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Ketene photodissociation in the wavelength range 193-215 nm: The H atom production channel. Emma J. Feltham,* Rafay H. Qadiri, Emily E.H. Cottrill, Phillip A. Cook,** John P. Cole, Gabriel G. Balint-Kurti and Michael N.R. Ashfold School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K. Figures: 10 Tables: 4 Author for correspondence: Prof. M.N.R. Ashfold (address as above) Tel: + 44 (0)117 9288312/3 Fax: + 44 (0)117 9250612 e-mail: [email protected] Present addresses: * EPSRC, Polaris House, North Star Avenue, Swindon, SN2 1ET, U.K. ** Orange, Parkgate, 2000 Aztec West, Almondsbury, Bristol, BS32 4TE, U.K. 1 Abstract The speed and angular distributions of H atom products arising in the photodissociation of jet-cooled ketene (CH2CO) molecules following excitation at 193.3, 203.3, 209 and 213.3 nm have been investigated by H Rydberg atom photofragment translational spectroscopy. The observed product energy disposal is interpreted in terms of one photon absorption to the 1B1 electronically excited state, internal conversion to high lying vibrational levels of the ground state and subsequent unimolecular decay to yield the observed H (+ HCCO) products. H atoms resulting from secondary photolysis of H containing primary products (most probably singlet CH2 radicals) are evident in the measured spectra, especially at high photolysis laser pulse energies. The kinetic energy distributions of the primary H + HCCO products span all energetically accessible product internal energies, peaking at ~1170 cm-1 in the case of parent excitation at 213.3 nm, and rising to ~1450 cm-1 (when exciting at 193.3 nm). These distributions are reproduced, qualitatively, by the Statistical Adiabatic Product Distribution (SAPD) method proposed recently by Cole and Balint-Kurti (J. Chem. Phys., preceding paper). This method is based on the use of a quantum mechanical, J conserving, Rice-Ramsperger-Kassel-Marcus (RRKM) treatment and provides a prediction of the product quantum state distributions and the total kinetic energy release spectra. Accurate, quadratic configuration interaction, intrinsic reaction coordinates have been computed for both the lowest singlet (S0) and triplet (T1) potential energy surfaces of CH2CO. Quantum mechanical SAPD calculations have been performed using both surfaces; the results favour the conclusion that the dissociation occurs on the S0 surface. This conclusion is further supported by comparison of the calculated and previously measured CO product vibrational quantum state distributions arising from photodissociation at 193.3 nm. The variational RRKM method has also been used to compute the branching ratios for forming H + HCCO and CH2 + CO products on both the S0 and T1 surfaces. Different aspects of the SAPD model, such as the inclusion of quantum mechanical tunnelling, the attractiveness of the long-range inter-fragment potential and the assumed adiabaticity of the fragmentation, have been varied in order to shed light on the nature of the dissociation process and the possible origins of the differences between the model calculations and the experimental results. It is found that the agreement between the quantum mechanical statistical model predictions and the experimentally observed total kinetic energy release spectra for the H atom dissociation channel can be greatly improved if the contribution of lower fragment relative orbital angular momenta is increased over that required by the use of a purely statistical model. This finding is equivalent to the conclusion 2 that the dissociation is not entirely statistical, but that the dynamics of the break-up process plays some role. In particular the initial geometry of the parent molecule may restrict the body-fixed angles into which the final products can scatter and, through this, may restrict the relative orbital angular momenta to be on average smaller than that predicted by a purely statistical theory. 3 Introduction Ketene has been identified in interstellar space,1,2 and has long found use as a ~ photochemical source of methylene (CH2) radicals in both their ground ( X 3B1) and first excited ( ~a 1A1) electronic states. More generally, its photodissociation has proven to be a popular test case for the validation of theories of unimolecular dissociation.3 Ketene has a C2v equilibrium ~ geometry in its ground (S0, or X 1A1) electronic state. Its electronic absorption spectrum exhibits a long progression of apparently diffuse bands spanning the region 260-470 nm 4-56 followed, at higher energies, by several short vibronic progressions attributable to Rydberg excitations from the highest occupied molecular orbital (HOMO).7-8910 This HOMO is doubly occupied in the ground state. It has b1 symmetry and substantial C=C bonding character, but is also weakly C=O anti-bonding.. Ab initio theory11,12 associates the extensive near UV absorption system with a * electronic promotion, resulting in population of a valence excited state of 1A" symmetry (S1, 1A2 at C2v geometries), but cannot exclude the possibility that the corresponding T1 (3A") excited state makes some (spin-forbidden) contribution to the overall absorption. The first of the Rydberg excitations is associated with the orbital promotion 3sa1 2b1. The origin of the resulting S2 S0 (1B1 X1A1) transition appears as a diffuse band centred at a wavelength, ~ 215 nm and with a peak cross-section ~1.510-17 cm2 molecule-1.13 Three bands of similar appearance and progressively diminished cross-section appear at higher energy with a mean band separation ~1050 cm-1. These have been variously assigned to members of both the 30n or 4 0n progressions (n = 1-3), 11,12,14 where 3 and 4 are, respectively, the CH2 scissor and C=C stretching vibrations, while a recent comparison of the corresponding features in the ultraviolet absorption spectra of both CH2CO and CD2CO suggests contributions from excited levels involving 3, 4 and 2 (the C=O stretching vibration). 