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MOLECULARPHYSICS, 1989, VOL. 66, No. 6, 1193-1202
Velocity modulation infrared laser spectroscopy of molecular ions The v4 band of ammonium by M A R K POLAK, MARTIN GRUEBELE, BRUCE W. DEKOCK and RICHARD J. SAYKALLY Department of Chemistry, University of California, Berkeley, California 94720, U.S.A. (Received 15 November 1988; accepted 18 November 1988)
We have measured 62 lines in the v4 band of the ammonium ion (NH~) using infrared diode laser velocity modulation spectroscopy of a hydrogen/ ammonia discharge. The transitions were fitted to a fourth order spherical rotor hamiltonian yielding v4 = 1447.2158(50) cm- 1, B4 _- 5.85121(24)cm- 1 and 2B 4 (4 = 5.3757(11)cm- 1. As in methane, the v4 band is strongly perturbed by the higher frequency v2 band. A comparison of the measured molecular properties with ab initio calculations is given. 1.
As one of the most fundamental molecules in chemistry and biology, the ammonium ion has been the subject of many experimental and theoretical studies examining its structural and dynamical properties. Very recently, NH~ and its deuterated analogs, NH3 D§ and ND~, have been investigated in detail by high resolution infrared laser spectroscopy. The first detailed studies of this ion in the gas phase were done simultaneously by the Oka [13 and Saykally 1-2] groups using velocity modulation spectroscopy of discharges. In these studies, the v3 band (triply degenerate stretch) was measured near 3350cm-1, its rotational structure confirming the postulated tetrahedral geometry of the molecule. Sch~ifer, Saykally and Robiette [33 analysed a large number of transitions in terms of a sixth order spherical rotor rovibrational hamiltonian, but the AR = 0 selection rule did not permit an independent determination of the rotational constants B o and B 3 o r the Coriolis parameter ~3. Consequently, a precise molecular structure was not extractable from that analysis. Subsequently two different approaches have been taken to deduce the molecular structure of NH~: isotopic substitution and detection of forbidden transitions. Nakanaga and Amano  have measured the v4 stretching band of NH3D +, and obtained B o for the symmetric top. The v4 mode is the nondegenerate vibration which results from the splitting of triply degenerate v 3 of NH~ in the lower symmetry isotopomer. This directly yielded the zero point averaged (ro) N - H bond distance, permitting an estimate of the equilibrium bond length for NH~ to be made. Since NH3 D§ has a permanent dipole moment ('-'0.26D), this work also provided predictions which could facilitate the detection of interstellar NH3D + in the millimeter or submillimeter wave region. Taking a different approach, Crofton and Oka [53 measured 24 forbidden transitions (AR ~ 0) in the v3 band of NH~. By fitting combination differences, the ground state values of B, D and D t w e r e determined independently, permitting the determination of B 3 , ~3 and the zero point (ro) 0026-8976/89 $3.00 9 1989 Taylor & Francis Ltd
M. Polak et al.
structure of ammonium. In addition, Crofton and Oka  observed the allowed transitions in the v3 band of ND~. None of the experimental work performed thus far has examined the bending vibrations of NH~ or its isotopomers. While quantum chemists have made great progress in predicting structures and stretching frequencies of polyatomic ions with high accuracy, the reliability of ab initio calculations for bending vibrations remains poorly tested. The only bending vibrations of non-linear ions studied with high resolution are those of H~- , H2C1§ , HaO + [8, 9], and their isotopomers. NH~ has been the subject of numerous ab initio calculations [10-13], however the accuracy of the bending frequencies has not yet been assessed. In the earliest high quality ab initio calculations [10-12], harmonic frequencies of all the NH~ vibrational modes were calculated, while anharmonic frequencies for bends and stretches were only estimated through empirical scaling procedures. More recently, Botschwina  has computed a pointwise potential surface to calculate directly anharmonic frequencies in a more rigorous fashion; however, the calculation was only carried out for the vl symmetric stretch. Such direct calculations of anharmonic bending frequencies are much more demanding than the corresponding calculations on stretching vibrations, in that they require a fairly rigorous treatment of the potential surface. The availability of experimental frequencies for more complex molecules such as NH~ should prove useful as a benchmark for future detailed calculations of the bending modes. In another context, condensed phase spectroscopy of both the bending and stretching vibrations of ammonium have been an important probe of hydrogen bonding and lattice dynamics [14, 15]. In such studies, various lattice effects can be characterized by the way in which they perturb the spectrum of the free ion. Clearly, direct measurement of spectroscopic properties of the isolated ion are needed to interpret fully such phenomena. In this work we report the measurement and analysis of the allowed transitions of the triply degenerate v4 bending vibration of NH~-. The spectrum was observed with a diode laser using velocity modulation spectroscopy of an NHa/H 2 discharge. Transitions up to J = 10 were observed and fitted to a fourth order spherical rotor hamiltonian with a standard deviation equal to twice the experimental uncertainty. This large standard deviation of the fit is due to perturbations of excited v4 states by the v2 vibration.
