J. Phys. Chem. 1995, 99, 2552-2560
2552
Controlled Dissociation of HgI2 via Optical Transitions between Electronic States J6zsef Soml6i Department of Photophysics, Institute of Isotopes of the Hungarian Academy of Sciences, P. 0. Box 77, Budapest, Hungary H-1525
David J. Tannor**+ Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556 Received: July 7, 1994; In Final Form: October 19, 1994@
The control of HgI2 photodissociation is proposed as a paradigm of control of polyatomic fragmentation using sequences of optical pulses. We focus on a collinear model, with the excited electronic state surface taken from the work of Zewail and co-workers and the ground electronic state surface adapted from the work of Bernstein and co-workers. We find that, using a sequence of two Gaussian pulses with a variable delay time and dump frequency, it is possible to obtain selectivity of fragmentation in the ground electronic state I I) with one pulse sequence to 78% for two-body ranging from 95% for three-body products (Hg products (HgI I) with a different sequence.
+
+ +
Introduction
Rabitz and co-workers have emphasized learning algorithms, which may overcome problems of system uncertainty via on In recent years, several theoretical approaches to controlling line experimental iteration of pulse design.22 chemical reactions via transitions between different electronic To find a system which is a meeting ground between theory states have emerged. Brumer and Shapiro have proposed and experiment is not easy. Theory is most reliable when the schemes that use the interference of two continuous-wave system is small. The smaller the number of electrons in the lasers.' Tannor and Rice2 have proposed a method which uses molecule, the more accurately one can calculate the potential two ultrashort laser pulses to break a desired chemical bond energy surfaces of the molecule and their couplings in various selectively. Rabitz and co-workers have formulated the problem excited states. In addition, the smaller the number of atoms of quantum state manipulation in terms of optimal control and the lighter they are, the more tractable is the simulation of t h e ~ r y . ~Kosloff et a1.: building on an earlier variational the quantum dissociation dynamics. On the experimental side, formulation of Tannor and Rice,2 arrived at the same formulation however, these considerations are reversed. The larger the independently. Theoretical simulations strongly suggest that optical control of photochemical products has a bright f ~ t u r e . ~ - ' ~ molecule, the more likely it is to have electronic transitions in the visible region, rather than the UV region; electronic Experimentally, there has been great progress in the technology spectroscopy is, in general, much easier in the visible region. of pulse shaping and sequencing, with applications to molecular Moreover, the heavier the atoms, the longer the vibrational systems. Zewail and co-workers pioneered the development and application of femtosecond pulse sequences to probe period and hence the more completely one can prepare and reaction dynamics. They have demonstrated how femtosecond manipulate localized wave packets in the laboratory with present pulse pairs can be used to clock dissociation times and to probe day technology. For example, a 30 fs pulse will not prepare a excited state potential surfaces." Scherer, Fleming, and colocalized wave packet in H2, which has a vibrational period of workers devised an elegant method to control the relative phase 7.5 fs, but it will prepare a localized wave packet in 12, which of two femtosecond pulses to fully exploit the coherence has a vibrational period of about 150 fs, since in the latter case properties of laser light. l2 Other pulse-shaping techniques have the time scale for the excitation is short compared with the been developed by Weiner and Heritage13 and Warren.14 The nuclear dynamics. new titanium-sapphire lasers may make the generation and Compounding the gap between theory and experiment are shaping of femtosecond pulses much simpler than has previously practical considerations. Many molecules are simply difficult been p0ssib1e.l~ In spite of promising preliminary attempts to to work with or lead to products which are difficult to attain pulse sequence control of chemical products,16 to date discriminate against experimentally. Others are not well there are no definitive experimental examples which achieve understood, either experimentally or theoretically. Rather than completely active control, as we define it below in this paper. searching in the abstract for the ideal experimental candidate Several approaches have been proposed to close the gap for