10 Most of the numerous previous studies of ketene photochemistry have concentrated on the channels leading to C=C bond fission following excitation within the extensive near UV absorption system,15-17 i.e. ~ H2CCO + h CH2 ( X 3B1) + CO CH2 ( ~a 1A1) + CO . (1) (2) Process (2) occurs via internal conversion (IC) from the initially populated S1 state to the ground state. As such, it provides a text-book example of a fragmentation occurring on a potential energy surface (PES) with no exit channel barrier. Careful studies at, and just above, the energetic threshold allow precise determination of the dissociation energy (30116 cm-1) of ground state 4 CH2CO molecules to singlet products.15 The electronic origin of the ~a 1A1 state of CH2 lies 3147 ~ cm-1 above that of the X 3B1 ground state.18 Process (1) is thus the lowest energy dissociation asymptote, but it is only accessible to those excited CH2CO(S1) molecules that undergo intersystem crossing (ISC), and dissociate on the T1 PES. Careful studies of the wavelength dependence of the CO product yield resulting from photolysis of jet-cooled CH2CO molecules have allowed characterisation of the height of the energy barrier (~1280 cm-1, measured relative ~ to the zero point energies of the CH2( X 3B1) + CO fragments) to dissociation on this T1 PES.15 Clearly, process (1) has to be the exclusive decay channel following excitation at photon energies less than the threshold for process (2) but, once over this threshold, the singlet products rapidly become dominant. For example, singlet products constitute >50% of the total dissociation yield at photon energies only 325 cm-1 above the channel (2) threshold19 and, when ketene is photolysed at 308 nm (~2350 cm-1 above the threshold for fragmentation channel (2)), the relative quantum yield of process (2) exceeds that of process (1) by at least a factor of ten.16,20,21 The present study focuses on the primary photochemistry of ketene molecules following excitation at higher energies, within the banded S2 S0 absorption system. fragmentation pathways now need to be considered, including: ~ H2CCO + h CH2( b 1B1) + CO >38450 cm-1)15,18 ~ HCCO( X 2A") + H >36800 cm-1)22 C2O + H2 >35560 cm-1). Additional (3) (4) (5) The wavenumbers in parentheses represent the respective energetic thresholds for forming the stated products in their lowest energy states. The thermodynamic threshold quoted for process (5) ~ is associated with formation of C2O fragments in their ground ( X 3) state, and has been derived using literature values for Δ f H 0o (CH 2 CO) 22 and Δ f H 0o (C 2 O) .23 The corresponding thermodynamic thresholds for forming C2O products in their metastable excited singlet ( ~a 1 and ~1 + b ) states will be, respectively, ~5270 cm-1 and ~8190 cm-1 higher in energy 23 and, given the extent of structural rearrangement involved, we anticipate that the actual thresholds for all of these H2 eliminations will be at yet higher energies due to the presence of activation barriers in the respective exit channels. Previous investigations of ketene photolysis at these shorter wavelengths have mainly involved excitation at the ArF excimer laser wavelength (193 nm). Analysis of the infrared (IR) emission from nascent CO fragments revealed them to be both rotationally and vibrationally excited;24,25 the deduced vibrational state population distribution was found to accord well with 5 that predicted by a statistical model assuming dissociation via process (2).24 Observations of ketenyl (HCCO) fragments, both by transient IR absorption spectroscopy 26 and by laser induced fluorescence (LIF),27-29 provide direct evidence for the participation of channel (4) at this ~ photolysis wavelength also. HCCO( X ) radicals show predissociation broadened absorption at excitation wavelengths shorter than 300 nm;30,31 Neumark and coworkers have identified CH(X2) and CH(a4) fragments, together with ground state CO molecules, as the products of this predissociation, but were unable to discern any contribution from the alternative H + C2O product channel.30,31 Visible emission observed following 212.5 nm photolysis of a room ~ temperature sample of CH2CO has been attributed to the CH2( b ~a ) transition,32 thereby suggesting a role for channel (3). The recent quantum yield estimates of Glass et al. 33 at 193 nm tend to contradict this conclusion, however. These latter workers used resonance absorption methods to monitor relative H atom yields following 193 nm photolysis of dilute ketene/Ar and ketene/H2 mixtures, together with the results of previous end product analysis studies, to infer a dominant role for channel (1), (quantum yield, 1 = 0.628), with 2 = 0.193 and 4 = 0.107. ~ Fragmentation pathway (5), forming C2O fragments specifically in their excited b 1+ state, was also deduced to contribute (~7.2% of the total dissociation yield), but this analysis implied negligible contribution from channel (3). The relative energies of the various parent excited states and product asymptotes discussed above are summarised in Fig. 1. If questions remain as to the relative importances of the various active dissociation channels following excitation of CH2CO molecules to their S2 excited state, they appear minor in comparison with the uncertainties regarding the actual fragmentation mechanism(s). The high value of 1 proposed by Glass et al. 33 in their study of CH2CO photolysis at 193 nm would suggest that the eventual dissociation occurs on a triplet PES, presumably accessed via ISC from the initially prepared S2 state. However, the deduced vibrational (following excitation at 193 nm) 24 and rotational (from photolysis at 230 nm) 34 energy disposal in the CO products has been modelled most satisfactorily on the assumption that these are formed together with CH2( ~a 1A1) co-fragments,24 while ab initio calculations of (limited regions of) the S2 PES have thus far failed to identify any energy barrier that might prevent CH2CO(S2) molecules dissociating directly via channel (3).11,12 Finally, we note that resonance Raman spectra of ketene molecules, recorded at several different excitation wavelengths in the range 200-217 nm, suggest that the initial motions away from the vertical (C2v) Franck-Condon region involve so-called C Is distortions in which the 6 C=C=O skeleton bends out of the CH2 plane35 - thereby hinting at somewhat more complex dynamics than suggested thus far by ab initio theory. The present study attempts to provide some clarification of this currently confused picture by applying the technique of H (Rydberg) atom photofragment translational spectroscopy (PTS) 36-38 to measure the velocity distributions of H atom products resulting from ketene photolysis in this same wavelength range. The results so obtained are then discussed in the context of a recently developed quantum mechanical, statistical, total angular momentum conserving theory (the Statistical Adiabatic Product Distribution or SAPD method) based on a variational RiceRamsperger-Kassel-Marcus (RRKM) treatment.39 This analysis supports the view that the eventual fragmentation occurs predominantly, if not exclusively, on the ground state PES. That being the case, it follows that there remains a pressing need for direct measurements of the various active product channels following UV photo-excitation of ketene, their respective quantum yields and the way these yields vary with excitation energy. Experimental H (Rydberg) atom PTS is a time-of-flight (TOF) technique, details of which have been described elsewhere. 