2. Experimental The diode laser velocity modulation spectrometer used in earlier work  has been modified considerably and is illustrated in figure 1. As in the older design, radiation is provided by a Laser Analytics LS-3 diode laser system and is passed through a 1 cm bore 1 metre long water cooled glass discharge cell. Mode selection is subsequently accomplished with a 0.25metre monochromator containing a diffraction grating blazed for 10microns. The monochromator is placed after the discharge in order to filter infrared and visible radiation emitted by the plasma. NaC1 beamsplitters are then used to couple about 10 per cent of the beam to a solid Ge etalon and to a gas reference cell. The etalon is used for relative frequency calibration, and the reference gases provide an absolute frequency reference. Three liquid nitrogen cooled H g : C d : T e detectors are used to detect the beams; the sample beam detector can detect a fractional absorbance of 1 part in 105 at 25 kHz
The v4 band of ammonium to P D P - I I
11 L _ _
i Figure 1. New version of the Berkeley diode laser velocity modulation absorption spectrometer. TDL, tunable diode laser; CTS, cryogenic temperature stabilizer; LCM, laser control module; fm, fm signal generator; PA, Pre-amplifier; LIA, lock-in amplifier. using a 100msec time constant. The reference gas and etalon signals are simultaneously detected by applying a small modulation to the laser current, resulting in a relatively low index frequency modulation, and by demodulation with lock-in amplifiers. The modulation amplitude is kept sufficiently small for there to be no apparent broadening of the velocity modulation signals. This triple detection scheme is the most important improvement to the spectrometer. Formerly the three measurements were performed in succession, which was more time consuming and resulted in measurement errors due to drifts in laser temperature and current. As in the previous work on ammonium I-2] the water cooled discharge plasma consisted of 1 Torr H2 and 100mTorr N H 3 . The plasma was driven at 25 kHz and 500 Watts resulting in a current of 500 mA. The Doppler modulated ion absorption signals were lock-in detected at the discharge frequency 1,17]. Approximately half of the assigned transitions were detected with the new spectrometer described above; the rest were measured on the older velocity modulation apparatus. Four diodes were required to observe the entire v4 spectrum, and signal to noise ratios ranged from 10 to 100 for the assigned transitions. The frequencies were calibrated with N H 3 1-18] to a precision of 0.003 c m - 1.
3. Assignment and analysis In the discussion that follows, we use the conventions of Hougen 1-19] for labelling the energy levels and the nomenclature conventions of Robiette et al. 1-20] for the molecular constants. In order to analyse the spectrum, a computer program
