J . Phys. Chem. 1989, 93, 1840-1851
1840
state in CS2 is approximately twice as long as the ‘Z+ state in OCS, allowing for a longer period of time for energy to flow into a mode responsible for dissociation of the weak bond in (CS,), before covalent dissociation takes place. 2. The exchange of a S-S bond for a C-S bond is exothermic in OCS by 0.7 eV but is endothermic by 0.05 in CS2. If the dimer covalent chemistry takes place through a mechanism as presented in reactions 7 and 10, then on the basis of the above energetics covalent chemistry in the CS2 dimer would be less favorable than in the OCS dimer. 3. The geometry of the dimers and the vibrational excitation in the excited states may play an important role as well. For example, the transition to the linear IZ+state of OCS leads to excitation of the symmetric stretch. Given the proposed “staggered parallel” geometry of the OCS dimer,15 this mode would not be disruptive to the van der Waals bond. In CS2 on the other hand, the transition to the bent lB2(IZu+)state leads to excitation in both the symmetric stretch and bending modes. Given the proposed linear geometry of the CS2 dimer,I5 both of these modes could be considered disruptive to the weak van der Waals bond. It is obvious from these results that photochemistry competes efficiently with energy transfer and that the covalent bond dissociates on a time scale shorter than that required for energy flow to complete randomization.
Conclusions In summary, the photodissociation of dimers of OCS and CS2, prepared in supersonic expansions, was investigated by using REMPI techniques. The results indicate that a significant amount of covalent chemistry occurs in the dimer, even though the van der Waals bond is much weaker, These results are consistent with recent studies of OCS cluster photodi~sociationl~ in the ‘A state at 222 nm and with evidence of CS2 cluster photodiss~ciation’~ of the ‘B2(lZU+)state at 193 nm. Comparatively more covalent chemistry is found to occur in the OCS dimer than in the CS2 dimer. This difference is presumed to be due to the difference in the energetics involved as well as the difference in excited-state dynamics for the two systems.
Acknowledgment. Financial support from the NSF, Grant C H E 8702486, is gratefully acknowledged. The authors thank Maureen McCarthy for many fruitful discussions. Registry No. (0CS)2, 463-58-1; (CS,),, 75-15-0; S2, 23550-45-0; C$,, 83917-77-5.
Supplementary Material Available: Tables of relative signal intensities from electron impact ionization of OCS and CS2 (4 pages), Ordering information is given on any current masthead page.
HOD Spectroscopy and Photodissociation Dynamics: Selectivity in OH/OD Bond Breaking Jinzhong Zhang, Dan G . Imre,* Department of Chemistry, University of Washington, Seattle, Washington 98195
and John H. Frederick Department of Chemistry, University of Nevada-Reno,
Reno, Nevada 89557 (Received: September 26, 1988)
We present a study of HOD photodissociation dynamics in the first electronically excited state for transitions originating from the ground as well as a few vibrationally excited states. The electronic absorption as well as emission spectra are calculated for the first time by using a quantum mechanical time-dependent formalism in the two stretching coordinates, and they are compared with those of H 2 0 and DzO.Good agreement between the calculated and experimental emission spectra is observed. Nuclear dynamics on both the ground and excited states are examined. A connection between the observed spectra and the photodissociation reaction is made. Branching ratios (H + OD)/(D + OH) as a function of laser frequency are obtained. There is generally a higher probability to break the OH bond than the OD bond, but to achieve selectivity in bond breaking to yield exclusively one of the two possible products requires a two-photon (IR + UV) scheme. Such a scheme is designed and presented.
I. Introduction The spectroscopy and photodissociation dynamics of water in its first absorption band have been the subject of many recent investigations. The first electronically excited state, the AIBI, is known to be repulsive, and the molecule dissociates directly to give H(2S) + OH(211). The water molecule presents a unique situation in which only one Born-Oppenheimer electronically excited state needs to be considered and no curve crossing is involved. Moreover, the small size of this molecule makes it feasible to calculate the relevant potential energy-surfaces (PES) from first principles. The ab initio PES for the A state has been calculated by Palma et al.’ and has since been used in several dynamical and spectroscopic studies.2” Schinke and co-workers14 ( I ) Staemmler, V.; Palma, A. Chem. Phys. 1985, 93, 63. (2) Engle, V.; Schinke, R.; Staemmler, V. J . Chem. Phys. 1988, 88, 129. (3) Henriksen, N.; Zhang, J.; Imre, D. G.J . Chem. Phys. 1988, 89, 5607.
0022-3654/89/2093- 1840$01.50/0
have calculated the absorption spectrum and photodissociation final product-state distributions, treating all three vibrational modes, and obtained good agreement with experimental result^.^^* We have very recently used the same surface to study the absorption3 and emission5 spectra. Our study was done in the two stretch coordinates while keeping the bend futed at the ground-state equilibrium geometry. We obtained excellent agreement with the absorption spectrum calculated by Schinke et al., which suggests that the photodissociation can to a good approximation be described in the two stretch coordinates. This is supported by the (4) Schinke, R.; Engel, V.; Andresen, P.; Hausler, D.; Baht-Kurti, G. G. Phys. Reu. Lett. 1985, 55, 1180. ( 5 ) Zhang, J.; Imre, D. G. J . Chem. Phys., in press. ( 6 ) Zhang, J.; Imre, D. G. Chem. Phys. Leff. 1988, 149, 233. (7) Andresen, P.; Ondrey, G. S.; Titze, B.; Rothe, E. W. J . Chem. Phys. 1980, 80, 2548. (8) Schinke, R.; Engel, V.; Staemmler. V. J. Chem. Phys. 1985,83,4522.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1841
H O D Spectroscopy and Photodissociation Dynamics recently measured resonance Raman (emission) spectrum, which shows a long progression in the two stretch modes with no hint of any bending a ~ t i v i t y . ~Our calculated resonance Raman spectrum fits the experimental spectrum extremely well. In our study, we were able to correlate the diffuse structure in the absorption spectrum with the dynamics on the excited state, showing that the observed diffuse vibrational progression is due to motion along the symmetric stretch ~ o o r d i n a t e .This ~ study indicated that the excited-state symmetric stretch frequency is almost a factor of 2 smaller than in the ground state. The excellent agreement between the calculated and observed absorption spectra and final product distribution further testifies to the high quality of the excited-state ab initio surface. To calculate the resonance Raman spectrum requires knowledge of three surfaces: the excited state, the ground state, and the transition moment surface. There exists a good PES for the ground state-it was obtained by Reimers and Watts1@IZby fitting to infrared data. In our study of the resonance Raman spectrum of HzO,Swe used this surface and obtained excellent agreement for both the line positions and intensities. In addition, we constructed for the study a simple transition moment surface in the two stretch coordinates that was used to fit the resonance Raman spectrum. ' The ground electronic state of H 2 0 has been the subject of a number of studies'@z0 that show that the dynamics and the vibrational eigenstates are of local mode character. Child13J4has shown that the ground-state eigenfunctions come in pairs, analogous to a tunneling pair in a symmetric double-minimum potential. In water, there is no actual potential barrier, yet energy transfer from one 0-H stretch to the other can occur via a process that has been termed dynamical tunneling. We will show that the broken symmetry of the HOD molecule enables us to localize vibrational energy in the OH or OD bond_exclusiuely and thus induce bond-specific dissociation on the A state. Isotope effects in chemical reactions have been an important tool in the study of chemical dynamics and kinetics throughout the years. The existence of high-quality PESs for the water molecule makes it possible to conduct a detailed study of the isotope effect in H O D photodissociation. Here the isotopic substitution results in symmetry breaking, and two distinct channels are open, one yielding H OD and the other D OH. Because of the symmetry breaking, we do not expect the two products to be formed with equal probability. In a recent paper Engle and Schinke2' presented a study of the isotope effect in the photodissociation of HOD. Their results show a branching ratio of ( H OD)/(D O H ) = 2.5 on the average. Moreover, they show that this ratio is wavelength dependent and it changes when one photodissociates vibrationally excited HOD rather than v" = 0. Unfortunately there are no experimental data available for HOD absorption spectra or final product-state distributions. This is due to the fact that HOD cannot be isolated from H 2 0 or D20, all of which will be present in the experiment. We will show here that a two-photon scheme can be used to create a spectral region where H O D is the only absorbing species, permitting a study of the final product distributions for pure HOD. Many interesting questions associated with symmetry breaking
