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Infrared diode laser spectroscopy of the ν2(2+ ← 1−) band of H3O+
335
Chemical Physics 108 (1986) 335-341 North-Holland, Amsterdam
INFRARED DIODE LASER SPECTROSCOPY
OF THE u2(2+ + l-)
BAND OF H,O +
P.B. DAVIES, S.A. JOHNSON Department
of Physical Chemistry,
University of Cumbridge, L.ensfield Roud, Cumbridge CB2 I EP, UK
P.A. HAMILTON Department
of Chemistry,
Queen Mary College, Mile End Road, London El 4NS. UK
and T.J. SEARS Department
of Chemistry,
Brookhaven Nutional Laboratory,
Upton. NY 11973. USA
Received 22 May 1986
Rotational lines in the va = 2 + + 1- “ hot” band of the inversion mode of the oxonium (H,O+ ) ion have been recorded by diode laser absorption spectroscopy. The ion was generated in low pressure gas discharges, and detected using both velocity modulation and modulated hollow cathode techniques. Analysis of the spectra using a simple oblate symmetric top model has allowed the rotational parameters describing the 2+ inversion state to be determined for the first time. The band origin lies at 521.4383(52) cm-‘. These data will be useful in refining the oxonium ion inversion potential function and should aid in the analysis of other bands involving or perturbed by the 2+ level.
1. Introduction
Over the past two years high resolution infrared laser spectroscopy has been remarkably effective in elucidating the structure of gaseous ions. The hydrated proton, HsO+, is a particularly good example of the fruitful collaboration between experiment and theory in this field and a precise structure and rovibrational potential function has been derived for this species [l]. Much of this work has centred on the v, “umbrella” mode of H30+, and the effective potential describing the inversion barrier has recently been determined from analysis of the IR laser spectra of HsO+ and D,O+, fitted to a model hamiltonian [l]. Fig. 1 shows this potential, its associated vibration-inversion levels and the transitions studied so far. These include rotational spectra of the O--O+ lowest inversion transition [2,3]. The barrier height in H30+ is about a third of its value in isoelec-
tronic NH,, and in SiH, (only recently determined [4]). One consequence of this is that the two components of the u2 = 1 + 0 transition are widely separated in HXO+ (526 and 954 cm-‘) and the O--O+ “inversion” spectrum, which lies in the microwave region in NH,, falls in the far infrared (mm) region for H,O+. Most of the high resolution spectroscopic effort so far has concentrated on transitions between the four lowest inversion levels I* and 0 *, and Oka and co-workers [5] have recently collected all the data on these transitions in a critical overall fit. Their results provide the parameters for these lowest levels up to quartic in centrifugal distortion and permit an extension to higher levels through transitions involving the I* and 0 * levels. Extension to these higher levels will enable the determination of a more accurate potential function, and also allows the possibility of investigating Coriolis interaction with other modes i.e. v,(2+)
0301-0104/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
/
P. B. Davies et al. / The ~~(2 + + I -) band
336
25oc
2ooc
2. Experimental
'503
k 0 6 t 5 1000
500
0
+
force field. It has already been pointed out [14] that several other transitions involving v2 levels have measureable intensity in addition to those involving the 0 *, 1 f set including Au, = 2 transitions. Based on theoretical intensity predictions [14] it should be possible to probe levels up to u = 4, well above the top of the barrier, using this type of infrared spectroscopy.
3000
=
of H,O
1
60
I
I
I
90
I
I
I
120
Pldegl
Fig. 1. Fitted inversion potential function for the oxonium ion with r = re fixed showing the lowest vibration levels and the vibrational transitions detected so far in H,O+. The displacement produced by excitation of one quanta of the v4 mode is also indicated schematically.
with ~~(1’). The present work reports the detection and analysis of the 2+ +- l- band of H30+. For ammonia the same band is centred at 629 cm-‘, and was studied first by grating spectrometry [6-81, then, in the last few years, at higher resolution by FTIR [9], and diode laser methods [lo-121. Recent theoretical calculations by Botschwina [13] in which the basis set was increased to over 100 functions have further reduced the difference between experiment [l] and ab initio results for H,O+. The determined barrier heights now agree within 7 cm- ’ [672 (expt) versus 678.9 (ab initio) cm- ‘1 and there is good agreement between geometrical parameters with the exception of r, - rp, the difference between equilibrium and planar O-H distances. It is suggested that further refinement in the experimental potential is feasible and this work is a step in that direction although advances await improvements in the experimental
Absorption spectra of H,O+ were recorded using two complementary spectrometers which are shown schematically in fig. 2. Both use Pb-salt diode lasers supplied by Spectra Physics Inc. At Cambridge, the spectra were recorded in an ac discharge, primarily using the velocity modulation technique introduced by Gudeman and Saykally [15] (fig. 2a). Improvements in the design, compared with the original spectrometer used for H30+ and D,O+ detection [1,16,17], include operating the ac discharge at considerably higher frequencies (20-80 kHz) and higher discharge currents up to 200 mA. The consequent improvements in detectivity (S/N = 2 for a 2 X 10e5 fractional absorption) and generated H,O+ concentrations were important for observation of the relatively weak hot band transitions reported here. An added feature of this spectrometer is the option to detect concentration-modulated species by synchronous detection of laser absorption at 2f. The salient features of the Brookhaven spectrometer have been described previously [1,18]. The ion source in this instrument is a 70 cm long, 3.8 cm diameter, cooled copper hollow cathode (fig. 2b), similar in design to that developed for use in the far-IR by van den Heuvel and Dymanus [19]. Here the hollow cathode is driven by a high voltage, high frequency (2: 10 kHz) transformer fed by an 800 W audio amplifier. With this arrangement the discharge only strikes during that half cycle of the ac in which the central copper electrode is negative with respect to that in the smali side arm. Lifetimes of ions are sufficiently short that efficient concentration modulation at lf occurs on the timescale of the ac. The subsequent amplitude modulation of ion absorption lines can
331
P.B. Davies et al. / The v,(2 + + I -) band of H,O ’ Audio amolifmr
a
f
---_--_
b
1
SiQ.
