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TheG0u+(61P1)–X0G+Excitation and Fluorescence Spectra of Hg2Excited in a Supersonic Jet
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
184, 300–308 (1997)
MS977345
The G0 u/ (6 1 P1 ) – X 0 g/ Excitation and Fluorescence Spectra of Hg2 Excited in a Supersonic Jet J. Koperski, 1 J. B. Atkinson, and L. Krause Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4 Received February 3, 1997; in revised form May 20, 1997
The G0 /u (6 1 P1 ) – X 0 /g excitation and fluorescence spectra of Hg2 van der Waals molecules, produced in a pulsed free-jet supersonic expansion beam crossed with a pulsed dye-laser beam, were studied using Ar as the carrier gas. A well-resolved vibrational structure of the G0 /u R X 0 /g excitation spectrum was recorded, as well as the isotopic structures of the vibrational components. A Condon internal diffraction pattern in the G0 /u r X 0 /g fluorescence band, emitted upon the selective excitation of the £* Å 39 vibrational component, was also observed and confirmed the assignments derived from the analysis of the isotopic structure. Analyses of the spectra yielded molecular constants for both states, as well as information on the ground state potential energy curve. The results are compared with those obtained from other experiments and from theoretical calculations. q 1997 Academic Press I. INTRODUCTION
The spectroscopy of the G0 u/ (6 1 P1 ) state of Hg2 has been studied mainly by laser-induced fluorescence (LIF) methods using vapor cells (1–3), and there has also been one report of a G0 u/ R X 0 g/ absorption spectrum observed in a supersonic jet, where the authors employed a (continuum) ultraviolet deuterium light source (4). The study of the rotationally resolved G0 u/ R A0 g/ spectrum of the ( 202Hg)2 molecule by pump and probe methods of laser spectroscopy (3) yielded accurate values of spectroscopic constants that were employed in an RKR calculation of the potential energy (PE) curve for the G0 u/ state. The spectroscopic constants of the X 0 g/ ground state were determined in experiments in which a laser beam was crossed with a supersonic molecular beam (5–8). However, the spectroscopic constants and the assignments of the vibrational components obtained from the various experiments show discrepancies which exceed the stated limits of error. As shown in Fig. 1, the G0 u/ state may be excited directly from the X 0 g/ ground state, or from the A0 g/ state by a stepwise method. The G0 u/ R A0 g/ excitation spectrum has been observed in an Hg vapor cell and, as expected from the Franck–Condon principle, its most prominent components corresponded to the excitation of £* õ 25 vibrational levels of the G0 u/ state (2). On the other hand, excitation from the X 0 g/ ground state, which is stable in a cooled expansion jet, resulted in the efficient population of £* ú 15 levels (4). We now report an experimental study of the G0 u/ R 1
On leave from the Institute of Physics, Jagiellonian University, Krako´w, Poland.
X 0 g/ excitation spectrum and the G0 u/ r X 0 g/ fluorescence spectrum, which were produced in a supersonic beam using methods of LIF. 2. EXPERIMENTAL DETAILS
The Hg2 beam, seeded in Ne or Ar as the carrier gas, was crossed with a beam of tunable laser light and the resulting fluorescence was observed at right angles to the plane containing the crossed beams, as shown in Fig. 2. The exciting radiation was scanned across the G0 u/ R X 0 g/ absorption, and variations in the fluorescence signal produced the excitation spectrum. The G0 u/ r X 0 g/ fluorescence bands were recorded by setting the laser frequency on a particular vibronic transition and scanning the resulting fluorescence spectrum with a monochromator. The beam source consisted of a high-temperature pulsed valve (General Valve Series 9) which was connected to a stainless steel Hg reservoir and to a carrier gas feed. A differential heating system maintained the valve nozzle at 10–15 K above the reservoir temperature to prevent condensation of Hg inside the valve. Two sizes of the valve nozzle were employed. A short nozzle with an orifice D Å 0.3 mm in diameter was used to record ‘‘cold’’ excitation spectra and a longer D Å 0.9 mm nozzle was used to increase the production of Hg2 molecules when recording the fluorescence bands. The exciting radiation was generated by an in-house built Nd:YAG laser-pumped dye laser utilizing a 1:3 mixture of Rhodamine 610 in ethanol and Rhodamine 640 in methanol, which emitted radiation in the wavelength range 5920–6220 ˚ . The second harmonic was produced by a KDP *C * crystal A
300 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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between the nozzle and the interaction region was varied in the range 5–12 mm. The strongest fluorescence signals were obtained with a backing pressure p0 Å 1 atm of Ar, while 1 atm of Ne produced signals approximately 10 times weaker. The signal-to-noise ratio was improved by gating the photomultiplier, which largely eliminated background due to scattered laser light. The scans of the laser radiation were repeated to average the signal and reduce the effects of noise, such as the pulse-to-pulse amplitude jitter. 3. THE EXCITATION SPECTRUM
Figure 3a shows a trace of the G0 u/ R X 0 g/ excitation spectrum which consists of 28 structured vibrational components belonging to the £* R £9 Å 0 progression. Figure 3b represents a Franck–Condon (FC) simulation of the spectrum, which will be described in some detail below. As shown in Fig. 4, each of the components consists of 12 peaks corresponding to the various combinations (m1 / m2 ) of the masses of the six most abundant Hg isotopes present in natural mercury (8). The £* assignments of the vibrational components in the spectrum were carried out by analyzing their isotopic shift Dnij which, for £* R £9 Å 0 vibronic transitions, may be represented by (9) / FIG. 1. A partial PE diagram for Hg2 , showing G0 / u } X 0 g excitation and decay processes (solid arrows). The decay takes place predominantly to the X 0 /g state (2). The dashed arrows show the alternative pump-andprobe excitation path.
Dnij Å v *e (1 0 r )( £* / 1/2) 0 v *e x *e 1 (1 0 r 2 )( £* / 1/2) 2 0 v e9 (1 0 r )/2 [1] / v e9 x 9e (1 0 r 2 )/4,
and was mixed with the fundamental in a BBO *C * crystal, resulting in the third harmonic and producing an output ˚ , which was made inciwavelength in the vicinity of 2000 A dent on the molecular beam. The scan of the fundamental dye-laser output was frequency calibrated with a 0.85 m SPEX double-grating monochromator which had been calibrated with a wavelength meter. The third harmonic beam was separated from the fundamental and second harmonic components by a set of prisms and was focused down to a diameter of 1 mm in the region where it crossed the molecular beam. The resulting fluorescence was focused either directly on the photocathode of an EMI 9813QB photomultiplier tube or on the entrance slit of an HR-320 Jobin–Yvon grating monochromator which was fitted with the above photomultiplier. The photomultiplier signal was registered with a Hewlett–Packard 54111D digitizing oscilloscope which acted as a transient digitizer and whose output was stored in a microcomputer. The optimal temperature of the reservoir was found to be in the range 500–510 K, corresponding to an Hg vapor pressure range of 38–51 Torr. The valve was driven at a repetition rate of 10 Hz, producing expansion beam pulses of 2 msec duration. The laser pulses were delayed 3–4 msec relative to the start of the valve pulses, to produce overlap in the interaction region. The distance X
where r Å ( mi / mj ) 1 / 2 , mi and mj are the reduced masses, m Å m1m2 /(m1 / m2 ), of two isotopic Hg2 molecules with different (m1 / m2 ) mass combinations, and v *e , v *e x *e , v e9 , v e9 x 9e are vibrational frequencies and anharmonicities of the G0 u/ and X 0 g/ states, respectively, taken from Ref. (3) for the G0 u/ state and from Ref. (8) for the X 0 g/ state. As shown in Fig. 5, the averaged measured isotopic shifts were found to be in the range 2.5–4.0 cm01 . The averages of the measured shifts were taken between peaks corresponding to (m1 / m2 ) Å 398 and 399, 399 and 400, 400 and 401, 401 and 402, 402 and 403, and 403 and 404. In most cases, the 396, 397, and 408 peaks were too faint to be detected. We have also plotted the shifts calculated from Eq. [1] for £*, £* / 2, and £* 0 2. We found that the plot of the measured isotopic shifts against the £* assignments given by the analysis lay within the limits of the shifts calculated for £* / 2 and £* 0 2, indicating that our £* assignments were correct within an error margin of {2. The vibrational assignments shown in Fig. 3 differ from those suggested elsewhere (4, 10), as do the measured frequencies of the vibrational components (10). The £* values given in (4) are lower by 13 and the frequencies of the vibrational components listed in (10) are lower by 2–35
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FIG. 2. Arrangement of the apparatus. V, pulsed valve; BD, laser beam dump; PM, photomultiplier.
