Vibrational relaxation dynamics of I35Cl(B, v′) induced by low-temperature collisions with He atoms

Using laser-induced fluorescence and two-laser, pump–probe spectroscopy, collision-induced vibrational relaxation is observed to compete with the dissociation of electronically excited ICl in a helium carrier gas expansion.

By thoroughly characterizing the expansion properties, we observe that collisions of ICl(B, v′ = 3) molecules with He atoms in the expansion induce vibrational relaxation of the initially prepared dihalogen down to rotor states in the next lower ICl(B,v′ = 2) level on timescales that compete with the rate for non-adiabatic transfer from the B state to the Z1 state.

The resulting ICl(B,v′ = 2,j′) product rotational distribution, along with the analogous ICl(B,v′ = 1,j′) distribution formed by collisional relaxation of molecules in the long-lived ICl(B,v′ = 2) level are compared to ICl(B,v′ = 2,j′) products formed by vibrational predissociation of He⋯ICl complexes prepared in different intermolecular vibrational levels within the He + ICl(B,v′ = 3) potential.

No evidence is observed for resonance-enhanced collisional cross sections, even at the low temperatures achieved, T < 1.0 K.


A fundamental goal of reaction dynamicists is to develop an understanding of a bimolecular encounter on the state-to-state level.

While this is particularly true for reactive systems, insights into the dynamics and mechanisms guiding energy transfer in non-reactive partners are also desirable.

With this goal in mind, groups have undertaken investigations into the collision dynamics of several systems, some of which include rare-gas atoms with halogen molecules, especially helium atoms with molecular iodine, I2.1–12

These rare gas–dihalogen systems have the advantage of being both experimentally and theoretically feasible.13,14

Experimentally, the dynamics are simplified within a supersonic expansion in which low temperatures, and consequently small initial-state distributions, are easily attainable.

Also, the halogens have a low-lying electronic state, the B3Π0+ state, with multiple vibrational levels that can be easily accessed.

The He + I2 system has received extra attention in these studies because of the significant absorption cross section of I2 in the visible wavelength region, and because it was noted near the advent of supersonic beam methods that there is a large cross section for collisions of He atoms to induce vibrational relaxation of I2(B,v′).6

Since then, a debate has ensued over the role that orbiting resonances, or weakly-bound collision complexes, have in the collisional relaxation of I2(B,v′).

An initial report suggested that orbiting resonances were the primary contributor to the large vibrational relaxation cross sections observed.7

Subsequent papers have suggested, however, that resonances need not be invoked to explain the large cross sections.8–10,12

These papers do acknowledge, however, that even though resonances are not required to explain the results, they could still be contributing to the observed behavior.

Because of this, the debate is still considered by some to be open.

A special subset of the experiments examining the collisional-relaxation dynamics of halogen molecules with rare gas atoms involves dissociation of rare gas–dihalogen van der Waals complexes, Rg⋯XY.

The dissociation of these complexes is often thought of as a half-collision event because it mimics the second half of a collision that occurs at a specified intermolecular geometry.

However, while numerous papers have been published on the dissociation dynamics of Rg⋯XY van der Waals complexes both by experimentalists and theoreticians,14,15 surprisingly little effort has been spent connecting the half-collision and full-collision regimes.

Presumably, this is because until recently the dynamics of Rg⋯XY complexes were only observed from one geometry, that of the T-shaped intermolecular orientation.13,14

Recent work by our group, however, has shown that different conformers of Rg⋯XY complexes can be stabilized within a supersonic expansion.16–19

Furthermore, these conformers have different Franck–Condon windows, enabling access to different excited-state intermolecular vibrational levels.18

A recent publication on He⋯ICl has shown that excitation to these different intermolecular vibrational levels gives rise to different vibrational predissociation dynamics due in large part to the region of the intermolecular potential that is populated.20

The experiments that are described in this manuscript were undertaken to identify the relaxation dynamics induced by collisions of a He carrier gas with ICl excited in the BX spectral region within a supersonic expansion.

The larger rotor constant of ICl in comparison to that of I2 permits rotational populations to be accurately determined.

A combination of laser-induced fluorescence (LIF) and two-color, pump–probe experiments are performed in conjunction with a systematic interrogation of the spectra recorded using different expansion conditions to shed light on these energy transfer processes.

The full-collision data can be analyzed to determine whether evidence exists for resonance-enhanced cross sections for collisions of ICl with He at low temperatures.

Also, the dynamics of the full-collision events are conveniently compared to those of the half-collision dynamics that were recently reported for vibrational predissociation of He⋯ICl van der Waals complexes from varying energy regions within the He + ICl(B,v′ = 3) intermolecular potential energy surface (PES)20.


These experiments were performed in a similar manner as reported previously.16–18,21

The ICl was seeded in a carrier gas by passing the gas over a vessel of solid ICl maintained at 274 K. A pure helium carrier gas was used unless otherwise noted.

The ICl/carrier gas mixture was pulsed through an orifice with a diameter, d, of 890(30) μm at 10 Hz into a vacuum chamber maintained at pressures <2.7 × 10−5 bar during an experiment using a roots blower mechanical pumping system.

