The rotationally resolved 1.5 &m spectrum of the HCN--HF ... · The rotationally resolved 1.5 pm...

The rotationally resolved 1.5 pm spectrum of the HCN-HF hydrogen-bonded complex

E. R. Th. Kerstel, H. Meyer,a) K. K. Lehmann, and G. Stoles Department of Chemistry Princeton University, New Jersey 08544

(Received 15 May 1992; accepted 17 August 1992)

We have measured the overtone spectrum of the CH stretching mode in HCN-HF. The vibrational predissociation rate is approximately twice that previously determined for fundamental excitation, whereas the complexation induced frequency shift is only marginally larger than that of the fundamental spectrum. These results are discussed in terms of a first-order perturbation theory treatment as set forth by LeRoy, Davies, and Lam [J. Phys. Chem. 95, 2167 (1991)]. We suggest that the frequency shift observed here might not only be due to complexation, but also to a long-range anharmonic interaction.

INTRODUCTION

Over the past few years the HCN-HF van der Waals heterodimer has emerged as a benchmark system for the spectroscopic study of linear hydrogen-bonded complexes, from the microwave to the (near) infrared regions of the spectrum. rm3 Microwave spectra of HCN-HF and its iso- topically substituted derivatives, recorded in a gas-cell experiment or a pulsed nozzle Fourier-transform IR (FTIR) spectrometer, have established its linear geometry (with the HF unit hydrogen bonded to the N atom) and allowed for the evaluation of ground-state rotational constants,4’5 electric quadrupole coupling constants,6 electric dipole moment,7’8 and the hydrogen-bond dissociation energy.’ Ex- ploiting the wide spectral coverage of their FTIR spectrometer and the relatively high sample temperature in a cooled static gas cell, Bevan and co-workers have been able to assign all seven fundamentals and several combination bands, hot bands, and overtones, including up to the 4~: third overtone of the high-frequency intermolecular bend,‘@19 and the first overtones of the CH and HF intramolecular stretching modes.20’21 Of the 34 anharmonic constants Xij and gii ( lQi<i<7) 22 are now known with reasonable accuracy. For no other hydrogen-bonded complex is such an extensive vibrational database, including anharmonicities, available for comparison with state-of- the-art calculations, such as have been performed for HCN-HF by Botschwina22 and Amos et ~1.~~ Whereas the gas-cell FTIR experiments have been instrumental in the rovibrational characterization of the complex, their limited spectral resolution, albeit sufficiently high to resolve the rotational structure, has precluded the accurate measure- ment, from the observed spectral linewidths, of the vibrational predissociation lifetimes associated with high- frequency intramolecular vibrations. It is in this respect that the much higher resolution afforded by a color-center laser, molecular beam, optothermal spectrometer can be applied to the further advancement of our knowledge of this benchmark system. Using such a spectrometer operat-

‘)Present address: Universitit Bern, Institut ftir anorganische, analytische und physikalische Chemie, Freierstrasse 3, CH-3000 Bern 9, Switzerland.

ing in the 3 pm region Miller and co-workers have uniquely determined the vibrational predissociation lifetimes of the vr (HF) (Ref. 24) and v2( CH) (Refs. 24 and 25) stretching fundamentals and of the associated combination band with the vi lowest-frequency bending mode.25

We have previously demonstrated the feasibility of ex- tending these measurements into the region of the CH- stretch first overtone, using a powerful commercial color- center laser operating near 1.5 ,um.26 In that study we recorded the 2vt spectrum of the HCN dimer. As in the study of the corresponding fundamental, the rotational linewidths, and therewith the vibrational predissociation lifetime, proved to be instrument limited. Here we report the 2v2 overtone spectrum of the CH stretching vibration in HCN-HF. Since the observed linewidths are not instrument limited, their Lorentzian component gives a direct measure of the predissociation lifetime of the excited complex at an energy of 6500 cm-‘, almost 4 times the dissociation energy. At the same time we can compare the complexation induced vibrational frequency (red-) shift for fundamental and overtone excitation, for the two systems HCN-HF and HCN dimer.

The HCN-HF complex, along with the HF dimer,27 are the first (hydrogen bonded) van der Waals systems for which the vibrational predissociation lifetimes have been determined for both fundamental and overtone excitation of the same high-frequency intramolecular vibration (i.e., the CH and HF oscillators, respectively). The (NO) 2 molecule is to our knowledge the only other dimer for which both fundamenta128-30 and overtone3’ vibrational predissociation (without simultaneous electronic excitation) data exist. In this case, due to the open-shell nature of the NO molecule, the dissociation process is believed not to occur on the ground-state electronic potential only, but instead to involve (at least) two electronic states, which are coupled through spin-orbit interaction. It may therefore be difficult to discuss this system in the same framework as used in this paper for van der Waals systems.

EXPERIMENT

The spectrometer used in these studies is based on the optothermal detection technique, an energy deposition technique that has been described extensively in the liter-

8896 J. Chem. Phys. 97 (12), 15 December 1992 0021-9606/92/248896-l 0$06.00 @ 1992 American Institute of Physics Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

ature.32’33 In short, a highly collimated molecular beam containing the species of interest impinges on the cold (l-2 K) surface of a semiconducting bolometer detector, after interaction with the IR laser radiation. Rovibrational energy deposited into the molecular beam by the laser is registered by the bolometer in a phase-sensitive detection scheme. If the excited molecules dissociate before reaching the detector (as in the case of vibrational predissociation of most weakly bound complexes) and most of their fragments leave the molecular beam, the resulting signal will have the opposite sign of a signal resulting from absorption by a stable molecule. This technique is particularly suited to studies involving vibrational overtone excitation, since the decrease in signal-to-noise ratio (S/N) resulting from the reduced transition strength of the overtone transition as compared to that of the fundamental transition (a difference of a factor of roughly 40 for most acetylenic CH stretch excitations), can be compensated for by an increase in laser power, if available. For a technique like direct absorption on the other hand, a decrease in oscillator strength translates directly in a proportional loss in S/N (provided the dominant noise source is technical noise of the laser system).