control, we consider those molecules for which femtosecond between theory and experiment. One approach is to restrict spectroscopy has already been demonstrated. This will guarattention to the observable effects of simple pulse sequences or antee that the molecule absorbs in a favorable region of the linearly chirped pulses. For example, several groups have spectrum, that it is not impossible to work with, that its focused on the use of sequences of Gaussian pulses, where the vibrational time scale is long compared with existing ultrashort Gaussian parameters may be obtained either by a constrained pulses, and that something is understood about its wave packet optimization or by a fit to the unconstrained optimal pulse wave dynamics on a time scale relevant to control of bond breaking. Others have focused on the use of chuped pulse^.^^-^^ This approach has been adopted b e f ~ r e , ' ~ ,although ' * ~ ~ ~to~ our ~~ knowledge all such earlier studies have been restricted to t Alfred P. Sloan Foundation Fellow 1991-95. diatomics. Abstract published in Advance ACS Abstracfs, February 1, 1995 @
0022-365419512099-2552$09.00/0 0 1995 American Chemical Society
Controlled Dissociation of Hg12
J. Phys. Chem., Vol. 99, No. 9, I995 2553
TABLE 1: Parameters of the Damped Morse Oscillator for the HgIz XZZ+Potential Surface Do(cm-') ~i(cm-') BO up@) ra(A) us+@) - 1000
2800
7.1
1
0.75
5.5
Y(A-')
re'@)
1 .o
0.2
2.8
2.5
2.3
Schrodinger equation reads
where and l y 2 denote the wave functions on the ground and excited electronic potential surfaces and p and c(r) are the dipole moment and the electric field associated with the laser pulses, respectively. The motion of the wave function on the potential surfaces is governed by the Born-Oppenheimer Hamiltonian:
ti2 2 -I-V1,, H,,, = --V 2m
2.1
7.5
4.8
IHg-I
(A)
Figure 1. (X2C+)"potential energy surface (the excited potential energy surface) used in our calculations.
The above considerations lead us to the study of control of HgI2 photodissociation as a paradigm of polyatomic control. This molecule has been the subject of detailed femtosecond optical pulse sequence inve~tigation?~-~~ It has many appealing experimental features, e.g. absorbing in the near UV region and having a relatively long time scale for vibrational motion. Because it is a triatomic, it has the richness of various possible photofragment pathways. As a result of the experimental femtosecond s t ~ d i e s *and ~ , the ~ ~ detailed wave packet modeling of the experiment^,^^ both carried out by Zewail's group, much is understood about the excited state wave packet dynamics. In particular, it is clear that there is a competition between twobody and three-body photofragments, i.e. HgI2 HgI I vs HgI2 I Hg 1. There is also a branching between production of I and I* (spin-orbit excited iodine) which may be controlled. Although it has not been observed in the femtosecond experiments, one can imagine selectively producing Hg I2 as well. In this paper we focus on control of the two-body (HgI I) vs three-body (Hg I I) branching ratio in HgI2. The study is limited in several ways. The dynamics on only two potential surfaces is considered, and there is no consideration of processes that lead to I* product. The bending degree of freedom is neglected in the study. One can argue that on the time scale of the pulse sequences there is little time for the slow bending motion to participate. However, inclusion of the bend degree of freedom would simply have rendered the quantum calculation intractable. Moreover, given the level of uncertainty in the potential energy surfaces in general and in the bend coordinate in particular, it seemed reasonable to neglect that degree of freedom in this preliminary study. Despite the shortcomings of the present study, it is believed that this represents an important intermediate step toward the meeting of theory and experiment on control of this benchmark system.
-
+
+
+
+ +
-
Vln stands for the potential in the groundexcited electronic state, while VZ is the Laplacian. The excited state surface we use is the analytical surface developed by Zewail and c o - ~ o r k e r son~ ~the basis of femtosecond pump-probe studies. Those workers developed a collinear model which seemed to reproduce the experimental data quite well. The model consists of a damped Morse oscillator with two sets of parameters:
I
.,
+
___e-yr1
("'
re)
where rl and r2 are the bond coordinates (IHg-I and I-HgI distances) and D, b, and re are the dissociation energy, the exponential coefficient (related to vibrational frequency), and the equilibrium distance, respectively, and are allowed to vary according to
+
+
1
V2(rl,r2) = D 1 - exp -#?
