Velocity modulation laser spectroscopy of molecular ions The hyperfine-resolved rovibrationai spectrum of HF

Transcription

1 MOLECULAR PHYSICS, 1989, VOL. 68, No. 3, Velocity modulation laser spectroscopy of molecular ions The hyperfine-resolved rovibrationai spectrum of HF by DAVID C. HOVDEf, ERIC R. KEIM and RICHARD J. SAYKALLY Department of Chemistry, University of California, Berkeley, California 94720, U.S.A. (Received 10 May 1989; accepted 26 May 1989) 34 v = 1 r 0 R branch infrared transitions in the X2H state of the HF molecular ion have been measured by velocity modulation laser absorption spectroscopy. Fluorine hyperfine structure was resolved for low J transitions. From a weighted fit of all available high resolution data, values were determined for the v = 0 and v = 1 fluorine hyperfine constants (except b(1)), 2- doubling parameters, rotational and centrifugal distortion constants and the vibrational band origin. Molecular expectation values derived from the hyperfine constants are compared to similar quantities for OH and NH-. An analysis is presented for the v = 0 proton hyperfine structure observed previously by laser magnetic resonance. 1. Introduction The HF + molecular ion is the simplest member of the hydrogen halide ion sequence HX + (X = F, C1, Br, I), and it is isoelectronic with the OH radical and NH- anion. A substantial effort has been dedicated to the study of this fundamental ion. Brundle [1] first observed HF + by photoelectron spectroscopy of HF, determining the vertical ionization energies to the X 2H ground and the A 2~+ excited states, and the approximate vibrational frequencies in these states. Higher resolution photoelectron and photo-ion experiments [2] refined these values and gave an estimate of the spin-orbit interaction. In 1975, Gewurtz, Lew and Flainek [3] observed the first rotationally resolved spectrum of the weak A 2~-~...r X 2H emission (z(rad) = 5 bts) [4]; they determined many important properties of the ion, including the dissociation limit of the weakly bound A 2E state. Hovde et al. [5] obtained the rotational spectrum of the v = 0 level of the X 2H state by laser magnetic resonance (L.M.R.) in Refined values of the rotational and A-doubling parameters were determined, and hyperfine structure due to both the F and H nuclei was observed. A complete determination of the hyperfine constants was not possible, however, due to the difficulty in assigning transitions in the nearly diamagnetic f~ = 89 spin sublevel. Theoretical studies [6, 7, 8, 9, 10] of HF have determined ab initio structural parameters for comparison with experiment. (The X 2H and higher electronic states were the subject of early studies) I-6, 7]. Because of the high ionization potential of the F atom, both the A and the X states correlate to the separated atom limit H + F (2p). Other excited electronic states correlate to higher energy states of the separated atoms. Hence the A and X states are well separated from all other electronic states at all bond lengths greater than r e. In contrast, the lowest separated ~" Present address: Department of Chemistry, Princeton University, Princeton, New Jersey 08544, U.S.A /89 $ Taylor & Francis Ltd

2 600 D.C. Hovde et al. atom limit of HCI +, H (2S) + CI + (3p), gives rise to the X 21-I ground state and a repulsive 4I-I surface that predissociates the A 252+ state I11]. HBr + is analogous to HCI + [12]. Wilson [13] and Hutson and Howard [14] calculated the A-doubling parameters p and q that describe the parity dependent perturbation of the X 2H state. Both bound and continuum levels of the shallow A 2E+ state made significant contributions to the computed parameters. Perturbations from higher E and A electronic states were ignored. Hutson and Cooper used a direct approach [15] for computing this perturbation that circumvented the need to explicitly sum over