J. Phys. Chem. 1994,98, 7313-7318
7313
Characterization of N2HF at 3v1 HF Stretch Susy N. Tsang, Huan-C. ChangJ and William Klemperer. Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 Receiued: February 1 , 1994; In Final Form: April 8, 1994’
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Vibrational excitation spectra of N2HF associated with the H F stretch of u1 = 3 are reported. Using the technique of intracavity laser-induced fluorescence, both the Z 2 second overtone band of pure HF stretch, (300OoO0) (OOOOoOo), and the II II hot band of N2 bend, (30OO0l1) (0000011), have been recorded. We determine a vibrational band origin of YO = 11 220.250 23(64) cm-l for the Z Z band and a rotational constant of B = 0.109 209( 13) cm-l for the state (u1u2u3uq’ug‘) = (300OoO0). For the combination state of the H F stretch with the N2 II bend (30OO0l1),the band origin relative to that of the state (0000011) is vo = 11229.489 cm-1 with B = 0.109 917(12) cm-l and 0.110 300(14) cm-l for the IIc and IIf components, respectively. Both the band origins and the rotational constants indicate that the N2-HF hydrogen bond is strengthened upon vibrational excitation of the H F stretch. We have also observed a line width broadening of 240(40) MHz due to vibrational predissociation at this second overtone state. The predissociation lifetime is 30-fold and 3-fold shorter than those at u1 = 1 and 2, respectively.
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possibility of viewing overtoneemission A q = -2 of the HF subunit in the detected signal. Preliminary studies of ArHF and HF The weakly bound van der Waals complex ArHF is among the dimer with u 1 = 3 0 excitation of the H F stretch with detection simplest of atom-diatom interactions that provide insight to the of the fluorescence using a liquid nitrogen cooled germanium anisotropy of the intermolecular potential of the hydrogen bond. detector have confirmed the Av1 = -2 overtone emission with Extensive experimental and theoretical studies of ArHF1-7have high signal-to-noise ratio, indicating that a considerable amount resulted in a nearly complete characterization of its threeof the dissociation product, HF, is in the v = 2 state. We assume dimensional potential energy surface.8 The natural extension of a similar behavior for the N2HF system and will examine this in this system is NzHF, which involves interactions between the the near future. relatively inert N2 diatom and the hydrogen-bonding HF dipole. Two stagnation compositions have been used here. We The studies of this complex should bridge our understanding of employed Ar expansion to observe the Z Z band, (300oooO) the interactions inherent in ArHF and HF dimer, another well(OOOOOOo), with H F and N2 concentrations of 2% and 1596, explored diatom-diatom s y ~ t e m . ~ J ~ respectively. To observe the ll ll hot band, (3000011) In this paper, we employ the state designation ( u ~ u ~ u J for u ~ ~ s ~(000001 ) l), we used pure N2 expansion to increase the “vibrational the seven vibrational modes of N2HF.11 The rotational spectrum temperature” of the jet. The HF concentration is also 2%, and of N2HFwas first studied by Soper, Legon, Read, and FlygareI2 the stagnation condition for both expansions is 800 Torr at 300 and was shown to have a linear equilibrium structure with zeroK. Two detection schemes, frequency modulation (FM) and point averaged bending angles of BN2 = 12O and eHF = 25O. With amplitude modulation (AM) with spectral resolutions of 10 and the availability of the quadrupole coupling constant for the free 180 MHz, respectively, were employed. The single frequency N2monomer,13ON2 is now calculated to be 17’. Infrared spectra FM allows precise frequency and line width measurements.7Jo of N2HF for u1 = 1 and 2 have been obtained.l1J4-I6 The work However, due to the limited possible modulation depth, 1180 we report extends these studies to the u = 3 level of HF. Second MHz, we used FM only to observe the strong and sharp features overtone spectroscopy of ArHF and (HF);! has been investigated of the Z Z band. The observation of the weak ll ll hot by laser-induced fluorescence that exploits the high intracavity band was accomplished by AM. In the FM detection of the pure power of a Ti-sapphire ring laser.7J0 The high detection sensitivity overtone band, the uncertainties in relative and absolute frequency of the intracavity laser-induced fluorescence technique allows measurements are f0.0006 and f 0.003 cm-1, respectively. In observations in N2HFof both the pure second OvertoneHFstretch, the AM mode of recording the hot band, weakness and congestion 3vl, and its combination mode with Nz bend, 3vl + US,through of the features limit the precision to f0.003 cm-1 in both absolute detection of the hot band (300001 l) (OOOOoll). However, our and relative frequency. attempts to observe the combination mode of HF bend failed probably because of the weakness of the transition (30010O0) Results and Analysis (0000000). The present work is preliminary to analyzing the fluorescent radiation. A. The (3000000) (OOOOW) Band. The spectrum of u1 = 3 0 pure H F stretch overtone of NzHF was recorded from Experiments 11 217 to 11 225 cm-1. Figure 1 shows the entire spectrum with a band center located near 11 220 cm-I. This spectrum was taken The intracavity laser-induced infrared fluorescence method in a single scan using Ti-sapphire intracavity power of 40 W, used to observe the second overtone transitions of the H F stretch laser scanning rate of 20 MHz/s, lock-in time constant of 1 s, in N2HF has been de~cribed.