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Blue-green bands of LiCd
Volume 200, number 1,2
CHEMICAL PHYSICS LETTERS
27 November 1992
Blue-greenbands of LiCd Marc C. van Hemert Departmentojchemistry, Gorkxus Laboratory, Universityojhiden, P.0. Box 9502,230ORA Leiden, The NetherIands
Davorka AzinoviC, Xinghua Li, Slobodan MiloBeviC, Goran Pichler ’ Instituteof Physics, Universityof Zagreb, P.0. Box 304, 41000 Zagreb, Croatia
and Rudolf Diiren Max-Planck-Institut flrStriimungsforschung,P.O.Box 2853, 3400 GOttingen,Germany Received 29 July 1992;in final form 16 September 1992
Excited LiCd molecules are formed in a photochemical reaction of Liz (C ‘II,) molecules with cadmium atoms in the ground state. Bound-free emission of LiCd molecules is observed in the region from 460 to 500 nm, which shows, in contrast to similar systems, a structured continuum with two distinct maxima at 482 and 489 nm. From ab iaitio SCF MRDCI calculations, augmented by an approximation for the spin-orbit splitting, the observed emission is interpreted as resulting from the 2211a,2-X1Z:,, and the 2 2111,2-X1X&x transitions of LiCd.
1. Introduction Recently we have reported the observation of bluegreen LiZn bands [ 1 ] where excited LiZn was formed in a photochemical reaction between electronically excited Liz molecules and ground-state Zn atoms, With calculated nonrelativistic potentials, this band was interpreted as being due to the 2 2Il-X 2C+transition of the LiZn molecule. The asymptote of the upper state was found to correspond to Li ( 3p) + Zn ( 4s)) with a substantial contribution of Zn( 3P) character to the 2 ‘II wavefunction at larger internuclear distances. In this Letter we present similar investigations for the lithium-cadmium molecule. It is another relatively simple intermetallic molecule where the cadmium 3P level has a prominent influence on the potential energy curves and the related molecular Correspondence to; R. Diiren, Max-Planck-Institut fir Striimungsforschung, P.O. Box 2853,340OGiittingen, Germany. 1 Presently at Max-Planck-Institut f& Quantenoptik, W-8046 Garching, Germany.
spectral features. This is induced by the fact that the 3Po, levels of Cd are energetically below the relevant Li(‘3p) level. We performed both experimental and theoretical studies of this molecule in order to gain more insight into the behavior of the relevant potential energy curves and the related spectral features in the series from the simplest case of LiZn towards the heavier representatives of the I-II B combinations like NaCd, NaHg, etc. The lithium-cadmium excimers are prepared through a photochemical reaction between a Li,( C ‘II,) molecule and a Cd( 5 ‘SO) atom in tbe same way as before with Liz-Zn [ 11. In contrast to the LiZn system, the experimental results show a spectral structure which suggests that fine structure plays a major role. To interpret our results the corresponding LiCd potentials were determined in an ah initio SCF MRDCI calculation. Therefore the spin-orbit splitting of the Zn(3P) level was included in an ad hoc way into the non-relativistic ab initio SCF MRDCI results based on the CI coefficients of the relevant LiCd( 2 ‘II) state.
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Volume 200, number I,2
2. Experiment The experimental arrangement is the same as described in our previous paper [ 11. The lithium-cadmium vapor mixture is prepared in a crossed heatpipe oven. The vapor contains mostly lithium and cadmium atoms and a few percent of lithium dimers. The preparation of electronically excited Liz molecules in specific rovibrational levels of the C ‘IIU state is achieved by means of a pulsed dye laser (LPD 3002E) working with DMQ dye and pumped by an excimer laser (LPX 105E) at 308 nm. Both the dye laser and pump laser output lines were used for excitation in separate sets of experiments. The fluerescence from the interaction volume was dispersed with a monochromator and the signals from a photomultiplier were averaged with a boxcar integrator. The analog output of the boxcar integrator was monitored on a strip chart recorder and also fed through an A/D converter to a PC computer. The heat-pipe oven was first filled with pure lithium metal, and after several days of operation with cadmium. When working with the lithium-cadmium mixture it was necessary to refill the heat-pipe oven with cadmium every few days, depending on the total pressure of the buffer gas and on the temperature setting. With respect to the vapor pressure curves of pure lithium and cadmium and lithium dimers [ 21, there are several modes of operation of the heat-pipe. Working with only one metal (lithium) “the heatpipe operation” mode means that the partial lithium pressure is equal to the pressure of the buffer gas (usually helium in the present experiment ) , This is achieved by applying sufficient heating power to make the temperature of the central zone correspond to the temperature determined by the vapor pressure curve. Applying higher heating power will not increase the temperature of the vapor but rather the length of the vapor column. Overheating will result in an escape of metal from the region where recycling is possible. In contrast to this, insufIicient heating power leads to a partial vapor pressure of lithium which is lower than that of the buffer gas, and as a consequence, a mixture of lithium vapor and buffer gas builds up in the central region. Working with two metals of substantially different vapor pressures like lithium and cadmium, one can choose the conditions (by setting buffer gas pressure and heating 98
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CHEMICAL PHYSICS LETTERS