cm01 than the frequencies of the (m1 / m2 ) Å 404 isotopic peaks of the corresponding vibrational components (the differences decrease as £* increases). To compare our results with those obtained in the highresolution experiment on monoisotopic ( 202Hg)2 (3), we drew a Birge–Sponer (B–S) plot of the (m1 / m2 ) Å 404 isotopic peaks of the spectrum shown in Fig. 3a and included
in the plot data taken from Ref. (3). It may be seen in Fig. 6 that the B–S plot of the G0 u/ R X 0 g/ spectrum is almost linear and appears to be an extension of the G0 u/ R A0 g/ plot with which it overlaps. Attempts to perform a linear regression analysis solely on the data of Fig. 3a were not successful in producing accurate results, because the DG£=/1/2 terms determined in this experiment were significantly less
/ FIG. 3. (a) An experimental trace of the G0 / u R X 0 g ( £9 Å 0) excitation spectrum, showing £* assignments. X/D Å 36.6, Meff (effective Mach number) Å 36.4. (b) A computer-simulated (11) spectrum showing the best fit to the £* R £9 Å 0 progression for the (m1 / m2 ) Å 401 isotopic peaks assuming the Morse function (dashed envelope) or a van der Waals function with n Å 6.21 (vertical lines) to represent of X 0 /g state.
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FIG. 5. The measured ( l ) and calculated ( s ) isotopic shifts Dn. j, data from Ref. (4).
/ FIG. 4. The isotopic structure of the G0 / u ( £* Å 49) R X 0 g ( £9 Å 0) vibrational component. The lower trace represents the simulation of the isotopic structure. The position of the central ( m1 / m2 ) Å 401 peak was obtained using program LEVEL 6.1 (11), the relative positions of the isotopic peaks were calculated using Eq. [1], and their amplitudes were weighted relative to the isotopic abundances in natural mercury. The individual isotopic peaks were represented by a Lorentzian curve with FWHM of 1.0 cm01 .
accurate than those in Ref. (3). The experimental data were, however, compared with the values calculated using v *e , v *e x *e , and v *e y *e from Ref. (3). The best fit between the experimental and calculated values was obtained for the £* assignments reported here. An extrapolation of the B–S data from Ref. (3) produced D *0 Å 8270 { 10 cm01 and D *e Å 8320 { 10 cm01 , values which will be compared with other estimates below. The quoted errors are statistical and take no account of possible variations in the shape of the PE curve at large internuclear distances. We believe that the discrepancy between our vibrational assignments and those given by Schlauf et al. (4) is due to the method which they employed in analyzing the absorption spectrum. They did not resolve the isotopic structure but simulated the vibrational spectrum using v *e , R *e (the equilibrium internuclear separation), and the vibrational temperature as adjustable parameters, taking v *e x *e from the B–S analysis of their spectrum, and using values of v e9 , v e9 x 9e , and R 9e from Ref. (6). Such a method would be less likely to produce unique assignments than that employed in the present study. To compound the problem, the v e9 value reported in Ref. (6) for the X 0 g/ state was interchanged there
with the value for v *e for the 0 u/ (6 3 P1 ) state, contributing to the resulting differences. The dissociation energies D *0 and D *e , of the G0 u/ state, can also be obtained from D *0 Å n(6 1 P1 r 6 1 S0 ) 0 n00 / D 90
[2]
D *e Å D *0 / v *e /2 0 v *e x *e /4 / v *e y *e /8,
[3]
where n(6 1 P1 r 6 1 S0 ) is the energy of the atomic transition, D 90 is taken from Ref. (8), and n00 Å 46201.7 cm01 is the energy of the G0 u/ ( £* Å 0) R X 0 g/ ( £9 Å 0) transition obtained from the extrapolation (9), using the experimental value for the energy of the G0 u/ R X 0 g/ ( £* Å 26 R £9 Å
/ FIG. 6. A Birge–Sponer plot of the G0 / u R X 0 g ( £9 Å 0) excitation spectrum shown in Fig. 3a, for (m1 / m2 ) Å 404 isotopic peaks ( h ), together with the data taken from Ref. ( 3) ( s ).
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FIG. 7. PE curve for the G0 / u state represented by the Morse function plotted with constants determined in Ref. ( 3) and this investigation. s, RKR calculation (3). l, Czuchaj et al. (12). The range of vibrational levels 25 õ £* õ 52 is also shown.
0) transition and the values of v *e , v *e x *e , and v *e y *e from Table IV of (3). Equations [2] and [3] yielded D *0 Å 8236 { 15 cm01 and D *e Å 8280 { 15 cm01 , respectively, in good agreement with the values yielded by the extrapolation shown in Fig. 6. Using the data from Refs. (3) and (8) and from this analysis, we attempted to simulate the G0 /u R X 0 /g ( £9 Å 0) excitation spectrum, using the LEVEL 6.1 FORTRAN code of LeRoy (11). This program solves the radial Schro¨dinger equation for bound levels and calculates the FC factors for transitions between rovibrational levels in the ground and excited states. The PE of the G0 u/ state was represented by turning-point pairs obtained from the RKR calculation (3), and the PE of the X 0 g/ ground state was represented by either a Morse, a van der Waals, or a Lennard–Jones (12-6) function with v e9 x e9 and D 9e from Ref. (8). Because the G0 u/ R X 0 g/ ( £* R £9 Å 0) progression begins from the £9 Å 0 vibrational level, the choice of the function representing the ground state potential was not expected to be crucial (9). However, we found during the simulation that the best results were produced by using for the X 0 g/ state the van der Waals potential U 9 (R) Å
D 9e n06
F S D S DG 6
R 9e R
n
0n
R 9e R
6
,
[4]
which had been used in the simulation of the G0 u/ ( £ * Å 12 ) r X 0 g/ fluorescence band (3), and also the Morse function. The simulation of the fluorescence band, which will be described below, yielded the parameter n Å 6.21 for the van der Waals function. Consequently, n Å 6.21 [rather than n Å 6.53 (3)] was used in the simulation of the excitation spectrum shown in Fig. 3a. Figure 3b represents the
best fit to the £* R £9 Å 0 progression of the (m1 / m2 ) Å ˚, a 401 isotope spectrum obtained for R 9e Å 3.69 { 0.01 A value larger than that obtained by van Zee et al. (6). Because the modeling of the excitation spectrum was found to be very sensitive to the difference DR Å R *e 0 R 9e , we assumed in the simulation the accurately known value R *e Å 2.8506 ˚ for the G0 u/ state (3) and varied R 9e . We also found that A the simulation was not noticeably affected when the parameter n was varied in the range 6.1–6.9. The program used in the simulation (11) generated the energies of the vibrational levels of the G0 u/ state, which allowed us to reexamine the report of Ehrlich and Osgood who claimed to ˚ laser have excited the £* Å 57 vibrational level with 1933 A radiation (1). We assumed that the excitation proceeded by photoassociation, from the energy of two separated ground state atoms, and found that they must have excited the £* Å 93 level for which the 401 isotope has an energy of 52 089 cm01 (relative to the energy of £9 Å 0), which should be compared with 51 716 cm01 , the energy of their laser radiation plus D 09 . This conclusion corroborates our previous estimate derived from the vibrational analysis of the G0 /u – A0 /g spectrum (2). Figure 7 shows the PE curve for the G0 u/ state, represented by the Morse function, plotted using constants obtained in Ref. (3) and this work, and compared with the result of an RKR calculation (3) and with the theoretical ab initio nonrelativistic pseudopotential calculation of Czuchaj et al. (12). There is good overall agreement between theory and experiment although the theoretical potential is somewhat shallower than the potential derived from the experimental data. 4. THE FLUORESCENCE SPECTRUM
The £* assignments in the G0 u/ R X 0 g/ excitation spectrum were confirmed on the basis of a fluorescence band
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/ FIG. 8. (a) The G0 / u ( £* Å 39) r X 0 g fluorescence band recorded with a 10 cm01 monochromator slit width. X/D Å 5.6, Meff Å 10.3. The sharp peak at the short-wavelength end of the band is due to £* Å 39 r £9 bound–bound transitions. (b) A computer simulation ( 19) of the bound– free part of the band showing the best fit obtained using the van der Waals function with n Å 6.21 to represent the X 0 /g potential.
