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The vibrational state (100O) of Ar…HCl excited in a pulsed jet by a glow discharge. Rotational spectrum and lifetime
Volume 198, number 3,4
CHEMICAL PHYSICS LETTERS
9 October 1992
The vibrational state ( 10’0) of Ar...HCl excited in a pulsed jet by a glow discharge. Rotational spectrum and lifetime J.W. Bevan ‘, AC Legon, CA. Rego and J. Roach Department of Chemistry, UniversityofExeter, Stocker Road, Exeter EX4 4QD. UK Received 14 July 1992; in final form 10 August 1992
Pure rotational spectra in the vibrationally excited state (10’0) of three isotopomers of the van der Waals molecule Ar...HCl have been detected with a pulsed nozzle, Fourier-transform microwave spectrometer that uses a dc glow discharge to excite molecules emerging from the nozzle. The spectroscopic constants B,, D, and x1(Cl) associated with the ( 10’0) state are reported. A comparison oflinewidths for the states ( 10’0) and (00’0) and time-of-flight arguments allow the conclusion that the lifetime for vibrational predissociation from the state (1 O”O)is rk 300 us.
1. Introduction The experimental accessibility and simplicity of Ar...HCl have made it, in many respects, the quintessential van der Waals molecule. Its existence was originally inferred from structure observed in the infrared spectrum of HCl in argon at relatively high pressure [ 1,2 1. Ground-state spectroscopic constants were later determined from the rotational spectrum observed via the molecular beam electric resonance technique [3,4] and were used in combination with data from molecular beam scattering, HCl line broadening by argon and with second virial coefficients to give model potential energy surfaces for Ar...HCl [ 5,6]. The latter proved accurate in their prediction of the wavenumbers of the van der Waals vibrational transitions that were subsequently observed by far-infrared spectroscopy [ 7-9 1. The rotationally resolved fundamental ( 10’0) t (00’0) observed by Howard and Pine [ IO] in the near-infrared region also provided important information about the potential energy function, especially an accurate dissociation energy Do from the abrupt cut-off in the spectrum at high J caused by rotational predissociation. Another phenomenon of particular inCorrespondence to: A.C. Legon, Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK. ’ Royal Society Guest Research Fellow. 0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers
B.V.
terest for Ar...HCl is vibrational predissociation from low J rotational states of ( 1O’O),for the vibrational energy of the state ( 1OOO)is approximately 25 times the energy required to dissociate the complex [lo]. This process may be viewed as a prototype of the elementary unimolecular step in a unimolecular reaction and the predissociative lifetime of the state ( 10’0) is therefore a quantity of importance. An accurate close-coupling calculation using the best potential energy function then available led Hutson [ II] to predict a value of about 2 us for the vibrationally predissociative lifetime of the state (10’0) of Ar...HCl. Contributions of the order 100 kHz from this source to the linewidths of low J transitions in the rotationally resolved fundamental ( 10’0) e (OOOO) band were therefore expected. Unfortunately, linewidths observed in the near-infrared spectra of the molecule [ 10,12,13] were in the range 40-100 MHz as a result of pressure broadening, Doppler broadening and other effects, thereby swamping the predicted contribution from predissociation. Another way to obtain information about the predissociative lifetime would be to observe the pure rotational spectrum of Ar...HCI in the state (lO”0) using a supersonically expanded gas jet. Linewidths of 10 kHz or less are routinely available from pulsed-nozzle, Fourier-transform microwave spectroscopy, see, for example, ref. [ 141. However, application of this technique has been restricted All rights reserved.
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largely to vibrational ground states as a result of the low effective temperatures in the jet. Even at room temperature the population of the (10’0) state of Ar...HCl is only 9X lo-’ times that of the ground state. How can a population of the state (10’0) of Ar...HCI be achieved in a supersonic jet sufficient to allow the pure rotational spectrum in that state to be observed? The application of a pulsed glow-discharge to a supersonically expanding jet is recognised as an effective method for producing significant populations of vibrationally and other excited states [ 151. The combination of a glow-discharge with a pulsed nozzle in Fourier-transform microwave spectroscopy offers a powerful method of observing the pure rotational spectra of van der Waals molecules in which one of the monomer vibrations is excited, given that the excited state is sufficiently long-lived. In this Letter, we describe the use of such a combination of techniques to observe the rotational spectrum of Ar...HCI in the state ( 10’0). As well as accurate Clnuclear quadrupole coupling constants, rotational constants and centrifugal distortion constants for the isotopomers Ar...H3SCl, Ar...H3’C1 and Ar...D3’Cl, we report an improved lower limit to the lifetime of the vibrationally predissociative state ( 10°O) of Ar...H35C1as determined from a comparison of linewidths of transitions in the ( 10’0) and (00’0) states and time-of-flight considerations.
composed of 1% hydrogen chloride (Argo International) in argon and held at a stagnation pressure of 3 atm, was expanded from the solenoid valve through the ring electrode, the instantaneous gas pressure allowed a dc glow discharge to be sustained in the gas at a peak current of ~600 LA. We estimate that a few percent of the HCl molecules in each gas pulse were thereby excited to the v= 1 state. Gas pulses emerging from the nozzle system then expanded further into the evacuated Fabry-Perot cavity of the spectrometer, forming in the process Ar...HCl molecules in the ( 10’0) state. The vibrational predissociative and fluorescence lifetimes of the excited dimers were sufficiently long for a detectable fraction to survive the approximately 20 cm of travel to reach the axis of the Fabry-Perot cavity and to be polarized by a 1 ps microwave pulse. Rotational spectra of the excited Ar...H35C1and Ar...H3’Cl were then recorded in the usual way [ 141. A frequency domain recordingoftheunresolvedF=7/2+5/2andF=9/ 2+7/2 pair of Cl nuclear quadrupole components in the J= 36-2 transition of ( 10’0) Ar...HjSC1is shown in fig. 1 and was obtained by averaging 427 gas pulses.
2. Experimental The rotational spectrum of Ar...HCl in the vibrationally excited state ( 10’0) was observed by using a pulsed glow-discharge nozzle as the source of supersonically expanded, vibrationally excited Ar...HCl molecules in our pulsed-nozzle, Fouriertransform microwave spectrometer [ 141. The pulsed glow-discharge nozzle consisted of a Series 9 (General Valve Corporation) solenoid valve but with a stainless-steel ring (5 mm inner diameter, 9 mm outer diameter) held concentrically with the 0.7 mm orifice and at 3 mm from the base plate. The ring was maintained at a nominal dc potential of - 1400 V while the case of the solenoid valve was at earth potential. When a pulse (Z 1 ms duration) of gas mixture, 348
2
50
150
100 Frequency
offset
200
, kHZ
Fig. 1. Frequency domain recording of the F=7/2+5/2 and F=9/2+7/2 unresolved pair of Cl-nuclear quadrupole components in the J=3+2 transition of Ar...HW in the vibrational state ( 10’0). The signals from 427 gas pulses, each subject to a dc glow discharge (see text), were averaged to give this spectrum. Frequencies are offset at a rate of 3.90625 kHz/point from the excitation frequency of 9975.8706 MHz and the dots have been joined by a cubic spline function. The doublet arises from the familiar Doppler effect.