~JO The excitation of U I = 3 0 and FM. Transitions from R( 16) to P( 18) have been detected is detected as total fundamental emission (Aul = -1) collected with a peak transition at J” = 6 with a signal-to-noise ratio (S/ by a large element (10 X 10 “2) infrared PbS detector whose N) of 40/1. The rotational temperature of the NzHF was detection sensitivity peaks at 3 pm. There is, in addition, a determinedfromthelineintensitiestobe 17(2) K. Themodulation depth of the FM was limited to 60 MHz to avoid any possible f Present address: Institute of Atomic and Molecular Sciences, Academia instrumental distortion of the band profile. A modulation depth Sinica, Taipei, Taiwan, 10764, R.O.C. *Abstract published in Aduance ACS Abstracts, June 15, 1994. of 80 MHz has also been used, and the Voigt profile showed no
Introduction
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0022-3654/94/2098-73 13%04.50/0 0 1994 American Chemical Society
Tsang et al.
7314 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994
N,HF (300OoO0) t (OOOOoOo)
11224.8
11221.0
11217.2
FREQUENCY (cm-I) Figure 1. Second overtone spectrum of the (3000") (OOOOW) band ofN2HF. ThebandcenterofthisZ-Ztransitionislocatedat 11 220.250 cm-1. +
tl U
-1 800
1800
0
Av (MHz) Figure 2. Comparison of the frequency modulation signals to first derivative Voigt profiles: (a) R(8) at 11 340.969 cm-l of ArHF (3000) (oo00)is fitted with a pure Gaussian width of 200(20) MHz; (b) R(8) at 11 222.403 cm-l of NsHF (3000") (OOOOW) with a Doppler width of 220(20) MHz and a vibrational predissociationwidth of 240(40)
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MHz.
significant alterations. A 2-fold improvement of the S/N can be obtained by using a larger modulation depth since the depth of 6&80 MHz is not adequate for maximizing signals from features with 200-MHzline widths. In a separate experiment, we used AM and obtained a peak S/N of 1SO/ 1, allowing therovibrational lines up to J" = 30 to be recorded (see Figure 3 as an example). Figure 2 shows the first-derivative line shapes of R(8) of the ArHF (3000) (1OOO) transition7 at 11 340.969 cm-l and R(8) of NzHF (SOOOW) (OOOOOO0) at 11 222.403 cm-1. The widths of the components in the lines, Gaussian and Lorentzian, of the two complexes are significantly different due to differences in the rate of vibrational predissociation. The ratio of the intensity of the line for N2HF to that for the ArHF line is 15 to 1. This intensity ratio is approximately equal to the concentration ratio of the twocomplexes. TheN2 to Ar ratio is 1to 5. Thedissociation
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energies are DO= 102(1) and 390(20) cm-1 for ArHF17and N2HF,16J8respectively. If a species equilibrium could exist, the "chemical temperature" is 100K. It isunclear whether theconcept of chemical temperature has sufficient transferability in argondominated expansions to be of appreciable utility. Also shown in Figure 2 is the fit of a Voigt profile for the R(8) of ArHF with a pure Gaussian component of 200(20) MHz (fwhm). TheArHFtransitionsatut 1 tou = 3oftheHFstretch have previously been determined to contain negligible Lorentzian c ~ m p o n e n t . ~ InpreviousstudiesofArHF(3000)-(1000),7 .~~~J~ the Gaussian width determined in a pure Ar expansion was 130 MHz, considerably less than that in the present measurement. This differencecan be attributed to the N2,the enthalpy of which is inherently higher than that of Ar, as is reflected in the higher effectivetranslational temperature. The 200(20)-MHz line width for ArHF implies the Doppler line width of NzHF to be AVD= 220(20) MHz. Using this Doppler component, the averagevalue of the Lorentzian component of all the lines from R( 16) to P( 18) is determined to be 240(40) MHz. The large standard residual indicates slightly different line widths obtained as a function of J! We note that the irregularity in line width is consistent with a related and apparent anomaly of the intensity variations in the manifold of the R and P branches shown in Figure 1. Analysis of the line widths shows some correlation with the intensity variations. Although the correlation is not fully regular, it does indicate the existence of a perturbation in the (3000000) state. We are unable to find a sharp crossing. At the present, the origin of this slight perturbation is not clear to us since there is no apparent nearby Zor II state that would perturb this pure second overtone transition. Perhaps a possible candidate is the II state (21OS1OO). Pursuing this speculation further is clearly not profitable at this time. Assignment of the transitions in Figure 1 is accomplished by combination differences. The term values are readily fit to a standard polynomial expression in J ( J + 1) for a semirigid linear molecule:
