Vector and scalar correlations in the photodissociation of NCCN

J. Photochem. Photobiol. A: Chem, 80 (1994) 45-52 45

Vector and scalar correlations in the photodissociation of NCCN

Ming Wu and Gregory E. Hall7 Department of Chemiay, Brookhaven National Laboratory, Upton, NY 11973~XXI0 (USA)

Abstract

The CN photofragments from the photodissociation of NCCN at 193 nm have been measured by high-resolution transient absorption spectroscopy. Doppler-broadened profiles of isolated rotational lines in the 2-O and 3-l vibrational bands of the CN A-X transition were observed under collisionless conditions with a tunable, single- frequency Ti:sapphire ring laser. Analysis of the Doppler profiles reveals a vector correlation between the translation and rotation of CN photoproducts, with the angular momentum of the high rotational states increasingly perpendicular to the recoil velocity. After correction for vector correlations, the laboratory-frame scalar speed distribution of state-selected photoproducts can be determined. The mean squared laboratory velocity is directly related to the average internal energy of coincident CN fragments. The wings of the Doppler profiles indicate that the available energy for a pair of ground state CN photoproducts following 193 nm dissociation of NCCN at 295 K is 5300& 150 cm-‘, which includes the average vibrational energy of the parent molecules selected by tbe photolysis laser. Phase space theory with an optimized available energy of 5300 cm-’ produces laboratory speed distributions that are in qualitatively reasonable agreement with the kinetic energy measurements, but overestimate the total internal energy of the photofragments. The measurements are good enough to warrant comparison with more sophisticated models of unimolecular decomposition.

1. Introduction

A handful of molecules have come to be considered as prototypes for the various limiting be- haviors that can be observed in the photodissociation of small molecules [l-3]. Theories for the treatment of photodissociation and unimolecular reactions in general depend on a deep and verified body of experimental knowledge about particular molecules that can be well described by a certain simplifying assumption which characterizes a dynamic or statistical model of photodissociation. Statistical models, in which only the total energy and angular momentum influence the fiagmen- tation process, are frequently appropriate for de- scribing predissociations where the only barrier to dissociation after internal conversion to the ground state is the reaction energy itself. Ketene [2] and NCNO [4] are two well-studied examples of such dissociations.

The photodissociation of NCCN has been considered as another classic case of statistical frag- mentation since the work of Eres et al. [5]. In this early fluorescence imaging experiment, CN vibrational and rotational distributions were measured following 193 nm dissociation in a skimmed

‘Author to whom correspondence should be addressed.

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molecular beam. From spatially resolved, laser- induced fluorescence (LIF) excited by a plane of delayed excitation light, rings of fluorescence were measured to give state-resolved CN velocity distributions. The total CN state distributions were

well fitted by the phase space theory (PST) of Pechukas and Light [6], provided that the available energy was adjusted down by about 1700 cm-’ from the then current literature values [3]. With allowances made for acknowledged experimental difficulties [5], the velocity distributions were not considered to be inconsistent with this model. Subsequent work on the photodissociation of NCCN has substantiated this general picture, e.g. investigation of the dissociation in the threshold region 17-91 and analysis of the spectroscopy and photophysics [9, lo] of the vibronically allowed ‘2; c ‘2,’ and ‘AU c ‘Zl transitions below 226 nm. A threshold for the detection of CN fragments has been reported at 212.2 nm [9], which coincides with the beginning of a reduction in the ‘2; fluorescence lifetime and quantum yield, and the onset of a continuum in the absorption spectrum.

The present workwas undertaken to characterize the CN coincident pair distribution using high- resolution transient absorption spectroscopy. Prob- ing CN in the A-X system with a single-frequency

46 M. Wu, GE. Hall / Vector and scalar comlotbns in the photodimociation of NCCN

Ti:sapphire laser allows us to measure state-resolved velocity distributions by means of Doppler profiles, following photodissociation of thermal NCCN at 193 nm. The measurements can be compared with PST and with the earlier molecular beam/LIF imaging measurements of Eres et al. [5]. The present experiments, using a thermal precursor, show approximate agreement with pre- vious measurements and PST. However, the higher velocity resolution of the present Doppler spectroscopic technique allows significant deviations from simple PST to be observed, both in the coincident product distributions and in the vector correlations of fragment velocity and angular momentum.

