2602
J . Phys. Chem. 1993,97, 2602-2608
Time-Dependent Quantum Dynamical Study of the Photodissociation of HOC1 Hua Guo Department of Chemistry, University of Toledo, Toledo, Ohio 43606 Received: September 8, 1992
We present a time-dependent quantum mechanical calculation of the photodissociation of hydrochlorous acid (HOCl). The dissociation dynamics is studied on a b initio potential energy surfaces of five excited states with two variables, Le., the 0-Cl bond length and H-O-Cl bending angle. The 0-H bond is frozen in all the calculations. Absorption spectra due to individual excited states are calculated and the total absorption cross section is compared with experimental measurements. Rotational state distributions of the OH fragment are obtained from the calculation, and the influence of the anisotropy of the excited state potential energy surfaces on the rotational excitation of the fragment is discussed.
I. Introduction Hydrochlorous acid (HOCl) has attracted much attention recently because of the possible role that it may play in the ozone depletion in the earth’s atmosphere.’-8 HOCl is believed to be formed in the stratosphere via the following r e a c t i ~ n : ~ . ~ HO,
+ C10
-
HOCl
+ 0,
(1)
Upon absorption of a UV photon in the 200400-nm region, hydrochlorous acid can dissociate to OH and a chlorine atom*
+
-.
+
HOCl hv O H C1 (2) The quantum yield of alternative dissociation products such as 0 HCl has been shown experimentally to be negligible.9 Both OH and C1 are very reactive and may participate in a series of reactions that destroy ozone in the upper atmosphere. The dissociation rate of reaction 2 is very important in determining the rate of ozone destruction in the stratosphere through the aforementioned mechanism. It has been proposed that HOCl may serve as a temporary reservoir for chlorine species if it has a long enough lifetime.4 On the other hand, if HOCl dissociates promptly, the fragments may accelerate the ozone depletion process (e.g., reaction 2). Therefore, an accurate determination of the photodissociation cross section for HOCl in the 200400nm region is very desirable. Many experimentalS-l0and theoretical’ ) - I 6 studies have been performed to determine the gas-phase absorption cross section of HOCl in the 200400-nm region. Although disagreement exists among experimentally measured absorption spectra of HOC1, it is generally acceptedI7 that there are two peaks in the spectrum centered at 320 and 240 nm, although the peak at long wavelength is probably weaker. The existence of a significant absorption band near 320 nm is especially important because it excludes the possibility that HOC1 serves as an efficient chlorine sink in the ozone depletion process. The absorption of HOCl at 240 nm is considered insignificant since ozone itself absorbs UV photon at X C 300 nme6s7Early theoretical studies’ did identify two contributions in the absorption spectrum from the transition to the two lowest excited states (1 ‘A’’ and 2lA’). However, the absorption due to the lower l l A ” state has a relatively weak oscillator strength and it peaks at a higher energy (270 nm) than observed in experiment (320 nm). The calculated lower peak is buried under the shoulder of the higher energy band, and the resulting total absorption cross section shows essentially only one peak, in disagreement with most experiments. Nanbu and I ~ a t a ’ ~have . ’ ~recently reported a new ab initio calculation on HOCl and have succeeded in qualitatively reproducing the experimental dual-peak structure in the absorption spectrum. In their calculations, the 0-H bond was frozen at its equilibrium
+
0022-3654/93/2097-2602S04.00/0
geometry. Two-dimensional potential energy functions were established for the excited singlet states of HOCl based on ab initio data. The classicalreflection principlewas used to calculate the absorption spectra due to transitions from the ground state to individual excited states.IsJ6 Classical mechanics was applied to investigate the photodissociation dynamics and calculate the OH fragment rotational state distributions at various wavelengths.I6 The photodissociation of hydrochlorous acid itself possesses many features worthy of theoretical exploration. The dissociation is much like that of water.Is The 0-H distance in HOCl is roughly the same as that in the OH free radical, and the OH group is hardly affected by the cleavage of the 0-C1 bond. It is therefore reasonable to assume that the OH vibrational mode can be separated from the dissociation as well as the bending (rotation) coordinates. The ab initio data show that all the singlet excited states of HOCl are strongly repulsive in the 0 4 1 coordinate and dissociation is expected to be direct and fast. The five lowest singlet excited states calculated by Nanbu and Iwata have different potential anisotropies that can influence the rotational excitation in the OH fragment. With the same initial wave function, the dissociation of HOCl at various excited states presents a realistic prototype for studying the relationship between the potential anisotropy