the rotational spectrum of ar–sih4 and ar–sid4

The Rotational Spectrum of Ar–SiH4 and Ar–SiD4

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Journal of Molecular Spectroscopy197,232–239 (1999)Article ID jmsp.1999.7926, available online at http://www.idealibrary.com on

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Yoshiyuki Kawashima,* R. D. Suenram,† G. T. Fraser,† F. J. Lovas,† and Eizi Hirota‡

*Department of Applied Chemistry, Kanagawa Institute of Technology, 1030 Shimo-ogino, Atsugi, Kanagawa 243-0292, Japan;†Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899; and

‡The Graduate University for Advanced Studies, Hayama, Kanagawa 240-0193, Japan

Received February 2, 1999; in revised form May 14, 1999

Microwave spectra of Ar–28SiH4, Ar–29SiH4, Ar–30SiH4, and Ar–28SiD4 were recorded using a pulsed molecular beamFourier transform microwave spectrometer. TheK 5 0 andK 5 1 components of theJ 5 3 4 2 through theJ 5 7 4 6transitions were measured and assigned in the 9–24 GHz region. For the primary28Si isotopic species, Ar–28SiH4 andAr–28SiD4, aK 5 0, A symmetry, aK 5 0, F symmetry, a doubly degenerateK 5 1, E symmetry, and anl /K-doubled,K 51, F symmetry rotational progression are observed at the'1 K rotational temperature of the supersonic expansion. Therotational constants for theK 5 0, A state for Ar–28SiH4 and Ar–28SiD4 areB 5 1700.40624(9) MHz and1630.687073(22)MHz and the centrifugal distortion constants areDJ 5 29.089(3) and20.0198(8) kHz andHJ 5 21.91(3) and20.851(8)Hz, respectively, where type A expanded uncertainties with a coverage factor,k 5 3, are given here and elsewhere. The valuesof the rotational constants for theK 5 0, A, and F states and for theK 5 1, E state are in good agreement with theinfrared-determined values for Ar–28SiH4. The measured linear Stark effect of theE-state transitions was analyzed to give adipole moment of 9.24(8)3 10232 C z m [0.0277(2) D]. © 1999 Academic Press

INTRODUCTION direct-absorption diode–laser spectroscopy. Brookeset al. (9)

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Because of their relative simplicity, the rare-gas complef the hydrides of the first- and second-row elementserved as simple model systems for the quantitative stuntermolecular potentials. These studies have led to accotential functions for such systems as Ar–HF (1), Ar–HCl (2),r–NH3 (3), and Ar–H2O (4). Potential functions of similaccuracy are not yet available for the rare-gas methaneilane interactions, primarily due to the vanishing elecipole moments of methane and silane which make it diffi

o observe the microwave and far-infrared spectra of tomplexes. The microwave studies provide electric dipoleents, precise centrifugal distortion constants, and isoependencies of the rotational constants, which are not evailable from infrared investigations, while the far-infratudies directly probe the large amplitude motions whichensitive to the anisotropy of the potential energy surfaceRecent increases in the sensitivity of pulsed molecular b

ourier transform microwave spectroscopy make it possibbserve rotational spectra for complexes with very small dioments, down to 33 10233 C z m [0.001 D]. In fact, spectrere observed for such “nonpolar” complexes as Ne–Ar5),r–Xe (6), and Ar–Kr (7). This increased sensitivity sugge

he potential for studying the rare-gas complexes of silaneethane using Fourier transform microwave spectroscop

he present paper we report the rotational spectrum of Ar–S4.he infrared spectrum of Ar–SiH4 was previously observed

he region of the SiH4 triply degenerate stretching vibration2189 cm21 by Randallet al. (8) in a molecular beam usin

232022-2852/99 $30.00opyright © 1999 by Academic Pressll rights of reproduction in any form reserved.

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ndertook a similar study of the Ne–SiH4 complex. For Ar–iH4 (8), 12 subbands were analyzed, yielding effective r

ional constants for theK 5 0, A andK 5 0, F states and th5 1, E and K 5 1, F states. Two anisotropic potentia

ere fit to the data, with one potential having aV3 term of 59.5m21 and noV4 term and the other potential having aV3 termf 91.2 cm21 and aV4 term of 27.8 cm21. The energy differnce between the minimum and maximum on the poteurface whenV4 5 0 is given by2

3=10VI 5 192 cm21.The present measurements furnish an additional test o

roposed potentials. For Ar–SiH4 we observe the smalll /K-ype doubling splitting of theDJ 5 1 transitions for theK 5, F state. This splitting was not obtained from the infratudies and is sensitive to the anisotropy of the potentiaddition, we have also measured the rotational spectrumr–SiD4 isotopic form, which further tests the proposed

entials since here the reduced mass is a factor of 2 less.iscrepancies are observed between predictions from th

entials of Randallet al.(8) and our experiments which sugghe need for inclusion of a radial dependence to the motentials. Finally, we provide precise values for the cental distortion constant and electric dipole moment, whichventually be used to help model the radial part of the potend to predict the intensity of the torsional modes.