2. Experimental section

The high-resolution transient absorption spectra of CN photoproducts were measured in the ap- paratus illustrated in Fig. 1 and previously described in more detail [ll]. The photolysis excimer laser (Questek 2240) delivered 5-10 mJ per pulse of unfocused 193 nm light at 10 Hz into a White cell (path length, 1 m). The probe laser was a Ti:sapphire ring laser (Coherent 899-29) pumped with 8 W from a multi-line Ar’ laser (Coherent 310), scanning over selected rotational lines of the 3-l and 2-O bands of the CN A(211)+X(Z~f) system. The continuous wave probe laser beam was attenuated to 20 mW or less on entering the White cell, where it made 20 passes, overlapping the nearly collinear excimer Iaser beam with an effective overlap path length of 2-3 m. The trans- mitted probe beam and a reference beam directly from the ring laser were measured with identical Si photodiodes (Hamamatsu 53072); d.c.-coupled

Al+ Ti:S

Gas

t In

r-7 Pump Out

1

Fig. 1. Experimental schematic diagram of the high-resolution transient absorption measurements.

signals from the photodiodes were acquired, time offset to compensate for optical path differences, ratioed and averaged in a fast digital oscilloscope (LeCroy 9450). A control computer archived the average ratio waveforms from the oscilloscope and sent step commands to the probe laser controller at the end of each signal averaging interval with a 100 MHz step size. Typically transients from 100 excimer laser shots were averaged at each probe frequency. Multiple scans were averaged for some of the weaker lines. A time resolution of 50-100 ns is dominated by the transit time of the probe laser beam through the White cell. Under our experimental conditions, the largest source of relative frequency uncertainty that could influence the Doppler profiles was the scan non- linearity; typical measured values were f 40 MHz.

Ethanedinitrile (often called cyanogen, NCCN) is an endangered chemical, no longer commercially available in the United States. Our NCCN (Mathe- son) was used without additional treatment. A slow flow of 2 standard cubic centimeters per minute through the White cell was set with a mass flow controller (MISS I47B; 1159B) at a pressure of 50 mTorr (6.7 Pa) measured with a capacitance manometer. Rotational line positions for the A-X system of CN were calculated from the spectroscopic constants of Cerny et al. [12] which produced unambiguous line assignments for the observed spectra.

3. Results

Preliminary measurements were made in a different sampIe cell where the probe laser multipass propagation was perpendicular to the photolysis beam, as described previously [ll]. In this cell, the velocity anisotropy can be measured by changing the polarization of the photolysis beam. We verified that no detectable change in transient absorption line shapes accompanied a change in the photolysis polarization, in agreement with the symmetrical rings of fluorescence observed by Eres ef al. [S] and the absence of significant CN rotational alignment observed by Wannenmacher et al. [8]. Having verified the velocity isotropy in the laboratory frame, we made all subsequent measurements in the long White cell, where the signals were about eight times larger than in the transverse cell, with no loss of information due to the restricted geometry.

In the 1 m White cell, we measured time- dependent absorption line shapes at 50 mTorr total pressure of NCCN, with better than 100 ns

time resolution and better than 50 MHz frequency resolution. We verified the indistinguishability of intensities and line shapes for F, and F2 spin- rotation components for a few test levels of the ground state, and arbitrarily restricted our subsequent attention to F, product states of CN fragments. Careful measurements were made for R,(N) and Q1(iV) lines for N= 17, 30, 35 and 40 in the 2-O band, and for N-6, 11, 16 and 21 in the 3-l band. These levels span the populated states and were selected to minimize accidentally blended lines and unresolved satellite lines. The R1 lines have no satellites; the Q, lines have Rzl satellites that are incompletely resolved at low values of N [12]. The Q,(6) and Q,(H) lines of the 3-l band were analyzed using the half of the Doppler profile not blended with the weaker satellite line. For Nz=16, the satellite intensities are much weaker, and the splitting exceeds the nascent Doppler width.

