Photodissociation dynamics of A state ammonia molecules. I. State dependent μ-V correlations in the NH2(ND2) products

Article abstract of DOI:10.1063/1.471367

The H(D) Rydberg atom photofragment translational spectroscopy technique has been applied to a further detailed investigation of the photodissociation dynamics of NH₃ and ND₃ molecules following excitation to the lowest two (v₂=0 and 1) vibrational levels of the first excited (A ¹A′₂) singlet electronic state. Analysis of the respective total kinetic energy release spectra, recorded at a number of scattering angles Θ [where Θ is the angle between the ε vector of the photolysis photon and the time-of-flight (TOF) axis], enables quantification of a striking, quantum state dependent, μ-v correlation in the NH₂(ND₂) products. The spatial distribution of the total flux of H(D) atom photofragments is rather isotropic (β_lab～0)- However, more careful analysis of the way in which the TOF spectra of the H(D) atom photofragments vary with Θ reveals that each H+NH₂(D+ND₂) product channel has a different partial anisotropy parameter, β_lab(v₂,N), associated with it: The H(D) atom ejected by those molecules that dissociate to yield NH₂(ND₂) fragments with little rotational excitation largely appear in the plane of the excited molecule (i.e., perpendicular to the transition moment and the C₃ axis of the parent, with β tending towards -1). Conversely, the H(D) atoms formed in association with the most highly rotationally excited partner NH₂(ND₂) fragments tend to recoil almost parallel to this C₃ axis (i.e., β→+2). Such behavior is rationalized in the context of the known potential energy surfaces of the A and X states of ammonia using a classical, energy and angular momentum conserving impact parameter model in which we assume that all of the product angular momentum is established at the point of the conical intersection in the H-NH₂(D-ND₂) dissociation coordinate. We conclude by reemphasizing the level of care needed in interpreting experimentally measured β parameters in situations where there is averaging over either the initial (parent) or final (product) quantum states.

Full text of DOI:10.1063/1.471367

Photodissociation dynamics of à state ammonia molecules. I. State dependent μv
correlations in the NH2(ND2) products
David H. Mordaunt, Michael N. R. Ashfold, and Richard N. Dixon
Citation: The Journal of Chemical Physics 104, 6460 (1996); doi: 10.1063/1.471367
View online: http://dx.doi.org/10.1063/1.471367
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˜
Photodissociation dynamics of A state ammonia molecules. I.
State dependent ␮-v correlations in the NH2(ND2) products
David H. Mordaunt,a) Michael N. R. Ashfold, and Richard N. Dixon
School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
͑Received 25 July 1995; accepted 12 January 1996͒
The H͑D͒ Rydberg atom photofragment translational spectroscopy technique has been applied to a
further detailed investigation of the photodissociation dynamics of NH3 and ND3 molecules
following excitation to the lowest two ͑ 2ϭ0 and 1͒ vibrational levels of the first excited
v
1
˜
(A A2Љ) singlet electronic state. Analysis of the respective total kinetic energy release spectra,
recorded at a number of scattering angles ⌰ ͓where ⌰ is the angle between the ⑀ vector of the
photolysis photon and the time-of-flight ͑TOF͒ axis͔, enables quantification of a striking, quantum
state dependent, ␮- correlation in the NH ͑ND ͒ products. The spatial distribution of the total flux
v
2
2
of H͑D͒ atom photofragments is rather isotropic ͑␤labϳ0͒. However, more careful analysis of the
way in which the TOF spectra of the H͑D͒ atom photofragments vary with ⌰ reveals that each
HϩNH ͑DϩND ͒ product channel has a different ‘‘partial’’ anisotropy parameter, ␤ ͑ 2 ,N͒,
v
2
2
lab
associated with it: The H͑D͒ atom ejected by those molecules that dissociate to yield NH2͑ND2͒
fragments with little rotational excitation largely appear in the plane of the excited molecule ͑i.e.,
perpendicular to the transition moment and the C3 axis of the parent, with ␤ tending towards Ϫ1͒.
Conversely, the H͑D͒ atoms formed in association with the most highly rotationally excited partner
NH2͑ND2͒ fragments tend to recoil almost parallel to this C3 axis ͑i.e., ␤→ϩ2͒. Such behavior is
rationalized in the context of the known potential energy surfaces of the ˜A and ˜X states of ammonia
using a classical, energy and angular momentum conserving impact parameter model in which we
assume that all of the product angular momentum is established at the ‘‘point’’ of the conical
intersection in the H–NH2͑D–ND2͒ dissociation coordinate. We conclude by reemphasizing the
level of care needed in interpreting experimentally measured ␤ parameters in situations where there
is averaging over either the initial ͑parent͒ or final ͑product͒ quantum states. © 1996 American
Institute of Physics. ͓S0021-9606͑96͒01615-0͔
I. INTRODUCTION
state out of plane ͑umbrella͒ bending mode, reflecting the
change in minimum energy configuration invoked by optical
excitation from the pyramidal ground state to the trigonal
Photodissociation studies that are fully state resolved,
both in the parent molecule and in the resulting products,
provide some of the most detailed insight possible into the
mechanisms and dynamics of molecular predissociation.
5,9,16
1
˜
planar A A2Љ state.
Such a structured absorption cross
section allows state selective excitation to specific Ј vibra-
v2
n
˜
tional levels of the A state. Each 20 vibronic band in the
Ammonia molecules in their first excited singlet state ͑the
˜
A
1A2Љ state͒ constitute one model system with properties
room temperature spectrum will consist of many overlapping
rovibronic transitions, each of which is lifetime broadened to
an extent that varies sensitively with H͑D͒ isotopic substitu-
tion and with the vibrational quantum number͑s͒ of the ex-
cited state level.1,5,8–13,21,26,32 These dramatic variations in
excited state lifetime have been rationalized in terms of vi-
appropriate for this purpose; indeed, given the number and
˜
range of recent studies of the dissociation dynamics of A
state ammonia molecules,1–33 this system must already have
acquired the status of being a text book example of a state-
selected molecular photodissociation.
Ammonia is a minor constituent of the atmospheres of
the outer planets and their satellites, in which photochemical
fission produces many important free-radical species which
can then participate in further, secondary reactions.34 Pho-
tolysis of ammonia initiates the formation of hydrazine. Con-
densation of this product competes with further photolysis,
yielding N2. This has been advanced as a possible mecha-
nism for the origins of nitrogen in the atmospheres of many
of the outer planets and their satellites, specifically Titan.34
˜
brational predissociation on the A state potential energy
surface.8,10,14,15,24 The A state of ammonia is quasibound;
˜
dissociation from the lowest vibrational levels ͑i.e., those
with Ј р 1͒ occurs predominantly via H͑D͒ atom tunneling
v2
through a barrier in the exit channel leading to the products
HϩNH2͑DϩND2͒. This barrier has been shown to arise as a
natural consequence of Rydberg (3s)→antibonding valence
2
*
͑␴ ͒ orbital evolution as one N–H͑N–D͒ bond is extended;
1
1
˜
˜
the barrier height is least ͑and tunnelling consequently most
The A A2Љ Ϫ X AЈ1 absorption band of ammonia is
facile͒ at planar geometries.8,14,15,24 A state ammonia mol-
˜
dominated by a well resolved progression in Ј , the excited
v2
ecules carrying more than one quantum of out of plane bend-
ing excitation, or excitation in other vibrational modes, have
sufficient internal energy that, if redistributed appropriately,
a͒
Present address: Department of Chemistry, University of California, Ber-
keley, CA 94720, USA.
