operation from 425 to 460 nm, was used to excite the LiHg x E E + - * 221-I3/2 transition. The ring dye laser was pumped by multi UV lines of an Ar E+ laser (Coherent INNOVA 100). The typical power of the dye laser was about 80-130 mW, depending mainly on the age of the dye. The linewidth of the laser light was about 1 MHz, which was much smaller than that of the Doppler-broadened spectra lines. The wavelength of the dye laser was measured by a lambdameter with a refresh rate of about 1 Hz and an accuracy better than 0.01 ,~. A temperature stabilized marker &alon whose mode spacing was about 0.75 GHz was used to monitor the frequency of the dye laser. The image of the fluorescence zone was rotated 90° by a set of mirrors onto the entrance slit of a grating ( 1 5 0 / 6 0 0 / 1 2 0 0 groves/ram selectable) monochromator (Acton SpectraPro-500). Two exit ports were available, of which one was connected with an OSMA (optical spectrometric multichannel analyzer, Princeton Instruments), and the other was connected to a photomultiplier (Hamamatsu R955). The dispersed fluorescence can be imaged directly by the OSMA, or deflected to the photomultiplier by rotating a mirror. The entrance slit was set to 100
~'--0~-~)"--0
~g
I
223oo
,
I
225oo
,
I
,
227oo
I
229oo
,
I
23~ oo
Wavenumber (cm -1) Fig. 2. Excitation spectrum of the LiHg X 2X + -o 22 II 3/2 transition at conditions of T = 1120 K, buffer gas (At) pressure 50 mbar. Note that the intensity is not corrected with respect to the laser power. At the top of each vibrational band an identification is marked.
466
X. Li et aL / Chemical Physics Letters 263 (1996) 463--470
spectrum. The absolute accuracy of the line positions was determined to be better than 0.03 cm -~.
Most of the vibronic transitions are overlapped with each other, with the v " = 0 ~ v ' = 1 transition to a lesser extent. We have thus chosen this vibronic transition as the starting point for a complete rotational analysis. In Fig. 3 we present the detailed spectrum of this vibronic transition. The spectrum beyond 22860 cm-t is overlapped with the v" = 0 v ' = 2 transition, which is generally weaker in intensity. A closer inspection of each rotational transition reveals the isotopic splitting, which is usually larger than the Doppler width of the rotational lines of LiHg. Among the 14 LiHg isotopic molecules, 7Li2°2Hg is the most abundant (about 27.5%), and thus the most pronounced line in each rotational transition. The isotopic splitting of the rotational lines of the 0-1 band is still too small to show completely separated components with the exception of the rotational lines near the dissociation limit. Hereafter, the spectral identification is made for 7Li2°2Hg, unless specified otherwise. The concentration of the 6LiHg molecules is about 1 order of magnitude smaller than that of the 7LiHg counter-
3. Results and analysis In Fi~. 2 we present the excitation spectrum of the LiHg X ~ + ~ 22H3/2 transition. Note that the total fluorescence intensity is not corrected with respect to the laser power. Nevertheless, the spectrum is in good agreement with theoretical calculations [3]. Difficulties are met when trying to make vibronic assignments using previous experimental results [4,5]. The main problem comes from the irregular vibrational spacing in the ground electronic state which cannot be explained. With the help of the ah initio calculations of Gleichmann and Hess [7], it was found that the previously obtained vibrational numbering of the excited state should be increased by 1. A detailed discussion will be given in the near future after the complete rotational analysis has been done. The new assignments are shown at the top of Fig. 2.
P
22760
22800
.~_.~-j.=~.Q ~
22840
22880
~
21
22920
Wavenumber (cm-~) Fig. 3. Spectrum of the 0 - , 1 vibronic band of the LiHg X ~ + ~ band starts at 22860 c m - i.
2~I13/2 and rotation identifications. The onset of the 0--, 2 vibronic
X. Li et al. / Chemical Physics Letters 263 (1996) 463-470
467
l~arts; as a consequence the transitions from the LiHg isotopic molecules are about 1 order of magnitude weaker in intensity. A detailed analysis of the 2E+~2FI3/2 transitions has been well described by Herzberg [8], and by many others, for example by Deile for CdH and CdD [9]. For the X2E + electronic state of LiHg, the energy levels of the molecule can be expressed as:
Based on the rotational selection rules, one obtained the following six branches for a X21~+~ 2 2Fl 3/2 transition,
E " ( v " , J " ) = G"(v") + F;'( J " ) ,
Q21(J) = vo + Fj( J ) - F','( J ) ,
(1)
where i = 1, 2. FT(J") are the two spin-coupling components, F," = B i N ( u + l ) - D i"N 2( U + 1) 2 +
, 3 I H~N ( U + 1)3+ ...+ 2TN,
(2)
Pz2(J) = v o + F~( J -
1) - F ~ ' ( J ) ,
Qzz(J) = v o + F!( J ) - F~'( J ) ,
(8) (9)
Rz2(J ) = v o + F ~ ( J + 1) - F ' z ' ( J ) ,
(10)
Pzl(J) = v o + F'( J - 1 )
(11)
- F'(( J ) ,
Rzl(J)=vo+F'c(J+l)-F'l'(J
(12) ),
(13)
where v 0 = T~ + G'(v') - G"(v"). It is easy to find that the following relations must hold: Q 2 2 ( J - 1) - e 2 t ( J )
F~ = B i N ( N + l) - D'_'N2( N + l) 2 +H~,N ,t 3( N + 1)3+ . - . ½ T. ( N. + 1)
= R22( J (3)
where 3/ is the spin-coupling constant, and y = y0(1 - 2 u 2 N ( N + 1)),
(4)
(5)
where T~ is the electronic term value of the excited state, j = c,d. F[ and Fit are the two A-doubling components of the 2 2[I3/2 state, Fj = B ; J ' ( J' + 1) - D'vjt2( J' + 1) 2 ++_16(j_½)(j + ½)(j + 3),
(6)
and 3=p/Y
2 + 2q/Y
(7)
is the A-doubling constant according to Mulliken and Christy [10]. The upper sign ( + ) in Eq. (6) applied to Tc, the lower ( - ) to Ta. Tc is the e-components of the A-doubled levels, and Ta is the f-components.