Lock-in
source
Gas in -5%
Fig. 2. (a) Velocity modulation
cooled
copper
hollow cathode
spectrometer used at Cambridge and (b) hollow cathode discharge source used at Brookhaven.
P.B. Daoies et al. / The vr(2 + + I -) band of H,O +
338
be synchronously detected using a lock-in-amplifier. Diode laser absorption is magnified by multi-passing of the beam through the discharge (20 times, typically), this being much easier to achieve in the wide bore hollow cathode, than for a long, narrow velocity-modulation tube. Lines were detected in the 450-670 cm-’ region on both spectrometers, and calibrated using the accurately known line positions of CO, [20-231, N,O [24], SO, [25] and H,O [21, 26-281. For Brookhaven measurements the calibration accuracy was better than 1 x lop3 cm-‘, this being achieved by simultaneously recording the ion and/or reference gas lines with the interpolating etalon. In Cambridge sequential calibration was employed yielding an accuracy of typically between (1-3)X lop3 cm-‘.
3. Results In the course of earlier work [17] on the l+ +- Oband of the u2 mode of H30+ (us = 525.83 cm-‘) in the region 500-800 cm-‘, many weak lines were observed which could not be assigned to this
f
band. Some of these belong to the l- + l+ band, which has recently been analysed by Oka and co-workers [5,29]. Calculations preceding any experimental result predicted that the 2+ +- lband should be centred in the 510-550 cm-’ region [14,30,31] and possess considerable dipole intensity. Many weak lines were found in this region which appeared to arise from the Q-branch of this band. Initially, the assignment of these and other lines was aided by a prediction by Sears et al. [l] of the form of the 2+ +- 1 - band from a fit of the inversion potential to experimental H30C and D30+ u2 = 0 * and l* vibration-rotation levels using the non-rigid invertor hamiltonian. A band centre near 518 cm-’ was predicted [l] and the line positions generated by the non-rigid inventor model were fitted to a conventional symmetric top formulation to generate oblate symmetric top rotational constants. Using these, several R-branch lines were assigned followed by a quantitative prediction and assignment of the Q-branch. The cycle of refinement was continued by measurement of more R- and Q-branch lines until most of the originally unassigned lines in the 517-525
0.3 % absorption
I
I
R(4,2)
(l++O-)
5212707 521.1355 521i72 O-009
Frequsncyhn-ll
Fig. 3. Scan through the transition using velocity with l/ detection). For from the hollow
R(5,2)
cm-l
--+
band centre of the H90+ v,(Z+ cl-) modulation (first derivative line shapes comparison a portion of the spectrum cathode source is shown inset.
(2+-l-)
------G
.z&Cd(cm-l)
639.2
142
Fig. 4. Scan through two R-branch lines of H,O+ recorded using concentration modulation at 100 kHz (2f) in the “velocity modulated” discharge.
P. B. Davies et al. / The ~~(2 + + I -) band of H,O + Table 1 Observed transition frequencies (cm-‘) band of H30+
in the Y* (2+ + 1- )
Assignment
Observed
10’ (obs. - cak.) a)
WW
386.4885 b, 455.8969 ” 456.9693 478.1001 517.8742 517.9118 517.9457 518.0576 =) 518.1313 518.4153 =) 518.4386 518.861 521.1139 521.1355 521.2164 521.2787 522.452 523.851 ‘) 524.8036 527.0402 542.2598 562.8470 582.5118 583.5451 601.6127 620.1907 638.2497 639.2142 640.8421 643.1653 646.2302 655.515 655.819 656.7576 658.343 660.5833 663.555
- 3.0 - 44.6 0.5 7.1 - 3.0 -11.7 -1.8 - 29.3 - 3.4 47.0 -0.8 -2 2.2 2.8 3.0 2.0 -3 -31 8.7 -1.4 0.9 - 2.2 - 5.6 -4.7 -11.7 -0.5 2.7 4.6 5.5 3.2 -3.7 -7 -11 -0.5 15 8.7 11
P(3,l) V3,2) VW 4(8>7) 4(9,8) Q(7,6) Q(lO,9) 4(6>5) Q(ll,lO) 4(5!4) 4(4,3) 4(2*2) Q(333) Q&l) 4(4,4) 4(7,7) Q(9,9) QWlO) QWJ2) R(O.0) fW1) R(2,l) N2,2) R(3S) R(4,l) W5,l) ~(5~2) R(5,3) R(5,4) R(5,5) R(6,O) R(6,l) W6,2) R(6,3) R(6.4) W6,5)
a) Calculated positions using parameters from table 2. b, Tentative assignment of a line reported in ref. [29]. ‘) Line measurement given zero weight in final fit (table 2).
