Δk = ±3 “forbidden” infrared transitions in the ν2-band of NH3

JOUR?r.4LOF BdOLRCULAR SPECTROSCOPY 62, 263-270

Ak=

(1976)

23 “Forbidden” Infrared Transitions in the Y2-Band of NH, D. LAUGHTON,~ S. M. FREUND,~ AND T. OKA Her&erg Institute of Astrophysics,

Natiod

Research

Council of Canada,

Ottaula, Ontario, Canada Two AK = f3 “forbidden” vibration-rotation transitions in the ut-band of NH3 have been measured by using infrared-microwave two-photon spectroscopy and laser Stark spectroscopy. Combining these results with Rao’s recent measurement of the band, xe have obtained the COrotational constant of 6.2280 ri 0.0008 cm-r. INTRODUCTION

In 1970, Shimizu (1) published a paper in which he described a systematic laser Stark spectroscopy study of the vz-band of NHs in the 10 pm region. While most of the observed signals were assigned unambiguously, he discovered two sets of signals which were definitely due to NH3 in the J = 3 level but could not be assigned t,o the normal Ak = 0 vibration-rotation transitions. We have found that these transitions are due to Ak = f3 transitions which become weakly allowed because of near degeneracies of rotation-inversion levels in the ~2 state. The purpose of the present paper is to discuss our further studies of Ak = f3 transitions in NH3 by using laser Stark spectroscopy and infrared-microwave two-photon spectroscopy. THEORY

The “forbidden” AK = f3 vibration-rotation transitions in molecules with Ch symmetry become allowed through AI k - Z/ = &3 mixing of wavefunctions due to vibration-rotation interaction. Such transitions were first reported by Olson for CHsD (2) and SiHsD (3) and were named as “perturbation allowed” transitions. The mechanism leading to these transitions is similar to that for “forbidden” rotational transitions in the ground state (4-8) but often the former is more strongly allowed than the latter because of the existence of vibrational near degeneracy. The general formula for the line strength of the “forbidden” vibration-rotation transition has recently been derived by Watson (9). Without accidental degeneracies, the matrix elements for “forbidden” transitions are smaller than those for allowed transition by a factor of K~ - lO_* for low J values and by a factor of -IO-* for f - 10. The “forbidden” transitions have been observed to be very strong in the ~1 and vr bands of AsH3 (IO) because of the near degeneracy between ~1 and v3 (I vl - v3] = 11.25 cm-l) and because this molecule is nearly spherical ((B - C)/B = 0.067). 1Present address: Department of Physics, Princeton University, Princeton, N. J. r Present address : Los Alamos Scientific Laboratories, Los Alamos, N. M. 263 Copyright @ 1976 by Academic Press, Inc. Al1 rights of reproduction in any form reserved.

264

J,.\I’GHTON,

I~REI’~I~

.\NJ)

OK\

FIG. 1. Vibration-rotation-inversion levels of ortho (A) NH, in the ~2 state. The lower inversion component of the f = 3, K = 0 level is very close (2.882 GHz) to the upper inversion component of the J = 3, K = 3 level and causes intensity borrowing. The same thing happens for the J = 5 levels. The f signs beside the levels indicate the parity. The inversion components for K = 0 which are not aflowed due to the Pauli exclusion principle are shown with broken lines. They are omitted for K = 3 levels and for J = 0, 1, and 2 levels for conciseness. The inversion splitting in the ground state is magnified for clarity.

The “forbidden” transitions were also sufficiently strong in the 3~2 band of PI-Is that they were observed with a conventional infrared spectrometer (II); for this molecule, 3~2 - (~VZ+ 4 - 100 cm-” and (B - C)/B = 0.120. For the vp-band of NH3, however, because of the lack of vibrationai near degeneracy (1~2 - ~4/ = 977.53 cm-r (I,?)) and its large deviation from a spherical top ((B - C)/Lr = 0.399), the AK = f3 transitions are much weaker than in PHa and AsH8. This situation is saved for a few transitions by an accidental near degeneracy between the lower inversion components of the k = 0 levels and upper inversion component of the k = f3 levels of ortho (A) - NH, (I = a) in the v2 state. The near degeneracy is caused because the inversion splitting of NH, in the v2 state (-3.5 cm-l) happens to be close to 9(B - C). Figure 1 shows energy levels of ortho NH3 in the v2 state. The separation between the near degenerate levels are 0.1 and 3.0 cm-’ for J = 3 and J = 5, respectively. Because of the Pauli principie, the lower inversion component is not allowed for the .J = even, K = 0 levels and the accidental degeneracy occurs only for the J = odd levels. The near degenerate levels (connected by broken lines in Fig. 1) have the same symmetry and are mixed by a centrifugal distortion term (5) H’ =

754 ~zrri[

(J+” + J-“) Jz + J,(J,3

+ J-3)],‘4.