arising from the decay of a selectively excited bound £* vibrational level to the repulsive part of the ground state. Ehrlich and Osgood (1) and Kedzierski et al. (3) had previously reported on CID patterns in the Hg2 fluorescence spectrum, which they interpreted as due to the bound-free radiative decays of the G0 u/ ( £* É 57) and G0 u/ ( £* Å 12) states, respectively, to the repulsive part of the X 0 g/ state. The (m1 / m2 ) Å 400 isotope in the G0 u/ ( £* Å 39) R X 0 g/ ( £9 Å 0) vibronic component was selectively excited and decayed to the repulsive part of the ground state, emitting the G0 u/ ( £* Å 39) r X 0 g/ fluorescence band. To favor the production of metal dimers in preference to the Hg– noble gas complexes (13), a relatively long 15-mm nozzle was employed to generate the molecular beam. The excitation region was located at a smaller distance from the orifice (X Å 5 mm) than in the case of the excitation spectrum. Figure 8a shows the gross structure of the resulting CID pattern, in which the number of maxima exceeds the £* vibrational quantum number of the emitting level by one. The band was recorded at relatively low resolution, using a 100 cm01 monochromator slit width. The intense peak at the short-wavelength end of the band is interpreted as being due mainly to unresolved bound–bound transitions to the closely spaced vibrational levels of the shallow ground state, while the broad maximum at the long-wavelength end corresponds to the inner turning point in the potential of the emitting £* level. Figure 8b represents a simulation of the bound-free part of the band, which will be described in some detail below. To confirm the vibrational £* level from which the
fluorescence was emitted, we recorded various parts of the fluorescence band at a higher resolution. Figure 9 shows two traces of the band recorded at slit widths of (a) 20 and (b) 10 cm01 . The results of a computer simulation are shown in Figs. 9c and 9d. The simulation (11) of the bound–bound part of the fluorescence band close to the region of the ˚ ), shown in Fig. 9c, emexcitation wavelength (2031.09 A ployed the spectroscopic constants obtained from the analysis of the excitation spectrum. We assumed either the Morse potential or the van der Waals potential with n Å 6.21 as representing the ground state PE curve. Since the simulation employed all the vibrational levels of the ground state, it was a good test for the particular representation of the ground state potential. From the simulation it became clear that the first seven peaks at the short-wavelength end of the fluorescence band were due to unresolved bound–bound transitions, while the remaining peaks were due to bound– free transitions. When the van der Waals potential was used in the simulation, a very good fit was obtained for the positions of the maxima and minima in the envelope of the bound–bound transitions (we were not able to resolve individual bound–bound transitions), but the relative intensities of the maxima in the envelope were better reproduced by the Morse function. The fit of the bound–bound part of the fluorescence band and of the excitation spectrum, was not very sensitive to the parameter n in the van der Waals potential. In the case of the bound–bound transitions, we obtained a satisfactory fit for a range of n values from 6.1 to 6.9. It was evident that variations in n within this range did not
/ FIG. 9. The G0 / u ( £* Å 39) r X 0 g fluorescence band in the 2020– ˚ 2150 A region, recorded with slit widths of (a) 20 and (b) 10 cm01 . The spectrum (a) is compared with (d), the simulation as in Fig. 8b. The spectrum (b), partially resolved bound–bound transitions, is juxtaposed with the result (c) of a simulation (11) of the individual bound–bound transitions.
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affect significantly the bound part of the potential curve of the ground state, but affected significantly the slope of the repulsive part above the dissociation limit, a conclusion which had also been reached in the modeling of the HgAr A0 / r X 0 / fluorescence spectrum (14). All the 40 maxima present in the CID pattern were identified in the traces in Figs. 8 and 9, confirming the assignments obtained from the analysis of the isotopic structure in the excitation spectrum. We attempted to resolve individual bound–bound components in the fluorescence band by increasing the resolution of the detection system (using a 2 cm01 monochromator slit) and by further cooling the molecules. We used a nozzle with a smaller orifice (D Å 0.3 mm) and increased X to 12 mm, obtaining an effective Mach number of 38.6 (15) which exceeded the terminal Mach number MT Å 33 beyond which no collisions should take place (16). The estimated effective temperatures were TT Å TR É 2 K and Tv É 20 K (15, 17). Even though, under these conditions, no collisional energy transfer should take place between the isotopic molecules within the excited £* state, we did not resolve any components that might be ascribed to individual bound–bound transitions. To construct a part of the repulsive section of the ground state PE curve from the G0 u/ ( £* Å 39) r X 0 g/ bound–free band, we adopted the semiclassical RKR-like inversion method of LeRoy (18). This approach, which is complementary to the ‘‘exact’’ computational and fitting procedures, offers one peculiar advantage—it distinguishes between the ‘‘phase’’ and ‘‘amplitude’’ information in the experimental spectrum and shows how the positions of the intensity extrema are determined by the shape of the repulsive potential while the peak heights depend on the transition dipole moment. The experimental input data in this case were the energy values of the intensity extrema (maxima and minima) in the recorded fluorescence band. A five-constant polynomial fit was used to represent the positions of the experimental intensity extrema, while the inner and outer turning points for the G0 u/ PE curve were taken from Ref. (3). The resulting X 0 g/ potential is shown in Fig. 10. To find the unique value n for the van der Waals function to make it overlap with the points obtained by the inversion method, it was necessary to assume the van der Waals X 0 g/ ground state potential with the parameter n as a free variable, simulate the bound–free band using this potential, and vary n to obtain the best fit between the observed and simulated positions of the oscillatory maxima and minima. We used a BCONT 1.4 FORTRAN code (19), in which the PE of the G0 u/ state was, as before, represented by the turning-point pairs yielded from the RKR calculation (3) while R 9e and D 9e for the ground state were obtained from the analysis of the excitation spectrum and Ref. (8), respectively. The program made provision for the variation of the electronic dipole transition moment M with R, the internuclear separa-
FIG. 10. PE curves for the X 0 / g state. ---, Morse function; – – – , van der Waals function (n Å 6.53), using v e9 x e9 and D e9 from Ref. (8), and ˚ . — , van der Waals function (n Å 6.21) from simulation (19) R e9 Å 3.69 A of the bound–free fluorescence band; l, Czuchaj et al. (12); 1, Dolg and Flad (22); s, repulsive part produced by the inversion procedure (18). The insert shows details of the bound part of the potential.