cm-’ region were incorporated in the fit. A scan showing the central Q-branch region of the spectrum is shown in fig. 3 using velocity modulation from a 5 kHz, 140 mA discharge through a mixture of 600 mTorr HJlO mTorr Oz. The insert in this figure shows part of the same spectrum obtained using the modulated hollow cathode discharge. Fig. 4 illustrates the use of
339
concentration modulation detection (at 2f) in a 50 kHz, 200 mA ac discharge to record one of the R-branch lines. Velocity-modulated first derivative signals of similar amplitude were recorded for this transition (i.e. at lf) but, in this case at least, superior noise reduction was achieved at 2f. A total of thirty-seven lines have so far been assigned to the y2(2+ + l-) band and these are listed in table 1. During the analysis, it became clear that the line reported by Liu and Oka [29] at 386.4885 cm-’ was the P(6, 2) transition of the v,(2+ + l-) band, and so it was included in the final fit. A satisfactory fit of thirty-three of these lines to the normal expression for the parallel band of a symmetric top, including quartic distortion terms, yielded the molecular parameters in table 2. The constants B”, DJ” and Df;, were constrained to the values determined by Liu et al. [5] from a fit of all published H30+ data involving u2 = 0 and 1.
4. Discussion The predicted u2 = 2+ constants derived from the non-rigid invertor model and inversion potential calculated from experimental data on the uz = 0 and 1 levels alone [l] are given in table 2, column 3. Satisfactory agreement with the experimental results determined in this work exists although the centrifugal distortion constants are relatively poorly determined and, unexpectedly, the sign of DiK is found to be positive rather than negative. The uniquely K-dependent constants C and DK cannot be determined from the analysis of allowed transitions in a parallel (AK = 0) band of a symmetric top. Instead two different sources of empirical estimates of these constants for the u2 = 1and 2+ levels are given in table 2 (column 4). Their accuracy is heavily reliant on the accuracy of the same constants calculated for the O+ ground state. In the first method C(O+) and DK(O+) are obtained from a symmetric top fit of O+ levels generated from the non-rigid invertor hamiltonian and the effective inversion potential [l], which itself is based on spectroscopic results for levels up to 1-. The second source of the ground state C
340
P. B. Davies et al. / The vr(2 + + I -) band of H,O +
Table 2 Molecular parameters (cm-‘) Parameter
VO
B” B’
C’-
C”
103D” 103D;
1O’D” JK 103D’ lo’& - D;;) C(O+) C(l_) C(2+) 103D,(O+ 103D,(l
103D,(2+ a) b, ‘) d, e, n
)
derived from analysis of the rz(2+ + 1~ ) band of HsO+
Fitted a,b) this work
Predicted d,
521.4383(52) 10.69741 =) 10.41062(54) 0.06170(33) 0.516 ” 0.1689(96) - 0.587 =) 0.306(19) - 0.568(12)
517.920 10.718 10.497 0.0785 0.94 0.73 -1.19 - 0.85 -0.23 6.1658 6.4037 1.58
- )
)
0.306
Empirical
541, 526 ‘), 540 ‘) 10.66
0.72 - 1.07
5.96 =), 6.1658 d, 6.09 O, 6.2958 n 6.15 g’, 6.3575 s) 1.5 ‘), 1.58 d, 0.1 0, 0.20 n -0.5 s), - 0.37 8)
Overall standard deviation of fit = 0.006 cm-’ (33 lines, table 1). Figures in parentheses are two standard errors in units of the last digit quoted. Constrained to values determined in ref. [5]. Derived from information in ref. [l]. From zero-point structure determined in ref. [l]. Ref. (51. g, From present fit. h, Ref. [32] i, Ref. [30], unless stated otherwise. ‘) Ref. [14].
constant is the experimentally determined zeropoint structure [l]. The perpendicular v3 band analysis [32] gives an alternative starting value for DK(O+). Using either estimates of C(O+) and &(O+) u2 = l- constants can then be determined from the parameter differences reported by Liu et al. [5] which can finally be combined with the present work to generate u2 = 2’ constants. This procedure gives a negative D,(2+) constant for both empirical approaches (table 2). Like the negative DJK(2+) this is unusual but may only reflect the uncertainty in the derived value of D, (o+). Although the quality of the v2(2+ + 1-) band fit was satisfactory (rms error of 0.006 cm-r), four of the lines were omitted as they fitted poorly. This is quite possibly the result of bad calibration, but an alternative explanation of this and the unexpected signs of the distortion constants is that a perturbation is operating - i.e. a Coriolis interaction between nearby u2, u, = 2+, 0’ and O-, 1’ levels. The approximate positions of the lowest few u, levels are indicated schematically in fig. 1.