power) to have a “heat-pipe mode of operation” either with respect to lithium or with respect to cadmium. The latter implies a high buffer gas pressure and the former a low buffer gas pressure accompanied by a gradual escape of cadmium. The first case establishes conditions with many more collisions of lithium dimers occurring with lithium atoms than with cadmium atoms. In the second case the number of Liz collisions with cadmium atoms increases relative to the number of those with lithium atoms. By changing the buffer gas pressure and the heating power it is thus possible to control the relative probabilities of the various energy transfer and reaction processes, which are subsequently observed in the fluorescence spectra. 3. Experimental results Fig. 1 shows a typical fluorescence spectrum of the Li-Cd vapor mixture from 400 to 900 nm due to excitation with the (excimer-) laser line at 308 nm. In this case higher vibrational levels within the Li2(C’II,) statearepopulated (~‘=18,OG’620). The spectrum consists of LiCd emission in the region from 450 to 500 nm as a result of the photochemical reaction of excited Liz with Cd and of several other Li and Liz collisionally induced features which partially overlap. More specifically, one observes the Liz triplet (2 3II,-1 3C: ) and/or the singlet (2 ‘2: -X ‘Zz ) bound-free emission at 458 and 452 nm, respectively [ 41, the Liz B-X bound-bound emission (450-550) nm [3], the Liz 1 3$-1 3C,
II
I
. z
4.0
c1
500
600
Wavelength
700
800
(nm)
Fig. 1. The fluorescence spectra from the Li-Cd mixturefor 308 nm excimer laser excitation. The vapor temperature, r, is 1010 K aad the buffer gas pressure, P, is 3 10 Ton
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bound-free emission (500-620) nm [ 51, and finally the Liz A-X bound-bound emission (600-850 nm), where the A state is populated collisionally or through radiative cascading. Atomic lithium transitions are also observed at 460.3,497.5, 610 and 810 nm, as well as the resonance line (2p-2s transition) which is strongly affected by self-absorption. Figs. 2a and 2b show the spectral region of the LiCd emission which is characterized by two main bands at about 482 and 489 nm. The small hump at about 460 nm is due to Liz emission. Atomic lithium lines are seen at 460.3 and 497.5 nm. For figs. 2a and 2b the ratio of lithium and cadmium vapor pressures is different. When the relative amount of cadmium (fig. 2b) is higher additional sharp structures are observed at about 481.2, 482.8 and 489.4, 491 nm. Figs. 3a-3c show the fluorescence spectra under different vapor pressure conditions and different dye laser wavelength excitations of Li2(C) . In these cases lower rovibrational levels of the C state are excited. The overall spectrum is seen to be less rich than the one described in fig. 1, especially in the region between 500 and 800 nm which is not shown here. No important change in the LiCd band shape is observed depending on the initial C state preparation, even comparing the dye-laser excitation at about 350 nm with excimer-laser excitation at 308 nm. Fig. 3a
a
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460
,
,
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I
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480
,
490
I
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Fig. 2. Spectral region 440-500 nm of LiCd emission with 308 nmlaserexcitation.(a)P=25Torr,T=1070K.(b)P=310Torr, T=lOlOK.
Wavelength
(nm)
Fig. 3. The fluorescence spectra of the Li-Cd mixture. (a) T= 1020K, P=205 Torr, and the laser wavelength, 1, is 351.095 run. (b) T= lOSOK,P=4OTo11,1=349.729 nm. The transition u”=7+‘=2, 15P is excited. (c) T= 1041K, P= 10.5Torr, and 1~349.338 nm.
is for a high Cd partial vapor pressure and low Li vapor pressure. Besides the LiCd emission only the atomic lithium emission is observed at 460.3 and 497.5 run. Again, additional sharp structures are observed in the LiCd emission. When the ratio of cadmium to lithium vapor pressures is decreased these structures appear to be smeared out. At present we cannot exclude the possibility that these additional structures are also influenced by the X-B Liz absorption which may appear in that wavelength region [ 31. But if so, one would expect an opposite effect as a function of the vapor pressure ratio. As the ratio of the vapor pressures decreases, collisionally induced Liz emission (the diffusive band [ 41) appears at 458 run (figs. 3b and 3~). Upon decrease of the vapor pressure ratio the frequency of collisions of Li2(C ‘II,) molecules with lithium atoms increases compared to the frequency of collisions with cadmium atoms. Therefore the population of the 2 311sstate and subsequent emission at 458 nm would also increase relative to LiCd emission, The emission from the B ‘II, state, which can 99
CHEMICAL PHYSICS LETTERS
Volume 200, number 1,2
4
I
a
at 490 nm
3:7L&
20
wav&ngth
tnrnj
Fig. 4. Selective absorption (excitation) spectra of the Li-Cd vapor mixture at detection wavelength of (a) 490 nm LiCd emission, (b) 335.3 nm V’ =0-m” =2 of the C-+X Liz transition.
be populated in a similar collision process, is also present in the region from 460 to 600 nm [ 31. Under the condition of high partial cadmium vapor pressure this emission is, however, hardly visible (figs. 2b and 3~). Fig. 4 shows portions of typical excitation spectra at two different detection wavelengths: at 490 nm where the LiCd emission occurs and at 335.3 nm which corresponds to the anti-stokes line of the Liz C-X transition. This demonstrates that the emission of LiCd is strictly correlated with the excitation of the Li2 C-X transitions. Some of the remaining resonances (fig. 4a) are due to the incidental excitation of LiH impurities, but in these cases no LiCd emission could be observed.