38 The present studies were carried out in two apparatuses. The first has been described previously. 38 Its successor is very similar in design, but has longer side arms and a longer (58 cm), more efficient tripling cell in which the Lyman- radiation used in the H atom detection step is generated. The interaction volume in the re-designed apparatus is 57 cm from the MgF2 lens that defines the exit of the tripling cell, and the photolysis laser radiation is focussed using a 75 cm f.l. lens. In both cases a skimmed, pulsed, molecular beam of ketene, seeded in argon (typically a 10% mixture at a total pressure of 1 atm), is crossed at right angles by pulses of photolysis laser radiation. This is either the frequency tripled output of a dye laser (in the range 203215 nm, generated using a KDP and a BBO crystal in series) pumped by an injection seeded Nd:YAG pumped dye laser (Spectra Physics GCR-270 with PDL 2), focussed into the interaction volume with a plano-convex lens of 30 cm focal length, or the 193.3 nm output of an ArF laser (Lambda-Physik, Optex). The latter output is unpolarised, but angular distributions of recoiling H atom photoproducts generated using the frequency tripled dye laser radiation were measured using a polarisation rotator (Newport RFU ½ Fresnel rhomb) to align its polarisation vector, phot, at any user selected angle, , relative to the TOF axis. 7 After a short time delay (~10 ns) the resulting H atom photofragments are tagged, in the photolysis region, using a two colour, two photon, double resonance excitation to a metastable Rydberg state. This process involves the successive absorption of a Lyman- photon at 121.6 nm, which excites the H atom from the n = 1 to n = 2 level, and a second photon of wavelength ~366 nm to excite these n=2 atoms to Rydberg states with high principal quantum number (n ~ 80) lying just below the ionisation threshold. The Lyman- radiation is generated by first combining the output of a second Nd:YAG pumped dye laser operating at ~554.8 nm with the Nd:YAG laser fundamental radiation (1064 nm) to give photons of wavelength 364.6 nm. The resulting UV beam is then focused into the tripling cell containing an optimised phase matched mixture of Kr and Ar gas where third harmonic radiation at 121.6 nm is generated. 40 The 366 nm radiation required for the second stage of the tagging process is generated by the frequency doubled output of a second dye laser pumped by the same Nd:YAG laser, thereby ensuring the synchronicity of the two 'tagging' laser pulses. Ketene was prepared by refluxing acetone over an electrically heated tungsten filament at a temperature ~750 C, 41 i.e: CH2CO + CH4. (CH3)2CO (6) The ketene thus formed was collected using an acetone-dry ice slush bath at –78 C, purified by vacuum distillation, and stored in a bulb maintained in the dark in an acetone-dry ice slush bath to prevent dimerisation. IR spectroscopy was used to confirm successful production of ketene,42 free from any detectable acetone or other impurities. Results and Discussion H atom TOF spectra. TOF spectra of H atoms resulting from the photolysis of jet-cooled ketene molecules were recorded at four separate excitation wavelengths (193.3, 203.3, 209.0 and 213.3 nm) within the S2 S0 absorption system, at a variety of incident pulse energies and, in the case of the three longer wavelengths, at = 0, 90 and 54.7 (the so-called 'magic' angle). At any given pulse energy, neither the profile nor the magnitude of TOF signals recorded at any of the three longer wavelengths showed any discernible sensitivity to the alignment of phot relative to the TOF axis implying that the H atom products are formed with an isotropic distribution of recoil velocities. As fig. 2 illustrates, however, for the case of H atom TOF spectra recorded at an excitation 8 wavelength of 209.0 nm, the profiles are dependent upon the photolysis laser pulse energy. Similar effects were observed following ketene photolysis at both 203.3 and at 213.3 nm. These spectra show clearly that the relative importance of the early time signal increases with increasing pulse energy. These fast H atoms are also evident, as a high-energy tail, in the corresponding total kinetic energy release (TKER) spectra (fig. 3) that result when the TOF data are transformed using the expression 1 d TKER = mH 2 t 2 mH 1 . mR (7) mH and mR in eq. (7) are the mass of the H atom and of the radical partner fragment, respectively, d is the TOF length, and t is the measured time of arrival. In constructing fig. 3, mR is assumed to be 41.03 amu, appropriate for the HCCO radical. As fig. 3 shows, much of the signal associated with the high energy tail appears at TKER >11000 cm1. This is the maximum permissible kinetic energy for fragments arising from one photon dissociation via channel (4) given the energy conserving relationship h = D0(H-HCCO) + Eint(HCCO) + TKER, (8) where Eint(HCCO) is the internal energy in the HCCO primary fragments and we neglect any (small) internal energy in the jet-cooled parent ketene molecules. H atom count rates with the photolysis laser blocked are negligible, thus eliminating unintentional photolysis by the Lyman- probe laser radiation as the source of such fast H atoms. We therefore conclude that these fast H atoms, most evident at high photolysis pulse energies (and thus intensities), must arise either as a result of two photon excitation of the parent ketene molecule or, more probably, from secondary photolysis of H containing primary photofragments like HCCO (from process (4)) or CH2 (from processes (1) and (2)) arising in the one photon dissociation process. The transformation used in constructing fig. 3 assumed that the fragments partnering the observed H atoms were in all cases HCCO. If the fastest H atoms evident in the TOF spectrum actually arise from secondary photolysis of primary CH2 fragments then the appropriate TOF to TKER conversion (eq. (7)) should involve mR = 13.02 amu and the TKER of the fastest H atoms should actually be ~5% larger than shown in fig. 3. Given the substantial yield of slow H atom products, the TKER spectra in fig. 3 have also been corrected to accommodate the reduced detector solid angle seen by the slower recoiling H atom fragments which arises from the laboratory to centre of mass transformation. For an isotropic H atom recoil velocity distribution (as in the present case) this laboratory to centre of mass correction is assumed to be purely geometric in origin and simply 9 involves division of the measured H atom count associated with any given velocity sub-group by a factor [1(vP/vH)2]3/2, where vP and vH are, respectively, the velocities of the parent molecule and the H atom fragment. Given vP ~ 550 m s-1, this scaling factor