(14)
R z 2 ( J - 1) - P22(J + 1) + Y = R21(g ) - P2,(g + 2) - y .
where u 2 is due to rotational distortion with increasing rotation [I0]. Since the ground state potential well is rather shallow, higher order rotational distortion terms in Eq. (2) and Eq. (3) are important due to the large anharmonicity. The Ftl ' levels are the ecomponents of the spin-doublet, and F 2 levels are the f-components. For the F~' levels J " = N + 1/2, for the F~ levels J" = N - 1/2. For the 2 21-i3/2 electronic state, the energy levels of the molecule can be expressed as: E ' ( v ' , J ' ) -~ Te + G ' ( v ' ) + Fj,
1) - O2,( J ) = "yJ ,
(15)
The analysis of the spectrum in Fig. 3 shows six branches, of which two are comparably stronger than the rest. Based on Ref. [8] and the HSnl-London factors [11] for the relevant transitions, it is easy to assign the progression at the red end of Fig. 3 (around 22770 cm - l ) to P22 and the two strong branches to Qze and Q21. Simple calculations based on the six observed branches reveal that the ground state of the LiHg molecule could be described by Hund's case (b), whereas the excited state could be assumed to belong to Hund's case (a), through Hund's case (c) might also be possible. Because the spectrum is congested in the bandhead region, most of the identified branches are incomplete. Assignment of the remaining three branches to P21, R22 and R21 is easy using Eq. (14) and Eq. (15) and a relative rotational quantum numbering could be made for all six branches. Since the spectrum is congested in the bandhead region, an absolute rotational quantum numbering is not obvious. This also prevented a direct vibrational numbering based on the isotopic shift of the 6LiHg and 7 • LiHg molecules since the 6LiHg lines are weaker and no rotational branches could be identified. The absolute rotational quantum numbering is based on the Chi-square output from a general linear leastsquares fitting program. The Chi-square for the rotational lines with the right quantum numbering is
468
X. Li
et
al. / Chemical Physics Letters 263 (1996) 463-470
found to be at least two-orders of magnitude smaller than those with incorrect ones. Increasing or decreasing the rotational quantum number from the correct
numbering will result in a dramatic increase in the chi-square and an increment or decrement of B values by 5% per unit J shift.
Table 1 List of identified rotational transitions J " - 1/2
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
P2~
P21
Q22
Q21
22774.756(b) 22775.013 22775.334 22775.698 22776.091 (h) 22776.571(h) 22777.121 22777.714(b) 22778.374 22779.084(b) 22779.870(b) 22780.711 22781.625 22782.604(b) 22783.640(b) 22784.768(b) 22785.951(b) 22787.223 22788.564 22789.988 22791.498 22793.087 22794.771 22796.552 22798.420 22800.402 22802.471(b) 22804.650 22806.940 22809.346 22811.873 22814.530 22817.306 22820.221 22823.28Zl(b) 22826.490(b) 22829.858 22833.390 22837.090 22840.968 22845.036 22849.322 22853.803
22775.635(b) 22776.036(b) 22776.500(b) 22776.985(h) 22777.532(b) 22778.145(h) 22778.805(h) 22779.494(h) 22780.268(b) 22781.077 22781.948 22782.875 22783.860 22784.900(b) 22786.005(b) 22787.162(b) 22788.387 22789.668 22791.017 22792.438 22793.923 22795.481 22797.107 22798.815 22800.605 22802.471(b) 22804.404 22806.435 22808.532 22810.739 22813.036 22815.428 22817.923 22820.512 22823.213 22826.035 22828.979 22832.032 22835.215 22838.518 22841.984(b) 22845.587(b) 22849.322 22853.241 22857.317 22861.568 22865.993 22870.615 22875.447
22771.490(h) 22770.950(h) 22770.450(h)
22768.717 22768.949 22769.255 22769.644 22770.094(b) 22770.623(b) 22771.210 22771.891 22772.642 22773.484(b) 22774.420(h) 22775.450(h) 22776.509 22777.645(b) 22778.990 22780.378(b) 22781.883 22783.487 22785.212 22787.046 22789.000(b) 22791.160(h) 22793.300(h) 22795.660(h) 22798.167 22800.836 22803.652(b) 22806.616(b) 22809.773 22813.112(b) 22816.637 22820.360(h) 22824.320
22778.644 22779.488(h) 22780.377(h) 22781.331(b) 22782.362 22783.487(h) 22784.680(b) 22785.948(b) 22787.280(b) 22788.720(h) 22790.264 22791.883 22793.602 22795.416(b) 22797.332 22799.370 22801.505 22803.753(h) 22806.120(h) 22808.605(b) 22811.234 22813.992 22816.881 22819.927 22823.130(b) 22826.500(h) 22830.012(b) 22833.715 22837.595 22841.686 22845.983