+
+
+
+
arise. The ratio ( H OD)/(D O H ) is expected to be wavelength dependent. This suggests the possibility that one might be able to devise a scheme for selectively inducing the molecule to dissociate by breaking one bond and not the other. We will present such a scheme that can be used to yield either of the two possible products at the experimentalist's will. The isotope substitution induces a significant change in the ground-state eigenstates as well. In some respects HOD is more like an asymmetric bent A-B-C type molecule than an analogue of H20. As a result, we will present an examination of the ground-state eigenstates for HOD. The paper is organized as follows: in section 11, we describe briefly the theoretical and numerical tools used in the calculations and the molecular model. We present absorption and emission spectra for transitions starting from u" = 0 and discuss the photodissociation dynamics on the electronically excited state in section 111. In section IV, eigenstates for the ground electronic state are calculated, and the ground-state dynamics are addressed. A scheme for selective bond breaking is discussed in section V. We use a variety of vibrationally excited states to uncover spectral regions that lead to a single product. Finally, our results are summarized in the last section. 11. Theory and Model A . Theory. We adopt here a time-dependent f o r m a l i ~ m ~ ~ - ~ ~ to treat the photodissociation process. This approach has been applied recently to several real molecular systems.3~s~6~25-29 The calculation procedure here follows closely that used in the study of HzO in ref 5 ; therefore, only a very brief outline of the theory is given. This treatment assumes the photodissociating laser is on for a long time compared to the dissociation time, which is consistent with most current experiments. According to the-dependent f ~ r m a l i s m , ~ the ' - ~ ~absorption spectrum is given by
in which
+
+
(9) Sension, R. J.; Brudzynski, R. J.; Hudson, B. Phys. Reu. Lett. 1988, 61, 694. (IO) Reimers, J. R.; Watts, R. 0. Mol. Phys. 1984, 52, 357. (11) Coker, D. F.; Watts, R. 0. J . Phys. Chem. 1987, 91, 2513. (12) Coker, D. F.; Miller, R. E.; Watts, R. 0. J . Chem. Phys. 1985, 82, 3554. (13) Lawton, R. T.; Child, M. S. Mol. Phys. 1979, 37, 1799. (14) Lawton, R. T.; Child, M. S. Mol. Phys. 1980, 40, 733. (15) Sorbie, K. S.; Murrell, J . N. Mol. Phys. 1975, 29, 1387. (16) Sibert, E. J.; Reinhardt, W. P.; Hynes, J. T. J . Chem. Phys. 1982, 77, 3583. (17) Davis, M. J.; Heller, E. J. J . Chem. Phys. 1981, 75, 246. (18) Hutchinson, J. S.; Sibert, E. L.; Hynes, J. T. J . Chem. Phys. 1984, 81, 1314. (19) Kellman, M. E. Chem. Phys. Left. 1985, 113, 489. (20) Jaffe, C.; Brumer, P. J . Chem. Phys. 1980, 73, 5646. (21) Engle, V.; Schinke, R. J . Chem. Phys. 1988, 88, 6831.
(3) Here, ,Zgeis the electronic transition moment (and is a function of the nuclear coordinates), ZI is the direction of polarization of the oncoming photons, and li) is the initial vibrational state. He is the nuclear Hamiltonian for the excited electronic state, and r is a phenomenological lifetime. From eq 1, we can see that all the spectroscopic and dynamical information is contained in the time dependence of the wave packet I$i(t)) on the excited state. The time-dependent expression for the Raman spectrum is similar, only now the dynamics occurs on the ground electronic state and the t = 0 wave packet depends on the incident photon frequency, wI: I ( w , w ~ )=
S _ ~ ~ e " ' ( ~ R ( w I ) l @ R ( W , ; t ) ) dt
(4)
where
(22) Heller, E. J. Acc. Chem. Res. 1981, 14, 368. (23) Lee, S.-Y.;Heller, E. J. J . Chem. Phys. 1979, 71, 4777. (24) Heller, E. J.; Sundberg, R. L.; Tannor, D. J . Phys. Chem. 1982,86, 1822. (25) Imre, D. G.; Kinsey, J. L.; Sinha, A,; Krenos, J. J . Phys. Chem. 1984, 88. 3956. (26) Imre, D. G.; Kinsey, J. L.; Field, R. W.; Katayama, D. H. J . Phys. Chem. 1982,86, 2564. (27) Zhang, J.; Heller, E. J.; Huber, D.; Imre, D. G.; Tannor, D. J . Chem. Phys. 1988, 89, 3602. (28) Zhang, J.; Imre, D. G. J . Chem. Phys. 1988, 89, 309. (29) Williams, S. 0.;Imre, D.G . J . Phys. Chem. 1988, 92, 3363.
1842 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
1@PR(q;t)) = e-(i/h)H81pR(wI)) l\kR(~I)j
&meiwl'-'tl+i(t))dt
(6) (7)
This last equation defines the Raman wave function, a time-independent function from which emission occurs back to the ground electronic state. According to these equations, the procedure for calculating absorption and Raman spectra is then very simple. First calculate the eigenstate li) on the ground electronic state, which is to be excited by the laser. This state is typically u " = 0. Then multiply the state li) by the transition moment pegto obtain I&). Finally, place 141)on the excited-state surface and calculate its time evolution, I&(t)). The absorption spectrum is given by the Fourier transform of the autocorrelation function (q5J+,(t)). While running the dynamics of I$l(t)), half Fourier transform I$,(t)) at the laser frequency wI to obtain I\kR(wI)). Multiply I\kR(wI)) by the transition moment to obtain I @ R ( ~ I ) ) and then place it on the ground-state potential. The dynamics of I @ R ( ~ I ) ) on the ground state produces a Raman spectrum by Fourier transforming the autocorrelation function ( @ R l @ R ( t ) ) . Note that this entire procedure requires calculating only one eigenstate, namely, li). This procedure, aside from being simple to implement, provides a very intuitive picture for the experiment. It follows very closely what actually happens in the lab. In the Raman experiment the incident photon transfers the ground-state wave function, multiplied by the transition moment, to the excited state. The excited-state Hamiltonian propagates it to dissociation. The laser continuously interacts with the molecule; in doing so it projects out of the moving wave packet I @ , ( t ) ) a frequency component, the one frequency that is resonant with the laser. This produces a time-independent wave function on the excited state, the Raman wave function. In the Raman experiment, a scattered photon transfers the Raman wave function back to the ground state, so that the observable in the experiment is the spectrum of the scattered photons. A side benefit from this approach is the dynamics of I d l ( t ) ) . Examination of the time evolution on the excited state provides valuable insight into the photodissociation process. When we describe dynamic processes, we usually imply a description of the motion of 141(t)).We talk about dissociation lifetime, intramolecular energy transfer, etc., even when describing an experiment performed with a continuous-wave narrow-band laser. What we really mean is if the molecules were excited with a short pulse and a wave packet is created, dynamics would ensue. Iq$(t)) is what would be prepared if the molecule were to be excited with a 6 pulse or a pulse short enough such that it would cover the entire electronic absorption profile homogeneously. B. Model. We treat HOD in exactly the same way as we did for H 2 0 in ref 5. The molecule is studied in two dimensions, with the H-0-D bond angle fixed at 104.52O. Freezing the bending motion has been justified for H 2 0 based on two observations: (i) the separability of the bending mode from the stretches in the H 2 0 and HOD photodissociation study of Schinke et al. and (ii) the absence of a bending progression in the experimental resonance Raman spectrum of Hudson and c o - w o r k e r ~ .We ~ ~ expect ~~ the same to be true for HOD as well; thus the bending motion is neglected in the present study. The calculation is performed in the internal coordinate system with R I and R 2 representing the 0-H and 0 - D stretches, respectively. In this coordinate system, the kinetic energy is not diagonal and we include the off-diagonal terms throughout the calculation. This is given as follows:
P,2 P22 T = - + - + 211, 21*2
PIP2cos 0
(8 1
m0 where PIand P2 are the momenta conjugate to R1 and R2, respectively. p] = mHmO/(mH + mol, 1 2 .= mDmol(mD + mol, and 0 is the H-0-D bond angle, which is fixed at 104.52'. (30) Hudson, B., private communication
Zhang et al.