The above considerations and the experimental setup, which combines an optothermally detected molecular beam with a Nd:YAG laser pumped, 1.5 ,um, 150 mW color-center laser (Burleigh FCL-120), have been discussed in detail in a previous publication (YAG denotes yttrium aluminum garnet).34 Here we will limit ourselves to discussing the experimental conditions specific to this study. The molecular beam is extracted, using a conical skimmer, from a room-temperature expansion of a 0.5% HCN and 1% HF in helium mixture through a 50 pm diameter nozzle, at a stagnation pressure of 4 bars. The gas mixture was obtained by on-line mixing of pre-mixed 1% HCN in helium (Matheson) with 2% HF in helium. Be- tween the recording of the full HCN-HF 2v2 spectrum and the measurements of the individual linewidths, we replaced both the mirrors and the spacers (with precision ground parallels) in the plano-parallel mirror multipass arrange- ment, to yield a slightly improved instrumental linewidth of 15 MHz [full width at half maximum (FWHM)], and improved S/N. We presently achieve a S/N of 2.5 x lo4 on the P( 1) transition of the acetylene v1 +v3 band near 1.5 pm, expanding an approximately 1% acetylene in helium mixture at 4 bars backing pressure. As the S/N ratio on the corresponding fundamental transition is actually slightly lower, this is a good indication of how efficiently we can pump overtone transitions. In the case that both fundamental and overtone transition are saturated one would expect the overtone signal to be twice as large due to the larger photon size. The spectra were linearized in frequency using reference signals derived from two scanning &talons of 8 GHz and 150 MHz free spectral range, as described in Ref. 34. Absolute frequency calibration was obtained from the P( 1) transition of the HCN 2v1 band. Its frequency was determined by Smith et aL3’ to be 6516.649 25 cm-‘, in reference to O2 calibration lines, whose accuracy we estimate at 4 to 5 x 10m4 cm-‘.

Kerstel et al.: Overtone spectroscopy of HCN-HF 8897

-2.01 I 6516.0 6517.0 6516.0 6519.0 6520.0

Frequency (cm-l)

FIG. 1. P(9) through R(6) of the 2~~ overtone spectrum of HCN-HF.

RESULTS

The spectrum of Fig. 1 shows the P( 9) through R (6) transitions of the linear HCN-HF complex. The negative features belong to the HC 14N and HC “N monomers [P( 1) and R(O), respectively]. At the present S/N level no hot band of the dimer is observed. The oscillations in the base-line level are caused by changes in the amount of scattered IR radiation received by the detector. The period of the oscillations is consistent with them being due to interference of overlapping laser beam paths occurring between the mirrors of the multipass (the mirror spacing is 25 mm). Realignment of the optical beam path indeed made the oscillations disappear.

The R (6) through P( 9) transitions were fitted to the standard expression for a rotating vibrator, with the ground-state constants constrained to the microwave values of Legon, Millen, and Rogers.4 A list of the transition frequencies is presented in Table I. The spectroscopic constants are given in Table II and include the values determined from the fundamental v2 spectrum by Dayton and Miller,24 and the FTIR gas-cell overtone spectrum of Be- van and co-workers.2’ The standard deviation of the fit is

TABLE I. Observed transition frequencies and residuals for the 2vz band of HCN-HF. The standard deviation of the fit is 5.4 MHz.

OBS OBS-CALC (cm-‘) (IO-” cm-‘)

R(6) 65 19.973 40 15.4 R(5) 6519.738 81 9.34 R(4) 6519.503 55 24.7 R(3) 65 19.267 27 17.8 R(2) 65 19.030 07 -6.27 R(l) 6518.792 29 - 19.0 R(O) 6518.554 06 -9.76 P(l) 6518.075 54 -9.30 P(2) 6517.835 54 9.63 P(3) 65 17.594 79 15.9 P(4) 6517.353 33 15.7 P(5) 6517.111 07 1.89 P(6) 6516.867 89 -32.8 P(7) 65 16.624 42 -20.8 P(8) 6516.380 05 -17.0 P(9) 6516.134 96 4.52

J. Chem. Phys., Vol. 97, No. 12, 15 December 1992 Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

8898 Kerstel et al.: Overtone spectroscopy of HCN-HF

TABLE II. Spectroscopic constants for the HCN-HF vz vibration.8 1 zoor

v=o v=l v=2 v=2 IOOO-

Ref. 4 Ref. 31 This work Ref. 21 c .2

800 - 3

B (cm-‘) 0.119 181 f

0.11973(S) 0.11958(5) z 600-

0.119 787b 0.119 478(7) .r"

2 400 - 0.119 817 0.119 489

,u

_c

AB (10-s 15(l) 31(l) 33 cm-‘)

D (lo-’ cm) 17 22(b) 16(h) 17b 63(11) 25 26

v. (cm-‘) 3310.3271(30) 6518.3152(l) 6518.3208

Av,, (cm-‘) -1.149(3) -1.2905(S) - 1.291

FL (MHz) 9.9(3) W2) < 45oE

r W 16.1(5) 9( 1.5)

‘The errors in parentheses represent one sigma. bConstrained to the microwave value of Ref. 4. ‘Gas-cell FIIR data (pressure is 5 Torr, temperature -31 “C).

-900 I. -60 I. -60 I. -40 *. -20 I. 0 I. 20 I. 40 8. 60 8. 80 *. 100 1

Frequency (MHz)

FIG. 2. Comparison of the experimentally observed (squares) rotational line shapes for the HCN P( 1) and the HCN-HF R( 3) lines. The solid lines give the results of a Gaussian line-shape fit to the monomer line, and of a Voigt profile fit to the HCN-HF line.

5.4 MHz. The results of the fit are in good agreement with the FIIR spectrum. The linewidths of the 5 Torr, - 3 1 “C gas-cell spectrum are approximately 450 MHz, which naturally limits the accuracy of the constants obtained from this spectrum. It should also be noted that in general the distortion constant D and the rotational constant B are highly correlated. For our fit the correlation between B’ and D’ is given by cos-’ (correlation) = 17”. In terms of a simplistic ball-and-stick model of the molecule, the AB’s for the fundamental and overtone spectrum can be entirely attributed to the extension of the excited CH bond, without the necessity of invoking a shortening of the hydrogen bond upon CH stretch excitation. The 2~~ band of the complex is observed to be shifted by only 1.2905 cm-’ to the red of the corresponding band in the HCN monomer. This redshift Av( U’ = 2, u” =O) is not only small when compared to the shifts observed for similar small hydrogen-bonded systems, like the HCN dimer, but also when compared with the redshift of the fundamental spectrum (1.149 cm-1).24

18(2) MHz (FWHM) was needed, which corresponds to an excited-state lifetime r of about 9 ns. The accuracy quoted for the Lorentzian width reflects the distribution in widths obtained from three different scans over the R (3) line. Also, within the experimental accuracy of the spectrum of Fig. 1, there is no indication of a J dependence of the linewidths. The absence of a Lorentzian component to the monomer line shape rules out a significant power broadening component to the linewidth of the complex, since no significant enhancement of the CH vibrational transition moment is expected upon hydrogen bonding to nitrogen.