The early Doppler profiles were extracted from a 50 ns-wide average of absorption intensities beginning 100 ns after the excimer laser photolysis. Negligible velocity relaxation was observed during the first few hundred nanoseconds under these conditions, and we consider these measurements to be representative of unrelaxed CN photoproducts. Figure 2 illustrates the early Q1- and R,- branch Doppler profiles measured for four v = 0 rotational states of CN. The Doppler shifts have been converted to velocity and the intensities have been scaled to the same maximum. These Doppler profiles of state-selected photofragments give information about the correlations of the velocity and angular momentum of the probed fragments, and the internal energy distribution of the undetected coincident fragment, through energy and linear momentllm conservation. A description of the analysis of the line shapes for the derivation of these vector and scalar correlations follows.

4. Analysis

4.1. v-J correlation We observe that the Q1- and RI-branch tran-

sitions probing the same lower level have different Doppler profiles, the signature of a correlation between the fragment recoil velocity v and its angular momentum J. In the particularly simple case of one-photon absorption for a system with no laboratory-frame alignment of velocity or angular momentum, the Doppler profile in the laboratory frame D’(w) is given by [ll, 131

1.0

jO.6 El

0.0

1.0

$0.5

3

0.0

1.0

QO.5

8

0.0

1.0

h Y 3 0.5

3

0.0

-1000 0 1000 m/a

Fig. 2. Doppler profiles for Q- and R-branch lines of selected rotational states in zr =O. The Doppler shift has been converted to veto&y, and the amplitudes have been scaled to the same maximum. Symbols show data and the full lines are simultaneous one-parameter fits, using eqn. (1) with an adjusted /3!(22).

D’(w) = 91 1

$

- [ 1 - h’2’B~(22)P2(~/2))]~2f’(2)) dv (I) WI 2v

where w is the Doppler shift, expressed in velocity units, hc2’ is unity for Q-branch absorption and --J/(21*+ 3) for R-branch absorption (approaching -t at high J), P&X) =@x* - 1) is tke second Legendre polynomial, pi(22) = {P2(8.J)) is the

48 M. Wu, G.E. HaN I VWor and scalar correIarions in the pho&Gsociarion of NCCN

bipolar moment characterizing the v-J correlation and v’fl(V,, is the angle-averaged speed distribution of the detected CN level in the laboratory frame. A (U+3)/kI weighted average of normalized R and Q lines eliminates the dependence on @$(22), resulting in the projection of the angle-averaged laboratory-frame velocity distribution onto a line, denoted by Do(w)

Do(w) = 4

$

vf’ (v) dv

WI (2)

The laboratory-frame speed distribution wy’(v) can be obtained from the derivative of this composite Doppler profile according to [ll, 14, 151

Figure 3 illustrates composite Doppler profiles D;(w) and the derived laboratory speed distributions for some of the measured CN states. The plotted symbols are the weighted averages of the measured absorption intensities plotted against the Doppler shift, expressed in velocity units. The smooth curves through the Doppler profiles are least-squares fits using a basis of five even Hermite

polynomials. The speed distributions were computed from the polynomial fits according to eqn.

(31. Values of pg(22) were determined by a simul-

taneous one-parameter fit to QI- and RI-branch Doppler profiles for each probed fragment state, using eqn. (1) and the function f’(v) obtained from the Q,- and R,-averaged Doppler profile. Table 1 summarizes the measured v-J correlations. The full lines in Fig. 2 show the resulting fits to the Doppler profiles. For low rotational levels, J and v are nearly uncorrelated; pg(22) is near zero. At higher rotational levels, the correlation ap- proaches -0.25, half of the limiting value for v _LJ.

The measured v = 1 states of CN display a weak correlation, similar to the same rotational levels of v=o.

4.2. Scalar correlations of coincident photofragments

The speed distributions of state-selected photofragments carry information about the internal energy distribution of the undetected coincident photofragments. The fastest fragments in a detected quantum state are those formed in coincidence with a minimum of internal energy in the coincident fragment; the slowest observed frag-

0 500 1000 1500 2000 Velocity (m/s) Velocity (m/s)

Fig. 3. Composite Doppler profiles D&J) for positive Doppler shifts: 0, selected CN photofragment states; -, corresponding speed distributions in the laboratory frame, v(*‘f’(v).

hf. Wu, G.E. Hall I Vector and scalar cotrelutions in the photodimobation of NCCN 49