-u 1
2
3
XOH (au)
Figure 1. Contour plot of the first excited-state PES (dashed lines) of
HOD for H-0-D bond angle at 104.52'. The solid contours represent the initial wave packet prepared on this surface starting from u " = 0: (a) ROHand RODare the 0-H and 0-D bond lengths, respectively; (b) mass-weighted coordinates XOHand YoD. L and H indicate low and high energies, respectively. (See text for deatils.) We use the ground-state PES developed by Reimers and Watts,11J2which has the simple form v = ~ ~ - ~( ~ I1( R I - R +o ) D) ~l ( l - e4R~-Ro))2+ g
fiZ(R1 - RoI(R2 - Ro) (9) where Dl = D, = 0.2092 au, cy1 = a2 = 1.1327, and Ro = 1.81 au. We chose the coupling termfi2 to be a function of the two stretch coordinates:
with constants y = 1.0 and F12= -6.76 X so that the correct dissociation limit is ~ b t a i n e d . ~ In the study of the resonance Raman spectrum of H 2 0 5we found that the nuclear dependence of the transition moment plays an important role in determining the relative Raman intensities. We use the same function here:
-
with p = 1 .O. This analytic form assures proper behavior (i.e., I.L 0) in the asymptotic region. The excited state PES of H 2 0 has been calculated by Palma et al.' in three dimensions using ab initio techniques. A contour plot of this surface in the two stretch coordinates is shown in Figure 1. Also shown in the figure is the initial wave function I+i(0)). The isotope-induced asymmetry can be viewed in two ways. Figure l a shows the potential in the R 1 and R2 coordinate system. In this representation the potential is symmetric as in H 2 0 , but the wave function is distorted. It is wider along the light O H displacement. Thus the initial wave function appears to be "leaning" toward O H breaking. Indeed we have found that more O D is produced on the average than OH. However, in this coordinate system one cannot use classical intuition to guide the motion of Iq5i(t)), since the masses are not the same for OH and OD. Figure l b shows the same system now scaled such that the masses in XoHand Yoo are both 1. In this coordinate system
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1843
n
H O D Spectroscopy and Photodissociation Dynamics
we need to energy analyze and I4OH) separately. The energy spectrum of each of these wave packets is the partial absorption spectrum for producing one of the two products. We set I 4 O H ) to zero; then the energy distribution of 140D)is given by
t=5 8
w.9
t-14.5
Since the dynamics of IdoD)is confined to only one of the exit channels, a smaller grid can be used. I+oD) moves mainly along RoH and very little in the R O D coordinate. A rectangular grid of 128 X 32 is thus sufficient. This procedure yields a partial absorption spectrum for producing H OD. Similarly eOH(w) can be obtained by setting to zero and calculating the dynamics of 140H),now on a grid of 32 X 128 points. Since the total wave function can always be written as
+
t~23.2
and to an excellent approximation, ( 4oDle-(l/h)Hc‘lf$OH) = (+oHIe-(’/h)He‘lf#JoD) = 0, the total absorption spectrum is then tOD(w) Q ~ ( w ) . As t m , this relationship becomes exact. This provides us with a convenient convergence test since we obtain the total absorption spectrum by two means. One uses the dynamics from t = 0, while the other comes from propagation at long time in the asymptotic regions.
-
+
Figure 2. Moving wave packet Ibi(r)) on the first excited-state PES of HOD for transition starting from u” = 0; time is in femtoseconds. In the first frame, the dashed lines are contours for the PES, and the black dot indicates the initial wave packet I&(O)).
neither the wave function nor the potential is symmetric. The slope along the XoH coordinate is noticeably larger than that along YoD. Thus we would predict that more O D will be formed and that the OH bond moving on a steeper potential will break more rapidly. Most of the figures in this paper are presented in the R& coordinates, but we need to keep in mind that when invoking classical ideas to describe the dynamics, there is a larger force “pushing” 14i(t))to break along OH. C. Numerical Procedure. We compute the dynamics of by solving the time-dependent Schrbdinger equation
a
ihzI4i(t)) = Hl4i(t))
(12)
numerically using a fast Fourier transform (FFT) grid technique, developed initially by Kosloff and K ~ s l o f f . ” - ~Our ~ procedure is identical with that used in ref 5 . For calculation of the dynamics on the excited stae, a fairly large grid is needed since Iq5i(t)) proceeds to dissociation. The initial wave function li) multiplied by the transition moment is placed on a 128 X 128 grid with grid spacings d R l = dRz = 0.1 au, and the dynamics is run until the wave packet reaches the asymptotic region. For calculation of the Raman spectrum, the Raman wave function is generated according to eq 7 . This is done while the dynamics of I&(t)) are calculated. I\kR(wI)) is then multiplied by the transition moment. Since peg goes to zero at large displacements, pcg13R(~I))= JQR(w1)) extends over much smaller displacements than does I\kR(wI)) and a smaller grid can then be used for the Raman spectrum calculation. IQR(~I)) is placed back on the ground state on a 64 X 64 grid with the same grid spacings, and the spectrum is obtained according to eq 4. The most interesting piece of information in this study is the wavelength dependence of the branching ratio between the two possible products H + OD and D + OH. We follow the procedure developed by Tannor et al.35 The dynamics of the total wave function results in the bifurcation of 14i(t)). These are clearly visible by inspecting Ic#J~(~)) at longer times (see Figure 2). Each of these two pieces corresponds to one of the two products, and we label them IdOD) and ( + O H ) , yielding H O D and D -+ OH, respectively. To calculate the branching ratio for all frequencies,
+
(31) Kosloff, R.;Kosloff, D. J . Phys. Chem. 1983, 79, 1823. (32) Gerber, R. B.; Kosloff, R.; Berman, M. Comput. Phys. Rep. 1986, 5, 59.
(33) Kosloff, D.; Kosloff, R. J . Comput. Phys. 1983, 52, 35. (34) Kosloff, R. J . Chem. Phys. 1988, 92, 2087. (35) Tannor, D., private communication.
111. Excited-State Dynamics: Starting from Y” = 0 A . Absorption Spectrum. The dynamics of I+,(t)) on the excited state represents the photodissociation only when the exciting laser pulse is a 6 function in time. A longer pulse does not create a simple wave packet but rather can be thought of as a train of pulses, each bringing a packet just like 141(0))up to the excited state. These packets then interfere with one another as they proceed to dissociation with the laser frequency determining which part of I4,(t)) interfere constructively or destructively. In the limit of a pulse that is long compared to the dissociation time, a delocalized wave function is created spanning displacements from the Franck-Condon (FC) region to infinite separation. In the continuous-wave limit, this delocalized function is the Raman wave function. Figure 2 shows snapshots of the photodissociation dynamics for 141(t)).At t = 0, I+,(O)) lands on the excited state in a region from the excited-state saddle point. displaced in both ROD and hH Thus, it feels a force that will cause it to move to larger displacements in both of these coordinates, with the force along RoH being larger than that along ROD. As I$,(t)) leaves the FC region and moves along the “symmetric stretch” direction, it begins to spread along the local mode directions which are no longer bound on the excited state and soon reaches a region in the potential surface that locally has negative curvature. At this point, which occurs approximately 6 fs after the &function laser pulse, spreading becomes very rapid (note that spreading in ROH is much more rapid than in ROD)and I4,(t))starts to bifurcate (see fourth frame in Figure 2). Eventually it breaks into two asymmetric pieces, each proceeding along almost purely local 0-H or 0-D stretches to yield H O D or D OH. At 30 fs following the laser pulse, over 90% of the wave packet is well into the two asymmptotic regions. Note that in the last frame 140D)is at larger displacement than (40H),clearly showing that the OH bond breaks faster than the OD bond. The fact that the amplitude of IdoD)is larger than that of also tells us that the OH bond is more likely to break. The two products are clearly visible as two separate wave packets, making it easy to analyze the energy distribution for each independently and to obtain partial absorption spectra. According to eq 1, we can obtain the total absorption spectrum by Fourier transforming the autocorrelation function (&(O)l4,(t)). Figure 3 shows a total of five absorption profiles. The dotted lines, a and c, are calculated absorption spectra for HzO and D20, both of which will be present under any experimental conditions, and thus are shown for reference. The HOD total absorption spectrum is indicated by the solid line labeled b. All three of these spectra exhibit diffuse structure whose origin has been discussed previo ~ s l yand , ~ the spacing between the diffuse peaks shows the ex-
+
+
1844
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Zhang et al.
c
I
0 8 -
\
10
40
7.0
100
130
ROH (a.u.)