DISCUSSION

The linewidths observed in the overtone spectrum are clearly broader than dictated by the residual Doppler broadening in the laser multipass. This is illustrated in Fig. 2, which shows both the HCN-HF R( 3) and the HCN monomer P( 1) transition. The monomer is well represented by a Gaussian of width 15.3 MHz (FWHM), which is taken as the instrumental line profile. The approximation that the monomer line shape represents the Gaussian con- tribution to the Voigt-shaped diameter lines is valid if both monomers and complexes have essentially the same velocity distribution. Since we expand rather dilute mixtures, we expect the velocity slip of the complexes with respect to the carrier gas to be small, and the approximation to be very good indeed.36 In order to fit a Voigt profile to the HCN-HF line an additional Lorentzian component of

It is interesting to discuss the present results for HCN-HF in the light of the data available for the HCN dimer, so far the only similar system for which a CH stretching overtone, sub-Doppler spectrum has been recorded. For HCN dimer both the v1 fundamental37 and the 2vi overtone26 spectrum of the “outside” CH stretch show linewidths that are instrument limited. Together with the observation that the excited dimers do dissociate before reaching the detector, these IR studies confined the HCN dimer vibrational predissociation lifetime to the range from 140 ns to 0.3 ms for fundamental,37 and to the range from 11 ns to 90 ps for overtone26 excitation. Recently, in our laboratory we have carried out microwave-infrared double- resonance experiments on (HCN)2 with the goal of nar- rowing the gap between the bounds for the fundamental (u= 1) vibrational predissociation lifetime.38 In a prelimi- nary experiment we observed rotational transitions in the vibrational upper state with a 220 kHz (FWHM) Lorent- zian component, indicating a U= 1 predissociation lifetime of approximately 1.5 ps.

It has been argued before37*39 that the long lifetime of the v1 excited HCN dimer is consistent with the observations that the hydrogen bond does not contract measurably and that the complexation induced redshift is rather small (3.16 cm-t for the fundamental, 6.39 cm-’ for the overtone) when compared to the redshift caused by excitation of the “inside” CH stretch (70 cm-’ for this fundamental


~2 band, which shows a lifetime of “only” 6 ns), since all of these observations can be attributed to the “outside” CH bond being decoupled to a much larger extend from the hydrogen bond than the inside CH bond participating in the hydrogen bonding. In fact, observations such as these for a wide range of weakly bound complexes have led Miller to propose his predissociation rate vs redshift correlation law:40

-r-la (Av)~. (1)

Even though the plot of log( 7-l) vs log( Av) presented by Miller, and containing data on over 20 systems shows sub- stantial scatter in a band nearly half an order of magnitude wide, around the proposed slope-equals-two line, the vibrational predissociation rates observed for HCN-HF (u= 1, as well as v=2) are at least 1 order of magnitude larger than the plot would suggest on the basis of the observed redshifts for the v2 and 2v2 bands. The results for ( HCN)2, on the other hand, are much more in line with the predictions of the correlation law.

The correlation law of Eq. ( 1) was rationalized by LeRoy and co-workers41 in a first-order perturbative treatment (including the use of Fermi’s golden rule to calculate the vibrational predissociation rate) for a hypothetical system involving only one internal degree of freedom (the initially excited intramolecular high-frequency mode). For example, their model would treat HCN-HF as the linear quasitriatomic H-( CN) v * * (HF), and also ignores vibrational modes associated with the van der Waals bond, as well as rotations of the complex or dissociation products. The authors showed that extension of their model to more than one internal degree of freedom (associated with other intramolecular modes in the monomer unit(s), or with the van der Waals bond, including motions that correlate with rotations of the free monomer units) leads to, the conclusion that the correlation law is no longer expected to hold. That it persists (as Miller’s observations show) is then taken as evidence for a two-step impulsive predissociation mechanism, in which the initial, rate-determining step involves only one internal degree of freedom. The redistribution over the product internal degrees of freedom of the energy released would then be decided during the process of fragment separation. It appears therefore that the preconditions for LeRoy’s theory are fulfilled for a series of systems in which the strength of the coupling function, which drives the vibrational predissociation process, varies over more than 2 orders of magnitude. LeRoy describes these preconditions as “all-else-being-equal” (if strictly applied this would limit the applicability of the theory to a single case), but in effect implying that the functional form of the coupling potential function be very similar for the systems considered. Since many of these systems involve the same type of monomer vibrational mode (e.g., the tri- ply bonded CH stretch), it seems reasonable to expect that at least the dependence of the coupling functions on the intramolecular (CH stretching) coordinate be very similar. The question now arises whether “all-else” can be considered equal when comparing overtone and fundamental ex-

FIG. 3. Schematic representation of the one-dimensional intra- and intermolecular potential-energy curves, and their wave functions, as discussed in the text. The potential U,(r) is the one-dimensional representation of the CH stretching potential in the complex, whereas U,(r) represents the corresponding potential in the isolated monomer. Note that the lowest vibrational levels (n=O) of the vibrationally averaged intermolecular (van der Waals) potentials correlate with the CH stretch energy levels in the complex, while their asymptotic values at large separation (R + m ) correlate with the monomer energy levels.

citation of the same mode in the same complex. To answer this question, we will first proceed with introducing Le- Roy’s formalism.