M. Polak et al.
[ i 1450
Frequency / c m - I Calculated
,, ,I I,Ib 1400
Frequency/em -1 Figure 2. A computer representation of the observed and calculated spectra of the v4 band of NH~. Calculated intensities at 400 K were used in both plots, and the plot of the observed spectrum contains only assigned lines. was developed to fit the transitions to the fourth order vibration-rotation spherical rotor hamiltonian developed by Hecht  and Moret-Bailley  and systemized by Robiette et al. . Matrix elements are calculated in the I J - IRKR) basis (R = J - l, where l = vibrational angular momentum), using formulae tabulated by Hecht  and corrected versions o f those tabulated by Susskind . The accuracy of the matrix elements was verified by independent calculation using the vibrational and rotational reduced matrix elements derived by Hecht  and standard angular momentum coupling techniques. For each J, the upper and lower state matrices are Wang transformed, and factored into their DZd symmetry components. The matrices are diagonalized and eigenvalues are assigned symmetry labels as shown by Dorney and Watson , using Hougen's labelling conventions for the upper state. The program can also be used to obtain eigenvectors and calculate intensities as described in . Assignment of the spectrum was complicated by three difficulties: lack of combination differences, incomplete coverage of the diode laser and perturbations by the v2 band. Because of the spherical rotor AR = 0 selection rule, none of the allowed transitions have common upper states. Not only does this preclude separation of upper and lower state constants, but it prevents use of previously assigned bands in assigning the spectrum. Incomplete spectral coverage, the most difficult aspect of analysing diode laser spectra, is a particular problem because of the v2 band perturbation. The Coriolis perturbation with the v2 vibration causes a dramatic increase
The v4 band o f ammonium
in the tetrahedral splittings of the v4 upper state. Since the diodes have 0.5-1.5 c m - 1 regions of single mode tunability, this meant very few single J multiplets were small enough to appear in one mode. The standard technique of assigning such spectra is the recognition of patterns in these multiplets, in this case by comparison with the v4 band of methane . Only the R branch of the spectrum (see figure 2) had sufficiently small splittings to permit such simple pattern recognition, although the multiplets already span more than 1 c m - 1 at R-- (5). The R branch multiplets were the key to assigning the spectrum. Recognition of intensity and spacing patterns in R - ( 2 ) , R - ( 6 ) (which spanned two diode laser modes) and part of R - ( 8 ) , resulted in the first assignment and fit. R - ( 5 ) was subsequently measured, and a fit of these lines yielded the first predictions of the P branch. These predictions were still in error by 2 cm-1 even at the low J value of the P + (4) transitions, but an assignment of the two lines near 1415 cm-1 (see table 1) was made based on spacing and relative intensities. The rest of the P branch was then easily predicted and fitted. The most difficult part of the assignment involved the Q branch. It was assigned through a combination of trial and error, comparison with CH4, and through use of measured relative intensities. Although accurate intensity measurements were not performed, relative intensities within a single scan were reliable. Figure 3 shows a portion of the Q branch where the frequencies and relative intensities have been fully accounted for. Finally, the assignment was verified by our ability to assign all of the strong transitions (signal to noise ratio > 20) that were measured within the range of the fit, and by being able to observe all of the predicted lines that were searched for. A total of 62 lines have been fitted to the fourth order spherical rotor hamiltonian. The ground state constants were fixed to those obtained by Crofton and Oka ; however, our own fits of their data indicate that the sign of D was misprinted in their paper, and this has been corrected in the present analysis. The observed transitions are tabulated in table 1 and the results of the fit are presented in table 2. The R branch extends only to J = 8 because of a cutoff in diode coverage. Although the Q and P branches were fitted only up to J = 10 and J = 9 respectively, if either of these branches was fitted with only the R branch, assignments could be extended to higher J. However, when these assignments were included in the entire fit, the quality of the fit became drastically worse. This is due to the Coriolis interaction with v2, and these higher J transitions were omitted from the fit. The parameters H, H4t and G244 were not determinable from the fit, and have been fixed at zero. The other highest order terms were clearly needed both to improve the fit, and to accurately predict high J lines during the assignment process. The constants obtained from the fit are similar in magnitude and sign to the corresponding constants in methane . The standard deviation of the fit is 0.006 c m - 1, about twice the measurement uncertainty. The existence of experimental ground state parameters permitted accurate prediction of the v4 forbidden ( A R ~ 0) transitions and their intensities. The most intense of these transitions are reduced by a factor of 100 from the strongest allowed transitions. Since the maximum signal-to-noise ratio for the allowed transitions was 100, the forbidden transitions should be at the threshold of our detectivity. Despite having searched over many of these transitions, they were not evident in any of the spectra. About 50 weak unassigned lines have been observed, mostly in the region of the P branch. Most likely they are due to both high-J Q branch transitions and hot band transitions.