6460
J. Chem. Phys. 104 (17), 1 May 1996
0021-9606/96/104(17)/6460/12/$10.00
© 1996 American Institute of Physics
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6461
dissociation can occur by passage over ͑rather than through͒
this exit channel barrier.
higher kinetic energy resolution. This allowed more detailed
determination both of the eigenvalues and the relative popu-
lations of the individual quantum states of the resulting
Planarity, or otherwise, affects not just the transmission
rate through ͑or over͒ the barrier in the N–H ͑N–D͒ bond
fission channel, but also the asymptotic product correlations.
At strictly planar geometries the ground electronic state of
ammonia correlates with the excited asymptote associated
NH2(X) photofragments.25 These data, in turn, permitted the
˜
first detailed analysis of the LIF excitation spectrum of the
˜
NH2(X) fragments resulting from near ultraviolet photolysis
of NH3.30 The greater detail provided through use of the
Rydberg tagging scheme also provided the first clear indica-
tions that the distribution of product recoil velocity vectors,
v, was markedly anisotropic, and that the detailed form of
with H͑D͒ atoms together with NH2͑ND2͒ products in their
2
˜
˜
excited A A1 state, whilst the first excited A state of the
parent correlates with the ground state products—an H͑D͒
2
˜
this anisotropy was
HϩNH2(X)v,N product channel being monitored.
a
function of the particular
atom plus an NH2͑ND2͒ fragment in its ground X B1 state.
˜
˜
Away from planarity, both the ground and the excited A state
of ammonia have the same (1AЈ) electronic symmetry. Thus
the ˜X and ˜A state surfaces of the parent can only ‘‘cross’’ at
Here we present new high resolution experimental mea-
surements of the kinetic energy distributions of the frag-
ments formed following photoexcitation via both the 000 and
planar geometries and, consequently, there is a conical inter-
section between these two surfaces, at planar geometries, in
1
˜ ˜
20 vibronic bands of the AϪX transitions of both NH3 and
˜
ND3. Complementary analyses of the fragments arising from
the corresponding photolyses of the much less studied mixed
isotopomers of ammonia, NH2D and NHD2, are described in
the accompanying publication.37 The present high resolution
data afford refined eigenvalues for rovibrational levels of
ground state ND2 fragments with rotational quantum number
NϳKa and for the bond dissociation energies D0͑H–NH2͒
and D0͑D–ND2͒. More importantly, it also provides the first
rigorous study of the previously recognized25 product quan-
tum state dependent correlations between the electric vector
of the photolysis laser ͑⑀͒, the transition dipole moment ͑␮͒,
and the recoil velocity vectors ͑v͒. This nonclassical stere-
ochemical behavior has been quantified for dissociations fol-
lowing excitation via the origin and the 210 vibronic bands of
the H–NH2͑D–ND2͒ exit channel. The parent A state surface
is therefore characterized by a deep well in this exit channel,
which acts as a funnel, accelerating most of the dissociating
trajectories through this narrow region of configuration space
˜
onto the X state surface and, hence, to the ground state prod-
ucts. Indeed, for parent excitation at all wavelengths longer
˜
than ca. 206 nm ͑i.e., for A state NH3 molecules with
Ј
v2
р 3 ͑р4 for the case of ND3͒ ground state fragments are the
sole products of this bond fission, excited state product for-
mation being an endoergic process.
The conical intersection has also been shown to have a
profound effect on the quantum state population distributions
within the resulting NH2͑ND2͒ fragments. An early laser-
˜
induced fluorescence ͑LIF͒ study of the NH2(X) fragments
˜ ˜
the AϪX transitions of both NH3 and ND3, by recording
resulting from ArF laser photolysis of a room temperature
NH3 sample yielded what, at the time, appeared to be an
impenetrably complex excitation spectrum, which merely
served to indicate that the nascent fragments were born with
substantial amounts of internal excitation.3 The first detailed
measure of the energy disposal within these products was
achieved using the photofragment translational spectroscopy
technique pioneered by Welge and co-workers.20,23,35 In
these early studies,20,23 the H atom photoproducts were
threshold ionized, at source, using a two color two-photon
excitation scheme, resonance enhanced at the one photon
energy by the nϭ2 Rydberg state, and their subsequent
times-of-flight monitored. Time-to-energy conversion
yielded a spectrum of the total fragment kinetic energy re-
total kinetic energy release spectra for several different val-
ues of ⌰ ͓the angle between ⑀ and the time-of-flight ͑TOF͒
axis͔ under otherwise strictly controlled experimental condi-
tions in order to determine effective laboratory frame recoil
anisotropy ͑␤͒ parameters for the dissociation processes
leading to each of the individual photofragment quantum
states; i.e., what we might view as a series of ‘‘partial’’ ␤
parameters. The observed variations in ␤ with product N are
reproduced, qualitatively at least, using a classical, energy
and angular momentum conserving, close-coupling impul-
sive model which approximates NH3 as a pseudotriatomic
͓H–N–͑H2͔͒ and assumes that all product angular momen-
tum is generated at the point of the conical intersection in the
H–NH2 dissociation coordinate. Discrepancies between the
absolute magnitudes of the experimentally measured labora-
tory frame anisotropy parameters, ␤lab , and those predicted
by this simple model are rationalised in terms of incomplete
alignment of the photoexcited parent molecules.
