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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 ~1.510-17 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 203215 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 cm1. 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.
(TKERmaxTKERi)) 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 CC and
CH 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 CC 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 CH 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 CC and CH 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 CH
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 HC 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 HC and CC 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, CC 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 CC and CH 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.
Rotational Constants / GHz
A
B
C
H2CCO(T1)
109.6
11.1
10.1
HCCO---H(TS)
117.3
9.7
9.0
CH2---CO (TS)
74.8
7.0
6.4
HCCO(2A”)
976.1
10.8
10.7

11.4
11.4
1637.6
247.8
215.3
3
3
CCO
3
CH2
Table 4
Most probable energies in the P(TKER) spectra obtained experimentally and through use of the
statistical ab initio quantum mechanical model assuming eventual break-up on the S0 PES of
CH2CO.
Photon Wavelength / nm
Most probable TKER / kJ mol-1
Experiment
Calculation
193.3
16 ± 1
28.58
203.3
14 ± 1
23.8
209.0
19 ± 1
21.6
213.3
14 ± 1
20.2
24
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b) Geometries of the intrinsic reaction coordinate for the H+HCCO dissociation process on the T 1 PES,
c) Normal mode vibrational frequencies in space perpendicular to the reaction coordinate for the S 0 surface,
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26