an infinite number of continuum levels. Their computed values for P0 and qo agreed well with those later determined from the rotational L.M.R. spectrum [5]. A more critical test of this theoretical technique would Compare the computed Pv and qv with accurate experimental values for several vibrational levels. Velocity modulation infrared laser spectroscopy has proven to be a powerful method for obtaining the vibrational spectra of both open and closed shell molecular ions [16, 17]. This technique is not limited to the study of transitions that can be magnetically tuned, and is thus far more general than laser magnetic resonance. Furthermore, due to the relatively narrow Doppler width observed at infrared frequencies, it is possible to measure the hyperfine structure of some open shell ions, whereas hyperfine structure is very rarely resolved in U.V. or visible studies. In the present work, we have measured 34 v = 1 ~- 0 R branch transitions of the X El-I state by velocity modulation infrared laser absorption spectroscopy. The lowest J lines showed resolved F-hyperfine structure. These new vibrational observations were combined with available L.M.R. rotational and electronic spectra in a weighted least squares fit to determine vibrational, rotational, centrifugal distortion, A-doubling and F-hyperfine constants for the v = 0 and v = 1 states. In addition, an analysis is presented here of the H-hyperfine structure obtained previously in this laboratory by laser magnetic resonance. 2. Experimental The radiation from a colour centre laser (20 mw at cm- 1) is split into a signal beam and a reference beam of approximately equal intensities. The signal beam is directed down the bore of the a.c. discharge plasma tube in which the ions are produced. The modulated drift velocity of charged species in the plasma results in a corresponding Doppler modulation of ion absorption features at the frequency of the discharge. The signal and reference beam intensities are measured by matched detectors; the difference signal is sent to a lock-in amplifier. A computer scans the laser, monitors the lock-in output and simultaneously reads a calibrated wavemeter to an accuracy of 0.003cm -1. Fractional absorptions as small as 3 x 10-6 can be detected with this system, which for the hydroxyl anion was shown to correspond to a minimum detectable ion density of 5 x 10 a cm -3 [18]. A detailed description of the colour centre laser velocity modulation spectrometer has been given in a recent review of velocity modulation spectroscopy by Owrutsky et al. [16]. HF was produced in a discharge through He and purified HF inside a 6mm diameter, 1 m long, water-cooled pyrex discharge cell. The discharge was driven by an ac power supply (ENI Plasmaloc-2) and high voltage transformer at 25 khz and 350Watts. The HF was purified by condensing it in a Teflon trap immersed in a dry ice-acetone bath, pumping off the H 2 that results from oxidation of the cylinder walls, and then allowing the trap to warm up. Optimum signals were observed using

3 Velocity modulation laser spectroscopy of molecular ions 601 HF + 9, : 7,/2 I R(6.5) H2F + v 3 826"-927 j I Figure I cm-i A velocity modulation (mode hop) scan showing the HF f2 = ~ R(6.5) transitions along with the H2 F v ~ 927. a gas mixture of 5 Torr of He and 30 mtorr of HF. While this mixture optimized the HF + signal, sufficient H2 F+ was also produced to be observed spectroscopically [19]. Figure 1 shows the 826 ~ 92~ transition of the v 3 band of H2F observed along with the f2 = ~ R(6-5) transitions of HF in a single scan taken with a 400ms time constant. ( HF + 2I13/2 R(2.5)e Figure 2, A scan (a) of the 2H3t 2 R(2,5)e transition of HF in which the hyperfine splitting is resolved by continuously tuning the colour centre laser. The upper etalon trace (b) was used for determination of the hyperfine splitting.

