State to state recoil anisotropies in the photodissociation of deuterated ammonia

Article abstract of DOI:10.1063/1.477411

The near ultraviolet photodissociation of deuterated ammonia, ND₃, allows particularly clear observation and quantification of the quantum state dependent angular anisotropy of the recoiling D+ND₂(X) photoproducts. The recoil anisotr

Full text of DOI:10.1063/1.477411

State to state recoil anisotropies in the photodissociation of deuterated ammonia
David H. Mordaunt, Michael N. R. Ashfold, and Richard N. Dixon
Citation: The Journal of Chemical Physics 109, 7659 (1998); doi: 10.1063/1.477411
View online: http://dx.doi.org/10.1063/1.477411
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 18
8 NOVEMBER 1998
COMMUNICATIONS
State to state recoil anisotropies in the photodissociation
of deuterated ammonia
David H. Mordaunt,a) Michael N. R. Ashfold,b) and Richard N. Dixon
School of Chemistry, University of Bristol, Bristol, BS8 1TS, United Kingdom
͑Received 5 August 1998; accepted 1 September 1998͒
The near ultraviolet photodissociation of deuterated ammonia, ND3, allows particularly clear
observation and quantification of the quantum state dependent angular anisotropy of the recoiling
˜
DϩND2(X) photoproducts. The recoil anisotropy is shown to depend upon five quantum numbers:
The rotational quantum numbers of the parent molecule selected in the absorption process, and the
rotational and vibrational quantum numbers of the resulting products. © 1998 American Institute
of Physics. ͓S0021-9606͑98͒01742-5͔
We report studies of the photodissociation of deuterated
ammonia (ND3) molecules which provide a particularly
clear demonstration that the recoil angular anisotropy of the
Photodissociation processes 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
dynamics of molecular photofragmentation processes. Disso-
˜
DϩND2(X) products is a sensitive function both of the par-
1
1
˜
˜
ent rotational quantum numbers selected in the absorption
process and of the resulting product rotational and vibra-
tional quantum numbers. Theory1 has long predicted such
quantum state dependent product recoil anisotropies, but
their experimental demonstration remains rare.
Classically, the spatial angular distribution of the recoil-
ing photofragments resulting from molecular photodissocia-
tion brought about using linearly polarized light is given by
ciation of ND3 via the origin band of its A AЉ–X A1Ј elec-
˜ 2 ˜
tronic transition is one such system. The A–X absorption
spectrum exhibits a long progression in ␯Ј2 , the excited state
out of plane bending mode—a direct consequence of the
Franck–Condon principle and the planar ← pyramidal
change in equilibrium geometry that accompanies this elec-
tronic transition. The spectroscopy of this transition is well
4
˜
established. The A state is predissociated, to the extent that
the jet-cooled absorption spectrum of NH3 shows vibrational
but no rotational structure; the advantage of studying the
fully deuterated isotopomer (ND3) is that it predissociates
sufficiently slowly that its ␯Јϭ0←␯ ϭ0and ␯Јϭ1←␯
1
I ␪͒ϭ
͑
1ϩ␤P cos ␪͒ .
͑1͒
͓
͑
͔
2
4␲
where ␤ is the classical anisotropy parameter, ␪ is the polar
angle between the velocity vector, ␯, of the recoiling frag-
ment and the electric vector, ⑀, of the photolysis laser, and
Љ
Љ
2
2
ϭ0 bands show resolved rotational structure, as illustrated in
Fig. 1. Thus by judicious choice of excitation wavelength we
can specify the rotational quantum numbers of both the ini-
tial and final states of the parent ND3 molecule. The only
P2 the second-order Legendre polynomial P (x)ϭ 1(3x2
͕
2
2
Ϫ1) .2,3 Measurement of ␤ can shed light on the character
͖
of the electronic transition dipole moment, ␮, and on the
time scale of the dissociation process. In the limit of a
prompt dissociation of a linear molecule, ␤ takes values of
ϩ2 or Ϫ1 according to whether ␮ is aligned parallel or per-
pendicular to the dissociating bond ͓i.e., from Eq. ͑1͒, the
fragments recoil with a sin2 ␪ or cos2 ␪ distribution, respec-
tively͔. Rotation of the excited molecule prior to fragmenta-
tion averages the angular dependence, partially degrading the
angular distribution so that it becomes more isotropic ͑i.e., ␤
tends towards zero͒. The present work illustrates additional
factors quantifying the recoil anisotropy in terms of the ex-
citation and fragmentation processes. The quantum recoil an-
isotropy parameter ␤͑␣͒ is shown to be dependent upon five
quantum numbers which, for simplicity, we denote collec-
tively as ␣ pending detailed discussion below.