(1)

Thus the “forbidden” transition “borrows” intensity from the allowed transitions as indicated in Fig. 1. There are other vibration-rotation terms which cause the

Ak = Lf 3 TRANSITIONS

IN NH8

26.5

forbidden transitions, but the mixing mentioned above dominates for such accidentally degenerate cases. The mixing between the (J, li) and (1, k - 3) levels is calculated to be e = (J, K1H’ 1J, k -

3)/AE

= (ltt4~&4AE)

(2k - 3)

X[(J-k+3)(J--++)(J--k+l)(J+k--)(J+k--)(J+k)]:,

(2)

where AE is the energy difference between the near degenerate levels. The intensity of a “forbidden” transition is smaller than the corresponding allowed transition by a factor of ]a(J, k)j2. Using the result of the normal coordinate calculations by Morino, Kuchitsu, and Yamamoto (13), we calculate rZZZZ to be 10.1 MHz. We then see that the intensity of the “forbidden” (3, O)+ +- (3, 3)_ transition is 5 X 1O-3 times that of the allowed Q(3, 3) transition. Similarly considering the value of the matrix element and the Boltzmann factor we find the intensity of the forbidden (5, O)+ +- (5, 3)_ transition is 2.7 X 1e5 of the Q(3, 3) transitions. These two are the only forbidden transitions observed in this paper. Transitions with much Iarger J values may have larger mixing but smaller Boltzmann factors which make them weaker. The intensities of other Ah = f3 lines are calculated to be weaker than the (5, O)++- (5, 3)_ line by a factor of 3.2 for (7, O), +- (7, 3)_, and 13 for (9, O)+ + (9, 3)_. For AK = f3 transitions with other k values, the factors for (J = 2 m 9) are 5.5 X 105 to 680 for (J, Al).._++ (J, f2)+, 110 to 28 for (J, &I)_++ (J, f4)+, 110 to 37 for (J, f2)+ ++ (J, =tS)_, and 51 to 20 for (J, &3)-t, (J, f6)+. These values are based on the mixing due to H’ only and for weaker transitions (for which the other mixings may be large), may differ appreciably from the real values. EXPER~~iENT

AND RESULTS

It is probably difficult to observe the forbidden transitions in NH8 by using a conventional infrared spectrometer because the transitions are either very weak or close to stronger lines. However, the resolution and sensitivity of laser spectroscopy enables us to observe these transitions. We use COZ and NzO lasers for which the frequencies are not continuously tunable, and the techniques of infrared-microwave two-photon spectroscopy (14-17) and Stark spectroscopy (1). Details of our apparatus are given in (16, 18), respectively.

A. To-P~tun

S~e&tr~s~~~~

Figure 2 shows the energy level system for observing the {3, 0) +- (3, 3) forbidden transition. The upper inversion component (parity +) for the J = 3, K = 3 level in the vz state of NH3 lies 2.9 GHz above the lower inversion component (parity +) for the J = 3, K = 0 level and, according to Eq. (2), their wavefunctions are mixed by about 7%. The NzO laser R(36) line at 967.30531 cm’-’ (19) happens to be close to both the allowed sQ(3, 3) line (P - VI - 1.2 GHz) and the forbidden (3, O), + (3, 3)- line (v - VL- - 1.7 GHz). We can use two-photon processes to subtract a microwave quantum kv, from the infrared quantum hvr as shown in Fig. 2(a). When the microwave frequency is varied and the two-photon condition YZ- vm = (E+’ - E+“>/h is satisfied, we observe a two-photon absorption signal. From the measured “resonant” microwave frequency and from the known inversion splitting,

266

r..\l‘GH’rON,

l~R1’1~Sl)

Two-Photon

.\SI)

OK.\

Stork

i

N20 laser

/ /

R(36)

to)

(b)