Ab initio i,
6.05 6.24 1.36 0.44
Ir) Ref. 1311.
The 0 *, 1’ term values are derived from ab initio results [30]. The same interaction has been extensively investigated for ammonia [8,9,33-501, where it has had to be incorporated to explain the structure, in particular, of the overlapping u2(2+ + O-) and ~~(0 * + 0 *) bands. Following the completion of this work the analysis of diode laser spectra of the v4 fundamental of H,O+ has been reported [51] and the existence of this perturbation can now be investigated further. The present measurements extend the data on H,O+ vibration-rotation levels to = 2400 cm-’ above the potential minimum and 1600 cm-’ above the inversion barrier. A definitive set of parameters for the v2 mode of H30f up to u = 2 would require further measurements on the high J and K lines of all bands detected so far, on P-branch lines of the present band, and on the 2- + 2+ transition, which is predicted to have measurable intensity and also lies between 500 and 600 cm-‘. This could be used to further refine the inversion potential.
P. B. Davies et al. / The v,(2 + + I -) band of H,O +
Acknowledgement Work at Brookhaven National Laboratory was carried out under contract DE-AC02-76CHOOO16 with the US Department of Energy supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. At Cambridge generous equipment grants were provided by the Science and Engineering Research Council and the Royal Society. We are grateful to Professor P. Botschwina for communicating his calculations on H30+ to us prior to publication.
References [l] T.J. Sears, P.R. Bunker, P.B. Davies, S.A. Johnson and V. Spirko, J. Chem. Phys. 83 (1985) 2676. [2] G.M. Plummer, E. Herbst and F.C. De Lucia, J. Chem. Phys. 83 (1985) 1428. [3] M. Bogey, C. Demuynck, M. Denis and J.L. Destombes, Astron. Astrophys. 148 (1985) Lll. [4] C. Yamada and E. Hirota, Phys. Rev. Letters 56 (1986) 923. [5] D.-J. Liu, T. Oka and T.J. Sears, J. Chem. Phys. 84 (1986) 1312. [6] H. Sheng, E.F. Barker and D.M. Dennison, Phys. Rev. 60 (1941) 786. [7] D.L. Wood, E.E. Bell and H.H. Nielsen, Proc. Nat. Acad. Sci. US 36 (1950) 497. [8] J.S. Garing, H.H. Nielsen and K.N. Rao, J. Mol. Spectry. 3 (1959) 496. [9] G. Di Lonardo, L. Fusina, A. Trombetti and I.M. Mills, J. Mol. Spectry. 92 (1982) 298. [lo] G. Baldacchini, S. Marchetti and V. Montelatici, J. Mol. Spectry. 103 (1984) 257. [ll] J. Hermanussen, A. Bizzari and G. Baldacchini, Report ENEA RT/TIB/84/40. [12] G. Baldacchini, S. Marchetti, V. Montelatici, G. Buffa and 0. Tarrini, J. Chem. Phys. 83 (1985) 4975. [13] P. Botschwina, J. Chem. Phys. 84 (1986) 6523. [14] P. Botschwina, P. Rosmus and E.-A. Reinsch, Chem. Phys. Letters 102 (1983) 299. 1151 C.S. Gudeman and R.J. Saykally, Ann. Rev. Phys. Chem. 35 (1984) 387. [16] P.B. Davies, P.A. Hamilton and S.A. Johnson, Astron. Astrophys. 141 (1984) L9. [17] P.B. Davies, P.A. Hamilton and S.A. Johnson, J. Opt. Sot. Am. B2 (1985) 794. [18] T.J. Sears, J. Opt. Sot. Am. B2 (1985) 786. (191 F.C. van den Heuvel and A. Dymanus, Chem. Phys. Letters 92 (1982) 219. [20] R. Paso, J. Kauppinen and R. Anttila, J. Mol. Spectry. 79 (1980) 236.