The pulsed valve and the supply lines, except for the sample reservoir, were kept at room temperature, ca. 294 K. The collision frequencies and densities in the expansion region were varied by utilizing different carrier-gas backing pressures within the range of 3.8 to 28.6 bar.

Regions with different local temperatures within the expansion, as well as varying densities and collision frequencies, were sampled by adjusting the downstream distance at which the laser axis intersected the supersonic expansion; most of these experiments were performed at downstream distances, x, ranging from 5.0 to 25.0 mm, or xd−1 = 5.6 to 28.1.

A commercial dye laser, pumped by the 532 nm output of a 10 Hz, Nd:YAG laser, was used in LIF spectroscopy experiments.

The laser pulse energies for most of the scans performed in the ICl BX, 2–0 and 3–0 region (560 to 567 nm) were ca. 20 mJ after the beam was spatially filtered to a diameter of 3 mm.

The frequency resolution of the dye laser was measured to be 0.06–0.07 cm−1.

Fluorescence was detected by imaging the interaction region of the laser with the expansion onto a photomultiplier tube (PMT) via a mirror and telescope assembly.

The fluorescence was filtered spatially using a 16.5 mm × 2.8 mm mask, with the long axis positioned parallel to the expansion, so that only fluorescence from the center, coldest region of the expansion was detected by the PMT.

The current signal from the PMT was amplified, integrated and averaged with a boxcar-gated integrator, and recorded as a function of laser wavelength.

The rotational contour of the I35Cl BX, 2–0 LIF band was fit using known spectroscopic constants22,23 in order to determine the Boltzmann rotational temperature representative of the I35Cl(X,v″ = 0) ground state level, Trot, in each set of experiments.

This is critical since Trot is dependent on the precise expansion conditions utilized, specifically the downstream distance that the laser crosses the expansion17 and, to a lesser extent, the backing pressure of the carrier gas.

In addition, the mechanical opening of the solenoid pulsed valve varied slightly on a day-to-day basis and, as a result, the pulsed valve widths and the temporal delay between the opening of pulsed valve and the firing of the laser were optimized for each set of experiments.

Slight deviations in the I35Cl(X,v″ = 0) rotational temperatures were found with these timing changes even when all other conditions were kept constant.

For two-color, pump–probe experiments, the laser system described above was used as the pump laser, and a second commercial Nd:YAG (355 nm) pumped dye laser was used as the probe laser.

The bandwidth was 0.06 cm−1, and neutral density filters were used to lower the laser pulse energies so that saturation effects were minimized; we found that pulse energies as low as 30 μJ were needed to avoid saturating individual rotational lines in the strong ICl EB, vv′ product spectra.

A dichroic mirror was used to co-propagate the pump and probe laser beams through the expansion region.

The temporal delay between the pump and probe lasers was typically 15 to 20 ns with a pulse-to-pulse timing jitter of ±1 ns.

A UG-1 filter was used to block laser scatter from both the pump and probe lasers and to minimize the detection of intense ICl BX emission induced by the pump laser.

Results and discussion

Laser-induced fluorescence spectra of ICl in He

High-resolution LIF spectra of ICl entrained in a He supersonic expansion were recorded in the ICl BX, 2–0 and 3–0 spectral regions, Fig. 1a and b, respectively.

These spectra were recorded using a He-backing pressure of 14.8 bar, at xd−1 = 11.9, and with the same laser pulse energies and PMT settings so that the relative intensities of the spectral features observed in both spectra can be compared.

The spectrum recorded in the ICl BX, 2–0 region was reported previously in Fig. 1 of ref. 20 but is plotted again in Fig. 1a for clarity of the discussion in these studies.

This spectrum is dominated by the I37Cl and I35Cl monomer bands near 17 659 and 17 664 cm−1, respectively.

To higher energy than the monomer bands are spectroscopic features attributed to transitions of He⋯I35,37Cl complexes with T-shaped and linear equilibrium orientations in the ground state to different intermolecular vibrational levels in the excited state.16,18,24

The intensities of the He⋯ICl features are ca. 100 times weaker than the ICl monomer bands.

(Note the ×100 magnification of the fluorescence intensity scale for transition energies >17 665 cm−1).

The LIF spectrum recorded in the ICl BX, 3–0 region, Fig. 1b, was also published previously, Fig. 2 of ref. 25, and is dominated by features attributed to transitions of the T-shaped and linear He⋯I35,37Cl(X,v″ = 0) complexes.16,18,24

The weak features near 17 821 and 17 828 cm−1 correspond to transitions of the I37,35Cl(X,v″ = 0) monomers to the short-lived I37,35Cl(B,v′ = 3,j′) rotational states.26,27

Based upon previous experimental investigations, the low ICl(B,v′ = 3,j′) rotor states accessed in these transitions have lifetimes on the order of 0.5 ns due to the presence of a nearby repulsive curve, the Z 1 state.27–30

However, because our integration gate is delayed 150 ns after the laser, I35,37Cl BX, 3 → v″ fluorescence is not detected.