The starting point of LeRoy’s4i analysis is the Hamil- tonian for the van der Waals molecule with only one intramolecular mode, which can be written as follows:

fMr,R) =H,,,(r) - (h2/8Gp)(d2/dR2)

+ VoWI +AV,(r,R). (2)

Here H,(r) describes the intramolecular vibration of the free monomer: H,@,(r) =E,( u) @J r) . The overall interaction potential is the sum of a “frozen” monomer potential V,(R) and a potential coupling term AV,(r,R). Intro- ducing a crude adiabatic separation of variables, the total wave function becomes

\I’tot,v(r,R)=~,(r)~v(R), (3)

where the wavefunctions $,(R) are associated with the radial van der Waals motion on the vibrationally averaged effective adiabatic potential ( V( R ) > uv (see Fig. 3) :

(V(R)),,= v~(R)+(%(r) IAVJr,R) I%,(r)). (4)

The next approximation is to expand the potential coupling term in a suitably chosen basis set:

AV,(r,R)= c h(r)VdR) k= 1,m

and to retain the leading term only:

AV,(r,R) z&(r) VI(R). (5)

If we take 4k( r) = (r- re) k, the expression corresponds to a Taylor expansion in the small-amplitude intramolecular vi-



8900 Kerstel et a/.: Overtone spectroscopy of HCN-HF

brational coordinate, an obvious approximation. At this point we follow LeRoy in allowing for a more general formulation.

In the following paragraphs we will discuss, in light of the above considerations, first the vibrational frequency shift Av that accompanies complexation, then the vibrational predissociation lifetime r, and finally we will return to the issue of the correlation law as represented by Eq. ( 1)

The vibrational frequency shift

Referring again to Fig. 3, it is easily seen that the vibrational frequency shift due to complexation is the quantity:

Av”,“,, = [Ec(v’) -mu”) I - [&Au’) -&(u”) I

=(D”m-DUt). (6) It can be shown that within first-order perturbation theory one can write the shift as

Avury,, = (4,(4)“~“4$“~(R) I V,(R) I$,r(R))

-(d,(T))u~‘u~‘(~,r,(R) I v,(R) IZC1”4R)).

elements were evaluated from the HCN monomer rotational constants, B, [i.e., the (r),, were approximated by ( ( (r) -2) ,“) - 1’2]. For the HCN dimer the ratio of the experimentally observed overtone and fundamental shifts is 2.024, in excellent agreement with the above result. It should be noted that the result of Eq. (8) is exactly what would be obtained from the electrostatic theory of Liu and Dykstra,42 when it is assumed that the effect of complex formation can be represented by the addition of an interaction potential linear in the CH stretching coordinate r to the intramolecular CH stretching potential. Liu and Dyk- stra have performed high-level ab initio calculations of the interaction potential for several systems containing HF that show that, within the limits of only considering the electrostatic forces, the approximation of a linear interaction potential is a very good one. Even for a strong interaction system such as the HF dimer with the inside HF stretch excited, the potential is certainly locally very nearly linear. For our case, where a nonbonded CH stretch is excited that is only slightly perturbed by the other molecule in the complex, the approximation should be even more valid.

(74 The notation (&(T))~~ is short for (Q”(r) [d,(r) (Q,(r)). We now make the simplifying assumption that the radial averages of Vi (R) do not significantly depend on the vibrational quantum number u, and obtain the result

Av,, “,, = [(~l(r))u~u~-(~1(T))u”v”l x (tCIP(R) I v,(R) I$“4R)). 0)

For HCN-HF the approximation made above is supported by the experimental redshifts and the dependence of the rotational constant on v. Since D,, = Dutt - Av~,~,,, the small redshifts indicate that the (hydrogen bond) dissociation energy, and consequently the van der Wards potential well depth, do not change significantly with excitation of the CH stretch. Also, the rotational constant B, does not indicate a vibrational dependence of the van der Waals bond length. Therefore, the radial van der Waals potential of our linear quasitriatomic complex appears not to change shape, or to shift position with respect to R, upon CH stretch excitation. Consequently, the same should be true for the wave functions supported by these potentials, and for the diagonal expectation values as they appear in Eq. (7b).

Using wave functions constructed to closely corre- spond to those of the CH oscillator in HCN,43 we have evaluated the expression on the right-hand side of Eq. (8)) replacing the matrix elements with ( ( r>2),, to obtain a numerical value of 2.18. Therefore, even if the second- order term had an appreciable magnitude, we would not expect the ratio of vibrational frequency shifts to change dramatically. Moreover, we expect Eq. (8) to be rather accurate since, to first order, the strength of the coupling function will cancel in the ratio of redshifts, eliminating the need to evaluate the absolute value of the coupling strength. It is therefore somewhat of a surprise to find the experimental value of the overtone redshift for CH excited HCN-HF to be only marginally larger than the fundamental shift: ( Av~,,/Av,,,)~~~ = 1.124.

If the dependence on the intramolecular coordinate r of the interaction potential is assumed to be linear, &(r) , =s (r-Q, we obtain for the ratio of vibrational frequency shifts:

Av,dAv,o=((r),,-((r),)/((r),,-(r),) =2.029. (8)

Since in the above expression the matrix elements are evaluated by integration over the monomer wave functions, the result is independent of the nature of the (ground state) partner in the complex. Consequently, we would predict the same ratio of u= 2 to u= 1 shifts for HCN-HF as for ( HCN)2. To obtain the numerical result the (T)“” matrix

We propose that the discrepancy is caused by the overtone band (or both fundamental and overtone bands) being displaced by a long-range anharmonic vibrational interaction. We do not see any evidence of J-dependent, local, near-resonant perturbations: there appears to be no correlation in the residuals of transitions connecting the same upper state-P( J” + 1) and R (J” - 1 )-nor are there irregularities in their intensities. Also, a Coriolis mediated interaction will not shift the band origin, but in general will effect the rotational constants (a Coriolis interaction can therefore not be positively ruled out because of the large difference in D” and D’ values of our fit). However, a long-range, low-order anharmonic perturbation, like a Fermi resonance, could be shifting the 2v2 state up by an amount equal to the predicted overtone redshift [based on Eq. (S)] minus the observed shift, i.e., 2.029 X 1.149- 1.2905=1.0 cm-‘. Together with the fact that we observe the HCN-HF spectrum at approximately the same S/N as the HCN dimer spectrum and that we have failed to observe the perturber in the region scanned, this leads to the estimate that the perturbing state must be at least 5 cm-’ below 2v2, and that the interaction matrix


Kerstel et aL: Overtone spectroscopy of HCN-HF 8901

TABLE III, Calculated frequencies for transitions from the ground state, for the HCN-HF vibrational states of A, symmetry, that appear in a 300 cm-’ wide window directly below the 2v2 state (0,2,0,0,0c,00,00). Also listed is their energy difference AhE with the 2vs state. The labeling of the normal-mode vibrations follows that used by Bevan and co-workers (Refs. 19 and 20). The total number of A, states in this region is 12 (16 when l-type doubling would be taken into account).

