6068
J. Phys. Chem. 1994,98, 60686074
High-Resolution Infrared Overtone Spectroscopy of Nz-HF: Vibrational Red Shifts and Predissociation Rate as a Function of HF Stretching Quanta John T. Farrell, Jr., Ofer Sneh, and David J. Nesbitt'vt Joint Institute for Laboratory Astrophysics, University of Colorado and National Institute of Standards and Technology, and Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0440 Received: February 10, 1994"
The high-resolution infrared spectrum of the UHF = 2 0 stretch in N r H F has been recorded using direct absorption of tunable infrared light in a slit jet spectrometer. The band origin is located at 7657.4057cm-1, red-shifted 93.39 cm-l from the U H F = 2 0 origin of the HF monomer. The changes in vibrational red shift with HF stretching quanta provide explicit information on the coupling between the high-frequency (Le., intramolecular) and low-frequency (i.e., intermolecular) degrees of freedom, which can be understood with a simple electrostatic model. Additional evidence for coupling between the low- and high-frequency modes is provided through an analysis of the rotational consants. Specifically, rotational-RKR techniques are used to invert the spectroscopic data to provide one-dimensional potential curves for the intermolecular van der Waals stretch coordinate for the UHF = 0, 1, and 2 levels of N2-HF. These potentials reproduce the experimentally observed increase in binding energy with incremental HFexcitation. Homogeneous broadening of therovibrational transitions is determined to be 79 f 11 MHz from a Voigt deconvolution of the individual absorption profiles and is independent of the upper state J within the experimental uncertainty. This broadening is attributed to a vibrational predissociation lifetime of 2.0 f 0.3 ns for the complex and reflects an 11-fold shorter vibrational predissociation lifetime than observed upon UHF = 1 0 excitation in Nz-HF.
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I. Introduction By virtue of the isolated nature of the reagents, photochemistry and spectroscopy of weakly bound binary complexes have served asvaluable tools for probing unimoleculardynamics.'-2 The field of molecular energy transfer has been an area of particularly active research, and our understanding of phenomena such as vibrational predissociation and intramolecular vibrational redistribution has improved dramatically as a result of studies incorporating these small molecular systems.' Recently, significant progress has been made in our ability to monitor stateto-state dissociation rates as well as the effects of intermolecular orientation on the rates of these processes. These studies have greatly furthered our understanding of intermolecular forcesand complement investigationsranging from the characterization of many-body forces in rare-gas hydrogen halide systems3p4 to the examination of phase transitions in larger clusters still to small to assume the properties of the associated bulk matter.5-6 There are a number of factors that make van der Waals complexes well suited for energy-transfer studies. First, the coupling between the constituents is often sufficiently weak that the nature of electronic and vibrational excitation is very similar to that of the isolated molecule. This allows the selective preparation of initial states that can be well described in terms of the quantum labels of themonomer. Second, the intermolecular bond is typically much weaker than a "true" chemicalbond, which allows relatively small amounts of energy to access states metastable with respect to dissociation. For example, there have been a large number of vibrationalpredissociation studies738carried out in the near-IR with excitation energies between 1000 and 4000 em-' in systems with dissociation energies ranging from 1000 to a few cm-1. Third, these complexes are readily formed in the cold environments of supersonic expansions, conditions that thermodynamically favor cluster formation through the absence of thermally dissociative collisions. The complexes f Quantum Physics Division, National Institute of Standards and Technology, Boulder, CO 80309. 0 Abstract published in Advance ACS Abstracrs, May 15, 1994.
formed under these conditions typicallyhave little or no excitation in the internal degrees of freedom, and this often leads to a relatively high degree of orientation of the subunits. This can significantly reduce the regions of phase space accessible to the metastable, vibrationally excited complex, thereby potentially reducing the number of degrees of freedom required to model the relevant dynamics. An additional benefit derived from the supersonic sources is the low temperature routinely obtained, which significantly reduces spectral congestion and considerably simplifies the interpretation of the spectrum. Vibrational predissociation dynamics in complexes formed between rare gas (RG) atoms and halogens, interhalogens, and radical diatoms have been extensively studied using laser-induced fluorescence (LIF) techniques.e1s In these experiments, the complexes are promoted to an electronically excited state with well-defined vibrational quanta in the diatom, and the lifetimes and products of the vibrational predissociation process are monitored. The observation of interesting dynamical effects such as rotational rainbowsl6andinterference structuresl2have helped elucidate the mechanism of the predissociation event. Additionally, these studies have allowed the determination of accurate potential energy surfaces and dissociationenergies for a number of complexes.12J3 Theoretical approaches ranging from classical to 3D full quantum calculations have been used to model results for complexesof Ne with IC1and C1213J7J8and have demonstrated good agreement with the experimental data. One potential limitation of electronic state preparation is the presence of nonadiabatic relaxation pathways which may complicate the analysis of the ensuing dynamics. These processes are nonexistent in the ground electronic state, and consequently infrared-based techniques can offer distinct advantages over electronic studies for some systems. Indeed, complexes of many of the simplest molecular species, such as H20, CH4, HF, HCI, etc., cannot be studied via LIF techniques but are quite amenable to investigationin the IR. The number of systemsthat have been studied using IR techniques is now quite large,8J9 and the predissociation dynamics observed in mid-infrared experiments have been shown to be quite complex for even the relatively simple