is insignificant when TKER > 5000 cm-1 and even for TKER = 1000 cm-1 it introduces a <2% increase in the signal deduced simply by re-binning of the measured H atom TOF data. 43 Secondary photolysis effects were not discernible in the H atom TOF spectra recorded at 193.3 nm, where the parent absorption cross-section is much smaller, but the photolysis pulse energies were varied by a factor of ~2 only in this case. In the remainder of this article we seek to demonstrate that the fragmentation of ketene molecules following excitation to the S2 state proceeds via radiationless transfer – either directly, or indirectly (via the S1 state) – to the ground S0 state, and then to comment on the various reported TKER spectra and product quantum state distributions. Modelling the TKER spectrum of the H + HCCO products. The following discussion concentrates on TKER spectra obtained by transforming H atom TOF spectra resulting from photolysis at 213.3 nm and 193.3 nm (figs. 4(a) and (b)), where the parent absorption cross-sections are, respectively, largest and smallest. i) Simple product density of states model All of the derived spectra peak at low (but non-zero) TKERs, implying substantial internal excitation of the polyatomic partner fragment. The general form, and the isotropy, of the observed TKER distributions match well with those observed previously for other molecules – e.g. allene 43 which are considered to fragment by IC and subsequent unimolecular decay of the resulting highly vibrationally excited ground state molecules. As in that case, we find that the observed TKER distributions are reproduced reasonably well by an unashamedly approximate model which assumes population of all energetically accessible product vibrational states, and that the relative probability of forming products with any particular TKERi, P(TKERi), is simply the product of the HCCO vibrational state density at the complementary internal energy (i.e. (TKERmaxTKERi)) and the corresponding 3-D translational density of states (which we model as (TKERi)1/2). The product vibrational state densities were calculated using the harmonic fundamental wavenumbers listed in Table II of the preceding paper, and the resulting state density partitioned into 50 cm-1 wide energy bins. As fig. 4 illustrates, this approximate model which has also been used to reproduce the observed form of the product energy disposal in the 10 photolysis of allene and propyne (amongst others) at similar wavelengths 43 replicates the TKER distribution measured at 213.3 nm rather well, though it predicts a broader TKER distribution than that observed following photolysis at 193.3 nm. This simple model is clearly flawed, however, since it ignores conservation of total angular momentum, and neglects possible fragment rotational excitation; additionally, since the calculation is based solely on properties of the asymptotic fragments the prediction is insensitive to the detail of the PES (S0 or T1) on which the dissociation proceeds. The general form of a P(TKER) curve predicted by this simple model will always be similar to those shown in fig. 4 and is likely to be appropriate in situations where the dissociation proceeds without a barrier and one of the fragments is a light atom like hydrogen. This form will not always be correct, however. Indeed, as shown previously, 39 the P(TKER) curve in the case of a statistical fragmentation yielding two molecular fragments (such as process (2)) will peak at zero TKER. ii) Statistical Adiabatic Product Distribution (SAPD) model The concurrent in-house development of a quantum mechanical, statistical, explicitly total angular momentum conserving theory 39 based on a variational RRKM treatment 44,45 of unimolecular dissociation processes encouraged us to embark on a much more detailed modelling of this fragmentation process. Thus we calculated minimum energy paths from the equilibrium ~ configuration out to the H + HCCO( X 2A”) and CH2( ~a 1A1) + CO(X) product asymptotes on the S0 PES, along with the normal mode vibrational frequencies in the coordinate space orthogonal to these respective intrinsic reaction coordinates (IRCs). Details of these calculations, and the energy profiles so derived, were presented in the preceding publication. 39 The equilibrium geometry and the IRCs were computed using a hybrid density functional theory (B3LYP) together with a cc-pvdz (Dunning’s correlation consistent double zeta) basis set 46 as implemented in the Gaussian 47 code. The energies of the equilibrium configuration, the products and all points along the IRC (reaction coordinate) were then evaluated using the quadratic configuration interaction method 48 (QCISD(T)) using a cc-pvqz basis set. 46 Thus the energies used were actually high level QCISD(T) energies, but the normal mode vibrational frequencies and the geometries were evaluated using B3LYP density functional theory. Having evaluated the energy profiles along the IRCs and the normal mode vibrational frequencies in the coordinate space perpendicular to these paths, we were then able to determine the configuration point on each IRC at which the sum of states is a minimum, i.e. the location of the ‘transition state’ for subsequent calculation of the respective RRKM decay rate constants, for 11 every total angular momentum J and photon energy, h. Such analysis permits us to calculate the quantum yield for process (4) on the S0 PES, 4(S0) = k4S/(k2 + k4S), where k4S represents the ~ contribution to HCCO( X 2A") + H formation occurring on the S0 PES. This ratio is calculated to be 4(S0) =0.18 in the case of photoexcitation of ground state CH2CO(J = 0) molecules at 213.3 nm (equivalent energy, E = 560 kJ mol-1), rising to 4(S0) =0.26 at 203.3 nm and to 4(S0) =0.35 at the most commonly studied excitation wavelength, 193.3 nm. Averaging over a weighted distribution of J states appropriate for Trot ~ 25 K – a typical parent rotational temperature has negligible effect on these calculated values for 4(S0). 39 We recognise that CH2CO(S2) molecules could, in principle at least, also decay by intersystem crossing (ISC) and subsequent dissociation on, most probably, the T1 PES. Thus we have also calculated minimum energy paths connecting the equilibrium configuration to the H + ~ ~ HCCO( X ) and CH2( X 3B1) + CO(X) product asymptotes on the T1 PES, and the normal mode vibrational frequencies in the coordinate space orthogonal to these respective coordinates. As for the S0 state, 39 the energies along the reaction paths are evaluated at the QCISD(T)/cc-pvqz level and the geometries and normal mode frequencies at the B3LYP/cc-pvdz level. Table 1 lists the calculated dissociation energies and other relevant energetics calculated using both the B3LYP/cc-pvdz and the QCISD(T)/cc-pvqz methods for the triplet spin symmetry surface. The calculated normal mode frequencies and rotational constants are listed in Tables 2 and 3, respectively. Our QCISD(T) computed energy difference between the CH2(3B1) + CO product asymptote on the T1 PES and the CH2(1A1) + CO asymptote on the S0 PES is 38.85 kJ mol-1, as compared with the experimental value of 37.65 0.06 kJ mol-1. 