and rotational excitation of the fragment. In this work, we report a quantum mechanical study of HOCl photodissociation dynamics using a time-dependent method. The wavepacket is represented on a two-dimensional grid and both the fast Fourier transform (FFT) and discrete variable representation (DVR) methods are used to evaluate the action of the Hamiltonian. The temporal propagation of the wavepacket is accomplishedby solving the time-dependent Schridinger equation by using the Chebychev method. The calculations are performed on the two-dimensional potential energy surfaces established by Nanbu and Iwata.I6 The details of the theory and its implementation will be discussed in next section. The absorption spectrum and final rotational state distributions obtained from our calculations will be presented in section 111. Conclusions are presented in section IV. 11. Theory
In this work, we use time-dependent quantum mechanics to study the photodissociation process (reaction 2). The photoinduced dissociation cross section can be approximated as the firstorder perturbation of the molecule/radiation interaction (Fermi’s 0 1993 American Chemical Society
Photodissociation of HOCl
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2603
golden rule) and written as follows~9
where w! and Eo are the wavelength of the incident photon and the ground-state energy of HOCl, respectively. tois the vacuum permittivity and c is the speed of light. The wave function 40 equalsCt+o,where +O is theground-state vibrational wave function and I.( is the appropriate transition dipole moment. In this work, the vibrational degree of freedom of O H is ignored since the OH internuclear distance is almost the same before and after the dissociation. We will focus on the rotational excitation of the O H fragment, which is treated as a rigid rotor. For the sake of simplicity, we also assume that the total angular momentum of the parent molecule is zero. The excited-state Hamiltonian can then be defined in a two-variable Jacobi coordinate system ( R J ) , using atomic units:
-- a sin 0%a
+ &+
+
V(R,d)= p2 V(R,B) (4) sin 8 a0 2PnO-ci where R is the distance between the chlorine atom and the center of mass of the OH and 8 is the Jacobi angle between the R and r vectors. Since the center of mass of OH is very close to the oxygen, the LHOCl angle can be approximated by the Jacobi angle through the relationship 8 = 180’ - LHOCl. In our calculation, the 0-H distance r is frozen at its equilibrium value (ro = 0.9643 A). P and j are the conjugate (angular) momenta of R and 8, respectively. The moment of inertia I for the system is defined as follows
_1 --
+-
1
1 (5) 2’ ~PHO-CIR’ 2PoHr; Note that the OH is treated as a three-dimensional rotor.20The reduced masses are given as follows:
The potentials V(R,8)are those of Nanbu and Iwata,I6 who fitted approximately 200 ab initio points for the five excited states by using anti-Morse functions with the following form:
by multiplying V(R,8)by the wave function at each ( R J ) grid point. Thecalculation of the action of the kinetic energy operator takes two steps. For the first term in eq 4, the wavepacket is first transformed from coordinate space to momentum space via a one-dimensional fast Fourier transform (FFT).21.22Since the kinetic energy operator for the Jacobi coordinate R is diagonal in momentum space, the action of the operator can be readily obtained by multiplying P2/
[email protected] on the wave function a t each momentum grid point. The resulting wave function is then transformed back to coordinate space via an inverse FFT. For the action of the second term in eq 4 involving the angular momentum operator, we use the discrete variable representation (DVR) method developed by Light et al.23s24The DVR includes a set of points that happen to be the abscissas of a Gaussian quadrature. This method then defines a unitary transformation matrix T between a discrete variable representation (DVR) and a finite basis representation (FBR) based on a Gauss quadrature:
where T+denotes the Hermitean conjugate of T. For the Jacobi angle 8 and its conjugate angular momentum j, the unitary matrix T can be defined on the basis of the Gauss-Legendre quadrature:
where xu = cos(8,) with 8, being the abscissas and o, is the corresponding weight factors of the underlying Gauss-Legendre quadrature. The FBR bases ( p j ) are the orthonormal eigenfunctions of the angular momentum operator j
where Pj are Legendre polynomials. To calculate the action of the angular kinetic energy operator, the wave function in the angular space is first transformed to the j-space by the T matrix. The angular kinetic energy operator (the second term in eq 4) is diagonal in the j-space, and its action is hence equivalent to multiplying the wave function by j(j 1)/21 for each j component. The final DVR wave function is obtained by carrying out an inverse transformation from the j-space to the @-space.In practice, this process can be simplified by a single multiplication of a new matrix t on the DVR coordinate wave fun~tions:25-~~
+
&4(R,S) = T + ’ v T $ ( R , O ) = t4(R,B)