4 602 D.C. Hovde et al. Transition frequencies were predicted to within 0.2 cm-1 using the vibrationalrotational parameters determined by Gewurtz, Lew and Flainek [3] in their optical emission study of HF +. In searching for transitions and calibrating the spectral lines observed, the laser was tuned in cavity-mode increments of 300 MHz (0"01 cm- 1) 'mode hop scanning'--by applying a ramp voltage to the interactivity etalon while simultaneously stepping the output grating. Scans up to 1.5 cm-1 were made using this method. For the R(2.5) transition of the f~ = ~ state the cavity mode hop scanning did not provide sufficient resolution, since for this transition the F hyperfine splitting is of the same order as the approximately Doppler limited linewidth of 0.01 cm-1. In this case, it was necessary to continuously tune the laser by synchronously ramping the etalon and the folding mirror inside the laser cavity, without stepping the output grating. By using the same voltage ramp to drive both elements it was straightforward to tune continuously the laser over 1200MHz (0.04cm -1) without an external feedback loop. The bottom trace in figure 2 is a continuous frequency scan of the R(2.5) transition, showing partial resolution of the hyperfine splitting. The top trace is the transmission of an external etalon used to measure precisely the splitting (free spectral range = 538 (1)MHz). All of the transitions listed in table 1 were measured to an absolute accuracy of cm-1 using a Burleigh WA20 wavemeter which was calibrated by measuring accurately known CH3I and CH 4 transitions [20, 21]. 3. Analysis Veseth's case (c~) hamiltonian [22] was incorporated into a weighted, non-linear least squares fitting program. The fitted parameters were defined by the case (a) approximation to the case (c) basis functions [23]. The A-doubling parameters were defined in the sense introduced by Mulliken and Christy [24] and thus conform to our work on HC1 + [23] and HBr + [25] but differ from the parameters given in our earlier work on HF + [5]. The velocity modulation data include 17 hyperfine resolved R-branch transitions and 17 higher J transitions, for which hyperfine structure was not observed. The infrared data were weighted by the square of the reciprocal uncertainty, (1/ cm-1)2. Ten laser magnetic resonance rotational transitions [5] in the v = 0, = az state were included in the fit with an experimental uncertainty of 2 MHz (7 10-Scm-t). From the electronic spectra [3] 43 v = 0 and 55 v = 1 combination differences were formed. Overlapped and partially resolved lines were omitted. The uncertainty of each combination difference was 0.05cm -1, but by averaging the values obtained from different bands, the uncertainty was usually reduced to 0.01 era- 1. Preliminary fits showed that centrifugal correction PD and qd to the A-doubling constants were essential to reproduce the velocity modulation data. However, H, the sextic centrifugal distortion constant, was not statistically significant, as it was highly correlated with D for our data set. Trial fits of the fluorine hyperfine splittings showed that values for all four v = 0 and three v = 1 constants were welldetermined: the seven F hyperfine parameters converged rapidly, although the correlation coefficients between d and d' (0.96) and h- and h-' (0.98) were high. The values obtained were independent of the number of hyperfine parameters in the trial fit.

5 Velocity modulation laser spectroscopy of molecular ions 603 Table 1. The v = 1 ~ 0 transitions of the X 217 state of HF observed by velocity modulation spectroscopy. Experimental precision = cm-~. Lines with hyperfine structure Frequency/ Obs-ealc/ J J' F F' P P' cm cm -~ = fl' = 89 sub-branch f~ = f~' = ~ sub-branch Lines without hyperfine structure Frequency/ Obs-calc/ J J' p p' cm-x 10-3 cm-1 fl = fg = 89 sub-branch 1' " " = f~' = ~ sub-branch ' ' The final fit included separate v = 0 and v = 1 values for the rotational and centrifugal constants B and D; the spin-orbit constant A, its centrifugal correction Ag; the A-doubling constant p and q, PD and qd; and the hyperfine parameters h+ =a+(b+c)/2, h- =a-(b+c)/2, and d. The hyperfine parameter