49 Figure 5 shows calculated minimum energy pathways for the corresponding CC and CH bond fissions on the T1 surface, yielding 3CH2 + CO and H + HCCO products via reactions 1 and 4, respectively. Establishing these IRCs required several hundred B3LYP/cc-pvdz calculations; about twenty QCISD(T)/cc-pvqz calculations were then performed to yield reliable energetics along each IRC. As for the S0 PES, the normal mode vibrational frequencies perpendicular to the IRC were computed at each point along the reaction path (using the B3LYP/cc-pvdz method). These frequencies and the details of the paths on the singlet and triplet surfaces have been tabulated and are available as auxiliary material. 50 Both profiles, when calculated at the QCISD(T)/cc-pvqz level, display small barriers to dissociation. The calculated barrier height in the CC bond fission channel on the T1 PES (~1650 cm-1 defined relative to the asymptotic products) is in very reasonable accord with the experimentally determined value 12 (~1280 cm-1 15 ), but we can find no previous reports of the small (~600 cm-1) energy barrier identified in the CH exit channel on this PES. The effect of these barriers is to ensure that the critical geometries (transition states) derived in our variational RRKM treatment always fall at smaller bond extensions than for the corresponding bond fissions on the S0 surface. . Given the ab initio data for the T1 PES we can locate the critical configuration point R‡, at which the sum of states W(E,J) is minimised as a function of J and photon energy, along each of the reaction coordinates, and deduce the corresponding unimolecular decay rate coefficients k(E,J) k(E,J) = W ‡ ( E .J ) , h( E , J ) (9) where W‡(E,J) is the sum of rovibrational states with total angular momentum J at and below energy E evaluated at R‡, and (E,J) is the parent density of states at the corresponding E and J. 39 Figure 6(a) shows calculated rate constants k(E) for the CC and CH bond fission channels (1) and (4), respectively, on the T1 PES, after averaging over a distribution of J states appropriate for a parent Trot = 25 K, along with the sum of the two. Averaging over the thermal distribution of parent ketene rotational states makes negligible difference undetectable on the scale of the figure. As with the fragmentation of CH2CO(S0) molecules discussed previously, 39 the displayed values of the k4 rate coefficient are twice the initially computed values, in recognition of the reaction path degeneracy introduced by the indistinguishability of the two CH bonds. Comparison with figure 6 of the preceding paper 39 clearly shows that, at any given E, the calculated unimolecular decay rates on the T1 PES are larger than those for dissociation on the S0 PES. This is a consequence of the smaller well depth of the T1 as compared with the S0 PES (recall Fig. 1). Both W‡(E,J) and (E,J) are reduced as a result of the smaller well depth, but the reduction in the magnitude of (E,J) dominates and the overall unimolecular rate constant is increased by one to two orders of magnitude over the energy range considered here. Given such k(E) data, variational RRKM theory then allows estimation of the quantum yield, or branching ratio, for process (4), now defined as 4(T1) = k4T/(k1 + k4T), as a function of E, for any CH2CO molecules that undergo radiationless transfer to, and dissociate on, the T1 PES, where k4T ~ represents the contribution to HCCO( X 2A") + H formation occurring through this process. Figure 6(b) shows the energy dependence of the branching ratio for forming H + HCCO products following fragmentation on both the T1 and the S0 PESs (i.e 4(T1) and 4(S0), respectively). From the figure it is apparent that HC bond fission is relatively more important on the S0 than 13 the T1 PES. This reflects the smaller energy gap between the ketenyl and the methylene products on the S0 surface. As fig. 6(b) shows, we deduce that 4(T1) ~0.034 at E = 560 kJ mol-1 (corresponding to an excitation wavelength of 213.3 nm), rising to ~0.091 at E = 620 kJ mol-1 ( 193.3 nm). Note, however, that none of this discussion addresses the relative probabilities of IC and ISC from the initially prepared S2 state; these variational RRKM calculations merely provide a prediction of the relative importance of HC and CC bond fission for CH2CO(S2) molecules that fragment via ISC to the T1 or via IC to the S0 PESs. The preceding paper 39 demonstrates the way in which, given knowledge of the intrinsic reaction coordinate, the conserved and transitional modes at R‡ and the assumption that the fragment angular momenta (J1 and J2), the product orbital angular momentum (L) and the quantum numbers of the conserved vibrational modes all evolve adiabatically once R > R‡, it is possible to predict rate constants (Eint, E, J) associated with formation of products with a specific internal energy Eint. As the total energy is conserved, these rate constants, when plotted against the relative kinetic energy of the two fragments, yield the TKER spectrum of the system. ~ Figs. 7a and 7b present such calculated relative kinetic energy distributions of the H + HCCO( X ) fragments arising following initial excitations at 213.3 nm and 193.3 nm. Each of the figures show the experimentally measured TKER spectra together with spectra calculated using the SAPD method assuming dissociation on both the S0 and T1 PESs. Both predicted distributions peak at higher TKER (i.e. lower Eint) than is observed experimentally but the (intuitively more likely) assumption that dissociation occurs on the S0 PES, after spin allowed radiationless transfer, gives the better match. We have explored in some detail possible ways of modifying the model calculations to bring about better agreement with the experimental results. Dissociations associated with high L quantum numbers are found to favour formation of fragments with higher TKERs. Our initial calculations were based on density functional B3LYP calculations, which had been corrected to account for the difference between these and the more accurate QCISD(T) values determined both at the equilibrium geometry and for the asymptotic fragments. To check that this procedure was not significantly influencing the form of the predicted TKER spectrum, we re-computed the energies of all points along the reaction path on the S0 PES at the QCISD(T)/cc-pvqz level of theory. A power series expression in 1/R (where R is the length of the extending bond of interest) was used to join the energy of the ‘molecular’ calculation at largest R to the QCISD(T) computed energies of the separated fragments, as described more fully in ref. 39. Use of this more accurate energy profile along the dissociation coordinate caused no significant change to any of our results. 