EXPERIMENTAL

The measurements were made using a Balle–Flygare10)ourier transform microwave spectrometer described p

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233ROTATIONAL SPECTRUM OF Ar–SiH4 AND Ar–SiD4

usly (11). The spectrometer was modified to allow forolecular beam to be directed along the cavity axis for

reased spectral resolution and sensitivity, as initially demtrated by Grabow and Stahl (12).The weakly polar Ar–SiH4 complexes were polarized usiicrowave radiation from a frequency synthesizer amplifie1 W, solid-state amplifier. A fast, single-pole, double-thIN diode switch was used to protect the low-noise hetero

eceiver from power reflected from the cavity input coupuring the excitation pulse. A molecular beam was formen ;1.5 3 105 Pa adiabatic expansion of a mixture of 1%olume SiH4 or SiD4 diluted in Ar. For the dominant Ar

28SiH4 species the free-induction decays from 100 noulses typically were averaged and then Fourier-transformbtain a spectrum. Rotational spectra of Ar–29SiH4 (4.7%) andr–30SiH4 (3.1%) were also recorded at reduced sensitivitatural abundance.For electric dipole measurements, two parallel plates (23

5 cm) separated by;25 cm were placed exterior to the cavs described previously (13). The nonzero field measuremeere made with the static electric-field vector fixed paralle

he microwave electric-field vector, givingDMJ 5 0 selectionules. The electric field was calibrated using the Stark effehe J 5 1 4 0 transition of OCS (14).

RESULTS

. Symmetry Considerations

Due to the extremely small cross section for nuclear–elaxation, complexes correlating asymptotically to all th

FIG. 1. Energy-level diagram showing the hindered-rotor state enerorrelating toj 5 0, 1, and 2 monomer states are shown. TheF, K 5 1, l /

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pin modifications of SiH4 ( A, E, F) are expected to bopulated in the molecular beam. The large rotational conf SiH4 (B ; 2.86 cm21) and low molecular-beam tempe

ure of 1–2 K allows only dimer states correlating to the lownergy monomerj rotational state of each spin modificatione populated;j 5 0 for A, j 5 1 for F, andj 5 2 for E. Theseonomer states have rotational energies of approximate.7, and 17.1 cm21, respectively. Neglecting nuclear–spin co

ng and differences in equilibrium constants and formainetics for the Ar1 SiH4 ^ Ar–SiH4 reaction leads to thonclusion that the relative populations of theA, E, and Fr–SiH4 spin modifications in the molecular beam willqual to the relative room-temperature populations of theA, E,ndF states of SiH4. These relative populations are 5, 2, afor theA, E, andF states of SiH4 and 5, 4, and 18 for theA,, andF states of SiD4.In Fig. 1 we show a theoretical plot of the energy level5 1 dimer states correlating toj 5 0, 1, and 2 SiH4

onomer states as a function of the leadingV3 tetrahedraindering potential term. Theoretically, thej 5 0, A state oiH4 correlates to aK 5 0, S state of the complex, thej 5 1,state correlates to both aK 5 0, S state, and anl /K-doubled5 1, P state, and thej 5 2, E state correlates to aK 5 0,

oubly degenerateS state, twoK 5 1 doubly degeneratePtates with first-order Stark effects, and twoK 5 2 doublyegenerateD states with first-order Stark effects. The spectates populated in the molecular beam depend on theemperature and the nature of the anisotropic potential. Inecause of their high energy relative to the rotational temture of the molecular beam, no transitions are observe

of Ar–SiH4 as a function of internal-rotation barrier,V3. Only J 5 1 dimer stateoubling splittings are not resolved on the scale of the figure.

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tween states correlating to thej 5 2, F-symmetry SiH4

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234 KAWASHIMA ET AL.

onomer states. In their infrared investigation, Randallet al.8) observed theA-symmetry, j 5 0, K 5 0 state, the-symmetry, j 5 1, K 5 0 and 1 states, with unresolv

/K-type doubling, and theE-symmetry,j 5 2, K 5 1 statehe same states are also observed in the present measureith the additional result that the splitting of thel /K-doubled5 1, F state is resolved. This splitting is too small to se

ig. 1.