4. Theoretical treatment Potential curves for the LiCd system were generated in essentially the same manner as in our previous study on the LiZn excimer emission [ 11, using suitable basis sets in an ab initio SCF MRDCI procedure. However, in comparison to LiZn, both the larger nuclear charge and the 18 additional electrons in Cd cause problems. Atomic SCF plus CI calculations find the 3P state nearly one full electron volt 100
27 November 1992
below the experimental value [ 61. The authors of ref. [ 6 ] put the origin of this too small energy gap in the too small computed correlation energy for the 5s’ state, in comparison with that for the 5s5p 3P state. Furthermore, our SCF CI calculations do not incorporate spin-orbit interaction, which in practice is responsible for a splitting of 540 cm-’ between the Cd 3P, and 3P, level [ 7 1. Finally, the 48 electrons in one atom put a heavy burden on the quality of the basis set. The choice of basis sets from the literature is rather limited [ 8 1. We have therefore followed the strategy adopted in ref. [ 61 and have used a primitive basis set of intermediate size ( 15s,1lp,7d Cartesian Gaussians, for the exponents see ref. [6] and a strong, general (Raffenetti-type) contraction [ 8). The 13s primitives were used in all 4 s-type core orbitals, with contraction coefficients taken from an uncontracted atomic SCF calculation for the Cd ground state, and the remaining 2 primitives were left uncontracted for the 5s valence shell. Similarly 9 p primitives were contracted in the 3 p-type core orbitals and 5 d primitives in the 2 d-type core orbitals, leaving again 2 uncontracted p and d primitives for the description of the 5p and 5d orbital, respectively. This contraction of course has no influence on the atomic SCF energy, but enormously reduces the basis set size in the calculation of the diatomic molecule. The basis set for Li was kept the same as in our previous LiZn studies [ 11. In our LiZn calculations it was already clear that the asymptotic Zn 3P level was too low by 3500 cm” compared to an error of 4100 cm-’ in ref. [ 61. This caused the calculated potential curves at long range to have an essentially incorrect ordering, since the Zn ‘P state was thus recovered below the Li 3p level. This caused no problems with further analyses because the spectroscopy of LiZn is determined by the shape of the potential curves at R values below 8 bohr. In that range the ordering of the relevant curves is presumably correct. The asymptotic error for the LiCd case is much larger, Cd 3P is, with the basis set of ref. [6] found at 23500 cm-’ compared to the experimental value of 3P, at 30114 cm-l, which is even below the Li 3s asymptote. By consequence, the avoided crossings between Li’Cd, LiCd’ and ionic potential curves occur at much too short an internuclear distance. Therefore, we considered that the
Volume 200, number 1,2
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CHEMICAL PHYSICS LETTERS
resulting potential curves were not immediately a suitable basis for a spectral simulation. In the studies of the Cd2 molecule the problems in the potential curves due to the too low Cd ‘P state were remedied by making a solid upward shift of the curves with respect to the ground state such that the asymptotic limits coincided with the experimental values [ 61. Such an approach is only feasible for a homonuclear system, if justifiable at all. The correct remedy would be to improve upon the description of the correlation energy in the Cd ground state. With all the available basis sets this appeared to be impossible when correlating the outermost 12,20 or 22 electrons. We made a similar observation for Zn. Recently calculations on the CdHg excimer have been performed [ 9 1, where an I-dependent empirical effective core potential (EECP) was used. In this manner a correct description of the singlet-triplet gap in the Cd atom could be realized by choice of the effective potential parameters. We did not have a computer program available for the use of these rather specific EECPs and therefore incorporated a strategy that has some similarity. Our strong contraction of the cadmium basis has merely the effect of generating a frozen Cd core that provides the largest part of the effective potential. Our approach lacks however part of the core polarizability specific to the EECPs in ref. [ 9 ] _The adjustable part of the EECP represented by a Gaussian pushes up the valence shell levels and is in ref. [ 5 ] l-dependent. By changing the exponents of the Gaussians for the 5p orbital that we can obtain just the same effect. In the calculation of the potential curves shown in fig. 5, we have modified the exponent of the most diffuse p function in the basis of ref. [ 61 such that the Cd ‘P asymptotic limit is found at around 30000 cm-‘. Of course, the variational approach for basis function optimization is violated, but we think that actually the 5p orbital obtained in this way will be much closer to reality than the one obtained with the Gaussian optimized for lowest energy. Due to the simplifications made by the strong contraction we only found it justified to do CI calculations on the basis of 3 active electrons, so we exclude the description of the Li inner shell electrons, which is presumably approximately constant over the internuclear distance as in Liz [lo] and exclude the description of correlation in the 46 Cd core elec-
35000 -
30000 -
-25000
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~~20000~ V B 15000 ii 4
10000 -
5000 -
O-
-5000--
2
4
6
8
10
R (bohr) Fig. 5. Potential energy curves of LiCd without spin-orbit interaction. The full lines are ‘Z+ potentials and dashed lines ‘II potentials.