˜
lease, the analysis of which showed that the NH2(X) frag-
ments resulting from dissociation of NH3 molecules follow-
ing photoexcitation into each of the first seven bending
˜
vibrational levels ( Ј ϭ 0–6) of the A state were formed
v2
with little vibrational excitation, but with substantial
amounts of rotational excitation, specifically distributed in
the form of a-axis rotation. Such markedly nonstatistical en-
ergy disposal was shown to be a natural consequence of the
conical intersection channelling ͑and indeed enhancing͒ any
out-of-plane bending motion in the parent NH3 molecule into
a-axis rotation in the fragment.23
II. EXPERIMENT
The photofragment translational spectrometer, the pho-
tolysis laser, and the laser systems used to ‘‘tag’’ the atomic
H͑D͒ fragments have all been described previously38–42 and
will only be summarized briefly here, along with operational
aspects specific to the present studies. A skimmed pulsed
supersonic beam of ammonia ͑or ammonia-d3͒—typically
More recent studies of the dissociation from the Ј ϭ 0
v2
˜
and 1 levels of A state NH3 employing the alternative neutral
͑Rydberg͒ H atom tagging scheme36 yielded significantly
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6462
FIG. 2. TKER spectrum for the HϩNH2 fragments resulting from photoly-
sis of a jet-cooled sample of NH3 molecules at 46 200 cmϪ1 with ⑀phot
aligned perpendicular to the TOF axis. Combs above the spectrum indicate
˜
the expected kinetic energies of NH2(X) fragments in their 2ϭ0 and 1
v
FIG. 1. H atom TOF spectrum resulting from photolysis of a jet-cooled
sample of NH3 molecules at 46 200 cmϪ1 with ⑀phot aligned perpendicular to
the TOF axis. The inset shows the early time part of this spectrum on a
much expanded time base.
levels with NϭKa and NϭKaϩ1, if we assume a bond dissociation energy
D0͑H–NH2͒ϭ37 115 cmϪ1
.
previously,20,23,25 the structure evident in this TOF spectrum
seeded as a 1% mixture in argon and held at a total backing
pressure of ca. 1 bar—is intercepted at right angles by the
output of the three pulsed laser systems used to effect the
photolysis and to ‘‘tag’’ the nascent H͑D͒ atom fragments.
The recoil kinetic energy distribution of these tagged atoms
is determined by recording their collision free TOF to a de-
tector ͑a Johnston multiplier, type MM1-SG͒ positioned
along the third orthogonal axis with its front face a well-
defined distance from the interaction region ͑825.6 mm for
most experiments but, simply because of the way the lab was
set up at the time, only 425.6 mm for some photolyses via
is indicative of the population of quantum states with NϳKa
˜
in the NH2(X) partner. Subsequent to the previous studies,
however, the eigenvalues of these levels are now known with
sufficient precision30 that a spectrum such as this actually
serves to provide the most accurate calibration of the dis-
tance separating the interaction region and the detector, d, in
our photofragment translational spectrometer. Figure 2
shows the total fragment kinetic energy release ͑TKER͒
spectrum derived from the TOF spectrum shown in Fig. 1
assuming a flight path dϭ825.6 mm, the value that affords
the minimum standard deviation when least squares fitting
the observed kinetic energies of the assigned features in Fig.
2 against their documented eigenvalues. The combs over the
spectrum reinforce the earlier findings that the most popu-
1
˜ ˜
the NH3(AϪX) 20 band͒. The photolysis photons are pro-
vided by a Nd-YAG pumped dye laser system ͑Quanta-Ray
GCR-5 plus PDL-3͒ operating with the dye DCM, the output
of which is first frequency doubled ͑in KDP͒; the doubled
͑2␻͒ and fundamental ͑␻͒ outputs are then mixed in BBO to
yield the required third harmonic ͑3␻͒ radiation. A home-
built Soleil–Babinet compensator positioned between the
two nonlinear crystals served to reorient the respective po-
larizations of the ␻ and 2␻ beams so as to optimize the sum
frequency generation process. The ⑀ vector of the resulting
3␻ radiation could be rotated ͑relative to the TOF/detection
axis͒, without any lateral beam displacement, using a New-
port RFU 1/2 Fresnel rhomb. The 3␻ radiation was then
focused ͑50 cm f.l. lens͒ so as to spatially overlap, and im-
mediately precede ͑⌬tϽ5 ns͒, the H͑D͒ atom tagging pulses
͑fully described previously38–42͒ in the interaction region.
˜
lated states of the NH2(X) product are indeed those with
ϭ0 and NϭK , with lesser contributions from states with
v
v
a
ϭ0 and NϭK ϩ1 and from the corresponding NϭK and
a
a
K ϩ1 rotational states built on the 2ϭ1 level. Naturally,
v
a
the availability of such precisely calibrated spectra allows a
further refinement of the value for the bond dissociation en-
ergy D0͑H–NH2͒: Energy conservation requires that
Eint͑NH3)ϩh␯ϭD0 H–NH ͒ϩE ͑H)ϩEkin͑NH2)
͑
2
kin
ϩEint͑NH2).
͑1͒
Under conditions of supersonic expansion the chosen pho-
Ϫ1
˜
tolysis wavelength ͑␯ϭ46 200 cm ͒ excites predominantly
the R0(1) and R1(1) transitions, thus allowing us to estimate
a value of ca. 18 cmϪ1 for Eint͑NH3͒, the average internal
energy of the parent molecules undergoing photoexcitation.
The input side of the energy balance ͓Eq. ͑1͔͒ is thus tightly
III. RESULTS
A. Bond dissociation energies
defined and, given the known NH2(X) eigenvalues,30 we can
˜
Figure 1 shows the TOF spectrum of H atoms resulting
from photolysis of a jet-cooled NH3 sample at 46 200 cmϪ1
,
derive a very precise value for the total kinetic energy ͑in the
˜
the wave number of the predissociation broadened R0(1)
and R1(1) transitions and the peak of the R branch in the
jet-cooled absorption band of the NH3(AϪX) origin transi-
tion. The polarization vector of the photolysis laser was
aligned perpendicular to the H atom TOF axis. As
laboratory frame͒ of the fragments HϩNH (X), ϭ0, Nϭ0.
v
2
We estimate the parent beam velocity ͑along an axis or-
thogonal to the TOF axis͒ at 450Ϯ75 m sϪ1. Applying the
laboratory to center-of-mass energy Jacobian results in a 9
cmϪ1 reduction in the deduced total fragment kinetic ener-
˜ ˜
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6463
other isotopomers of ammonia to similar accuracy. Here we
concentrate on a comparable analysis yielding D0͑D–ND2͒.
Discussion of the H–N and D–N bond strengths in the
mixed isotopomers NH2D and NHD2 is reserved for a com-
panion paper. The lower ͑ Ј ϭ 0 and 1͒ vibronic levels of the
v2
˜
A
state of ND3 predissociate an order of magnitude more
slowly than the corresponding levels in NH3,1,8–10 with the
0
1
˜ ˜
result that the ND3(AϪX) 00 and 20 bands show ͑at least
partially͒ resolved rovibronic structure ͑Fig. 3͒ and the initial
photoselection of the parent state selection can be that much
better defined. Figure 4 shows total kinetic energy release
spectra for the DϩND2 fragments ͑derived using the previ-
ously determined value of d͒ obtained following photoexci-
tation of jet-cooled samples of ND3 ͑1% mixture in Ar͒ at
two different wave numbers—46 708 and 46 724 cmϪ1, cor-
responding to the Q1(1) and R0(0) transitions in the
FIG. 3. Calculated absorption profiles ͑at 15 K͒ for the 000 and 201 bands of
the ˜AϪ˜X transitions of NH
ND (˜AϪ˜X) origin band—and two orthogonal polarizations.