. Analysis

The observed transitions for the various isotopic formrgon–silane are listed in Table 1. Figures 2 and 3 show supectra of theJ 5 5 4 4 andJ 5 3 4 2 or J 5 4 4 3egions of28SiH4 and Ar–28SiD4. For Ar–28SiH4 and Ar–28SiD4,btained using an isotopically enriched sample, transiere observed for theK 5 0, A; K 5 0, F; K 5 1, E; and

he l /K-doubledK 5 1, F state, as expected from the infranalysis. For the Ar–29SiH4 and Ar–30SiH4 isotopic forms, theigher energyK 5 1, F state was not observed due to theatural abundances of29Si (4.7%) and30Si (3.1%) reducing thignal-to-noise ratio of the transitions. No proton spin–yperfine was resolved on any transitions in the present se note that for theK 5 0, F state in CH4–H2O (15), the CH4

pin–spin hyperfine was resolved, giving an interactiontant ofD aa 5 25 kHz. Since the magnitude ofD aa scales a1/r HH

3 &, wherer HH is the proton–proton separation, it shoe approximately a factor of 2.4 smaller in the present cnd thus not measurable at our resolution.Assignments of the symmetries to the observed transias aided by the previous infrared analysis, the obse

elative intensities, and the Stark effects of the transitioniscussed below. The frequencies of the transitions for–28SiH4 isotopic form are well predicted from the infrareasurements (8). Moreover, the relative intensities of t5 0, A; K 5 0, F; and K 5 1, E states should b

pproximately 5, 9, and 2 for the protonated species and 5nd 4 for the deuterated species, roughly consistent witbserved intensities of the spectra shown in Figs. 2 andThe transitions are fit using the linear-molecule Ham

ian:

H 5 B0J~ J 1 1! 2 DJ@ J~ J 1 1!# 2 1 HJ@ J~ J 1 1!# 3. @1#

he HJ constant was needed to fit the observed transitionoth Ar–SiH4 and Ar–SiD4 to experimental precision. Table

ists the molecular constants for Ar–28SiH4, Ar–29SiH4, Ar–30SiH4, and Ar–28SiD4.

. Dipole Moment Determination

Because of the small induced dipole moment of Ar–SiH4, noplitting of the K 5 0 lines were observed for fields up


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tark effects from which an electric-dipole moment canetermined. The observed Stark splitting of theJ 5 3 4 2,5 1 line for Ar–28SiH4 is shown in Fig. 4. The figure show

hat each of theKM components are resolved at an applectric field of 42 V/cm. In addition, the Stark componentsymmetrically split about the zero-field line center as expeor a linear Stark effect. Figure 5 shows a plot of the Shifts for theKM components of theJ 5 3 4 2, K 5 1ransition used in the dipole moment determination foriH4. The dipole moment was obtained from frequency-sersus applied electric field measurements for theKM 5 11nd12 components, which were fit to the equation,

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econd and higher-order effects were not included innalysis. The results of these fits yield a value of the eleipole moment of 9.24(8)3 10232 C z m [0.0277(2) D], wher

ype-A expanded uncertainties are given with a coverageor, k 5 3. Relative uncertainties in our knowledge oflectric field value (0.13%) are included in the reported un

ainty.

. Structure

The center-of-mass separation of the silane molecule anrgon atom can be determined from the observed rotatonstant of the complex. Each internal rotor state of the solecule has a different rotational constant, and, if these

erences are totally due to variations in the effective adiaadial potentials, different zero-point van der Waals centeass separations,Rcm. The value ofRcm can be estimated for

igid complex using the expression

I dimer 5 mRcm2 1 I monomer,

herem is a pseudodiatomic reduced mass of the complexdimer andI monomerare the moments of inertia of the complex ahe monomer, respectively. The calculated values ofRcm areiven in Table 2 for Ar–SiH4 and Ar–SiD4. TheRcm value forr–28SiH4 for the K 5 0, A state is significantly greater th

he value obtained for theK 5 0, A state of Ar–28SiD4. Thisesult holds even if we assume that the SiH4 or SiD4 subunit isreely rotating. In the free-rotor limit for theA state,I dimer 5Rcm

2 , giving Rcm values of 4.0893 and 4.0443 Å for Ar–28SiH4

nd Ar–28SiD4, respectively. For intermediate internal rotatarriers, the value ofI dimer obtained from the reciprocal of thotational constant has slightly different contributions frmonomerfor each of the internal rotor states. In addition, theI dimer

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TABLE 1Observed Microwave Transitions for Ar–28 29 30 28


SiH4, Ar– SiH4, Ar– SiH4, and Ar– SiD4

Note.Observed-calculated values are kHz. Standard uncertainties (Type B) on the line positions are estimated to be 1 kHz.

