Pure rotational Q-branch spectrum of silane-28Si in the vibrational ground state observed by microwave Fourier transform spectroscopy

JOURNAL OF MOLECULAR SPECTROSCOPY

117,60-68 (1986)

Pure Rotational Q-Branch Spectrum of Silane-28Si in the Vibrational Ground State Observed by Microwave Fourier Transform Spectroscopy M. OLDANI AND A. BAUDER Laboratorium ftir Physiktdische Chemie, Eidgeniissische Technische Hochschule Ziirich, CH-8092 Zurich, Switzerland

AND

A. G. ROBIETTE Oxford University Computing Service, 13 Banbury Road, Oxford OX2 6NN, England

A pulsed microwave Fourier transform (MWFT)spectrometer operating in the 8- to 184X2 frequency range has been used to observe pure rotational Q-branch microwave transitions of silane-2*Si. The 49 measured transitions are of all three parity-allowed types A,-A), E-E, and F,F2, and cover the range 13 =ZJ < 25. A set of refinedtensorkl centrifugaldistortionconstants 4, HdT, HeT, L4~, &T, and L*T has heen determined by a least-squares fit from a total of 70 measurements. The fit included the 49 MWFI measurements of this work, I 1 transitions observed with Stark spectroscopy, nine infrared-radio frequency double-resonance measurements, and one zero-field splitting determined from an avoided-crossing molecular-beam experiment. 0 1986 AcademicPress,Inc.

I. INTRODUCTION

The “forbidden” pure rotational microwave spectra of tetrahedral XY,-type molecules in their vibrational and electronic ground state arise from an electric dipole moment induced by centrifugal distortion of the molecule (1). The magnitude of the electric dipole moment is of the order of 10m5D (2) for Y = H or D. Despite the weakness of the corresponding electric dipole transitions, XY,-top spectra have been recorded so far by a variety of experimental methods. Q-branch pure rotational transitions of silane-28Si have been observed by intracavity infrared laser-radio frequency double-resonance (3, 4), and by sensitivity-enhanced Stark microwave spectroscopy (5). The R branch of the pure rotational spectrum of silane-28Si has been studied in the far-infrared region by FTIR spectroscopy (6). Both rotational and centrifugal distortion constants of the vibrational ground state have been determined from the measured R- and Q-branch transition frequencies. Efforts have been made to determine the induced electric dipole moment (4, 6-8) and the octopole (7) moment of silane28Si.In addition, ground state molecular constants of silane-**Si have been determined by fitting combination differences obtained from high-resolution infrared (9-12) and Raman (13, 14) spectra. Silane nuclear radio-frequency spectra (15) and avoided crossings in the J = 2 state (16) have been observed by molecular beam methods. 0022-2852186 $3.00 CopyrightQ 1986 by Academic Press Inc. All rigbls of reproductionin any form reserved.

60

MWFT ROTATIONAL

SPECTRUM OF **SiH.,

61

Recently, we applied time-resolved microwave Fourier transform (MWFT) spectroscopy to record the pure rotational spectra of methane and methane-d4 in their ground state (17). In the present paper, we report on the pure rotational microwave spectrum of silane-28Si in the vibronic ground state obtained by the same experimental method. A total of 49 transition frequencies was measured in the frequency range between 8 and 18 GHz. All types of parity-allowed AJ = 0 transitions A,-&, E-E, and PI-F2 were observed. The measured transition frequencies were combined with 21 data acquired with other methods in a weighted least-squares fit of the tensorial centrifugal distortion constants. The fit yielded a set of refined constants. A brief account of the theory is given in Section 2. The experimental procedure and the assignment are presented in Section 3. The least-squares analysis is described in Section 4. In Section 5, the results of the present work are compared to those of previous investigations and the relevance of this work for astronomical searches of silane is stressed. 2. THEORY

The calculation of the Q-branch transition frequencies of silane-28Si was based on the expression used in our previous study (27) restricted to the eighth order in J, v = [& + IIL,~J(J + 1) + LTJ2(J + l)‘](fi4) + [J&T + J%TJ(J + 1>1(~6) + &T(%).