14 We also investigated whether inclusion of tunnelling in our calculations of the energy disposal in the H + HCCO fragments formed via dissociation on the S0 PES might improve the agreement between the calculated and experimental TKER spectra. This was achieved using a simple one-dimensional tunnelling formula developed by Nikitin, 51,52 but its inclusion led to no discernable change in the form of the calculated TKER spectrum. One of the underlying assumptions of the present model is the adiabatic nature of the dynamics from the critical (or transition state) geometry, out to the infinitely separated fragments. Recent exact dynamical calculations of fragmentation process (2) at energies a little above the dissociation threshold 53 have revealed a degree of non-adiabatic energy exchange in the exit channel, beyond the critical geometry. In that particular case, however, the effect of the non-adiabaticity appears to be to shift the product translational energy release in the opposite direction from that which would be needed in the present case to improve agreement with experiment. The conservation, or otherwise, of the body-fixed z component of the fragment rotational angular momentum, K, is a problematic issue. A crucial aspect of our model involves the tracking of the available kinetic energy for every set of assigned fragment quantum numbers as the fragments evolve from the transition state to the asymptotic fragments. If this available kinetic energy decreases to zero at any point, the fragment quantum states in question do not contribute to the TKER spectrum. To explore the effect of this implicit K-conservation we investigated a variant of the model in which the adiabaticity requirement on the K quantum number was relaxed so as to permit K to change and the energy associated with K to contribute to surmounting the centrifugal barrier on the S0 PES. Such relaxation of the K-conservation constraint was found to have only a very small effect. It in fact resulted in a small increase in the energy at which the computed TKER spectrum peaked (rather than the decrease that would be required to achieve better match with experiment). Table 4 compares the most probable energies in the measured TKER distributions with those resulting from the K-conserving calculations on the S0 PES. The peaks of the calculated distributions show an essentially linear shift to higher kinetic energy with increasing photon energy whereas, particularly in view of varying contributions made by H atoms from secondary photolysis, the peaks of the experimental TKER spectra show no obvious variation with the excitation frequency. Experiment and theory at each excitation energy can be brought into reasonable coincidence if, rather than assuming completely statistical, ergodic behaviour during the photon absorption, subsequent IC, and eventual break-up on the S0 PES, we assume that some (excitation energy dependent) portion of the available energy is localised in vibrational modes 15 that do not couple strongly to the other modes of the system. 53 Our knowledge of the radiationless transition(s) leading to population of the S0 PES is insufficient for us to be able to assess the likely validity of such speculation, or the nature of the required ‘localised’ vibrations, however. We now proceed to consider a possible dynamical modification to the TKER distributions predicted by the SAPD model. iii) Dynamical modification of the SAPD predictions The systematic differences between the experimental TKER spectra and those predicted by the SAPD model might reflect the fact that the underlying dynamics of the fragmentation is not completely statistical in nature54,55,56,57. Non-statistical dynamical effects could arise if, for example, bond stretching along the IRC occurred too fast to permit full sampling of all bending and torsional states, or if there was a preference for particular dissociation geometries (e.g. bond angles). Such dynamical influences might well result in a selective weighting of the orbital angular momentum quantum numbers for the relative motion of the two dissociating fragments. Detailed examination of the contributions made by different values of L to the TKER spectrum predicted by the SAPD model revealed that low L quantum numbers favour small kinetic energy releases. This suggested that it would be possible to achieve a better match between the experimentally observed and the predicted TKER spectra if the contributions associated with the various different L values in our calculations were weighted appropriately. Figure 8 shows the relative contributions associated with different L values in the SAPD modelling of the TKER spectra of the H + HCCO products following excitation at (a) 213.3 nm and (b) 193.3 nm. As fig. 9 illustrates, it is possible to obtain much better agreement with the experimental distributions measured at both wavelengths if we assume a scaling function S of the form S = exp[-L2], with = 0.001 (at 213.3 nm) and 0.0015 (at 193.3 nm). The revised weightings of the various L contributions after application of these distorting functions are shown in fig. 8 also. The distorting functions have been chosen so as to bring the peaks of the model spectra close to those measured experimentally. Agreement between theory and experiment remains imperfect, but we note the limitations of the experimental data. Photofragment translational spectroscopy experiments based on time-of-flight measurements such as are used in the present study cannot, by definition, measure zero kinetic energy particles, so discrepancies between experiment and theory at near zero kinetic energies could well be due to experimental limitations. There are also significant uncertainties regarding the contributions that secondary photolyses make to the measured TKER spectra. Such contributions almost certainly account for 16 the measured yield of H atoms with TKER > TKERmax that is particularly evident in the data recorded at 213.3 nm. In summarising this section, we note that the SAPD model reproduces the general form of the experimental TKER spectrum of the H + HCCO products arising in the near UV photolysis of CH2CO. Whether the eventual dissociation is assumed to occur on the S0 or T1 PES, the model successfully captures the observation that the distribution peaks at TKER > 0, and that there is negligible