(13)
The initial wave function in the DVR is obtained from the ground-state wave function 40:
where Pi is a polynomial of 8
The coefficients C , are optimized to fit the ab initio points and are given in ref 16. The propagation of the wavepacket on an excited state is equivalent to solving the corresponding time-dependent SchrBdinger equation (in atomic units):
4DVR(Rlea,t= 0) = w,”240(R,e,) (14) where the definition of the ground-state vibrational wave function will be given later. Note that the square root of the weight factor o, is multiplied by the initial coordinate space wave function at each grid point. The wave function in the coordinate space is actually different from the DVR wave function by a factor of
In this work, the wavepacket is discretized on a two-dimensional grid. The grid in the R coordinate is chosen to be uniform in order to facilitate the discrete Fourier transform that will be discussed later. The grid in the 8 coordinate is selected as the abscissas for a Gauss-Legendre quadrature. The basic idea behind such a choice is to establish a basis for an efficient formula to evaluate the action of the Hamiltonian on the wavepacket. The action of the Hamiltonian is evaluated at each time step. The action of the potential energy operator can be easily obtained
An alternative method in solving the Schriidinger equation (9) is to expand the total wave function to an N-dimensional FBR basis set {1p~}.*~-3~Such an expansion generates Nso-called channel wave functions that can be propagated via a one-dimensional FFT method. However, such a basis set/FFT approach requires a construction of an N X N X M potential matrix, where Nand M are the dimension of the 8 and R bases, respectively. This potential matrix is not needed in the DVR method because the potential is handled in coordinate space. The transformation matrix between the DVR and FBR has a dimension of N X N and can be stored for every operation. The DVR method is
j=O
o,’J2*
2604
TABLE I: Parameters for the Ground-State Wave Function ~
Guo
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
~~
Ro,A BO, deg @R,
bohr
00,rad-2
HOCl
DOC1
1.7667 77.04 70.102 3 1.039
1.7667 77.04 7 1.456 41.897
therefore a more efficient approach in treating dynamics involving angular variables. The initial wavepacket is the ground-state vibrational wave function multiplied by the transitiondipole moment. Thegroundstate wave function is approximated by a product of two Gaussians (unnormalized):
where all the parameters determined from ground-state equilibrium data32are listed in Table I. For the time propagator, we choose to use the Chebychev scheme suggested by Tal-Ezer and K o ~ l o f f .In~ this ~ method the time propagator exp(-Mt) is expanded in Chebychev polynomials of iH with the Bessel functions of the first kind of the coefficients. This method allows one to use a significantly larger time step than other local propagators. It has been shownj4 that the Chebychev scheme is extremely efficient in propagating a timeindependent Hamiltonian. It should be pointed out that the wavepacketflt) in eq 9 is not an eigenfunction of the excited-state Hamiltonian. Rather, it is a manifold of all the energy components. For a specific photon frequency w ~the , asymptotic rotational state distribution (partial cross-section) of the O H fragment can be calculated by projecting the final wavepacket onto the asymptotic states:*6J9JO
where v,(O) is the rotational basis representing the free O H rotor state and the wave function in the R coordinate is a plane wave. The wave vector in the plane wave of the translational coordinate is given by
111. Results
In all the calculations presented here, we have chosen a 512point grid in the R coordinate from 2.0 to 14.0 au and 40 DVR points. The time interval for the propagation is set at 100 au and 50 Chebychev terms are used in the expansion. The propagation usually requires 2000-3000 au for the wavepacket to reach the asymptotic limit. A. AbsorptionSpectrum. Theground-state hydrochlorous acid isa bent moleculewith theLHOClof 102.96’ (notethat8 = 180’ - LHOCl). The ground-state force field and equilibrium geometry have been determined spectroscopically~2and confirmed by a b initio calculations.ll-13.15.16.35 The ground-state HOCl is a ‘Z+ state, which dissociates to HO(A2Z+) C1(2P) in linear configurationsdue to angular momentum conservation. It forms an avoided crossing with a higher excited I l l state at bent geometries and dissociates to HO(X2II) + C1(2P), according to the Wigner-Witmer rule.36 The dissociation mechanism is much like that of ~ a t e r . 3 ~ In the ab initio calculation of Nanbu and Iwata,l6 five singlet excited sZates were included. They are l l n , lIA, and 112- in linear configurations. The first two excited states split into four components (two ‘A’and two IA”) when the molecule bends (the Renner-Teller effect). The A’ component of the lower 1I I I state interacts with the ground state to form a conical intersection near
+