Figure 4. Raman wave function (*R(158.7)) of HOD on the excited state generated at 158.7 nm for transition starting from u’’ = 0.
55
65
60
frequency (XI 0 3 c m - l )
Figure 3. Absorption spectrum (dotted lines) for (a) H20 and (c) D2O starting from u “ = 0, and partial absorption spectra (solid lines) for (d) H + OD, and (e) D + OH for transition starting from u ” = 0 in HOD. The solid line (b) is the absorption spectrum of HOD, which is the sum of the two partial spectra d and e. The bottom part of the figure shows the branching ratio (H + OD)/(D + OH) as a function of frequency.
pected isotope shifts. We also note a shift in the origins of the total absorption spectra with isotope, which is simply due to the difference in the ground vibrational energy levels for the various isotopically substituted molecules. Figure 3 also shows the branching ratio ( H OD)/(D + OH) as a function of excitation wavelength. This figure confirms the observation we made by looking at the dynamics of I&(?)): over the entire frequency region the OH bond breaks with higher probability. The two partial spectra also exhibit diffuse structure but with two different frequencies. As one might expect, the H OD spectrum exhibits a progression spaced by the OD frequency, while the progression in the D OH spectrum is spaced by the O H frequency. In the very red end of the spectrum the branching ratio ( H + OD)/(D + OH) is large, suggesting the possibility of selectivity; however, this spectral region is overlapped by the H 2 0 spectrum, and one could not excite H O D without exciting H 2 0 at the same time. Moreover, in this region the absorption coefficient is rather small and the frequency region where high selectivity occurs is narrow. Figure 3 illustrates why we prefer to show the two partial spectra rather than ratio plots. The ratio plot will give an apparent high selectivity with no hint as to the absorption probability. Experimentally, it will be nearly impossible to use u” = 0 as the initial state and induce selective bond breaking. Our calculated branching ratio agrees extremely well with the results obtained by Engel and Schinke2’ using a time-independent formalism. We can provide a qualitative explanation for the wavelength dependence of the branching ratio. To do so we return to Figure 1 where the A state potential and the initial wave function are shown. The ratio plot shows maxima at both low and high energies and an overall higher probability for producing OD. As we mentioned earlier, the force along the OH coordinate is larger than that in the OD, resulting in an overall “stronger push” of the wave packet to move along OH. To understand the wavelength dependence, we can identify different regions of the wave function with their corresponding absorption wavelength. We resort here to simple ideas invoked in the reflection a p p r ~ x i m a t i o n . The ~~ reflection principle implies that the high-energy part of the spectrum can be correlated with the piece of the wave packet
+
+
+
(36) Herzkrg, G. Molecular Spectra and Molecular Struture I . Spectra of Diatomic Molecules, 2nd 4.;Van Nostrand: Princeton, 1950 pp 391-394.
located in coordinate space over the high-energy part of the potential. Similarly, the low-energy region of the absorption spectrum is correlated with the piece of the wave packet located over the lowest region of the potential. These simple ideas ignore the initial momentum distribution; however, here the forces on the wave packet are large and thus will dominate the dynamics. In Figure l b we label the two potential energy extremes, where I&(O)) is nonzero, L and H for low and high energies, respectively. The arrows indicate the direction of the force at these points. The lowest energy part of the t = 0 wave packet is located below the barrier, in the H O D exit channel. There is no corresponding region at the same energy in the D + OH exit channel. We then predict that HOD will dissociate to yield predominantly H OD, when the excitation wavelength is tuned to the very red end of the absorption spectrum. Since the amplitude of I+,(O)) in this region is small, the absorption cross section will be very low. The high-energy region of Iq+(O)) is well above the barrier, yet the branching ratio indicates that the high-frequency components correlate almost exclusively with H + OD. The arrow in Figure l b indicates that the force on the high-energy region of the wave packet also points toward the H + OD exit channel. This qualitative analysis is based on classical arguments. The recent work by Engel and Schinke2*shows very good agreement between classical and quantal results for this system, suggesting that despite the low masses, classical intuition can be used to a large extent to understand the dynamics. B. Raman Wave Function and the Emission Spectrum. The resonance Raman (emission) spectrum provides a unique probe of HOD photodissociation dynamics. First, it is one of the simplest observables to obtain that can be assigned to HOD unambiguously even in the presence of the other isotopic species. The resonance Raman spectrum for the mixture shows H20, D20, and HOD Raman lines; however, because of the isotope shift on the ground state it should be possible to assign each line to the corresponding isotope. On the other hand, the three absorption spectra are overlapped (see Figure 3), and the HOD spectrum cannot be isolated. The same is true for a probe of the fragment product-state distributions, making it impossible to tell whether the OH/OD originated in H20, D20, or HOD. Moreover, as we have shown for H20,5the resonance Raman spectrum probes the dynamics in the interaction region, where the fate of the reaction is determined. Hudson and c o - w ~ r k e r shave ~ ~ recently recorded the resonance Raman spectrum for HOD. Since the experimental data are only preliminary at this point, we will not offer a direct comparison but rather present our calculated results. In general, agreement between calculated and observed spectra is good although many of the HOD lines are overlapped by H 2 0 or D 2 0 at the present experimental resolution. To calculate the Raman spectrum according to eq 4, we first need to calculate the Raman wave function at the incident laser frequency wI,which we choose to be oI= 158.7 nm (63012 cm-I). We implement eq 7 and project out of Iq$(t)) the Raman wave function, 19,(158.7)), which is shown in Figure 4. By examining
+
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HOD Spectroscopy and Photodissociation Dynamics
.he Journal of Physical Chemisiry, Vol. 93, No. 5. 1989 1845
3
0
4000
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Figure 5. Calculated emission spectrum of HOD excited at 158.7 nm with transition starting from 0’‘ = 0. The peaks are labeled according to the local mode assignmentsgiven by Watts in ref 11: n.m refer to n quanta in O-H and m quanta in O-D stretches. The peaks are shaded differently for different progressions.