1211J. Kauppinen,
341
K. Jolma and V.-M. Homeman, Appl. Opt. 21 (1982) 3332. (221 K. Jolma, J. Kauppinen and V.-M. Homeman, J. Mol. Spectry. 101 (1983) 300. v31 K. Jolma, J. Mol. Spectry. 111 (1985) 211. and V.-M. Homeman, J. Mol. 1241 K. Jolma, J. Kauppinen Spectry. 101 (1983) 278. v51 S.C. Foster and J.W.C. Johns, N.R.C. Canada, private communication. T. Karkkainen and E. Kyro, J. Mol. Spec1261 J. Kauppinen, try. 71 (1978) 15. 1271 J. Kauppinen and E. KyrB, J. Mol. Spectry. 84 (1980) 405. and R.A. Toth, Selected WI J.-M. Flaud, C. Camy-Peyret constants: water vapour line parameters from microwave to medium infrared (Pergamon Press, Oxford, 1981). 1291 D.-J. Liu and T. Oka, Phys. Rev. Letters 54 (1985) 1787. 1301 P.R. Bunker, W.P. Kraemer and V. spirko, J. Mol. Spectry. 101 (1983) 180. [311 N. Shida, K. Tanaka and K. Ohno, Chem. Phys. Letters 104 (1984) 575. 1321 M.H. Begemann and R.J. Saykally, J. Chem. Phys. 82 (1985) 3570. 1331 E.A. Cohen and R.L. Poynter, J. Mol. Spectry. 53 (1974) 131. 1341 J.W.C. Johns, A.R.W. McKellar and A. Trombetti, J. Mol. SpFtry. 55 (1975) 131. 1351 V. Spirko, J.M.R. Stone and D. PapouSek. J. Mol. Spectry. 60 (1976) 159. 1361 W.K. Bischel, P.J. Kelly and C.K. Rhodes, Phys. Rev. Al3 (1976) 1829. 1371 L.A. Farrow and R.E. Richton, J. Chem. Phys. 70 (1979) 2166. [38] S. Urban, V. Spirko, D. Papousek, R.S. McDowell, N.G. Nereson, S.P. Belov, L.I. Gershstein, A.V. Maslovskij, A.F. Krupnov, J. Curtis and K.N. Rao, J. Mol. Spectry. 79 (1980) 455. [39] E.A. Cohen, J. Mol. Spectry. 79 (1980) 496. [40] W.H. Weber and R.W. Terhune, Opt. Letters 6 (1981) 455. [41] H. Sasada, Y. Hasegawa, T. Amano and T. Shimizu, J. Mol. Spectry. 96 (1982) 106. [42] W.H. Weber and E.A. Cohen, Opt. Letters 8 (1983) 488. [43] W.H. Weber and R.W. Terhune, J. Chem. Phys. 78 (1983) 6422. [44] E.A. Cohen, W.H. Weber, R.L. Poynter and J.S. Margolis, MO!. Phys. 50 (1983) 727. (451 V. Spirko, J. Mol. Spectry. 101 (1983) 30. [46] S. Urban, D. PapouZek, V.M. Devy, B. Fridovich, R. DCunha and K.N. Rao, J. Mol. Spectry. 106 (1984) 38. [47] S. Urban, R. DCunha and K.N. Rao, J. Mol. Spectry. 106 (1984) 64. [48] S. Urban, R. D’Cunha, K.N. Rao and D. PapouSek, Can. J. Phys. 62 (1984) 1775. [49] W.H. Weber, J. Mol. Spectry. 107 (1984) 405. [50] S. Urban, R. D’Cunha, K.N. Rao and D. Papougek, J. Mol. Spectry. 111 (1985) 361. [51] M. Gruebele, M. Polak and R.J. Saykally, 41st Annual Symposium on Molecular Spectroscopy, Columbus OH, June 1986, paper FA 12.
Chemical Physics 108 (1986) 335-341 North-Holland, Amsterdam
INFRARED DIODE LASER SPECTROSCOPY
OF THE u2(2+ + l-)
BAND OF H,O +
P.B. DAVIES, S.A. JOHNSON Department
of Physical Chemistry,
University of Cumbridge, L.ensfield Roud, Cumbridge CB2 I EP, UK
P.A. HAMILTON Department
of Chemistry,
Queen Mary College, Mile End Road, London El 4NS. UK
and T.J. SEARS Department
of Chemistry,
Brookhaven Nutional Laboratory,
Upton. NY 11973. USA
Received 22 May 1986
Rotational lines in the va = 2 + + 1- “ hot” band of the inversion mode of the oxonium (H,O+ ) ion have been recorded by diode laser absorption spectroscopy. The ion was generated in low pressure gas discharges, and detected using both velocity modulation and modulated hollow cathode techniques. Analysis of the spectra using a simple oblate symmetric top model has allowed the rotational parameters describing the 2+ inversion state to be determined for the first time. The band origin lies at 521.4383(52) cm-‘. These data will be useful in refining the oxonium ion inversion potential function and should aid in the analysis of other bands involving or perturbed by the 2+ level.