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The linewidth of the two familiar Doppler doublets is discussed in detail below. Rotational spectra of ( 10°O) Ar...D35Clwere recorded similarly but by using DC1 prepared by dehydrating a solution of 20% DC1 in DzO (Aldrich Chemical Company) with PZ05.
3. Results 3.1. Rotational transitions and spectroscopic constants of Ar...HCl in the state (10’0) The search for rotational transitions of Ar...H35C1 in the ( 10’0) state was carried out in the region suggested by the rotational constant B, and the centrifugal distortion constant D, obtained in the analysis of the ( 10’0) t (00’0) fundamental band in the nearinfrared spectrum [ lo]. The Cl-nuclear quadrupole coupling constant x( 35C1)used in the prediction was assumed unchanged from the ground state [ 4,161. Transitions were readily observed near to the predicted frequencies with good signal-to-noiseratio (see fig. 1). Observed frequencies of hyperfine components in the J=3+2 and 4-3 transitions of Ar...Hj$Cl, Ar...H37Cl and Ar...D3sC1,each in the ( 10’0) state, are recorded in table 1. Full widths at half maximum were approximately 10 kHz and hence allowed frequencies to be measured with an accuracy of 1 kHz for the H-species but unresolved D-nuclear quadrupole hyperfine structure in Ar...D3V1 gave
9 October 1992
broader lines and slightly less accurate frequencies. The rotational spectrum in the ( 10’0) state was fitted for each isotopomer in a standard iterative least-squares analysis in which the complete matrix of the linear-molecule Hamiltonian H=B,J2-D,J4-;Q:VE
(1)
was constructed in the coupled basis I+J=F and diagonalised in blocks of F. The residuals obtained in the final cycle of the fit are included in table 1 and indicate that the Hamiltonian ( 1) was entirely satisfactory for Ar...H35C1and Ar...H37CI.The neglect of D-nuclear quadrupole effects in Ar...D3’C1led, as expected, to larger residuals. The determined spectroscopic constants B,, D,, and xl (Cl) = eq, Q are displayed in table 2. The values of BL and D1 for Ar...H3’C1and Ar...H37C1are in excellent agreement with those from the infrared spectrum [ lo]. The x1(Cl) values are larger in magnitude, by *9% for the HCl species and x 5Ohfor the DC1 species, than the corresponding ground-state quantities xo(Cl) [4,161. 3.2.Dynamics of Ar...HCl in the vibrational state (10%)
The principal dynamical interest of the present work centres on the lifetime for vibrational predissociation from the excited state (10’0) of Ar...HCl. Once in collisionless expansion in a supersonic jet, a ( 10°O) state Ar...HCl molecule can lose its vibra-
Table 1 Observed and calculated rotational transition frequencies in the vibrational state ( 10’0) of Ar...H”CI, Ar...H”CI and Ar...D3W Transition
ArII.H3’CI
Ar...H3’Cl
Ar...D35CI
J’eJ”
F’eF”
3-2
512-312 3/2cl/2 7/2+5/2 9/2+7/2
9974.0831 9974.0831 9975.6316 9975.6316
1.1 -1.4 0.3 0.0
9695.0768 9695.0768 9696.2957 9696.2957
0.8 -0.8 0.1 -0.1
9869.0190 9869.0190 9871.3728 9871.3728
1.8 -4.0 1.4 0.8
4-3
7/2+5/2 5/2+3/2 9/2+7/2 11/2+9/2
13297.6822 13297.6822 13298.4071 13298.4071
0.0 0.7 -0.3 -0.4
12925.5576 12925.5576 12926.1288 12926.1288
0.2 -0.2 0.1 -0.1
13158.5277 13158.5277 13159.6254 13159.6254
3.1 1.5 -2.1 -2.5
u (MHz)
Au &Hz) a)
v(MHz)
Au (kHz) a)
Y (MHz)
Au (kHz) ‘I
a1Au= v,~,- v,,,~
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Table 2 Spectroscopic constants of three isotopic species of Ar...HCl in the vibrational state ( 10’0) Spectroscopic constant
Ar...H3CI
Ar ..H3’C1
AI.. D3>C1
4 (MHz)
1662.9135(2) 19.883(7) -24.998( 13)
1616,3480(l) 18.768(4) -19.683(g)
1645.4563(7) 16.838(23) -37.96(4)
J% (kHz) x,(Cl) (MHz)
tional through
excitation coupling
in two ways:
by predissociation
to the translational
continuum
of
Ar and (v=O, J)HCl molecules and by fluorescence. Since the vibrational energy of the state (10%) is ~25 times the ground-state dissociation energy Do of Ar..,HCI, the first mechanism is clearly available, If the lifetime of the vibrationally predissociating state is short enough, it will be reflected in a contribution to the breadth of rotational transitions in the ( 10’0) state detectable by the present technique. The contribution of fluorescence to the breadth of the ( 10’0) state will be negligible ( < 0.01 kHz) if the fluoresence lifetime is similar to that of (u=l)HCl [17]. Figs. 1 and 2 show the same hyperfine component of the same rotational transition (J=3+2) of Ar...H3?Z1in the states (10’0) and (OOOO),respectively, recorded under identical instrumental conthe separate
50
100 Frequency
150 offset
200
.I
I kHZ
Fig. 2. Frequency domain recording of the F=7/2+5/2 and F=9/2+7/2 pair of Cl-nuclear quadrupole components in the I- 3~2 transition of Ar...H%l in the ground state (00’0). The conditions are identical to those for fig. 1, except that only four gas pulses were employed. Frequencies are offset at a rate of 3.90625 kHz/point from 10069.4806MHz.