the entire path taken by I*([)) can be seen. It clearly shows the asymmetry induced by the isotope substitution. Since the propagation is stopped when the first piece of the wave packet reaches the edge of the grid, I*R) appears to be extended further on the OH side. This is because the OH bond breaks more rapidly. The Raman wave function also shows that the OH bond a t this laser frequency breaks more readily, since the amplitude of I*,) in the H O D product channel is higher. According to Figure 3 the ratio H + OD/D + OH = 4 at 158.7 nm. The vibrational excitation in the final O H and O D products is also quite evident in lqR(158.7)) and appears in the form of oscillation in the asymptotic region perpendicular to the pure OH or OD local modes. The next step in the calculation of the Raman spectrum involves transferring the Raman wave function, multiplied by the transition moment, back to the ground state: Since the transition moment goes to zero at large internuclear separations, laR)has vanishing amplitude in these regions. W e expect then that the spectrum will exhibit an overall decay in intensity at higher vibrational levels. The Raman spectrum can be thought of as a probe of the dynamics on the ground-state PES because it is a signature of the dynamics of Ian)on that surface. However, it is also a n intrinsic probe of the dynamics that occur on the excited-state potential because it is this motion that determines Ian)in the first place. Thus, the complexity of the Raman spectrum depends entirely on the relationship between the two dynamics occurring on the two surfaces. Since the transition moment surface goes to zero at large bond displacements, it effectively imposes an upper time limit on the amount of excited-state dynamics that contributes to the spectrum. For this reason, it is the early time dynamics on the excited state of HOD that dominates the shape of I*,). This early time dynamics corresponds to motion along a symmetric-stretch-like coordinate. If the dynamics on the ground state also consisted of motion along the symmetric stretch coordinate so that the vibrational eigenstates were oriented along this direction, then the Raman spectrum would appear as a simple progression in the symmetric stretch. On the other band, if the predominant dynamics on the HOD ground state were along the local mode cmrdinates with the nodal patterns of the vibrational eigenstates oriented along these directions, then the resulting Raman spectrum would appear very complicated with many lines. While the ground-state dynamics of H 2 0 is largely local mode in character, as we shall see below, due to the large mass difference between OH and OD, the ground-state vibrational eigenstates of HOD are all almosi pure local mode states. For a diffuse initial state such as laR), the dynamics on the ground electronic state is very complex, giving very little insight, and thus is not shown. W e calculate I%([)) by propagation for IOstime-steps with di = 0.25 au (total time z 600 fs) on a grid of 64 X 64 points with the same grid spacings as before. The
+
1
2
kH (a u.)
3
1
2
3
kH (a u.)
Figure 6. Vibrational eigenstates (absolutevalues) on the ground electronic surface of H20 (a) the (5.0) state, (b) the (1.0) state, and (c) the (0.1) state. State labeling here is given in normal mode quanta.
Fourier transform of (aRI%(i)) then gives the Raman spectrum, shown in Figure 5. This spectrum is noticeably more complex than the H,O spectrum (see ref 5 ) ; nevertheless, the lines can all be labeled according to their local mode quantum numbers n,m for C-H and C-D stretches, respectively. From these assignments, we see that the spectrum consists of an 0-H stretch progression n.0, an 0-D stretch progression O,m, as well as many of the possible combinations n,m. As discussed above, the behavior of the transition moment accounts for the overall decay in line intensity a t higher vibrational levels. Understanding the correspondence between the motion of l@l(i))on the excited state and the observed spectral lines is no straightforward matter: however, if we consider the early time motion of IQL(i))and the local mode character of the ground-strate eigenfunctions, the complexity of the spectrum is not surprising. To describe a motion along the “symmetric stretch” direction requires the superposition of many local mode eigenstates, each of which gives rise to a line in the spectrum.
IV. Dynamics on the Ground-State Surface To gain some insight into the resonance Raman spectrum, it is useful a t this point to examine the dynamics that occur on the ground-state electronic surface of HOD. Just as in the case of the excited-state surface, the effect of the isotopic substitution leads to substantial qualitative changes in the dynamics on the grounq state. These changes arise as the result of a combination of two effects: (i) a reorientation of the normal modes due to the isotope effect and (ii) the elimination of the dynamical tunneling between the local stretch modes due to the broken symmetry of the molecule. In H20, the ground-state dynamics is normal-mode-like only at very low energies and becomes local mode in character a t higher energie~.”.’~J~.’’Classically, this implies that an initial excitation of more than 2 quanta in one C-H bond remains forever in that bond.16 Quantum mechanically, however, there is a dynamical tunneling effect"^"^" that allows the excitation to flow between the two 0-H bonds on a time scale that is long compared to the 0-H vibrational period.’8 This tunneling interaction is reflected in the vibrational eigenstates of H20 in which amplitude is shared equally between the two 0-H bonds (see Figure 6a) so that the eigenstates all have the C , symmetry of the Hamiltonian. The (37) Siben. E. L.: Hynes, J. T.: Reinhardt, W. P. J. Chem. Phys. 1982.
77, 3595.
1846 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
I rHoH
45 I
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Zhang et al.
I
I
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1
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3
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1.0
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Mass Figure 7. Variation of the angle between the normal and local bond mode
directions as a function of continuously changing one of the hydrogen atom masses between mH = 1 and mD = 2 (solid line). H20corresponds to an angle of 4 5 O , while HOD exhibits an angle of - 2 O between the two sets of coordinates. Solid circles indicate the (quamtum mechanically) estimated angle between the nodal line of the first vibrational excited (0,l) and the local bond mode directions for several of the “hydrogen” masses. Open circles give the estimated angle for states corresponding to 5 quanta (0,5) in the local mode. lowest vibrational excited states (Figure 6b,c) have nodal lines along the normal mode directions, reflecting the predominance of this type of motion at low energies. By deuteriation of one of the hydrogens, a profound effect on the character of the normal modes is observed. In H20, the normal coordinates are rotated by an angle of 45’ relative to the local mode (0-H bond) coordinates. This is, in fact, always true when the zeroth order modes have degenerate frequencies. For HOD, however, the frequency degeneracy is broken and the normal coordinates are only rotated by an angle of < 2 O relative to the local mode directions. In Figure 7, we have represented the normal coordinate directions as a function of continuously changing one of the hydrogen masses between mH = 1 and mD = 2. From this figure, we see not only that the normal modes of HOD are almost identical with the local mode coordinates but also that only a very slight change in the mass of one of the hydrogens is sufficient to induce this effect. To demonstrate that this effect is reflected in the quantum mechanics of this system, we have estimated the same angle by examining the nodal line of the first vibrational excited state, 0,1, for several different “hydrogen” masses and indicated these results as solid circles in Figure 7 . A more subtle effect is the elimination of the tunneling interaction between the two bonds in HOD. By analogy, we can picture this interaction as a barrier tunneling process in a double-well potential. For H 2 0 , the proper analogy is a symmetric d o ~ b l e - w e l l so l ~that ~ ~ ~the eigenstates contain equal amounts of amplitude in each well. By slightly changing one of the hydrogen masses, however, we destroy the symmetry of the double-well and the eigenstates now have amplitude in one well or the other but not b ~ t h . ’ ~In , ’ effect, ~ by breaking the symmetry, we have cut off the “communication” between the two wells. This implies that many of the vibrational eigenstates of HOD will be approximately separable in the local mode coordinates (RoH and ROD)and thus will have nodal lines roughly parallel to the ROHand ROD axes. Examples of such states are shown in Figure 8. The essence of the difference between the HOD eigenstates and those for H 2 0 are most apparent when one compares Figure 8e,f with Figure 6a-these are all pictures of states with 5 quanta in the local modes. Interestingly, Figure 7 indicates that the 0,5 vibrational eigenstates for a variety of “hydrogen” masses between mH = 1 and mD = 2 are all oriented roughly parallel to the local mode axes. In the case of the first excited state (O,l), the agreement between the quantum eigenstates and the normal mode prediction is almost perfect for all masses; however, for the 0,5 state, the eigenstates are oriented along the normal mode directions only for large molecular asymmetry, as in HOD. At intermediate
Figure 8. Representative vibrational eigenstates on the ground electronic
surface of HOD. The local mode quantum number labels for each state are listed on the figure with n,m referring to n quanta in the OH bond and m quanta in the OD bond. masses (e.g., mH = l.Ol), 0,5 is almost purely local mode in character despite the fact that the normal modes are not parallel to the local modes. In HOD, the dynamics is local-mode-like because the normal modes are so nearly identical with the local modes; whereas, in H 2 0 , local mode behavior arises as the result of a 1:1 nonlinear resonance between the normal m ~ d e ~ . ~In ~other , ~ words, ~ * ~ ~ , ~ ~ the underlying classical phase space is very different for these two molecules. This is demonstrated in Figure 9, where we show composite surface of section plo@ for H 2 0 and H O D at three different energies. These plots show that while H O D has a very simple phase space structure indicating normal (local) modes that are only weakly coupled, the phase space of H 2 0 is noticeably more complicated. An interesting intermediate case is that of mH = 1.01. For this idealized model, the classical phase space is very similar to that for H 2 0 , yet the quantum eigenstates in the local mode energy regime do not exhibit the dynamical tunneling interaction found in H 2 0 and have amplitude along only one bond or the other, but not both. Apparently, the 1% change in the mass is not enough to significantly alter the classical dynamics but does introduce enough asymmetry to eliminate the tunneling interaction between the two stretches. Quantum mechanically, these surfaces of section suggest that the nodal lines of HOD eigenstates will run the same directions throughout the energy range probed by the resonance Raman spectrum (see Figure 8), but the same will not be true for H 2 0 (see Figure 6). This also means that, contrary to the double-well analogy used above, the dynamics of HOD is actually better represented by a pair of weakly interacting oscillators for which tunneling plays no role whatsoever. Regardless of the reasons for the elimination of tunneling effects, however, their absence in HOD represents an important distinction between the two molecules. The stretching dynamics implied by the HOD eigenstates shown in Figure 8, then, is much simpler than in the case of H 2 0 . A wave packet that is initially displaced only along the 0 - D bond will move along the ROD coordinate but will not develop any coordinate (see Figure 10). appreciable amplitude along the hH The same will be true for an initial displacement only in the 0-H bond. Interestingly, this means that, in contrast to H 2 0 , the (38) Lichtenberg, A. J.; Lieberman, M. A. Regular and Stochasric Motion; Spring-Verlag: New York, 1983.