6 604 D.C. Hovde et al. Table 2. Results of the simultaneous fit of vibrational, rotational, [5] and electronic spectra of HF [3], showing the parameters (in MHz) and their statistical uncertainties (2tr). Magnetic 9-factors used to fit L.M.R. rotational data were fixed at the values determined in [5]. The proton hyperfine constant was obtained from a separate fit to the rotational spectra only [5] (130) (2912"5223 (43) cm-1) v=0 v=l B (92) (12) D 66"21 (12) (16) A (430) (500) A (14) (12) p (76) (80) q "3 (32) (12) PD --4"9 (32) --2"2 (16) qo 0'58 (22) 0"40 (16) d h h- b h + Fluorine hyperfine parameters 4900 (1000) 4800 (1400) 3354 (14) 3520 (370) 5500 (1800) 6200 (4400) 1270 (140) 1347 (fixed) Proton hyperfine parameter (determined separately) 83.2 (44) b = b(f) - c/3 was adjusted only for the v = 0 level; its value for v = 1 was set at the ab initio value. The spin-rotation constant, ~, [8] was constrained to zero, so an effective value for A~ = Ao- 2~B/(A- 2B) was determined for both vibrational levels. Finally, the vibrational band origin v o was fit. Thus 142 measurements were fit with 25 parameters. The normalized standard deviation was 1.4. The constants and their 2tr statistical uncertainties are reported in table 2 [26]. Proton hyperfine constants were obtained from a separate fit to the laser magnetic resonance data [5]. The same single nuclear spin hamiltonian [22] was used to fit the data, except that the much larger F hyperfine structure was averaged out with the following procedure. Resonant fields were predicted by setting all hyperfine constants to zero. Then the observed proton hyperfine splittings were superimposed onto these predicted fields, and the proton hyperfine constants h and b were varied. Although this procedure ignores the correlations of the proton hyperfine parameters with other fitted parameters, typically these correlations are small (absolute values are less than 0.3 for the F hyperfine parameters). The correlation of the H hyperfine parameters to the F hyperfine parameters is not determined in the single nuclear spin model. More fundamentally, the model ignores the interaction between the two nuclear spins. The nuclear dipole-dipole interaction is of the order t~f 9 flh/r 3. Furthermore, for the AM~ = 0 transitions observed, this energy is the same in the upper and lower states, and so does not contribute to the observed transition frequency. The v = 0 proton hyperfine constant h = a + (b + c)/2 is listed in table 2.

7 Velocity modulation laser spectroscopy of molecular ions 605 Table 3. Comparison of A-doubling constants (GHz). Experimental Theoretical Electronic Hutson and This work spectrum [3] Cooper [15] Wilson [13] Po Pl qo ql Results and discussion Improved values were obtained for the v = 0 and v = 1 molecular constants, listed in table 2, and the hyperfine constants describing the unpaired electron distribution around the F nucleus were fully determined for the first time. Because the velocity modulation experiment probes both the t2 = 89 and t2 = ~ 2 substates, both A-doubling parameters p and q are well determined. The precision with which p can be determined depends primarily upon the quality of the fl = 89 observations, since in the case (a) limit, the fl = 3 parity splittings are independent of p. Centrifugal corrections to the A-doubling constants were determined for the first time. For the isoelectronic hydroxyl radical, Po = MHz, qo = MHz [27]. Experimentally determined A-doubling constants are compared to theoretical results in table 3. The direct summation approach of Hutson and Cooper is in good agreement with the results presented here, with errors of 15 per cent for p and 8 per cent for q. The success of this theoretical method is seen in the excellent reproduction of the vibrational