350
ditions. It is clear that in each, the two components of the familiar Doppler doublet have full widths at half maximum, Av,,~, of x 10 kHz. In fact, the mean of 10 measurements of Av,,~ gave values of 10.9( 8 ) kHz and 10.2( 5) kHz for the states (10’0) and (OO’O),respectively. Although there is an indication of a slight increase of 0.7 kHz in AY,,~on excitation of one quantum of the mode Y,, this is probably not experimentally significant, as will be made clear when the time-of-flight of the excited molecules before detection is considered below. Even if the determined increase in Av,,, on vibrational excitation were experimentally significant, it would be difficult to relate it to an accurate value for z, the predissociative lifetime of the excited state. The observed lineshapes in the pulsed-nozzle FT microwave experiment are complicated by the Doppler doubling effect, the origin [ I S] of which appears to be in dispute [ 191 and for which there is no simple lineshape function. In the case of the J=3+2 transitions of Ar...H3’Cl, shown in figs. 1 and 2, there is the additional complication that each Doppler component is the result of the blending of an unresolved pair (separation 4 kHz ). The problem is how to deconvolute the various contributions to Av,,~. Two limiting approaches are possible. If the observed increase in Avl ,2 on vibrational excitation were all assigned to predissociative broadening of rotational transitions in the state (10'0) (i.e. if the various other contributions such as transit time broadening, T2damping, etc. were all unchanged on vibrational excitation) and if all contributions were assumed additive (i.e. Lorentzian ), the implied value of the predissociation lifetime would be r= (2kA~)-’ ~230 ps. If, on the other hand, the observed Av,/~ results from the convolution of Lorentzians (for the homogeneous broadening effects) and a Gaussian (for the Doppler effect) the appropriate expression is Au,,, x (Av~+Av&)‘/~ [ 201 and the increase of Av,,~ on vibrational excitation then corresponds to a predissociation width of
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about 3.5 kHz and hence to za45 ps for the state ( 10’0). However, the time of flight of molecules from the nozzle to the point of detection in the present experiment shows that 5 must be significantly greater than 45 ps. Gas pulses that have been subjected to the dc glow discharge travel at a speed of 5 x lo4 cm s- ’ [ 181 in a direction perpendicular to the axis of the FabryPer& cavity. The geometry of the experiment is such that a molecule must travel in collisionless expansion for 15 cm before it reaches the microwave beam waist, i.e. the point at which the microwave standing wave electric field of the cavity has the value of l/ e of its maximum (axis) value. We can assume [ 181 that the polarization of molecules lying between the nozzle and the beam waist, and its subsequent contribution to the spontaneous coherent emission recorded at the detector, is not significant. Hence,the time of flight of molecules that reach the beam waist and are detected is at least 300 ps. Measurements, under identical conditions, of the ratio of the amplitudes of time-domain signals collected from Ar...H3’Cl molecules in the states ( 10’0) and (00’0) led to the ratio (N, /No)t in the range 0.03-0.05 for the populations of these states after the time of flight t> 300 ps. If T were, say, 100 ps the value (NJ&,), at time zero (i.e. immediately after excitation at the nozzle) would then have to be in the range 0.6 to 1.0, implying an effective vibrational temperature between T,x 8000 and co K. Even for z= 200 ks, the ranges would have to be 0.13-0.22 and 2050-2750 Kfor (N,/N,), and TV,respectively. But these vibrational temperatures are too high. In separate discharge experiments carried out under similar conditions but detecting signals from the monomer 160’2C32Sin argon, the ratio’of the population of the v3= 1 state (2062 cm- ’ ) to that of the ground state after the same time of flight was found to be (N3/No),=0.05 and corresponds to TV= 1000 K (losses due to fluorescence are negligible on this timescale). If similar vibrational temperatures and populations of ( 10’0) Ar...H35C1are produced in the discharge, it therefore seems likely that ~3300 ps. Interestingly, Huang et al. [ 2 1 ] find a lower limit of 300 ps for the lifetime of ( lO’O)Ar...HF from an infrared experiment in which the excited molecules survive long enough in a beam without dissociation to reach a bolometer.
9 October 1992
The other dynamical aspect of interest in the ( 10’0) state of Ar...HCl is the angular oscillation of the HCl subunit. It has been shown for Ar...HCl [ 16]
that the coupling constant x0( Cl) in the ground state is given accurately by the projection of the free HCl value xz(Cl) onto the a axis of the dimer. In the present case, xl(Cl) is therefore related to the coupling constant #(Cl) of the v= 1 state of free HCl by XI(Cl) = fxY(Cl) (3 coszO- 1 > ,
(2)
where 8 is the angle between the HCl direction and the a axis, as defined in fig. 3, and the average is over the state uI= 1. When the $(Cl) collected in table 3 [ 221 are used in eq. (2) with the appropriate xl (Cl) of table 2, the operationally defined angles e,,=cos-‘(cos2e> I/* shown in table 4 result. Also included in table 4 is the corresponding set of 0,, for the (OOOO)states of the three isotopomers investigated [ 3,4,16]. We note that excitation of v, = 1 leads in each case to a decrease in 0,“. This is consistent with a strengthening of the van der Waals bond when the HCl stretch is excited. Such an effect is also apparent in a small increase in the wavenumber of the intermolecular stretching mode vj when v, is excited [ 121. A recent potential energy function [ 231 shows that the barrier to internal rotation of the HCl subunit increases from the state (OOOO)to the state ( 10°O), a result consistent with the changes in x(C1) established experimentally. 3.3. Dimer geometry and van der Waals stretching force constant in the state (1000) For a complex such as Ar...HCl, in which the vibrations are anharmonic and in which the bending and stretching modes are strongly mixed, there are obvious difficulties in applying the usual models [ 24-
Fig. 3. Definition of the angles 0 and a and the distance rc.m.for the model of Ar...HCl described in the text.
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Volume 198, number 3,4
Table 3 Spectroscopic and geometrical properties of hydrogen chloride in the vibrational state u- 1 Property
H’%ZI
H3’C1
D”CI
B, (MHz) a) x,(Cl) (MHz) a) I1 (A) b,
303876.51 -69.2729(9) 1.30298
303414.14 - 54.5985 1.30298
158284.92 -68.5831(10) 1.29481
a) Ref. 1221. The value ofX,(“‘Cl) was obtained by scalingx, (%l) by the ratio Q”/Q”. b, Calculated from B, =h/llx’pr:.
Table 4 Structural parameters of the Ar...HCl dimer in the ( 10’0) and (00’0) vibrational states a) Vibrational state
Ar...H35CI Ar...H3’C1 Ar...D’5CI
(OOOO) b,
(1OOO) 0,” (deg)
<&n.>“* (A)
r(Ar...Cl) (A)
0,” (deg)
<&.>“‘(A)
r(Ar...Cl)
40.750(S) 40.764(6) 33.065(25)
3.9956 3.9988 3.981 I
4.0233 4.0250 4.0402
41.531(l) 41.53 33.750(l)
3.9795 3.9801 3.9667
4.0065 4.0059 4.0247
(A)
a) Errors in (rim, ) 1’2and r(Ar...Cl) propagated from errors in the spectroscopic constants are less significant than the last digit quoted. Errors from limitations in the model used to calculate these quantities are likely to be larger. b, Calculated from spectroscopic constants in refs. [ 3,4,16] using the methods discussed in the text.