State Energy (cm-‘) AE(cm-‘)

w,o,o,oqoq~) 6519.22 0.00 (o,1,1,1,00,2°,00) 6511.65 7.57 (1,0,1,0@,1’,1’) 6478.50 40.72 (10003’ 1’00) 91,) *, 6435.63 83.59 (0,0,3,1,~,~,~) 6397.88 121.34 w,Lo,~,2°,~) 6375.40 143.82 (0 0 3 0 00,00,2e) t , , , 6361.16 158.06 ( 1,0,1,3,0c,0e,0? 6327.07 192.15 (0,1,1,1,1’,00,1’) 6325.75 193.47 ( 1 0 0 0 2’,22,00) , I , 9 6318.88 200.34 (0 0 3 0 oo,@,$) 9 9 , I 6227.02 292.20 ( wNv2,22,@v 6225.77 293.45

element is larger than roughly 2 cm-‘, since the frequency shift yields ( Wi”,)‘/AE= 1 cm- ‘, while the intensity argu- ment leads to ( B’i”,/AE)2 < 0.2. As mentioned above, there exists of course also the possibility that both the fundamental 5r2 and the overtone 2v2 levels are shifted (presumably both up from their unperturbed positions, thus only in- creasing the required size of the interaction matrix element). We note too, that for a weak, long-range perturbation it is reasonable to consider the change in linewidth insignificant, unless the perturber is intrinsically much broader (shorter lived).

We have attempted a direct count of the density of states of HCN-HF using the harmonic frequencies and anharmonicities determined for the complex by Bevan and co-workers, supplemented with those of the HCN monomer and assuming those that are not (yet) available to be zero. Only states of A, symmetry, which can couple to 2v2 via an anharmonic interaction, were counted. The total number of quanta in the molecule was (arbitrarily) limited to 5, while we searched in a 300 cm-’ window below 2v2. The results are summarized in Tables III and IV. Clearly

TABLE IV. The harmonic frequencies and anharmonicities (in units of cm-‘) as used in the calculation of the HCN-HF vibrational energy levels (Refs. 10-20).

1 1 2 3 4 5 6 7

wi 3891.80 3440.94 2127.71 190.22 726.95 611.72 75.0 XI, -116.9 0 0 8.025 0 54.1 4.214

Xl/ -51.355 - 14.85 -0.161 -19.352 0 -0.409 X3/. - 10.224 0 -3.107 0 -0.61 x4j -4.341 2.61 - 17.231 0.015

XSJ -2.497 0 0 xbj -32.717 -7.701 xlj 0

gsJ 5.23 0 0 gbj 18.047 0.8

g7J 0

there is potential for a vibrational interaction of the kind we are looking for to occur, even at this density of states, e.g., transferring one quantum from the CH stretch to one quantum in the CN stretch and two quanta in the high- frequency HF bend (and possibly one quantum in the van der Waals stretch). We are, however, hesitant to choose any one state with certainty, especially due to the uncer- tainties in the anharmonic cross terms, and because a 144 cm-’ detuning as for the (O,l, 1,0,0,2,0) state would re- quire a rather large interaction matrix element of 12 cm-‘.

As one last note here, we would like to mention that we recently observed the fundamental and overtone spectra associated with CH stretch excitation in HCN-BF3.44 Both spectra (vi and 2vi) appear very regular, showing no signs of short-range (Coriolis mediated) perturbations. The fundamental spectrum is shifted by 0. lO( 1) cm-’ to the red of the corresponding monomer band. However, the overtone is observed approximately 0.65 ( 1) cm- ’ to the blue, presumably also due to a vibrational perturbation.

The vibrational predissociation rate

We will attempt to predict the ratio of u=2 to U= 1 vibrational predissociation rates within the same framework. The Fermi’s golden rule formula yields the following expression for the rate:

r-‘=2rK c I @&9>“QJ12 U<U’

x I (&E(R) I VI(R) lb(R)) 12. (9)

The “free” wave function @“JR) is associated with the dissociation channel with v < U’ and a kinetic-energy release E= [E,( v’) - EC( u”)] -Do- E,( 0). The density-of- states factor usually present in the expression for the Golden rule45 is implicit in the summation over all energetically allowed dissociation channels and the normaliza- tion of the wave functions.46 In general, a strong preference for the v = v’ - 1 dissociation channel is observed.4749 We will therefore drop the summation from Eq. (9) and obtain for the ratio of overtone to fundamental rates:

=( I (h(r))2,l/l (hW)ml j2

x ( I Ww2,(R) I VI(R) 1$2(R)) I

x I %,E,~(R) I V,(R) IA(R)) I -‘12. (10)

If the vibrationally averaged van der Waals potentials ( V(R)),, do not depend strongly on the vibrational quantum number U, then both the free and the bound (metastable) wave functions appearing in Eq. (10) will be fairly similar for U= 0 and u= 1, respectively, for U= 1 and U= 2. Consequently, the rightmost factor in Eq. ( 10) reduces, in a first approximation, to unity:



This approximation can of course be justified with the same arguments presented earlier to justify the approximation made to arrive at Eq. (7b) from Eq. (7a).

We have numerically evaluated [see the discussion following Eq. (8)] the matrix elements appearing in Eq. ( 11) and find for the linear term, #r(r) =s* (r-rc), that ~-‘(u’=~)/T-~(u’= 1) =2.03, while for the quadratic term, f$i(r)=t*(r-ra)*, we calculate r-l(0’=2)/ r-‘(v’=1)=8.42. This compares to a ratio of 1.8 (0.3) observed experimentally.