trons. Nevertheless, after selection, configuration spaces of 5000 for C states and 4000 for II states resulted) in which we searched for the 5 and 4 lowest eigenvalues, respectively. The effect of spin-orbit interaction was added to the computed potential curves in an ad hoc way. We used the experience of the only calculations on a similar system that have included spin-orbit effects for NaHg [ 111. These calculations show a nearly linear dependence of diagonal (1 *II-l *II) and off-diagonal (1 *IT-2%) spin-orbit coupling matrix elements upon the internuclear distance in the the range form 4.5 to 8.5 bohr. In NaHg this coupling scrambles the II and Z states to a large extent. We assume that with the smaller spin-orbit coupling in Cd, we will no longer have scrambling but just a simple splitting of the 211state into a l/2 and a 3/2 component, with the l/2 component lowest. The size of the splitting at a particular internuclear distance can be related to the amount of Cd 3P character in the 2 ‘Il wavefunction [ 121. When going from R= 5.5 bohr to R=6.5 bohr in 101
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CHEMICAL PHYSICS LETTERS
our CI wavefunctions we observe a linear increase of the fraction of configurations with three open shells, resulting from couplings between the Li electron and the Cd 3P electrons. At R= 5.5 bohr this fraction amounts to 15%and at R= 6.5 bohr to 19%.Adopting an atomic spin-orbit parameter value of about 1200 cm-l, we derive a molecular splitting of about 190 cm-’ at the equilibrium internuclear distance for the LiCd C state of 5.7 bohr. This value is presumably an underestimate since off-diagonal spinorbit coupling, i.e. interaction with the 3 2Y&+ state may also be important. In summary spin-orbit coupling has the consequence that the C 211potential is split into l/2 and 3/2 components that are more or less parallel in the internuclear distance region of interest.
5. Discussion With the potential curves shown in fig. 5, where spin-orbit contributions were not included, one could already perform spectral simulations for the C’IIX IZf bound-free spectrum. The relevant difference potential has a minimum at 5.7 bohr. This minimum is responsible for the enhancement in the bound-free spectrum peaking at about 489 nm. In spectral simulations where we assume that the main contribution to the intensity results from partial waves with J=37, which is the most probable value at 1000 K, we obtain a spectrum which consists mainly of a single peak at 489 nm with a full width at half maximum of about 7 nm. Additional structures due to the contributions from different vibrational levels are observed as well, analogous to the LiZn emission [ 11. We assume that the two pronounced maxima in the observed LiCd spectrum at 482 and 489 nm result from the extrema in two difference potentials. The minima in these difference potentials should then be separated by about 300 cm-‘. In our interpretation of the spectrum this separation should correspond to the separation of the CzI11,2 and CzI13,2 potentials at about 5.7 bohr. Our theoretical estimate of 190 cm-’ seems thus somewhat too low. Work is in progress in order to include the spin-orbit interaction in more detail and at the same time possible further effects of a relativistic treatment. Based on present calculations we also predict some 102
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other spectral features of LiCd. As for the LiZn molecule, enhanced emission due to the minimum in the B 2Zt-X 2Z+ difference potential at about 4.5 bohr is expected at 904 nm. The A211-X2Z’ difference potential has no extrema and consequently emission in the red wing of the Li 2~42s resonance line of a pure reflection type is expected. The 32Z’-X2Z+ difference potential has a more complicated structure, and due to minima at about Yand 4 bohr the enhanced emission is expected at about 473 nm. However, as in the LiZn case, the corresponding dipole transition moment is much ‘smaller than that for the C 211+X2E+ transition.
Acknowledgement This work has been done under the contract CI 1*0525-C (MB) with the European Community and was also supported in part by the Ministry for Science of the Republic of Croatia.
References [ 1] S. MiIo&iC, X. Li, D. Azinovic, G. Pichler, M.C. van Hemert, A. Stehouwer and R. Diiren, J. Chem. Phys. 96 (1992) 7364. [2 ] A.N. Nesmeyanov, Vapor pressure of the chemical elements, ed. R. Gray (Else+, Amsterdam, 1963). [3]C. EnennandCh.Ottinger,J. Chem.Phys. 76 (1982) 5812. [4] J.T. Bahns, WC. Stwalley and G. Pichler, J. Chem. Phys. 90 (1989) 2841. [ 5] F. Engelke and H. Hage, Chem. Phys. Letters 103 ( 1983) 98. [6 ] CF. Bender, T.N. Rescigno,H.F. SchaeferIII and A.E. Orel, J. Chem. Phys. 71 (1979) 1122. [7] C.E. Moore, NBS Circular No. 467, Vol. 1 (US GPO, Washington, 1949). [8 ] R. Piorier, R. Kari and LG. Csizmadia, Handbook of Gaussian basis sets (Elsevier, Amsterdam, 1985). [9] E. Czuchaj, F. Rebentrost, H. Stall and H. Preuss, Chem. Phys. Letters 197 (1992) 187. [lo] I. Schmidt-Mink, W. Mllller and W. Meyer, Chem. Plays.92 (1985) 263. [ 111L. Windholz, G. Zerza, G. Pichler and B. Hess, Z. Physik D 18 (1991) 373. L. Windholz, M. Musso, G. Pichler and B. Hess, J. Chem. Phys. 94 (1991) 3366. [ lZ]H. Lefebvre-Brion and R.W. Field, Perturbation in the spectra of diatomic molecules (Academic Press, New York, 1986) p. 216.