R~2
R21
22776.898 22777.510(h) 22778.180(b) 22778.915(b) 22779.690(b) 22780.547(h) 22781.380(h) 22782.292(b) 22783.260(h) 22784.282 22785.344(b) 22786.509 22787.712(b) 22788.968(b) 22790.263(b) 22791.640(b) 22793.070(b) 22794.589 22796.161 22797.803 22799.509(b) 22801.305 22803.154 22805.086 22807.101(b) 22809.185 22811.361(b) 22813.634 22815.980 22818.433 22820.971 22823.613 22826.377(b) 22829.234 22832.218(b) 22835.294 22838.507(h) 22841.848(h) 22845.312 22848.955(h) 22852.701 22856.610 22860.688 22864.956(I)) 22869.359
22787.250(h) 22788.640(h) 22790.108(h) 22791.680(h) 22793.260(h) 22794.900(h) 22796.610(h) 22798.335(b) 22800.175 22802.062 22804.001 22806.023(b) 22808.100 22810.246 22812.460(b) 22814.760(h) 22817.116(b) 22819.557 22822.085 22824.700 22827.387 22830.165(b) 22833.040(h) 22836.008 22839.070 22842.239 22845.500(h) 22848.940(h) 22852.396 22856.020 22859.759 22863.631 (h) 22867.64Zl(h) 22871.794(h) 22876.097 22880.499(h) 22885.168 22889.967
X. Li et a l . / Chemical Physics Letters 263 (1996) 463-470
469
Table 1 J" - 1 / 2
P2z
P2I
Q22
Q21
R22
51 52 53 54 55
22828.487
22850.483 22855.230 22860.212 22865.448 22870.975
22858.506 22863.450 22868.654 22874.123(b)
22880.498 22885.766 22891.271 22897.044 22903.087
R2I
Transition energies in c m - 1. Letters in brackets: b - blended with other transitions; h - heavily blended or weak rotational lines which are superimposed on strong transitions.
The identified rotational transitions with the correct rotational quantum numbering are listed in Table 1 and are shown on the top of Fig. 3. In Figi 4 we present the Fortrat diagram for the LiHg X X + ~ 22H3/2 v" = 0 "-¢ v' - 1 band. While performing the fitting it is found that the rotational distortion up to 5th order for the ground state must be included in order to obtain a reasonable fit. The A-doubling constant of the excited state is fond to be rather small and is undetermined by the fitting program. Subsequently 8 is fixed at 0. Isolated lines are weighted with l, blended lines are weighted with 1/2, heavily blended or very weak lines which are superimposed on strong transitions with 1/3. The obtained molecular constants are listed in Table 2, together with the results from ab initio calculations [7]. The agreement between the experimental values
and those from ab initio calculations is very good, indicating that the quality of the theoretical calculations is high. The calculated line positions using the obtained molecular constants agree with the observed ones within the experimental accuracy (0.03 c m - 1).
4. Conclusion We have investigated the rotationally resolved excitation spectrum of the LiHg X2X+--*22II3/2 transition. A rotational analysis is made for the 0 ~ 1 vibrational band, and the molecular constants are obtained. The analysis of the rest of the observed vibronic transitions is in progress. Once the transitions from the ground state have been determined,
60.5 P
P
21
Q
~
40.5
30.5
Q21 R21
20.5
10.5
0.5
22760
22800
22840
22880
22920
Wavenumber (cm-]) Fig, 4. Fortrat diagram of the LiHg X 2 ~ + ~ 22H3/2 ( v " = 0 ~ v ' = 1) transition. ( • ) observed rotation lines; ( • ) rotational lines predicted by calculation using the obtained molecular constants.
470
X. Li et aL / Chemical Physics Letters 263 (1996) 463-470
Table 2 Molecular constants for the LiHg 22[I3/:~ (v' = 1) and X 2 ~ + (v" = 0) electronic states a Quantity
Fitting results
ab initio [7]
vo
B'v Dvr X l06 8
22774.735(14) b 0.3038685(1180) 2.3638(326) 0¢ 0.278555(103)
22761 0.31
O~"x l0°
4.5950(79)
H~' X I0 I° 1,~ × 10 ~3 J~ X 1 0 1 7 70 u 2 × 105
-8.5397(4890) 2.1813(1340) -3.3871(1320) O. 106831(518) 1.3651(439)
Jubil~iumsfonds der 0sterreichischen Nationalbank, Project No. 4873. XL acknowledges the receipt of a Lise Meitner postdoctoral stipendium from the Austrian Science Foundation (No. M-108-PHY). He would like to thank for the help of H. Skenderovic at the early stage of the experiment.