In fitting the spectroscopic constants at the excited state, we constrained the term values for the ground state to those obtained by Lovejoy and Nesbitt.11 The ground- and excited-state term energies are listed in Table 1, and they are used to fit eq 1. The fit including the cubic term results in both the values of H(u) and D(u) being essentially undetermined. Hence, the value of H(3000000) is constrained in the final fit to obtain spectroscopic constants of vo(3000000) = 11 220.250 23(64) cm-1, B(3000000) = 0.109 209(13) cm-I, and D(3000000) = 3.98(44) X le7cm-1. Using thevalueofHdetermined at (1000000),11 thespectroscopic constantsobtained are essentiallyidentical to those obtainedwhen H is set equal to zero. The standard deviation of the fit is 0.0015 cm-I, considerably larger than our experimental uncertainty of a0.0006cm-1. We attribute this to a slight perturbation which is consistent with the observations of irregular line widths and intensitiesstated earlier. For the NzHF complex, the band origin Vo(300@@) is red-shifted by -152.557 cm-1 from that of the HF monomer at u = 3,20 the constant B(3000000) is increased by 2.596, and D(3000000) is reduced by 31% from their ground-state values. The vibrational dependences observed in the rotational and distortion constants require a small quadratic term to fit those observed at the H F stretch from ul = 0 to uI = 3 of N2HF, as shown in Table 3.11JZl6 B. The (3OOO@ll) (-11) Hot Band. We recorded the spectrum of the (3000011) (0000011) hot band from 11 226 to 11 230 cm-1. A portion of the spectrum taken in a single scan using Ti-sapphire intracavity power of 40 W, laser scanning rate of 10 MHz/s, lock-in time constant of 3 s, and AM detection is
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Characterization of N2HF at 3ul HF Stretch
The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7315
TABLE 1: Observed and Calculated Term Values (in cm-1) for the (3000aOO) HF Stretch and Its Ground State (OOOOW) of NJIF'
TABLE 2 Observed and Calculated Relative Term Values (in cm-l) for the (300001l)N2 Bend and Its Ground State ~ooOool1) of NJIF'
Ed4 -VO(OO~O~')~ ~ooooo0O)
J 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(3000000) 11 220.2535(32) 11 220.4698(10) 11 220.9056(1) 11 221.5596(-11) 11 222.4322(-20) 11 223.5249(-12) 11 224.8347(-16) 11 226.3658( 11) 11 228.1 106(-6) 11 230.0745(-12) 11 232.2586(3) 11 234.6593(5) 11 237.2793(22) 11 240.1135(4) 11 243.1664(-1) 11 246.4368(-6) 11 249.9250(-5) 11 253.6309( 1)
0.000000 0.213 170 0.63950 1.27895 2.13 150 3.1971 4.4756 5.9670 7.6713 9.5882 11.7176 14.0595 16.6137 19.3800 22.3582 25.5482 28.950 32.563
J 1 2 3 4 5
6 7 8
9 10 11 12 13 14 15 16 17
(00OOO1IC)E 0.107327 0.53662 1.18053 2.03899 3.1120 4.3993 5.9010 7.6169 9.5469 11.6909 14.0486 16.6199 19.4046 22.403 25.613 29.037 32.673
(OOO@1'1)c 0.107783 0.53890 1.18554 2.04766 3.1252 4.4180 5.9261 7.6493 9.5875 11.7406 14.1083 16.6906 19.4872 22.498 25.722 29.161 32.812
(3000011C) 11 229.493(2) 11 229.928(-2) 11 230.589(0) 11 231.470(1) 11 232.568( 1) 11 233.885(-1) 11 235.423(-1) 11 237.181(-1) 11 239.160(1) 11 241.355(0) 11 243.769(-1) 11 246.405(1) 11 249.256(-1) 11 252.328( 1) 11 255.617(0) 11 259.124(0) 11 262.851(0)
(3oooo11/) 11 229.491(-2) 11 229.933(-2) 11 230.597(1) 11 231.479(1) 11 232.582( 1) 11 233.904(0) 11 235.448(2) 11 237.213(2) 11 239.198(2) 11 241.400(1) 11 243.822(-2) 11 246.465(-2) 11 249.330(-1) 11 252.412(-1) 11 255.715(0) 11 259.237(1) 11 262.976(0)
Numbers in parentheses are deviations (observed minus calculated) of the frequency measurements, in units of the last significant digits. Uncertainty in both absolute and relative frequency measurements is f0.003 cm-I. VO(OOOOO~~) is the band origin of the U J II bend at the ground vibrational state of the H F stretch and is undetermined. Calculated from ref. 11. (I
The quantum numbers in parentheses are defined as (ulu~upJu+) following ref 11. All the observed energies are averages of at least two independent experiments with standard deviations of k0.003 cm-I in absolute frequency measurements and i0.0006 cm-I in relative frequency measurements. Numbers in parenthesesdenote residuals (observedminus calculated) in units of the last significant digits. Calculated from ref 11.