The correlation law

That the correlation law of Eq. ( 1) can be misleading when comparing overtone with fundamental vibrational predissociation is easily seen by combining the estimates of Eqs. (8) and ( 11)) with a linear approximation for & (r), into

tion channel considered. Especially when one (or both) of the dissociation products has more than one internal degree of freedom, it is possible that the vibrational predissociation following overtone excitation shows a very different redistribution of the excitation energy over the internal degrees of freedom of the products than the predissociation following fundamental excitation. But even in the case of only one internal degree of freedom, the degree of rotational excitation of the products may be quite different. Indeed, the beautiful work of Miller’s group on HF dimer has clearly demonstrated the importance of near-resonant channels in the vibrational dissociation process.50 There- fore, even if the Au= - 1 preference holds rigidly, the 1c11,~~~ CR 1 and $o,.Q~(R 1 wave functions might not just be simply displaced by AE=E,(v=2) -EJv= l), but also be of rather different shape and displaced along the van der Waals coordinate.

x (~)~*-(r)~)/((r),~-(r)~))*=2.03. (12)

If the correlation law of Eq. ( 1) could be applied as im- plied above, the ratio on the left-hand side in Eq. (12) should be unity. Clearly then, when comparing v=2 to v = 1 predissociation, “all-else” is not equal in the same sense as one needs to assume to make Eq. ( 1) valid. How- ever, if it can be assumed that the monomer vibrational wave functions Q’,(r), and therefore the matrix elements (4t (r) ), are not much affected by complexation, the factors containing the matrix elements (+t (r) ) in Eqs. (7) and (9) can be treated as constants, for a given series of complexes involving the same intramolecular vibrational excitation (from v” to v’). In this case the correlation law relies on the coupling function having very much the same shape for all members of this series, so that in first approximation one can assume a simple scaling of the coupling function with a constant factor. In contrast, when comparing overtone and fundamental vibrational predissociation in the same complex, the coupling function is naturally unchanged, but the monomer vibrational wave functions, and thus the matrix elements (+t (r) ), change dramatically with the vibrational quantum number.

In conclusion, the requirement that the diagonal radial matrix elements appearing in the expression for the frequency shifts [Eq. (7a)] do not depend strongly on v is more easily satisfied than the corresponding requirement for the off-diagonal coupling matrix elements in the expres- sions for the predissociation rate [Eqs. (9) and (lo)]. The first-order description of the predissociation rate behavior, and therewith the correlation law, is potentially much more troublesome than the frequency-shift prediction within the same framework.

As we have already pointed out, the validity of the correlations derived for this case [specially the one formu- lated in Eq. ( 1 1 )] now depends on changes with the quantum number v in the radial van der Waals wave functions being negligible, in both the metastable and the unbound, dissociative state. This appears to be a reasonable assumption for the case of the metastable wave function r&(,,(R): since it is presumed that the initial excitation does not involve a hot band or combination band transition associated with the van der Waals mode(s), the function r,&(R) has the smooth shape without nodes, characteristic of the lowest vibrational level (with quantum number n =O). However, the wave function $JR) associated with the dissociation products is a rapidly oscillating function and its exact behavior could depend strongly on the dissocia-

This may very well be the main reason for the faster predissociation of the overtone, “free” HF-stretch excited HF dimer, compared to the corresponding fundamental case, as observed very recently by Nesbitt and co- workers.*’ The linewidths in their 2~~ spectrum are indic- ative of predissociation rates that are sensitively dependent on the rotational quantum numbers (including the inter- conversion tunneling symmetry of the levels), and that are generally about 1 order of magnitude faster than for the fundamental. Due to the small moment of inertia of HF and the highly anisotropic hydrogen bond (resulting in a strong mixing of the rotational states), rotational excitation of the fragments is expected to result in efficient vibrational predissociation of the HF dimer. However, as for our HCN-HF system, the number of accessible dissociation channels for (HF), is not expected to increase dramatically from fundamental to overtone excitation, in view of the harmonic preference for Au = - 1. Still, it should not surprise us if the HF dimer, with its more strongly anhar- manic HF oscillator and nonlinear hydrogen bond, defies treatment in such a simple model as presented here. Al- ready its overtone frequency redshift is larger than approximately twice the fundamental shift (71 vs 30 cm-‘); the experimental ratio of redshifts is 2.37, whereas an evaluation of Eq. (8), with as input the monomer rotational constants of HF,51 yields a predicted ratio of 2.033.

King and co-workers have observed the NO stretching v1 + v5 combination band and the 2v5 overtone of the NO dimer.3 ’ The vi and v5 fundamentals were previously recorded in both time29 and frequency28*30 domain experiments. For the present discussion the v5 (antisymmetric NO stretches) measurements are the most interesting. For

J. Chem. Phys., Vol. 97, No. 12, 15 December 1992

Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

this mode, the fundamental and overtone frequency redshifts are -87 and - 165 cm-‘, respectively (i.e., Av2d Avlo= 1.9), whereas the lifetimes were determined to be 39(8) and 20(3) psec, respectively [yielding a ratio r-‘(u’=2)/r-l(v’= 1) =2.0]. Both the ratio of redshifts and the ratio of the lifetimes agree remarkably well with the predictions based on Eqs. (8) and ( 1 l), especially when taking into account that the large redshifts suggest a relatively strong potential coupling. However, there exists strong evidence that the predissociation of the NO dimer evolves, at least partially, through a nonadiabatic spin- orbit coupling mechanism which involves the electronic ground state ( ‘A 1 ) and the repulsive surface of a low-lying electronically excited state. As already pointed out in the Introduction, this level of agreement might well turn out to be fortuitous as our understanding of the (NO), dissociation mechanism increases.

Predissociation rate vs density of exit channels

The last issue we would like to discuss is the much shorter lifetime of the HCN-HF complex, compared to the HCN dimer, for both fundamental and overtone excitation. While the total density of dissociation channels is undoubtedly much larger for the HCN dimer, many of these channels are not likely to play an important role for reasons explained below. For the sake of simplicity, we will assume for the following discussion that the complex is excited to the J=O level of the predissociating state. This is not a serious restriction in view of the very low rotational temperatures attained in molecular-beam experiments. Conservation of angular momentum then requires that

J,-tJ2+Jort,=O, (13) where J, and J2 are the internal angular momenta associated with the fragments, while Jorb represents the orbital angular momentum associated with the reduced mass p, relative velocity g, and impact parameter b (i.e., the short- est line segment between the asymptotic straight-line tra- jectories of the fragments at large separation) of the separating fragments. Similarly, conservation of energy requires that

hv=Do-Einit+ C (EY+ER+ET)i, (14) i= I,2

where hv represents the energy of the photoexcitation, Einit the internal energy of the complex before excitation (relative to the zero-point energy), and E, ERt and ET the vibrational, rotational, and translational energy of each fragment. The total number of energetically allowed dissociation channels is obtained from Eq. ( 14), given the energy levels of the monomer fragments, as the number of ways in which we can combine the energies deposited into vibrational and rotational motions of the fragments under the condition that the kinetic-energy release is zero or pos- itive (the ratio of ET1 to En is determined by conservation of linear momentum).