0.27
Units in cm-1 except U 2 which is dimensionless. Numbers in parentheses are one standard deviation. I" and Jo" are the 4 th and 5 th order distortion terms. b Vo = G ' ( 1 ) - 6"(0). e Fixed at 0. a
we plan to use the inverted perturbation approach (IPA) to obtain an ac curate description of the ground state potential.
Acknowledgements
This work was supported by Austrian Science Foundation, Project No. P-9929-PHY, and by the
References
[1] S. Miiosevic, in: Spectral Line Shapes, eds. A.D. May, J.R. Drummond and E. Oks, AlP Conf. Prod. No. 328 (AIP, New York, 1995) pp. 391-405. [2] S. Barrat, Trans. Faraday Soc. 25 (1929) 758. [3] X. Li, S. Milosevic, D. Azinovic, G. Pichler, R. Diiren and M.C. van Hemert, Z. Phys. D. 30 (1994) 39. [4] D. Gruber and X. Li, Chem. Phys. Lett. 240 (1995) 42. [5] D. Gruber, X. Li, L. Windholz, M.M. Gleichmann, B.A. Hess, I. Vezmar and G. Pichler, J. Phys. Chem., in press. [6] C.R. Vidal and W.C. Stwalley, J. Chem. Phys. 77 (1982) 883. [7] M.M. Gleichmann and B.A. Hess, J. Chem. Phys. 101 (1994) 9691. [8] G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950). [9] O. Deile, Z. Phys. 106 (1937) 405. [10] R.S. Mulliken and A. Christy, Phys. Rev. 38 (1931) 87; J.H. Van Vleck, Phys. Rev. 33 (1929) 502. [11] R.N. Zare, Angular Momentum (Wiley, New York, 1988); L.T. Earls, Phys. Rev. 48 (1935) 423.
13 December 1996
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 263 (1996) 463-470
The LiHg X2X ÷ 22II3/2 transition: excitation spectrum and rotational analysis of the v" = 0-v' = 1 band X. Li ', P. Pircher, D. Gruber, L. Windholz Institut ffir Experimentalphysik, Technische Unioersit~t Graz, Petersgasse 16, A-8010 Graz, Austria Received 3 July 1996; in final form 3 October 1996
Abstract
We report the rotationally-resolved excitation spectrum of the LiHg X 2~ + ~ 22I~3/2 transition, the first case among Ia(Li, Na, K, Cs)-IIb(Zn, Cd, Hg) intermetallic molecules. Different vibronic transitions are assigned. A rotational analysis is made for the o" = 0 ~ v' = 1 band, and rotational constants have been obtained.
1. Introduction
Although spectra of Ia(Li, Na, K, Rb, Cs)-IIb(Zn, Cd, Hg) intermetallic molecules [1] were observed by Barrat [2] in 1920s, high resolution spectroscopy on these molecules remains reclusive. The reasons are manifold: because of the nature of their potentials, and of the increased bonding and decreased internuclear separation in the upper states, only the lowest o' levels of the excited states emit into the bound levels of the ground states, only the lowest v' levels of the excited states emit into the bound levels of the ground state. The Franck-Condon factors for the higher v' levels favor bound-free emission onto the repulsive part of the ground state potential. The high temperature emission spectra exhibit therefore mainly continuous emission from the high v' levels, and no vibrational or rotational structure is observed. In addition, because of the weak bonding in their
'Present address: Max-Planck-lnstitut fiir Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching bei Miinchen, Germany.
ground states, the equilibrium concentrations of the heteronuclear molecules are much smaller than those of their homonuclear alkali dimer counterparts. These facts make the investigation of the rotational structure of the Ia-IIb intermetallic molecules difficult. Using theoretical potential energy curves, Li et al. [3] gave the first theoretical interpretation on the emission spectra of the Ia-IIb molecules produced through photochemical reaction processes [1]. It was shown that the bound-bound transitions play an important role for the lowest vibrational levels of the excited states. The Franck-Condon factors of the bound-bound transitions decrease with increasing vibrational quantum number, whereas those of the bound-free transitions decrease with increasing vibrational quantum number, whereas those of the bound-free transitions behave otherwise. They further pointed out the possibility of direct excitation of these molecules through bound-bound transitions [3]. Subsequently, Gruber and Li [4] and Gruber et al. [5] successfully observed bound-bound transitions of the LiHg blue-green band. However, the rotational structure remained unresolved due to the
000%2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0009-261 4(96)01 222-5
464
X. Li et al. / Chemical Physics Letters 263 (1996) 463-470
ences among LiH, Li 2 and LiHg molecules, it is possible to distinguish transitions from different molecules by determining the Doppler width of the spectral lines whenever the spectral lines are well isolated. In this Letter we present the excitation spectrum of the LiHg X 2 X + ~ 221-I3/2 transition. The spectrum is vibrationally identified and a rotational analysis is made for the 0 ~ 1 vibronic transition. Rotational constants have been obtained for the first time.