I
I
11229.7
11229.2
11228.7
11228.2
11227.7
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FREQUENCY(cm-')
Figure 3. Portion of the second overtone spectrum of the (300@11) (000001~)hot band of NzHF. The transitions labeled with solid squares are R(26)-R(30) of the (300oooO) (OOOoooO) fundamental band, with R(26), R(27), and R(28) blended respectively with P(7), P(5), and P(3) of the (300@11) (O0OOOl1) combination band. The weak Q branch centered at 11 229.4 cm-I is indicative of the nature of II II transition.
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displayed in Figure 3. It shows the rovibrational transitions of a Q branch and P(2) to P(8) of the (30OO0l1) (0000011) hot band and several high J value R branch features of the pure overtonestretch (3000000) (0000000)of N2HF. The weakness of the Q branch is characteristic of a parallel band, AK = 0 with
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K'= K"
# 0.21
The hot band is surprisingly intense since it can be observed without difficulty,with a peak intensity of 6%of the pure overtone stretch. Moving the laser beam closer to the nozzle (to =l mm) to probe the supersonic jet at a warmer region is required for observations of V I = 1 in a pulsed slit jet11 where the hot band is much weaker in intensity (less than 2% of the pure overtone band). However, we found that to increase the intensity of the observed hot band at V I = 3, a pure N2 expansion is sufficient, without the necessity of moving the laser beam. This significantly improves the signal, by d o % , with peak S/N approaching 10/ 1 with a lock-in time constant of 3 s. A rotational temperature of 15(2) K for the pure N2 expansion is observed for the rI ll transition, similar to the rotational temperatures of the Z Z band in 15% Nz.
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TABLE 3 Spectroscopic Constants (in cm-l) of NJIF at the HF Stretch from VI = 0 to VI = 3. 01 = o b UI = lb UI = 2e UI = 3 H F stretch (~1000000) VO(U1000o0O) 0.0000 3918.2434 A~o(~l00oooO) 0.0000 43.1795 B(u~oooo0O) 0. 10658552e 0.107178 ~(~~oooo00) x 107 5.74~ 5.28 Nz II bend (u~0OOOl1) Vo(~100OOl')O.OOO0 3920.9598 YO( 00Ooo11) Avo(~lOOOO1')d O.OOO0 2.7160 B( UI OOOO1IC) 0.107328 0.107903 B(u100001'f) 0.107784 0.108342 D(~100OOl~~) X lo7 6.6 6.3 ~ ( ~ ~ o o o oxi 1107 ~ )6.64 6.24 q(u1O0Ool1)X 10' 4.61 4.45
7657.4057 -93.3892 0.108022 4.8
11220.250 -152.557 0.1092 1 4.0 11229.489 9.239 0.10992 0.11030 5.9 5.3 3.8
a AVO is the shift of the frequency of the H F stretch in N2HF(ul000000) from thatoftheHF(u) monomer (refs 20and 35). Spectroscopicconstants are rounded off to the least significant digit. Reference 11. Reference 12. Shift of bending frequency from that at U I = 0. Reference 16.