energetically allowed fragmentation pathway for ND3 mol-
˜
ecules following excitation to the A,␯ ϭ0 level is D atom
Ј
elimination following cleavage of a D–ND2 bond.
The photodissociation of ND3 is investigated experimen-
tally using the technique of D atom photofragment transla-
tional spectroscopy5 which offers sufficient energy resolution
to reveal the rovibrational quantum state population distribu-
tions within the partner ND2 photofragments. Two photolysis
energies are chosen: 46 708 and 46 724 cmϪ1, appropriate
for excitation of, respectively, the Q1(1) ͓and, to a lesser
˜ ˜
extent, Q1(2)͔ and R0(0) transitions within the ND3(A–X)
origin band. The resulting D atom photofragments are
tagged, state selectively, prior to escaping the interaction re-
gion, by a two-color two-photon electronic excitation
scheme ͑␭ϭ121.6 nm and ϳ365.6 nm, respectively͒ result-
ing in population of a Rydberg state with principal quantum
number, nϳ80. The D atom translational energies and thus,
by momentum conservation, the total fragment kinetic-
a͒
Present address: Coherent Inc., Medical Group, 2400 Condensa Street,
Santa Clara, CA 95051.
b͒
Electronic mail: mike.ashfold@bristol.ac.uk
0021-9606/98/109(18)/7659/4/$15.00
7659
© 1998 American Institute of Physics
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7660
J. Chem. Phys., Vol. 109, No. 18, 8 November 1998
˜ ˜
FIG. 1. Simulated absorption spectra of the ND3(A–X)origin band assum-
ing a parent rotational temperature of 15 K ͑but a 300 K nuclear spin
temperature͒ and a lifetime broadened transition width of 4.2 cmϪ1 ͑Ref. 4͒,
together with a stick spectrum indicating the contributing transitions. The
full circles ͑᭹͒ indicate the transitions chosen for investigation.
FIG. 3. Experimentally resolved ͑᭹͒ and theoretical predicted ͓—, by Eq.
˜
͑5͔͒ anisotropy parameters for photodissociation of ND3(A)
molecules
␯ϭ0
following preparation via the ͑A͒ R0(0) and ͑B͒ Q1(1) transitions.
energy release (ET), are determined by measuring the D
atom times of flight to a detector mounted 825 mm distant
along the axis orthogonal to the plane containing the molecu-
lar beam and the photolysis and tagging laser beams.
tion. The angular distributions are obtained by rotating the ⑀
vector of the photolysis laser radiation so as to sample both
parallel and perpendicular orientations with respect to the
detection axis. Clearly, the detailed intensity distributions
observed are sensitive both to the alignment of ⑀ ͓compare
Figs. 2͑A͒ with 2͑B͒, and Figs. 2͑C͒ with 2͑D͔͒ and to the
detail of the parent rovibronic transition excited ͓compare
Figs. 2͑A͒ with 2͑C͒ and Figs. 2͑B͒ with 2͑D͔͒. The recoil
angular anisotropy parameter may be determined experimen-
tally, as a function of product ND2 vibrational and rotational
quantum states, via the relationship
As Fig. 2 shows, the P(ET) spectra exhibit structure
reflecting the energies of the various quantum states of the
ND2 partner fragment that are populated in the fragmentation
process. Analysis shows that nearly all the ND2 fragments
are formed with only zero-point vibrational energy, but with
a high degree of rotational excitation. This rotational excita-
tion is concentrated about the a-inertial axis ͑i.e., states with
product rotational quantum numbers NϭKa and NϭKa
ϩ1). Such observations are consistent with previous discus-
sions of the dissociation dynamics of ammonia.5–7 The rela-
tive populations of these product states are deduced from the
intensities of the corresponding peaks in the P(ET) spec-
trum. Thus the experiment yields a one-dimensional ͑1D͒
radial cut through the three-dimensional ͑3D͒ recoil distribu-
Ipara ␯,N͒ϪI
␯,N͒
͑
͑
perp
␤ ␯,N͒ϭ2
͑
.