(1)

The peak absorption coefficients of the individual transitions were calculated by the procedure of Domey and Watson (18). A temperature of 293 K, an electric dipole moment KY of 3.73 - 10m5D (19), a pressure-broadening coefficient a(Av of 9.6 MHz (Tori)-’ (5), and a rotational constant B0 of 2.859056 cm-’ (12) were used. All calculations were performed with the computer program discussed in Ref. (I 7). 3. EXPERIMENTAL

DETAILS AND ASSIGNMENT

A commercial sample of silane (Matheson; semiconductor grade) was used without further purification. Exclusively the rotational transitions of the most abundant isotopic species 28SiH4 (92 mole% in natural abundance) were studied. The MWFI spectrometer operating in the 8- to 18-GHz frequency range used for all measurements will be described elsewhere (20). Its operational principles have been briefly outlined in Ref. (17). The transitions of silane-28Si are more intense than those of methane and methaned., (17) due to the larger electric dipole moment of 3.73 - 10m5D (19) of silane-28Si as compared to methane. Ozier et al. (5) observed 11 Q-branch E-type microwave transitions of silane-28Si with a sensitivity-enhanced Stark spectrometer. They determined the six tensorial centrifugal distortion constants (up to the eighth order in J) from these data. Starting from their distortion constants the Q-branch microwave spectrum was calculated with prediction errors of less than 600 kHz for the transitions under consideration. Searches were carried out using experimental conditions similar to those applied in the study on methane (I 7), except for the higher available pulse power of up to 45 W. Owing to the high prediction accuracy and the enhanced sensitivity

62

OLDANI, BAUDER, AND ROBIETTE

(at higher pulse power), observation of the transitions and their assignment were straightforward. Virtually all transitions were found within the predicted frequency interval. In the absence of any Stark information, the assignment of the transitions was solely based on the reliability of the frequency predictions and on the internal consistency of the data. The strongest transitions were recorded within a few minutes with a signal-to-noise ratio of better than 20. For the weakest transitions, an averaging time of up to 4 hr was required. The weakest observed transition has a peak absorption coefficient of 4.24 X lo-l2 cm-‘. Finally, a total of 49 transitions of all types of symmetry A,-&, E-E, and FI-F2, with J between 13 and 25, was observed. Transitions with J less than 13 were not observed since they fall below the frequency range of the instrument. Transitions with J greater than 25 were either too weak or too high in frequency to be measured. Accurate peak frequencies were determined from the maximum of a parabola fitted to seven points of the discrete power spectrum around the center of a transition. As was pointed out by Ozier et al. (5), the silane isotope shifts of most of the transitions are larger than the experimental half-width at half maximum of 300-400 kHz. Hence, it was assumed that small perturbations of the lineshape due to the isotopic transitions would not affect the frequency measurements. At least three independent measurements of every transition were performed with different carrier frequencies and the peak frequencies were averaged. An experimental accuracy of +50 kHz is estimated for all measured peak frequencies. Recordings of a free electric polarization decay and of the corresponding power spectrum of a transition are presented in Figs. 1 and 2, respectively. 4. ANALYSIS

The 49 measured transition frequencies, together with 11 transitions measured previously by Stark spectroscopy (S), nine measurements from a former study with infrared

r ,.

I

0

I

I

1

I

I 5.12 p*

FIG. 1. Microwave electric polarization decay of the J = 15, Fz(3)-F,( 1) Q-branch transition of **SiH4at 13848.549 MHz. The sample was irradiated with 100~nsec pulses of a power of I5 W at a carrier frequency of 13850 MHz. The signals were down converted to about 25 MHz and digitized at a rate of 100 MHz. The pulses were repeated at a rate of 50 kHz and the individual decays were accumulated for 5 min. The pressure was 70 mTorr at 295 K.