The larger number of energetically accessible channels for the HCN dimer is mostly a result of the additional internal degrees of freedom in the nonexcited HCN mole-

TABLE V. Direct count of the accessible dissociation channels following excitation of the “outside” CH stretch. The maximum kinetic-energy release is 200 cm-‘. The dimer is assumed to be prepared in the predis- sociative state with J=O. The spectroscopic data for the HCN monomer was taken from Ref. 54, that of HF from Ref. 51. D, (HCN-HF) = 1737 cm-‘. Do (HCN-HCN) = 1330 cm-‘.

(a) No rotational excitation of the products

(b) Only Au= - 1 channels, with no vibrational excitation of the partner; bc0.3 8,

(c) Same as (b), except that b<lti

(d) Same as (b), no limit to the impact parameter b

HCN-HF (HCNh

u=l v=2 lJ=l v=2

2 3 0 0

20 17 0 0

48 35 6 14

55 49 81 83

cule and the rotational constant being much smaller for HCN than for HF. However, the additional channels associated with the intramolecular vibrational modes of the nonexcited HCN partner in the HCN dimer are rather remote from the excited, outside CH stretching mode. That is to say that in this case the overlap between the metastable and the free wave functions appearing in the Golden rule expression of Eq. (9) is expected to be small. It can therefore be argued that their excitation in the vibrational predissociation process is unlikley, as we also expect the excitation of the HF stretch to be unlikely. In both cases, the energy leaking out of the excited CH stretch would have to pass through the van der Waals bond. But even when we consider only those dissociation channels that leave the other molecule in the vibrational ground state, the HCN dimer has, in principle, many more channels at its disposal by virtue of the much smaller rotational level spacing in HCN than in HF. However, again it can be anticipated that these are not very effective in accelerating the dissociation process. Indeed, in order to dispose of the same amount of energy, the HCN fragment would have to be excited to much higher angular momentum states than the HF fragment. It is generally accepted that V-R energy transfer processes are much less efficient than V- V processes.49 Moreover, the large-amplitude zero-point motion of the internal hydrogen atom in HCN-HF, correlat- ing with HF free rotation, allows the HCN-HF complex to access dissociation channels with, for a linear complex, remarkably different angular momenta, whereas for the much more rigid HCN dimer we expect both fragments to have very nearly the same angular momentum (the “impact parameter” is at every instant close to zero, corresponding to zero orbital angular momentum associated with the separating fragments).

For the above reasons we have tabulated in Table V (for both fundamental and overtone excitation, and for both systems) the number of energetically accessible dissociation channels (with an upper limit to the kinetic- energy release of 200 cm-‘) for the following cases: (a) counting only the vibrational channels, i.e., excluding ro-

Kerstel et a/.: Overtone spectroscopy of HCN-HF 8903



tational excitation of the products, (b) counting only the Av= - 1 channels that leave the partner molecule in the vibrational ground state and with the range of product angular momenta limited such that the maximum impact parameter b is limited to 0.3 A, (c) ditto, but with the impact parameter b < 1 A, and (d) including all rotational channels. The expectations based on the above arguments are clearly born out. The large difference in the number of available vibrational (rotationless) channels for the two systems can be attributed to the different dissociation energies (Da=1737 cm-’ for HCN-HF,9 while Da=1330 cm - ’ for HCN dimer52V53 ) . For HCN dimer, for which the energy to be redistributed after dissociation is larger, the energy is still not sufficient to excite the second overtone of the bend. The remaining energy, however, is now much larger than can be accommodated by the next lower vibrational state, the first overtone of the bend. Necessarily, this amount of excess energy has to be disposed of in the form of rotational and kinetic excitation of the fragments, both in themselves rather inefficient processes. Note too, that the increase in density of dissociation channels from fundamental to overtone excitation is at most very modest. In conclusion, we can state that a reasonable constraint on the number of channels that are considered accessible by the system, such as the kinetic constraint of limiting the range of impact parameters, suffices to rationalize the observed trends in the vibrational predissociation rates for these systems.

ACKNOWLEDGMENTS

CONCLUSIONS

We have observed the spectrum of HCN-HF involving overtone excitation of the CH stretch. The vibrational predissociation lifetime is about a factor of 2 shorter than for the corresponding fundamental spectrum. This result is not inconsistent with a simple picture based on first-order perturbation theory, if we assume the dependence on the intramolecular CH stretching coordinate of the coupling potential function to be linear. This appears to be a reasonable choice for a system in which the CH stretching potential is only slightly affected by the formation of the complex. It is then disconcerting to see that the vibrational frequency shift for the overtone spectrum is very different from that predicted by the same model. We have therefore proposed that the experimentally observed frequency shift reflects not only the effect of complexation, but also the effect of a long-range vibrational interaction that shifts the relevant energy levels in the complex. Perhaps isotopic sub- stitution, by selectively shifting the vibrational energy levels in the complex, will allow us to assess the correctness of our proposed vibrational interaction. A good understanding of the driving forces behind the complexation induced vibrational frequency shift is important, so the measured shift can be reliably used as a sensitive test for the effects of electron correlation in ab initio calculations. Another issue is that calculations of dimer properties often neglect the effects of anharmonicities. Overtone data should allow us to decide whether observed discrepancies with experiment are due to this simplification or to other factors (such as basis-set errors).

We are grateful to Professor R. LeRoy for sending a preprint of his publication (Ref. 41), for discussing his work with us, and for his critical reading of this manuscript under difficult circumstances, and to Professor J. W. Bevan for sharing with us a manuscript of Ref. 19 and the unpublished FTIR spectrum of the HCN-HF 2~~ band.21

This work was supported by the NSF under Grant No. CHE-901649 1.

‘A. C. Legon and D. J. Millen, Faraday Discuss. Chem. Sot. 73, 71 (1982); Chem. Rev. 86, 635 (1986).

‘J. W. Bevan, in Structure and Dynamics of Weakly Bound Molecular Complexes, edited by A. Weber, Vol. 212 in NATO ASI Series C (Rei- del, Dordrecht, 1986); W. Klemperer, ibid.

‘D. J. Nesbitt, Chem. Rev. 88, 843 (1988). 4A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Sot. London Ser.