͑2͒
Ipara ␯,N͒ϩ2I
␯,N͒
͑
perp
͑
where Ipara(␯,N) and Iperp(␯,N) represent the relative popu-
lation of the ND2 photofragment with vibrational and rota-
tional quantum numbers ␯ and N, measured with ⑀ parallel
and perpendicular to the detection axis.
The most striking aspect of the present work is the quan-
titative measure of the state selective recoil anisotropy pa-
rameter, ␤͑␣͒, obtained using Eq. ͑2͒. Two effects are clearly
apparent from the plots shown in Fig. 3. First, the magnitude
of ␤͑␣͒ depends sensitively upon the initial rotational state of
the parent molecule from which dissociation occurs. Second,
the value of ␤͑␣͒ is not constant for all of the product quan-
tum states, but varies from a negative value for low N levels
of ND2 to a positive value for levels with high NϳKa . The
full recoil angular distributions resulting from photodissocia-
tion through these two different parent transitions are recon-
structed in Fig. 4. The concentric circles represent the flux of
ND2 photofragments with a given rotational quantum num-
ber NϳKa , and thus a given recoil velocity and kinetic en-
˜
FIG. 2. DϩND2 photofragment translational energy distributions, P(ET),
ergy. The A state of ammonia has a trigonal planar geometry
resulting from dissociation of ND3 following excitation via the
˜ ˜
with the A–X transition dipole moment parallel to the C3
˜ ˜
A–X,(0,0),R0(0), and Q1(1) transitions with the detection axis respec-
axis. The laser preferentially excites molecules aligned with
their transition dipole aligned parallel to ⑀, i.e., with their
molecular plane perpendicular to the laser polarization. For
tively parallel ͑A͒ and ͑C͒ and perpendicular ͑B͒ and ͑D͒ to the laser polar-
ization axis. Combs superimposed above the spectra indicate the various
˜
populated rotational levels of ND2(X)
.
␯ϭ0
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J. Chem. Phys., Vol. 109, No. 18, 8 November 1998
7661
than its rotational period, the degree of spatial alignment can
be described by the alignment parameter, A (J ,J ,K). The
Ј Љ
0
photofragment recoil anisotropy can then be expressed as
␤ ␣͒ϭA P cos ␹͒,
͑3͒
͑
͑
0
2
where ␹ represents the angle between the transition dipole
and the dissociating bond. The A˜ –˜X transition in ammonia is
parallel, thus there are three important quantum numbers:
The projection of the total angular momentum on the C3 top
axis (Kc , henceforth denoted simply as K for both initial and
final states͒, and the initial and final rotational angular mo-
menta ͑ J and J ͒. The A (J ,J ,K) value is dependent on
Ј Љ
Љ
Ј
0
the specific rotational transition selected, i.e.,
J
J
2
0
Ј
Ј
J ϩK
Ј
ͱ30 2J ϩ1͒
͑
A0 J ,J ,K͒ϭ Ϫ1͒
͑
͑
Ј Љ
Ј
ͩ
ͪ
K
ϪK
J
J
1
Љ
Ј
ϫ
,
͑4͒
ͭ
ͮ
2
1
J
Ј
where ͑ ͒ and ͕ ͖ denote 3-jand 6-j symbols, respectively.3,8
The rotationally resolved R0(0) and Q1(1)transitions have
A (J ,J ,K) values of ϩ2.0 and ϩ0.5, respectively, not-
Ј Љ
0
withstanding the fact that J ϭ1in both cases. At this point,
Ј
since ␹ϭ90°, we would thus predict that the products of the
dissociation of ND3 from these particular excited-state levels
should yield constant anisotropy parameters ␤͑␣͒ of Ϫ1.0
and Ϫ0.25, respectively.