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s also affected by Coriolis interactions betweenK states of thame rovibronic symmetry.The proton–deuteron isotopic shift in the bond lengt

etween20.045 and20.082 Å, depending on the barriernternal rotation. This shift is rather large when comparedelated molecules. The shift in bond lengths between CH4–HClnd CD4–HCl is only 0.0384 Å, for example (16). Consistenith the shorter bond length for the deuterated isotopic f

he weak-bond pseudodiatomic stretching force constantrequencies obtained from

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nd listed in Table 2 show similar trends, with the deuted isotopic form having a larger stretching force cons

FIG. 2. Survey scan of theJ 5 5 4 4 andJ 5 3 4 2 transitions or–28SiH4.


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DISCUSSION

The present results are in reasonable agreement witnfrared measurements of Randallet al. (8). As shown in Table, the values for the infrared ground-state rotational cons

or the Ar–28SiH4 isotopic form are consistent with the morecise microwave measurements. Moreover, the Stark end relative intensities of the observed lines further validatssignments of Randallet al. (8). The present data also testandallet al. (8) anisotropic potential for Ar–SiH4.Close examination reveals that thel /K-doubling splitting o

heK 5 1, F state, not obtained in the Randallet al. (8) study,re well predicted by the Randallet al. (8) potentials. For the

FIG. 3. Survey scan of theJ 5 5 4 4 andJ 5 4 4 3 transitions or–28SiD4. Note that theA-state transition overlaps with one component of

/K-doubledK 5 1, F-state transition.

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3 5 60 cm21, V4 5 0 potential theB value difference,DB,etween the twoF states for the protonated and deuterapecies are 3.3 and 3.0 MHz, respectively, while for theV3 51.2 cm21, V4 5 27.8 cm21 potential theDB splittings are.0 and 2.6 MHz. These calculations were made by usispherical-top-ball” Hamiltonian with a frozen radial coorate, as discussed by Ohshima and Endo (16) and other17–18). The experimental values for the splittings are

FIG. 4. Observed Stark splitting of theE StateJ 5 3 4

FIG. 5. Plot of the frequency shift versus electric field for theKM 5 11nd12 components of theJ 5 3 4 2, K 5 1 transition.


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Hz for Ar–28SiH4 and 1.9 MHz for Ar–28SiD4. Neither thesotopic data nor thel /K-doubling splittings, however, caiscriminate between the two proposed potentials. More

he overall splitting patterns are in poor agreement withictions from the Randallet al.(8) potential. This is most likelconsequence of the neglect of the radial motion, which wllow the possibility of different radial minima for the differeymmetry andK states. Such an effect could explain,nstance, the reversal inA/E symmetry of the rotational linrequency ordering for the Ar–SiH4 isotopomer. For Ar–SiD4he A/E experimental ordering agrees with the model calcions. Further infrared studies of torsional hot bands and

5 1 transition with an applied electric field of 42 V/cm.

TABLE 3Comparison of the Rotational Constants

for Ar–28SiH4 (MHz)

Note.Type A expanded uncertainties are given with the coveragefactor, k 5 3.

2, K

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infrared studies, if feasible with the expected small oscillators ved

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6. W. Jager, Y. Xu, and M. C. L. Gerry,J. Chem. Phys.99, 919 –927(1993).

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trengths of the torsional modes, should allow an improescription of the anisotropic potential for argon–silane.

ACKNOWLEDGMENTS

The present study was supported in part by grants (05044045 and 096rom the Japanese Ministry of Education International Scientific Resrogram.

REFERENCES

1. J. M. Hutson,J. Chem. Phys.96, 6752–6767 (1992).2. J. M. Hutson,J. Phys. Chem.96, 4237–4247 (1992).3. C. A. Schmuttenmaer, R. C. Cohen, and R. J. Saykally,J. Chem. Phys

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171,189–199 (1995).2. J.-U. Grabow and W. Stahl,Z. Naturforsch. A45, 1043–1044 (1990).3. L. H. Coudert, F. J. Lovas, R. D. Suenram, and J. T. Hougen,J. Chem

Phys.87, 6290–6299 (1987).4. J. S. Muenter,J. Chem. Phys.48, 4544–4547 (1968).5. R. D. Suenram, G. T. Fraser, F. J. Lovas, and Y. Kawashima,J. Chem

Phys.101,7230–7240 (1994).6. Y. Ohshima and Y. Endo,J. Chem. Phys.93, 6256–6265 (1990).7. R. W. Randall, J. B. Ibbotson, and B. J. Howard,J. Chem. Phys.100,

7042–7050 (1994).8. J. M. Hutson and A. E. Thornley,J. Chem. Phys.100,2505 (1994).

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the rotational spectrum of ar–sih4 and ar–sid4

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