M. P o l a k et al.
Table 1. Observed transitions (cm -1) in the v4 band of ammonium. Residuals are in 10 -3 cm -1. The relative intensities are calculated for a rotational temperature of 400 K, and are in arbitrary units. The experimental precision is 0.003 cm- 1. Assignment
P + (9) P + (9) P + (8) P + (9) P + (9) P + (8) P + (7) P + (7) P + (7) P + (7) P + (7) P + (6) P + (5) P + (5) P + (4) P + (4) P + (4) P + (3) Q0 (8) Q0 (8) Q0 (8) Qo (lO) QO (7) Q0 (7) (20 (lO) Q0 (9) QO (8) QO (9) Q0 (10) QO (5) (20 (8) QO (9) Q0 (3) OO (6) Q0 (5) QO (2) (20 (lO) Qo (8) (20 (2) Oo (5) QO (7) Q0 (1) O0 (4) Q0 (9) Q0 (6) Q0 (3) R - (2) R - (2) R-- (5) R - (5) R - (5) R - (5)
F2 (2)-F1 (2) E (1)-E (1) E (2)-E (2) F1 (1)-F2 (1) F2 (1)-F1 (1) F2 (2)-F1 (2) F2 (2)-F1 (2) E (1)-E (1) F1 (2)-F2 (2) F1 (1)-F2 (1) F2 (1)-F1 (1) F2 (1)-El (1) E (1)-E (1) F2 (1)-F1 (1) F1 (1)-F2 (1) E (1)-E (1) F2 (1)-F1 (1) A1 (1)-A2 (1) A2 (1)-A1 (1) F2 (1)-F1 (1) E (1)-E (1) F1 (2)-F2 (2) F2 (1)-F1 (1) F1 (1)-F2 (1) F2 (1)-F1 (1) E (1)-E (1) F1 (1)-F2 (1) A2 (1)-A1 (1) A2 (1)-A1 (1) F2 (1)-El (1) E (2)-E (2) F1 (2)-F2 (2) F1 (1)-F2 (1) F2 (1)-F1 (1) E (1)-E (1) E (1)-E (1) F1 (3)-F2 (3) F1 (2)-F2 (2) F1 (1)-F2 (1) F2 (2)-F1 (2) F2 (2)-F1 (2) F2 (1)-El (1) F1 (1)-F2 (1) A1 (1)-A2 (1)
Figure 3. A single velocity modulation scan over the most dense region of the Q branch. Each dot indicates an assignment which is given in table 1.
M. Polak et al.
Table 2. Table of molecular constants (cm- 1) for NH + obtained from the least squares fit. All uncertainties are 2~r.A correlation table is available on request from the authors. Ground state constants (fixed at values in ) B0 D Dt
5.92932 1-282 x 10 -4 4.80 x 10 -6 Upper state constants
~22o x 103 ~224 • 103 Fla o x 103 F13 4 • 103 D • 10 6 D, x 10 6 G220 • 106 G224 • 106 G244 • 10 6
G2a6 • 106 H x 106 H4t • 106 H6t • 106
The spectral structure evident in figure 2 demonstrates the effect of the Coriolis perturbation by v2. We observe a spectrum similar to that of m e t h a n e - - t h e P and Q branch exhibit much larger splittings than the R branch. This difference in splittings is due to each branch accessing a different manifold of rotational levels; the P and Q branch access levels which are more strongly perturbed because they are closer in energy to v2 and because they have larger coupling matrix elements with v z levels . DeFrees and McLean  have calculated v2 to be 1660 cm-1. As in methane, v z lies only about 200cm-1 above v4, facilitating extensive mixing between these states. Hence the parameters obtained in this analysis should be regarded as effective constants; a more thorough analysis would require experimental observation of the v2 band. The v2 band is dipole forbidden in zeroth order, but Coriolis mixing with v4 makes it weakly dipole allowed. The strongest lines in the vz band of methane are a factor of 1000 weaker than those of v4 , therefore v2 of ammonium is most likely too weak for detection with our spectrometer. A b initio calculations of the vibrational frequencies of N H ~ show quite good agreement with the observed values for both the v3 and v4 bands. These calculations, particularly [101 were very important in guiding experimental studies of both bands. In the first high level calculation, Yamaguchi and Schaefer  attempted to predict v4 by scaling a D Z CI harmonic frequency based on the results of the same level of theory applied to methane. This resulted in a prediction of 1569cm -1, about 120cm -1 too high. The large discrepancy with experiment is likely due to insufficient empirical information on scaling harmonic frequencies at the time of this pioneering calculation. In addition, the v4 bending frequency shows
The v# band of ammonium
Table 3. Comparison of SCF ab initio calculations with experimental results for NH~. Frequencies are in cm- 1, bond distances in A.