MWFT ROTATIONAL

63

SPECTRUM OF **SiH,

II

13646.00

13851.27 MHZ

FIG. 2. A section of the power spectrum showing the J = 15, F*(3)-FI( 1) Q-branch microwave transition of %I& with a calculated DL- of 1.22 X lo-" cm-’ (cf. Fig. 1). The dashed line links the points of the discrete power spectrum. The solid line is the best fit Lorentzian to the points.

laser-radio frequency double-resonance (4), and a zero-field splitting determined by avoided-crossing molecular-beam spectroscopy (16), were used to determine the tensorial centrifugal distortion constants DT, HdT, HhT, LhT, Lb=, and LBT in a leastsquares fit. Owing to the different absolute accuracies of the measured frequencies, they were weighted as the inverse square of their estimated absolute uncertainties. A tentative inclusion of the tenth-order constants P4r, PbT, PST, and PloT in the fit, however, showed that the present amount of information does not allow their determination. The four tenth-order constants were indeterminate and the standard deviations (SD) of the lower order constants increased drastically compared to the eighthorder fit. The mean residual error for a typical weight of 400 (corresponding to 50 kHz uncertainty) of the fit with 10 constants was 22 kHz compared to 26 kHz for the fit with six constants. The improvement of the fit on inclusion of the higher order constants is only marginal. Hence, the analysis was restricted to eighth order in J. Table I includes the observed transition frequencies and their differences to the values calculated from the adjusted constants. The calculated peak absorption coefficients of the observed transitions covering the range between 4.24 X lo-l2 and 3.14 X 1O-” cm-’ are also included in Table I. It does not appear that there is any correlation between the J values and the residuals, indicating that the neglect of higher order constants is justified and no systematic error is introduced. The tensorial centrifugal distortion constants determined in the fit are given in Table II together with their standard deviations. The correlation matrix of the fitted constants is given in Table III. 5. DISCUSSION

Pulsed MWFI spectroscopy was shown earlier to be an excellent method of observation of pure rotational microwave spectra of tetrahedral spherical tops (17). This work on 28SiH4 confirms the merits of this experimental technique. The number of observed transitions, including all symmetry-allowed types, was increased greatly. The results of the present work may be compared to those obtained by Ozier et al.

64

OLDANI, BAUDER, AND ROBIETTE TABLE I Observed Pure Rotational Q-Branch Microwave Transitions of Silane-**Si Transition lower level

J z:;

ohs.

cabs.-talc.

ErrOra

MHZ

MHZ

MHZ

b 'max cm-l

2

F*(l)

- E(1)

0.0007

0.001

5

F2(1)

- Fl(l)

60.69

d

0.225

0.3

1.26

5

Fl(2)

- F2(1)

185.68

d

0.072

0.2

2.15 E-14

9

Fl(3)

- F2(1)

2279.46

d

-0.356

0.3

5.30 E-12

9

F2(2)

- F1(3)

270.10

d

-0.003

0.Z

1.35

9

F2(21

- F2(3)

170.26

d

0.157

0.2

1.35 E-13

13

F*(2)

- F1(l)

8440.269

0.023

0.05

5.19

E-11

13

F2(3)

- Fi(l)

10972.476

-0.009

0.05

1.38

E-11

14

E(2)

- E(1)

10976.358

-0.008

0.05

5.88

E-11

14

E(2)

- E(1)

10976.37

0.005

0.1

5.88 E-11

14

Fl(2)

- F*(l)

10539.720

0.008

0.05

8.78

1.