0022-3654/94/2098-6068$04.50/00 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6069
IR Overtone Spectroscopy of Nz-HF
binary systems.2bz5 As one classic example of mode-specific established through the use of rotational-RKR techniques,52.53 which allow the generation of one-dimensional (Le., collinear) behavior, excitation of the “bound” vs the “free” H F in (HF)2 potentials for the interaction between the N2 and H F in a given leads to vibrational predissociationrates that differ by more than vibrational level. Additionally, the faster vibrational predissoa factor of 30.26 Furthermore, these rates can vary dramatically ciation rate for N2-HF excited to 2v1 vs V I is examined. The upon isotopic substitution, as has been demonstrated recently for possibility of near-resonant Nz(u) + H F continuum states (HF)z/(DF)2 (ref 27), (HCl)z/(DC1)2 (refs 28 and 29), and the accelerating the predissociationof 2vl is discussed, as is the role mixed dimers of HF/DF30and HCl/DC1.31 The faster vibrational increased coupling between the intramolecularand intermolecular predissociation rate for HC1-DCl upon HCl vs DCl excitation coordinates could play in enhancing V V energy-transfer has been rationalized in terms of intermolecular V V transfer channels. from the excited HCI to the DCl concomitant with the predissociation event, a channel not available upon excitation of the 11. Experimental Section lower-frequency DC1 stretch. Similar differences in vibrational predissociationrates have also been explained in terms of nearThe slit jet difference frequency infrared spectrometer used in resonant V V transfer for the mixed dimers of HF/HC1,32 as these studies54 and the modificationsthat allow access to the first well as Dz/Hz-HF,23.33 NzHF/DF,’~and C ~ H Z - H C ~ / D C ~ . ~ ~overtone stretching region of HF42have been described in detail Several theoretical models have been developed to rationalize previously. The high-resolution, tunable 1.3-pm light is generated the wide range of predissociation rates for these weakly bound via a variation of the difference frequency generation technique systems. Early progress in this area led to the momentum gap developed by Pine.55 The single-frequencyoutput of a CW Nd: law36and subsequent refinements there0f.3~4 Additionally, a YAG laser and tunable ring dye laser are rendered collinear and correlation law has been developed by Miller41based on a Golden focused into a 4 X 4 X 50 mm LiNbO3 crystal. The crystal is Rule treatment of the predissociation rate and a perturbative housed in a temperature-controlled oven, whose temperature is treatment of the coupling between the monomer and complex ramped synchronously with the scanning of the dye laser to vibrational potentials. These methods have provided a semipreserve 90° noncritical phase matching conditions. This scheme quantitative understanding of the predissociationdynamics, but can typically generate approximately 50 pW of infrared light the development of more quantitative models has been hampered with 2-3-MHz line widths for 300 and 400 mW of Nd:YAG and by the lack of detailed potential energy surfaces which explicitly dye laser radiation, respectively. After exiting the oven, the account for the intermode coupling, i.e., the coupling between differencefrequencylight is transmitted through a series of bandthe high-frequency intramolecular and the low-frequency interpass filters that reflect the dye and Nd:YAG beams. The infrared molecular (van der Waals) modes. Construction of such light is then recollimated and split into signaland referencebeams, multidimensionalpotentials has in general not been possible due with the former directed along the long axis of a supersonic to the lack of experimental data which probe sufficient regions expansion generated by a 4-cm X 130-pm pulsed slit jet. of the potential surface sensitive to this coupling. The Nz-HF clusters are formed via the adiabatic expansion of an HF/Nz/rare gas mixture through the pulsed slit valve. The Two approaches have recently been introduced that provide gas mixture found to maximizeNz-HF cluster formation consists the experimental data necessary to bridge this gap. Techniques of 1.5%H F in a 60:40 mix of Nz with “first-run” Ne (Le., a 70:30 that access ouertone vibrations in the chromophoreshave recently Ne:He mixture from the first distillation of Ne) at a total backing been devel0ped,4~~~ providing information on how the intermode pressure of 600-800 Torr. Multipass optics are used to obtain coupling changes as a function of the high-frequency stretching 16 passes through the expansion which provides a 64-cm coordinate. The complexes that have been studied in this manner absorption path length. Both the signal and reference beams are include Ar-HF,44v45(HF)2,46,47(HCN)2,43 and HCN-HF.48 In monitored with room temperature intrinsic germanium photoaddition, King and co-workers49and