small resolution of the monochromator, the limited set of observed transitions and the strong Li 2 B - X and LiH (A-X) transitions. Although the LiHg X 2 X + ~ 22II3/2 transition falls into the blue absorption wing of the Li 2 X IX~B IHu transition, the absorption and emission of the Li 2 (B-X) band is still about two or three orders of magnitude stronger than that of the LiHg. The major difference between these two molecular transitions is that the LiHg 22II3/2 ~ X 2 E + emission concentrates in the 430-450 nm spectral range, whereas the emission of the Li 2 (B-X) emission in the 430-450 nm region is rather weak. This enables us to obtain a relatively clean excitation spectrum of the LiHg X22~+~ 22I]3/2 transition by detecting fluorescence in the 430-450 nm spectral region. Emission from the LiH (A-X) transition (LiH is present as impurities in lithium) could also be attenuated with this method, due to the large vibrational spacing of the LiH molecule ( ~ 1400 cm -1) [6]. In addition, because of the relatively large mass differ-
2. E x p e r i m e n t a l
In Fig. 1 we present the experimental apparatus. The lithium-mercury vapor mixture, both of natural isotopic compositions (6Li: 7.5%, 7Li: 92.5%; 196Hg: 0.2%, 19SHg: 10.1%, ]99Hg: 16.9%, 2°°Hg: 23.1%, 2°lHg: 13.2%, 2°2Hg: 29.7%, 2°4Hg: 6.8%), was generated in a crossed heat-pipe oven. Argon was used as buffer gas. A modified ring dye laser (Coher-
{ Marker Etalon
I-(
)7
"Me'er
I
Hea P,peOven
Ar ++ laser I
I
i
"'
I
'
'
Chopper
' ' ~
/
'
±
J i_
~ ---' i i
i i i
IRM
tJ it
RS 232C IEEE488
1Loc-,:o,,,er)_
I'
onocrom.or ~
PMT
Fig. 1. Experimental apparatus. PD: photodiode; PMT: photomulitplier tube; IRM: image rotating mirros; OSMA: optical spectrometric multichannel analyzer.
X. Li et al./ Chemical Physics Letters 263 (1996) 463-470
465
ixm, whereas the exit slit in front of the photomultiplier was set to about 2.5 mm. Combined with the 150 grooves/mm grating, this gives a band pass from 430 to 450 nm when the central wavelength is set to approximately 440 nm. Throughout the scans the spectra were monitored by the OSMA in order to identify the source of molecular transitions. Each scan of the exciting laser was about 30 GHz long and about 1600 individual scans were taken in order to obtain the whole excitation spectrum. The signal from the photomultiplier was processed by an E G & G 5210 lock-in amplifier. The analog intensity signal from the marker &alon was digitized by one of the A / D ports of the Lock-in amplifier, which in turn was connected to a PC 486 through an IEEE-488 interface. An RS 232C interface was used to collect the signal from the lambdameter. The refresh rate of the lambdameter and the A / D conversion speed of the lock-amplifier set the time limit of each scan to about 30 s in order to achieve a reasonable spectral resolution. Each individual scan file contains the information on the readings of the lambdameter, intensity signals from the photomultiplier and the marker &alon. A computer program reads these data files and effectively 'glues' the individual scans into a complete
ent CR699-21) operated with Stilbene 3, and tunable in single mode operation from 425 to 460 nm, was used to excite the LiHg x E E + - * 221-I3/2 transition. The ring dye laser was pumped by multi UV lines of an Ar E+ laser (Coherent INNOVA 100). The typical power of the dye laser was about 80-130 mW, depending mainly on the age of the dye. The linewidth of the laser light was about 1 MHz, which was much smaller than that of the Doppler-broadened spectra lines. The wavelength of the dye laser was measured by a lambdameter with a refresh rate of about 1 Hz and an accuracy better than 0.01 ,~. A temperature stabilized marker &alon whose mode spacing was about 0.75 GHz was used to monitor the frequency of the dye laser. The image of the fluorescence zone was rotated 90° by a set of mirrors onto the entrance slit of a grating ( 1 5 0 / 6 0 0 / 1 2 0 0 groves/ram selectable) monochromator (Acton SpectraPro-500). Two exit ports were available, of which one was connected with an OSMA (optical spectrometric multichannel analyzer, Princeton Instruments), and the other was connected to a photomultiplier (Hamamatsu R955). The dispersed fluorescence can be imaged directly by the OSMA, or deflected to the photomultiplier by rotating a mirror. The entrance slit was set to 100
~'--0~-~)"--0
~g
I
223oo
,
I
225oo
,
I
,
227oo
I
229oo
,
I
23~ oo
Wavenumber (cm -1) Fig. 2. Excitation spectrum of the LiHg X 2X + -o 22 II 3/2 transition at conditions of T = 1120 K, buffer gas (At) pressure 50 mbar. Note that the intensity is not corrected with respect to the laser power. At the top of each vibrational band an identification is marked.
466
X. Li et aL / Chemical Physics Letters 263 (1996) 463--470
spectrum. The absolute accuracy of the line positions was determined to be better than 0.03 cm -~.