Al(l)

- AZ(l)

9844.501

0.006

0.05

1.5, E-10

14

F1(3)

- F2(2)

8706.826

0.028

0.05

6.72

15

F2(3)

- Fl(l)

23848.549

-0.039

0.05

1.22 E-10

15

F3(2)

- F2(1)

12903.775

-0.019

0.05

1.18 E-1C

15

Al(l)

- AZ(l)

12049.495

0.030

0.05

1.85 E-10

15

Fl(31

- F2(2)

8627.804

0.023

0.05

8.13

15

F1(4)

- F2(2)

12322.917

0.023

0.05

2.92

E-11

15

E(2)

- E(1)

8069.927

0.007

0.05

7.76

E-11

15

E(2)

- E(l)

8069.92

=

-0.001

0.075

7.76

E-11

322.36

d

0.005

0.2

1.07 E-12

4.48217'

=

E-16

E-13

E-11

E-11

E-11

15

F2(4)

- F2(4)

16

A2(1)

- Al(l)

17543.552

0.003

0.05

2.57

E-10

-0.038

0.05

1.43

E-10

-0.010

0.05

9.74

E-11

0.1

9.74

E-11

-0.017

0.05

1.07 E-10

16

F*(Z)

- F2(2)

16555.391

16

E(2)

- E(1)

16213.956

16

E(2)

- E(l)

16214.01

16

Fl(3)

- F*(l)

11750.715

16

F1(4)

- F2(1)

16637.683

0.013

0.05

4.95

16

F2(3)

- Fl(2)

10677.435

-0.008

0.05

1.47

E-10

16

E(3)

- E(2)

10465.792

0.038

0.05

3.94

E-11

16

E(3)

- E(2)

10465.76

0.005

0.075

3.94 E-11

16

Fl(4)

- F2(2)

0.031

0.05

4.20

E-11

17

E(2)

- E(1)

0.075

1.13

E-10

a Estimated

mOment

peak

Of e;y

15127.22

absorption

avoided-crossing

d From

infrared

measurements Stark

used

= 3.73.10-5

' From

e From

e

9789.037

uncertainty,

b Calculated

e

-0.026

for statistical coefficient

based

weights:

see

on a dipole

II (191.

molecular-beam

laser-radio

frequency

141. spectroscopy

e

0.044

[Sl.

spectroscopy double-resonance

1161.

E-21

text.

MWFI’

ROTATIONAL

SPECTRUM

OF 28SiH,

65

TABLE I-Continued Transition .J

lower level

P%

17

E(Z)

- EC11

17

F2(3)

- F3(2)

17

AI(I)

- AI(l)

17

Fz(4)

- F1(31

17

F1(4)

- F2C21

I*

E(Z)

- E(1)

18

F*(3)

- F1(l)

18

Fz(4)

- F1(Z)

18

E(3)

- E(Z)

18

E(3)

- E(2)

18

FIO)

- F2(3)

I8

FtCSJ

- F1t3)

18

AI(Z)

- A2(21

18

F1(4)

- F20)

19

E(2)

- E(1)

19

Fz(4)

- F1(2)

19

F3(4)

- F213)

19

E(3)

- E(Z)

19

F*(S)

-

20

EC31

- E(2)

7.0

F1(3)

- F2(2)

20

AI(Z)

- AZ(l)

20

Ft(4)

- F2(3)

20

Fz(4)

- F1(3)

20

E(4)

- E(3)

20

E(4)

- E(3)

21

F3(51

- F2(3)

21

E(3)

- EC?.)

21

F1(6)

- F2(41

21

AZ(Z)

- AI(Z)

22

F*(4)

- F1(3)

22

F3(4)

- F*(4)

23

F2(4)

- F3(3)

23

A*(Z)

- AI(I)

23

Ft(3)

- F1(4)

23

F1(S)

- F3(4)

25

F1(3)

- FZ(4)

25

F2(51

- F1C5)

F1t3J

b

obs.

ohs.-talc.