͓͑a͒ and ͑b͒, respectively͔ and ND3 ͓͑c͒ and
3
3
͑d͔͒, with the dominant rovibronic transitions indicated in each case. Spec-
troscopic parameters for the respective excited states are from Ref. 32.
These spectra are also dominated by progressions associated
with rovibrational levels of the partner fragment with
NϳKa . In the case of ND2(X), however, the energies of the
˜
gies, and a value for D0͑H–NH2͒: 37 115Ϯ20 cmϪ1 ͑4.602
Ϯ0.002 eV͒. This serves to further refine both the value de-
termined in the earlier photofragment translational
spectroscopy experiment in which the H atoms were moni-
tored via the ion,20 and the currently recommended literature
value.43
higher NϳKa levels are not yet available from high resolu-
tion optical spectroscopy. Thus the data shown here, which
are substantially better resolved than was apparent in the
earlier TOF study of this system23 ͑in which the D fragments
were monitored via the ion͒, provides the best measure yet of
the eigenvalues of these highly rotationally excited levels of
˜
the ND2(X) fragment.
Having established a precise measure of the flight path,
d, we are in a position to determine bond strengths for the
Our assignments were guided by comparison with esti-
FIG. 4. TKER spectra for the DϩND2 fragments resulting from photolysis of a jet-cooled sample of ND3 molecules at 46 708 cmϪ1 ͓͑a͒ and ͑b͔͒ and 46 724
cmϪ1 ͓͑c͒ and ͑d͔͒ with ⑀phot aligned, respectively, parallel ͓͑a͒ and ͑c͔͒ and perpendicular ͓͑b͒ and ͑d͔͒ to the TOF axis. Combs above each spectrum indicate
the expected kinetic energies of ND2(X) 2ϭ0 fragments with NϭKa and NϭKaϩ1 if we assume a bond dissociation energy D0͑D–ND2͒ϭ38 010 cmϪ1
.
˜
v
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
6464
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
˜
mated eigenvalues for the NϭKa levels of ND2(X) calcu-
lated using
a
‘‘semirigid bender’’ Renner–Teller
2
Hamiltonian44,45 with the bending potentials ͑for the X B1
˜
2
˜
and A A1 states͒ optimized by fitting the existing NH2
data30 with an appropriate change of masses. The calculated
term values were then refined by least squares to fit the ex-
perimental data. Experimental and predicted eigenvalues for
˜
the NϳKa rovibrational levels of ND2(X) are listed in the
Appendix. Having established the comb of NϭKa rovibra-
tional energy levels it is then a straightforward matter to
determine the total recoil energy of the D atoms formed in
˜
association with ND2(X), ϭ0, Nϭ0 fragments and thus,
v
after, the necessary small lab to center-of-mass energy cor-
rection, to establish a value for D0͑D–ND2͒ϭ38 010Ϯ20
cmϪ1. As shown in more detail in the following paper, the
difference between D0͑D–ND2͒ and D0͑H–NH2͒ is wholly
consistent with the zero-point energy differences between the
respective parents ͑ND3 and NH3͒ and products ͑ND2 and
NH2͒.
B. Product quantum state dependent vector
correlations
A previous H atom photofragment translational spectros-
copy study25 of the near UV photolysis of NH3 showed,
qualitatively, that the relative intensities of the various peaks
appearing in the total kinetic energy release spectra such as
those shown in Figs. 2 and 4 were a sensitive function of ⌰,
the angle between ⑀ and the TOF axis. This implies that the
fragmentation channels leading to the different HϩNH2
product quantum states have different associated anisotropy
FIG. 5. Plots showing the way in which total detected H atom flux, QH ͑i.e.,
integrated over all TOF’s͒ resulting from NH3 photolysis at ͑a͒ 46 200 cmϪ1
0
Ϫ1
͑within the AϪX 00 band͒ and ͑b͒ 47 069 cm ͑within the 210 band͒ varies
as a function of ⌰, the angle between ⑀phot and the TOF axis. For conve-
nience, the vertical scaling has been chosen such that this ratio of H atom
fluxes is set to unity at the most favored laboratory scattering angle.
˜ ˜
netic energies in both sets of spectra, which appears as a
pedestal for EϽ3000 cmϪ1 in each of the spectra shown in
Fig. 6. As discussed more fully in the following paper, we
attribute this signal to an alternative predissociation mecha-
nism ͑internal conversion to high levels of the ground state͒
which will lead to a much more nearly statistical distribution
parameters, ␤͑ 2 ,N͒. To further elucidate on the nonclassical
v
angular distribution of photofragments resulting from pho-
˜
tolysis via the A state of ammonia, we recorded TOF spectra
of the H atoms formed following dissociation of the 00 and
1
˜
2 levels of A state NH3 ͑out to tϭ380 ␮s͒ for a range of ⌰
values Ϫ0°, 15°, 30°, 45°, 60°, 75°, and 90°—while all other
experimental conditions were maintained, as near as pos-
sible, identical. The angular dependence of the total H atom
flux, QH͑⌰͒, for excitation via both the 000 and 201 bands, is
shown in Fig. 5, while the resultant total fragment kinetic
energy release spectra at a selection of these angles are dis-
played in Figs. 6 and 7. ͑The latter set of spectra were re-
˜
over all of the energetically available NH2(X) product quan-
tum states. For the purposes of the present analysis, this un-
derlying continuum signal has been removed by least squares
fitting an appropriate function and subtracting its contribu-
tion from the experimental result. From the remainder, we
can obtain best estimates of the ⌰ dependence of the relative
˜
populations P( 2 ,N;⌰) of the various NH2(X) product
v
corded using a shorter flight path, 425.6 mm.͒
˜
quantum states arising solely from dissociation on the A state
˜
The corresponding NH2(X), 2 , N rovibrational quan-
v
surface via the normalization
tum state population distributions were estimated via simu-
lation of the individual spectra.46 These simulations pro-
W
2 ,N;⌰͒
QH ⌰͒
͑
͑v
P
2 ,N;⌰͒ϭ
.