Most of the vibronic transitions are overlapped with each other, with the v " = 0 ~ v ' = 1 transition to a lesser extent. We have thus chosen this vibronic transition as the starting point for a complete rotational analysis. In Fig. 3 we present the detailed spectrum of this vibronic transition. The spectrum beyond 22860 cm-t is overlapped with the v" = 0 v ' = 2 transition, which is generally weaker in intensity. A closer inspection of each rotational transition reveals the isotopic splitting, which is usually larger than the Doppler width of the rotational lines of LiHg. Among the 14 LiHg isotopic molecules, 7Li2°2Hg is the most abundant (about 27.5%), and thus the most pronounced line in each rotational transition. The isotopic splitting of the rotational lines of the 0-1 band is still too small to show completely separated components with the exception of the rotational lines near the dissociation limit. Hereafter, the spectral identification is made for 7Li2°2Hg, unless specified otherwise. The concentration of the 6LiHg molecules is about 1 order of magnitude smaller than that of the 7LiHg counter-
3. Results and analysis In Fi~. 2 we present the excitation spectrum of the LiHg X ~ + ~ 22H3/2 transition. Note that the total fluorescence intensity is not corrected with respect to the laser power. Nevertheless, the spectrum is in good agreement with theoretical calculations [3]. Difficulties are met when trying to make vibronic assignments using previous experimental results [4,5]. The main problem comes from the irregular vibrational spacing in the ground electronic state which cannot be explained. With the help of the ah initio calculations of Gleichmann and Hess [7], it was found that the previously obtained vibrational numbering of the excited state should be increased by 1. A detailed discussion will be given in the near future after the complete rotational analysis has been done. The new assignments are shown at the top of Fig. 2.
P
22760
22800
.~_.~-j.=~.Q ~
22840
22880
~
21
22920
Wavenumber (cm-~) Fig. 3. Spectrum of the 0 - , 1 vibronic band of the LiHg X ~ + ~ band starts at 22860 c m - i.
2~I13/2 and rotation identifications. The onset of the 0--, 2 vibronic
X. Li et al. / Chemical Physics Letters 263 (1996) 463-470
467
l~arts; as a consequence the transitions from the LiHg isotopic molecules are about 1 order of magnitude weaker in intensity. A detailed analysis of the 2E+~2FI3/2 transitions has been well described by Herzberg [8], and by many others, for example by Deile for CdH and CdD [9]. For the X2E + electronic state of LiHg, the energy levels of the molecule can be expressed as:
Based on the rotational selection rules, one obtained the following six branches for a X21~+~ 2 2Fl 3/2 transition,
E " ( v " , J " ) = G"(v") + F;'( J " ) ,
Q21(J) = vo + Fj( J ) - F','( J ) ,
(1)
where i = 1, 2. FT(J") are the two spin-coupling components, F," = B i N ( u + l ) - D i"N 2( U + 1) 2 +
, 3 I H~N ( U + 1)3+ ...+ 2TN,
(2)
Pz2(J) = v o + F~( J -
1) - F ~ ' ( J ) ,
Qzz(J) = v o + F!( J ) - F~'( J ) ,
(8) (9)
Rz2(J ) = v o + F ~ ( J + 1) - F ' z ' ( J ) ,
(10)
Pzl(J) = v o + F'( J - 1 )
(11)
- F'(( J ) ,
Rzl(J)=vo+F'c(J+l)-F'l'(J
(12) ),
(13)
where v 0 = T~ + G'(v') - G"(v"). It is easy to find that the following relations must hold: Q 2 2 ( J - 1) - e 2 t ( J )
F~ = B i N ( N + l) - D'_'N2( N + l) 2 +H~,N ,t 3( N + 1)3+ . - . ½ T. ( N. + 1)
= R22( J (3)
where 3/ is the spin-coupling constant, and y = y0(1 - 2 u 2 N ( N + 1)),
(4)
(5)
where T~ is the electronic term value of the excited state, j = c,d. F[ and Fit are the two A-doubling components of the 2 2[I3/2 state, Fj = B ; J ' ( J' + 1) - D'vjt2( J' + 1) 2 ++_16(j_½)(j + ½)(j + 3),
(6)
and 3=p/Y
2 + 2q/Y
(7)
is the A-doubling constant according to Mulliken and Christy [10]. The upper sign ( + ) in Eq. (6) applied to Tc, the lower ( - ) to Ta. Tc is the e-components of the A-doubled levels, and Ta is the f-components.
(14)
R z 2 ( J - 1) - P22(J + 1) + Y = R21(g ) - P2,(g + 2) - y .