FIG. 2. Energy diagram for the forbidden AK = f3 transition observed with (a) infrared-microwave two-photon method and (b) with laser Stark method. The frequency of the X&I laser R(36) line (967.30531 cm-‘) is 1229 i: 5 MHz smaller than the allowed AK = 0 transition and is 1653 i 30 MHz larger than the forbidden Ak = 3 transition. In the two-photon experiment a microwave quantum is subtracted from the infrared quantum (16). In the laser Stark experiment, transitions are tuned into resonance by an applied electric field. The very small shift for the upper state is neglected in the figure. Note that the Ak = 0 transition cannot be reached by the laser line using the Stark shift.

we can determine the frequency of the infrared transitions accurately. For the allowed transition, the two-photon process had sufficient intensity to be observed with a Lamb dip method (15, 16) and thus the transition was measured with an accuracy of 6 MHz. For the forbidden transitions, the frequency was measured with an accuracy of 30 MHz by a straightfo~ard two-photon absorption method (16). The result is given in TabIe I. N. Stark Spectroscopy The results of Stark spectroscopy are also given in Table I. As was already reported by Shimizu (I), the Stark resonance for the J = 3 line was obtained for both the R(36) line of the NzO laser and the R(8) line of the CO2 laser. The latter line permitted the allowed and forbidden lines displayed in a single sweep, and enabled us to compare the relative intensities of the two. They were different by a factor of more than 100, in agreement with the theoretical estimate. If the laser power is high, this ratio is reduced by as much as a factor of 10 because of saturation of the allowed transition. The J = 5 forbidden transition was observed using both the R(10) line of the Cot laser and the R(39) line of the h’s0 laser. The J = 5 resonances observed using the CO2 line are shown in Fig. 3. This same transition has been recently observed independently by Ueda (20). The analysis of the Stark spectrum employed to obtain A.v = Y - ~1 was similar to that used br- Shimizu (1); we treated the Stark shift between the ground state

AA = f

3 TRANSITIONS

IN NH,

267

inversion doublet exactly and others by using second order perturbation theory. Since the second order shift in the excited state and that in the ground state tend to cancel each other, for all the resonance analyzed, more than 997, of the shift is caused by the shift in the ground state inversion doublet. The variation of mixing due to small shifts of (J, 0) and (J, 3) levels in the excited state is quite negligible. The calculated values of AV and the extrapolated line positions are given in Table I. The error was caused primarily by the uncertainties of dipole moment (I) for the ground state (1.475 f 0.0060) and for the excited state (1.25 f O.OlD). ANALYSIS

The experiments described above have determined accurate frequencies of two K = 0 +- 3 Q branch transitions; that is, E(uz, J, 0, +) - E(0, J, 3, -) for J = 3 and 5. In order to obtain information on the C rotational constant in the ground state, we need combination difference between the above frequencies and frequencies of some allowed transitions with k = 0; that is, E(vz, J, 0, -I-) - E(0, J f 1, 0, -). Unfortunately, neither two-photon spectroscopy nor laser Stark spectroscopy can be conveniently used for measuring the latter transitions because, for K = 0 rotational levels, one component of inversion doublet is missing due to the Pauli principle. We therefore used the most recent infrared measurement of the a&(2, 0), usP(4, 0), asR(4, 0), and asP(6, 0) transitions kindly supplied to us by K. Narahari Rao (21). These frequencies gave us four combination differences, E(0, J, 0, - ) - E(0, J f 1, 3, -) for J = 3 and 5 with an accuracy of 0.005 cm-‘. These combination differences were then reduced to hypothetical energy differences between inversion-free (J, 0) and (J, 3) levels after adding or subtracting frequencies of pure rotational TABLE

I

Summary of the Observed Results’” mixing e = 0.071 (3, O), + (3,3)N20 R(36) line YI = 967.30531 cm-1 Two-photon spectroscopy Y,,, = 25.522 f 0.03 GHz Av = -1.652 f 0.03 GHz Stark spectroscopy E(M = 3) = 11.70 kV/cm Au = E(M = 2) = 17.43 kV/cm Av = E(M = 1) = 33.64 kV/cm Au = YI = 967.70723 cm-’ CO2 R(8) line E(M = 3) = 40.79 kV/cm AY = (5,0)+ +- (5,3)COS R(10) line E(M = 5) E(M = 4) E(M = 3) NzO R(39) line E(M = 5)

= = = =

mixing e = 0.012 YZ= 969.13955 cm-1 25.33 kV/cm Av = 31.63 kV/cm Av = 41.90 kV/cm Av = YI = 969.40061 cm-1 51.69 kV/cm Av =

a Av = Y - vi = vi,,” - P,,,.