2.0 A.16 Nonadiabatic coupling can be important in two cases, namely, the conical intersection and Renner-Teller splitting near the linear configurations.38 It has been shown that both types of coupling are important in radiationless decay and/or photod i s ~ o c i a t i o n . ~Transitions ~ J ~ - ~ ~ ~from ~ singlet states to triplet states may also be important. Unfortunately, the nonadiabatic interactions between different states are not available from the ab initio work16 and we will, in this work, ignore all the possible nonadiabatic transitions during the dissociation process. The contour plots of the five excited states are presented in Figure 1. All of the five states are repulsive in the dissociation (0421) coordinate and possess different angular anisotropies, aV/dO. For example, 1IA” and 2IA“ are bent in the FranckCondon region with their equilibrium LHOCl angle similar to the equilibrium angle of the ground state. It can be expected that the rotational excitation of the dissociated OH fragment from these two states will be limited. On the other hand, the other threestates (2IA’, 3IA’,and 3IA”) arelinear in theFranckCondon region. Rotational excitation of the O H fragment can be anticipated for the dissociation on these surfaces because of the strong potential angular anisotropy. Figure 2 presents the wavepacket dynamics of the dissociation on the first two excited states (1IA” and 2IA’). Due to the repulsive nature of the potentials, the wavepackets move quickly downhill to the asymptote. The wavepackets start with a Gaussian shape and maintain such a shape during the dissociation. The time interval for the wavepackets is 300 au and the wavepackets reach the asymptote in approximately 2500 au or 60 fs. The initial wavepacket on the 2IA‘ state surface has a small peak on the shoulder of the main packet. This is due to a dip in the transition dipole function near the ground-state equilibrium geometry (see Figure 2a in ref 16). The absorption cross section for all the excited states is plotted in Figure 3. The transition dipole functions from the a b initio work of Nanbu and IwataI6 are used in our calculations. For the A’ states, the transition dipole moments are taken as an average of the x- and y-components, namely, p = ( p x 2 p,,2)1/2.The transition dipole moments for the A” states are simply the r-component, p = M,. The transition dipole moment for the 2IA’ state is the largest and its absorption peak predominates. The transition to the l l A ” state is extremely weak since the corresponding dipole is approximately 1 order of magnitude smaller than that of the 2IA’ state in the Franck-Condon region. The three highest excited states in our calculation (2IA’, 3lA’, and 3IA”) have comparable transition dipole moments and their cross sections are approximately the same. The absorption spectra to these three states peak at 168, 147, and 138 nm, respectively. The absorption bands near 240 nm due to the 2IA’ state and 330 nm due to the 1IA” state are the w s t important for the atmospheric chemistry of ozone depletion. In Figure 4, we have plotted the logarithm of the absorption spectra in the 200400-nm region with experimentally measured data. It can be readily seen that there are two peaks in the calculated total absorption cross section. The intensity of the lower peak (1 IA” 1 ]A’) is approximately weaker than that of the second peak (2IA’- 1IA’) due to a smaller transition dipole moment. The experimental curves are due to Molina and Molina6 (triangle), Knauth et al.7 (circle), and Mishalanie et a1.I0(square). All threemeasurementsshow a second peakaround 320 nm. Our quantum calculation agrees reasonably well with the overall shape of the spectrum. However, the absolute value of our calculated cross section is slightly smaller than the experimental values. The classical &function spectrum of Nanbu and IwataI6 is also very close to our results. Therefore, the speculation that HOCl may act as a chlorine sink in the upper atmosphere is probably unreasonable. B. Rotational State Distribution of OH. There has been no experimental report on the rotational distribution of the O H
+
-
Photodissociation of HOC1
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2605
140.00
148.00
140.00
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120.00
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e0.00
8 0 . 00
60.00
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40.00
20.00
20. 00
20.00 0.00
t Bul\l!i i 1.00
1.50 2.00
I
\I 2.50
3.00
I
1
0.00
3 . 5 0 4.00
140.00
140.00
120.00
120.00
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aO. 00
60,00
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0.00
1 . 0 8 1.50 2.00
2.50
3.00 3.50
1.00 1.50 2.00
2 . 5 0 3.00
4.00
1.00
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3.00
3.50 4.00
0.00 1.00
1 . 5 0 2.00
2.50
3 . 0 0 3.50
4.00
4.00
3.50
Figure 1. Contour plots of the potential energy surfaces for the first five singlet excited states of HOCI: (a) the 1 'A" state, (b) the 2IA' state, (c) the 2IA" state, (d) the 3IA' state, and (e) the 3'A" state. The x-axis is the R coordinate I
0 00 1
(A) and the y-axis is the angle 0 (degree).