CHEMICAL PHYSICS LETTERS
27 November 1992
Blue-greenbands of LiCd Marc C. van Hemert Departmentojchemistry, Gorkxus Laboratory, Universityojhiden, P.0. Box 9502,230ORA Leiden, The NetherIands
Davorka AzinoviC, Xinghua Li, Slobodan MiloBeviC, Goran Pichler ’ Instituteof Physics, Universityof Zagreb, P.0. Box 304, 41000 Zagreb, Croatia
and Rudolf Diiren Max-Planck-Institut flrStriimungsforschung,P.O.Box 2853, 3400 GOttingen,Germany Received 29 July 1992;in final form 16 September 1992
Excited LiCd molecules are formed in a photochemical reaction of Liz (C ‘II,) molecules with cadmium atoms in the ground state. Bound-free emission of LiCd molecules is observed in the region from 460 to 500 nm, which shows, in contrast to similar systems, a structured continuum with two distinct maxima at 482 and 489 nm. From ab iaitio SCF MRDCI calculations, augmented by an approximation for the spin-orbit splitting, the observed emission is interpreted as resulting from the 2211a,2-X1Z:,, and the 2 2111,2-X1X&x transitions of LiCd.
1. Introduction Recently we have reported the observation of bluegreen LiZn bands [ 1 ] where excited LiZn was formed in a photochemical reaction between electronically excited Liz molecules and ground-state Zn atoms, With calculated nonrelativistic potentials, this band was interpreted as being due to the 2 2Il-X 2C+transition of the LiZn molecule. The asymptote of the upper state was found to correspond to Li ( 3p) + Zn ( 4s)) with a substantial contribution of Zn( 3P) character to the 2 ‘II wavefunction at larger internuclear distances. In this Letter we present similar investigations for the lithium-cadmium molecule. It is another relatively simple intermetallic molecule where the cadmium 3P level has a prominent influence on the potential energy curves and the related molecular Correspondence to; R. Diiren, Max-Planck-Institut fir Striimungsforschung, P.O. Box 2853,340OGiittingen, Germany. 1 Presently at Max-Planck-Institut f& Quantenoptik, W-8046 Garching, Germany.
spectral features. This is induced by the fact that the 3Po, levels of Cd are energetically below the relevant Li(‘3p) level. We performed both experimental and theoretical studies of this molecule in order to gain more insight into the behavior of the relevant potential energy curves and the related spectral features in the series from the simplest case of LiZn towards the heavier representatives of the I-II B combinations like NaCd, NaHg, etc. The lithium-cadmium excimers are prepared through a photochemical reaction between a Li,( C ‘II,) molecule and a Cd( 5 ‘SO) atom in tbe same way as before with Liz-Zn [ 11. In contrast to the LiZn system, the experimental results show a spectral structure which suggests that fine structure plays a major role. To interpret our results the corresponding LiCd potentials were determined in an ah initio SCF MRDCI calculation. Therefore the spin-orbit splitting of the Zn(3P) level was included in an ad hoc way into the non-relativistic ab initio SCF MRDCI results based on the CI coefficients of the relevant LiCd( 2 ‘II) state.
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2. Experiment The experimental arrangement is the same as described in our previous paper [ 11. The lithium-cadmium vapor mixture is prepared in a crossed heatpipe oven. The vapor contains mostly lithium and cadmium atoms and a few percent of lithium dimers. The preparation of electronically excited Liz molecules in specific rovibrational levels of the C ‘IIU state is achieved by means of a pulsed dye laser (LPD 3002E) working with DMQ dye and pumped by an excimer laser (LPX 105E) at 308 nm. Both the dye laser and pump laser output lines were used for excitation in separate sets of experiments. The fluerescence from the interaction volume was dispersed with a monochromator and the signals from a photomultiplier were averaged with a boxcar integrator. The analog output of the boxcar integrator was monitored on a strip chart recorder and also fed through an A/D converter to a PC computer. The heat-pipe oven was first filled with pure lithium metal, and after several days of operation with cadmium. When working with the lithium-cadmium mixture it was necessary to refill the heat-pipe oven with cadmium every few days, depending on the total pressure of the buffer gas and on the temperature setting. With respect to the vapor pressure curves of pure lithium and cadmium and lithium dimers [ 21, there are several modes of operation of the heat-pipe. Working with only one metal (lithium) “the heatpipe operation” mode means that the partial lithium pressure is equal to the pressure of the buffer gas (usually helium in the present experiment ) , This is achieved by applying sufficient heating power to make the temperature of the central zone correspond to the temperature determined by the vapor pressure curve. Applying higher heating power will not increase the temperature of the vapor but rather the length of the vapor column. Overheating will result in an escape of metal from the region where recycling is possible. In contrast to this, insufIicient heating power leads to a partial vapor pressure of lithium which is lower than that of the buffer gas, and as a consequence, a mixture of lithium vapor and buffer gas builds up in the central region. Working with two metals of substantially different vapor pressures like lithium and cadmium, one can choose the conditions (by setting buffer gas pressure and heating 98