dependence of constants. In principle, the A-doubling distortion constants Po and qo can also be calculated. Comparison with the experimental values presented here would provide a further test of theory. As described initially by Frosh and Foley [28] the hyperfine constants are defined in terms of expectation values over the electronic wavefunction. In order to extract the best equilibrium values for these expectation values from the experimentally determined parameters in table 2, we combined the v = 0 and v = 1 parameters by assuming the vibrational dependence of the hyperfine parameters is adequately described by equations of the form P(v) = Pe + (V + 89 The equilibrium hyperfine constants a, b(f), c and d were evaluated from the fitted h+(0), h-(0), d(0), b(0), h h-(1) and d(1), and the value fixed for b(1). Because the hyperfine constant b(1) was constrained to its ab initio value in the fit, the value obtained for b(f) is effective and may differ from the true equilibrium b(f) by b'. The hyperfine constant c(e) also depends on this choice of b(1) to a lesser extent; the values of a(e) and d(e) are not affected. The molecular expectation values derived from the constants are listed in Table 4. The quoted uncertainties were obtained by propagating correlated errors [29] in the fitted parameters. The expectation values are compared to ab initio values [10] for HF and to values for the OH radical [30]. Expectation values for atomic fluorine [31] and hyperfine results measured for NH- are also included for comparison [32]. The effect of the net molecular charge in contracting the electron

8 606 D.C. Hovde et al. Table 4. Expectation values derived from the hyperfine parameters of HF listed in table 2, with 2a statistical uncertainties (this work), ab initio MBPT calculations for HF +, and expectation values for the isoelectronic species 17OH and 14NH-. For NH-, a complete determination of the hyperfine constants has not been achieved. HF + HF + F this work MBPT [10] OH [30] NH- [32] atom [31] sin 20\ 3 1"3 /s 133 (26) 3 cos rs 1)l --27'4(61) (r- 3), 56"2 (46) I~ 2(0) O" 35 (44) Heavy nucleus Proton 3' th- =a-89 F-~C. h + =a+89 F+89 distribution is evident in the expectation values that depend upon (r-a>, which takes its largest value for the positive ion. From table 4, one sees that the ab initio fluorine nucleus values are in good agreement with experiment, except for the Fermi contact constant, which is rather poorly determined by our experiments. The situation for the proton hyperfine constant h+= a c) is less satisfactory. The calculated value is 60 per cent greater than the observed value. The reason for this discrepancy is not clear. The proton hyperfine parameters of other first row hydrides were accurately predicted at this level of theory. The calculations for HF were performed at r = A, whereas the experimental v = 0 value represents an average over the zero point vibrational motion with classical turning points at and 1.108A. Vibrational averaging gives a 3.3 per cent correction to the theoretical results for the X 21-1 state of OH; for CH it amounts to 2-6 per cent. The vibrational frequency of HF (oge= 3090cm -t) is intermediate between that of OH (3650 cm-1), and CH (2830cm -1) [33]. Thus an exceptionally large vibrational dependence would be required to explain this disagreement. Proton hyperfine resolved observations of the v = 1 level would directly measure the vibrational state dependence. With such ideas in mind, we have begun an investigation of this spectrum by the newly developed technique of Direct Laser Absorption Spectroscopy of Fast Ion Beams with substantially ( x 10) improved resolution [34]. This work was supported by the Experimental Physical Chemistry Program of the National Science Foundation (Grant CHE ) and the NSF Presidential Young Investigator Program. We thank the IBM Corporation for a NSF-PYI Matching Grant. Thanks to Beth Kuchinsky for valuable help in preparing the HF HC1 and HBr manuscripts.