Miller and co-workers5O5l voltaic detectors, the photocurrents from which are subtracted have developed techniquesthat resolve the final state distributions in order to eliminate common mode amplitude noise on the laser of the vibrational predissociation products. Since vibrational light. The transient imbalance due to differential absorption is predissociationof weakly bound complexes is analogousto a halfdigitized, signal-averaged, and stored as a function of laser collision event, the analysis of product states accessed from a frequency to yield the spectrum. Transition frequencies are well-characterized initial state provides information about the measured with a traveling Michelson interferometer referenced anisotropy in the potential as well as thegeometry of the transition to a polarization-stabilized HeNe laser,56with the P( l), UHF = state. Both of these experimental approaches provide comple2 0 absorption of H F monomer at 7709.6839 cm-I 57 serving mentary information and indeed establish rigorous tests of as an absolute frequency standard. theoretical models designed to model dynamics sensitive to this Line-shape analysis is performed by taking small (5-8 MHz) intermode coupling. incremental laser steps over each rovibrational transition. To In this paper we present data for Nz-HF excited to the first improve the signal-to-noise ratios, 16 averages are recorded at overtonestretching level of the HF. The results from the present each laser step, and multiple scans over each transition are study can be compared with those reported from mid-IR and performed to reduce the statistical uncertainties. The resulting microwave experiments to help elucidate the effect of H F stretch line shapes are least-squares fit to a Voigt profiles to deconvolve excitation on the vibrationally averaged structure and vibrational the Gaussian and Lorentzian componentsof each transition. The predissociation dynamics of the complex. The spectroscopic Gaussian component arises from residual Doppler broadening in observables that provide this information are the red shift (Le., the expansion and is determined as an unconstrained parameter the frequency shift of the chromophore upon complexation), the in the Voigt fits. The results are in good agreement with the changes in rotational and centrifugal distortion constants as a Gaussian component determined for UHF = 2 0 transitions in function of UHF, and vibrational predissociationrate. The approach Ar-HF, for which there is nodetectablevibrationalpredissociation used to understand the changes in the vibrational red shift with broadening45 at our 12-3-MHz resolution. The Lorentzian increasing U H F incorporates a perturbative treatment of the component provides a spectroscopic determination of the precoupling between the intermolecular and intramolecular mordissociative lifetime of the complex via T = I/27rAvprdida. dinates. The Darticular model emdoved is based on electrostatics. correlating the changes in the potential with changes of the III. Results and Analysis monomer’s electrical properties upon vibrational excitation. The Throughout the remainder of the paper, we will refer to the correlation between the changes in the rotational and centrifugal UHF = 2 0 and U H F = 1 0 transitions of Nz-HF as 2vl and distortion constants with U H F and the intermolecular potential is
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Farrell et al.
6070 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 NzHF P BRANCH 10
5 0.5
=2 0 R BRANCH
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0
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TABLE 2 Molecular Constants Obtained from Least-Squares Analysis of the N2-HF 2vl Transitions Listed in Table 1 (in c d ) * ground state VI 2Vl YO
B” Dv X lo7
z 4
m
O.oo00 0.10658548(3) 5.673(41) -1.38(27)
3918.24332( 14) 0.1071782(14) 5.295(47) -1.33(30)
7657.40573(33) 0.1080225(76) 4.84(30)
H,X 10” 0.0b a Uncertainties in parentheses represent 95% confidence limits. The experimentaldata from the ground59and firsts*vibrationalHF levels are included in the fit, weighted by theinverseofthesquareof the measurement uncertainity. b Parameter constrained to be 0.0.
8
0
m Q
h
8
v
0
,
I 7655
I 7660
FREQUENCY (cm-’ ) Figure 1. Spectrum of N r H F excited to the first overtone stretching level of the HF. The spectrum was constructed by overlapping 1.5-cm-I scans, averaging 15 pulses per 14-MHzfrequency step.
TABLE 1: Observed Transitions to the 2vl Level of NrHF* J’+ J” Y (cm-1) J’- J” Y (cm-1) J’+ J” Y (cm-*) 14- 15 7654.5210 (-5) 13 6 14 7654.6920 (0) 12 13 7654.8659 (1) 11 12 7655.0426 (-1) 10 1 1 7655.2232 (4) 9 10 7655.4065 (3) 8 9 7655.5923 (1) 7 8 7655.7823 (1) 6-7 7655.9749 (2) 5 6 7656.1705 (2) 4 5 7656.3685 (-4)
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3-4 2 3 1 2 0- 1 1 0 2+ 1 3 2 4+ 3 5-4 6 5 7 6
7656.5704 (0) 8 -7 7659.2138 (1) 7656.7749 (0) 9 8 7659.4522 (-3) 7656.9822 (0) 10 9 7659.6944 (3) 7657.1922 (4) 1 1 10 7659.9386 (0) 7657.6218 (0) 12 1 1 7660.1860 (0) 7657.8408 (1) 13 12 7660.4364 (2) 7658.0624 (0) 14 13 7660.6892 (-3) 7658.2869 (-1) 15 14 7660.9454 (-2) 7658.5147 (-3) 16- 15 7661.2045 (-1) 7658.7449 (2) 7658.9778 (0)
TABLE 3 Average hedimciation Line Widths for P- and R-Branch Transitions of 2q of Nz-HF’ line width line width line width J’ (MHZ) J’ (MHz) J’ (MHz) 0 1 2 3
90(25) 90(30) 80(25) 65(30)
4 5 6 7
75(20) 85(10) 80( 10) 90(20)
8 9
10 11
70(10) 80(20) 55(30) 85(30)
The numbers in parentheses represent 1u standard deviation. The variation in uncertainty reflects the increase in signal/noise near the peak of the Boltzmann distribution. The overall average is Auprcdh, = 79 f 11 MHz, corresponding to a predissociation lifetime of 2.0 i 0.3 ns.