Previously reported pump–probe experiments indicate that the I35,37Cl BX, 3–0 LIF features are observed as a result of a mechanism that populates rotational states of the long-lived I35,37Cl(B,v′ = 2) vibrational level following the preparation of rotor states in the short-lived I35,37Cl(B,v′ = 3) level.25

The rotational structure within the I35,37Cl BX, 3–0 LIF features is accurately simulated using published ground and excited-state rotational constants and term values.22,23

These features, therefore, cannot be attributed to transitions originating from bound He⋯I35,37Cl(X,v″ = 0) intermolecular vibrational levels or from weakly interacting He + I35,37Cl(X,v″ = 0) collision complexes that would have different rotational contours than those observed.

In order to best characterize the dynamics and mechanism of the collision processes occurring in the expansion, special attention was focused on characterizing the local environment within the supersonic expansion and on tracking the experimental observables as a function of the expansion conditions.

These measurements are used to estimate the physical parameters associated with the collisions of He atoms with ICl(B,v′ = 3,j′) molecules that compete with the non-adiabatic dissociation dynamics of the excited-state molecules.

Finally, a comparison of the full-collision measurements with half-collision dynamics of He⋯ICl(B,v′ = 3) complexes will be made.

Characterization of the supersonic expansion

Local temperature within the expansion

Extensive experimental and theoretical investigations have been undertaken to characterize the properties of atoms and molecules within isentropic supersonic expansions.31–35

The thermodynamics for a perfect gas require the temperature T, pressure P, and density ρ, within the expansion region to be related byT/T0 = (P/P0)(γ−1)/γ = (ρ/ρ0)γ−1,where T0, P0, and ρ0 represent the temperature, pressure, and density of the reservoir gas behind the nozzle, and γ is the heat capacity ratio, Cp/Cv, or 5/3 for a monatomic gas.36

These quantities can be related to the Mach number, M, and consequently the distance downstream in nozzle diameters, xd−1, byT/T0 = [1 + M2 (γ – 1)/2]−1, where M = A (xd−1) γ−1,where A is a constant, 3.26 for a monatomic gas expansion.36

Eqn (2) is only valid for the region within an expansion where the two-body collision frequency is sufficient for continued cooling.

Previous experiments performed in our laboratory20 indicate that collisions of He atoms with ICl(X,v″ = 0) molecules and He⋯ICl(X,v″ = 0) complexes occur at downstream distances of at least xd−1 = 69, and thus eqns (1) and (2) would be expected to hold for regions in the expansion up to this distance.

The local temperatures associated with each xd−1 at which LIF spectra were recorded are calculated using eqn (2).

These temperatures, Tcalc, are shown in Fig. 2 as open squares, as are the I35Cl(X,v″ = 0) Boltzmann rotational temperatures Trot, that were experimentally determined by fitting the rotational contour of the I35Cl BX, 2–0 LIF band, black squares.

There is poor agreement between the values of Tcalc and Trot, especially at low xd−1, as Tcalc is more than a factor of two greater than Trot up to xd−1 = 14.0.

A fit of the experimental data indicates that the functional form of eqn (2) is appropriate only with a larger value for the constant A, 5.28(5), black line in Fig. 2.

Similar behavior has been reported for a He/I2 expansion using a slit nozzle.3

As noted previously,33 the reason for the discrepancy may be that for He expansions the terminal Mach number reached is much larger than that predicted using classical equations.

The intermolecular translational energy that arises from the different terminal velocities of the seeded molecules and the carrier-gas atoms in an expansion gives rise to another temperature value, Tslip, that is not necessarily represented by either Tcalc or Trot.8,31,37–40

The difference in the velocities along the expansion direction results from the different masses of the species and is referred to as a velocity slip, with the heavier species travelling more slowly than the lighter species.

The ICl molecules in a He expansion are thus predicted to be travelling slower than the lighter He atoms, and collisions between the two species will occur with a temperature of Tslip.

Furthermore, each species in the expansion will have a different velocity distribution, which can be characterized by a translational temperature, Ttrans.

The distribution of the lighter species is broader than that of the heavier species, which will also contribute to the slip between the light and heavy species in the expansion.

In order to estimate a value for the velocity slip between the ICl molecules and the He atoms in the expansion as well as the velocity distribution of the ICl molecules, we have directly measured the time-of-flight of excited-state ICl* molecules that is needed to travel a fixed distance along the expansion using a pump–probe experimental scheme.

The pump laser was fixed at the wavelength of the I35Cl BX, 2–0 bandhead, at 17 664 cm−1, and the probe laser was fixed on the I35Cl EB, 11–2 bandhead, 23 066 cm−1.

The laser beams were spatially filtered down to ca. 1 mm diameters, and a 0.5 m focal length lens was inserted after the iris to focus the lasers to diameters of ca. 320 and ca. 180 μm for the pump and probe lasers, respectively, in the expansion region.

The probe laser was aligned so that it crossed the expansion 3.5(1) mm downstream from the pump laser.

The intensity of the I35Cl EX, 11 → v″ fluorescence induced by the probe laser was then monitored as a function of the temporal delay between the pump and probe lasers.

The maximum probe signal was observed at a temporal delay of 2.00 μs with the pump laser crossing the expansion 9.9 mm downstream from the pulsed valve orifice, xd−1 = 11.1, when using a backing pressure of 14.8 bar.