1. Introduction
Over the past two years high resolution infrared laser spectroscopy has been remarkably effective in elucidating the structure of gaseous ions. The hydrated proton, HsO+, is a particularly good example of the fruitful collaboration between experiment and theory in this field and a precise structure and rovibrational potential function has been derived for this species [l]. Much of this work has centred on the v, “umbrella” mode of H30+, and the effective potential describing the inversion barrier has recently been determined from analysis of the IR laser spectra of HsO+ and D,O+, fitted to a model hamiltonian [l]. Fig. 1 shows this potential, its associated vibration-inversion levels and the transitions studied so far. These include rotational spectra of the O--O+ lowest inversion transition [2,3]. The barrier height in H30+ is about a third of its value in isoelec-
tronic NH,, and in SiH, (only recently determined [4]). One consequence of this is that the two components of the u2 = 1 + 0 transition are widely separated in HXO+ (526 and 954 cm-‘) and the O--O+ “inversion” spectrum, which lies in the microwave region in NH,, falls in the far infrared (mm) region for H,O+. Most of the high resolution spectroscopic effort so far has concentrated on transitions between the four lowest inversion levels I* and 0 *, and Oka and co-workers [5] have recently collected all the data on these transitions in a critical overall fit. Their results provide the parameters for these lowest levels up to quartic in centrifugal distortion and permit an extension to higher levels through transitions involving the I* and 0 * levels. Extension to these higher levels will enable the determination of a more accurate potential function, and also allows the possibility of investigating Coriolis interaction with other modes i.e. v,(2+)
0301-0104/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
/
P. B. Davies et al. / The ~~(2 + + I -) band
336
25oc
2ooc
2. Experimental
'503
k 0 6 t 5 1000
500
0
+
force field. It has already been pointed out [14] that several other transitions involving v2 levels have measureable intensity in addition to those involving the 0 *, 1 f set including Au, = 2 transitions. Based on theoretical intensity predictions [14] it should be possible to probe levels up to u = 4, well above the top of the barrier, using this type of infrared spectroscopy.
3000
=
of H,O
1
60
I
I
I
90
I
I
I
120
Pldegl
Fig. 1. Fitted inversion potential function for the oxonium ion with r = re fixed showing the lowest vibration levels and the vibrational transitions detected so far in H,O+. The displacement produced by excitation of one quanta of the v4 mode is also indicated schematically.
with ~~(1’). The present work reports the detection and analysis of the 2+ +- l- band of H30+. For ammonia the same band is centred at 629 cm-‘, and was studied first by grating spectrometry [6-81, then, in the last few years, at higher resolution by FTIR [9], and diode laser methods [lo-121. Recent theoretical calculations by Botschwina [13] in which the basis set was increased to over 100 functions have further reduced the difference between experiment [l] and ab initio results for H,O+. The determined barrier heights now agree within 7 cm- ’ [672 (expt) versus 678.9 (ab initio) cm- ‘1 and there is good agreement between geometrical parameters with the exception of r, - rp, the difference between equilibrium and planar O-H distances. It is suggested that further refinement in the experimental potential is feasible and this work is a step in that direction although advances await improvements in the experimental
Absorption spectra of H,O+ were recorded using two complementary spectrometers which are shown schematically in fig. 2. Both use Pb-salt diode lasers supplied by Spectra Physics Inc. At Cambridge, the spectra were recorded in an ac discharge, primarily using the velocity modulation technique introduced by Gudeman and Saykally [15] (fig. 2a). Improvements in the design, compared with the original spectrometer used for H30+ and D,O+ detection [1,16,17], include operating the ac discharge at considerably higher frequencies (20-80 kHz) and higher discharge currents up to 200 mA. The consequent improvements in detectivity (S/N = 2 for a 2 X 10e5 fractional absorption) and generated H,O+ concentrations were important for observation of the relatively weak hot band transitions reported here. An added feature of this spectrometer is the option to detect concentration-modulated species by synchronous detection of laser absorption at 2f. The salient features of the Brookhaven spectrometer have been described previously [1,18]. The ion source in this instrument is a 70 cm long, 3.8 cm diameter, cooled copper hollow cathode (fig. 2b), similar in design to that developed for use in the far-IR by van den Heuvel and Dymanus [19]. Here the hollow cathode is driven by a high voltage, high frequency (2: 10 kHz) transformer fed by an 800 W audio amplifier. With this arrangement the discharge only strikes during that half cycle of the ac in which the central copper electrode is negative with respect to that in the smali side arm. Lifetimes of ions are sufficiently short that efficient concentration modulation at lf occurs on the timescale of the ac. The subsequent amplitude modulation of ion absorption lines can
331
P.B. Davies et al. / The v,(2 + + I -) band of H,O ’ Audio amolifmr
a
f
---_--_
b
1
SiQ.
Lock-in
source
Gas in -5%
Fig. 2. (a) Velocity modulation
cooled
copper
hollow cathode
spectrometer used at Cambridge and (b) hollow cathode discharge source used at Brookhaven.
P.B. Daoies et al. / The vr(2 + + I -) band of H,O +
338
be synchronously detected using a lock-in-amplifier. Diode laser absorption is magnified by multi-passing of the beam through the discharge (20 times, typically), this being much easier to achieve in the wide bore hollow cathode, than for a long, narrow velocity-modulation tube. Lines were detected in the 450-670 cm-’ region on both spectrometers, and calibrated using the accurately known line positions of CO, [20-231, N,O [24], SO, [25] and H,O [21, 26-281. For Brookhaven measurements the calibration accuracy was better than 1 x lop3 cm-‘, this being achieved by simultaneously recording the ion and/or reference gas lines with the interpolating etalon. In Cambridge sequential calibration was employed yielding an accuracy of typically between (1-3)X lop3 cm-‘.