~3 V4 r~(N-H)
Yamaguchi and Schaefer [I0]
DeFrees and McLean  (a)
Dixon  (b)
Botschwina  (c)
3343-1399 (21)(d) 1447.2158 (50) 1.0208 (20)(f)
3379 (e) 1569 (e) 1.0185(0)
3305 1466 --
3315 1452 --
(a) HF/6-31G* basis SCF, scaled harmonic frequencies. (b) basis set unspecified SCF, scaled. (c) CEPA-1. (d) . (e) DZ CI scaled. (f) , estimated from experimental r o . (g) CI, extended basis.
the largest variation with basis set in these calculations, indicating particular difficulty in calculating this bending frequency. DeFrees and McLean  and Dixon and Komornicki  have subsequently predicted v4 at 1466 c m - 1 and 1452 c m - 1 respectively, using scaled SCF values. Similar predictions for the v3 band are also within 40 cm-1 of the experimental values. These results are summarized in table 3, from which it is apparent that scaled SCF frequencies provide predictions of N H ~ vibrational frequencies for both the stretching and bending motions, which are reliable to approximately 40cm-1. By treating the potential surface rigorously to directly compute the anharmonic frequencies, as has been done by Botschwina for the v1 mode , the level of accuracy can be improved dramatically, and it is hoped that this paper will inspire such efforts. Dixon and Komornicki  have also calculated the absolute intensities for the v3 and v4 fundamental bands, predicting them to be at 193 km/mol and 153 km/mol respectively. Accurate experimental determination of ion band intensities is not feasible with the velocity modulation spectrometer because of the lack of reliable ion density information. The absolute intensity of the v3 band of NH~ is currently under investigation using Fast Ion Beam Laser Absorption Spectroscopy , recently developed at Berkeley, where the N H + density can be directly measured. This work was supported by the National Science Foundation (Grant No. CHE8612296). The authors would also like to thank H. S. Johnston for the loan of a laser diode.
       
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GRUEBELE,M., POLAK,M., and SAYKALLY,R. J., 1987, J. chem. Phys., 87, 3347. YAMAGUCHI,Y., and SCHAEFERIII, H. F., 1980, J. chem. Phys., 73, 2310. DEFREES,D. J., and MCLEAN, A. D., 1985, J. chem. Phys., 82, 333. DIXON,D. A., and KOMORNICKI,A. (to be published). BOTSCHWINA,P., 1987, J. chem. Phys., 87, 1453. KEARLEY,G. J., and OXTON, I. A., 1983, Advances in Infrared and Raman Spectroscopy, Vol. 10, edited by R. J. H. Clark, and R. E. Hester (Wiley), p. 111. ROBERTS,M. P., CLAVELL-GRUNBAUM,D., and STRAUSS, H. L., 1987, J. chem. Phys., 87, 6393. GRUEBELE,M., POLAK,M., BLAKE,G. A., and SAYKALLY,R. J., 1986, J. chem. Phys., 85, 6276. GUDEMAN,C. S., and SAYKALLY,R. J., 1984, A. Rev. Phys. Chem., 35, 387. WEBER,W. (private communication). HOUGEN, J., 1976, International Review of Science, Physical Chemistry Series Two, Vol. 3, Spectroscopy, edited by D. A. Ramsay (Butterworths), p. 75. ROBIETTE,A. G., GRAY,D. L., and BIRSS,F. W., 1976, Molec. Phys., 32, 1591. HECHT, K. T., 1960, J. molec. Spectrosc., 5, 355. MORET-BAILLY,J., 1961, Cah. Phys., 15, 237. SUSSKIND,J., 1972, J. chem. Phys., 56, 5152. DORNEY,A. J., and WATSON,J. K. G., 1972, J. molec. Spectrosc., 42, 135. (a) BOTINEAU,J., 1972, J. molec. Spectrosc., 41, 182. (b) SUSSKIND,J., 1973, J. molec. Spectrosc., 45, 457. GRAY, D. L., and ROBIETTE,A. G., 1976, Molec. Phys., 32, 1609. JAHN, H. A., 1938, Proc. R. Soc., A, 168, 495. BERGER,H., 1975, J. molec. Spectrosc., 55, 48. KEIM, E. R., COL, J. V., OWRUTSKY,J. C., AGMAN,N. V., and SAYKALLY,R. J., 1988, 43rd Symposium on Molecular Spectroscopy, Columbus, Ohio.