LovejoyandNesbittlIestimatedthe(OOOOOll)state tobe85(20) cm-1. There has been no direct determination of it or related levels. We note that we were unsuccessful in observing the HF bending vibration which we expect to be more intense than the N2 bend. We therefore calculate only relative term energies E(J) - uo(OOOOol l) based on the rotational and centrifugal distortion constants of the e and f components of the ll bend reported at u1 = 1 by Lovejoy and Nesbitt." As those authors pointed out, labeling of the two components is tentative since unambiguous assignments at the ground vibrational states of the HF stretch have not yet been established. The term energies at V I = 3 listed in Table 2 are fit separately, to the standard polynomial expansion for both e and f ll components, E"(J) = u&)
+ B(u)[J(J + 1) - 11 - D(u)[J(J + 1) - 112 (2)
yielding u 0 ( 3 0 0 0 ~ 1 ~-~u)0 ( 0 0 0 0 ~ 1 ~=) 11 229.487 72(63) cm-I, B(3000°11C) = 0,109 917(12) cm-l, 0(3000°1~c)= 5.88(40) X lo-' cm-1 and ~o(300001Sf)- u0(000001~)= 11 229.490 61(75) cm-1, B(30000l19 = 0.110 300(14) cm-1, and D(30OWlSf) = 5.26(48) X 10-7 cm-I, respectively, for the two components. The
7316 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994
TABLE 4: Observed Vibrrtioepl Baed Origin Red Shifts (in cm-1) and predissoclrtion Wetimes (in GHz) of ArHF, N a F , and (HF)z as a Function of the Hydrogen-Bonded HF Stretchidg State AVO(VHP)
ArHF N2HF HFHFg
mF’1
mF’2
-9.6541’ -43.1795d -93.3435
-20.9118’ -93.389e
UHF=
3
-33.773e -152.557f -329.72
AVPd(WF)
N2HF 0.0072h 0.079# 0.24f HFHP 0.33 10 4 References 4 and 5. b Reference 6. Reference 7. d Reference 11. Reference 16. f This work. g Constants of the hydrogen-bonded HF stretch (ref 10 and references therein). Reference 15. band origins of the two independent fits are essentially identical, with a difference smaller than our experimental uncertainty of f0.003 cm-I in all the frequencies measured. The /-doubling is calculated to be qr( 3oooO1I ) =B( 3oooO1v) -B( 3oooO1*e) = 3.8( 2) X 10-4 cm-I, compared to the values of 4.45(7) X lO-, cm-I at u1 = 1 and 4.61(8) X 10-4 cm-1 at u1 = 0.” The large uncertainty in qr at u1= 3 is fromseveral contributions. First, the splitting, Avr = q,[J’(J’+ 1) - 11-qr[J”(J”+ 1) - I], due to the difference in qr at u1 = 0 and u1 = 3 is less than 0.01 cm-I (or 300 MHz) for the rovibrational lines of J” I 10. Compared even to the N2HF Doppler width of 220(20) MHz, this splitting is too small to be resolved for more than half of the lines observed. The splittings can be detected only in high J value lines of the P branch, but not in the R branch. Second, the experiment was performed with AM, which results in an effective laser line width of 200 MHz and thus further diminishes some observations of the splittings. Finally, the intrinsic vibrational predissociation broadening of the ll bend at the second overtone state of the HF stretch could be comparable to the splitting. The weakness and breadth of the features prevent the use of a FM scheme for precise measurements of the lifetime broadenings. However, by carefully comparing the P branch features of the II band with that of the R branch of the pure I:overtone stretch, we donot observe any appreciabledifferencesin line width between these two bands (see Figure 3). We therefore estimate that the broadening in the vibrational predissociation of this ll bend at uI = 3 of the HF stretch is also about 240 MHz. We hope that future stabilization of our system using AM will allow a direct comparison of the predissociation line widths for the I: and II bands. Discussion A. Vibrational Red Shifts. As stated, N2HF is a model system for the studies of diatomdiatom hydrogen bond interactions. The redshiftsin thevibrational bandorigins which increasenearly linearly with u1 are evidence of the change in the interaction potential as a function of the vibrational excitation. The red shift indicates a larger binding energy in the excited state as in the ArHF system.’ A comparison of the red shifts of the two complexes at UHF = 1-3 is shown in Table 4. The refatiue red shifts in the vibrational band origins between these two complexes are remarkably similar, a trend also noted recently by Nesbitt and co-workers.16 The red shifts listed in Table 4 for both the N2HF and ArHF complexes have componentsthat approximately increase quadratically as
where A depends on the complex of interest. Also listed in Table 4 are the band origin shifts of the hydrogen-bonded H F in (HF)2. Although the results are incomplete for (HF)2 in Table 4, they do show some similarities in the magnitude of the relative red
Tsang et al. shifts a t the fundamental and the second overtone states to those of ArHF and N2HF. A simple first-order perturbation theory model can explain the quadratic increase in the red shifts. We use a general treatment and assume that the potential energy of the complex is given as V = V(r,,R,) where rf is the internal valence coordinates of the subunits and Rj is the soft intermolecular coordinates of the complex which include for a binary complex the centers of mass separation &M between the two subunits and orientation angles of the subunits. The potential of the complex is