by the inverse square of the measurement uncertainty. Leastsquares fitting of these data yields the band origins, rotational constants,and centrifugaldistortion constantsfor each vibrational level of the complex; these values are listed in Table 2. The origin of this band determined from the fit is 7657.4057(3) cm-l, which is red-shifted 93.39 cm-1 from the UHF = 2 0 origin of the HF monomer. This is slightly more than twice the 43.18cm-I redshift exhibited upon vl excitationand reflectsa systematic deepening of the intermolecular potential as a function of H F vibrationalexcitation. TheB rotational constant exhibits a similar a Numbers in parentheses represent (observed-calculated) deviations, in units of the least significant digit. The residual standard deviation of trend, increasingmonotonically from the ground vibrational state the fit is 0.000 25 cm-l. to u = 1 to u = 2 (see Table 2). This correponds to a systematic decrease in the vibrationally averaged center-of-massseparation vl, respectively, to avoid confusion with vibrational transitions of between the Nz and H F and together with the red shift provides the HF monomer. Similarly, the levels accessed by the V I and explicit information on changes in the intermolecular potential 2vl transitions will be denoted u = 1 and v = 2, respectively, with as a function of H F stretching quanta. These interactions are the understanding that only the H F within the complex is discussed in more detail in the Discussion section. undergoing excitation. The average Doppler and Lorentzian components of the The initial search for the 2vl origin was guided by the results individual rovibrational line shapes for 2vl transitions are from previous overtone studies of van der Waals c l ~ s t e r s , ~ ~ , ~determined ~-~ via a Voigt analysis. For transitions near the peak for which the frequencyshift upon complexationis approximately of the Boltzmann distribution, the signal-to-noiseratio is sufficient twice that observed upon fundamental excitation. Based on a to float both the Doppler and Lorentzian widths, yielding an 43-cm-1 red shift for vl excitation,sS the 2vl band is anticipated average Doppler width of 80 f 10 MHz. This is approximately to be near 7660 cm-l, Le., approximately 90 cm-l to the red of a factor of 2 larger than the 38 f 6 MHz determined for the the U H F = 2 0 origin of H F at 7750.8 cm-l. Figure 1 shows transitions of N r H F under similar expansion conditions,which a band centered at 7657 cm-l, which exhibits simple P/R branch is quantitatively consistent with the 2-fold higher infrared structure indicative of a Z 2 transition for a near-linear frequencies observed in the overtone region. For the peaks with molecule. The spectrum is observed only when Nz and H F are lower signal-to-noise, the Doppler contributions are fiied at 80 simultaneously present in the expansion. The location of the MHz in order to reduce uncertainties in the Lorentzian comorigin, band structure, and dependence upon expansion gas ponents. Factors that could inhomogeneously broaden the composition strongly indicate that N t H F is the complex giving rovibrational line shapes, such as collisionaland power broadening, rise to this spectrum;this assignmentis unambiguously confirmed are negligible in the low-density environment of the free jet by agreement (* 0.0005 cm-I) with ground-state combination expansion and 550-pW difference frequency power levels. differences from previous microwave studies.s9 The observed Consequently, the Lorentzian component determined from the transition frequencies for N r H F are listed in Table 1. Voigt deconvolution described above can be directly related to The band shows no evidence of local perturbations, and the time scale for energy transfer from the excited H F to the consequently transitions to this level are fit to the standard intermolecular modes, which by analogy to the results for vls8 expansion in J(J + l), excitation is attributable to vibrational predissociation. The predissociationline widths for J’= 1-1 1 are listed in Table 3 and E YO + B’J’(J’+ 1) - DIJ’(J’+ I)]* + ...within the accuracy of the measurements do not reflect a J’ dependence. The average Lorentziancomponentof 79 f 1 1 MHz B”J”(J”+ 1) D’TJ’’(J’’+ 1)]* + ... (1) corresponds to a lifetime of 2.0 f 0.3 ns, which translates into an 11-fold faster vibrational predissociation for 2vl than for v1 To enhance the quality of the fit, data from the microwave59 and excitation. These results are discussed in more detail below. v 1 studies56 of Nz-HF are also included in the analysis, weighted
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IR Overtone Spectroscopy of NTHF
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6071 one has
100
-90 -80 -70
I
with associated harmonic force constant k,, harmonic frequency we, and anharmonicity ode. Addition of the interaction term yields V'(r), the modified stretching potential
-60 -50 -40
x -30 -1 w
20
0
-20 -1 0 0
0
I
2
3
NUMBER OF VIBRATIONAL STRETCHING QUANTA
Figure 2. Vibrationalred shifts vs the quanta of stretch excitationin the infrared chromophore of all complexes for which rotationally resolved data have been reported in an overtone level. The experimentaldata for N r H F (u = 1) are from ref 58 and for N2-HF (u = 2) from present work; for (HF)2 (u = 1, 2, and 3) the data are from refs 74, 46, and 47, respectively; for Ar-HF (u = 1 , 2, and 3) the data are from refs 75,45, and 44, respectively; for (HCN)2 (u = 1 and 2) the data are from refs 25 and 43; and for HCN-HF (u = 1 and 2), the data are from refs 24 and 48. The linearity of the plot arises from a perturbative interaction between the intermolecular (van der Waals) bond and the high-frequency intramolecular bond, as described in the text.