261 to determine the radial geometry and the intermolecular stretching force constant from rotational and centrifugal distortion constants, respectively. It is nevertheless of interest to apply the models here to obtain an indication of the changes that occur in these molecular properties on excitation of v, and, if possible, identify trends. When determining the separation of the two subunits in a weakly bound dimer, such as Ar...HCl, from rotational constants, partial allowance for the contribution of the intermolecular modes of vibration is often made by using a model of the type shown in fig. 3. The HCl subunit is assumed rigid and to oscillate about its centre of mass through the angle LX. The distance r,.,. is taken as fixed, an assumption equivalent to ignoring the effect of the van der Waals stretching mode. This model leads for Ar...HCl to the expression [ 24,251 (~bb)=1((~~.,.)+t~bHC’(l+(cos2~)),
(3)
where the moment of inertia lEcl = h/81cZBzC’is defined operationally in terms of the rotational constant BFc’ of the appropriate state v of free HCl [ 221. The average in eq. (3) is over the angular motion of the HCl subunit and~u=mA’mHC’/(mAr+mHC1).In 352
the approximation that eq. (3 ) is valid for the state (10’0) of Ar...HCl, that (&,,) =I,=h/87c2B, and that (cos2@ can be used in place of (cos201), ( r&,.,.} I/* can be estimated using eq. ( 3). Values for the state ( 10’0) of the three isotopomers of Ar...HCl investigated are given in table 4. The necessary values of 0,” are also recorded in table 4 while the rotational constants are in tables 2 and 3. A measure of the distance r(Ar...Cl) in the state ( 10’0) is then given by r(Ar...Cl)= ( rf,,,)1/2+r(cos
a> ,
(4)
where r is the distance of Cl from the HCl mass centre. The various r(Ar...Cl) so calculated are also collected in table 4. For purposes of comparison, the corresponding set of quantities for the ground state (OO”O)of Ar...HCI, calculated from previously published spectroscopic constants [ 3,161, are included in table 4. Interestingly, r(Ar...Cl) is longer in the (10’0) state by about 0.02 A, which is also the lengthening of the free HCl molecule on excitation from v= 0 to v= 1. We have observed a similar effect in Kr...HCl [ 271. Finally, the centrifugal distortion constant D, has been used in the expression
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Table 5 Effective force constants /c~and wavenumbers Fs of the van der Waals stretching mode of the dimer Ar...HCl in the ( 10’0) and (00’0) vibrational states Vibrational state
Ar...HJsCl Ar...H3’Cl Ar...D%Zl
(1000)
(OOOO) n)
kl (Nm-I)
v; (cm-‘) b,
k, (Nm-I)
fl, (cm-‘) b,
1.1419 (5) 1.1428 (3) 1.319 (2)
31.973 (6) 31.538 (3) 34.12 (3)
1.1640 (3) 1.1658 (3) 1.33 (3)
32.281 (4) 31.856 (2) 34.2 (3)
‘) Calculated from centrifugal distortion constants Do=20.058 (5) and 18.920 (4) kHz for Ar...H%I and Ar...H”CI, respectively, from unpublished measurements. k, for Ar...D3’Cl was obtained from Do given in ref. [ 31. b, Cahxdated from k, using & = (2rc) - ’ ( k,/p) I’*.
k3 = ( 161r*B;~/D,) ( 1-I?,/B;c’)
,
(5)
due to Millen [26] to estimate the quadratic force constant k3 associated with the van der Waals stretching mode in each of the states ( 10°O) and ( 00’0 ) . The required spectroscopic constants B, , D, and BrC’ for the ( lOoft) state are given in tables 2 and 3 while those (B,, Do and BfC’) for the state (00’0) are available elsewhere [ 3,4,16,22]. The results for k, and for the corresponding wavenumbers ~~=(2~-‘(k,/~)“~aresetoutintable5.Wenote that the strength of the van der Waals bond, as measured by kJ,is essentially unaffected by excitation of V, and that the & are in good agreement with those available from far- and near-infrared spectroscopy [ 7,121, that is 32.44 and 32.64 cm -r from the transitions (OO”l)t(OOoO) and (lO”l)t(OOoO), respectively, for Ar...H35C1.Such agreement also obtains for Kr...HCl [ 271.
4. Conclusion We have used a dc glow discharge in conjunction with a pulsed-nozzle, Fourier-transform microwave spectrometer to excite and detect the rotational spectrum of each of three isotopomers of Ar...HCl in the vibrationally excited state ( 10’0). A comparison of observed full-widths at half maximum of rotational transitions in the states (10’0) and (00’0) of Ar...H3’Cland time-of-flight considerations allow the lower limit of 7~300 ps to be placed on the vibrationally predissociative lifetime of the ( 10’0) state. We note that the technique introduced here has
wider applications than reported in this publication. It is generally applicable to the investigation of rotational spectra in the vibrationally excited states of a wide range of molecules and possibly to the production of other types of short-lived species. The adaptation of a pulsed nozzle to allow emergent molecules to be subjected to an electrical discharge is part of a general programme to use modified nozzles for the generation (by, e.g., fast mixing [28], pyrolysis [ 291, electrical and microwave discharge) of transient molecules.
Acknowledgement
We thank Dr. Peter Hamilton of QMWC London for helpful advice and discussion. One of us (ACL) thanks the SERC for a research grant in support of our work in the detection of transient species using modified nozzles and the Royal Society for the award of a Guest Research Fellowship (for JWB). JWB thanks the Texas A & M Former Students Association Sabbatical Leave Program, NSF and the Robert A. Welch Foundation for additional support.
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[4] S.E. Novick, KC Janda, S.L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys. 65 (1976) 1114. [ 51 J.M. Hutson and B.J. Howard, Mol. Phys. 43 ( 1981) 493. [6] J.M. Hutson and B.J. Howard, Mol. Phys. 45 ( 1982) 769. [ 7 ] R.L. Robinson, D.-H. Gwo and R.J. Saykally,J. Chem. Phys. 87 (1987) 5156. [8] R.L. Robinson, D. Ray, D.-H. Gwo and R.J. Saykally, J. Chem. Phys. 87 ( 1987) 5149. [9] K.L. Busarow, GA. Blake, KB. Laughlin, R.C. Cohen, Y.T. Lee and R.J. Saykally,J. Chem. Phys. 89 (1988) 1268. [IO] B.J. Howardand A.S. Pine, Chem. Phys. Letters 122 (1985)
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[ 181E.J. Campbell, L.W. Buxton, T.J. Balle, M.R. Keenan and W.H.Flygare, J.Chem. Phys. 74 (1981) 813,829; T.J. Balle and W.H. Flygare, Rev. Sci. Instrum. 52 ( 1981) 33. [19] F.J. Lovas and R.D. Suenram, J. Chem. Phys. 87 (1987) 2010. [20] C.H. Townes and A.L. Schawlow, Microwave spectroscopy (McGraw-Hill, New York, 1955) p. 375. [ 2 I] Z.S. Huang, K.W. Jucks and R.E. Miller, J. Chem. Phys. 85 (1986) 6905. [22] E.W. Kaiser, J. Chem. Phys. 53 (1970) 1686. [23] J.M. Hutson, J. Phys. Chem. 96 ( 1992) 4237. [24] AC. Legon and L.C. Willoughby, Chem. Phys. 85 (1984) 443. [25 ] G.T. Fraser, KR. Leopold, D.D. Nelson Jr., A. Tung and W. Klemperer, J. Chem. Phys. 80 (1984) 3073. [26] D.J. Millen, Can. J. Chem. 63 (1985) 1477. [27 ] J.W. Bevan, AC. Legon and C.A. Rego, unpublished results. [ 28 ] A.C. Legon and C.A. Rego, Angew. Chem. Intern. Ed. Engl. 29 (1990) 72. [29]A.C. Legon and D. Stephenson, J. Chem. Sot. Faraday Trans. 87 (1991) 3325.