t""
"
"
A"
'
I
I
2 a0 3 00 4 0 0 5 00 6 00 7 00 8 00
0 00
,
30,00 60.00 90.00
/1/ll!'/ ! lllll i / /
'
J
'
I
/
I
-
-
120 00
-
150.00
-
180 00
1
100
150
200
250
300
350
400
h(nm) Figure 3. Absorption spectra of five excited states of HOCI. The spectrum for the 1'A" state has been multiplied by a factor of IO.
2 00 3 00 4 00 5 00 6 00 7 00 8 00
Figure 2. Snapshots of dissociating wavepackets on the 1 'A" state (a, top panel) and on the 2IA' state (b, bottom panel). The x-axis is the R coordinate in bohr and the y-axis is the 0 angle in degrees. The time interval is 300 au.
fragment from the UV dissociation of HOCI, to our best knowledge. However, we present here theoretical predictions of the final OH rotational distributions at various photon wavelengths based on a b initio potential energy surfaces. It is our hope that this calculation will stimulate future experimental work on the underlying dissociation process. The rotziional state distribution of the O H fragment depends on two factors: the initial bending wave function of HOC1 and the final state interaction, which is specified by the angular anisotropy of the relevant excited-state potential. The potential energy surfaces of the five excited states at the ground-state equilibrium 0-CI distance are plotted in Figure 5 , along with the ground-state bending wave function of HOCI. It can be seen that the two lowest A" states are bent and their equilibrium
bending angles are roughly at the ground-state equilibrium angle ( 0 = 77.04"). The 3lA' and 3lA" states have their equilibrium angle at linear configuration (e = 0"). The 2IA'state has a near isotropic potential in the 90-O0 region. It can be expected that the rotational excitation will be most conspicuous for the two highest states 3IA'and 3IA", while therotatioanlstatedistribution of OH will be cold for the lowest excited states, Le., 1 lA", 2'A', and 2'A". If there were no final-state interaction, the bending motion would decouple from the dissociation coordinate. In other words, the fragmentation of the molecule proceeds as if the potential energy surface were isotropic. Under such circumstances, the final rotational state distribution of the OH is completely determined by the overlap of the initial bending wave function of HOC1 with the free rotor state wave functions of the OH fragment. This is the so-called Franck-Condon (FC) limit.45 The rotational distribution of O H in the Franck-Condon limit has been calculated and presented in Figure 6 . It is an oscillating function of the rotational quantum numberj, but it decreases to
Guo
2606 The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 -18
0.6
-
0.5
-D
0.4
.-C0
3
-19
I
In .U
-
0.3
.-
0.2
mC 0
b 0)
-0
I
m
-20
I
0
a
0.1
0 0
-21
1
2
3
4
5
6
7
8
9
Rotational state
Figure 7. Rotational state distribution of the OH fragment dissociated from the 1 !A” state at three photon wavelengths, 300,330, and 360 nm. The FC distribution is also given in the figure.
-22 200
250
350
300
400
h(nm)
Figure 4. Log plot of the absorption spectra in the 200-400-nm region. Theexperimentalcurvesaredueto Molina and Molina6(triangle), Knauth et al.’ (circle), and Mishalanie et a1.I0 (square). The dashed lines are the logarithms of the individual absorption spectra of the two lowest excited states and the solid line is the logarithm of the total absorption spectrum. 12
0.5
-
.-C0
S
0.4
-
C.’:
9 ul .U
0.3
mC 0
0.2
300 nm
Bl 330 nm
3
360nm
__._ F - C
.-
I
m c 0
a
0.1
i 0
10
0
1
2
3
4
5
6
7
0
9
Rotational state
Figure 8. Rotational state distribution of the OD fragment dissociated from the 1 !A” state at three photon wavelengths, 300,330, and 360 nm. The FC distribution is also given in the figure.