tion. We used the three theoretical values for M(R) reported in Ref. (20), ranging from 3.27 to 3.97 D, which were calculated at the three corresponding values of R (in the ˚ ) and assumed a linear relationship berange 2.64–3.70 A tween M and R. The best fit, which was obtained for n Å 6.21, is shown in Figs. 8b and 9d. We should stress that even a slight departure of n from this value (by {0.03) changed the slope of the van der Waals repulsive curve and the profile of the simulated band to the extent that it no longer fitted the experimental trace. This was particularly apparent in the long-wavelength region, where the profile of the simulated band is governed by the slope of the ground state potential energy curve. The van der Waals potential with n Å 6.21 is shown in Fig. 10 together with the potentials represented by the van der Waals function for n Å 6.53 (3) and the Morse function plotted using v e9 x 9e and D 9e from ˚ obtained in this investigation. A Ref. (8), and R 9e Å 3.69 A comparison is also made with the calculations of Czuchaj et al. (12) and Dolg and Flad (21, 22) whose result agrees most closely with our experimental curves. The repulsive part of the ground state potential obtained by the inversion method (18) and the van der Waals potential with n Å 6.21 lie closer to the van der Waals curve with n Å 6.53 (3) than to the Morse curve. This supports the conclusion reached also in the modeling of the G0 u/ ( £* Å 12) r X 0 g/ fluorescence band (3) that the Morse function does not adequately describe the repulsive part of the PE curve of the X 0 g/ state. 5. CONCLUSIONS
The G0 u/ (6 1 P1 ) – X 0 g/ excitation and fluorescence spectra of the Hg2 van der Waals molecules were studied in a
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TABLE 1 / Spectroscopic Constants for the G0 / u and X 0 g States of Hg2
pulsed free-jet supersonic expansion beam crossed with a pulsed dye-laser beam. A well-resolved vibrational structure in the G0 u/ ( £* ) R X 0 g/ ( £9 Å 0) excitation spectrum was recorded, as well as the isotopic structures of the individual vibrational components. An isotope shift analysis produced £* assignments which differ by 13 from those reported by Schlauf et al. (4). An improved value for the equilibrium internuclear separation R 9e in the X 0 g/ ground state was determined by modeling the excitation spectrum. A Birge– Sponer plot of the G0 u/ (25 õ £* õ 52) R X 0 g/ ( £9 Å 0) progression recorded for the (m1 / m2 ) Å 404 isotope could be interpreted as an extension of the G0 u/ (0 õ £* õ 32) R A0 g/ (0 õ £9 õ 7) vibronic band origins found from the rotational analysis of the spectrum obtained with monoisotopic ( 202Hg)2 (3). The analysis of the CID pattern in the G0 u/ r X 0 g/ fluorescence band, emitted upon selective excitation of the £* Å 39 vibrational component, confirmed the vibrational assignments of the peaks in the excitation spectrum. Simulation of the excitation spectrum and of the bound–bound and bound–free parts of the fluorescence band showed that a van der Waals potential with n Å 6.21 was a good representation of the ground state potential below and above the dissociation limit. Below the dissociation limit the ground state potential could also be represented by the Morse function. An analysis of the excitation spectrum yielded molecular constants that are compared in Table 1 with those obtained from other experiments and from theoretical calculations. This comparison, especially with the re-
cent result of Dolg and Flad (21, 22), suggests that relativistic effects should be included in ab initio calculations for the massive Hg2 molecule. ACKNOWLEDGMENTS We thank R. J. LeRoy for helpful discussions facilitating the use of his LEVEL 6.1, RPOT, and BCONT 4.1 computer programs and H. J. Flad for permission to quote his unpublished theoretical data. This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
REFERENCES 1. D. J. Ehrlich and R. R. Osgood, Jr., Phys. Rev. Lett. 41, 547–550 (1978). 2. J. Supronowicz, R. J. Niefer, J. B. Atkinson, and L. Krause, J. Phys. B 19, L717–L721 (1986). 3. W. Kedzierski, J. Supronowicz, A. Czajkowski, J. B. Atkinson, and L. Krause, J. Mol. Spectrosc. 173, 510–531 (1995). 4. M. Schlauf, O. Dimopoulou-Rademann, K. Rademann, U. Even, and F. Hensel, J. Chem. Phys. 90, 4630–4631 (1989). 5. A. Zehnacker, M. C., Duval, C. Jouvet, C. Lardeux-Dedonder, D. Solgadi, B. Soep, and O. Benoist d’Azy, J. Chem. Phys. 86, 6565–6566 (1987). 6. R. D. van Zee, S. C. Blankespoor, and T. S. Zwier, J. Chem. Phys. 88, 4650–4654 (1988). 7. J. Koperski, J. B. Atkinson, and L. Krause, Chem. Phys. Lett. 219, 161–168 (1994). 8. J. Koperski, J. B. Atkinson, and L. Krause, Can. J. Phys. 72, 1070– 1077 (1994).
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9. G. Herzberg, ‘‘Spectra of Diatomic Molecules,’’ Van Nostrand, New York, 1950. 10. M. Schlauf, Ph.D. thesis, Phillipps-Universita¨t Marburg, 1989. [In German] 11. R. J. Le Roy, ‘‘LEVEL 6.1: A Computer Program Solving the Radial Schro¨dinger Equation for Bound and Quasibound Levels, and Calculating Various Expectation Values and Matrix Elements,’’ University of Waterloo Chemical Physics Research Report CP-555R, 1996. 12. E. Czuchaj, F. Rebentrost, H. Stoll, and H. Preuss, Chem. Phys. 214, 277–289 (1997). 13. C. L. Callender, S. A. Mitchell, and P. A. Hackett, J. Chem. Phys. 90, 2535–2543 (1989). 14. J. Koperski, Chem. Phys. 211, 191–201 (1996); 214, 431–432 (1997). 15. D. M. Lubman, C. T. Rettner, and R. N. Zare, J. Phys. Chem. 86, 1129–1135 (1982). 16. J. B. Anderson, R. P. Andres, and J. B. Fenn, Adv. Chem. Phys. 10, 275–317 (1966). 17. G. M. McClelland, K. L. Saenger, J. J. Valentini, and D. R. Herschbach, J. Phys. Chem. 83, 947–959 (1979).
18. R. J. LeRoy, ‘‘A Computer Programs for Inversion of Oscillatory Bound-Continuum Spectra,’’ University of Waterloo Chemical Physics Research Report CP-327, 1988; M. S. Child, H. Esse´n, and R. J. LeRoy, J. Chem. Phys. 78, 6732–6740 (1983). 19. R. J. LeRoy, Comput. Phys. Comm. 52, 383–395 (1989); R. J. LeRoy, ‘‘BCONT 1.4. A Computer Program for Calculating Absorption Coefficients, Emission Intensities or (Golden Rule) Predissociation Rates,’’ University of Waterloo Chemical Physics Research Report CP-329R 3 , 1993. 20. F. H. Mies, W. J. Stevens, and M. Krauss, J. Mol. Spectrosc. 72, 303– 331 (1978). 21. M. Dolg and H.-J. Flad, J. Phys. Chem. 100, 6147–6151 (1996). 22. M. Dolg and H.-J. Flad, unpublished result. 23. N. Bras and C. Bousquet, J. Phys. (Paris) 40, 945–960 (1979). 24. W. E. Baylis, J. Phys. B 10, L583–L587 (1977). 25. J. R. Bieron´ and W. E. Baylis, Chem. Phys. 197, 129–137 (1995). 26. C. F. Kunz, C. Ha¨ttig, and B. A. Hess, Mol. Phys. 89, 139–156 (1996).