probability of forming products with the maximum kinetic energy allowed by energy conservation (TKERmax). The agreement with experiment is somewhat better if the product distribution is assumed to arise following IC and subsequent decay of ‘hot’ S0 molecules. Agreement with experiment can be further improved in either of two ways – by assuming that some portion of the available energy is locked up in vibrational modes and is not randomised amongst the other vibrational modes of the system on the timescale of the bond fission process, or that the dynamics of the dissociation is not completely statistical and that this may be modelled by distorting the statistical weighting of the orbital angular momenta of the relative motion of the two dissociating fragments. Modelling the vibrational state population distribution in the CO products. The form of the nascent CO product vibrational state population distribution resulting from 193 nm photolysis of ketene provides further support for the view that fragmentation following excitation at such wavelengths occurs following IC to the S0 PES. Figure 10 compares the experimentally determined CO vibrational state population distribution 26 with that predicted by the SAPD model assuming that the eventual fragmentation occurs on the S0 PES (i.e. via dissociation channel (2)) and on the T1 PES (channel (1)) PES, respectively. The calculated vibrational state population distribution is actually for a parent CH2CO sample with Trot = 25 K, but it is indistinguishable from that calculated for J = 0 parent molecules; we would not expect any significant difference in the form of this predicted vibrational state population distribution if we were to perform a more expensive calculation using the Trot value (300 K) appropriate for the experimental measurements. Again, the result of the comparison is not definitive, but the calculation employing the S0 PES provides the better fit with experiment. Clearly, the unambiguous route to establishing the relative importances of the IC and ISC routes to forming CO products following excitation of CH2CO molecules at 193.3 nm (and other near UV wavelengths), must involve direct detection of nascent singlet and/or triplet methylene fragments. 17 This is particularly so given the probability of secondary photolysis of the primary HCCO fragments – the products of which will certainly include CH and CO. 30,31 Implications for previous estimates of dissociation quantum yields. The present analysis strongly favours the view that dissociation of ketene molecules following excitation to their S2 state at wavelengths ~200 nm proceeds predominantly, if not exclusively, via internal conversion to the S0 state and subsequent unimolecular decay of these highly internally excited ground state species. pathways will be channels (2) and (4). That being so, the dominant fragmentation The quantum mechanical, statistical, total angular momentum conserving calculations based on a variational RRKM treatment reported here provide estimates of the wavelength dependence of the branching ratio between these two channels. Dynamical effects have been invoked as a possible explanation for deviations between the experimentally measured TKER spectra of the H (+ HCCO) products and those predicted by the SAPD model; such effects, if valid, could plausibly modify the wavelength dependent branching between channels (2) and (4) predicted in fig. 6(b) also. Even allowing for such dynamical effects, however, none of the preceding analysis would point to any significant role for product ~ channels (1) – forming 3CH2, (3) – leading to electronically excited CH2( b 1B1) fragments or (5) – involving elimination of H2 molecules and the formation of C2O radicals. Such a conclusion is in marked contradiction with the (indirect) quantum yield estimates reported by Glass et al., 33 who suggested 3CH2 as a major product and some formation of electronically excited C2O fragments via process (5). One other recent study, of HCNO and HCN product formation in the 193 nm photolysis of ketene in the presence of excess NO, 58 impacts on this discrepancy. These workers used time resolved mass spectrometry to determine yields of HCNO and HCN products and derived the values: HCNO = 0.78 0.18 and HCN = 0.19 0.04. 58 These yields were rationalised in terms of the competing reactions: CH2 + NO HCNO + H (10a) HCN + OH (10b) and HCCO + NO HCNO + CO (11a) HCN + CO2. (11b) The measured yields were shown to be broadly compatible with the ketene photolysis quantum yield estimates of Glass et al. 33 and the branching ratios k10a/k10, k10b/k10, k11a/k11 and k11b/k11 18 determined in previous Fourier transform infra red end product analyses, 59-61 although the measured HCN yield was rather higher than such an analysis would predict (but still within the combined uncertainties). 58 Under the relatively high pressure conditions of these experiments any methylene photoproducts will be rapidly quenched to, and react as, 3CH2. An equivalent analysis to that reported in ref. 58, but using the photolysis quantum yields 2 = 0.65 and 4 = 0.35 suggested by the current work, return values of 0.80 0.08 and 0.17 0.07 for HCNO and HCN – in quantitative accord with the experimental measurements. Conclusions The H atom products arising in the near UV (193.3 – 213.3 nm) photodissociation of jetcooled CH2CO molecules have been investigated by photofragment translational spectroscopy (PTS). The spectra of the primary H + HCCO products span all energetically accessible product internal energies, peaking in the range 1200 – 1500 cm-1 at all excitation wavelengths investigated. H atoms resulting from secondary photolysis of H containing primary products are also clearly evident in the measured spectra, especially at the longer wavelengths and at high photolysis laser pulse energies. The observed energy disposal in the primary products is most plausibly interpreted in terms of one photon absorption to the S2 excited state, radiationless transfer to high vibrational levels of the S0 state and subsequent unimolecular decay. To gain further insight into this fragmentation process we have used the SAPD method, a recently developed, quantum mechanical, statistical, total angular momentum conserving theory based on a variational RRKM treatment, 39 together with computed quadratic configuration interaction, intrinsic reaction coordinates for both the S0 and T1 PESs, to predict the measured TKER spectra for both product channels. The method was also used to predict rate constants and branching ratios for forming H + HCCO and CH2 + CO products on both of these PESs, and CO product vibrational state distributions resulting from CH2CO photolysis at 193.3 nm. Comparison between the predicted CO