8 h
> 2 6 > 4
2
0 20
40
60
80
100
120
Weg) Figure 5. Anisotropy of the excited-statepotential energy surfaces. The O-CI distance is fixzed at the equilibrium value (1.7667 A). The initial bending wave function is also plotted in the same figure.
0 C
.-
I
3
-D I
ul .U
mC
0 1 2 3 4 5 6 7 8 9 1011121314
Rotational state
Figure 6. Rotational state distribution of the OH(0D) fragment in the Franck-Condon limit.
zero at large quantum numbers. This type of distribution is very similar to what Schinkeobtained in the photodissociation of water in the A which was confirmed by experimentalist^?^ In the same figure, we have also plotted the Franck-Condon distribution for OD from the dissociation of DOCl. The OD rotational distribution in the Franck-Condon limit is slightly hotter than that of OH.
However, there is always a final-state interaction in photodissociation, although it may be very small in some cases. The fragment rotational distribution can be distorted, or completely altered in some cases, from the FC limit, depending on the strength of the potential anisotropy. In Figure 7, the rotational state distributions of the OH fragment from the dissociation on the 1IA” state are presented. The OH distribution is calculated at three wavelengths, one at the absorption maximum (330 nm) and two on each side (300 and 360 nm). The Franck-Condon distribution is also given in the same figure. The rotational distributionsof the OH fragment exhibit a very weakdependence on the photon wavelength, as the OH rotational excitation increases only slightly with the photon energy. The distribution from the exact treatment is colder than the FC distribution, indicative of final-state interaction. However, the final-state interaction is not very strong since the FC oscillatory structure is largely retained for small j . The calculated OH distribution is negligible for j larger than four. This behavior of the OH distribution can be easily understood by analyzing the potential anisotropy. Although the 1’A” potential energy surface has a large overall angular anisotropy, it is relatively isotropic near the ground-state equilibrium angle where the molecule is excited. As a result, the parent molecule experiences little torque when it is promoted to the excited state. The dissociation is basically the recoil of the C1 from OH with a fixed 8. This can be seen from the snapshots of the wavepacket in Figure 2a. Similar calculationsare performed for the isotropic substitute DOCl. The deuterated hydrochlorous acid dissociates slower than HOC1 and the rotational state distribution of the OD fragment is hotter, as shown in Figure 8. The calculated distribution is also very close to the FC limit. The rotational distribution for OH dissociated from the 2’A’ state is also very FC-like. Figure 9 shows three rotational distributionsfor OH dissociated out of the 2IA’state at 210,240, and 270 nm. The OH rotational state becomes slightly more excited at shorter wavelengths. Theexcitation in the OH rotation is higher than that of the 1 ‘A” state, due to the anisotropy of the
The Journal of Physical Chemistry, Vol. 97, No. I I , I993 2607
Photodissociation of HOCl
w
210 nm 240 nm _ ,270 nm F.C
.-C0
0
c
3
D v) .c
U
-m
0.15
.-
0.1
-
0 C
.c m
0.05
L
0
U n 0
1
2
3
4
5
6
7
8
Rotational state
Rotational state
Figure 9. Rotational state distribution of the OH fragment dissociated from the 2IA’state at three photon wavelengths, 210,240, and 270 nm. The FC distribution is also given in the figure.
R
quantum
B classical
...... . . .
.
0.5
L
0 1 2 3 4 5 6 7 8 9 101112131415
9
-
;
:i c
C
.g c
0.4
-*
0.3
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F :
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2’A’ 3lA‘ 3lA’
3
U
0 1 2 3 4 5 6 7 8 9 101112131415
Rotational state 0
2
4
6
8
1 0 1 2 14
16 18 20
Rotational state
Figure 10. Rotational state distribution of the OH fragment dissociated from the three highest excited states, Le., the 2IA” state, the 3IA’ state, and the 3’A”state. Thephotonwavelengthischosentobeat themaximum of the corresponding absorption spectra.