͑2͒
͑v
˜
ceeded as follows. The eigenvalues for the NH2(X) partner
͚ ͚ W 2 ,N;⌰͒ ͚⌰QH ⌰͒
͑v
͑
N
v
2
photofragment are known. Thus we can produce a ‘‘spec-
trum’’ of ␦ functions, each of which is then convoluted with
a kinetic energy dependent Gaussian line shape function
given by ⌬E/cmϪ1 ͓full width at half maximum ͑FWHM͔͒
ϭ25ϩ0.0007E, where E is the corresponding total kinetic
energy release, in order to reproduce the experimental reso-
lution. The only adjustable parameters then required to
model the experimental spectra are the individual peak
Representative plots for many of the HϩNH2 product chan-
nels resulting from photolysis via the 000 and 201 bands of the
˜ ˜
NH3(AϪX) transition are shown in Figs. 8 and 9, respec-
tively. Given the recoil anisotropy relation
1
P
2 ,N;⌰͒ϭ
1ϩ␤ 2 ,N͒P2 cos ⌰͒ ,
͑v
͑3͒
͑v
͓
͑
͔
4␲
where P2͑cos ⌰͒ϭ12͑3 cos2 ⌰Ϫ1͒, we can then estimate a
partial anisotropy parameter ␤( 2 ,N) for each of these rovi-
heights, W( 2 ,N;⌰). At this point we should comment
v
briefly on the rising background at the lowest fragment ki-
v
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6465
FIG. 6. Representative TKER spectra for the HϩNH2 products resulting from fragmentation of a jet-cooled sample of NH3 molecules following photoexci-
˜ ˜
tation within the AϪX 00 band at 46 200 cmϪ1. These illustrate the way in which the detailed form of this spectrum depends on the relative orientation of ⑀phot
0
˜
and the TOF axis. Combs above each spectrum indicate peaks associated with NH (X) fragments in their 2ϭ0 and 1 levels with NϭKa and NϭKaϩ1.
v
2
brational product state channels simply by least squares fit-
ting the observed P( 2 ,N;⌰) in terms of Eq. ͑3͒ with
D0͑H–NH2͒ and D0͑D–ND2͒. However, the most notable
and original observation, and the one meriting discussion, is
the product state dependent recoil anisotropy. A product state
dependent anisotropy parameter is not entirely without pre-
cedent. For example, the near UV photodissociation of HI
v
␤( ,N) as the only unknown. The resultant ␤( 2 ,N) are
v2
v
reported in Figs. 10 and 11. These show that, for NH3 disso-
0
˜
ciation via the 0 level of the A state, ␤( 2 ,N) ranges from
v
˜
2
2
ca. Ϫ0.7 in the case that the resulting NH2(X) products are
yields iodine atoms in both their P1/2 and P3/2 spin–orbit
states; the recoil of the former are consistent with a ␤ param-
eter of ca. ϩ2 ͑i.e., recoil parallel to the ⑀ vector of the
photolysis source͒ while the latter arise via a perpendicular
transition ͑␤ϳϪ1͒.47 This is a somewhat trivial example,
reflecting the fact that the near UV photons excite two over-
lapping electronic transitions ͑the transition moments for
which are, respectively, parallel and perpendicular to the in-
ternuclear axis͒ which correlate with the two different spin–
orbit states of atomic iodine. More pertinent to the present
work are recent observations of subtle differences in the ef-
fective ␤ parameters for forming various low rotational states
of the NO(X) products resulting from near threshold ͑ca. 396
formed with little rotational excitation to ca. ϩ1.4 ͑for the
highest NϭKa product states permitted by energy conserva-
tion͒. The observed ␤( 2 ,N) parameters for dissociation via
v
1
˜
the 2 level of the A state ͑Fig. 11͒ show an even greater
sensitivity to the angular momentum and total kinetic energy
release; dissociation channels leading to low N products
show ␤ϳϪ1 ͑characteristic of a perpendicular transition; i.e.,
the detected H atom recoils in the plane perpendicular to the
C3 axis of the parent͒ whilst the most rotationally excited
products arise via a process characterized by a ␤( 2 ,N)
v
value of ca. ϩ2 ͑i.e., the detected H atoms recoil parallel to
this axis͒.
nm͒ photolysis of NO ͑Ref. 48͒ and for the ϭ0 and ϭ1
v
v
2
IV. DISCUSSION
NO(X) products resulting from NO2 photolysis at both 351
and 355 nm,49 although our understanding of the number and
nature of the excited electronic states of NO2 involved in
these dissociations precludes particularly detailed interpreta-
tion of these results.
This latest study of the near UV photodissociation of
jet-cooled ammonia molecules confirms earlier conclusions
regarding the very specific channeling of excess energy into
a-axis rotation of the ground state NH2͑ND2͒ fragments, and
provides refined eigenvalues for levels of ND2(X) with
NϳKa and for the respective bond dissociation energies
˜
In contrast, the very striking product N-dependent ␮, v
correlations observed in the present work are amenable to
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6466
FIG. 7. Representative TKER spectra for the HϩNH2 products resulting from fragmentation of a jet-cooled sample of NH3 molecules following photoexci-
˜ ˜
tation within the AϪX 20 band at 47 069 cmϪ1. These illustrate the way in which the detailed form of this spectrum depends on the relative orientation of ⑀phot
1
˜
and the TOF axis. Combs above each spectrum indicate peaks associated with NH (X) fragments in their 2ϭ0, 1, and 2 levels with NϭKa .
v
2
detailed explanation. They are an inevitable consequence of
the combined requirements of energy and angular momen-
tum conservation during the passage through, and ultimate
fragmentation at, the conical intersection in the
H–NH2͑D–ND2͒ dissociation coordinate. In what follows
we account for the general form of the observed product state
dependent ␮, v correlations using an extension of the close-
coupling impulse model41,50 developed to account for the
observed rotational state population distribution in the
OH(X) products resulting from the Lyman-␣ photolysis of
˜
FIG. 8. NH (X, 2 ,N) quantum state population distributions, P(N), de-
v
2
˜
rived from the experimental spectra displayed in Fig. 6 for ⌰ϭ͑a͒ 0°, ͑b͒
FIG. 9. NH (X, 2 ,N) quantum state population distributions, P(N), de-
v
2
30°, ͑c͒ 60°, and ͑d͒ 90° ͑ࡗ, 2ϭ0, NϭKa ; ᭿, 2ϭ0, NϭKaϩ1; छ,
rived from the experimental spectra displayed in Fig. 7 for ⌰ϭ͑a͒ 0°, ͑b͒
v
v
ϭ1, NϭK ; ᭺, 2ϭ1, NϭKaϩ1; the joining lines are included simply
30°, ͑c͒ 60°, and ͑d͒ 90° ͑ࡗ, ϭ0, NϭK ; ᮀ, ϭ1, NϭK ; ᭺, 2ϭ2,
v2 v2
NϭKa ; the joining lines are included simply to guide the eye͒.
v2
to guide the eye͒.
v
v
a
a
a
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6467
FIG. 10. Plots highlighting the variation of the deduced anisotropy
parameters, 2 ,N) associated with channels leading to
␤
(
v
lab
˜
HϩNH (X, 2 ,NϳKa) produces resulting from photolysis of NH3 at 46 200
v
2
cmϪ1 ͑000 band͒ ͑ࡗ, 2ϭ0, NϭKa ; ᭿, 2ϭ0, NϭKaϩ1; छ, 2ϭ1,
v
v
v
NϭK ; ᭺, 2ϭ1, NϭKaϩ1 products͒. The solid curves show the result of
v
a
model calculations employing Eqs. ͑8͒–͑10͒ and assuming a value of ϩ1.1
for the alignment parameter A0 ͑see text for further discussion͒.