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power) to have a “heat-pipe mode of operation” either with respect to lithium or with respect to cadmium. The latter implies a high buffer gas pressure and the former a low buffer gas pressure accompanied by a gradual escape of cadmium. The first case establishes conditions with many more collisions of lithium dimers occurring with lithium atoms than with cadmium atoms. In the second case the number of Liz collisions with cadmium atoms increases relative to the number of those with lithium atoms. By changing the buffer gas pressure and the heating power it is thus possible to control the relative probabilities of the various energy transfer and reaction processes, which are subsequently observed in the fluorescence spectra. 3. Experimental results Fig. 1 shows a typical fluorescence spectrum of the Li-Cd vapor mixture from 400 to 900 nm due to excitation with the (excimer-) laser line at 308 nm. In this case higher vibrational levels within the Li2(C’II,) statearepopulated (~‘=18,OG’620). The spectrum consists of LiCd emission in the region from 450 to 500 nm as a result of the photochemical reaction of excited Liz with Cd and of several other Li and Liz collisionally induced features which partially overlap. More specifically, one observes the Liz triplet (2 3II,-1 3C: ) and/or the singlet (2 ‘2: -X ‘Zz ) bound-free emission at 458 and 452 nm, respectively [ 41, the Liz B-X bound-bound emission (450-550) nm [3], the Liz 1 3$-1 3C,
II
I
. z
4.0
c1
500
600
Wavelength
700
800
(nm)
Fig. 1. The fluorescence spectra from the Li-Cd mixturefor 308 nm excimer laser excitation. The vapor temperature, r, is 1010 K aad the buffer gas pressure, P, is 3 10 Ton
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bound-free emission (500-620) nm [ 51, and finally the Liz A-X bound-bound emission (600-850 nm), where the A state is populated collisionally or through radiative cascading. Atomic lithium transitions are also observed at 460.3,497.5, 610 and 810 nm, as well as the resonance line (2p-2s transition) which is strongly affected by self-absorption. Figs. 2a and 2b show the spectral region of the LiCd emission which is characterized by two main bands at about 482 and 489 nm. The small hump at about 460 nm is due to Liz emission. Atomic lithium lines are seen at 460.3 and 497.5 nm. For figs. 2a and 2b the ratio of lithium and cadmium vapor pressures is different. When the relative amount of cadmium (fig. 2b) is higher additional sharp structures are observed at about 481.2, 482.8 and 489.4, 491 nm. Figs. 3a-3c show the fluorescence spectra under different vapor pressure conditions and different dye laser wavelength excitations of Li2(C) . In these cases lower rovibrational levels of the C state are excited. The overall spectrum is seen to be less rich than the one described in fig. 1, especially in the region between 500 and 800 nm which is not shown here. No important change in the LiCd band shape is observed depending on the initial C state preparation, even comparing the dye-laser excitation at about 350 nm with excimer-laser excitation at 308 nm. Fig. 3a
a
0.0
I’ 440
!
,
I
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(
460
,
,
470
Wavelength
I
I
,
480
,
490
I
I 500
(nm)
Fig. 2. Spectral region 440-500 nm of LiCd emission with 308 nmlaserexcitation.(a)P=25Torr,T=1070K.(b)P=310Torr, T=lOlOK.
Wavelength
(nm)
Fig. 3. The fluorescence spectra of the Li-Cd mixture. (a) T= 1020K, P=205 Torr, and the laser wavelength, 1, is 351.095 run. (b) T= lOSOK,P=4OTo11,1=349.729 nm. The transition u”=7+‘=2, 15P is excited. (c) T= 1041K, P= 10.5Torr, and 1~349.338 nm.
is for a high Cd partial vapor pressure and low Li vapor pressure. Besides the LiCd emission only the atomic lithium emission is observed at 460.3 and 497.5 run. Again, additional sharp structures are observed in the LiCd emission. When the ratio of cadmium to lithium vapor pressures is decreased these structures appear to be smeared out. At present we cannot exclude the possibility that these additional structures are also influenced by the X-B Liz absorption which may appear in that wavelength region [ 31. But if so, one would expect an opposite effect as a function of the vapor pressure ratio. As the ratio of the vapor pressures decreases, collisionally induced Liz emission (the diffusive band [ 41) appears at 458 run (figs. 3b and 3~). Upon decrease of the vapor pressure ratio the frequency of collisions of Li2(C ‘II,) molecules with lithium atoms increases compared to the frequency of collisions with cadmium atoms. Therefore the population of the 2 311sstate and subsequent emission at 458 nm would also increase relative to LiCd emission, The emission from the B ‘II, state, which can 99
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wav&ngth
tnrnj
Fig. 4. Selective absorption (excitation) spectra of the Li-Cd vapor mixture at detection wavelength of (a) 490 nm LiCd emission, (b) 335.3 nm V’ =0-m” =2 of the C-+X Liz transition.
be populated in a similar collision process, is also present in the region from 460 to 600 nm [ 31. Under the condition of high partial cadmium vapor pressure this emission is, however, hardly visible (figs. 2b and 3~). Fig. 4 shows portions of typical excitation spectra at two different detection wavelengths: at 490 nm where the LiCd emission occurs and at 335.3 nm which corresponds to the anti-stokes line of the Liz C-X transition. This demonstrates that the emission of LiCd is strictly correlated with the excitation of the Li2 C-X transitions. Some of the remaining resonances (fig. 4a) are due to the incidental excitation of LiH impurities, but in these cases no LiCd emission could be observed.