where &V(r,,R==) is the general form of the anharmonic potentialsof the free HFmonomer and its partner. The interaction potential Z&V’(r,,R,) can be expanded as a power series in terms of the displacementsof the set of internal valence coordinates (r, - rd) as
Similar arguments for the functional form of the interaction potential have been givensz2 The change in the valence mode vibrational energy, AE(u), or, equivalently, the frequency shift of the band origin for the valence bond coordinate rf is perturbatively treated as
to the lowest order where vibrational averaging of the soft modes is not explicitly shown. Since for any realistic valence vibration (v((r, - r.&) = a(u + l/2) b(u + 1/2)2 and (vl(r, - rd)2b) = A(u + l/2) + B (u + 1/2)2to lowest approximations,the equation for AE(u) simplifies to
+
AE(v) = ‘d
for the first-order approximation. If a >> b and A >> B, a linear shift is expected. However, a quadratic term in the frequency shift of the band origin will arise from a variety of physical effects. The form of eq 7 is adequate to model the quadratic increase in red shifts observed in the ArHF and N2HF complexes at UHF = 1 to UHF = 3. The magnitude of the red shift for each complex is largely reflected in [aV’(r,,R,)/a&,, whose sign depends on the nature of the interaction and the specific valence coordinate considered. For all HF complexes studied to date, this term for the HF stretch valence coordinate is negative. This model
Characterization of N2HF at 3vl HF Stretch
The Journal of Physical Chemistry, Vol. 98, No. 30, 1994 7317
essentially reduces to the linear interaction potential model of Liu and Dykstra;23 however, (vl(ri - r&) has a nonnegligible quadratic dependence with increasing u due to anharmonicity of the potential of the HF monomer. We note that, for hydrogen-bonded binary complexes with linear equilibriumgeometries, the values of the absolute red shifts are much greater than their experimentally observed vibrationally averaged values. Liu and Dykstra's theoretical red shifts for several complexes in the linear configuration are smaller than the experimentally determined values.23.24 The red shifts predicted for the fundamental transition of the H F stretch in ArHF24and N2HF23 at their linear equilibrium geometries are -9.4 and -34 cm-1, respectively, vs the vibrationally averaged experimental values of -9.654143 and -43.1795 cm-1.11 The Liu and Dykstra theory of vibrational transition frequency shifts in hydrogenbonded complexes23J4 does not treat vibrational averaging or dispersion interactions. These effects may not be negligible and result in significant undervaluation of the red shifts at the linear equilibrium structures. From isotopic studies of N Q H F / D F , ~ ~ the zero-point bending motion affects the value of DO,which is larger for the latter isotopomer as a result of reduced vibrational averaging. Wecanextrapolate theredshiftsof theHFstretchasafunction of UHF for ArHF at the linear equilibrium structure in the absence of zero-point motion by using the band origins of the II ( ~ ~ ~ 1 1 0 or Z ( ~ ~ ~ 1bend 0 0 )of ArHF. The band origins for the II bends (0110)and(l1lO),respectively65.712 204~and4022.1062cm-1,s imply a red shift of -5.029 cm-I from that of the HF monomer at u = 1.35 The smaller red shift in the II (1 110) bend of ArHF compared to that of the pure fundamental HF stretch (1000) is due to the simultaneous one quantum excitation of the H F bend. The effect of zero-point vibration of the H F subunit in ArHF is removed by linear extrapolation to give a red shift of -14.3 cm-l for the experimental linear arrangement compared to the theoretical value of -9.4 cm-I.z4 The ratio of -9.65 to-14.3 cm-1 is between Pl(cos e) and P2 for the ArHF complex.2 Similar analysis and extrapolation at UHF = 3 by comparing the red shifts of the HF stretch in (3000) and in the (31 10) II bend of ArHF7 yield a red shift of -5 1.4 cm-I at the linear equilibrium structure. Using the above P1 projection,2 this gives a vibrationallyaveraged red shift of -34 cm-I and compares favorably with the experimentally determined value of -33.773 ~ m - 1 . ~ Unfortunately, complete data for extrapolation of the red shift to the linear configuration are not available for the NzHFsystem. From the change in red shift of the HF stretch (or, equivalently, the blue shift of the N2 bending frequency) observed in the II II hot band of -2.7 cm-1 at U I = 111 and -9.2 cm-1 at u1 = 3, we may readily correct for the effect of NZzero-point bending. For the effect of H F bending, we anticipate a reduction of the red shift to lie somewhere between PIand Pz of the zero-point averaged bending angle of HF. Thus, we estimate that the experimental value of the red shift at UHF = 1 of linear NzHF is -43.2 + -2.7 -10 =-56 cm-1. Thisvalue is much larger than the theoretical estimate of -34 cm-1. Unfortunately, the approximate correction for H F bending of -10 cm-l is uncertain. We hope that the steady increase in experimental sensitivity will soon permit observationof the (3001000) ( O O O W ) transition, theHF bend. While the prediction of the equilibrium geometry red shift for NzHF is not exact, the arguments presented here stress that the purely electrostatic theoretical values for the red shifts are largely underestimated at the linear equilibrium of the complexes. We finally note that for ArHF the variation of intermolecular interaction energy as a function of HF distance has been calculated.27 It is found that for the distances of u = 0-3 there is negligible variation of the interaction energy at the SCF level; virtually the entire distance variation is found at MP4 in the