where u 2 is due to rotational distortion with increasing rotation [I0]. Since the ground state potential well is rather shallow, higher order rotational distortion terms in Eq. (2) and Eq. (3) are important due to the large anharmonicity. The Ftl ' levels are the ecomponents of the spin-doublet, and F 2 levels are the f-components. For the F~' levels J " = N + 1/2, for the F~ levels J" = N - 1/2. For the 2 21-i3/2 electronic state, the energy levels of the molecule can be expressed as: E ' ( v ' , J ' ) -~ Te + G ' ( v ' ) + Fj,
1) - O2,( J ) = "yJ ,
(15)
The analysis of the spectrum in Fig. 3 shows six branches, of which two are comparably stronger than the rest. Based on Ref. [8] and the HSnl-London factors [11] for the relevant transitions, it is easy to assign the progression at the red end of Fig. 3 (around 22770 cm - l ) to P22 and the two strong branches to Qze and Q21. Simple calculations based on the six observed branches reveal that the ground state of the LiHg molecule could be described by Hund's case (b), whereas the excited state could be assumed to belong to Hund's case (a), through Hund's case (c) might also be possible. Because the spectrum is congested in the bandhead region, most of the identified branches are incomplete. Assignment of the remaining three branches to P21, R22 and R21 is easy using Eq. (14) and Eq. (15) and a relative rotational quantum numbering could be made for all six branches. Since the spectrum is congested in the bandhead region, an absolute rotational quantum numbering is not obvious. This also prevented a direct vibrational numbering based on the isotopic shift of the 6LiHg and 7 • LiHg molecules since the 6LiHg lines are weaker and no rotational branches could be identified. The absolute rotational quantum numbering is based on the Chi-square output from a general linear leastsquares fitting program. The Chi-square for the rotational lines with the right quantum numbering is
468
X. Li
et
al. / Chemical Physics Letters 263 (1996) 463-470
found to be at least two-orders of magnitude smaller than those with incorrect ones. Increasing or decreasing the rotational quantum number from the correct
numbering will result in a dramatic increase in the chi-square and an increment or decrement of B values by 5% per unit J shift.
Table 1 List of identified rotational transitions J " - 1/2
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
P2~
P21
Q22
Q21
22774.756(b) 22775.013 22775.334 22775.698 22776.091 (h) 22776.571(h) 22777.121 22777.714(b) 22778.374 22779.084(b) 22779.870(b) 22780.711 22781.625 22782.604(b) 22783.640(b) 22784.768(b) 22785.951(b) 22787.223 22788.564 22789.988 22791.498 22793.087 22794.771 22796.552 22798.420 22800.402 22802.471(b) 22804.650 22806.940 22809.346 22811.873 22814.530 22817.306 22820.221 22823.28Zl(b) 22826.490(b) 22829.858 22833.390 22837.090 22840.968 22845.036 22849.322 22853.803
22775.635(b) 22776.036(b) 22776.500(b) 22776.985(h) 22777.532(b) 22778.145(h) 22778.805(h) 22779.494(h) 22780.268(b) 22781.077 22781.948 22782.875 22783.860 22784.900(b) 22786.005(b) 22787.162(b) 22788.387 22789.668 22791.017 22792.438 22793.923 22795.481 22797.107 22798.815 22800.605 22802.471(b) 22804.404 22806.435 22808.532 22810.739 22813.036 22815.428 22817.923 22820.512 22823.213 22826.035 22828.979 22832.032 22835.215 22838.518 22841.984(b) 22845.587(b) 22849.322 22853.241 22857.317 22861.568 22865.993 22870.615 22875.447
22771.490(h) 22770.950(h) 22770.450(h)
22768.717 22768.949 22769.255 22769.644 22770.094(b) 22770.623(b) 22771.210 22771.891 22772.642 22773.484(b) 22774.420(h) 22775.450(h) 22776.509 22777.645(b) 22778.990 22780.378(b) 22781.883 22783.487 22785.212 22787.046 22789.000(b) 22791.160(h) 22793.300(h) 22795.660(h) 22798.167 22800.836 22803.652(b) 22806.616(b) 22809.773 22813.112(b) 22816.637 22820.360(h) 22824.320
22778.644 22779.488(h) 22780.377(h) 22781.331(b) 22782.362 22783.487(h) 22784.680(b) 22785.948(b) 22787.280(b) 22788.720(h) 22790.264 22791.883 22793.602 22795.416(b) 22797.332 22799.370 22801.505 22803.753(h) 22806.120(h) 22808.605(b) 22811.234 22813.992 22816.881 22819.927 22823.130(b) 22826.500(h) 22830.012(b) 22833.715 22837.595 22841.686 22845.983
R~2
R21
22776.898 22777.510(h) 22778.180(b) 22778.915(b) 22779.690(b) 22780.547(h) 22781.380(h) 22782.292(b) 22783.260(h) 22784.282 22785.344(b) 22786.509 22787.712(b) 22788.968(b) 22790.263(b) 22791.640(b) 22793.070(b) 22794.589 22796.161 22797.803 22799.509(b) 22801.305 22803.154 22805.086 22807.101(b) 22809.185 22811.361(b) 22813.634 22815.980 22818.433 22820.971 22823.613 22826.377(b) 22829.234 22832.218(b) 22835.294 22838.507(h) 22841.848(h) 22845.312 22848.955(h) 22852.701 22856.610 22860.688 22864.956(I)) 22869.359
22787.250(h) 22788.640(h) 22790.108(h) 22791.680(h) 22793.260(h) 22794.900(h) 22796.610(h) 22798.335(b) 22800.175 22802.062 22804.001 22806.023(b) 22808.100 22810.246 22812.460(b) 22814.760(h) 22817.116(b) 22819.557 22822.085 22824.700 22827.387 22830.165(b) 22833.040(h) 22836.008 22839.070 22842.239 22845.500(h) 22848.940(h) 22852.396 22856.020 22859.759 22863.631 (h) 22867.64Zl(h) 22871.794(h) 22876.097 22880.499(h) 22885.168 22889.967
X. Li et a l . / Chemical Physics Letters 263 (1996) 463-470
469
Table 1 J" - 1 / 2
P2z
P2I
Q22
Q21
R22
51 52 53 54 55
22828.487
22850.483 22855.230 22860.212 22865.448 22870.975
22858.506 22863.450 22868.654 22874.123(b)
22880.498 22885.766 22891.271 22897.044 22903.087
R2I
Transition energies in c m - 1. Letters in brackets: b - blended with other transitions; h - heavily blended or weak rotational lines which are superimposed on strong transitions.