CHEMICAL PHYSICS LETTERS
9 October 1992
The vibrational state ( 10’0) of Ar...HCl excited in a pulsed jet by a glow discharge. Rotational spectrum and lifetime J.W. Bevan ‘, AC Legon, CA. Rego and J. Roach Department of Chemistry, UniversityofExeter, Stocker Road, Exeter EX4 4QD. UK Received 14 July 1992; in final form 10 August 1992
Pure rotational spectra in the vibrationally excited state (10’0) of three isotopomers of the van der Waals molecule Ar...HCl have been detected with a pulsed nozzle, Fourier-transform microwave spectrometer that uses a dc glow discharge to excite molecules emerging from the nozzle. The spectroscopic constants B,, D, and x1(Cl) associated with the ( 10’0) state are reported. A comparison oflinewidths for the states ( 10’0) and (00’0) and time-of-flight arguments allow the conclusion that the lifetime for vibrational predissociation from the state (1 O”O)is rk 300 us.
1. Introduction The experimental accessibility and simplicity of Ar...HCl have made it, in many respects, the quintessential van der Waals molecule. Its existence was originally inferred from structure observed in the infrared spectrum of HCl in argon at relatively high pressure [ 1,2 1. Ground-state spectroscopic constants were later determined from the rotational spectrum observed via the molecular beam electric resonance technique [3,4] and were used in combination with data from molecular beam scattering, HCl line broadening by argon and with second virial coefficients to give model potential energy surfaces for Ar...HCl [ 5,6]. The latter proved accurate in their prediction of the wavenumbers of the van der Waals vibrational transitions that were subsequently observed by far-infrared spectroscopy [ 7-9 1. The rotationally resolved fundamental ( 10’0) t (00’0) observed by Howard and Pine [ IO] in the near-infrared region also provided important information about the potential energy function, especially an accurate dissociation energy Do from the abrupt cut-off in the spectrum at high J caused by rotational predissociation. Another phenomenon of particular inCorrespondence to: A.C. Legon, Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK. ’ Royal Society Guest Research Fellow. 0009-2614/92/$ 05.00 0 1992 Elsevier Science Publishers
B.V.
terest for Ar...HCl is vibrational predissociation from low J rotational states of ( 1O’O),for the vibrational energy of the state ( 1OOO)is approximately 25 times the energy required to dissociate the complex [lo]. This process may be viewed as a prototype of the elementary unimolecular step in a unimolecular reaction and the predissociative lifetime of the state ( 10’0) is therefore a quantity of importance. An accurate close-coupling calculation using the best potential energy function then available led Hutson [ II] to predict a value of about 2 us for the vibrationally predissociative lifetime of the state (10’0) of Ar...HCl. Contributions of the order 100 kHz from this source to the linewidths of low J transitions in the rotationally resolved fundamental ( 10’0) e (OOOO) band were therefore expected. Unfortunately, linewidths observed in the near-infrared spectra of the molecule [ 10,12,13] were in the range 40-100 MHz as a result of pressure broadening, Doppler broadening and other effects, thereby swamping the predicted contribution from predissociation. Another way to obtain information about the predissociative lifetime would be to observe the pure rotational spectrum of Ar...HCI in the state (lO”0) using a supersonically expanded gas jet. Linewidths of 10 kHz or less are routinely available from pulsed-nozzle, Fourier-transform microwave spectroscopy, see, for example, ref. [ 141. However, application of this technique has been restricted All rights reserved.
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largely to vibrational ground states as a result of the low effective temperatures in the jet. Even at room temperature the population of the (10’0) state of Ar...HCl is only 9X lo-’ times that of the ground state. How can a population of the state (10’0) of Ar...HCI be achieved in a supersonic jet sufficient to allow the pure rotational spectrum in that state to be observed? The application of a pulsed glow-discharge to a supersonically expanding jet is recognised as an effective method for producing significant populations of vibrationally and other excited states [ 151. The combination of a glow-discharge with a pulsed nozzle in Fourier-transform microwave spectroscopy offers a powerful method of observing the pure rotational spectra of van der Waals molecules in which one of the monomer vibrations is excited, given that the excited state is sufficiently long-lived. In this Letter, we describe the use of such a combination of techniques to observe the rotational spectrum of Ar...HCI in the state ( 10’0). As well as accurate Clnuclear quadrupole coupling constants, rotational constants and centrifugal distortion constants for the isotopomers Ar...H3SCl, Ar...H3’C1 and Ar...D3’Cl, we report an improved lower limit to the lifetime of the vibrationally predissociative state ( 10°O) of Ar...H35C1as determined from a comparison of linewidths of transitions in the ( 10’0) and (00’0) states and time-of-flight considerations.
composed of 1% hydrogen chloride (Argo International) in argon and held at a stagnation pressure of 3 atm, was expanded from the solenoid valve through the ring electrode, the instantaneous gas pressure allowed a dc glow discharge to be sustained in the gas at a peak current of ~600 LA. We estimate that a few percent of the HCl molecules in each gas pulse were thereby excited to the v= 1 state. Gas pulses emerging from the nozzle system then expanded further into the evacuated Fabry-Perot cavity of the spectrometer, forming in the process Ar...HCl molecules in the ( 10’0) state. The vibrational predissociative and fluorescence lifetimes of the excited dimers were sufficiently long for a detectable fraction to survive the approximately 20 cm of travel to reach the axis of the Fabry-Perot cavity and to be polarized by a 1 ps microwave pulse. Rotational spectra of the excited Ar...H35C1and Ar...H3’Cl were then recorded in the usual way [ 141. A frequency domain recordingoftheunresolvedF=7/2+5/2andF=9/ 2+7/2 pair of Cl nuclear quadrupole components in the J= 36-2 transition of ( 10’0) Ar...HjSC1is shown in fig. 1 and was obtained by averaging 427 gas pulses.
2. Experimental The rotational spectrum of Ar...HCl in the vibrationally excited state ( 10’0) was observed by using a pulsed glow-discharge nozzle as the source of supersonically expanded, vibrationally excited Ar...HCl molecules in our pulsed-nozzle, Fouriertransform microwave spectrometer [ 141. The pulsed glow-discharge nozzle consisted of a Series 9 (General Valve Corporation) solenoid valve but with a stainless-steel ring (5 mm inner diameter, 9 mm outer diameter) held concentrically with the 0.7 mm orifice and at 3 mm from the base plate. The ring was maintained at a nominal dc potential of - 1400 V while the case of the solenoid valve was at earth potential. When a pulse (Z 1 ms duration) of gas mixture, 348
2
50
150
100 Frequency
offset
200
, kHZ
Fig. 1. Frequency domain recording of the F=7/2+5/2 and F=9/2+7/2 unresolved pair of Cl-nuclear quadrupole components in the J=3+2 transition of Ar...HW in the vibrational state ( 10’0). The signals from 427 gas pulses, each subject to a dc glow discharge (see text), were averaged to give this spectrum. Frequencies are offset at a rate of 3.90625 kHz/point from the excitation frequency of 9975.8706 MHz and the dots have been joined by a cubic spline function. The doublet arises from the familiar Doppler effect.