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 1847
HOD Spectroscopy and Photodissociation Dynamics 20 1
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Figure 10. Time evolution of the u” = 0 eigenstate displaced initially along the 0-D stretch coordinate away from the equilibrium point on the ground-state PES (dashed lines in the first frame) of HOD. Time is in femtoseconds.
3
m
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a0
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io
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ROH Figure 9. Surfaces of section of H20(a, c, and e) and HOD (b, d, and f) at three different energies: (a), (b) 7500 cm-I; (c), (d) 14000 cm-’; (e), (f) 22000 cm-’. These surfaces are generated by running a set of classical trajectories with random initial conditions at each of the energies for each of the molecules. Points are generated for (RoH,PoH) whenever R O H(Roo) ~ passes through its equilibrium position with positive momentum. Local and normal mode regions of phase space are indicated.
classical dynamics of the stretch modes in HOD will be consistent with the quantum wave packet dynamics for all times-that is, initially localized excitations will remain localized. What impact do these results have upon observable quantities such as the resonance Raman spectrum? The almost separable local mode character of the ground state implies that the spectrum of a wave packet displaced, as in Figure 10, along Roo only, will be very simple as shown in Figure 11, top. As expected the spectrum exhibits a nearly pure progression in the 0-D stretch-this is confirmed by looking at the eigenstates represented by each line (Figure 11, bottom). Correspondingly similar results are found for a wave packet displaced in the 0-H stretch only. To simulate the actual Raman wave function, we present results for a wave packet displaced in both the ROHand RODcoordinates. Figure 12 shows the spectrum for this wave packet,’which consists of progressions in both O H and OD, as well as all combination modes, similar to the actual Raman spectrum (Figure 5). As noted in the previous section, these results indicate that to interpret the resonance Raman spectrum requires knowledge of the dynamics on both the ground and excited surfaces. The ground-state wave functions serve as templates for learning about the dynamics on the excited state, so we need to know how the templates are oriented. A similar effect has been observed in the resonance Raman spectra of CH31 and CD31.2s*39340 A 1.2 res(39)Hale, M.0.;Galica, G. E.; Glogover, S.G.; Kinsey, J. L. J . Phys. Chem. 1986, 90, 4991. (40)Sundberg, R. L.;Imre, D. G.; Hale, M. 0.;Kinsey, J. L. J . Phys. Chem. 1986, 90, 5001.
L
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Figure 11. Top: emission spectrum obtained by propagating the u“ = 0 eigenstate displaced along the 0-D stretch coordinates away from the equilibrium point on the ground-state PES of HOD (refer to Figure 10). The labeling is the same as in Figure 5 . Bottom: vibrational eigenstates of the ground electronic surface projected out for some of the peaks in the spectrum in Figure 11, top.
onance between the CD, umbrella bend and the C-I stretch on the ground electronic state results in a rotation of the template with respect to the CHJ template. As a consequence, the CDJ spectrum shows a very different intensity distribution from the CH31 spectrum, despite the fact that the dynamics on the excited-state surface for these two molecules a r e very similar.
1848 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
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Figure 12. Emission spectrum obtained by propagating u"= 0 eigenstate displaced along both the G-H and G-D stretch mrdinates away from the equilibrium p i n t an the ground-state PES of HOD. The labeling is the same as in Figure 5 . The H 2 0 resonance Raman spectrum has fewer lines than the corresponding HOD spectrum and thus appears to be easier to interpret. What is not immediately obvious from the spectrum is the fact that the template in H20 changes direction as we move up the vibrational ladder. The low-energy states are normal modes and thus provide information about the motion on the excited state along the symmetric and antisymmetric stretch omrdinates. Above u"= 2 the eigenstates are local modes and the template is rotated by 4 5 O . This effect is expected to be even more important in D p , where the transition from normal to local modes occurs at higher vibrational levels and the region over which states cannot be assigned to either category is wider. Because of the large mass effect in HOD, its template is oriented along the local (normal) modes for all vibrational levels. In that respect the HOD spectrum is simple and the assignments are consistent throughout the entire spectrum. Nevertheless, this points out a very important observation: the presence of many lines in a spectrum can be due to intrinsic differences in the dynamie of the two electronic surfaces and need not arise as a result of IVR on the ground electronic state. V. Photodissociation of Vibrationally Excited H O D Selectivity in Bond Breaking In this section, we present a simple two-photon scheme by which one can control the process of bond breaking in HOD. However, some practical obstacles must be overcome to be able to achieve a high degree of selectivity in a real experiment. First of all, a mixture of H 2 0 , D20, and HOD will always be present; therefore, our scheme must provide a frequency region in which only HOD absorbs. Achieving this objective is important in and of itself if one is interested in experimentally studying HOD photodis+ation by looking at the final product distribution. Secondly, the A state absorption is in the vacuum UV region of the spectrum where experimental work is difficult, so our selective bond-breaking scheme would be more practical if we could shift the useful frequency region for HOD absorption to the red ofthe H 2 0 and D 2 0 absorptions. This is further motivated by the existence of another X electronic transition that overlaps the blue end of the A absorption. Third, the useful frequency range in our proposed scheme should k broad enough so that slight broadening effects due to finite temperature do not serve to mask the desired result. Finally, we reemphasize the importance of having an absorption coefficient in the frequency range leading to selective photodissociation that is substantial enough to make the experiment feasible (see section IIIA). To design our "ideal" experiment, we will utilize the knowledge we have gained of both the ground-state surface and the photo-
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Fipurc 13. lnilial wave packets (solid c3nloursJ prepared on the excited-sutc PES (dash:d liner1 of HOD for lrdnsitiom starling from (a) u'kH = 1. (b) c'kH= 2 . (e) u'hD= 1, (d) u",," = 3. The ,haded regions are u r d to indicate the low encrgy p r t m n s u l each U ~ Y Cpacket.