TABLE 1. o-J correlations in CN photofragments

v=o 8%22) v=l &x22)

N=17 -0.08*0.04 N=6 -0.01 f0.04 N=30 -0.15*0.04 N= 11 - 0.02f 0.06 N=35 -0.21*0.04 N= 16 -0.14f0.06 N=40 -0.23*0.04 N=21 -0.08f0.06

ments are formed in coincidence with the most highly excited coincident fragments. Because the parent NCCN molecules have a thermal distribution of velocities prior to dissociation, the observed Doppler profiles are a convolution of the Gaussian distribution of parent speeds along the probe direction with the true center-of-mass (CM) line shape function D,,(w) which reflects the coincident CN state distribution for each observed CN state. Extracting the scalar correlation between photofragment pairs thus requires deconvolution of the measured Doppler profiles, as previously described by Ticktin and Huber [14]. The present data constitute a relatively favorable case for such analysis, since no significant additional broadening is introduced by the laser linewidth, and the required deconvolution function is accurately described by the known gaussian parent velocity distribution. Furthermore, the diatomic fragments have a low density of states, and the total photofragment state distribution has been measured previously [S, 10, 161. Several of the Doppler profiles were measured with enough signal averaging to attain signal-to-noise ratios in excess of 1OO:l. In spite of these favorable conditions, we find the deconvolutions poorly suited for de- termining the maximum velocity in the CM frame, since this requires representing a discontinuity with a small number of smooth functions. Details of this analysis will be described elsewhere [17]. For now, we extract average coincident internal energies from the laboratory frame measurements and compare our measurements with the predic- tions of PST.

The laboratory-frame speed distributions, as shown in Fig. 3, were used to compute a mean squared velocity, and thence an average translational energy in the laboratory frame: &z(v~>. Table 2 lists the average translational energies observed for each detected state. The convolution of the center-of-mass recoil velocity distribution with the parent velocity distribution increases the mean translational energy and broadens the distribution. The result is to increase each mean squared fragment velocity by the mean squared thermal velocity of the parent molecule [18]. The

TABLE 2. Scalar correlations in CN photofragmennts

Detected state @t)lsb @i”t(Cwb PST&&V) 2)’ =o only

w=O, N=17 1470 2105 1569 ~-0, N=30 1350 1185 1331 v=o, iv=35 1190 890 1169 v=O, N=4O 900 765 952 v=l, N-6 1140 1190 1145 v=l, iv=11 1055 1190 1109 v=l, N=16 1050 940 1063 v=l, N=21 920 850 980

“Laboratory-frame average translational energy (en-‘) of the detected CN photofragment. Uncertainties are k40 cm-’ in each case. bAverage internal energy of coincident CN’ states for each observed CN state. E,, is assumed to be 53W cm-’ in the energy balance calcularion, computed according to eqn. (5). Uncertainties are dominated by the uncertainties in the available energy. ‘Calculated average rotational energy of coincident CN’ v’=O photofragment using PST and E,lI=5300 cm-‘.

thermal motion of the parent thus adds fmCN(~NCCN2) = 3kT/4 = 158 cm- ’ to the mean kinetic energy in the CM frame. In the CM frame, both CN fragments have the same kinetic energy, determined from energy balance including the internal energy of the coincident CN, denoted CN’

=Ei,,(CN) +Ei&CN’) + x,(CN),, (4)

The average internal energy of the unmeasured CN’ fragment is thus given by

(Eht(CN’)) =Eavti, -Ei,,(CN)

-2 (E,(CN),) - y 1 Table 2 also lists the average internal energies of the coincident CN’ photofragments, calculated using eqn. (5) and E,,il=5300 cm-‘, a value derived from the analysis below. While the detailed line shape data should be able to address higher resolution features of the coincident energy distribution, these mean values are well determined and offer a check on the consistency of other more ambitious analyses.

PST [6] has been used successfully to describe the rotational state distribution of CN fragments from jet-cooled NCCN dissociated at 193 nm [5] as well as from room temperature NCCN dissociated at various longer wavelengths [7, 81. This statistical theory counts the combinations of fragment states consistent with a fixed total energy

50 M. Wu, G.E. Hall I Vector and scalar correlations in the photodissociation of NCCN

and angular momentum. Prior to calculating the total distribution of fragment quantum states, PST necessarily counts the distribution of coincident fragment states for each specified fragment quantum state - the correlated state distribution probed with a state-resolved velocity measurement.