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The linewidth of the two familiar Doppler doublets is discussed in detail below. Rotational spectra of ( 10°O) Ar...D35Clwere recorded similarly but by using DC1 prepared by dehydrating a solution of 20% DC1 in DzO (Aldrich Chemical Company) with PZ05.
3. Results 3.1. Rotational transitions and spectroscopic constants of Ar...HCl in the state (10’0) The search for rotational transitions of Ar...H35C1 in the ( 10’0) state was carried out in the region suggested by the rotational constant B, and the centrifugal distortion constant D, obtained in the analysis of the ( 10’0) t (00’0) fundamental band in the nearinfrared spectrum [ lo]. The Cl-nuclear quadrupole coupling constant x( 35C1)used in the prediction was assumed unchanged from the ground state [ 4,161. Transitions were readily observed near to the predicted frequencies with good signal-to-noiseratio (see fig. 1). Observed frequencies of hyperfine components in the J=3+2 and 4-3 transitions of Ar...Hj$Cl, Ar...H37Cl and Ar...D3sC1,each in the ( 10’0) state, are recorded in table 1. Full widths at half maximum were approximately 10 kHz and hence allowed frequencies to be measured with an accuracy of 1 kHz for the H-species but unresolved D-nuclear quadrupole hyperfine structure in Ar...D3V1 gave
9 October 1992
broader lines and slightly less accurate frequencies. The rotational spectrum in the ( 10’0) state was fitted for each isotopomer in a standard iterative least-squares analysis in which the complete matrix of the linear-molecule Hamiltonian H=B,J2-D,J4-;Q:VE
(1)
was constructed in the coupled basis I+J=F and diagonalised in blocks of F. The residuals obtained in the final cycle of the fit are included in table 1 and indicate that the Hamiltonian ( 1) was entirely satisfactory for Ar...H35C1and Ar...H37CI.The neglect of D-nuclear quadrupole effects in Ar...D3’C1led, as expected, to larger residuals. The determined spectroscopic constants B,, D,, and xl (Cl) = eq, Q are displayed in table 2. The values of BL and D1 for Ar...H3’C1and Ar...H37C1are in excellent agreement with those from the infrared spectrum [ lo]. The x1(Cl) values are larger in magnitude, by *9% for the HCl species and x 5Ohfor the DC1 species, than the corresponding ground-state quantities xo(Cl) [4,161. 3.2.Dynamics of Ar...HCl in the vibrational state (10%)
The principal dynamical interest of the present work centres on the lifetime for vibrational predissociation from the excited state (10’0) of Ar...HCl. Once in collisionless expansion in a supersonic jet, a ( 10°O) state Ar...HCl molecule can lose its vibra-
Table 1 Observed and calculated rotational transition frequencies in the vibrational state ( 10’0) of Ar...H”CI, Ar...H”CI and Ar...D3W Transition
ArII.H3’CI
Ar...H3’Cl
Ar...D35CI
J’eJ”
F’eF”
3-2
512-312 3/2cl/2 7/2+5/2 9/2+7/2
9974.0831 9974.0831 9975.6316 9975.6316
1.1 -1.4 0.3 0.0
9695.0768 9695.0768 9696.2957 9696.2957
0.8 -0.8 0.1 -0.1
9869.0190 9869.0190 9871.3728 9871.3728
1.8 -4.0 1.4 0.8
4-3
7/2+5/2 5/2+3/2 9/2+7/2 11/2+9/2
13297.6822 13297.6822 13298.4071 13298.4071
0.0 0.7 -0.3 -0.4
12925.5576 12925.5576 12926.1288 12926.1288
0.2 -0.2 0.1 -0.1
13158.5277 13158.5277 13159.6254 13159.6254
3.1 1.5 -2.1 -2.5
u (MHz)
Au &Hz) a)
v(MHz)
Au (kHz) a)
Y (MHz)
Au (kHz) ‘I
a1Au= v,~,- v,,,~
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Volume 198, number 3,4
Table 2 Spectroscopic constants of three isotopic species of Ar...HCl in the vibrational state ( 10’0) Spectroscopic constant
Ar...H3CI
Ar ..H3’C1
AI.. D3>C1
4 (MHz)
1662.9135(2) 19.883(7) -24.998( 13)
1616,3480(l) 18.768(4) -19.683(g)
1645.4563(7) 16.838(23) -37.96(4)
J% (kHz) x,(Cl) (MHz)
tional through
excitation coupling
in two ways:
by predissociation
to the translational
continuum
of
Ar and (v=O, J)HCl molecules and by fluorescence. Since the vibrational energy of the state (10%) is ~25 times the ground-state dissociation energy Do of Ar..,HCI, the first mechanism is clearly available, If the lifetime of the vibrationally predissociating state is short enough, it will be reflected in a contribution to the breadth of rotational transitions in the ( 10’0) state detectable by the present technique. The contribution of fluorescence to the breadth of the ( 10’0) state will be negligible ( < 0.01 kHz) if the fluoresence lifetime is similar to that of (u=l)HCl [17]. Figs. 1 and 2 show the same hyperfine component of the same rotational transition (J=3+2) of Ar...H3?Z1in the states (10’0) and (OOOO),respectively, recorded under identical instrumental conthe separate
50
100 Frequency
150 offset
200
.I
I kHZ
Fig. 2. Frequency domain recording of the F=7/2+5/2 and F=9/2+7/2 pair of Cl-nuclear quadrupole components in the I- 3~2 transition of Ar...H%l in the ground state (00’0). The conditions are identical to those for fig. 1, except that only four gas pulses were employed. Frequencies are offset at a rate of 3.90625 kHz/point from 10069.4806MHz.