TABLE 4 Vibrational Red Shifts (in cm-1) of van der Waals Complexes Containing HF for Which Rotationally Resolved Overtone Data Have Been Reported' complex VI YI/YI 2u1 2vl/v1 3v1 3v1/vl N r H F -43.18ob 1.000 -93.389' 2.163 -152.557d 3.533 (HF)2 -30.523' 1.000 4 7 . 9 7 2 f 2.227 -99.306g 3.254 Ar-HF -9.654* 1.000 -20.912' 2.166 -33.773' 3.498 v1 refers to HF stretch excitation (for (HF)z the data are for the "free"HF). Reference 58. This work. Reference 67. Reference 74. /Reference 46. Reference 47. Reference 75. Reference 45. I Reference 44. IV. Discussion
A. Vibrational Red Shifts. Figure 2 shows thevibrational red shifts vs the number of vibrational quanta in the IR chromophore of all van der Waals complexes for which rotationally resolved overtone data have been reported. These values are also listed in Table 4. The small magnitude of the red shifts with respect to the monomer frequencies (Avrd shift/vO I1%) suggests that a perturbative treatment of the interaction of the intermolecular and intramolecular bonds is justified. Liu and Dysktra have presented calculations6M2 in which the change in the intramolecular stretchingpotential V(r)upon hydrogen bond formation is represented by an interaction term, Vnt(r)= sr, where s is the slope of the perturbing interaction potential as determined from ab initio calculations and r is the intramolecular stretching coordinate. The model is electrostatic in nature; the interaction of the molecule's polarizabilities and multipole moments with the electric field of a nearby molecule leads to changes in the intramolecular stretching potential of the molecule. This interaction has been found to be nearly linear with r for a large number of molecules, including HF.60 The addition of a linear term to the anharmonic stretching potential changes the equilibrium curvature and hence the potential force constant. As a consequence, the vibrationaltransition frequenciesof the monomer within the complex are shifted with respect to that of the free molecule. The red shift predicted by this model for v1 excitation of N2HF is 34 cm-1, in fair agreement with the experimental value of 43 cm-1. While quantitative agreement between the calculated and experimental red shifts requires that the slopes be accurately determined, the calculation of the red shift ratios do not. Consequently, we can extend this formalism to determine the vibrational dependence of the red shifts. By modeling the anharmonic stretching potential of the H F as a Morse oscillator,
(3) Evaluation of the curvature of this potential near the new equilibrium value of r allows k', the modified harmonic force constant, to be determined, from which it is possible to derive expressions for w: and w:x,'. Neglecting terms higher than first order in s, we calculate the ratios of the frequency shifts for u = 2 / u = 1 and u = 3/u = 1 for H F containing complexes to be 2.01 and 3.03, respectively, and independent of the value of s. This is in reasonable agreement with the experimentallyobserved ratios listed in Table4 for NTHF (2.16 and 3.53), Ar-HF (2.17 and 3.50), and (HF)2 (2.23 and 3.25). This simple one-dimensional model correctly reproduces the qualitative behavior of thevibrational dependenceof the red shifts but consistentlyunderpredicts the experimentallyobserved ratios. This discrepancycan at least be partially attributed to the effects of angular interactions not accounted for in this one-dimensional treatment. Specifically, the increase in angular anisotropy of the intermolecular potential with increasing UHF will tend to increase the alignment of the H F along the intermolecular axis, effectively further increasing both the strength of the hydrogen bond and the coupling with the intramolecularstretch. This effect has been experimentally observed from infrared Stark spectroscopy of Ar-HF,63 where the vibrationally averaged bend angle of the H F decreases from (ez)V 2 = 48' in UHF = 0 to 43' in U H F = 1. Similar results have been reported from Stark spectroscopy of u1 ofNrHF,64although thedecreasein theaverageHFbending angle could not be quantified. The work of Liu and Dykstra on which the above calculation is based lends a plausible physical picture to the origin of the vibrational red shifts for weakly bound complexes. Further support for the role of electrostatic interactions as a primary contributor to the red shifts has been given by Huts0n6~for ArHF. It was found that thevibrationally averaged inductionenergy could explain approximately 80% of the red shift for both u = 1 and 2. This can be contrasted, however, by the recent high-level ab initio calculationson Ar-HF by Tao and KlempereF in which the increase in electrostatic interactions is apparently offset by terms such as the exchange repulsion, and the dominant factor contributing to the red shift is actually the dispersion energy. Whether this is alsovalid for more stronglyinteracting, hydrogenbonding systems such as N r H F is unclear. A detailed ab initio analysis of how and why intermolecular potentials for hydrogen bonding change with intramolecular vibrational excitation of the subunits clearly merits further theoretical attention. B. Rotational Constants. Analysis of the rotational and centrifugal distortion constants as a function of H F stretching quanta provides information about the intermode coupling that is complementary to that obtained from the red shift analysis. In particular, the rotational constant provides the vibrationally averaged center-of-mass separation for a given H F vibrational level of the complex. Previous overtone studies of Ar-HF44s4S and (HF)246.47haveshown that theB rotationalconstant increases with monomer vibrational level, reflecting a decrease in the vibrationally averaged center-of-mass separation. This is consistent with a contraction of the complex and strengthening of the intermolecular bond. Further supporting evidence lies in the behavior of thecentrifugal distortion constant D, which decreases as a function of monomer vibrational level. These trends are
Farrell et al.