3. Results In the course of earlier work [17] on the l+ +- Oband of the u2 mode of H30+ (us = 525.83 cm-‘) in the region 500-800 cm-‘, many weak lines were observed which could not be assigned to this
f
band. Some of these belong to the l- + l+ band, which has recently been analysed by Oka and co-workers [5,29]. Calculations preceding any experimental result predicted that the 2+ +- lband should be centred in the 510-550 cm-’ region [14,30,31] and possess considerable dipole intensity. Many weak lines were found in this region which appeared to arise from the Q-branch of this band. Initially, the assignment of these and other lines was aided by a prediction by Sears et al. [l] of the form of the 2+ +- 1 - band from a fit of the inversion potential to experimental H30C and D30+ u2 = 0 * and l* vibration-rotation levels using the non-rigid invertor hamiltonian. A band centre near 518 cm-’ was predicted [l] and the line positions generated by the non-rigid inventor model were fitted to a conventional symmetric top formulation to generate oblate symmetric top rotational constants. Using these, several R-branch lines were assigned followed by a quantitative prediction and assignment of the Q-branch. The cycle of refinement was continued by measurement of more R- and Q-branch lines until most of the originally unassigned lines in the 517-525
0.3 % absorption
I
I
R(4,2)
(l++O-)
5212707 521.1355 521i72 O-009
Frequsncyhn-ll
Fig. 3. Scan through the transition using velocity with l/ detection). For from the hollow
R(5,2)
cm-l
--+
band centre of the H90+ v,(Z+ cl-) modulation (first derivative line shapes comparison a portion of the spectrum cathode source is shown inset.
(2+-l-)
------G
.z&Cd(cm-l)
639.2
142
Fig. 4. Scan through two R-branch lines of H,O+ recorded using concentration modulation at 100 kHz (2f) in the “velocity modulated” discharge.
P. B. Davies et al. / The ~~(2 + + I -) band of H,O + Table 1 Observed transition frequencies (cm-‘) band of H30+
in the Y* (2+ + 1- )
Assignment
Observed
10’ (obs. - cak.) a)
WW
386.4885 b, 455.8969 ” 456.9693 478.1001 517.8742 517.9118 517.9457 518.0576 =) 518.1313 518.4153 =) 518.4386 518.861 521.1139 521.1355 521.2164 521.2787 522.452 523.851 ‘) 524.8036 527.0402 542.2598 562.8470 582.5118 583.5451 601.6127 620.1907 638.2497 639.2142 640.8421 643.1653 646.2302 655.515 655.819 656.7576 658.343 660.5833 663.555
- 3.0 - 44.6 0.5 7.1 - 3.0 -11.7 -1.8 - 29.3 - 3.4 47.0 -0.8 -2 2.2 2.8 3.0 2.0 -3 -31 8.7 -1.4 0.9 - 2.2 - 5.6 -4.7 -11.7 -0.5 2.7 4.6 5.5 3.2 -3.7 -7 -11 -0.5 15 8.7 11
P(3,l) V3,2) VW 4(8>7) 4(9,8) Q(7,6) Q(lO,9) 4(6>5) Q(ll,lO) 4(5!4) 4(4,3) 4(2*2) Q(333) Q&l) 4(4,4) 4(7,7) Q(9,9) QWlO) QWJ2) R(O.0) fW1) R(2,l) N2,2) R(3S) R(4,l) W5,l) ~(5~2) R(5,3) R(5,4) R(5,5) R(6,O) R(6,l) W6,2) R(6,3) R(6.4) W6,5)
a) Calculated positions using parameters from table 2. b, Tentative assignment of a line reported in ref. [29]. ‘) Line measurement given zero weight in final fit (table 2).
cm-’ region were incorporated in the fit. A scan showing the central Q-branch region of the spectrum is shown in fig. 3 using velocity modulation from a 5 kHz, 140 mA discharge through a mixture of 600 mTorr HJlO mTorr Oz. The insert in this figure shows part of the same spectrum obtained using the modulated hollow cathode discharge. Fig. 4 illustrates the use of
339
concentration modulation detection (at 2f) in a 50 kHz, 200 mA ac discharge to record one of the R-branch lines. Velocity-modulated first derivative signals of similar amplitude were recorded for this transition (i.e. at lf) but, in this case at least, superior noise reduction was achieved at 2f. A total of thirty-seven lines have so far been assigned to the y2(2+ + l-) band and these are listed in table 1. During the analysis, it became clear that the line reported by Liu and Oka [29] at 386.4885 cm-’ was the P(6, 2) transition of the v,(2+ + l-) band, and so it was included in the final fit. A satisfactory fit of thirty-three of these lines to the normal expression for the parallel band of a symmetric top, including quartic distortion terms, yielded the molecular parameters in table 2. The constants B”, DJ” and Df;, were constrained to the values determined by Liu et al. [5] from a fit of all published H30+ data involving u2 = 0 and 1.