(4) (f= D, b, re). We used the second set of parameters suggested in ref 25 (the b potential surface), since they gave better agreement with the experimental results. These parameters are listed in Table 1. Figure 1 shows equipotential contours for this potential surface. The ground state potential energy surface was constructed to give good agreement with the surface of Bernstein and coworkers, on the basis of experimental data.26 The twodimensional space of the bond coordinates is divided into two parts, the interaction region (up to 4.5 A in both coordinates) and the asymptotic region. The overall potential is the weighted sum of potentials for each of these two regions, where the weight function is the Fermi distribution function in both coordinates:
and
Model and Numerics
The HgI2 molecule was treated in the framework of the Born-Oppenheimer approximation. Two electronic states, namely the X ' c i and the (X2C+)estates, were considered. The
Here rl and r2 are the bond coordinates, and r11 and r21 are the borders of the region governed by the interaction potential, while sx and sy determine how wide the intermediate region between
2554 J. Phys. Chem., Vol. 99, No. 9, 1995
Soml6i and Tannor
7.5
25 20
n
i t
1
I \
’”i ;Ir
5.7
5
4
5
U
%F=i
P U
1
3
3.9
3
2.1
2.1
7.5
4.8
IHg-I
(A)
Figure 2. Ground state potential energy surface of Hg12. TABLE 2: Parameters of the Ground Potential Energy Surface interaction asymptotic used in region region both regions
(A) rzI (A) r w x k (A) rswyk (A) 111
PK)
Pkl
uPk
DK)(ev) Dki
(eV)
ffDk
rem (A) reki
ffrk
(4
4.5 4.5
5.5 5.5
10.0 10.0
12.0 -6.558 0.6 0.39 2.6 0.014 32 2.4 1.68 0.02
12.0 3.1 0.007
0.39 2.6
SYMMETRIC C9OROIIUATE
i
Figure 3. Slices of the potentials along the symmetric coordinate in the ground and excited electronic states. 0 1 , 0 2 , and 03 show the pump frequency (identical for the two pulse sequences) and the dump frequencies for the second and for the first pulse sequences, respectively.
the equilibrium value of the excited state is larger than that of the ground state, and the excited state well is much shallower than that of the ground state. A complex potential was used to absorb the dissociating part of the wave function and to measure the yields of different final products. The rate of absorption induced by the complex potential is proportional to the expectation value of the imaginary part of the potential, i.e.
0.0017
6.85 0.68 0.006 0.13 0.13
sx SY
The complex potential covers a 0.3 A wide region on two edges of the examined area:
the interaction and asymptotic regions is. Each potential is a Morse function rotated around the swing points of (5.5 A, 5.5 A) for the interaction and (10.0 A, 10.0 A) for the asymptotic potential. The parameters of the Morse functions depend on the angle of the rotation about the swing point, ak,where k = I, A denotes either the interaction or the asymptotic region:
Vk ( l ,r21-- Dk{[ 1 - $t(rk-rek)lrek]2
Vc(rl,r2)= 0 i f r , < rc and r2 < rc
- 1}
(9)
+
Vc(r1,r2)= i(VIml V,m2)otherwise
where f stands for
or D. The swing angle a is given by
Parameters used for the ground state potential energy surface in our calculations are summarized in Table 2. Figure 2 shows equipotential contours for the surface. Slices of the potential surfaces along the symmetric coordinate are shown in Figure 3 to highlight the energetics of the processes involved. Note that
rc and rm, denote the beginning of the complex potential and the maximal value of each coordinate, respectively. Since the coordinates can vary from 2.165 to 6.773 A, rc was chosen as 6.473 A, while VOwas chosen to be 13170 cm-’. The wave function absorbed in the regions of rl E [2.165 A, 4.0 A], r2 1 rc or r2 E [2.165 A, 4.0 A], r1 1 rc was considered to dissociate into two-body products, while the amplitudes absorbed in the regions rl 2 rc, rz > 4.0 8, and r2 1 rc, r1 > 4.0 A (note that these two regions overlap) were assigned to three-body dissociation. The time dependent SchrBdinger equation was solved using the Fourier method on a 512 x 512 point grid. The time propagation was performed using the Split operator m e t h ~ d . ~ ’ . ~ ~ HgI2
-.HgI + I vs HgIz --.. I + Hg + I
-
We explore what is perhaps the simplest possible control scenario to discriminate between HgIz HgI I vs HgIz I
+
-
Controlled Dissociation of HgI2
J. Phys. Chem., Vol. 99, No. 9, 1995 2555
+