This time delay corresponds to an I35Cl velocity of ca. 1750(50) m s−1.

The measurement was repeated with the pump laser set at 21.7 mm downstream, xd−1 = 24.4, and with backing pressures of 7.9 and 14.8 bar, and the same velocity was obtained in all measurements.

Within the experimental error, this value is the same as both the terminal velocity of pure He in a supersonic expansion, 1760 m s−1,38 and the mass weighted terminal velocity of 360 ppm ICl in a He expansion, 1747 m s−1.

Consequently, we can only deduce an upper limit for the velocity slip between the I35Cl molecules and the He atoms of 60 m s−1.

This velocity would correspond to Tslip < 0.6 K, suggesting that Tslip may be either within or below the range of Trot, 0.19 to 3.0 K. Consequently, we do include Tslip in some of the analyses described below to investigate what contribution the velocity slip may have on the observed dynamics.

We also attempted to estimate the velocity distribution of the ICl molecules in the expansion by recording the temporal breadth of the pump–probe delay signals recorded as described above and with the pump laser at xd−1 = 11.1 and 24.4, and with backing pressures of 7.9 and 14.8 bar.

The temporal breadth of the pump–probe signals in all the measurements was approximately the same, ca. 0.22 μs, and appears to be limited by the diameters of the focused lasers in the expansion region.

Thus, we do not include effects from the velocity distribution in the analyses below.

Local densities within the expansion

Since Trot is the most reliable measurement of the expansion temperature for our current apparatus, and Trot is known to be an upper limit for the equilibrium temperature, Teq,40Trot is used in eqn (1) to approximate the total density (He atoms and ICl molecules) ρ at each distance in the expansion.

As will be shown below, the general trend observed of decreasing I35Cl density as a function of xd−1 is reproduced using Trot in eqn (1).

This provides some validity for using Trot as the local temperature in eqn (1), despite the fact that eqn (2) does not quantitatively reproduce our temperature measurements.

The calculated total densities range from 3.8 × 1017 cm−3 at xd−1 = 5.8 down to 0.6 × 1017 cm−3 at xd−1 = 14.0.

The densities of the ground state I35Cl(X,v″ = 0) molecules ρI35Cl are then estimated by multiplying ρ by the partial pressure of ICl in a He carrier gas, ca. 360 ppm at 14.8 bar and 274 K,41 and by the isotopic abundance of the I35Cl isotope, 0..757742

The resultant estimates of ρI35Cl vary from 1.0 × 1014 cm−3 at xd−1 = 5.8 down to 1.6 × 1013 cm−3 at xd−1 = 14.0, as shown in Fig. 3 as open squares.

Since the I35Cl(X,v″ = 0) densities are orders of magnitude less than the total density in the expansion, the He-carrier gas density at each downstream distance is approximately ρ.

Local ICl–He collision frequency

Several models and methods have been implemented in calculations of the collision frequencies of molecules with carrier gas atoms within supersonic expansions.

The simplistic equation for collisions between hard spheres43 is most often implemented to estimate order-of-magnitude collision frequencies of a molecule A with carrier gas atoms B:ZHS = πd2AB (8kTABμAB)1/2ρBThe collision diameter dAB is taken to be the average of the diameters of A and B, dAB = ½(dA + dB).

The relative temperature between A and B is TAB, the local density of B within the expansion is ρB, the reduced mass of the collision pair is μAB, and k is Bolzmann’s constant.

The different values of the temperatures within the expansion, Tcalc, Trot, and Tslip, indicate the complexity of fully characterizing the properties of an expansion comprised of multiple species.

Rather than attempting to incorporate each of the temperatures in estimating ZHS, we have chosen to use Ttot = Trot + Tslip for TAB and ρ for ρB in eqn (3) to provide an upper limit for ZHS.

We also assume dHe(ICl) = 3.7 Å, based on approximations of atomic He and molecular ICl diameters.43

Calculations of the He + ICl(B,v′ = 2) PES44 indicate that this approximation may be a slight overestimate for dHe(ICl).

Examining a slice through the T-shaped orientation reveals a hard-sphere radius of 3.34 Å.

However, considering that collisions will occur at multiple orientations, including the linear orientation, which has a longer hard-sphere radius than the T-shaped orientation,21 we believe that dHe(ICl) = 3.7 Å is a reasonable estimate.

Using this value, we calculate hard-sphere collision frequencies ranging from 2.2 × 107 collisions s−1 at xd−1 = 5.8 down to 2.7 × 106 collisions s−1 at xd−1 = 14.0.

Previous studies have shown, however, that for the low temperatures prevalent in a free-jet expansion a hard-sphere model is not appropriate.8,39,45–47

Because of the low temperatures, a potential incorporating an attractive term gives much more reasonable estimates of collision frequencies.

One such model that has worked well is the Lennard-Jones 6–12 potential.8,39,45–47

The Lennard-Jones 6–12 model is especially convenient because the collision frequency, ZLJ, can be related to the hard sphere collision frequency, ZHS, using published Ω(2,2)* collision integrals: ZLJ = Ω(2,2)*ZHSThe collision integrals have been tabulated as a function of the reduced temperature, T*, whereT* = kT/εand ε corresponds to the well depth of the potential.