9 Velocity modulation laser spectroscopy of molecular ions 607 References [1] BRUNDLE, C. R., 1970, Chem. Phys. Lett., 7, 317. [2] BERKOWITZ, J., CHUPKA, W. A., GUYON, P. M., HOLLOWAY, J. H., and SPOrm, R., 1971, J. chem. Phys., 54, BERKOWlTZ, J., 1971, Chem. Phys. Lett., 11, 21. GUYON, P. M., SPOHR, R., CHUPKA, W. A., and BERKOWITZ, J., 1976, J. chem. Phys., 65, [3] GEWURTZ, S., LEW, H., and FLAINEK, P., 1975, Can. J. Phys., 53, [4] VAN SPRANG, H. A., and DE HEER, F. J., 1978, Chem. Phys., 33, 73. [5] HOVDE, D. C., SCHAEFER, E., STRAHAN, S. E., FERRARI, C. A., RAY, D., LUBIC, K. G., and SAYKALLY, R. J., 1984, Molec. Phys., 52, 245. [6] JULIENNE, P. S., KRAUSS, M., and WAHL, A. C., 1971, Chem. Phys. Lett., 11, 16. [7] RAFTERY, J., and RICHARDS, W. G., 1972, J. Phys. B, 5, 425. [8"] GREEN, S., and ZARE, R. N., 1976, J. molec. Spectrosc., 64, 217. [9] ROSMUS, P., and MEYER, W., 1977, J. chem. Phys., 66, 13. [10] KRISTIANSEN, P., and VESETH, L., 1986, J. chem. Phys., 84, [11] LUBIC, K. G., RAY, D., HORDE, D. C., VESETH, L., and SAYKALLY, R. J., 1989, J. molec. Spectrosc. (in the press). [12] LUBIC, K. G., RAY, D., HOVDE, D. C., VESETH, L., and SAYKALLY, R. J., 1989, J. molec. Spectrosc. (in the press). [13] WILSON, I. D. L., 1978, J. molec. Spectrosc., 70, 394. [14.] HUTSON, J. M., and HOWARD, B. J., 1980, Molec. Phys., 41, [15] HUTSON, J. M., and COOPER, D. L., 1981, J. chem. Phys., 75, [16] OWRUTSKY, J. C., ROSENBAUM, N., TACK, L., GRUEBEEE, M., POLAK, M., and SAYKALLY, R. J., 1971, Phil. Trans. R. Soc. A, 324, 97. [17] COL, J. V., and SAYKALLY, R. J., 1989, Ion and Ion Cluster Spectroscopy and Structure, edited by J. Maier (Elsevier Science Press), pp [18] ROSENBAUM, N. H., OWRUTSKY, J. C., TACK, L. M., and SAYKALLY, R. J., 1986, J. chem. Phys., 84, [19] SCHAEFER, E., and SAYKALLY, R. J., 1984, J. chem. Phys., 81, [20] ANTTILA, R., PASO, R., and GUELACHVILI, G., 1986, J. molec. Spectrosc., 119, 190. [21] PINE, A. S., 1976, J. opt. Soc. Am., 66, 97. [22] VESETH, L., 1976, J. molec. Spectrosc., 59, 51; 1976, Ibid., 63, 180; 1979, Ibid., 77, 195. [23] LUBIC, K. G., RAY, D., HOVDE, D. C., VESETH, L., and SAYKALLY, R. J., 1989, J. molec. Spectrosc., 134, 1. [24] MULLIKEN, R. S., and CHRISTY, A., 1931, Phys. Rev., 38, 87. [25] LUBIC, K. G., RAY, R., HOVDE, D. C., VESETH, L., and SAYKALLY, R. J., 1989, J. molec. Spectrosc., 134, 21. [26] A copy of the correlation matrix is available on request from the authors. [27] COOPER, D. L., and VESETH, L., 1981, J. chem. Phys., 74, [28] FROSCH, R. A., and FOLEY, H. M., 1952, Phys. Rev., 88, [29] ALBRITTON, D. L., SCHMELTEKOPF, A. L., and ZARE, R. N., 1976, Molecular Spectroscopy Modern Research, Vol. II, edited by K. N. Rao (Academic Press). [30] LEOPOLD, K. R., EVENSON, K. M., COMBEN, E. R., and BROWN, J. M., 1987, J. molec. Spectrosc., 122, 440. [31] HARVEY, J. M. S., 1965, Proc. R. Soc. A, 285, 581. [32] MILLER, H. C., AL-ZA'AL, M., and FARLEY, J. W., 1985, Phys. Rev. Lett., 58, [33] HUBER, K. P., and HERZBERG, G., 1979, Molecular Spectra and Molecular Structure. Vol. IV, Constants of Diatomic Molecules (Van Nostrand Reinhold). [34] COL, J. V., OWRUTSKY, J. C., KEIM, E. R., AGMAN, N. V., HOVDE, D. C., and SAYKALLY, R. J., 1989, J. chem. Phys., 90, 3893.