6072 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 1000
-VHF - - - - VHF
800
600
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=0
=1 =2
400 7-
E
v
>
200
o -200 -400
-600 -800 2
3
4
5
6
7
8
R(A)
Figure 3, One-dimensional potential curves for N t H F generated by inversion of the rotational and centrifugal distortion constants using the rotational-RKRtechnique of Nesbitt and Child.53 The rotational-RKR procedure provides the inner and outer classical turning points of the
intermolecular potential near the equilibrium position. The long-range 'behavior of the potentials is approximated by electrostatic terms as discussed in ref 53. The three curves are for the (HF) vibrationalground state and the first and second vibrationallyexcited states and reflect the increasing well depth with increased stretch excitation of the monomer.
present for N l H F as well and are a manifestation of the same physical interactions responsible for the vibrational red shifts. This behavior is most simply rationalized by examining the changes in the electrical properties of the H F as a function of U H F . Since both the H F dipole moment and polarizability increase upon vibrational excitation, the dipole-induced dipole and dispersion interactions also increase. Regardless of whether the dominant contribution to the red shift arises from induction or dispersion, the net result is an increase in the intermolecular bond strength and corresponding decrease in bond length. Nesbitt and Child53 have shown that it is possible to invert experimental rotational and centrifugal distortion constants of van der Waals complexes to obtain informationabout the potential energy surface for a given vibrational level of the monomer constituents. This "rotational-RKR" procedure is analogous to the RKR inversion used for generating potential energy surfaces for diatomics from vibrational spectroscopicdata and similarly provides the classical inner and outer turning points of the intermolecular potential. The quantitative accuracy of this inversion procedure has been tested on rotational eigenvalues derived from model 1-Dpotentialss3as well as through comparison of potential parameters determinedfor N r H F and its isotopomers in the ground and first vibrational levels of the HF stretch.34In the latter study, a high level of consistency is found between the predicted force constants and equilibrium well depths for the different 15N/14N isotopomers, as is expected within the BornOppenheimer approximation. Furthermore, this method is able to reproduce quantitatively the u = 1 vibrational red shifts for both the N2-HF and N2-DF complexes. By incorporating the rotational and centrifugal distortion constants listed in Table 2 for u = 2 of N r H F , it is possible to generatea similarone-dimensional radial potentialfor the complex excited to the first overtone stretching level of HF. It is worth emphasizing that these potential curves represent adiabatic averages over all other coordinates, i.e., the intramolecular H F and N2 stretches and intermolecular bends. Figure 3 shows the one-dimensional potential curves for the three lowest H F vibrational levels in N2-HF, obtained from fitting the inner and outer turning points of the potential to a Lennard-Jones 6-12 functional form. The deepening of the potential with increasing quanta of HF stretch is clearly evident from the figure and demonstrates that the changes in the intermolecular potential
between different H F vibrational levels of the complex are qualitatively reproduced. An assessment of the quantitative accuracy of these potential curves is available from a comparison of the predicted red shifts with thoseobservedexperimentally. Since our spectroscopicdata are most sensitive to the region near the potential minimum, fitting to any of severalfunctional forms is sufficient to reproduce the harmonic and low-order anharmonic behavior of the potential. The calculated red shifts are obtained by subtracting the value of DOfor the ground vibrational state from Do of and 2vl. For ~ 1 the , calculated red shift for I4NrHFis 40 f 2 cm-1, in excellent agreement with the experimentally observed value of 43 cm-I. Likewise, good agreement is achieved for 2vl, where the predicted red shift is 106 f 20 cm-I vs the observed 93 cm-I. The larger uncertaintyfor 2vl simplyreflectsthesmaller range ofSs observed and the correspondingly smaller precision of the higher-order centrifugal constants determined from the spectral fit. However, even though the error bars bracket the experimental value for 2v1, the calculated red shift for 3vl of 250 f 80 cm-I differs somewhat from the recently reported value of 153 cm-1.6' Once again, while the experimental trend of a near-linear red shift with UHF remains valid for higher vibrational excitation of the HF, the one-dimensional model appears to systematicallyoverpredictthe magnitude of the red shifts. It is worth restating, however, that the rotational-RKR method is most sensitive to the equilibrium region of the potential and that reproducing the red shifts also requires a reliable characterization of the long-range potential, where the 1-Dcollinear approximation eventually must break down. C. Vibrationalpredissociation. Thevibrational predissociation lifetime of N r H F following 2vl excitation is 2.0 f 0.3 ns, which is 11-fold faster than the 22 f 5 ns reported for The shorter lifetime for the u = 2 vs u = 1 level is in qualitative agreement with statistical theories, which predict a monotonic increase in thevibrationalpredissociationrate with increasing internal energy. Additionally, thisvalue agreesqualitatively with the ratio reported for vibrational relaxation of H F by N2 in cell experiments at 295 K,a in which Nz relaxes H F (UHF = 2) 6 times faster than HF(UHF = 1). Given the extensive averaging over energy and orientation implicit in the bimolecular relaxation rate constants, it is difficult to extract any quantitative comparison with the vibrational predissociation rates. However, the similarity in the vibrationaldependenceof the unimolecularand bimolecular rates suggests the importance of complex formation in the collisional process. In fact, the rate constants from these cell studies do show an inverse temperature dependencebelow 400 K, supporting the role of complex formation in the bimolecular relaxation event. It is interesting