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MS977345
The G0 u/ (6 1 P1 ) – X 0 g/ Excitation and Fluorescence Spectra of Hg2 Excited in a Supersonic Jet J. Koperski, 1 J. B. Atkinson, and L. Krause Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4 Received February 3, 1997; in revised form May 20, 1997
The G0 /u (6 1 P1 ) – X 0 /g excitation and fluorescence spectra of Hg2 van der Waals molecules, produced in a pulsed free-jet supersonic expansion beam crossed with a pulsed dye-laser beam, were studied using Ar as the carrier gas. A well-resolved vibrational structure of the G0 /u R X 0 /g excitation spectrum was recorded, as well as the isotopic structures of the vibrational components. A Condon internal diffraction pattern in the G0 /u r X 0 /g fluorescence band, emitted upon the selective excitation of the £* Å 39 vibrational component, was also observed and confirmed the assignments derived from the analysis of the isotopic structure. Analyses of the spectra yielded molecular constants for both states, as well as information on the ground state potential energy curve. The results are compared with those obtained from other experiments and from theoretical calculations. q 1997 Academic Press I. INTRODUCTION
The spectroscopy of the G0 u/ (6 1 P1 ) state of Hg2 has been studied mainly by laser-induced fluorescence (LIF) methods using vapor cells (1–3), and there has also been one report of a G0 u/ R X 0 g/ absorption spectrum observed in a supersonic jet, where the authors employed a (continuum) ultraviolet deuterium light source (4). The study of the rotationally resolved G0 u/ R A0 g/ spectrum of the ( 202Hg)2 molecule by pump and probe methods of laser spectroscopy (3) yielded accurate values of spectroscopic constants that were employed in an RKR calculation of the potential energy (PE) curve for the G0 u/ state. The spectroscopic constants of the X 0 g/ ground state were determined in experiments in which a laser beam was crossed with a supersonic molecular beam (5–8). However, the spectroscopic constants and the assignments of the vibrational components obtained from the various experiments show discrepancies which exceed the stated limits of error. As shown in Fig. 1, the G0 u/ state may be excited directly from the X 0 g/ ground state, or from the A0 g/ state by a stepwise method. The G0 u/ R A0 g/ excitation spectrum has been observed in an Hg vapor cell and, as expected from the Franck–Condon principle, its most prominent components corresponded to the excitation of £* õ 25 vibrational levels of the G0 u/ state (2). On the other hand, excitation from the X 0 g/ ground state, which is stable in a cooled expansion jet, resulted in the efficient population of £* ú 15 levels (4). We now report an experimental study of the G0 u/ R 1
On leave from the Institute of Physics, Jagiellonian University, Krako´w, Poland.
X 0 g/ excitation spectrum and the G0 u/ r X 0 g/ fluorescence spectrum, which were produced in a supersonic beam using methods of LIF. 2. EXPERIMENTAL DETAILS
The Hg2 beam, seeded in Ne or Ar as the carrier gas, was crossed with a beam of tunable laser light and the resulting fluorescence was observed at right angles to the plane containing the crossed beams, as shown in Fig. 2. The exciting radiation was scanned across the G0 u/ R X 0 g/ absorption, and variations in the fluorescence signal produced the excitation spectrum. The G0 u/ r X 0 g/ fluorescence bands were recorded by setting the laser frequency on a particular vibronic transition and scanning the resulting fluorescence spectrum with a monochromator. The beam source consisted of a high-temperature pulsed valve (General Valve Series 9) which was connected to a stainless steel Hg reservoir and to a carrier gas feed. A differential heating system maintained the valve nozzle at 10–15 K above the reservoir temperature to prevent condensation of Hg inside the valve. Two sizes of the valve nozzle were employed. A short nozzle with an orifice D Å 0.3 mm in diameter was used to record ‘‘cold’’ excitation spectra and a longer D Å 0.9 mm nozzle was used to increase the production of Hg2 molecules when recording the fluorescence bands. The exciting radiation was generated by an in-house built Nd:YAG laser-pumped dye laser utilizing a 1:3 mixture of Rhodamine 610 in ethanol and Rhodamine 640 in methanol, which emitted radiation in the wavelength range 5920–6220 ˚ . The second harmonic was produced by a KDP *C * crystal A
300 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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between the nozzle and the interaction region was varied in the range 5–12 mm. The strongest fluorescence signals were obtained with a backing pressure p0 Å 1 atm of Ar, while 1 atm of Ne produced signals approximately 10 times weaker. The signal-to-noise ratio was improved by gating the photomultiplier, which largely eliminated background due to scattered laser light. The scans of the laser radiation were repeated to average the signal and reduce the effects of noise, such as the pulse-to-pulse amplitude jitter. 3. THE EXCITATION SPECTRUM
Figure 3a shows a trace of the G0 u/ R X 0 g/ excitation spectrum which consists of 28 structured vibrational components belonging to the £* R £9 Å 0 progression. Figure 3b represents a Franck–Condon (FC) simulation of the spectrum, which will be described in some detail below. As shown in Fig. 4, each of the components consists of 12 peaks corresponding to the various combinations (m1 / m2 ) of the masses of the six most abundant Hg isotopes present in natural mercury (8). The £* assignments of the vibrational components in the spectrum were carried out by analyzing their isotopic shift Dnij which, for £* R £9 Å 0 vibronic transitions, may be represented by (9) / FIG. 1. A partial PE diagram for Hg2 , showing G0 / u } X 0 g excitation and decay processes (solid arrows). The decay takes place predominantly to the X 0 /g state (2). The dashed arrows show the alternative pump-andprobe excitation path.
Dnij Å v *e (1 0 r )( £* / 1/2) 0 v *e x *e 1 (1 0 r 2 )( £* / 1/2) 2 0 v e9 (1 0 r )/2 [1] / v e9 x 9e (1 0 r 2 )/4,
and was mixed with the fundamental in a BBO *C * crystal, resulting in the third harmonic and producing an output ˚ , which was made inciwavelength in the vicinity of 2000 A dent on the molecular beam. The scan of the fundamental dye-laser output was frequency calibrated with a 0.85 m SPEX double-grating monochromator which had been calibrated with a wavelength meter. The third harmonic beam was separated from the fundamental and second harmonic components by a set of prisms and was focused down to a diameter of 1 mm in the region where it crossed the molecular beam. The resulting fluorescence was focused either directly on the photocathode of an EMI 9813QB photomultiplier tube or on the entrance slit of an HR-320 Jobin–Yvon grating monochromator which was fitted with the above photomultiplier. The photomultiplier signal was registered with a Hewlett–Packard 54111D digitizing oscilloscope which acted as a transient digitizer and whose output was stored in a microcomputer. The optimal temperature of the reservoir was found to be in the range 500–510 K, corresponding to an Hg vapor pressure range of 38–51 Torr. The valve was driven at a repetition rate of 10 Hz, producing expansion beam pulses of 2 msec duration. The laser pulses were delayed 3–4 msec relative to the start of the valve pulses, to produce overlap in the interaction region. The distance X
where r Å ( mi / mj ) 1 / 2 , mi and mj are the reduced masses, m Å m1m2 /(m1 / m2 ), of two isotopic Hg2 molecules with different (m1 / m2 ) mass combinations, and v *e , v *e x *e , v e9 , v e9 x 9e are vibrational frequencies and anharmonicities of the G0 u/ and X 0 g/ states, respectively, taken from Ref. (3) for the G0 u/ state and from Ref. (8) for the X 0 g/ state. As shown in Fig. 5, the averaged measured isotopic shifts were found to be in the range 2.5–4.0 cm01 . The averages of the measured shifts were taken between peaks corresponding to (m1 / m2 ) Å 398 and 399, 399 and 400, 400 and 401, 401 and 402, 402 and 403, and 403 and 404. In most cases, the 396, 397, and 408 peaks were too faint to be detected. We have also plotted the shifts calculated from Eq. [1] for £*, £* / 2, and £* 0 2. We found that the plot of the measured isotopic shifts against the £* assignments given by the analysis lay within the limits of the shifts calculated for £* / 2 and £* 0 2, indicating that our £* assignments were correct within an error margin of {2. The vibrational assignments shown in Fig. 3 differ from those suggested elsewhere (4, 10), as do the measured frequencies of the vibrational components (10). The £* values given in (4) are lower by 13 and the frequencies of the vibrational components listed in (10) are lower by 2–35
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FIG. 2. Arrangement of the apparatus. V, pulsed valve; BD, laser beam dump; PM, photomultiplier.