4-Hg I, in which the first laser pulse (pump pulse) excites the molecule to the excited state potential surface and a second pulse (dump pulse) stimulates emission to the ground electronic state at some later time. In favorable cases the excited state wave packet stays localized, and by controlling the time delay between the pump and dump pulses, one can control the propagation time on the excited state surface and hence the dissociation products (this is also known as the Tannor-Rice scheme2). Due to the symmetry of HgI2 there are only two distinct exit channels in the ground electronic state under collinear geometry, the I Hg I and the HgI I channels. (If bending motion is allowed, a third product, Hg 12, becomes possible, and the control of this product would be very interesting; this point is discussed further in the Conclusion.) Note, that the I Hg I final products produced in either of the two electronic states are indistinguishable. The goal o f this paper is to construct pulse sequences to significantly enhance the fraction of three-body product (Hg I I) over two-body product (HgI I) and vice versa. These pulse sequences should be producible using current or imminently available technology. To solve the time dependent Schrodinger equation for a heavy three-atom molecule like HgI2 is quite a CPU intensive problem; therefore, it is practically impossible to carry out a complete optimization of the pulse sequence. On the basis of our previous we have restricted our attention to twopulse pump-dump pulse sequences, with the goal of control of two-body vs three-body dissociation on the ground electronic state. The functional form of the electric field is taken to be a sequence of two Gaussian pulses
+ +
44
a
I
E 0 \
r3
33
6 l
.--
m
*
22
0
Z
W
+ +
3 r 3 11 w
U LL
+ +
+
0 0
200
100
TIME
+ +
IFSI
44
b
5 m Q
3
*
22
3
p
0
z
w
2
2
11
U LL
The temporal width (a)of the amplitude of all pulses was set to 21.3 fs. This corresponds to a fwhm of 33.5 fs in the intensity, a value which is quite tractable with present technology. The corresponding spread in frequency is a o of about 250 cm-'. The pump pulse is the same for both sequences: its central frequency is chosen to be 310 nm, the value used in the experiments of Dantus et al.24 This excitation energy deposits 8950 cm-' of potential energy more than is required for three-body dissociation of the molecule in the excited electronic state. Since the initial displacement is directed entirely along the symmetric stretch coordinate, this excitation leads to direct and virtually complete three body breakup in the excited state. This greatly constrains the possible control: the dump pulse must come in within 200 fs, since that is the time scale for irreversible exit to three-body products. Moreover, the excitation of the wave packet prepared by the dump pulse on the ground state is of necessity along the symmetric stretch. The function of the second pulse is therefore only to determine the position and momentum of the dump wave packet along the symmetric stretch: long time delays (> 150 fs) will prepare a ground state wave packet with a large displacement along the symmetric stretch, while short time delays will prepare smaller displacements. Note that the energy required for threebody dissociation on the ground state is 24125 cm-'. Only a part o f this energy can be obtained from kinetic energy on the excited state, which is limited to 11750 cm-'. However, the full amount of energy required for three-body dissociation can be deposited in the form of potential energy: the large amplitude symmetric stretch motion on the excited state is capable o f "airlifting" the wave packet arbitrarily far into the asymptotic region of the ground state potential in our model. Thus, the control scenario is this: with a longer delay time between pulses the dump pulse prepares a ground state wave packet which is
100
0
200
TIME (FSI
Figure 4. Husimi transform of the pulse sequences leading to mostly (a) three-body and (b) two-body final products. The central frequencies of these pulses are compared to the difference between the potential surfaces in Figure 3. Parameters of the pulse sequences are summarized in Table 3.
TABLE 3: Parameters of the Pulse Sequences Leading to I He: I or He:I I Final Products
+
+
+
goal: I + H g + I A l 2 (W
cm-*) Az2 (W cm-2) w1 (cm-') 0 2 (cm-') t l (fs) t 2 (fs) at (fs)
3.15 x 1013 1.26 x 10" 32 880 4850 32 152 21.3
goal: H g I + I 3.15 x 1013
5.04 x 10" 32 880 8400 32 121 21.3
so far displaced along the symmetric stretch coordinate that the exit out the three-body channel is irreversible. With a shorter delay time, the symmetric stretch displacement is not as large. Although there is still enough energy available for three-body dissociation, the energies are much lower, and the majority of amplitude on the ground state does not exit directly. While some fraction of the amplitude does exit directly, the remainder reflects back from the three-body region, leading to long-lived trajectories in the ground state interaction region which ultimately exit primarily via the two-body channels. Two time delays were chosen: 120 and 89 fs. The frequencies of the dump pulses were chosen to stimulate the most possible population back to the ground electronic state, i.e. to be equal to the Franck-Condon energy associated with that timing. The parameters of the pulse sequences are summarized in Table 3.