to speculate about the factors giving rise to the differences in the u = 1 vs u = 2 rates, since the predissociation dynamics in each case are governed by the same BornOppenheimerpotential surface. From previous studiesof weakly bound clusters, it is known that one of the factors that can accelerate the rate of vibrational predissociation is a nearresonance with product vibrational and rotational continuum states; i.e., the rate increases when there is little translational energy imparted into the recoiling fragments. As an example, vibrational predissociationfollowing ~1 excitation of N r D F (i.e., UDF = 1 0) occurs more than an order of magnitude faster than observed following v1 excitation of N T H F . ~ This ~ increase can be rationalized as arising from a near-resonant V V channel to form N2 (wt= 1) and DF (UDF = 0), which would serve to reduce dramatically the energy deposited as rotational and translational excitation of the products. Conversely, vibrational predissociation of N r H F via the same mechanism requires an additional -loo0 cm-I to be partitioned between rotational and translational energy of the fragments. Bohac and Miller69have recently characterized the final state distribution of the Nz and HFvibrational predissociation products
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IR Overtone Spectroscopy of NTHF
TABLE 5 Vibrational Relaxation Channels for Vibrational
hedissociation following Y = 1 and Y = 2 Excitation of Nz-HF' vibrational predissociation products excitation UHF Q4I E AE (cm-I) VI 0 0 12 374 0 1 7 54 2Vl 1 0 12 107 1 1 6 233 0 0 18 489 0 1 15 128 0 2 10 401 0 3 3 117 a UHF and m1refer to the final vibrational levels of the HF and N2 products, jz refers to the largest values of HF rotation that can be accessed energetically,and AE refers to the remaining energy that must be partitioned between N2 rotation and relative translational energy of the fragments. The values of HF jz and mIfor V I excitation are from ref 69 and representexperimentallyobserved quantities, while the values for 2vl are predictions based on a N r H F binding energy of DO= 390 cm-I. following V I excitation of Nz-HF. Their results indicate nearly equal probability of populating U N =~ 1 and U N = ~ 0 and population of the highest corresponding ~ H Flevel accessible in each N2 vibrational channel such as to minimize the relative translational energy of the products. Similar distributions have been observed by King and c o - ~ o r k e r following s~~ HF excitation of NO-HF, in which U N O = 1 and U N O = 0 are formed with equal probability. From analysis of the Doppler profiles of the NO, values for ~ H F in each NO vibrational channel were determined again to be the highest energetically available and minimize the translational center-of-mass energy of the product fragments. In the gas-phase collisional relaxation studies of HF (UHF = 1-3) by N2, the dominant relaxation channel proceeds via AVHF = -1.68 This is of course the pathway accessed for vibrational predissociation of N2-HF from u = 1, and if N2-HF excited to the u = 2 level follows this trend, similar quantum state distributions of the H F and Nz might be expected. The dissociation energy of N2-HF has recently been determined to be 390 f 20 ~m-l,~O and it is thus possible to determine whether a near-resonant product channel exists for 2vl vs V I which could accelerate the rate of predissociation. Table 5 shows the ~ H F values observed69for both U N =~ 1 and = 0 following vibrational predissociation from u = 1 of N2-HF and the remaining energy which must be partitioned as N2 rotational energy and relative translational energy of the fragments. Also listed in Table 5 are the maximum j values for HF (denoted j:rx) energetically allowed for u = 2 for the AUHF= -1 pathway. As anticipated above, the AE values are quite similar for the u = 1 and u = 2 initial states, suggesting that a simple energetic nonresonant Au = -1 channel cannot satisfactorily explain the 11-fold increased vibrational predissociation rate for u = 2. It is possible, however, that vibrational predissociation of the complex following excitation to u = 2 proceeds via the AUHF= -2 channel, and access to this pathway might contribute to the increased rate. In this scenariothere is sufficient energy available to populate up to U N ~= 3. Although such multiple-quantum changes in vibrational level are typically unfavorable in bimolecular relaxations, the highly oriented collinear geometry of the N2 and HF in the complex could potentially enhance such intermolecular V V transfer. Listed in Table 5 are the N2 vibrational and corresponding jzxlevels which could be populated if vibrational predissociation occurred via a AVHF = -2 pathway. The U H F = 0, U N = ~ 3 channel is of particular interest, since three quanta of N2 vibration act as a sink for 6904 cm-1, leaving only -370 cm-1 of energy to partition as rotational and translational energy of the products. With ~ H F= 3, only 117 cm-I would remain to be partitioned between N2 rotation and product translation. While this near resonance and the low
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The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6073 angular momentum of the diatom could explain the increased rate for u = 2 vibrational predissociation, the necessary fivequantum transfer of vibrational excitation would reflect a surprising, though intriguing, energy-transfer event. It is worth mentioning that this reasoning implicitly assumes that the availability of resonant V V channels accelerates predissociation, although the results of Bohac and show that predissociation of Nz-HF following V I excitation occurs as readily via the V V channel as the V R,T channel, even though the latter requires much more energy to be imparted as rotational and relative translational energy. Clearly, resolution of the HF and Nz rovibrational distributions following vibrational predissociation of the complex excited to overtone vibrational levels would be invaluable in determining whether large multiplequantum V V channels constitute significant dissociation pathways. The above treatment based on simple energetic grounds neglects the effects of H F excitation on the coupling between the intramolecular and intermolecular coordinates. This type of coupling is also responsible for the vibrational relaxation of molecules in solution, in which the coupling with bulk modes of the solvent determine the efficiency of vibrational relaxati0n.