We also observe that the photofragment recoil anisot-
ropy parameter is dependent on the product rotational quan-
tum number (NϳKa). The D atom ejected by molecules that
dissociate to yield ND2 fragments with low rotational angu-
lar momentum are preferentially directed in the plane of the
excited molecule ͓i.e., perpendicular to ␮, with ␤(Nϭ0
FIG. 4. Polar plot illustrating a 2D cut through the 3D distribution of
˜
DϩND2(X)
product recoil energies arising in the photodissociation of
␯ϭ0
ND3 molecules following excitation on the ͑A͒ R0(0) and ͑B͒ Q1(1) tran-
sitions of the A˜ –˜X(0,0) band derived from the experimental measurements
displayed in Figs. 2 and 3. The radial axis is product translational energy,
the ⑀ vector of the photolysis laser is vertical, and the angle is between ⑀ and
the recoil axis. Azimuthal symmetry is assumed about the laser polarization
axis. The bare central region in each plot reflects the inability of the time-
of-flight experiment to monitor the slowest D atom products.
ϳϪ 1A (J ,J ,K) as predicted by Eq. ͑3͔͒. Conversely, the
Ј Љ
2
0
D atoms formed in association with the most highly rotation-
ally excited ND2 partners tend to recoil almost parallel to the
transition dipole, i.e., ␤(NϭKϳ26)→A (J ,J ,K). such
Ј Љ
0
dynamics are a consequence of the conical intersection be-
excitation via the R0(0) transition, D atoms formed with
ND2 products appearing in low N levels preserve this align-
ment with maximum flux orthogonal to the laser polariza-
tion; however, as the value of N increases the trend is re-
versed, with the maximum flux of photofragments appearing
parallel to the laser polarization axis. For excitation via the
Q1(1) transition the recoil distribution for all ND2 product
levels is more isotropic, however, there is a small anisotropy
following the same trend as for the R0(0) transition, as in-
˜
˜
tween the A and X state potential-energy surfaces, at planar
geometries, in the D–ND2 dissociation coordinate, which
gives rise to a large out of plane torque.9,10 Products with a
small degree of rotational excitation arise from fragmenting
parent molecules with internuclear trajectories which pass
through the conical intersection without experiencing this
torque, and behave as predicted by Eq. ͑3͒. However, prod-
ucts with considerable rotational excitation have been accel-
erated by the torque tangential to the molecular plane, this
enhances the rotational motion and perturbs the recoil anisot-
ropy. The measured energy and angular momentum disposal
within the products are reproduced well by an impact param-
eter model,6 which predicts the quantum recoil anisotropy for
each product N state
dicated by the ␤͑␣͒ values in Fig. 3.
˜
The lifetime of ND molecules in their A,␯ ϭ0 state
Ј
3
that result from excitation via the R0(0) and
Q1(1)transitions is ϳ2.7 ps.4 This lifetime exceeds its rota-
tional period ͑ϳ2.2 ps for molecules with N ϭ1). Thus the
Ј
excited molecules typically make at least one complete rota-
tion prior to dissociation. Classically, we would expect this
to degrade the photofragment recoil anisotropy, thereby
tending towards an isotropic recoil distribution. Clearly this
is not the case, the excited molecules remain aligned and the
degree of the alignment is dependent upon the particular par-
ent rotational transition excited.
␤ ␣͒
3N Nϩ1͒ប2
2␮R2TSET
N
͒
͑
͑
͑
ϭ
Ϫ1.