Soml6i and Tannor
2556 J. Phys. Chem., Vol. 99, No. 9, 1995 I
1.01
z
0
c
4 J
3
a 0 a
I 100
200
TIME I F S I
0 W
2 .I0
U W
w
c 7. e
.05
5
10 TINE
15
0
5
10
15
20
25
30
TIME Il@0 FSI
Figure 5. (a) (valva)and (b) ( v b l v b ) as a function of time, using the fiist pulse sequence. The pump pulse excites 52% of the molecules, and the second pulse dumps 27% of them.
"0
0
20
25
30
I100 FSI
Figure 6. Integrated dissociation probability from 0 ps to t. The probability of (a) the two-body and (b) the three-body dissociation in the ground electronic state; (c) the two-body and (d) three-body dissociation in the excited electronic state using the fiist pulse sequence. Curve a has not reached its maximum, but a significant increase is not expected.
The Husimi transforms of the pulse sequences, shown in Figure 4, allow one to visualize the pulse sequence in time and frequency simultaneously. The Husimi transform is defined as follows:
The pump pulse excites 52% of the amplitude onto the excited potential surface (Figure 5 ) . In the case of the first pulse sequence the excited state wave packet has reached the beginning of the three-body asymptotic region with large positive momentum before the second pulse dumps 27% of the population at 120 fs (Figure 5 ) . Thus, by the Franck-Condon principle, after the dump pulse most of the ground state wave packet dissociates into three atoms. This can be seen clearly in Figure 6 , which shows the integrated dissociation probability as a function of time (curve b). Only a small portion of the
Figure 7. F'robability of (a) the two-body dissociation and (b) the threebody dissociation in the ground electronic state using the first pulse sequence.
dumped 27% does not have enough energy to reach the threebody asymptotic region: 6% of the dumped population does not dissociate at all, while 2% breaks into two-body products (Figure 6, curve a). Most of the 24-25% amplitude left on the excited surface by the second pulse dissociates into three atoms (Figure 6, curve d). The time dependence of the exit probability is a good indicator of the dynamics and is shown in Figure 7. The wave function reaches the three-body dissociation region in the first 900 fs in both electronic states; after that the two-body dissociation dominates despite the low overall yield for this process. After the first two-body dissociation peak, which belongs to direct dissociation, a second peak appears due to indirect processes. The molecules which do not have enough kinetic energy after the dump pulse to reach the three-body asymptotic region reflect back to the equilibrium region of the ground state potential. This amplitude is subsequently scattered off the inner turning point of the ground state potential and directed into the two-body channels. This indirect process is responsible for the second peak starting at 1.2 ps. This phenomenon represents only a small portion of the dissociation in the case of the first pulse sequence but will be seen to play a very significant role in the second pulse sequence. Equal amplitude contours of the wave packet on both surfaces at t = 162 fs and t = 2.85 ps are shown in Figure 8. Most of the three-body amplitude has already been absorbed by this later time. Note the lack of significant amplitude in the two-body channels on the ground state. Using the second pulse sequence the two-body (HgI I) yield is increased significantly. The pump pulse again excites 52% of the molecules (Figure 9). The time delay between the laser pulses is 89 fs; in this case molecules do not have enough time to reach the three-body asymptotic region on the excited state potential energy surface. Although the second pulse was more efficient in this case and 40% was dumped to the ground potential surface (Figure 9), only 4.5% of the amplitude is able to reach the three-body asymptotic region in the ground electronic state (Figure 10, curve b). The potential energy barrier between the interaction region and the two-body asymptotic region in the ground electronic state is small; hence, those molecules which are reflected back to the equilibrium region still have a chance to dissociate into two-body products. The two-body dissociation probability is 15- 16% using the