We begin by computing the PST fragment distributions assuming a dissociation energy of 47 100 cm-l [8,9]. This corresponds to an available energy for rotationless NCCN of 4600 cm-’ at 193.4 mn, the center of the ArF excimer emission which has a bandwidth near 250 cm-‘_ We use a value of 80x 10d60 erg cm6 for the c coefficient in the c/r” term influencing the centrifugal barrier [6]. The PST calculations were performed with Boltz- mann weighting of parent rotational states, appropriate for the 295 K sample and no rotational selectivity in the excitation step. For each exper- imentally detected rotational state of CN, the PST distribution of coincident fragment states was expressed as a sum-of-rectangles Doppler profile, and convolved with the one-dimensional gaussian parent velocity distribution (~=219 m s-‘). The highest rotational states of v=O and v=l states have no significant coincident v = 1 fragments, so the partitioning of energy between vibrational states, not well described by PST according to Eres et al. [5], does not affect these calculated line shapes. For each of these levels, the calculated laboratory-frame Doppler profiles are significantly narrower than the observed profiles_ Figure 4 shows

I I I I I -2000 - 1000 0 1000 2000

Velocity (m/s)

Fig. 4. Composite Doppler profiles and simulations based on PST. Measured Do(w) for v = 0, N = 40 is plotted as open circles. PST velocity distributions in the laboratov frame are plotted for different assumed available energy parameters: chain line, 4600 cm-‘; broken line, 5300 cm-‘; full line. 5800 cm-‘. All curves have been normalized to the same area.

a typical fit using PST for the v =O, N=40 state. The circles are averaged Q and R data and the chain line is the PST calculation for an available energy of 4600 cm-‘.

The wings of the Doppler profiles are dominated by Eavail and are relatively insensitive to the details of the CN’ internal state distribution, since all the low-energy coincident states contribute to a peak in the kinetic energy distribution near the maximum value: I_[JY~~~~-E~,~(CN)]. A value of E avail larger than 4600 cm-’ is required to match the wings of the Doppler profiles. This can be due either to vibrational energy in the parent molecules or a bond dissociation energy of less than 47 100 cm-‘. The PST calculations already account for the additional available energy due to thermal rotation of NCCN. The effect of in- creasing Eavail to 5300 and 5800 cm-’ in the PST calculation is shown by the broken and full curves of Fig. 4 respectively. The fit to the wings at 5300 cm-l is acceptable for this line and the rest of the higher rotational states observed in both 2, = 0 and w=l.

Some quantitative discrepancies persist for some states at low velocities, corresponding to an excess of high-energy coincident CN’ photofragments in the PST calculations. The total fragment internal energy distribution is probably too hot in this calculation, based on the recent bulb measurements of v = 0 CN by Huang [lo], where N< 31 levels were well described by a temperature of 1400 K. The PST calculation for these levels shows only a small deviation from a linear Boltzmann plot, with a slope corresponding to about 3000 K for ~1 =O in coincidence with v’ =O, and 2100 K for 21 =O in coincidence with v’ = 1. We also list in Table 2 the PST average rotational energy of coincident CN’ v’ =O for each of the measured states, based on the calculations with E,, = 5300 cm-‘. It should be noted that the v =O, N&30 states are observed to have even colder coincident partners than the calculated u’=O states. If a contribution of the v’ = 1 states is included, the discrepancy becomes worse. Of the v =O states measured, only N= 17 appears to have a significant amount of coincident ZI’ = 1. To fit the N= 17 line shape data with the PST internal energy distributions and Email= cm-’ requires a total u = 1:v = 0 ratio of 0.5 & 0.1, significantly larger than the ratios previously observed in a molecular beam [S, 191 (0.15) or at room temperature [16, 191 (0.35). Interestingly, the fits to the low velocities of the v = 1, N = 7 and N = 11 states can be improved by including up to about 5% of a contribution from a v = 1, v’ = 1 channel. Improving the line

M. WY, G. E. Hall I Vector and scalar correlarions in the photodismciation of NCCN 51

shape fit would have the effect of worsening the agreement of the average energy in Table 2 for these two states.