~~~~2 Consequently, a knowledge of how this coupling varies as a function of monomer excitation is necessary to reproduce the observed predissociation rates. The theoretical framework for understanding the influence of intermode coupling on the vibrational predissociation rate of weakly bound complexes has been established by Beswick and J ~ r t n e r and ~ ~ E, ~ i~n g . ~ ~ " ' Recently, Miller has proposed an empirical relationship discerned from a number of complexes studied in the near-IR. This model incorporates a Golden Rule treatment of the vibrational predissociation and a perturbative treatment of the coupling between intramolecular and intermolecular potentials and predicts that the vibrational predissociation rate should scale with the square of the red shift for different complexes containing the same chromophore. Comparison with experimental data for a series of HF-containing complexes excited to the U H F = 1 manifold shows reasonable agreement with the experimentally observed rates. Scoles and co-worker~4~ have recently extended this treatment to permit a comparison of vibrational predissociation rates for thesame complex in different vibrational levels. Within their stated assumptions, i.e., (i) the intermolecular wave functions are identical in the first overtone and fundamental levels of the monomer, (ii) the monomer wave functions are negligibly affected by complexation, and (iii) the intermode potential coupling function does not change with the monomer vibrational level, the ratio of predissociation rates between the fundamental and first overtone levels of the monomer for any complex is predicted to be k,=z/k,,l 2. While this is in qualitative agreement with their results for HCN-HF48 where the ratio is 1.8, the agreement is poor for the present Nz-HF results where kv=2/ku=l= 11 and for V I excitation of (HF)2 where ku=2/kU=l= It is evident from these overtone studies that the predissociation dynamics of these simple systems are sufficiently complex that even qualitatively accurate models for predicting vibrational predissociation trends are difficult to formulate and may depend on details of the potential energy surfaces that have proven hard to measure. However, with the increasing sensitivity of experimental methods, the spectroscopic data necessary to construct accurate potential energy surfaces for individual complexes are becoming available. Furthermore, concurrent advances in computational methodology are permitting the extraction of highly accurate potentials from spectroscopic data for increasingly larger systems, and the prospect of full quantum dynamical calculations on these potentials has improved dramatically. The sensitivity of the rotational-RKR inversion to the near-equilibrium region of the intermolecular potential suggests that these v-dependent potentials may prove useful in theoretical predissociation models
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6074 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994
for linear hydrogen-bondedcomplexes. Extension toother systems is quite feasible, and experimental results from isotope and overtone studies, as well as those that resolve the final product state distributions, will provide the necessary, rigorous tests of these theoretical models.
V. Summary The high-resolutionspectrumof the first overtone H F stretching level of N2-HF has been recorded using direct absorption of tunable infrared light. The band origin, at 7657.4057 cm-1, is red-shifted 93.39 cm-I from the U H F = 2 0 origin of free HF. This red shift is slightly more than twice that observed for V I excitation of N2-HF and can be rationalized in terms of electrostatic-based perturbations in the monomer vibrational potential induced by complex formation. The changes in the intermolecular/intramolecularcouplingwith monomer vibrational level manifested in the red shift are also evident in the rotational constants. The rotational and centrifugal distortion constants are used to generate a one-dimensional radial potential from rotational RKR inversion, as has been done for N r H F in the ground and first H F stretching level. These potentialsare capable of reproducing the vibrational red shifts of the complexes within experimental error. Analysis of the homogeneous broadening of the rovibrational line shapes allows a vibrational predissociation life-time of 2.0 f 0.3 ns to be determined, which is more than an order of magnitude faster than observed upon u = 1excitation. This magnitude of rate increase cannot be rationalized solely on the basis of a simple energetic resonance and most likely reflects greater dynamical coupling between the intermolecular and intramolecular coordinates for u = 2 vs u = 1. In addition, nearresonant, multiple-quantum V V channels not available for u = 1 may acceleratevibrational predissociationfrom u = 2. While theories developed to model vibrational predissociation trends cannot satisfactorily explain the observed rates, calculations on potentials constructed from spectroscopicdata such as the RKRbased potentials described above are promising candidates for more quantitative studies.
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Farrell et al. (16) Waterland, R. L.; Skene, J. M.; Lester, M. I. J . Chem. Phys. 1988, 89,7277. (17) Lipkin, N.; Moiseyev, N.; Leforestier, C. J. Chem. Phys. 1993,98, 1888. (18) Villarreal, P.; Miret-Art&, S.;Roncero, 0.; Delgado-Barrio, G.; Beswick, J. A.; Halbentadt, N.; Coalson, R. D. J . Chem. Phys. 1991,94, 4230. (19) Cohen, R. C.;Saykally,R. J. Annu. Rev. Phys. Chem. 1991,42,369. (20) Block, P. A.; Jucks, K. W.; Pedersen, L. G.; Miller, R. E. Chem. Phys. 1989,139, 15. (21) Nesbitt, D. J.; Lovejoy, C. M. J. Chem. Phys. 1990,93,7716. (22) Lovejoy, C. M.; Nesbitt, D. J. J. Chem. Phys. 1990,93,5387. (23) Lovejoy, C. M.; Nelson, D. D., Jr.; Nesbitt, D. J. J . Chem. Phys. 1988,89,7180. (24) Dayton, D. C.; Miller, R. E. Chem. Phys. Lett. 1988,143,181. (25) Jucks, K. W.; Miller, R. E. J. Chem. Phys. 1988,88.6059. (26) Pine, A. S.;Fraser, G. T. J . Chem. Phys. 1988. 89,6636. (27) Pine, A. S.;Lafferty, W. J.; Howard, B. J. J. Chem. Phys. 1984,81, 2939. (28) Schuder, M. D.; Lovejoy, C. M.; Lascola, R.; Nesbitt, D. J. J. Chem. Phvs. 1993.99,4346.