4. Discussion The predicted u2 = 2+ constants derived from the non-rigid invertor model and inversion potential calculated from experimental data on the uz = 0 and 1 levels alone [l] are given in table 2, column 3. Satisfactory agreement with the experimental results determined in this work exists although the centrifugal distortion constants are relatively poorly determined and, unexpectedly, the sign of DiK is found to be positive rather than negative. The uniquely K-dependent constants C and DK cannot be determined from the analysis of allowed transitions in a parallel (AK = 0) band of a symmetric top. Instead two different sources of empirical estimates of these constants for the u2 = 1and 2+ levels are given in table 2 (column 4). Their accuracy is heavily reliant on the accuracy of the same constants calculated for the O+ ground state. In the first method C(O+) and DK(O+) are obtained from a symmetric top fit of O+ levels generated from the non-rigid invertor hamiltonian and the effective inversion potential [l], which itself is based on spectroscopic results for levels up to 1-. The second source of the ground state C
340
P. B. Davies et al. / The vr(2 + + I -) band of H,O +
Table 2 Molecular parameters (cm-‘) Parameter
VO
B” B’
C’-
C”
103D” 103D;
1O’D” JK 103D’ lo’& - D;;) C(O+) C(l_) C(2+) 103D,(O+ 103D,(l
103D,(2+ a) b, ‘) d, e, n
)
derived from analysis of the rz(2+ + 1~ ) band of HsO+
Fitted a,b) this work
Predicted d,
521.4383(52) 10.69741 =) 10.41062(54) 0.06170(33) 0.516 ” 0.1689(96) - 0.587 =) 0.306(19) - 0.568(12)
517.920 10.718 10.497 0.0785 0.94 0.73 -1.19 - 0.85 -0.23 6.1658 6.4037 1.58
- )
)
0.306
Empirical
541, 526 ‘), 540 ‘) 10.66
0.72 - 1.07
5.96 =), 6.1658 d, 6.09 O, 6.2958 n 6.15 g’, 6.3575 s) 1.5 ‘), 1.58 d, 0.1 0, 0.20 n -0.5 s), - 0.37 8)
Overall standard deviation of fit = 0.006 cm-’ (33 lines, table 1). Figures in parentheses are two standard errors in units of the last digit quoted. Constrained to values determined in ref. [5]. Derived from information in ref. [l]. From zero-point structure determined in ref. [l]. Ref. (51. g, From present fit. h, Ref. [32] i, Ref. [30], unless stated otherwise. ‘) Ref. [14].
constant is the experimentally determined zeropoint structure [l]. The perpendicular v3 band analysis [32] gives an alternative starting value for DK(O+). Using either estimates of C(O+) and &(O+) u2 = l- constants can then be determined from the parameter differences reported by Liu et al. [5] which can finally be combined with the present work to generate u2 = 2’ constants. This procedure gives a negative D,(2+) constant for both empirical approaches (table 2). Like the negative DJK(2+) this is unusual but may only reflect the uncertainty in the derived value of D, (o+). Although the quality of the v2(2+ + 1-) band fit was satisfactory (rms error of 0.006 cm-r), four of the lines were omitted as they fitted poorly. This is quite possibly the result of bad calibration, but an alternative explanation of this and the unexpected signs of the distortion constants is that a perturbation is operating - i.e. a Coriolis interaction between nearby u2, u, = 2+, 0’ and O-, 1’ levels. The approximate positions of the lowest few u, levels are indicated schematically in fig. 1.
Ab initio i,
6.05 6.24 1.36 0.44
Ir) Ref. 1311.
The 0 *, 1’ term values are derived from ab initio results [30]. The same interaction has been extensively investigated for ammonia [8,9,33-501, where it has had to be incorporated to explain the structure, in particular, of the overlapping u2(2+ + O-) and ~~(0 * + 0 *) bands. Following the completion of this work the analysis of diode laser spectra of the v4 fundamental of H,O+ has been reported [51] and the existence of this perturbation can now be investigated further. The present measurements extend the data on H,O+ vibration-rotation levels to = 2400 cm-’ above the potential minimum and 1600 cm-’ above the inversion barrier. A definitive set of parameters for the v2 mode of H30f up to u = 2 would require further measurements on the high J and K lines of all bands detected so far, on P-branch lines of the present band, and on the 2- + 2+ transition, which is predicted to have measurable intensity and also lies between 500 and 600 cm-‘. This could be used to further refine the inversion potential.
P. B. Davies et al. / The v,(2 + + I -) band of H,O +
Acknowledgement Work at Brookhaven National Laboratory was carried out under contract DE-AC02-76CHOOO16 with the US Department of Energy supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. At Cambridge generous equipment grants were provided by the Science and Engineering Research Council and the Royal Society. We are grateful to Professor P. Botschwina for communicating his calculations on H30+ to us prior to publication.
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