͑5͒
A0 J ,J ,K͒
͑
Ј Љ
The model assumes that the transition state for dissociation is
located at the conical intersection. The reduced mass ͑␮͒ and
bond distance (RTS) of the departing D atom are evaluated at
the conical intersection. ET(N) denotes the translation en-
For a molecule that dissociates on a time scale longer
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7662
J. Chem. Phys., Vol. 109, No. 18, 8 November 1998
ergy release for the product quantum states. As Fig. 3 shows,
these calculated values of ␤͑␣͒ are in excellent accord with
those obtained from experiment, confirming this dynamical
interpretation.
In conclusion, the quantum anisotropy parameter is de-
pendent on five quantum numbers, such that ␤(␣)
in a very confined region of configuration space ͑the conical
intersection͒ and a well defined mapping of the extent of
some parent motion orthogonal to the dissociation axis at this
transition state ͑out of plane bending in this case͒ onto the
eventual product quantum states. Although the quantum state
sensitivity of the spatial anisotropy parameter ␤͑␣͒ is readily
understandable and predicted theoretically, clear experimen-
tal demonstrations are likely to remain rather elusive.
ϵ␤(J ,J ,K;N). Ammonia is the first molecule for which
Ј Љ
such detailed quantum effects in product recoil anisotropies
have been observed and quantified. The state dependence of
The authors are grateful to the EPSRC for equipment
grants and a Senior Research Fellowship ͑MNRA͒, and the
Leverhulme Trust for a Senior Research Fellowship ͑RND͒.
␤(J ,J ,K;N) is brought about by two processes: First op-
Ј Љ
tical excitation ͑which determines the alignment of the par-
ent molecular frame in the laboratory frame of reference͒;
second, the dissociation dynamics ͑which can be dependent
on product quantum state͒.
Finally, it is worth commenting on the generality of such
observations. The creation and retention of significant align-
ment in these ND3 molecules, notwithstanding their predis-
sociating on a time scale longer than the rotational period, is
a consequence of the pure parent state selection ͑excitation
1 G. G. Balint-Kurti and M. Shapiro, Chem. Phys. 61, 137 ͑1981͒.
2 R. N. Zare and D. R. Herschbach, Proc. IEEE 51, 173 ͑1963͒; R. N. Zare,
Mol. Photochem. 4, 1 ͑1972͒.
3 R. N. Zare, Angular Momentum ͑Wiley, New York, 1988͒.
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Chem. Phys. 102, 4772 ͑1995͒; 102, 4783 ͑1995͒, and references therein.
5 M. N. R. Ashfold, D. H. Mordaunt, and S. H. S. Wilson, Advances in
Photochemistry edited by D. C. Neckers, D. H. Volman, and G. von
Bunau ͑Wiley, New York, 1996͒, Vol. 21, p. 217.
of a range of J ,K levels would result in a more isotropic
Ј
Ј
ensemble of excited-state molecules͒ and the lack of suitable
͑Coriolis͒ couplings by which the well defined precession
might be scrambled. Both of these necessary attributes will
generally be harder to achieve in heavier, more predissoci-
ated systems ͑where spectral congestion would be more
problematic͒ or in molecules carrying higher levels of inter-
nal excitation. The observation of a dramatic product quan-
tum state dependence of ␤͑␣͒ also requires a rather favorable
set of circumstances. For example, in the case of ammonia,
we picture the ultimate energy disposal as being established
6 D. H. Mordaunt, M. N. R. Ashfold, and R. N. Dixon, J. Chem. Phys. 104,
6460 ͑1996͒; 104, 6472 ͑1996͒, and references therein.
7 R. N. Dixon, Mol. Phys. 88, 949 ͑1996͒.
8 This expression is derived by integrating the rotational wave functions
over two Euler angles ͑the molecular and space-fixed frame azimuthal
angles͒, following the work of S. E. Choi and R. B. Bernstein, J. Chem.
Phys. 85, 150 ͑1986͒, and that described in Ref. 3.
9 P. Rosmus, P. Botschwina, H.-J. Werner, V. Vaida, P. C. Engelking, and
M. I. McCarthy, J. Chem. Phys. 86, 6677 ͑1987͒.
10 R. Polak, I. Paidarova, V. Spirko, and P. J. Kuntz, Int. J. Quantum Chem.
54, 429 ͑1996͒.
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