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+
-
correlation energy. Since this corresponds to the dispersion energy, it is likely that this is relevant to the red shift observed in NzHF. B. Nz BendingAngle and Frequency Blueshift. The tightening of the hydrogen bond between the N2 and the HF subunits is seen not only in the pure H F stretch, nu1, but also in the combination mode of nv1 + v5. Shown in Table 3 are the blue shifts of the bending frequency of the Nz subunit at various vibrational states of the HF stretch. In spite of the lack of data at the first overtone region, the change in bending frequency apparently increases quadratically in frequency from 2.7 cm-1 at u1 = 1'1 to 9.2 cm-1 at u 1 = 3. This blue shift is a natural consequenceof the hydrogen bond tightening sincethe bending forceconstant increasesbetween the two subunits and is in perfect accord with the observations for ArHF.7 The observed blue shifts are also consistent with the decrease of the I-doubling constants, qis, listed in Table 3. An approximation of the complex as a linear triatomic shows that Wb scales inversely to the Idoubling parameter.28 The reduction of the I-doubling parameter for the II II band suggests an increase in the N2 bending frequency. The kinds of structural alteration in the NzHF complex also can be inferred from the changes in the molecular constants. As shown in Table 3, the changes in spectroscopic constants upon vibrational excitation of u1 = 3 in both the Z 2 and II II bands follow a pattern seen in earlier studies of the system at uI )= 1 and 2.11J23 In the Z Z band, the rotational constant as a function of the vibrational states of the u1 HF stretch increases nearly linearly. The same behavior has been exhibited in the Z Z band involving only the pure HF stretch in ArHF at UHF = 0 to U H F = 3.&l As has been suggested earlier concerning the ArHF complex: increase in the rotational constant can be due to both a smaller amplitude in the bending motion of the HF unit and a contraction in distance between the centers of mass of the two subunits, as a result of an increase in hydrogen bond strength upon vibrational excitation of the HF stretch. Similar changes in the molecular constants are also observed in the ll II hot band due to variation in the anisotropy of the NzHF potential. Uponexcitationofthe HFstretch, therotationalconstant increases linearly and the centrifugal distortion constant decreases also nearly linearly as a function of VI. This is clearly due to the same influences as that cited for the 2- I:band, which are the decrease in hydrogen bond length and greater alignment of the two monomer subunits to the intermolecularaxis. These effects result in a larger bending force constant and hence a higher bending frequency evidenced in the blue shifts. C. Vibrational Predimchtion. In spiteof the many similarities between ArHF and NzHF, the two complexes are vastly different in binding energy as well as in vibrational predissociation. At u1 = 1, the predissociation lifetime of NzHF is 22 ns," in sharp contrast with 20.6 ms of ArHF.19 This contrast has been readily explained by the momentum gap model proposed for the vibrational predissociation of hydrogen-bonded complexes.29-33 In NzHF, an additional dissociation channel can be opened by the vibration and rotation of the N2 fragment,
-
-
-
-
-
-
N~HF(uI,u~=O) HF(uI-l,J,) +
+ N ~ ( u ~ = O ,+J ~M) I
(8)
where J. and J b are the rotational quantum numbers of the HF and Nz fragments, respectively. The opening of both channels, with nearly equal probability, has been demonstrated recently by Bohac and Miller'* in the studies of the spatial angular distributions of the dissociating products at u1 = 1. Their results determinethe interestingcompetitionof rotational and vibrational energy transfer in the second channel, which is favored by the smallness of the rotational quantum number change but is limited by the weakness of the vibrational mode coupling of the N2 molecule. At the overtone HF stretch of u1 = 3, it is expected
7318 The Journal of Physical Chemistry, Vol. 98, No. 30, 1994