350
ditions. It is clear that in each, the two components of the familiar Doppler doublet have full widths at half maximum, Av,,~, of x 10 kHz. In fact, the mean of 10 measurements of Av,,~ gave values of 10.9( 8 ) kHz and 10.2( 5) kHz for the states (10’0) and (OO’O),respectively. Although there is an indication of a slight increase of 0.7 kHz in AY,,~on excitation of one quantum of the mode Y,, this is probably not experimentally significant, as will be made clear when the time-of-flight of the excited molecules before detection is considered below. Even if the determined increase in Av,,, on vibrational excitation were experimentally significant, it would be difficult to relate it to an accurate value for z, the predissociative lifetime of the excited state. The observed lineshapes in the pulsed-nozzle FT microwave experiment are complicated by the Doppler doubling effect, the origin [ I S] of which appears to be in dispute [ 191 and for which there is no simple lineshape function. In the case of the J=3+2 transitions of Ar...H3’Cl, shown in figs. 1 and 2, there is the additional complication that each Doppler component is the result of the blending of an unresolved pair (separation 4 kHz ). The problem is how to deconvolute the various contributions to Av,,~. Two limiting approaches are possible. If the observed increase in Avl ,2 on vibrational excitation were all assigned to predissociative broadening of rotational transitions in the state (10'0) (i.e. if the various other contributions such as transit time broadening, T2damping, etc. were all unchanged on vibrational excitation) and if all contributions were assumed additive (i.e. Lorentzian ), the implied value of the predissociation lifetime would be r= (2kA~)-’ ~230 ps. If, on the other hand, the observed Av,/~ results from the convolution of Lorentzians (for the homogeneous broadening effects) and a Gaussian (for the Doppler effect) the appropriate expression is Au,,, x (Av~+Av&)‘/~ [ 201 and the increase of Av,,~ on vibrational excitation then corresponds to a predissociation width of
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about 3.5 kHz and hence to za45 ps for the state ( 10’0). However, the time of flight of molecules from the nozzle to the point of detection in the present experiment shows that 5 must be significantly greater than 45 ps. Gas pulses that have been subjected to the dc glow discharge travel at a speed of 5 x lo4 cm s- ’ [ 181 in a direction perpendicular to the axis of the FabryPer& cavity. The geometry of the experiment is such that a molecule must travel in collisionless expansion for 15 cm before it reaches the microwave beam waist, i.e. the point at which the microwave standing wave electric field of the cavity has the value of l/ e of its maximum (axis) value. We can assume [ 181 that the polarization of molecules lying between the nozzle and the beam waist, and its subsequent contribution to the spontaneous coherent emission recorded at the detector, is not significant. Hence,the time of flight of molecules that reach the beam waist and are detected is at least 300 ps. Measurements, under identical conditions, of the ratio of the amplitudes of time-domain signals collected from Ar...H3’Cl molecules in the states ( 10’0) and (00’0) led to the ratio (N, /No)t in the range 0.03-0.05 for the populations of these states after the time of flight t> 300 ps. If T were, say, 100 ps the value (NJ&,), at time zero (i.e. immediately after excitation at the nozzle) would then have to be in the range 0.6 to 1.0, implying an effective vibrational temperature between T,x 8000 and co K. Even for z= 200 ks, the ranges would have to be 0.13-0.22 and 2050-2750 Kfor (N,/N,), and TV,respectively. But these vibrational temperatures are too high. In separate discharge experiments carried out under similar conditions but detecting signals from the monomer 160’2C32Sin argon, the ratio’of the population of the v3= 1 state (2062 cm- ’ ) to that of the ground state after the same time of flight was found to be (N3/No),=0.05 and corresponds to TV= 1000 K (losses due to fluorescence are negligible on this timescale). If similar vibrational temperatures and populations of ( 10’0) Ar...H35C1are produced in the discharge, it therefore seems likely that ~3300 ps. Interestingly, Huang et al. [ 2 1 ] find a lower limit of 300 ps for the lifetime of ( lO’O)Ar...HF from an infrared experiment in which the excited molecules survive long enough in a beam without dissociation to reach a bolometer.
9 October 1992
The other dynamical aspect of interest in the ( 10’0) state of Ar...HCl is the angular oscillation of the HCl subunit. It has been shown for Ar...HCl [ 16]
that the coupling constant x0( Cl) in the ground state is given accurately by the projection of the free HCl value xz(Cl) onto the a axis of the dimer. In the present case, xl(Cl) is therefore related to the coupling constant #(Cl) of the v= 1 state of free HCl by XI(Cl) = fxY(Cl) (3 coszO- 1 > ,
(2)
where 8 is the angle between the HCl direction and the a axis, as defined in fig. 3, and the average is over the state uI= 1. When the $(Cl) collected in table 3 [ 221 are used in eq. (2) with the appropriate xl (Cl) of table 2, the operationally defined angles e,,=cos-‘(cos2e> I/* shown in table 4 result. Also included in table 4 is the corresponding set of 0,, for the (OOOO)states of the three isotopomers investigated [ 3,4,16]. We note that excitation of v, = 1 leads in each case to a decrease in 0,“. This is consistent with a strengthening of the van der Waals bond when the HCl stretch is excited. Such an effect is also apparent in a small increase in the wavenumber of the intermolecular stretching mode vj when v, is excited [ 121. A recent potential energy function [ 231 shows that the barrier to internal rotation of the HCl subunit increases from the state (OOOO)to the state ( 10°O), a result consistent with the changes in x(C1) established experimentally. 3.3. Dimer geometry and van der Waals stretching force constant in the state (1000) For a complex such as Ar...HCl, in which the vibrations are anharmonic and in which the bending and stretching modes are strongly mixed, there are obvious difficulties in applying the usual models [ 24-
Fig. 3. Definition of the angles 0 and a and the distance rc.m.for the model of Ar...HCl described in the text.
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Volume 198, number 3,4
Table 3 Spectroscopic and geometrical properties of hydrogen chloride in the vibrational state u- 1 Property
H’%ZI
H3’C1
D”CI
B, (MHz) a) x,(Cl) (MHz) a) I1 (A) b,
303876.51 -69.2729(9) 1.30298
303414.14 - 54.5985 1.30298
158284.92 -68.5831(10) 1.29481
a) Ref. 1221. The value ofX,(“‘Cl) was obtained by scalingx, (%l) by the ratio Q”/Q”. b, Calculated from B, =h/llx’pr:.
Table 4 Structural parameters of the Ar...HCl dimer in the ( 10’0) and (00’0) vibrational states a) Vibrational state
Ar...H35CI Ar...H3’C1 Ar...D’5CI
(OOOO) b,
(1OOO) 0,” (deg)
<&n.>“* (A)
r(Ar...Cl) (A)
0,” (deg)
<&.>“‘(A)
r(Ar...Cl)
40.750(S) 40.764(6) 33.065(25)
3.9956 3.9988 3.981 I
4.0233 4.0250 4.0402
41.531(l) 41.53 33.750(l)
3.9795 3.9801 3.9667
4.0065 4.0059 4.0247
(A)
a) Errors in (rim, ) 1’2and r(Ar...Cl) propagated from errors in the spectroscopic constants are less significant than the last digit quoted. Errors from limitations in the model used to calculate these quantities are likely to be larger. b, Calculated from spectroscopic constants in refs. [ 3,4,16] using the methods discussed in the text.