Equally good fits to the wings and somewhat better fits at low velocities can be obtained by fixing the correlated internal energy distribution with a PST calculation using E,ir = 4800 cm-’ (as was used to describe the product distribution for a jet-cooled sample [5]) and calculating the fragment velocity with a larger available energy. The best energy in this model was found to be 5200 f 100

-‘. This apparently inconsistent model would iFappropriate if the dissociation had a small exit barrier that defined the dissociation threshold and gave approximately statistical energy partitioning at the barrier. The asymptotic products could then be accelerated to their final velocities consistent with a bond dissociation energy below the recently published values by about 700 cm-‘. This picture is in accord with the relatively flat-topped Doppler lines, indicative of a deficiency of the highest internal energy coincident states allowed by energy conservation. This barrier cannot be the centrifugal barrier, since that is already taken into account in the PST, and it does not change the asymptotic energies.

5. Discussion

The 700 cm-’ difference in Eavail deduced from the product distribution following dissociation in a skimmed molecular beam [5] and from the present kinetic energy analysis could be a result of hot band excitation in the thermal vapor. The absorption spectrum of NCCN vapor between 193 and 194 nm contains one strong feature assigned to the 1:44:, band of the ‘2; +-lx,’ system and a weak feature assigned to the 1;4: band of the IA; t ‘2: system (with about 500 cm-’ of vibrational energy), with about 75% of the total intensity in a background continuum [lo]. Only a minor contribution due to hot bands is therefore anticipated in this spectral region.

PST with an adjustable Eavsil value has been used in two quite different ways. Other workers [S, 7, $1 have used the fall-off population of the highest rotational states to estimate Esvsii. In the present analysis, Eavail has been adjusted to fit the maximum CM velocities of photofragments. The maximum velocities are dominated by the lowest rotational states of the coincident photoproducts, and so the changing rotational distributions with EaVar, are a minor part of the line shape fits. That E,,, estimated from the kinetic energies is larger

than the value estimated from the internal state distribution suggests that there are dynamic reasons for not populating the highest energetically allowed states.

The observed V-J correlations reinforce the argument that a dynamic bias affects the most energetic product states. The observed vector correlations can be expressed as an under-rep- resentation of some helicity levels (J projections quantized along the axis parallel to v), reducing the effective degeneracy below W+ 1 for the highest J levels. This would be manifested as a faster fall- off in rotational population at high rotational levels than predicted by the fully statistical PST for a given Eavail. The discrepancies in the shape of the product distribution may be approximated using a value of Eavair less than the true asymptotic value.

6. Conclusions

The photodissociation of NCCN at 193 nm has been reinvestigated using high-resolution transient absorption to measure Doppler profiles of collisionless CN photofragments. Using the red A-X system and a Ti:sapphire ring laser, the vector properties of the dissociation have been fully char- acterized. The predissociation is slow enough to wash away all memory of the laboratory polarization of the excitation step, and a J-dependent correlation of the velocity with the rotation axis has been observed, with u and J increasingly perpendicular in higher rotational states of CN. The maximum speeds observed for each quantum state detected are consistent with an available energy for dissociation of 5300 f 150 cm- ‘, about 700 cm-’ more than the difference between the average photon energy and the recently published bond dissociation energy [9]. Based on the average internal energies of the coincident CN’ photofragments, it seems unlikely that the total product distribution is as hot as a PST distribution with this available energy. Doppler experiments with a tunable photolysis wavelength would be helpful in narrowing the uncertainties in parent energy, as would a careful measurement of the total pop- ulations at the highest rotational levels formed at 193 nm in a thermal vapor. The existing Doppler data warrant comparison with more sophisticated models of dissociation in order to arrive at a dissociation model consistent with total product distributions, coincident product distributions and vector correlations.

52 M. Wi, G.E. Hull I Vector and scalar correlations in the pkotodissociation of NCCN

Acknowledgments

We are grateful to J. Halpem for sharing pre- prints of recent spectroscopic and photophysical studies of C,N,. This work was performed at Brookhaven National Laboratory under contract DE-AC02-76CH00016 with the US Department ofEnergy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences.

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Vector and scalar correlations in the photodissociation of NCCN

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