2IA’ state potential. It is weakly linear in the Franck-Condon region, but the potential minimum gradually changes to approximately 90°, as shown in Figure 2b. The wavepacket initially moves toward a linear H-O-CI geometry and then turns back to dissociate, with C1 recoiling perpendicular to the OH axis. The dynamics of the dissociation described here explains the slight rotational excitation in the OH rotation. The anisotropy of the potential along the dissociation path is small enough to permit the OH fragment to retain some FC feature. The OH rotational state distributions for the highest three states are calculated at the peak wavelength of each corresponding absorption band, namely, 168 nm for the 2IA” state, 148 nm for the 3’A’state, and 138 nm for the 3IA”state. The OH fragment from the 2lA”statedissociationhasavery low rotationalexcitation (see Figure 10). Forty-seven percent of the fragment are unexcited, while the rest distribute in the first five excited rotational states. This is consistent with the angular anisotropy of the 2’A” state potential, which has a minimum at the groundstate equilibrium angle. This is not the case for the dissociation of HOCl on either the 3IA” or 3IA’ state. Both excited states are linear and have strong anisotropic potentials in the FranckCondon region. The excited HOCl is subjected to a strong torque to bend the molecule to linearity. Such a strong bending force causes the OH to rotate while it dissociates and finally leads to rotational excitation. As shown in Figure 10, the rotational distributions for the OH fragment dissociated from these two states have maxima near j = 10 and extend to j = 18. The rotational distributions obtained from our quantum calculations are in qualitative agreement with the results from a classical treatment.I6 For example, the classical dynamicsshow strong rotational excitation in the OH fragment from photodissociationon the 3IA”or 3lA’states but cold rotationaldistributions for the three lowest excited states. Figure 11 shows both the quantum and classical distributionsat 193 nm for the two highest states, Le., 3IA” or 3lA’. The agreement is fairly good except for some oscillatory features characteristic of a quantum dis-
Figure 11. Rotational state distributionof the OH fragment dissociated from the 3’A’ state (lower panel) and the 3‘A” state (upper panel) at 193 nm. The classical distributionsi6are also given in the figure.
tribution. This discrepancy exists even in the Franck-Condon limit. The classical EC limit distribution, for instance, is a smooth monotonically decaying function of j , while the quantum FC distributiondisplays strong oscillations. This point has been well addressed in the photodissociation of a similar system, the first absorption band of H20,43*48$49 even when a Wigner initial distribution is used. Finally, a few comments on the functional form used to fit the potential energy surfaces are warranted. We have noticed that the anti-Morse form used by Nanbu and Iwata has several undesirable features. First, it may give a very deep hole in the linear CI-H-O geometry because of a positive value of P3 at large 8 angles. The potential may also have improper asymptotic behavior. For example, the potential should be isotropic when R approaches infinity. The functionalform used to represent the surface may still have an angular dependence due to P4. Furthermore, this functional form is not capable of representing the conical intersection well, as pointed out by Nanbu and Iwata.I6 A more general and well-behaved potential energy function form suggested by Murre11 and co-workersS0provides a much better representation of potential energy surfaces.
IV. Conclusions Time-dependent quantum mechanical calculationshave been carried out for the dissociation of HOCl. The dynamics is characterized by a wavepacket on two-dimensional ab initio potential energy surfaces, but nonadiabatic couplings among different states are ignored. The total absorption spectrum in the 200-400-nm region has been calculated and it shows two peaks centered at 240 and 330 nm, respectively,in good agreement with experiment. The peak at 330 nm is approximately 100 times weaker than the predominant peak at 240 nm. Our quantum absorption cross section speculation that HOCl may act as a chlorine sink in the upper atmosphere is probably unreasonable. The rotational state distributions of the OH fragments upon dissociation on all five excited states have been calculated at various wavelengths. It has been shown that the potential anisotropy plays an important role in the rotational excitation of the OH fragment. The OH rotational distributionsof the lowest
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three states are relatively cold and resemble more or less the Franck-Condon distribution. The OH fragment from the highest two states is found to be highly excited rotationally. This is due to the bending forces exerted on the excited molecule during the dissociation. The deuterated hydroxyl radical exhibits higher rotational excitation than OH. Acknowledgment. This work was supported by the National Science Foundation (Grant CHE-9116501).I wish to thank Dr. S. Nanbu and Professor S. Iwata for sending us a copy of their potential code and Professor A. D. Jorgensen for some useful discussions. References and Notes ( I ) Solomon, S.; Garcia, R. R.; Rowland, F. S.; Wuebbles, D. J . Nature 1986, 321, 755.
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