Y =

967.2502f 0.001 cm-1

-1.663 -1.663 -1.663

GHz GHz GHz

v = 967.250 f

0.001 cm-’

-13.77

GHz

Y = 967.248 f

0.02 cm-1

-3.561 -3.564 -3.554

GHz GHz GHz

Y = 969.021 f

0.003 cm-1

-11.308

GHz

Y = 969.023 •t 0.007 cm-’

268

IAI’GHTON,

I--

25

~--*-

FREI’XC’I,

.\ND-OR,\

1

35

40

~-

ECkV/cm)

FIG. 3. Laser Stark spectrum of the “forbidden” (J = 5, K = 0,+) +- (J= 5,K = 3, -) spectrum of NH3 using the CO2 R(lO) line at 969.13955 cm-l. The sample pressure was 2 mTorr and the time constant of detection was 0.3 sec. This transition is calculated to be a factor of 3 X 104 weaker than the allowed Q(3, 3) transition.

P- and Q-branch transitions and correcting for inversion splittings. The rotational constants B. DJ,and DJK needed for the former calculation were derived from combination differences determined by two-photon spectroscopy (16) and the accurate millimeter wave measurement by Helminger and Gordy (22). The constants HJJJ, HJJK, and HJKK determined by Dowling (23) were used for small higher-order corrections, and the inversion splitting for the K = 0 levels were calculated by using Costain’s formula (23). The four combinations gave values 9(B -

C) + 81

DK - 729 HK = 33.518 cm-r 33.514 cm-’ 33.512 cm-’ 33.511 cm-r.

(4)

Since we observed AK = f3 transitions of only one type, we could not separate B - C, DK, and HK in Eq. (4). We neglected the HK term assuming that HK is of the same order of magnitude as other sextic constants (- lO+ cm-l). The value of DK calculated by Sundaram, Suszek, and Cleveland (25) was used after being scaled by a factor (1.05) which was obtained by comparing observed values of other quartic constants DJ and DK with their calculated values. The C rotational constant of NH3 thus determined is given in Table II together with other rotational constants used in the calculation. The value of CO was previously determined by Benedict and Plyler to be 6.196 cm-’ from combining ~3 and 2~3~ spectra of NH3 (26). Considering the approximation 2 (Cl)“, = - (C{)zylp used in their deviation, the agreement of their Co constant with ours is very good. Garing et al. (12) gives Co = 6.090 from an analysis of the v2 and vq bands. The values of DJ and D JK determined in our work agree excellently with those of Dowling (23) and with those of Mould, Price, and Wilkinson (27) within their quoted uncertainties. After the completion of this paper we learned of a paper by Ueda and Shimoda (28) in which they describe a very detailed analysis of the vz-band of NH3 by laser

Ak = f 3 TRANSITIONS

IN NH3

269

TABLE II ~o~tional

Constants for NH86

BO = 9.94413 f 0.00009 cm-1 CO = 6.2280 f 0.0008 cm-l DJ = (8.406 f 0.026) X IO+ cm-t D JK = - (15.507 f 0.076) X 10-4 cm-r DK = (8.4 i 0.9) X 1w4 cm-l HJJJ = (2.38 z&0.34) X lo-’ cm-l HJJK =I - (8.78 f 0.91) X lo-’ cm-* HJKK = (1.05 f 0.12) X IO-@ cm-’

assumed” assumed” assumedc assumedc

fl The constants are derived from the center of inversion doublets. b The value of DK is based on Ref. (25) with an appropriate scaling factor. c These values are taken from Ref. (23).

Stark spectroscopy. They have also observed the same two forbidden transitions reported in our paper. Their value of CO - ~DK agrees with our value within the quoted uncertainties. Their quoted uncertainties for the centrifugal distortion constants are much less than ours because they included more high 1, K transitions. They have also determined vibration-rotation-inve~ion constants in the ~2 state. ACKNOWLEDGMENT We would like to thank K. Narahari Rao for informing us of the four frequencies used in our analysis prior to the publication. We also wish to thank J. K. G. Watson for having worked out the general formula and J. W. C. Johns and J. K. G. Watson for critical reading of the manuscript. RECEIVED:

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Con