+
Controlled Dissociation of HgI2
J. Phys. Chem., Vol. 99, No. 9, 1995 2557 6.8
a 5.2
5.2
n
n
*s
5
n
n
q*
T
H
n
3.7
2.2
3.7
l o
2.2
4.5
IHg-I
2.2 2.2
6.8
4.5
(A)
(A)
IHg-I
6.8
6.8
6.8
b
n
5.2
n
5.2
*s
O S
r
Y
T
$ H
Y
3.7
3.7
2.2 2.2
2.2 4.5
IHg-I
6.8
2.2
4.5
(A)
IHg-I
6.8
(A)
Figure 8. Snapshots of the amplitudes on the (a) ground and (b) excited potential surfaces at time 162 fs and on the (cj ground and (dj excited
surfaces at time 2.85 ps using the fist pulse sequence, which leads to mainly three-body products. second pulse sequence, as is shown in Figure 10, curve a. Due to the smaller kinetic energy the total dissociation probability decreases from 49% to 34%. Molecules left in the excited state by the second pulse again dissociate primarily into three-body products (Figure 10, curve d). The dissociation probability in the ground electronic state as a function of time, using the second pulse sequence, is shown in Figure 11. The highest values of the two- and three-body dissociations are almost equal, but the broad second peak due to the indirect processes is the source of the much higher yield for the two-body product. The wave function driven by this pulse sequence has virtually no component going into the threebody channel at later times (Figure 12). The effect of the two different pulse sequences on the molecule is summarized in Table 4. Selectivity is defined as the ratio of the objective (either three-body or two-body dissociation in the ground electronic state) to the total dissociation in the ground electronic state. Using the fiist pulse sequence, 19% goes into the ground state three-body channel and only 2% into the ground state two-body channel, for a selectivity of 90%. Using the second pulse sequence, the probability of the three-atom dissociation in the ground state decreases to 4.5% while the ground state two-body dissociation increases to 15.5%, for a selectivity of 78%. The remainder of the probability (the discrepancy between the sum of the
probabilities in Table 4 and unity) is due to the probability for formation of undissociated HgI2.
Conclusion We have presented a model study of HgI2 photodissociation using two different pulse sequences. The study considers only two electronic states and neglects the bending degree of freedom; thus, HgI I*, Hg I* -t I*, and Hg 12 products are not included in the model. The objective was to control two-body vs three-body products, i.e. HgI I vs Hg I I. The pulse sequences were restricted to forms deemed accessible with current technology. They consist of a pair of Gaussian pulses with an adjustable time delay and central frequency. The width of the pulses in all cases was taken to be 21 fs (a),corresponding to a fwhm of 33.5 fs in the intensity. A great deal of control was found to be achievable. With a time delay of 120 fs, the ratio of three-body to two-body product on the ground state was about a factor of 10; with a time delay of 89 fs, the ratio of two-body to 3-body product on the ground state was about a factor of 3.5. These results require some further discussion, however. The experiments and simulations of Zewail’s group on the FTS of Hg1223-25 suggest that three-body product dominates at high excitation energies (3 10 nm) while two-body product dominates
+
+
+
+
+ +
Soml6i and Tannor
2558 J. Phys. Chem., Vol. 99, No. 9, 1995 ! .01
I
3 a 0
a
0' 0
I
100
200 TIME
TIME lFSl
Figure 9. (a) (l/)all/)a)and (b) (l/)t,ll/)t,) as a function of time, using the second pulse sequence. The pump pulse excites 52% of the molecules, and the second pulse dumps 40% back to the ground electronic state.