A 370, 213 (1980). ‘Z. Kisiel, A. C. Legon, and D. J. Millen, Proc. R. Sot. London Ser. A 381, 419 (1982).

‘A. C. Legon, D. J. Millen, and L. C. Willoughby, Proc. R. Sot. London Ser. A 401, 327 (1985).

‘A. C. Legon, D. J. Millen, and S. C. Rogers, Chem. Phys. Lett. 41, 137 (1976).

s A. C. Legon, D. J. Millen, and S. C. Rogers, J. Mol. Spectrosc. 70, 209 (1978).

9B. A. Wofford, M. E. Eliades, S. G. Lieb, and J. W. Bevan, J. Chem. Phys. 87, 5674 (1987); 88, 6678 (1988).

“B A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, J. Chem. Phys. 83, 6188 (1985).

“B. A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, Chem. Phys. Lett. 124, 579 (1986).

“B. A. Wofford, M. W. Jackson, J. W. Bevan, W. B. Olson, and W. L. Lafferty, J. Chem. Phys. 84, 6115 (1986).

13E Kyro, M. Eliades, A. M. Gallegos, P. Shoja-Chagervand, and J. W. Bkvan, J. Chem. Phys. 85, 1283 (1986).

14M W. Jackson, B. A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, J. Chem. Phys. 85, 2401 (1986).

“D Bender, M. Eliades, D. A. Danzeiser, M. W. Jackson, and J. W. Bevan, J. Chem. Phys. 86, 1225 (1987).

16M. W. Jackson, B. A. Wofford, and J. W. Bevan, J. Chem. Phys. 86, 2518 (1987).

“B A. Wofford, M. W. Jackson, S. G. Lieb, and J. W. Bevan, J. Chem. Phys. 89, 2775 (1988).

‘*B A Wofford R. S. Ram, A. Quinonez, J. W. Bevan, W. B. Olson, and w. J: Lafferty: Chem. Phys. Lett. 152, 299 (1988).

IsA. Quinones, R. S. Ram, G. Banderage, R. R. Lucchese, and J. W. Bevan, J. Chem. Phys. (submitted).

“B. A. Wofford, S. G. Lieb, and J. W. Bevan, J. Chem. Phys. 87, 4478 (1987).

“J. W. Bevan (private communication). 22P. Botschwina, Structure and Dynamics of Weakly Bound Complexes,

edited by A. Weber, Vol. 212 in NATO ASI Series C (Reidel, Dordrecht, 1987).

23R. Amos T. Gaw, N. Handy, E. Simandiras, and K. Somasundram, Theor. dim. Acta 71, 41 (1987).

24D. C. Dayton and R. E. Miller, Chem. Phys. Lett. 143, 181 (1988). “D. C. Dayton and R. E. Miller, Chem. Phys. Lett. 150, 217 (1988). 26H Meyer, E. R. Kerstel, D. Zhuang, and G. Stoles, J. Chem. Phys. 90,

4623 (1989). *‘M. A. Suhm, J. T. Farrel, A. McIlroy, and D. J. Nesbitt (unpublished). 28Ph. Brechignac, S. De Benedicts, N. Halberstadt, B. J. Whitaker, and S.

Avrillier, J. Chem. Phys. 83, 2064 (1985). 29M P Casassa, J. C. Stephenson, and D. S. King, J. Chem. Phys. 89,

1966’(1988). “Y. Matsumoto, Y. Ohshima, and M. Takami, J. Chem. Phys. 92, 937

(1990). “J R. Hetzler, M. P. Casassa, and D. S. King, J. Phys. Chem. 95, 8086

(‘1991). “T. E. Gough, R. E. Miller, and G. Stoles, Appl. Phys. Lett. 30, 338

(1977).



“M Zen, in Atomic and Molecular Beam Methods, edited by G. Stoles (dxford University, New York, 1988), Vol. 1.

UE. R. Th. Kerstel, K. K. Lehmann, T. F. Mentel, B. H. Pate, and G. SC&S, J. Phys. Chem. 95, 8282 (1991).

“A. M. Smith, S. L. Coy, W. Klemperer, and K. K. Lehmann, J. Mol. Spectrosc. 134, 134 (1989).

I’D. R. Miller, in Atomic and Molecular Beam Methods, edited by G. Stoles (Oxford University, New York, 1988). Vol. 1.

“K. W. Jucks and R. E. Miller, J. Chem. Phys. 88, 6059 (1988). ‘*E. R. Th. Kerstel, X. Yang, K. K. Lehmann, and G. Stoles (to be

published). ‘sR. E. Miller, in Dynamics of Polyatomic van der Waals Complexes,

edited by N. Halberstadt and K. C. Janda, Vol. 227 in NATO AS1 Series B (Plenum, New York, 1990).

‘OR. E. Miller, Science 240,447 (1988). ” R. J. LeRoy, M. R. Davies, and M. E. Lam, J. Phys. Chem. 95, 2167

(1991).

“S. Liu and C. E. Dykstra, J. Phys. Chem. 90, 3079 (1986). 43K. K. Lehmann and A. M. Smith, J. Chem. Phys. 93, 6140 (1990). “E. R. Th. Kerstel, X. Yang, and G. Stoles (to be published). 45See, e.g., A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York,

1975). 46R. J. LeRoy, Comput. Phys. Commun. 52, 383 ( 1989). 47D. H. Levy, Adv. Chem. Phys. 47, 323 (1981). 48J M. Skene, J. C. Drobits, and M. I. Lester, J. Chem. Phys. 85, 2329

(‘1986). 49G. E. Ewing, J. Chem. Phys. 91,4662 (1987). %D. C. Dayton, K. W. Jucks, and R. E. Miller, J. Chem. Phys. 90, 2631

(1989). “G. Guelachvili, Opt. Commun. 19, 150 (1976). ‘*H. D. Mettee, J. Phys. Chem. 77, 1762 (1973). 53L. W. Buxton, E. J. Campbell, and W. H. Flygare, Chem. Phys. 56, 399

(1981). 54W. Quapp, J. Mol. Spectrosc. 125, 122 (1987).


The rotationally resolved 1.5 &m spectrum of the HCN--HF ... · The rotationally resolved 1.5 pm...

Documents

Transcript of The rotationally resolved 1.5 &m spectrum of the HCN--HF ... · The rotationally resolved 1.5 pm...