that there are more channels opened in the vibration of the N2 fragment, up to Au2 = 4. Since we haveobserved the fundamental emission (Au = -1) of the HF stretch and, as has been pointed by Farrell et ~1.16that multiple quantum transition is highly improbable, it is most likely that the channels depicted in eq 8 and 9 also dominate at the overtone states. We have previously noted that the production of H F at u = 2 is large in both (HF)2 and ArHF when u = 3 in H F is excited. The ratio of the distribution of the rotational fragments of the II II hot band transition in the two fragment channels should be interesting as the extent of the coupling between the intramolecular and intermolecular coordinates of the complex has been reduced by the excitation of the N2 bend. The effects should be present in the line widths of the hot band, but the presently large 200-MHz laser line width from the AM prevents sufficientlyaccurate measurementof the changesin the line width of the II II hot band excitation compared to that of the Z Z second overtone band of the pure H F stretch excitation. We hope in the future that less than 100%amplitude modulation of the argon ion pump laser will allow single mode operation of the Ti-sapphire laser. This will allow determination of small changes in the lifetime. It is possible that the first channel might be favored in the bend excitation because V-V coupling would be less effective. A comparison of the vibrational predissociation rates can be made between N2HF and the hydrogen-bonded H F stretch in (HF)2. Although there is insufficient data for the hydrogenbonded HF stretch, it remains a better comparison than using the results of the free-HF stretch since the two stretches have dramatically different characteristics in many respects.10 If we compare the predissociation rate at UHF = 3 to that at UHF = 1 shown in Table 4, the ratio of Avpd(u~~=3)/Avpd(w~=I) 30 is found for both complexes. The similarity suggests that the predissociation line width of the bound-HF stretch at UHF = 2 is approximately 3 GHz, a factor of 10 enhancement from the fundamental to the first overtone. We note that the identity in the ratio b v , , , 1 ( ~ ~ ~ = 3 ) / A u p d1)( ~may ~ = not be coincidental, considering the large differences in the rotational constants and transition dipole moments between the N2 and H F bases. Thus, it seems that from UHF = 1to UHF = 3 the increase in the vibrational predissociation rate in the bound-HF stretch is greatly above linear and somewhat below geometric. These trends contrast predictions of the vibrational predissociation rate from an elementary first-order perturbation theory based on a linear interaction potential and the Fermi golden rule where an arithmetic increase as a function of IF is expected.32J4 A much more complex model involving detailed examination of the curve crossing or, better yet, the multidimensional intersections of the potential energy surfaces arising from different vibrational states of the HF subunit in NzHF may be needed to explain the larger than expected vibrational predissociation rate as a function of UHF. Curve crossing and its influence on the vibrational predissociation rates have been discussed by EwingP2 and the model may be applicable to N2HF. The measurement of dispersed fluorescence and its polarization should be quite helpful in providing a more detailed data set for the higher vibrational levels as has the angular distributionI8 for U I = 1.
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Tsang et al.
Conclmion The present observations, in conjunction with the previous measurements, provide an extensive data base that allows for a detailed investigation, both experimentally and theoretically, of thenatureofvibrationalenergytransfer procasesin weaklybound molecular complexes. Future investigation of the NlHFcomplex involving the H F bend excitation, dispersed fluorescence, and amustooptic modulation will answer some fundamental questions of dynamics.
Acknowledgment. The research is supported by the National Science Foundation. We thank John Farrell Jr. and DavidNesbitt for making their results available to us prior publication. We also thank Dr. Reza Mollaaghababa for helpful discussions throughout this work. References a d Notes (1) Hutson, J. M.J. Chem. Phys. 1992, 96,6752. (2) Dixon,T. A.; Joyner, C. H.; Baimhi, F. A,; Klemperer,W. J . Chem. Phys. 1981, 74, 6539. (3) Lovejoy, C. M.; Schuder, M.D.; Nesbitt, D. J. Chem. Phys. Lerr. 1986, 127,374. (4) Lovejoy, C. M.; Schuder, M. D.; Nesbitt, D. J. J. Chem. Phys. 1986, 85,4890. ( 5 ) Lovejoy, C. M.;Ntsbitt, D. J. J . Chem. Phys. 1989, 91, 2790. (6) Farrcll, Jr., J. T.; Sneh, 0.;McIlroy, A.; Knight, A. E. W.; Nesbitt, D. J. J . Chem. Phys. 1992,97,7967. (7) Chang, H.-C.; Klcmperer, W. J. Chem. Phys. 1993, 98, 2497. (8) Chang,H.-C.;Tao,F.-M.;Klemperer, W.;Healey,C.;Hutson, J. M. J. Chem. Phys. 1993,99,9337. (9) Truhlar, D. G. In Dynamicsof Polyatomic Vander WaalsComplexes; Halberstadt, N., Janda, K. C., Eds.; Plenum Press: New York, 1990. (10) Chang, H A ; Klemperer, W. J. Chem. Phys. 1993,98,9266. (11) Lovejoy, C. M.;Nesbitt, D. J. J. Chem. Phys. 1987,86, 3151. (12) Soper, P. D.; Legon, A. C.; Read, W. G.; Flygare, W. H. J. Chem. Phys. 1982, 76, 292. (13) JHger, W.; Gerry, M.C. L. Chem. Phys. Lett. 1992, 196, 274. (14) Kolenbrander, K. D.; Liey, J. M.J. Chem. Phys. 1986,85, 2463. (15) Jucks, K. W.; Huang, Z. S.;Miller, R. E. J. Chem. Phys. 1987,86, 1098. (16) Farrell, Jr., J. T.; Sneh, 0.;Nesbitt, D. J., submitted to J. Phys.
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