The values of the collision integrals in ref. 48 only extend to T* = 0.3; however, lower values of T* have been reported by Knight and co-workers.39

We use here a fit of Knight’s reported values to determine the Ω(2,2)* values that correspond to our experimentally determined values for Ttot.

We take the Lennard-Jones well depth, ε, to be equal to that of the calculated He + ICl(B,v′ = 3) PES, 32 cm−1 in the T-shaped orientation;18 the potential will be more shallow at other collision geometries.

The estimated values of ZLJ decrease almost an order of magnitude from ca. 9.7 × 107 collisions s−1 down to ca. 1.5 × 107 collisions s−1 with increasing distances in the range investigated.

The assumption that Ttot = TAB will be qualitatively justified in the following section.

Collisional relaxation of ICl(B,v′ = 3) to ICl(B,v′ = 2)

Propensities for ICl(B,v′ = 3)–He collisions

Using the aforementioned equations for density and collision frequency, eqns (1), (3), and (4), as well as the characterization of the temperature of the expansion, we can model the downstream-distance and backing-pressure dependences of the intensities of the I35Cl BX, 2–0 and 3–0 features in an attempt to gain insight into the collision dynamics that give rise to the observed signals.

The LIF spectra recorded in the ICl BX, 2–0 and 3–0 regions at several distances downstream are used to characterize the dependence of the I35Cl BX, 3–0 band intensity on carrier gas density and I35Cl–He collision frequency.

The integrated intensities of the I35Cl BX, 2–0 and 3–0 bands recorded using a backing pressure of 14.8 bar and at four different distances downstream are shown in Fig. 3 as black squares and circles, respectively.

The error bars were estimated using the signal-to-noise levels of the LIF features.

Weighted fits of the data to power dependencies were made to provide a guide for the experimental trends of the intensities, shown as solid lines.

The data points and the fits were normalized by dividing each data point by the value of the fit at xd−1 = 5.8.

The intensities of the I35Cl BX, 2–0 and 3–0 bands decay monotonically with increasing distance with the 3–0 band decaying more rapidly than the 2–0 band.

The intensities of the I35Cl BX, 2–0 band are found to be proportional to the density of the ground-state I35Cl(X,v″ = 0) molecules at each distance, ρI35Cl, calculated as described in Section III. b.

2, and, as a result, we use the intensity of the I35Cl BX, 2–0 band to monitor changes in the I35Cl(X,v″ = 0) ground-state density.

Note that some collisional relaxation of ICl(B,v′ = 2) to ICl(B,v′ = 1) does occur, but this represents only ca. 1% of the ICl molecules excited.20

Any ICl signals that arise from collisions of the ICl molecules with He atoms should be proportional to the product of the I35Cl–He collision frequency and the I35Cl density, ZLJ*ρI35Cl, at each downstream distance.

These products are fit to a power dependence, lower dashed curve in Fig. 3, and normalized using the value of the fit at the shortest xd−1, open circles.

Strong agreement between the integrated intensity of the I35Cl BX, 3–0 band, filled circles, and ZLJ*ρI35Cl, open circles, is observed in Fig. 3.

The agreement of ZHS*ρI35Cl with the I35Cl BX, 3–0 band is reasonable but not quite as good as the agreement with ZLJ*ρI35Cl.

This indicates that the Lennard-Jones potential is a slightly better model for calculating collision frequencies than the simplistic hard-sphere potential.

Furthermore, the effectiveness of both of these potentials in modeling collision frequencies eliminates the necessity of invoking a resonance enhancement to the collision cross section.

The data in Fig. 3 also indicates that following the preparation of the short-lived rotational states within the I35Cl(B,v′ = 3) level, some of these excited-state molecules undergo collisions with He atoms in the expansion.

The collisions vibrationally relax a fraction, f3–2, of the predissociative I35Cl(B,v′ = 3) states down to the long-lived I35Cl(B,v′ = 2) rotor states, which in turn fluoresce.

Recall that since we have monitored the intensity of the fluorescence signal using a boxcar integration gate positioned 150 ns after the excitation laser pulse, we detect fluorescence from only those excited-state molecules that undergo collisions and not from a vast majority of the prepared molecules that non-adiabatically dissociate.

It is also important to emphasize that the rotational structure indicates that bare I35Cl molecules are being promoted to rotational states within the I35Cl(B,v′ = 3) level, not He⋯I35Cl complexes that would form I35Cl(B,v′ = 2) products via vibrational predissociation of metastable He⋯I35Cl(B,v′ = 3) intermolecular vibrational levels.

The rates and cross sections for the collision-induced, vibrational energy relaxation of I35Cl(B,v′ = 3) rotor states down to I35Cl(B,v′ = 2) states, k3–2 and σ3–2, can be estimated using the f3–2 values measured at varying downstream distances.