cm01 than the frequencies of the (m1 / m2 ) Å 404 isotopic peaks of the corresponding vibrational components (the differences decrease as £* increases). To compare our results with those obtained in the highresolution experiment on monoisotopic ( 202Hg)2 (3), we drew a Birge–Sponer (B–S) plot of the (m1 / m2 ) Å 404 isotopic peaks of the spectrum shown in Fig. 3a and included
in the plot data taken from Ref. (3). It may be seen in Fig. 6 that the B–S plot of the G0 u/ R X 0 g/ spectrum is almost linear and appears to be an extension of the G0 u/ R A0 g/ plot with which it overlaps. Attempts to perform a linear regression analysis solely on the data of Fig. 3a were not successful in producing accurate results, because the DG£=/1/2 terms determined in this experiment were significantly less
/ FIG. 3. (a) An experimental trace of the G0 / u R X 0 g ( £9 Å 0) excitation spectrum, showing £* assignments. X/D Å 36.6, Meff (effective Mach number) Å 36.4. (b) A computer-simulated (11) spectrum showing the best fit to the £* R £9 Å 0 progression for the (m1 / m2 ) Å 401 isotopic peaks assuming the Morse function (dashed envelope) or a van der Waals function with n Å 6.21 (vertical lines) to represent of X 0 /g state.
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FIG. 5. The measured ( l ) and calculated ( s ) isotopic shifts Dn. j, data from Ref. (4).
/ FIG. 4. The isotopic structure of the G0 / u ( £* Å 49) R X 0 g ( £9 Å 0) vibrational component. The lower trace represents the simulation of the isotopic structure. The position of the central ( m1 / m2 ) Å 401 peak was obtained using program LEVEL 6.1 (11), the relative positions of the isotopic peaks were calculated using Eq. [1], and their amplitudes were weighted relative to the isotopic abundances in natural mercury. The individual isotopic peaks were represented by a Lorentzian curve with FWHM of 1.0 cm01 .
accurate than those in Ref. (3). The experimental data were, however, compared with the values calculated using v *e , v *e x *e , and v *e y *e from Ref. (3). The best fit between the experimental and calculated values was obtained for the £* assignments reported here. An extrapolation of the B–S data from Ref. (3) produced D *0 Å 8270 { 10 cm01 and D *e Å 8320 { 10 cm01 , values which will be compared with other estimates below. The quoted errors are statistical and take no account of possible variations in the shape of the PE curve at large internuclear distances. We believe that the discrepancy between our vibrational assignments and those given by Schlauf et al. (4) is due to the method which they employed in analyzing the absorption spectrum. They did not resolve the isotopic structure but simulated the vibrational spectrum using v *e , R *e (the equilibrium internuclear separation), and the vibrational temperature as adjustable parameters, taking v *e x *e from the B–S analysis of their spectrum, and using values of v e9 , v e9 x 9e , and R 9e from Ref. (6). Such a method would be less likely to produce unique assignments than that employed in the present study. To compound the problem, the v e9 value reported in Ref. (6) for the X 0 g/ state was interchanged there
with the value for v *e for the 0 u/ (6 3 P1 ) state, contributing to the resulting differences. The dissociation energies D *0 and D *e , of the G0 u/ state, can also be obtained from D *0 Å n(6 1 P1 r 6 1 S0 ) 0 n00 / D 90
[2]
D *e Å D *0 / v *e /2 0 v *e x *e /4 / v *e y *e /8,
[3]
where n(6 1 P1 r 6 1 S0 ) is the energy of the atomic transition, D 90 is taken from Ref. (8), and n00 Å 46201.7 cm01 is the energy of the G0 u/ ( £* Å 0) R X 0 g/ ( £9 Å 0) transition obtained from the extrapolation (9), using the experimental value for the energy of the G0 u/ R X 0 g/ ( £* Å 26 R £9 Å
/ FIG. 6. A Birge–Sponer plot of the G0 / u R X 0 g ( £9 Å 0) excitation spectrum shown in Fig. 3a, for (m1 / m2 ) Å 404 isotopic peaks ( h ), together with the data taken from Ref. ( 3) ( s ).
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FIG. 7. PE curve for the G0 / u state represented by the Morse function plotted with constants determined in Ref. ( 3) and this investigation. s, RKR calculation (3). l, Czuchaj et al. (12). The range of vibrational levels 25 õ £* õ 52 is also shown.
0) transition and the values of v *e , v *e x *e , and v *e y *e from Table IV of (3). Equations [2] and [3] yielded D *0 Å 8236 { 15 cm01 and D *e Å 8280 { 15 cm01 , respectively, in good agreement with the values yielded by the extrapolation shown in Fig. 6. Using the data from Refs. (3) and (8) and from this analysis, we attempted to simulate the G0 /u R X 0 /g ( £9 Å 0) excitation spectrum, using the LEVEL 6.1 FORTRAN code of LeRoy (11). This program solves the radial Schro¨dinger equation for bound levels and calculates the FC factors for transitions between rovibrational levels in the ground and excited states. The PE of the G0 u/ state was represented by turning-point pairs obtained from the RKR calculation (3), and the PE of the X 0 g/ ground state was represented by either a Morse, a van der Waals, or a Lennard–Jones (12-6) function with v e9 x e9 and D 9e from Ref. (8). Because the G0 u/ R X 0 g/ ( £* R £9 Å 0) progression begins from the £9 Å 0 vibrational level, the choice of the function representing the ground state potential was not expected to be crucial (9). However, we found during the simulation that the best results were produced by using for the X 0 g/ state the van der Waals potential U 9 (R) Å
D 9e n06
F S D S DG 6
R 9e R
n
0n
R 9e R
6
,
[4]
which had been used in the simulation of the G0 u/ ( £ * Å 12 ) r X 0 g/ fluorescence band (3), and also the Morse function. The simulation of the fluorescence band, which will be described below, yielded the parameter n Å 6.21 for the van der Waals function. Consequently, n Å 6.21 [rather than n Å 6.53 (3)] was used in the simulation of the excitation spectrum shown in Fig. 3a. Figure 3b represents the
best fit to the £* R £9 Å 0 progression of the (m1 / m2 ) Å ˚, a 401 isotope spectrum obtained for R 9e Å 3.69 { 0.01 A value larger than that obtained by van Zee et al. (6). Because the modeling of the excitation spectrum was found to be very sensitive to the difference DR Å R *e 0 R 9e , we assumed in the simulation the accurately known value R *e Å 2.8506 ˚ for the G0 u/ state (3) and varied R 9e . We also found that A the simulation was not noticeably affected when the parameter n was varied in the range 6.1–6.9. The program used in the simulation (11) generated the energies of the vibrational levels of the G0 u/ state, which allowed us to reexamine the report of Ehrlich and Osgood who claimed to ˚ laser have excited the £* Å 57 vibrational level with 1933 A radiation (1). We assumed that the excitation proceeded by photoassociation, from the energy of two separated ground state atoms, and found that they must have excited the £* Å 93 level for which the 401 isotope has an energy of 52 089 cm01 (relative to the energy of £9 Å 0), which should be compared with 51 716 cm01 , the energy of their laser radiation plus D 09 . This conclusion corroborates our previous estimate derived from the vibrational analysis of the G0 /u – A0 /g spectrum (2). Figure 7 shows the PE curve for the G0 u/ state, represented by the Morse function, plotted using constants obtained in Ref. (3) and this work, and compared with the result of an RKR calculation (3) and with the theoretical ab initio nonrelativistic pseudopotential calculation of Czuchaj et al. (12). There is good overall agreement between theory and experiment although the theoretical potential is somewhat shallower than the potential derived from the experimental data. 4. THE FLUORESCENCE SPECTRUM
The £* assignments in the G0 u/ R X 0 g/ excitation spectrum were confirmed on the basis of a fluorescence band
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/ FIG. 8. (a) The G0 / u ( £* Å 39) r X 0 g fluorescence band recorded with a 10 cm01 monochromator slit width. X/D Å 5.6, Meff Å 10.3. The sharp peak at the short-wavelength end of the band is due to £* Å 39 r £9 bound–bound transitions. (b) A computer simulation ( 19) of the bound– free part of the band showing the best fit obtained using the van der Waals function with n Å 6.21 to represent the X 0 /g potential.