4. Theoretical treatment Potential curves for the LiCd system were generated in essentially the same manner as in our previous study on the LiZn excimer emission [ 11, using suitable basis sets in an ab initio SCF MRDCI procedure. However, in comparison to LiZn, both the larger nuclear charge and the 18 additional electrons in Cd cause problems. Atomic SCF plus CI calculations find the 3P state nearly one full electron volt 100
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below the experimental value [ 61. The authors of ref. [ 6 ] put the origin of this too small energy gap in the too small computed correlation energy for the 5s’ state, in comparison with that for the 5s5p 3P state. Furthermore, our SCF CI calculations do not incorporate spin-orbit interaction, which in practice is responsible for a splitting of 540 cm-’ between the Cd 3P, and 3P, level [ 7 1. Finally, the 48 electrons in one atom put a heavy burden on the quality of the basis set. The choice of basis sets from the literature is rather limited [ 8 1. We have therefore followed the strategy adopted in ref. [ 61 and have used a primitive basis set of intermediate size ( 15s,1lp,7d Cartesian Gaussians, for the exponents see ref. [6] and a strong, general (Raffenetti-type) contraction [ 8). The 13s primitives were used in all 4 s-type core orbitals, with contraction coefficients taken from an uncontracted atomic SCF calculation for the Cd ground state, and the remaining 2 primitives were left uncontracted for the 5s valence shell. Similarly 9 p primitives were contracted in the 3 p-type core orbitals and 5 d primitives in the 2 d-type core orbitals, leaving again 2 uncontracted p and d primitives for the description of the 5p and 5d orbital, respectively. This contraction of course has no influence on the atomic SCF energy, but enormously reduces the basis set size in the calculation of the diatomic molecule. The basis set for Li was kept the same as in our previous LiZn studies [ 11. In our LiZn calculations it was already clear that the asymptotic Zn 3P level was too low by 3500 cm” compared to an error of 4100 cm-’ in ref. [ 61. This caused the calculated potential curves at long range to have an essentially incorrect ordering, since the Zn ‘P state was thus recovered below the Li 3p level. This caused no problems with further analyses because the spectroscopy of LiZn is determined by the shape of the potential curves at R values below 8 bohr. In that range the ordering of the relevant curves is presumably correct. The asymptotic error for the LiCd case is much larger, Cd 3P is, with the basis set of ref. [6] found at 23500 cm-’ compared to the experimental value of 3P, at 30114 cm-l, which is even below the Li 3s asymptote. By consequence, the avoided crossings between Li’Cd, LiCd’ and ionic potential curves occur at much too short an internuclear distance. Therefore, we considered that the
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resulting potential curves were not immediately a suitable basis for a spectral simulation. In the studies of the Cd2 molecule the problems in the potential curves due to the too low Cd ‘P state were remedied by making a solid upward shift of the curves with respect to the ground state such that the asymptotic limits coincided with the experimental values [ 61. Such an approach is only feasible for a homonuclear system, if justifiable at all. The correct remedy would be to improve upon the description of the correlation energy in the Cd ground state. With all the available basis sets this appeared to be impossible when correlating the outermost 12,20 or 22 electrons. We made a similar observation for Zn. Recently calculations on the CdHg excimer have been performed [ 9 1, where an I-dependent empirical effective core potential (EECP) was used. In this manner a correct description of the singlet-triplet gap in the Cd atom could be realized by choice of the effective potential parameters. We did not have a computer program available for the use of these rather specific EECPs and therefore incorporated a strategy that has some similarity. Our strong contraction of the cadmium basis has merely the effect of generating a frozen Cd core that provides the largest part of the effective potential. Our approach lacks however part of the core polarizability specific to the EECPs in ref. [ 9 ] _The adjustable part of the EECP represented by a Gaussian pushes up the valence shell levels and is in ref. [ 5 ] l-dependent. By changing the exponents of the Gaussians for the 5p orbital that we can obtain just the same effect. In the calculation of the potential curves shown in fig. 5, we have modified the exponent of the most diffuse p function in the basis of ref. [ 61 such that the Cd ‘P asymptotic limit is found at around 30000 cm-‘. Of course, the variational approach for basis function optimization is violated, but we think that actually the 5p orbital obtained in this way will be much closer to reality than the one obtained with the Gaussian optimized for lowest energy. Due to the simplifications made by the strong contraction we only found it justified to do CI calculations on the basis of 3 active electrons, so we exclude the description of the Li inner shell electrons, which is presumably approximately constant over the internuclear distance as in Liz [lo] and exclude the description of correlation in the 46 Cd core elec-
35000 -
30000 -
-25000
-
~~20000~ V B 15000 ii 4
10000 -
5000 -
O-
-5000--
2
4
6
8
10
R (bohr) Fig. 5. Potential energy curves of LiCd without spin-orbit interaction. The full lines are ‘Z+ potentials and dashed lines ‘II potentials.