H2O. This purely classical model requires conservation of
the total energy and angular momentum, but also involves a
number of simplifying assumptions. The ammonia molecule
is treated as a pseudotriatomic ͓͑H2͒–N–H͔. As discussed
earlier, fragmentation to ground state products involves pas-
sage through the conical intersection in the H–NH2 dissocia-
tion coordinate. The model assumes that bond rupture is in-
stantaneous at this point of intersection and that it is at this
point that the final angular momentum of the products is
established; i.e., that this point of conical intersection would
represent the ‘transition state’ for the scattering wave packet.
FIG. 11. Plots highlighting the variation of the anisotropy parameters,
˜
␤
(
2 ,N) associated with channels leading to HϩNH (X, 2 ,NϳKa)
v
v
lab
2
products resulting from photolysis of NH3 at 47 069 cmϪ1 ͑201 band͒ ͑ࡗ,
ϭ0, NϭK ; ᮀ, ϭ1, NϭK ; ᭺, 2ϭ2, NϭKa products͒. The solid
v2
v2
v
a
a
Given our knowledge of the potential energy surfaces for the
A˜ and ˜X states of ammonia and the earlier classical trajec-
curves show the result of model calculations employing Eqs. ͑8͒–͑10͒ and
assuming a value of ϩ2.0 for the alignment parameter A0 ͑see text for
further discussion͒.
tory calculations,24 it is unrealistic to expect the impulsive
force to be purely along the dissociating N–H bond—indeed,
if this was the case, we should expect the bulk of the avail-
able energy to be partitioned into product translation. A more
realistic view is that the conical intersection generates a sub-
stantial out of plane torque, which carries through as product
angular momentum.
the H atom recoil velocity recoil , and its reduced mass
v
␮
. Given our assumption that the torque acts at the
H–NH
2
point of surface intersection, basic geometry implies that
We begin by considering the angular momentum of the
bNϭRCI sin ␣,
͑5͒
NH2 photofragments, jNH . This must equal the vector sum
2
of the angular momentum generated by the recoiling H atom,
lH , and any angular momentum initially present in the parent
where RCI is the H–NH2 distance at the conical intersection
and ␣ is the final angle of recoil measured relative to the D3h
plane of the excited state molecule as shown in Fig. 12. Thus
we can write
(JNH ). Given that the parent molecules in the present study
3
are internally ‘‘cold,’’ this latter contribution will be negli-
gible. Thus,
͉
jNH
͉
Ϸ
͉
lH͉
ϭbN␮
recoilϭRCI sin ␣␮
.
vrecoil
v
HϪNH
H–NH
2
2
2
jNH ϭϪlHϩJNH ϷϪlH .
͑4͒
2
3
͑6͒
The angular momentum associated with the recoiling H atom
is the cross product of its recoil momentum and its perpen-
dicular displacement from the center of mass. The magnitude
of lH can be expressed in terms of an impact parameter bN ,
Simple energy conservation ͓Eq. ͑1͔͒ allows us to write
h␯ϪD0 H–NH ͒ϭ1 ␮
ϩEint͑NH2͒,
͑7͒
2
͑
vrecoil
2
2
H–NH
2
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6468
tively, being negative for the low N product states, approach-
ing zero at intermediate N and then becoming strongly posi-
tive for the highest NϳKa product states. Thus we conclude
that low angular momentum states are created when the H
atom is ejected perpendicular to the C3 top axis of NH3, but
that the combination of energy and angular momentum con-
servation requires that the recoil velocity vectors of those H
atoms that are formed in association with the highest NϭKa
product states must be aligned almost parallel to this top
axis. It should be noted that for Kaϭ21 and this total energy
Eq. ͑8͒ is inapplicable with RCIϭ0.196 nm. Thus this prod-
uct channel must become populated with an impact param-
eter bN larger than the chosen value of RCI , thereby indicat-
ing a limitation of the assumption of simple rectilinear
trajectories through a single action point.
FIG. 12. Illustration of the impact parameter model used to account for the
experimentally observed correlation between the recoil velocity, v, and the
rotational angular momentum, j, of the NϩNH2 products resulting from near
UV photolysis of jet-cooled NH3 molecules. The model treats NH3 as a
pseudotriatomic molecule ͓͑H2͒–N–H͔ and assumes that all product angular
momentum is established at the point of the conical intersection between the
X˜ and ˜A state potential energy surfaces of the dissociating parent molecule
͑see text for further details͒.
Finally we need to address the fact that our measure-
ments are made in the laboratory, not the body fixed, frame
and, although the trends in the experimentally derived
␤ ( 2 ,N) values observed for dissociation via the 00 and 21
v
lab
˜
levels of A state NH3 are very similar, their absolute magni-
tudes differ by some 30% ͑see Figs. 10 and 11͒. This reflects
a combination of two factors, neglected in our discussion
thus far: parent alignment, and the finite time scale of the
fragmentation process.25 Concentrating on the former first;
the respective photoexcitation processes produce excited
state populations with differing degrees of alignment, which
should be reflected in the measured lab frame anisotropy
parameters according to
1
2
v2
recoil is the total kinetic energy of the recoil-
H–NH
2
where
␮
ing fragments. Rearranging Eqs. ͑6͒ and ͑7͒ so as to elimi-
nate recoil , and reexpressing
͉
jNH
͉
in terms of N ͑ϵKa in
v
2
this model͒, we obtain
1/2
N Nϩ1͒ប
͓ ͑
͔
sin ␣ϭ
.
1/2
RCI͕2␮
h␯ϪD H–NH ͒ϪE ͑NH ͒]
͑
͖
0 2 int 2
͓
H–NH
2
͑8͒
␤
labϭA0 J ,K ͒ P cos ␣͒ .
͑10͒
͑
͑
Ј
Ј
͗
͘
2
Thus we have established a simple relationship between
the out-of-plane recoil angle ␣ ͑in the body-fixed frame of
the molecule͒ and the final rotational angular momentum of
the products. The corresponding anisotropy parameter, ␤ ͑in
the body fixed frame with a parallel transition dipole͒ asso-
As Fig. 3 shows, the jet-cooled absorption associated with
the NH3(AϪX) 20 band is dominated by the R0(0) transi-
tion, for which the excited state alignment parameter A0 will
take the limiting value ϩ2.0, and our impact parameter
1
˜ ˜
model thus predicts ␤ ( 2 ,N) values ranging from Ϫ1 to
v
ciated with each
͉
,N product channel is therefore
lab
v2
2 ,N͒ϭ2P2 cos ␲/2Ϫ␣͒
͔
͘
ϩ2 ͓Eq. ͑10͔͒. However, the corresponding transition is sym-
␤
͑v
͓
͑
˜ ˜
metry forbidden in the NH3(AϪX) origin band and, under
3N Nϩ1͒ប2
the prevailing experimental conditions, our photoexcitation
will involve ͑predominantly͒ the predissociation broadened
R0(1) and R1(1) lines, having relative intensities ca. 2:1 at
15 K. The spatial alignment parameters associated with these
two excitations are ϩ1.0 and ϩ0.5, respectively, with the
weighted mean ca. ϩ0.83. This would imply that the result-
ing excited state molecules would precess such that the plane
containing the nuclei makes an average angle of ca. 62° with
the transition dipole ␮. In practice, the experimental
͑
ϭ
Ϫ1.