The complex potential absorbs the amplitude as it reaches the asymptotic regions. ,
2
0
/--I
a
/ d l
a W t-
4
a w
b
W * Z C
'
C ------I
2'0
'
25
'
i0
'
35
T I M E I100 FSi
Figure 10. Integrated dissociation probability from 0 ps to t. The probability of (a) the two-body and (b) the three-body dissociation in the ground electronic state; (c) the two-body and (d) three-body
dissociation in the excited electronic state using the second pulse sequence. Curve a has not reached its maximum, but a significant increase is not expected. at lower excitation energies. One can therefore say that twobody vs three-body control can be controlled via sweeping through the excitation frequency. Although this is a form of control, it is passive, in the sense that it uses nature's FranckCondon factors. A more active form of control, which is at the heart of the Tannor-Rice scheme, as well as the schemes of Brumer and Shapiro, and Rabitz and co-workers, is to prepare states with the same energy content but which lead to different bond breakage. We call this completely active control. Technically speaking, in completely active control one exploits the degeneracy of the dissociative continuum corresponding to different chemical arrangement channels (i.e. the degenerate eigenstates corresponding to different chemical products), and the goal is to excite only those that lead to the desired chemical product. In the case of HgI2 studied in this paper, above the energy for three-body dissociation, two-body dissociation is still
(100 F S i
Figure 11. Probability of (a) the two-body dissociation and (b) the
three-body dissociation in the ground electronic state using the second pulse sequence. energetically accessible. If the excess excitation energy can be directed selectively into translational motion of the two-body fragments, those products can be energetically identical to slower ~ three-body fragments. This would be completely active control according to our definition. Despite the significant degree of control over branching ratio as a function of time delay described above, it must be recognized that the energy contents of the wave packets produced by the two dump pulses differ significantly. Thus, the control is only partially active: although the energy content of the ground state wave packets is actively controlled via time delay and central frequency, the selection of Franck-Condon factors within that degenerate energy region is not actively controlled. This is an inevitable consequence of the excited state potential surface and the excitation at 310 nm, which leads to three-body dissociation in 500 fs. Thus, there is only one temporal window to access each region of the ground state potential and therefore a unique dump time corresponding to a particular energy content of the ground state wave packet. In contrast, the earlier studies on the model HHD system were below the excited state dissociation limit; the broken symmetry of the model led to a Lissajous motion of the wave packet on the excited state potential and hence multiple time windows to dump back to the ground state within the same energy band but with different Franck-Condon f a ~ t o r s . * ~ ~ , * ~ Note that this situation may be considerably altered in solution,33where solvent caging could lead to multiple passes through the same frequency window. The real HgI2 molecule has the additional possibility of fragmenting to Hg 12, and it is interesting to consider the possibility of laboratory control of this arrangement vs the other two channels. From Walsh diagrams and relativistic calculations on the homologous molecules HgCl2 and HgBr2, it is believed that the excited state has a bent geometry; thus, excitation and deexcitation should lead to a certain amount of energy in the bending coordinate, which is the coordinate leading to Hg 12. We can speculate that for early dump times (90 fs) there will be a very interesting competition between dissociation to HgI -t- I and Hg I2 on the ground state. However again, if the potential surfaces used in the present study are even qualitatively correct, the direct three-body exit on the excited state at excitation energies of 310 nm allows only one time window for each energy range; even if a large yield of Hg 12 is obtained, again it can be considered only partly active control.
+
+
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Controlled Dissociation of HgI2
J. Phys. Chem., Vol. 99, No. 9, 1995 2559
6.8
a
h
5.2
OS I
$
I
3.7
2.2 2.2
4.5
IHg-I 6.8
6.8
2.2
(A)
4.5
IHg-I 6 . 8- 1
1
I
6.8
(A)
b
n
5.2
5 Y
? Y
3.7
'
2.2 2.2
IHg-I
(A)
4.5
IHg-I
6.8
(A)
Figure 12. Snapshots of the amplitudes on the (a) ground and (b) excited potential surfaces at time 162 fs and on the (c) ground and (d) excited
surfaces at time 2.41 ps using the second pulse sequence, which leads to mainly two-body products.