The fraction of the predissociative I35Cl(B,v′ = 3) excited-state molecules that re-stabilize in rotational states of the I35Cl(B,v′ = 2) level, f3–2, is estimated using the LIF spectra, Fig. 1, and published Franck–Condon factors; the I35Cl BX, 3–0 Franck–Condon factors are three times greater than those of the 2–0 band.49

The integrated intensity of the 2–0 band is 30.4 on this intensity scale, and we would expect the 3–0 band to have an integrated intensity of 91.2 on the same scale if the v′ = 3 rotational states were not predissociative.

Since the fluorescence following excitation of the 3–0 band is from the I35Cl(B,v′ = 2) level, we can directly compare the value of 91.2 to the integrated intensity of the 3–0 band, 0.12, and we find that f3–2 ≈ 1.3 × 10−3 at xd−1 = 11.2 and with a He-backing pressure of 14.8 bar.

The rates, k3–2, can be approximated using the f3–2 values at each distance and the I35Cl(B,v′ = 3) excited-state lifetime.

We assume that the contribution of the spontaneous emission of ICl(B,v′ = 3) is negligible.

In order to calculate k3–2, we use f3–2 to determine the relative yields of the I35Cl(B,v′ = 2) and I 2P3/2 + Cl 2P3/2 products that result from collisional relaxation and non-adiabatic dissociation, respectively.

We then assume a lifetime of 0.5 ns for non-adiabatic dissociation onto the ICl(Z 1) state, τNA, corresponding to the lifetimes of I35Cl(B,v′ = 3) states with little rotational excitation.26,27

The values of f3–2 and τNA are then used to determine k3–2:k3–2 = f3–2/((1 − f3–2)τNA)The estimates of k3–2 at each xd−1 drop an order of magnitude, from ca. 107 s−1 down to ca. 106 s−1, with increasing downstream distance over the range investigated.

The cross sections for vibrational relaxation induced by collisions with He atoms along the expansion, σ3–2, are then found usingσ3–2 = k3–2(μABπ/8kTAB)1/2/ρB,43where TAB is represented by either Trot or Ttot.

The values of σ3–2 are in the range of 20–50 Å2 under these conditions and are comparable to the hard-sphere scattering cross section of 43 Å2 obtained using dHe(ICl) = 3.7 Å.

The values of σ3–2 as well as f3–2, and k3–2 at each xd−1 are listed in Table 1.

While several approximations and assumptions were made in extracting these cross sections, the large values are suggestive of the significant probability for vibrational relaxation of ICl(B,v′ = 3) rotor states induced by collisions with He atoms in the supersonic expansion.

Our estimates of the vibrational relaxation cross sections of ICl(B,v′ = 3), 20–50 Å2, are in accord with the reported cross sections for vibrational relaxation of I2(B,v′) molecules in a He expansion, which are found to be in the range of 15 to 700 Å2 with a dependence on the initially prepared vibrational level, v′.5,6

The collision-induced vibrational relaxation of ICl* molecules should be proportional to the product of the He-atom carrier gas density and the ICl*–He collision frequency, as mentioned above.

We have also monitored the dependence of the intensities of the I35Cl BX, 2–0 and 3–0 LIF bands as a function of He-backing pressure; LIF spectra in each vibronic region were recorded at xd−1 = 10.7 nozzle diameters using various He-backing pressures between 11.4 and 28.6 bar.

The values of Trot were found to change only slightly with increasing backing pressure throughout this pressure range, varying from 1.36(3) to 1.49(3) K. The I35Cl–He collision frequency, which should be approximately proportional to the I35Cl*–He collision frequency, was calculated using eqns (1), (3), and (4) and assuming TAB is equal to either Trot or Ttot at each pressure.

The collision frequency increased linearly with backing pressure, as expected.

The intensity of the I35Cl BX, 3–0 band also increases with He-backing pressure and tracks roughly with the collision frequency of ICl molecules with He atoms in the expansion.

This similar dependence on the backing pressures supports the conclusion that the I35Cl(B,v′ = 2) molecules that are detected following preparation of I35Cl(B,v′ = 3) rotor states are a consequence of collision-induced vibrational relaxation.

ICl(B,v′) product-state distributions

Having observed that the I35Cl BX, 3–0 band is detected as a result of collision-induced vibrational relaxation with He atoms in the expansion, we sought to characterize the full-collision dynamical process by examining the I35Cl(B,v′ = 2,j′) rotational product-state distribution.

This distribution could then be compared to the recently published He⋯ICl half-collision data20 in an effort to understand the relationships, if any, between the two processes.

In order to do this, high-resolution pump–probe spectra were recorded by probing the Δv = −1 channel that results from collisions between molecules initially prepared in the long-lived I35Cl(B,v′ = 2) and short-lived I35Cl(B,v′ = 3) levels and He atoms in the expansion.

The spectra were taken using a He-backing pressure of 14.8 bar, and at a downstream distance of xd−1 = 11.2.

Under these conditions an I35Cl(X,v″ = 0) rotational temperature of ca. 1.5 K was measured.

The rotationally resolved spectrum of the I35Cl EB, 10–2 band recorded with the pump laser fixed on the I35Cl BX, 3–0 bandhead, which corresponds to excitation of the j′ = 1–3 rotor levels, is shown in Fig. 4a.

The spectrum of the I35Cl EB, 9–1 band recorded with the pump laser fixed on the I35Cl BX, 2–0 bandhead, which also corresponds to excitation of the j′ = 1–3 rotor levels, is plotted in Fig. 4b for comparison.