trons. Nevertheless, after selection, configuration spaces of 5000 for C states and 4000 for II states resulted) in which we searched for the 5 and 4 lowest eigenvalues, respectively. The effect of spin-orbit interaction was added to the computed potential curves in an ad hoc way. We used the experience of the only calculations on a similar system that have included spin-orbit effects for NaHg [ 111. These calculations show a nearly linear dependence of diagonal (1 *II-l *II) and off-diagonal (1 *IT-2%) spin-orbit coupling matrix elements upon the internuclear distance in the the range form 4.5 to 8.5 bohr. In NaHg this coupling scrambles the II and Z states to a large extent. We assume that with the smaller spin-orbit coupling in Cd, we will no longer have scrambling but just a simple splitting of the 211state into a l/2 and a 3/2 component, with the l/2 component lowest. The size of the splitting at a particular internuclear distance can be related to the amount of Cd 3P character in the 2 ‘Il wavefunction [ 121. When going from R= 5.5 bohr to R=6.5 bohr in 101
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our CI wavefunctions we observe a linear increase of the fraction of configurations with three open shells, resulting from couplings between the Li electron and the Cd 3P electrons. At R= 5.5 bohr this fraction amounts to 15%and at R= 6.5 bohr to 19%.Adopting an atomic spin-orbit parameter value of about 1200 cm-l, we derive a molecular splitting of about 190 cm-’ at the equilibrium internuclear distance for the LiCd C state of 5.7 bohr. This value is presumably an underestimate since off-diagonal spinorbit coupling, i.e. interaction with the 3 2Y&+ state may also be important. In summary spin-orbit coupling has the consequence that the C 211potential is split into l/2 and 3/2 components that are more or less parallel in the internuclear distance region of interest.
5. Discussion With the potential curves shown in fig. 5, where spin-orbit contributions were not included, one could already perform spectral simulations for the C’IIX IZf bound-free spectrum. The relevant difference potential has a minimum at 5.7 bohr. This minimum is responsible for the enhancement in the bound-free spectrum peaking at about 489 nm. In spectral simulations where we assume that the main contribution to the intensity results from partial waves with J=37, which is the most probable value at 1000 K, we obtain a spectrum which consists mainly of a single peak at 489 nm with a full width at half maximum of about 7 nm. Additional structures due to the contributions from different vibrational levels are observed as well, analogous to the LiZn emission [ 11. We assume that the two pronounced maxima in the observed LiCd spectrum at 482 and 489 nm result from the extrema in two difference potentials. The minima in these difference potentials should then be separated by about 300 cm-‘. In our interpretation of the spectrum this separation should correspond to the separation of the CzI11,2 and CzI13,2 potentials at about 5.7 bohr. Our theoretical estimate of 190 cm-’ seems thus somewhat too low. Work is in progress in order to include the spin-orbit interaction in more detail and at the same time possible further effects of a relativistic treatment. Based on present calculations we also predict some 102
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other spectral features of LiCd. As for the LiZn molecule, enhanced emission due to the minimum in the B 2Zt-X 2Z+ difference potential at about 4.5 bohr is expected at 904 nm. The A211-X2Z’ difference potential has no extrema and consequently emission in the red wing of the Li 2~42s resonance line of a pure reflection type is expected. The 32Z’-X2Z+ difference potential has a more complicated structure, and due to minima at about Yand 4 bohr the enhanced emission is expected at about 473 nm. However, as in the LiZn case, the corresponding dipole transition moment is much ‘smaller than that for the C 211+X2E+ transition.
Acknowledgement This work has been done under the contract CI 1*0525-C (MB) with the European Community and was also supported in part by the Ministry for Science of the Republic of Croatia.
References [ 1] S. MiIo&iC, X. Li, D. Azinovic, G. Pichler, M.C. van Hemert, A. Stehouwer and R. Diiren, J. Chem. Phys. 96 (1992) 7364. [2 ] A.N. Nesmeyanov, Vapor pressure of the chemical elements, ed. R. Gray (Else+, Amsterdam, 1963). [3]C. EnennandCh.Ottinger,J. Chem.Phys. 76 (1982) 5812. [4] J.T. Bahns, WC. Stwalley and G. Pichler, J. Chem. Phys. 90 (1989) 2841. [ 5] F. Engelke and H. Hage, Chem. Phys. Letters 103 ( 1983) 98. [6 ] CF. Bender, T.N. Rescigno,H.F. SchaeferIII and A.E. Orel, J. Chem. Phys. 71 (1979) 1122. [7] C.E. Moore, NBS Circular No. 467, Vol. 1 (US GPO, Washington, 1949). [8 ] R. Piorier, R. Kari and LG. Csizmadia, Handbook of Gaussian basis sets (Elsevier, Amsterdam, 1985). [9] E. Czuchaj, F. Rebentrost, H. Stall and H. Preuss, Chem. Phys. Letters 197 (1992) 187. [lo] I. Schmidt-Mink, W. Mllller and W. Meyer, Chem. Plays.92 (1985) 263. [ 111L. Windholz, G. Zerza, G. Pichler and B. Hess, Z. Physik D 18 (1991) 373. L. Windholz, M. Musso, G. Pichler and B. Hess, J. Chem. Phys. 94 (1991) 3366. [ lZ]H. Lefebvre-Brion and R.W. Field, Perturbation in the spectra of diatomic molecules (Academic Press, New York, 1986) p. 216.