arising from the decay of a selectively excited bound £* vibrational level to the repulsive part of the ground state. Ehrlich and Osgood (1) and Kedzierski et al. (3) had previously reported on CID patterns in the Hg2 fluorescence spectrum, which they interpreted as due to the bound-free radiative decays of the G0 u/ ( £* É 57) and G0 u/ ( £* Å 12) states, respectively, to the repulsive part of the X 0 g/ state. The (m1 / m2 ) Å 400 isotope in the G0 u/ ( £* Å 39) R X 0 g/ ( £9 Å 0) vibronic component was selectively excited and decayed to the repulsive part of the ground state, emitting the G0 u/ ( £* Å 39) r X 0 g/ fluorescence band. To favor the production of metal dimers in preference to the Hg– noble gas complexes (13), a relatively long 15-mm nozzle was employed to generate the molecular beam. The excitation region was located at a smaller distance from the orifice (X Å 5 mm) than in the case of the excitation spectrum. Figure 8a shows the gross structure of the resulting CID pattern, in which the number of maxima exceeds the £* vibrational quantum number of the emitting level by one. The band was recorded at relatively low resolution, using a 100 cm01 monochromator slit width. The intense peak at the short-wavelength end of the band is interpreted as being due mainly to unresolved bound–bound transitions to the closely spaced vibrational levels of the shallow ground state, while the broad maximum at the long-wavelength end corresponds to the inner turning point in the potential of the emitting £* level. Figure 8b represents a simulation of the bound-free part of the band, which will be described in some detail below. To confirm the vibrational £* level from which the
fluorescence was emitted, we recorded various parts of the fluorescence band at a higher resolution. Figure 9 shows two traces of the band recorded at slit widths of (a) 20 and (b) 10 cm01 . The results of a computer simulation are shown in Figs. 9c and 9d. The simulation (11) of the bound–bound part of the fluorescence band close to the region of the ˚ ), shown in Fig. 9c, emexcitation wavelength (2031.09 A ployed the spectroscopic constants obtained from the analysis of the excitation spectrum. We assumed either the Morse potential or the van der Waals potential with n Å 6.21 as representing the ground state PE curve. Since the simulation employed all the vibrational levels of the ground state, it was a good test for the particular representation of the ground state potential. From the simulation it became clear that the first seven peaks at the short-wavelength end of the fluorescence band were due to unresolved bound–bound transitions, while the remaining peaks were due to bound– free transitions. When the van der Waals potential was used in the simulation, a very good fit was obtained for the positions of the maxima and minima in the envelope of the bound–bound transitions (we were not able to resolve individual bound–bound transitions), but the relative intensities of the maxima in the envelope were better reproduced by the Morse function. The fit of the bound–bound part of the fluorescence band and of the excitation spectrum, was not very sensitive to the parameter n in the van der Waals potential. In the case of the bound–bound transitions, we obtained a satisfactory fit for a range of n values from 6.1 to 6.9. It was evident that variations in n within this range did not
/ FIG. 9. The G0 / u ( £* Å 39) r X 0 g fluorescence band in the 2020– ˚ 2150 A region, recorded with slit widths of (a) 20 and (b) 10 cm01 . The spectrum (a) is compared with (d), the simulation as in Fig. 8b. The spectrum (b), partially resolved bound–bound transitions, is juxtaposed with the result (c) of a simulation (11) of the individual bound–bound transitions.
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affect significantly the bound part of the potential curve of the ground state, but affected significantly the slope of the repulsive part above the dissociation limit, a conclusion which had also been reached in the modeling of the HgAr A0 / r X 0 / fluorescence spectrum (14). All the 40 maxima present in the CID pattern were identified in the traces in Figs. 8 and 9, confirming the assignments obtained from the analysis of the isotopic structure in the excitation spectrum. We attempted to resolve individual bound–bound components in the fluorescence band by increasing the resolution of the detection system (using a 2 cm01 monochromator slit) and by further cooling the molecules. We used a nozzle with a smaller orifice (D Å 0.3 mm) and increased X to 12 mm, obtaining an effective Mach number of 38.6 (15) which exceeded the terminal Mach number MT Å 33 beyond which no collisions should take place (16). The estimated effective temperatures were TT Å TR É 2 K and Tv É 20 K (15, 17). Even though, under these conditions, no collisional energy transfer should take place between the isotopic molecules within the excited £* state, we did not resolve any components that might be ascribed to individual bound–bound transitions. To construct a part of the repulsive section of the ground state PE curve from the G0 u/ ( £* Å 39) r X 0 g/ bound–free band, we adopted the semiclassical RKR-like inversion method of LeRoy (18). This approach, which is complementary to the ‘‘exact’’ computational and fitting procedures, offers one peculiar advantage—it distinguishes between the ‘‘phase’’ and ‘‘amplitude’’ information in the experimental spectrum and shows how the positions of the intensity extrema are determined by the shape of the repulsive potential while the peak heights depend on the transition dipole moment. The experimental input data in this case were the energy values of the intensity extrema (maxima and minima) in the recorded fluorescence band. A five-constant polynomial fit was used to represent the positions of the experimental intensity extrema, while the inner and outer turning points for the G0 u/ PE curve were taken from Ref. (3). The resulting X 0 g/ potential is shown in Fig. 10. To find the unique value n for the van der Waals function to make it overlap with the points obtained by the inversion method, it was necessary to assume the van der Waals X 0 g/ ground state potential with the parameter n as a free variable, simulate the bound–free band using this potential, and vary n to obtain the best fit between the observed and simulated positions of the oscillatory maxima and minima. We used a BCONT 1.4 FORTRAN code (19), in which the PE of the G0 u/ state was, as before, represented by the turning-point pairs yielded from the RKR calculation (3) while R 9e and D 9e for the ground state were obtained from the analysis of the excitation spectrum and Ref. (8), respectively. The program made provision for the variation of the electronic dipole transition moment M with R, the internuclear separa-
FIG. 10. PE curves for the X 0 / g state. ---, Morse function; – – – , van der Waals function (n Å 6.53), using v e9 x e9 and D e9 from Ref. (8), and ˚ . — , van der Waals function (n Å 6.21) from simulation (19) R e9 Å 3.69 A of the bound–free fluorescence band; l, Czuchaj et al. (12); 1, Dolg and Flad (22); s, repulsive part produced by the inversion procedure (18). The insert shows details of the bound part of the potential.