The rotational quantum number of the I35Cl(B,v′) state associated with several of the P-lines are shown to emphasize the degree of rotational excitation in the product channels.

Note that the P-rotor lines are overlapped by weaker R-lines originating from states with higher rotational excitation.

The highest observed rotor lines are the P(21) and the P(23) lines in the 10–2 and 9–1 spectra, respectively.

We believe that these spectra are of the nascent product-state distributions since pump–probe spectra were recorded at two extreme distances downstream, 5 mm and 20 mm, and therefore in regions with different collision frequencies, and no significant changes in the rotational distributions were observed.

The rotational-state distributions of the Δv = −1 vibrational relaxation channels were determined using a linear least-squares fitting algorithm, known spectroscopic constants,22,50 and the appropriate rotational linestrength factors51 to fit the rotational contours.

The distributions obtained from the I35Cl EB, 10–2 and 9–1 bands, Fig. 4a and b, are plotted as a function of I35Cl(B,v′) internal rotational energy in Fig. 5a as black circles and open squares, respectively.

The rotational-state distributions are bimodal with an overall maximum at j′ = 6 and another maximum at j′ = 12 in both of the Δv = −1 channels.

Minima were observed at j′ = 8 and 10 for the I35Cl(B,v′ = 2) and I35Cl(B,v′ = 1) products, respectively.

The mean rotational energy found in each of these product levels is 9.5 and 10.9 cm−1.

Since the energy difference between the I35Cl(B,v′ = 3,j′ = 0) and I35Cl(B,v′ = 2,j′ = 0) states and the I35Cl(B,v′ = 2,j′ = 0) and I35Cl(B,v′ = 1,j′ = 0) states is 163.4 and 182.7 cm−1, respectively,22 we can estimate the fraction of the available energy that is found in rotational excitation of the products.

The amount of energy found in the I35Cl(B,v′ = 2) and I35Cl(B,v′ = 1), Δv = −1 vibrational relaxation channels represents ca. 6% of the total available energy.

Thus, most of the available energy is converted into kinetic energy of the ICl* and He collision partners.

Propensities for collisions of ICl(B,v′ = 3) with other gases

We have recorded LIF spectra of ICl entrained in a number of different carrier gases to qualitatively check for the effect of the collision partner on the vibrational relaxation of ICl(B,v′ = 3).

Recall that the intensity of the I35Cl BX, 3–0 band is ca. 103 times weaker than the 2–0 band when using a He-carrier gas with a backing pressure of 14.8 bar and at xd−1 = 10.7.

In contrast, the intensity of the 3–0 band is significantly smaller, ca. 106 times weaker, than the 2–0 when using a 90% Ne in He carrier gas at the same backing pressure and distance.

When using a 100% Ar carrier gas, no ICl BX, 3–0 LIF signals were observed.

It should be noted, though, that the intensity of the I35Cl BX, 2–0 LIF feature is weaker when using an Ar-carrier gas and, consequently, the signal-to-noise levels are worse than those of the ICl in He or Ne/He spectra.

Finally, LIF spectra were also recorded using a pure hydrogen expansion.

The intensities of the ICl BX, 3–0 features in these ICl/H2 spectra are about twice those measured in the helium expansion.

The different efficiencies for vibrational relaxation with the He, Ne, Ar, and H2 collision partners do not appear to be a result of the corresponding attractive intermolecular potential wells in the excited state.

The intermolecular potential energy surfaces for He + ICl(B,v′ = 3), Ne + ICl(B,v′ = 3), and ortho-H2 + ICl(B,v′ = 3) have all been shown to have minima in the T-shaped orientation with binding energies of 16.2(7),52 65(5),53 and 69.5(3)–76.3(3) cm−1,54 respectively.

Of these three collision partners, Ne is observed to have the smallest probability for inducing vibrational relaxation even though the excited-state binding energy of I35Cl(B,v′ = 3) with Ne is significantly larger than that with He and comparable to that with H2.

The lighter H2 partner, in contrast, is the most efficient vibrational relaxation partner.

This might lead one to believe that it is the mass mismatch, and thus the velocity slip, between the ICl molecule and the collision partner that gives rise to the different probabilities for collisional relaxation.

However, using the aforementioned binding energies of the He⋯ICl, Ne⋯ICl, and H2⋯ICl complexes to estimate their well depth, as well as our velocity-slip experiments to determine Ttot, we find that the velocity slip is not nearly large enough to account for the different values of ZLJ that would be required to justify the observed vibrational-relaxation efficiencies.

For instance, in order to be in accord with our observed efficiencies, the ZLJ for the Ne expansion would have to be three orders of magnitude less than ZLJ for the He expansion.

Using our observed upper limit for the slip temperature for the He calculations and assuming no slip for the Ne calculations, the worst case scenario, we find that there is a factor of 2.5 more collisions in the Ne expansion than in the He expansion.

This indicates that some other phenomenon must be giving rise to the observed trends.

Thus, we propose an alternative possibility.