EIIOX=

amax

MHZ

MHZ

MHZ

.K1

66

OLDANI, BAUDER, AND ROBIETTE TABLE II Tensorial Centrifugal Distortion Constants’ (MHz) of Silane-%i present

work

transitions et al.

of Ozier

[5lb

DT

74.74987(22)

E-3

74.75136(163)

H4T

-6.03530~120~

E-6

-6.04403(1013)

E-6

H6~

2.59885(51)

E-6

2.59786(284,

E-6

4.647(155)

E-10

E-3

L4T

4.530(18)

E-10

L6T

-3.809(131

E-10

-3.794(76)

E-30

LET

-7.790(103)

E-10

-7.659(311)

E-10

a Errors

in parentheses

as obtained b Obtained al.

from

i51. The

the

represent

one

least-squares

a separate constants

moredigits

however. column

from

fit of the agree

with

are displayed

standard

deviation

fit. 11 transitions

the

results

here

of ozier

of Ozier

for comparison

et

et al.; with

1.

(5). Six microwave measurements of Ozier et al. were repeated in this study. The differences between the two independent measurements of 7-54 kI-Iz are well within the combined experimental uncertainties of the measurements. The results of a separate fit of the 11 transitions of Ozier et al. are included in Table II. Despite some large correlations among these fitted constants as shown in Table III, their reliability is quite satisfactory. The mean residual error of the fit of Ozier et al. is 41 kHz for a typical weight of 100 (corresponding to 100 kHz uncertainty). This error is much smaller than the typical experimental uncertainty of 75 kHz reported by the authors. This is most likely a consequence of the small number of degrees of freedom (df) of their fit. They determined six constants from a set of 11 transition frequencies. No correlation between the residuals and the J value is observed. These results reflect the excellent adaptation of the eighth-order Hamiltonian to their data set which was limited to transitions with 14 < J < 20. The mean residual error of the fit of this work is 26 kHz for a typical weight of 400, i.e., for an estimated uncertainty of 50 kHz of a measurement. In view of the large number of measured data, the discrepancy between the mean residual error and the estimated uncertainty means that the latter has been judged too large. The tensorial centrifugal distortion constants of Ozier et al. are compared to those of this work most conveniently using 95% confidence intervals. The latter are obtained for the results of Ozier et al. as 2.57 SD (5 df). Those of our work are 2.00 SD (64 df). The results of the two fits are identical within the 95% confidence limits and even within 1 SD. However, the standard deviations on the individual constants are smaller by factors of 2 to 8 in our work. Recently, Pierre et al. (II) have determined the four scalar and the six tensorial centrifugal distortion constants up to eighth order in J from 9 19 infrared combination differences, 11 microwave transitions of Ozier et al. (5), and five double-resonance

MWFI

ROTATIONAL

SPECTRUM OF **SiH.+

67

TABLE III Correlation Matrices’ of the Constants of the Least-Squares Fits

11 transitions %

H4T

"6T

of Ozier

et al.

L4T

IS1 L6T

LET

measurements of Kreiner et al. (4). They obtained virtually the same results on the tensorial constants as Ozier et al. (5). As the authors stress, the tensorial part of their result is dominated by the measurements of Ozier et al., and their new FIIR information was mainly absorbed by the scalar constants. The results of the present work are of some relevance for the search of silane in interstellar space. Two Q-branch microwave transitions in every tetrahedral X&-type molecule may show maser action (21). Due to the improved prediction accuracy now available, the search for the possible interstellar silane-28Si masers is facilitated. From the refined constants of this work, the two maser transitions are calculated as J = 6, AI-AZ at 428.9084( 10) MHz and J = 12, A2-Ar( 1) at 75 14.1236(79) MHz. The levels are 120 cm-’ (172 K) and 446 cm-’ (641 K), respectively, above the ground state. Searches for silane in the Jovian atmosphere have been reported (22) but only upper concentration limits could be determined. ACKNOWLEDGMENTS Financial support by the Swiss National Science Foundation (Project No. 2.223-0.84) is gratefully acknowledged. We thank Mr. M. Andrist and Mr. W. Groth for their contributions during the construction of the MWFT spectrometer.

RECEIVED:

October 14, 1985

68

OLDANI, BAUDER, AND ROBIETTE REFERENCES

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