tion. We used the three theoretical values for M(R) reported in Ref. (20), ranging from 3.27 to 3.97 D, which were calculated at the three corresponding values of R (in the ˚ ) and assumed a linear relationship berange 2.64–3.70 A tween M and R. The best fit, which was obtained for n Å 6.21, is shown in Figs. 8b and 9d. We should stress that even a slight departure of n from this value (by {0.03) changed the slope of the van der Waals repulsive curve and the profile of the simulated band to the extent that it no longer fitted the experimental trace. This was particularly apparent in the long-wavelength region, where the profile of the simulated band is governed by the slope of the ground state potential energy curve. The van der Waals potential with n Å 6.21 is shown in Fig. 10 together with the potentials represented by the van der Waals function for n Å 6.53 (3) and the Morse function plotted using v e9 x 9e and D 9e from ˚ obtained in this investigation. A Ref. (8), and R 9e Å 3.69 A comparison is also made with the calculations of Czuchaj et al. (12) and Dolg and Flad (21, 22) whose result agrees most closely with our experimental curves. The repulsive part of the ground state potential obtained by the inversion method (18) and the van der Waals potential with n Å 6.21 lie closer to the van der Waals curve with n Å 6.53 (3) than to the Morse curve. This supports the conclusion reached also in the modeling of the G0 u/ ( £* Å 12) r X 0 g/ fluorescence band (3) that the Morse function does not adequately describe the repulsive part of the PE curve of the X 0 g/ state. 5. CONCLUSIONS
The G0 u/ (6 1 P1 ) – X 0 g/ excitation and fluorescence spectra of the Hg2 van der Waals molecules were studied in a
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G0 /u (6 1 P1 ) – X 0 /g SPECTRA OF Hg2
TABLE 1 / Spectroscopic Constants for the G0 / u and X 0 g States of Hg2
pulsed free-jet supersonic expansion beam crossed with a pulsed dye-laser beam. A well-resolved vibrational structure in the G0 u/ ( £* ) R X 0 g/ ( £9 Å 0) excitation spectrum was recorded, as well as the isotopic structures of the individual vibrational components. An isotope shift analysis produced £* assignments which differ by 13 from those reported by Schlauf et al. (4). An improved value for the equilibrium internuclear separation R 9e in the X 0 g/ ground state was determined by modeling the excitation spectrum. A Birge– Sponer plot of the G0 u/ (25 õ £* õ 52) R X 0 g/ ( £9 Å 0) progression recorded for the (m1 / m2 ) Å 404 isotope could be interpreted as an extension of the G0 u/ (0 õ £* õ 32) R A0 g/ (0 õ £9 õ 7) vibronic band origins found from the rotational analysis of the spectrum obtained with monoisotopic ( 202Hg)2 (3). The analysis of the CID pattern in the G0 u/ r X 0 g/ fluorescence band, emitted upon selective excitation of the £* Å 39 vibrational component, confirmed the vibrational assignments of the peaks in the excitation spectrum. Simulation of the excitation spectrum and of the bound–bound and bound–free parts of the fluorescence band showed that a van der Waals potential with n Å 6.21 was a good representation of the ground state potential below and above the dissociation limit. Below the dissociation limit the ground state potential could also be represented by the Morse function. An analysis of the excitation spectrum yielded molecular constants that are compared in Table 1 with those obtained from other experiments and from theoretical calculations. This comparison, especially with the re-
cent result of Dolg and Flad (21, 22), suggests that relativistic effects should be included in ab initio calculations for the massive Hg2 molecule. ACKNOWLEDGMENTS We thank R. J. LeRoy for helpful discussions facilitating the use of his LEVEL 6.1, RPOT, and BCONT 4.1 computer programs and H. J. Flad for permission to quote his unpublished theoretical data. This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
REFERENCES 1. D. J. Ehrlich and R. R. Osgood, Jr., Phys. Rev. Lett. 41, 547–550 (1978). 2. J. Supronowicz, R. J. Niefer, J. B. Atkinson, and L. Krause, J. Phys. B 19, L717–L721 (1986). 3. W. Kedzierski, J. Supronowicz, A. Czajkowski, J. B. Atkinson, and L. Krause, J. Mol. Spectrosc. 173, 510–531 (1995). 4. M. Schlauf, O. Dimopoulou-Rademann, K. Rademann, U. Even, and F. Hensel, J. Chem. Phys. 90, 4630–4631 (1989). 5. A. Zehnacker, M. C., Duval, C. Jouvet, C. Lardeux-Dedonder, D. Solgadi, B. Soep, and O. Benoist d’Azy, J. Chem. Phys. 86, 6565–6566 (1987). 6. R. D. van Zee, S. C. Blankespoor, and T. S. Zwier, J. Chem. Phys. 88, 4650–4654 (1988). 7. J. Koperski, J. B. Atkinson, and L. Krause, Chem. Phys. Lett. 219, 161–168 (1994). 8. J. Koperski, J. B. Atkinson, and L. Krause, Can. J. Phys. 72, 1070– 1077 (1994).
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9. G. Herzberg, ‘‘Spectra of Diatomic Molecules,’’ Van Nostrand, New York, 1950. 10. M. Schlauf, Ph.D. thesis, Phillipps-Universita¨t Marburg, 1989. [In German] 11. R. J. Le Roy, ‘‘LEVEL 6.1: A Computer Program Solving the Radial Schro¨dinger Equation for Bound and Quasibound Levels, and Calculating Various Expectation Values and Matrix Elements,’’ University of Waterloo Chemical Physics Research Report CP-555R, 1996. 12. E. Czuchaj, F. Rebentrost, H. Stoll, and H. Preuss, Chem. Phys. 214, 277–289 (1997). 13. C. L. Callender, S. A. Mitchell, and P. A. Hackett, J. Chem. Phys. 90, 2535–2543 (1989). 14. J. Koperski, Chem. Phys. 211, 191–201 (1996); 214, 431–432 (1997). 15. D. M. Lubman, C. T. Rettner, and R. N. Zare, J. Phys. Chem. 86, 1129–1135 (1982). 16. J. B. Anderson, R. P. Andres, and J. B. Fenn, Adv. Chem. Phys. 10, 275–317 (1966). 17. G. M. McClelland, K. L. Saenger, J. J. Valentini, and D. R. Herschbach, J. Phys. Chem. 83, 947–959 (1979).
18. R. J. LeRoy, ‘‘A Computer Programs for Inversion of Oscillatory Bound-Continuum Spectra,’’ University of Waterloo Chemical Physics Research Report CP-327, 1988; M. S. Child, H. Esse´n, and R. J. LeRoy, J. Chem. Phys. 78, 6732–6740 (1983). 19. R. J. LeRoy, Comput. Phys. Comm. 52, 383–395 (1989); R. J. LeRoy, ‘‘BCONT 1.4. A Computer Program for Calculating Absorption Coefficients, Emission Intensities or (Golden Rule) Predissociation Rates,’’ University of Waterloo Chemical Physics Research Report CP-329R 3 , 1993. 20. F. H. Mies, W. J. Stevens, and M. Krauss, J. Mol. Spectrosc. 72, 303– 331 (1978). 21. M. Dolg and H.-J. Flad, J. Phys. Chem. 100, 6147–6151 (1996). 22. M. Dolg and H.-J. Flad, unpublished result. 23. N. Bras and C. Bousquet, J. Phys. (Paris) 40, 945–960 (1979). 24. W. E. Baylis, J. Phys. B 10, L583–L587 (1977). 25. J. R. Bieron´ and W. E. Baylis, Chem. Phys. 197, 129–137 (1995). 26. C. F. Kunz, C. Ha¨ttig, and B. A. Hess, Mol. Phys. 89, 139–156 (1996).
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