͑9͒
2␮R2CI
EavailϪEint͑NH2͒]
͓
Note from Eqs. ͑8͒ and ͑9͒ that, for a given available energy
and RCI , there is an upper limiting value of N for which
these equations are applicable. This occurs when a product
channel is closed at finite RCI by a high centrifugal barrier.
Quantifying RCI is not trivial, since the ‘‘point’’ of coni-
cal intersection is in fact a surface involving four of the six
dimensions needed to represent the complete potential en-
ergy surface of NH3. For the purpose of this calculation we
assume a value of RCIϭ0.196 nm derived from inspection of
Figs. 2 and 4 of Ref. 15, but a 10% variation in this value
would have little effect on the overall conclusions that fol-
␤ ( 2 ,N) values measured following excitation via the
v
lab
˜ ˜
NH3(AϪX) origin band are less degraded than would be
predicted by including this value of A0 in Eq. ͑10͒. This is
understandable given the finite time scale of the dissociation
process. The parent absorption spectrum shows predissocia-
tion broadened linewidths of ca. 38 cmϪ1 ͑FWHM͒,10,12,26
implying an excited state lifetime with respect to fragmenta-
tion ͑ca. 1.4ϫ10Ϫ13 s͒ that is short in comparison with one
complete rotational period for an NH3 molecule with Jϭ1.
Thus it should come as little surprise that the recoil anisotro-
low. The calculated values so obtained for the NH2
͉ 2ϭ0,
v
NϭKa products arising from photolysis via the 21 level of
͘
˜
Ϫ1
NH3(A) at 47 069 cm are shown by the smooth curve
superimposed upon the experimental data in Fig. 11͑a͒.
Clearly, the general form of the calculated ␤( 2 ,N) values
reproduces the trends of the measured ␤ ( 2 ,N) values for
v
˜ ˜
pies we observe following excitation via the NH3(AϪX) ori-
v
lab
this and the other sets of populated states almost quantita-
gin band are ͑i͒ smaller than those we measure following
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6469
TABLE I. Observed and calculated term values ͑in cmϪ1͒ for levels of the
X
tirely attributable to the much poorer alignment of the ex-
2B1 state of ND2 .
˜
cited state molecules (A0ϭϩ0.5); note that these two JЈϭ1
levels differ in total energy by just 2.6 cmϪ1
.
2ϭ0
2ϭ1
v
v
NϭKa
Obs. Calc.͑a͒ Calc.͑b͒
NϭKaϩ1 NϭKaϩ2
NϭKa
V. CONCLUSIONS
Ka
Calc.͑b͒
Calc.͑b͒
Calc.͑a͒
0
0
19
64
136
234
358
506
680
877
1097
1339
1603
1888
2193
2517
2860
3221
3600
3995
4406
4832
5273
5728
6197
6679
7174
7681
8200
8730
9270
9821
0
19
64
136
234
357
506
679
876
1096
1338
1602
1886
2191
2515
2857
3218
3595
3989
4399
4824
5264
5718
6186
6668
7162
7668
8186
8716
9257
9809
11
40
96
179
287
421
581
765
973
1204
1457
1732
2028
2345
2680
3034
3406
3796
4202
4624
5062
5514
5981
6462
6956
7464
7983
8515
9058
9613
10 178
32
72
139
232
351
496
666
861
1100
1120
1168
1244
1348
1479
1637
1820
2027
2258
2512
2788
3085
3402
3739
4093
4466
4855
5261
5682
6119
6569
7034
7511
8001
8503
9017
9542
10 077
10 623
11 178
H ͑Rydberg͒ atom photofragment translational spectros-
copy has been applied to a further detailed investigation of
the photodissociation dynamics of NH3 and ND3 molecules
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
64
136
234
356
506
following excitation to the lowest two ͑ 2ϭ0 and 1͒ vibra-
v
1
˜
tional levels of the first excited (A AЉ2) singlet electronic
state. Analysis of the respective total kinetic energy release
spectra confirm earlier conclusions that, in each case,
the NH2͑ND2͒ fragments are formed with little vibrational
excitation but with high levels of rotational excitation,
specifically distributed in the form of rotation about the
a-inertial axis. The present work provides refined values for
the respective bond dissociation energies: D0͑H–NH2͒
677
874
1080
1322
1587
1874
2181
2509
2856
3222
3606
4008
4426
4861
5311
5776
6256
6749
7256
7777
8309
8854
9411
9980
10 559
1096
1340
1604
1886
2192
2516
2857
3221
3600
3996
4408
4843
5270
5723
6200
6686
7181
7693
ϭ37 115Ϯ20 cmϪ1, D0͑D–ND2͒ϭ38 010Ϯ20 cmϪ1
.
The most striking aspect of the present work, however,
is the particularly clear demonstration of, and quantification
of, the way in which the measured recoil anisotropy param-
eter depends on the particular quantum state in which the
NH2͑ND2͒ product is formed. The spatial distribution of the
total flux of H͑D͒ atom photofragments is fairly isotropic
͑␤labϳ0͒. However, more careful analysis of the way in
which the TOF spectrum of the H͑D͒ atom photofragment
varies with ⌰, the angle between ⑀ and the TOF axis, reveals
that each HϩNH2͑DϩND2͒ product channel in fact has a
different effective anisotropy parameter, ␤lab , associated
with it. The H͑D͒ atom ejected by those molecules that dis-
sociate to yield NH2͑ND2͒ fragments with little rotational
excitation appear largely in the plane of the excited molecule
͑i.e., perpendicular to the transition moment and the C3 axis
of the parent, with ␤ tending towards Ϫ1͒. Conversely, the
H͑D͒ atoms formed in association with the most highly ro-
tationally excited partner NH2͑ND2͒ fragments tend to recoil
almost parallel to this C3 axis ͑i.e., ␤→ϩ2͒. Such behavior
1
˜
excitation of the fully aligned NH3(A,2 ) molecules but ͑ii͒
not as degraded as might be predicted in the limit that the
excited state alignment was allowed to develop over several
rotational periods. The solid curves in Fig. 10 are fits to the
experimental data derived using Eqs. ͑8͒–͑10͒ and an ‘‘ef-
fective’’ A0 value of ϩ1.1.