vibrational state population distributions and previous experimentally measurements supports previous suggestions 26 that dissociation occurs primarily, if not exclusively, on the S0 PES. Such an analysis leads to the conclusion that the most abundant H containing primary products arising in the photodissociation of CH2CO molecules at wavelengths ~ 200 nm will be CH2( ~a 1A1) fragments. This, when considered together with previous reports that the major products of HCCO photolysis in this wavelength range are CH + CO, 30,31 encourages the view that secondary photolysis of 1CH2 radicals is the main source of the 19 secondary H atoms observed at higher photolysis fluences. Given these conclusions, and the obvious ease of inadvertent secondary photolysis, there must be some doubt concerning the validity of the recently reported (indirect) quantum yield estimates of Glass et al. 33 following 193.3 nm photolysis of CH2CO and, in particular, the deduced dominance of channel (1) leading to formation of 3CH2 radicals. There would appear to be a need for further, direct, measurements of the molecular products of this photolysis before we can have a secure knowledge of the fragment channel branching ratios and product quantum yields. Acknowledgements The authors wish to acknowledge the financial support of the Leverhulme Trust and the EPSRC, in the form of equipment grants, a post-doctoral fellowship (EJF), studentships (to RHQ, PAC and JPC), and equipment grants. We are also grateful to EPSRC for providing facilities through the U.K. Computational Chemistry facility on which some of the larger ab initio calculations were performed. Finally, we thank K.N. Rosser for his outstanding technical support, Dr N. Taniguchi (Kyoto University) and R. Perez Garcia for their contributions to the experimental work, Dr. J.N. Harvey for advice and assistance with the molecular electronic structure calculations and Professor R.N. Dixon FRS for his help and interest in this work. 20 Figure Captions Fig. 1. Schematic energy level diagram illustrating various of the lower energy dissociation limits available to ketene. The shaded areas represent schematically the extent of the S1 S0(v=0) and S2 S0(v=0) absorptions; the depth of the shading within any one band is intended to indicate the energy dependence of the relative absorption strength. Fig. 2. H atom TOF spectra resulting from photolysis of jet-cooled ketene molecules at 209 nm, using incident pulse energies of (a) 1.5 J , (b) 9 J and (c) 21 J pulse-1 with, in all cases, = 90. Each is the summation of signal accumulated over 20,000 photolysis laser pulses and has been arbitrarily scaled so as to appear with the same peak intensity. Fig. 3. TKER spectra obtained by conversion of the TOF spectra shown in fig. 2 using eq. 7, assuming mR = 41.03 amu, and corrected for the velocity dependence of the H atom detection efficiency. The dashed vertical line at high TKER indicates the maximum kinetic energy release possible assuming that all of the observed H atoms arise via primary fragmentation process (4). Fig. 4. TKER spectra obtained by conversion of H atom TOF data from photolysis of jet-cooled ketene molecules at (a) 213.3 nm (using incident pulse energies, E ~ 1.5 J and = 90 (open circles)) and at (b) 193.3 nm (unpolarised light, with E ~ 130 J) together with, in each case, that ~ calculated for the H + HCCO( X ) fragments using the simple product density of states model (solid curve). Fig. 5. Variation of electronic energy with dissociating bond length on lowest triplet spin symmetry potential energy surface. Reaction 4, C-H bond fission; Reaction 1, CC bond fission. The distance is that between the atoms connected by the dissociating bond. The energies are calculated using the QCISD(T)/cc-pvqz method (at 20 geometries in each case) and are given relative to the computed energy of CH2CO(S0) at its equilibrium geometry as predicted using the DFT/B3LYP/cc-pvdz method. 21 Fig. 6. (a) Energy dependent rate constants k1 and k4T (i.e. for CC and CH bond fission) on the T1 PES calculated using eq. (9), after averaging over a distribution of parent J states appropriate for Trot = 25 K, together with the sum (k1 + k4T). (b) Calculated energy dependences of the quantum yield for H + HCCO product formation on the T1 and S0 PESs [4(T1) = k4T/(k1 + k4T), 4(S0) = k4S/(k2 + k4S)]. Fig. 7. Comparison of experimental TKER spectrum obtained by conversion of H atom TOF data from photolysis of jet-cooled ketene molecules at (a) 213.3 nm using incident pulse energies ~ 1.5 J and = 90 and (b) unpolarised 193.3 nm radiation with E ~ 130 J pulse-1 - ( ), with those ~ predicted for the H + HCCO( X ) products using the statistical ab initio quantum mechanical model assuming eventual break-up on the S0 PES ( ) and the T1 PES ( ). Fig. 8 Plots showing the relative contributions associated with different L values in the SAPD modelling ( ) of the TKER spectra of the H + HCCO products following excitation at (a) 213.3 nm and (b) 193.3 nm, together with the distorted distributions obtained by applying a scaling function of the form S = exp[-L2] ( ) that provide a better match with experiment as illustrated in fig. 9. Fig. 9 Plots comparing the experimental ( ) TKER spectra measured at (a) 213.3 nm and (b) 193.3 nm with those predicted using the SAPD model ( ) and when using the distorted L weightings illustrated in fig. 8 ( ). Fig. 10. Comparison of the previously reported experimental CO vibrational state population distribution resulting from 193.3 nm photolysis of ketene (from ref. 26) ( ) and that predicted by the SAPD model assuming that fragmentation occurs on the S0 ( ) and the T1 ( ) PESs. 22 Table 1 Calculated dissociation energies, energies of other key critical configurations, and asymptotic energy separations associated with T1 PES, including zero-point energy contributions. TS = transition state Energies in kJ mol-1 B3LYP/cc-pvdz QCISD/cc-pvqz 237.770 210.599 ------- 217.871 144.064 88.269 ------- 107.932 H2CCO(T1) 3CCO + H2 216.162 190.958 E [H2CCO(S0) H2CCO(T1)] 212.276 225.220 E [3CH2 1CH2] 51.513 38.848 E [3CCO 1CCO] 106.072 80.292 H2CCO(T1) HCCO + H H2CCO(T1) HCCO---H(TS) H2CCO(T1) 3CH2 + CO H2CCO(T1) 3CH2---CO (TS) Table 2 Computed normal mode frequencies for critical geometries and asymptotic fragments associated with the T1 PES. Normal Mode Frequencies / cm-1 H2CCO(T1) 3251 3091 1780 1409 1055 981 783 454 HCCO---H(TS) 3308 2074 1230 634 541 518 374 265 3 CH2--- CO(TS) 3323 3104 2069 1098 423 331 228 139 HCCO 3323 2088 1254 567 503 499 3 CCO 2025 1099 368 367 3 3363 3114 1051 CH2 23 390 Table 3 Computed rotational constants for critical geometries and asymptotic fragments associated with the T1 PES. 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