+ + + I Final goal: I + Hg + I goal: HgI + I
TABLE 4: Yield of the I Hg I and HgI Products Using the Two-Pulse Sequences
+ + + +
Hg I (excited state) I Hg I (ground state) I HgI (excited state) I HgI (ground state) selectivity
I
+ +
25%
13.5%
19%
4.5%
0.7% 2%
0.4% 15.5%
0.95
0.78
Despite these qualifications, HgIz is still a strong candidate for experimental control studies. The presence of the I* fragmentation channel in the excited state, with a dissociation threshold 7600 cm-l higher than that of the I channel, will have a profound effect on the energetics of at least a portion of the dissociation process, removing much of the excess energy available in the symmetric stretch coordinate. Moreover, excitation at energies below 310 nm (e.g. 450 nm) will deposit less energy in the symmetric stretch and lead to longer lived and richer excited state dynamics. At these lower excitation energies the energy acquired in the excited electronic state will not be sufficient to give three-body products in the ground state; however, the HgI I and Hg 12 channels should still be energetically accessible, and one could conceivably achieve completely active control between these channels via the choice
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of time delay. The model of Zewail and co-workersZ5predicts that, even for excitation at 450 nm, dissociation to HgI I proceeds on a time scale of less than a picosecond, which again would preclude multiple passes to regions with the same dump frequency and hence completely active control. However, it appears there is no direct experimental evidence for this, and in the absence of accurate ab initio calculations there is a lot of uncertainty remaining with regard to both the surface and the dynamics at these excitation energies. We conclude that HgI2 remains a leading contender for experiments demonstrating active control of polyatomic dissociation. Despite, or perhaps because of, the remaining uncertainties in the potentials, exploratory experimental studies would be timely. We suggest that excitation at 400-500 nm and deexcitation at 800-900 nm, with a variable time delay of 100 fs up to several picoseconds, is an appropriate parameter range to begin exploratory studies of control over HgI I vs Hg 12. Clearly, high-quality 3-D ab initio surfaces and dipoles for this system would allow one to be much more confident and specific in making predictions. Such calculations for systems with heavy atoms are just coming on line.34 Because of the heavy masses of the atoms and the fact that the pulse sequence ideas used here do not exploit phase information, classical
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2560 J. Phys. Chem., Vol. 99, No. 9, 1995
trajectories should provide an accurate assessment of the branching ratio as a function of time delay. Such a classical study including the bend degree of freedom would serve as a valuable prognosis of the feasibility of successful control experiments. Acknowledgment. This work was supported by a grant from the U.S. Office of Naval Research, with partial support from OTKA grant number 14330. We are grateful to Jiwen Qian for assistance with the graphics. Most of the computations were carried out on a Cray-YMP machine of the NCSA at UrbanaChampaign. References and Notes (1) Shapiro, M.; Brumer, P. J . Chem. Phys. 1986, 84, 4103. Brumer, P.; Shapiro, M. Chem. Phys. Lett. 1986, 126, 54. (2) Tannor, D. J.; Rice, S. A. J . Chem. Phys. 1985,83,5013. Tannor, D. J.; Kosloff, R.; Rice, S. A. J . Chem. Phys. 1986, 85, 5805. Tannor, D. J.; Rice, S. A. Adv. Chem. Phys. 1988, 70, 441. (3) Peirce, A.; Dahleh, M.; Rabitz, H. Phys. Rev. A 1988, 37, 4950. (4) Kosloff, R.; Rice, S. A,; Gaspard, P.; Tersigni, S.; Tannor, D. J. Chem. Phys. 1989, 139, 201. (5) Shi, S.; Rabitz, H. Chem. Phys. 1989, 139, 185. Shi, S.; Rabitz, H. J . Chem. Phvs. 1990. 92. 2927. Shi, S.; Rabitz, H. ComDut. Phvs. Commun. 1991,63, 71. (6) Judson, R. S.; Lehmann, K. K.; Rabitz, H.: Warren, W. S. J . Mol. Struct. 1990, 223, 425. (7) Kim, Y. S.; Rabitz, H.; Askar, A.; McManus, J. B. Phys. Rev. B 1991, 44, 4892. (8) Gross, P.; Neuhauser, D.; Rabitz, H. J . Chem. Phys. 1992,96,2834. (9) Yan, Y.; Gillilan, R. E.; Whitnell, R. M.; Wilson, K. R.; Mukamel, S. J . Phys. Chem. 1993, 97, 2320. (10) Amstrup, B.; Lorincz, A.; Rice, S. A. J . Chem. Phys. 1993, 97, 6175. (11) Zewail, A. H. Science 1988,242, 1645. Zewail, A. H.; Bemstein, R. B. Chem. Eng. News 1988,66,24. Rose, T. S.; Rosker, J.; Zewail, A. H. J . Chem. Phys. 1989, 91, 7415. (12) Scherer, N. F.; Ruggiero, A. J.; Du, M.; Fleming, G. R. J . Chem. Phys. 1990, 93, 856. Scherer, N. F.; Carlson, R. L.; Matro, A,; Du, M.; Ruggiero, A. J.; Romero-Rochin, V.; Cina, J. A,; Fleming, G. R.; Rice, S. A. J . Chem. Phys. 1991, 95, 1487.
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