Our measurements involving ND3 are less extensive in
the sense that we only made measurements with two or-
thogonal photolysis laser polarisations, but they do involve a
very high degree of initial state selection. The angular depen-
dence of the data shown in Fig. 4 are entirely consistent with
all of the foregoing discussion. Excitation at 46 724 cmϪ1
has been rationalized in the context of the known potential
energy surfaces of the ˜A and ˜X states of ammonia using a
classical, energy and angular momentum conserving impact
parameter model in which we assume that all of the product
angular momentum is established at the ‘‘point’’ of the coni-
cal intersection in the H–NH2͑D–ND2͒ dissociation coordi-
nate. Other simple systems where we can anticipate that such
product state dependent ␮, v correlations might be observ-
able are ͑obviously͒ the heavier Group V hydrides, but also
˜ ˜
invokes the R0(0) transition of the ND3(AϪX) origin band;
the resulting excited state molecules having JЈϭ1 and
KЈϭ0 will be fully aligned (A0ϭϩ2.0). Once again, not-
withstanding the longer excited state lifetime with respect to
dissociation ͑ca. 1.3ϫ10Ϫ12 s͒, we observe a marked
N-dependent ␮, v correlation in the products as predicted in
the original theoretical treatment of such correlations.51 This
correlation is much less evident in the data taken at 46 708
cmϪ1 ͓Figs. 4͑a͒ and ͑b͔͒. In this latter case we are exciting,
predominantly, the Q1(1) transition, leading to population of
the JЈϭ1, KЈϭ1 level and the reduced correlation is en-
TABLE II. Potential energy parameters for ND2(X 2B1) used for calcula-
tions (b) of Table I.
˜
fsϭ3.0ϫ105(cmϪ1ÅϪ1
͒
fbϭ33 271.2 ͑cmϪ1 radϪ2
͒
hϭ12 023.6 ͑cmϪ1
␪0ϭ76.0 ͑deg͒
͒
r0ϭ1.0 ͑Å͒
c1ϭϪ167.8 ͑cmϪ1
͒
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
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˜
Mordaunt, Ashfold, and Dixon: Photodissociation of A state ammonia molecules. I
6470
APPENDIX: TERM VALUES FOR ROTATIONAL
any bent triatomic molecules where photodissociation occurs
following a linear ← bent transition for which the transition
dipole moment lies in the molecular plane.
LEVELS OF THE GROUND STATE OF ND2(X 2B1)
˜
The assignments of the TKER spectra were based on
calculated eigenvalues using the ‘‘semirigid bender’’
Renner–Teller Hamiltonian,44,45 with the bending potentials
This study serves as a timely reminder of the need for
caution when interpreting ␤ parameters determined from non
fully quantum state resolved experimental measurements of
the photofragments arising even from as small and simple a
polyatomic molecule as ammonia. Traditionally, it has long
been recognized that measured ␤ parameters intermediate
between the limiting values of ϩ2.0 and Ϫ1.0 ͑correspond-
ing to the case of prompt dissociation following photoexci-
tation via a transition whose dipole moment lies, respec-
tively, parallel and perpendicular to the molecular plane͒ can
reflect ͑i͒ the presence of overlapping transitions in the par-
ent absorption spectrum and/or ͑ii͒ a reduction in anisotropy
due to parent rotation during the lifetime of the photoexcited
molecule. The present study highlights more of the subtleties
that may be ‘buried’ in such measurements. For example,
dynamical factors may dictate ͑as here͒ that each product
channel has its own, well defined ␤ parameter: as we show, a
simple measurement of the angular dependence of the total
flux of either product returns an average ͑and dynamically
meaningless͒ ␤ value. By way of further complication we
demonstrate that, in the case of predissociative systems at
least, one should give detailed consideration to the way in
which parent alignment will affect the actual magnitude of
any measured ␤ parameter, even when measured with full
quantum state resolution of the products. From the aforemen-
tioned discussion it should be obvious that we would expect
that simply changing the photolysis energy by a few cmϪ1
would result in population of a different ‘‘mix’’ of excited
state levels, with different alignments, leading to products
with somewhat different recoil anisotropies and thus
2
2
˜
˜
͑for the X B1 and A A1 states͒ optimized by fitting the
existing NH2 data,30 and with an appropriate change of
masses for ND2. The experimental rotational term values for
2ϭ0 and NϭKa ͑Table I͒ were then derived from the
v
TKER spectrum for ͓ND3͑000͒→DϩND2͔ ͑Fig. 4͒, with an
extrapolated dissociation energy of D00͑DϪND2͒ϭ38 010
cmϪ1
.
These Renner–Teller calculations slightly underestimate
the experimental term values, indicating a small mass depen-
dence to the variation with Ka of the contribution from the
zero-point energy of the neglected stretching vibrations. The
term values denoted as calc.͑a͒ in Table I are derived from
these Renner–Teller calculations by applying a uniform scal-
ing increase of 0.9%.
The experimental term values for 2ϭ0 and NϭKa
v
were also fitted by least squares to a more empirical model in
which, for each level ͉N,Ka , the term value was estimated
͘
as the minimum value with respect to ␪ and r of a single
effective potential function:
2
Erot N,K ͒ϭV ␪,r͒ϩA ␪,r͒ K ͒
͑
͑
͑
͑
a
a
ϩ 12 B ␪,r͒ϩC ␪,r͒ N Nϩ1͒Ϫ K ͒
,
2
͓ ͑ ͔͓ ͑ ͔
͑
͑
a
͑A1͒
where ␪ is the external inter bond angle, r is the NH bond
length, A(␪,r), B(␪,r), and C(␪,r) are ‘‘rotational con-
stants’’ in the principal axis system, and V(␪,r) is a potential
function to be optimized. This model takes explicit account
of both centrifugal stretching and centrifugal bending. The
chosen potential function was30,44
␤( 2 ,N) values which, whilst showing similar trends to
v
those displayed in Figs. 10 and 11, can be expected to differ
in their absolute magnitudes.
2
hfb ␪2Ϫ␪ ͒
͑
0
V ␪,r͒ϭf rϪr ͒2ϩ
͑
͑
r
0
2
0
2
0
2
f ␪ ϩ 8hϪ␪ ͒␪
͔
͓
͑
b
4
c1 3␪4Ϫ␪ ͒cos 2␲␪/5␪ ͒sin2 ␲␪/␪ ͒
͑
͑
͑
0
0
0
ϩ
.
͑A2͒
4
␪4ϩ␪ ͒
ACKNOWLEDGMENTS
͑
0
The optimum parameters, most of which were taken over
from NH2,30 are given in Table II. This model was then used
Once again it is a pleasure to acknowledge Professor K.
¨
H. Welge and Dr. L. Schnieder ͑Universitat Bielefeld͒ for the
to calculate term values for 2ϭ0 and NϾKa . Term values
v
help, advice, and encouragement they have given us with all
of our H atom photofragment translational spectroscopy
work. We are also grateful to colleagues in Bristol ͑espe-
cially Keith Rosser and Leon Rogers͒ for their contributions
to this work, and to SERC ͑now EPSRC͒ for equipment
grants and a studentship ͑to D.H.M.͒. D.H.M. is also grateful
to Professor J. P. Simons ͑Oxford University͒ and Professor
calculated by this method are denoted as calc.͑b͒.
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