di~rw.iationstarting from I"'=0. I n section I V . our study of thc ground electronic state of HOD demonstrated that it is possible to prepsrc vibrational cigenntatcs that repre,xnt pure 0 - 1 1 or O-D stretches via infrared excitation. As a result. one can store vibrational energy exclusively in one bond or the other in this molecule. This cncrgy can thcn give the mnlecule a 'push" along (?H or OD before it is excitcd with a UV photon to the diswciative A state. The hope is that this -push" will then induce the molecule to dissociate selectively along the vibrationally excited coordinate. Our use of the word "push" ma) be misleading because it givcs the impression that a time-evolving state along a local mode coordinate must be prepared for our scheme to be nucccssful. In fact, because the vibrational eigenstates of ground-slate HOD are of nearly local mode in character (see Figures 8 and 11, bottom), we wuld uw a continuous-wavc infrared l a w to prepare the initial vibrational state with no restrictions on the timing between the I R and UV photons. To get a feel for whether such a scheme might work, we return to the reflectiun approximatiun used in scction 111 to explain the branching ratio for photodiswiation initiated from u"= 0. From this point of view, u e would like the initial wave function to have substantial overlap with the low-energy part of the excited-state potential surface in one of the exit channels and not the other. For the purpose of this qualitative discussion, wc once again ignore the momentum distribution inherent in the initial wave function. To illustrate these ideas, four different initial wave functions are pictured on the excited-state potential in Figure 13. Since our goal is to achieve selectivity in the low-energy region of the absorption spectrum. we look for thc lowest cncrgy region ufthc potential where the initial wave function has appreciable amplitude. I n Figure I3a, the shaded area drawn on the initial state i")OH = I indicates the louest energy portion of this wave function which is located in the I I + O D dissociation chinnel. The corresponding low-energ) region in the D + O H dissociation channel overlaps onl) portions of the initial state whose amplitude is negligible-only higher energy parts of the D t OH channel corrcspond IO regions where the initial state has appreciable 3mplitude. Thus. if we could exclusively extract the low-energy component of this wave function. it would be well.approximated in coordinated space by the shaded area in Figure 13a and selective dissociation to II + O D would ensue. This can be accomplishcd by using a narrow-band laser tuned to the low-energy part of the absorption spectrum. Such a laser effectively projects out of the moving wave packet the frequency components corresponding to the energy range of the l a w photons.
The Journal of Physical Chemistry, Vol 93, No 5. 1989 1849
HOD Spectroscopy and Photodissociation Dynamics 4
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RoH (a.u.1 Figure 14. Schematic representations of the two possible dissociation channels: shaded area for D + OH and blank area for H + OD. Dashed contours represent the excited-state PES.
50
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frequency (xio3cm-’) Fipre 15. Absorption spectra (dotted lines) for (a) H20, (b) HOD, and (c) D,O starting from u”= 0; partial absorption spectra (solid lines) for (d) H + O D and (e) D + OH for transition starting from v‘bH= 1 in HOD. The solid line f is the sum of the two partial spectra d and e. The shaded region indicates where the selective bond breaking is possible. We can approximately map out which regions of the excitedstate potential surface lead to either the H + O D or D + OH dissociation channels by investigating the classical dynamics of the system for trajectories initiated at r a t (i.e., with P = 0). Figure 14 outlines the regions in which such trajectories lead to H + OD or D OH formation. While the area near the FC region for u” = 0 exhibits a more complicated dependence of product formation on the initial conditions, it is clear that there are substantial regions in the two exit channels and along the steep wall of the potential that can be identified with one product or the other. In particular, this picture reinforces the description given above for the photodissociation from v’bH = 1. The shaded low-energy portion of the u’bH= 1 initial wave packet (Figure 13a) clearly corresponds to a region of the potential in which only H + O D is produced. Although pieces of this wave packet do overlap areas that lead to D + OH formation, these pieces primarily correspond to higher energy trajectories. These same ideas can be expressed within the framework of stationary states as well. On the excited-state potential, the eigenstates (scattering states) form a continuum; nevertheless, those states that lie well below the top of the barrier in energy can be associated with one exit channel or the other. The relative probability of making a transition to those continuum states is simply given by the Franck-Condon factor \(+il$E(k’)12, where represents a continuum state a t energy E in exit channel k (k = H O D or D + OH), and (6il = (u’lg,. For continuum states at a given energy below the barrier, it is clear that the = 1 ) with I$B(HCoD)) Franck-Condon overlap of I+i) = GgcIu’bH
+
+
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frequency (xlo3cm-’) Figure 16. Absorption spectra (dotted lines) for (a) H,O, (b) HOD, ai (c) D,O starting from u“= 0; partial absorption spectra (solid lines) f (d) H + O D and (e) D + OH for transition starting from u’bH = 2 HOD. The d i d line f is the sum of the two partial spectra d and e. No : that the band-selective region (shaded area) is larger than that in Figure 15.
1
5
9
13
Ron(au)
Figure 17. Raman wave function IY1.(213)) of HOD (solid contours) on the excited-state PES (dashed lines) generated at 213 nm (center of the shaded area in Figure 16) for transition initiated from o’bs = 2. will be much greater than that with ($B(D+oH’). so excitation to that energy will lead almost exclusively to H + O D production. This can be seen from the partial absorption spectra shown in Figure 15. This reaction selectivity is enhanced even further by starting in u’bH= 2 (Figure 13b). Qualitatively, this is indicated by the larger shaded region drawn on the v’bH= 2 eigenstate in Figure 13b. This can also be seen more clearly from the partial absorption spectrum in Figure 16. The Raman wave function (Figure 17) calculated for an incident frequency at the center of the shaded region in Figure 16 shows that H + O D will be produced almost exclusively with this two-photon scheme. Selective production of D OH via an IR plus UV two-photon scheme is also possible but is much harder to achieve for low vibrational excitations. Using u’bn = I as an initial state for photodissociation (shown in Figure 13c) does not significantly enhance the reaction selectivity. This result may seem a t first sight to be a bit surprising since we are giving the O-D bond an initial push, yet still no special preference is obtained for the dissociation of the O-D bond. If we look a t the dynamics of the u’kD = 1 state after it has been promoted to the excited electronic state (Figure IB), we see that the wave packet bifurcates, flowing into both exit channels more or less equally, very similar to the case of u ” = 0. A look at the partial absorption spectra for each product (Figure 19) further confirms the fact that there is no reasonable frequency range over which the molecule could be excited to preferentially form the D + OH products. Similar ~ results are also obtained for excitations beginning with u ’ b = 2. When we vibrationally excite HOD tou’b, = 3 (Figure 13d), however, we are able to create a reasonable frequency range over
+
1850 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
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t=a.9
ROH (au)
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z
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t-20.3
Figure 20. Absorption spectra (dotted lines) for (a) H20, (b) HOD, and (c) D20starting from u " = 0; partial absorption spectra (solid lines) for (d) H OD and (e) D OH for transition starting from U ' ~ D= 3 in HOD. The solid line f is the sum of the two partial spectra d and e.
0
+
I '$OD >
+
8
Figure 18. Moving wave packet IQi(t)) on the first excited-statePES of HOD for transition starting from u'bD = 1; time is in femtoseconds. In the first frame, the dashed lines are contours for the PES.
......................... .........................
......................... ............................. .........................
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i 13
R OH (au)
Figure 21. Raman wave function (9,(216.5))
frequency ( ~ 1 0 ~ c m . ' ) Figure 19. Absorption spectra (dotted lines) for (a) H20,(b) HOD, and (c) D20 starting from u " = 0; partial absorption spectra (solid lines) for (d) H + OD and (e) D + OH for transition starting from U ' ~ D= 1 in HOD. The solid line f is the sum of the two partial spectra d and e. No bond-selective region can be seen here. which UV excitation leads almost exclusively to D + OH formation (Figure 20). This is borne out by the Raman wave function shown in Figure 21, which is calculated for an incident frequency at the center of the shaded region in Figure 20. Note that this function has appreciable amplitude only in the D + OH exit channel, indicating that only the 0-D bond is broken by using this two-photon transition. Referring to Figure 14, it is easy to understand why we must prepare a higher vibrational excitation to achieve exclusive 0-D bond fission. The initial state must have appreciable amplitude in the low-energy parts of the dark gray region while having negligible amplitude in the low-energy parts of the white region. This requirement is met only for v'bD= 3 and higher. By contrast, since the white area is much more predominant in the FC region, the converse requirement for selective production of H O D is satisfied for the more modest vibrational excitations.