261 to determine the radial geometry and the intermolecular stretching force constant from rotational and centrifugal distortion constants, respectively. It is nevertheless of interest to apply the models here to obtain an indication of the changes that occur in these molecular properties on excitation of v, and, if possible, identify trends. When determining the separation of the two subunits in a weakly bound dimer, such as Ar...HCl, from rotational constants, partial allowance for the contribution of the intermolecular modes of vibration is often made by using a model of the type shown in fig. 3. The HCl subunit is assumed rigid and to oscillate about its centre of mass through the angle LX. The distance r,.,. is taken as fixed, an assumption equivalent to ignoring the effect of the van der Waals stretching mode. This model leads for Ar...HCl to the expression [ 24,251 (~bb)=1((~~.,.)+t~bHC’(l+(cos2~)),
(3)
where the moment of inertia lEcl = h/81cZBzC’is defined operationally in terms of the rotational constant BFc’ of the appropriate state v of free HCl [ 221. The average in eq. (3) is over the angular motion of the HCl subunit and~u=mA’mHC’/(mAr+mHC1).In 352
the approximation that eq. (3 ) is valid for the state (10’0) of Ar...HCl, that (&,,) =I,=h/87c2B, and that (cos2@ can be used in place of (cos201), ( r&,.,.} I/* can be estimated using eq. ( 3). Values for the state ( 10’0) of the three isotopomers of Ar...HCl investigated are given in table 4. The necessary values of 0,” are also recorded in table 4 while the rotational constants are in tables 2 and 3. A measure of the distance r(Ar...Cl) in the state ( 10’0) is then given by r(Ar...Cl)= ( rf,,,)1/2+r(cos
a> ,
(4)
where r is the distance of Cl from the HCl mass centre. The various r(Ar...Cl) so calculated are also collected in table 4. For purposes of comparison, the corresponding set of quantities for the ground state (OO”O)of Ar...HCI, calculated from previously published spectroscopic constants [ 3,161, are included in table 4. Interestingly, r(Ar...Cl) is longer in the (10’0) state by about 0.02 A, which is also the lengthening of the free HCl molecule on excitation from v= 0 to v= 1. We have observed a similar effect in Kr...HCl [ 271. Finally, the centrifugal distortion constant D, has been used in the expression
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Table 5 Effective force constants /c~and wavenumbers Fs of the van der Waals stretching mode of the dimer Ar...HCl in the ( 10’0) and (00’0) vibrational states Vibrational state
Ar...HJsCl Ar...H3’Cl Ar...D%Zl
(1000)
(OOOO) n)
kl (Nm-I)
v; (cm-‘) b,
k, (Nm-I)
fl, (cm-‘) b,
1.1419 (5) 1.1428 (3) 1.319 (2)
31.973 (6) 31.538 (3) 34.12 (3)
1.1640 (3) 1.1658 (3) 1.33 (3)
32.281 (4) 31.856 (2) 34.2 (3)
‘) Calculated from centrifugal distortion constants Do=20.058 (5) and 18.920 (4) kHz for Ar...H%I and Ar...H”CI, respectively, from unpublished measurements. k, for Ar...D3’Cl was obtained from Do given in ref. [ 31. b, Cahxdated from k, using & = (2rc) - ’ ( k,/p) I’*.
k3 = ( 161r*B;~/D,) ( 1-I?,/B;c’)
,
(5)
due to Millen [26] to estimate the quadratic force constant k3 associated with the van der Waals stretching mode in each of the states ( 10°O) and ( 00’0 ) . The required spectroscopic constants B, , D, and BrC’ for the ( lOoft) state are given in tables 2 and 3 while those (B,, Do and BfC’) for the state (00’0) are available elsewhere [ 3,4,16,22]. The results for k, and for the corresponding wavenumbers ~~=(2~-‘(k,/~)“~aresetoutintable5.Wenote that the strength of the van der Waals bond, as measured by kJ,is essentially unaffected by excitation of V, and that the & are in good agreement with those available from far- and near-infrared spectroscopy [ 7,121, that is 32.44 and 32.64 cm -r from the transitions (OO”l)t(OOoO) and (lO”l)t(OOoO), respectively, for Ar...H35C1.Such agreement also obtains for Kr...HCl [ 271.
4. Conclusion We have used a dc glow discharge in conjunction with a pulsed-nozzle, Fourier-transform microwave spectrometer to excite and detect the rotational spectrum of each of three isotopomers of Ar...HCl in the vibrationally excited state ( 10’0). A comparison of observed full-widths at half maximum of rotational transitions in the states (10’0) and (00’0) of Ar...H3’Cland time-of-flight considerations allow the lower limit of 7~300 ps to be placed on the vibrationally predissociative lifetime of the ( 10’0) state. We note that the technique introduced here has
wider applications than reported in this publication. It is generally applicable to the investigation of rotational spectra in the vibrationally excited states of a wide range of molecules and possibly to the production of other types of short-lived species. The adaptation of a pulsed nozzle to allow emergent molecules to be subjected to an electrical discharge is part of a general programme to use modified nozzles for the generation (by, e.g., fast mixing [28], pyrolysis [ 291, electrical and microwave discharge) of transient molecules.
Acknowledgement
We thank Dr. Peter Hamilton of QMWC London for helpful advice and discussion. One of us (ACL) thanks the SERC for a research grant in support of our work in the detection of transient species using modified nozzles and the Royal Society for the award of a Guest Research Fellowship (for JWB). JWB thanks the Texas A & M Former Students Association Sabbatical Leave Program, NSF and the Robert A. Welch Foundation for additional support.
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[4] S.E. Novick, KC Janda, S.L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys. 65 (1976) 1114. [ 51 J.M. Hutson and B.J. Howard, Mol. Phys. 43 ( 1981) 493. [6] J.M. Hutson and B.J. Howard, Mol. Phys. 45 ( 1982) 769. [ 7 ] R.L. Robinson, D.-H. Gwo and R.J. Saykally,J. Chem. Phys. 87 (1987) 5156. [8] R.L. Robinson, D. Ray, D.-H. Gwo and R.J. Saykally, J. Chem. Phys. 87 ( 1987) 5149. [9] K.L. Busarow, GA. Blake, KB. Laughlin, R.C. Cohen, Y.T. Lee and R.J. Saykally,J. Chem. Phys. 89 (1988) 1268. [IO] B.J. Howardand A.S. Pine, Chem. Phys. Letters 122 (1985)
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[ 181E.J. Campbell, L.W. Buxton, T.J. Balle, M.R. Keenan and W.H.Flygare, J.Chem. Phys. 74 (1981) 813,829; T.J. Balle and W.H. Flygare, Rev. Sci. Instrum. 52 ( 1981) 33. [19] F.J. Lovas and R.D. Suenram, J. Chem. Phys. 87 (1987) 2010. [20] C.H. Townes and A.L. Schawlow, Microwave spectroscopy (McGraw-Hill, New York, 1955) p. 375. [ 2 I] Z.S. Huang, K.W. Jucks and R.E. Miller, J. Chem. Phys. 85 (1986) 6905. [22] E.W. Kaiser, J. Chem. Phys. 53 (1970) 1686. [23] J.M. Hutson, J. Phys. Chem. 96 ( 1992) 4237. [24] AC. Legon and L.C. Willoughby, Chem. Phys. 85 (1984) 443. [25 ] G.T. Fraser, KR. Leopold, D.D. Nelson Jr., A. Tung and W. Klemperer, J. Chem. Phys. 80 (1984) 3073. [26] D.J. Millen, Can. J. Chem. 63 (1985) 1477. [27 ] J.W. Bevan, AC. Legon and C.A. Rego, unpublished results. [ 28 ] A.C. Legon and C.A. Rego, Angew. Chem. Intern. Ed. Engl. 29 (1990) 72. [29]A.C. Legon and D. Stephenson, J. Chem. Sot. Faraday Trans. 87 (1991) 3325.