The identified rotational transitions with the correct rotational quantum numbering are listed in Table 1 and are shown on the top of Fig. 3. In Figi 4 we present the Fortrat diagram for the LiHg X X + ~ 22H3/2 v" = 0 "-¢ v' - 1 band. While performing the fitting it is found that the rotational distortion up to 5th order for the ground state must be included in order to obtain a reasonable fit. The A-doubling constant of the excited state is fond to be rather small and is undetermined by the fitting program. Subsequently 8 is fixed at 0. Isolated lines are weighted with l, blended lines are weighted with 1/2, heavily blended or very weak lines which are superimposed on strong transitions with 1/3. The obtained molecular constants are listed in Table 2, together with the results from ab initio calculations [7]. The agreement between the experimental values
and those from ab initio calculations is very good, indicating that the quality of the theoretical calculations is high. The calculated line positions using the obtained molecular constants agree with the observed ones within the experimental accuracy (0.03 c m - 1).
4. Conclusion We have investigated the rotationally resolved excitation spectrum of the LiHg X2X+--*22II3/2 transition. A rotational analysis is made for the 0 ~ 1 vibrational band, and the molecular constants are obtained. The analysis of the rest of the observed vibronic transitions is in progress. Once the transitions from the ground state have been determined,
60.5 P
P
21
Q
~
40.5
30.5
Q21 R21
20.5
10.5
0.5
22760
22800
22840
22880
22920
Wavenumber (cm-]) Fig, 4. Fortrat diagram of the LiHg X 2 ~ + ~ 22H3/2 ( v " = 0 ~ v ' = 1) transition. ( • ) observed rotation lines; ( • ) rotational lines predicted by calculation using the obtained molecular constants.
470
X. Li et aL / Chemical Physics Letters 263 (1996) 463-470
Table 2 Molecular constants for the LiHg 22[I3/:~ (v' = 1) and X 2 ~ + (v" = 0) electronic states a Quantity
Fitting results
ab initio [7]
vo
B'v Dvr X l06 8
22774.735(14) b 0.3038685(1180) 2.3638(326) 0¢ 0.278555(103)
22761 0.31
O~"x l0°
4.5950(79)
H~' X I0 I° 1,~ × 10 ~3 J~ X 1 0 1 7 70 u 2 × 105
-8.5397(4890) 2.1813(1340) -3.3871(1320) O. 106831(518) 1.3651(439)
Jubil~iumsfonds der 0sterreichischen Nationalbank, Project No. 4873. XL acknowledges the receipt of a Lise Meitner postdoctoral stipendium from the Austrian Science Foundation (No. M-108-PHY). He would like to thank for the help of H. Skenderovic at the early stage of the experiment.
0.27
Units in cm-1 except U 2 which is dimensionless. Numbers in parentheses are one standard deviation. I" and Jo" are the 4 th and 5 th order distortion terms. b Vo = G ' ( 1 ) - 6"(0). e Fixed at 0. a
we plan to use the inverted perturbation approach (IPA) to obtain an ac curate description of the ground state potential.
Acknowledgements
This work was supported by Austrian Science Foundation, Project No. P-9929-PHY, and by the
References
[1] S. Miiosevic, in: Spectral Line Shapes, eds. A.D. May, J.R. Drummond and E. Oks, AlP Conf. Prod. No. 328 (AIP, New York, 1995) pp. 391-405. [2] S. Barrat, Trans. Faraday Soc. 25 (1929) 758. [3] X. Li, S. Milosevic, D. Azinovic, G. Pichler, R. Diiren and M.C. van Hemert, Z. Phys. D. 30 (1994) 39. [4] D. Gruber and X. Li, Chem. Phys. Lett. 240 (1995) 42. [5] D. Gruber, X. Li, L. Windholz, M.M. Gleichmann, B.A. Hess, I. Vezmar and G. Pichler, J. Phys. Chem., in press. [6] C.R. Vidal and W.C. Stwalley, J. Chem. Phys. 77 (1982) 883. [7] M.M. Gleichmann and B.A. Hess, J. Chem. Phys. 101 (1994) 9691. [8] G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950). [9] O. Deile, Z. Phys. 106 (1937) 405. [10] R.S. Mulliken and A. Christy, Phys. Rev. 38 (1931) 87; J.H. Van Vleck, Phys. Rev. 33 (1929) 502. [11] R.N. Zare, Angular Momentum (Wiley, New York, 1988); L.T. Earls, Phys. Rev. 48 (1935) 423.