+
VI. Summary We have presented a detailed study of the spectroscopic observables arising from the direct photodissociation of HOD. Along the way, we have investigated the connection between the observed spectral information and the inferred nuclear dynamics on the two electronic potential surfaces. This has been facilitated by using a quantum mechanical time-dependent wave packet approach to
of HOD (solid contours) on the excited-state PES (dashed lines) generated at 216.5 nm for transition initiated from u'bD = 3.
study the photodissociation process. Because the photodissociation occurs on a single electronic surface, the water molecule provides an excellent test case for the theoretical description of photodissociation and we have obtained excellent agreement between our calculated results and the experimental absorption and emission spectra. The absorption spectrum of HOD is very similar to that of H20 but blue-shified due to the isotope shift of the ground vibrational state on the X surface. HOD displays the weak diffuse structure that is observed in the H 2 0 absorption; however, the spacing between adjacent bands is narrower due to the isotope effect. Unfortunately, because the absorption profiles of HzO, HOD, and D 2 0 overlap so completely, it is virtually impossible to extract the absorption spectrum of HOD experimentally. The emission spectrum of HOD, on the other hand, can be more easily sorted out from the isotopic mixture, and our calculated results are in good agreement with the recently measured experimental spectrum. This spectrum is much more complex than that for H 2 0 because the broken symmetry causes more than twice as many states to be Raman active. Despite this complexity, the spectrum can be readily assigned by using local mode quantum number labels. Our use of a time-dependent approach to study HOD photodissociation has led to a better physical understanding of the origins of the complexity in the resonance Raman spectrum. The early time dynamics of on the A state surface, which provides the dominant contribution to the spectrum, is along a symmetric-stretch-like coordinate. On the ground electronic surface, however, the dynamics is almost purely along the local mode
J . Phys. Chem. 1989, 93, 1851-1859
Because this scheme utilizes a UV photon that is red-shifted relative to excitation from u” = 0, it not only eliminates the need to control the timing between the two laser photons but also allows one to selectively excite only HOD in a mixture with H 2 0 and DzO. Our calculations indicate that photodissociation from v’bH = 1 and higher leads to a reasonable frequency range over which UV photon excitation will lead to exclusive production of H OD. Surprisingly, the converse is not true for excitation from v’bD= 1. In fact, one must initially prepare vfbD= 3 or higher before the two-photon scheme leading to exclusive D OH formation becomes practical. Such experiments are currently being planned.
coordinates. Since the spectrum is simply a projection of the excited-state dynamics (in the guise of the Raman wave function) onto the template created by the ground-state vibrational eigenfunctions, the fundamental difference in the dynamics on the two surfaces leads to a more complicated resonance Raman spectrum. The time-dependent approach also gives us some insight into the behavior of the OD/OH branching ratio as a function of the incident laser frequency. Using arguments based on the _reflection principle and knowledge of the classical dynamics on the A surface, we can correlate the lowest and highest energy parts of the initial wave packet almost exclusively with the H + OD exit channel. Although the OD/OH branching ratio becomes very large at the low and high ends of the absorption profile for excitation from v” = 0, the absorption coefficient is very small in these regions. This means that it would be very difficult experimentally to induce selective bond breaking via a one-photon excitation from v” = 0. We have shown that a two-photon scheme can be concocted that does lead to almost exclusive formation of H OD or D OH. This procedure invoJves first promoting HOD to an excited vibrational state on the X surface with an IR photon and then adding a UV photon to selectively photodissociate the molecule.
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Acknowledgment. We gratefully acknowledge the financial support for this project by the National Science Foundation (Grant No. CHE-8707168 and CHE-8507138) and the donors of the Petroleum Research Fund, administered by the American Chemical Society. In addition, we thank Professors Eric Heller, Robert Watts, Bruce Hudson, David Tannor, and Dr. Niels Henricksen for helpful discussions.
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Registry No. HOD,14940-63-7.
Spectral Diffusion in Molecular Aggregates Yi Lin and David M. Hanson* Department of Chemistry, State University of New York, Stony Brook, New York I 1794-3400 (Received: October 3, 1988)
Spectral diffusion in 4-bromo-4’-chlorobenzophenoneaggregates in polystyrene films at 4.2K is characterized. Steady-state and time-resolved phosphorescence spectra for different concentrations and excitation energies are reported. The spectral features and energy-transfer dynamics provide evidence for delocalized aggregate states (DAS), localized aggregate states (LAS), and discrete molecule states (DMS). The DAS are strongly coupled to the LAS, and relaxation from DAS to LAS occurs at a rate faster than 5 X 104/s.The LAS are strongly coupled to the DMS with a relaxation rate around 5 X 103/s, depending upon the energy of the LAS. The DAS have the highest excitation energies and appear to be associated with the interior regions of the aggregate. The DMS, in the polymer environment, have the lowest excitation energies. The LAS appear to be associated with the boundary regions of the aggregate. A theoretical model is shown to mimic the experimental observations.
I. Introduction Spectral diffusion is the process of energy transfer between like species with different transition energies. Characterization of spectral diffusion in disordered materials has attracted considerable attention from both experimentalists14 and theoretician^.^-^ The techniques of time-resolved fluorescence line narrowing*-I0 (TRFLN) and time-resolved phosphorescence line n a r r o ~ i n g ~ - ~ J (TRPLN), together with measurements of the resonant donor decay as a function of time, have made it possible to study spectral diffusion within inhomogeneously broadened optical l i n e ~ . ~InJ ~ the TRFLN experiment, a narrow-band pulsed laser is used to (1) Richert, R.; Bassler, H. J. Chem. Phys. 1986, 84, 3567. (2) Prasad, P. N.; Morgan, J. R.; El-Sayed, M. A. J. Phys. Chem. 1981, 85, 3569. (3) Chu, S.; Gibbs, H.; McCall, S. L.; Passner, A. Phys. Rev. Lett. 1980, 45, 1715. (4)Kook, S. K.; Hanson, D. M., to be published. ( 5 ) Hostein, T.; Lyo,S. K.; Orbach, R. In Topics in Applied Physics; Yen, W. M., Selzer, P. M., Eds.; Springer: Berlin, 1981;Vol. 49,Chapter 2,and references therein. (6) Blumen, A. J . Chem. Phys. 1980, 72, 2632. (7) Blumen, A.; Klafter, J.; Silbey, R. J . Chem. Phys. 1980, 72, 5320. (8) Szabo, A. Phys. Rev. Lett. 1970, 25, 924. (9) Selzer, P. M.; Huber, D. L.;Hamilton, D. S.;Yen, W. M.; Weber, M. J. Phys. Rev. Lett. 1976, 36, 813. (IO) Hegarty, J.; Yen, W. M. Phys. Reu. Lett. 1976, 43, 1126. ( I 1) Talapatra, G. B.; Rao, D. N.; Prasad, P. N. J . Phys. Chem. 1984, 88, 4636.
0022-3654189 12093-185 1$01.50/0
excite molecules with resonance frequencies spanning a small segment of the inhomogeneous band. After the source is turned off, the fluorescence spectrum evolves in time. Initially there is only sharp luminescence coming from the molecules that were excited directly by the incident light. As time passes, molecules with resonant frequencies outside the bandwidth of the source begin to luminesce. The broad luminescence arises from energy transfer to those molecules that were not excited by the light. The time-dependent ratio between the sharp component and the broad background provides information about the microscopic transfer processes. In the case of phonon-assited energy transfer, the line shape depends on the phonon population. When the thermal energy is greater than the inhomogeneous line width, the broad line is symmetric; otherwise, the broadening is predominantly toward the lower energy side. Recently, spectral diffusion and site-selected excitation in “orientationally disordered” organic solids have been investigated by El-Sayed and c ~ - w o r k e r s . ~ J They ~ J ~ reported observations of spectral diffusion in I-bromo-4-chloronaphthalene.Time-resolved phosphorescence line narrowing experiments were performed under conditions where kT was much smaller than the inhomogeneous line width. The results were interpreted in terms of phonon-assisted unidirectional energy transfer. Similar spectral (12)Morgan, J. R.; El-Sayed, M. A. J. Phys. Chem. 1983, 87, 200. (13)Morgan, J. R.; El-Sayed, M. A. J. Phys. Chem. 1983, 87, 3 8 3 .
0 1989 American Chemical Societv