In our group’s work on the Ne⋯ICl complex,53 we noted that the signals observed in the ICl BX, 2–0 region were larger than the signals observed in the 3–0 region.

This was attributed to the competition between electronic predissociation and vibrational predissociation that is present in the 3–0 region due to the presence of the nearby repulsive ICl(Z 1) electronic state.26

Because of the strong possibility that Ne⋯ICl(B,v′ = 3) van der Waals complexes undergo electronic predissociation, we find it plausible that collisions between Ne atoms and ICl(B,v′ = 3) excited-state molecules can induce non-adiabatic dissociation of ICl via the repulsive Z1 state.

This mechanism would compete with vibrational relaxation and thereby reduce the observed yields for the collisional-relaxation products.

Furthermore, because of the relatively large mass and polarizability of Ne compared to H2 or He, collision-induced non-adiabatic dissociation should be much more prevalent with a Ne carrier gas than with H2 or He.

Comparison of full-collision and half-collision dynamics

It is interesting to compare the results of the full-collision dynamics with those of the recently reported half-collision, vibrational predissociation dynamics of He⋯I35Cl(B,v′ = 3) van der Waals complexes prepared with varying amounts of intermolecular vibrational excitation.20

Collision-induced vibrational relaxation results in a bimodal I35Cl(B,v′ − 1) rotational state distribution with maxima at j′ = 6 and 12 and a minimum at j′ = 8 or 10, Fig. 5a.

Bimodal distributions are also evident in the vibrational predissociation measurements of He⋯ICl(B,v′ = 3) when preparing the complex in the lowest, n′ = 0, and second excited, n′ = 2, intermolecular vibrational levels.

When more highly excited intermolecular vibrational levels are prepared, however, the bimodal structure blurs out.

The ICl(B,v′ = 2) rotational product-state distributions that result from vibrational predissociation for these two extreme cases was reported previously, Fig. 5 of ref. 20, and is plotted here in Fig. 5b.

The ICl(B,v′ = 2) rotational populations that result following the preparation of complexes in the metastable He⋯ICl(B,v′ = 3,n′ = 0,J′ = 0) and He⋯ICl(B,v′ = 3, n′ = 4, J′ = 1) states are shown as black diamonds and open triangles, respectively.

While both of these vibrational predissociation product-state distributions bear some resemblance to those of the collision-induced product-state distribution, Fig. 5a, the distribution formed from the vibrational predissociation of the n′ = 0, J′ = 0 level is quantitatively more similar.

Qualitatively, the bimodal structure for this channel is reproduced almost identically, with maxima at j′ = 5 and 13 and a minimum at j′ = 10.

The main difference is that in the collisional-relaxation data the two maxima have comparable populations, while vibrational predissociation from the n′ = 0, J′ = 0 level has the first maxima with significantly more population.

Vibrational predissociation from the n′ = 4,J′ = 1 level is better in this respect, but lacks a definitive bimodal distribution as well as non-negligible population at Erot > 20 cm−1.

Quantitatively, a comparison of the residuals between the collisional-relaxation product-state distribution and the half-collision n′ = 0, J′ = 0 distribution is ca. 35% less than for the comparison with the n′ = 4, J′ = 1 distribution.

Somewhat surprisingly, then, collision-induced vibrational relaxation mimics vibrational predissociation from lower intermolecular vibrational levels that tend to more localized in the T-shaped region, n′ = 0 or 2, more closely than vibrational predissociation from more highly excited intermolecular vibrational levels with states that are delocalized in the angular coordinate, such as the n′ = 4 level.

A possible explanation for this behavior may be that in colliding with the ICl molecule at the low temperatures achieved in the expansion, the He atom is steered by the He + ICl(B,v′ = 3) potential where it tends to find the region of the minimum of the multi-dimensional PES, which is also where the lowest bound intermolecular vibrational level is localized.

Hence, similar rotational product-state distributions are observed.


Pathways that compete with the non-adiabatic dissociation of electronically excited ICl(B,v′ = 3) in a He-carrier gas expansion are investigated using LIF and two-laser, pump–probe spectroscopy.

We find that collisions between ICl molecules and He atoms occur over extended distances along the expansion direction.

The collision frequency between molecules prepared in the short-lived I35Cl(B,v′ = 3) level and the He atoms is high enough that vibrational relaxation down to rotational states in the next lower I35Cl(B,v′ = 2) level can occur with measurable yields.

At the same time, the vibrational relaxation can be modeled using a Lennard-Jones 6–12 collision-frequency model, arguing that there is no need to invoke a resonance-enhancement to the collisional cross section.

The rotational-state distributions of the low-energy, collision-induced vibrational relaxation and of the vibrational predissociation from low-lying He⋯ICl(B,v′) intermolecular vibrational levels are seen to match quite well as opposed to the agreement with the distributions from the vibrational predissociation of levels that have more intermolecular vibrational excitation and are delocalized in the angular coordinate.

This suggests that at low temperatures, the He atoms are steered toward the minimum of the He + ICl(B,v′ = 3) intermolecular potential before scattering off the repulsive wall.

The ability to accurately measure the ICl vibrational and rotational product-state distributions suggests that this system would be well-suited for complimentary theoretical investigations of intermolecular energy transfer.