8013
J. Phys. Cbem. 1991, 95.8013-8018
parent beam. Excessive population in the K = 0 levels was observed, indicating a preferred rotation of the methyl fragment around a C, axis. A quite differing, but to some extent complementary study, was done by Black and Powis,’OJ’ who photolyzed an effusive warm methyl iodide beam. Rotational population in levels up to N = 15-20 was found, and mainly high-K levels were populated in the methyl fragment. From an analysis of the changes in the REMPI spectrum form perpendicular plarization of the photolysis and probe laser to the magic angle REMPI spectrum (polarization of probe laser at 5 4 . 7 O ) an ‘‘overall” alignment moment Ah2)= 0.5 f 0.2 was extracted. This positive alignment is in agreement with the expectation for a parallel dissociation of an internally warm parent molecule. The initial relatively high-K quantum number of the parent is conserved in the dissociation to the spinning rotation of the methyl fragment and N will be directed preferentially along the C3 symmetry axis. The maximum attainable alignment from the total recoil distribution of the photofragments is Ag) = 0.8.39A somewhat smaller extracted average alignment of A&) = 0.5 was proposed to originate from the rotational excitation induced in the photodissociation from the Yg wagging mode, populated to about 7% in the CD31at room temperature, and zero-point energy, lowering the initial parallel alignment on N along the C3 axis.” From inspection of Figure 5 it can be seen that the rotational energy transfer to the fragment CD3 has a smooth dependence on energy gap. It is also noted that as the value of N becomes larger the energy gap between (N”, K” = N’? and (N‘ = N”+ 1, K’= N ’ - l ) , the smallest allowed rotational energy transfer, increases. By N = 9 this smallest energy gap, (9,9) (10,9), is 100 cm-I, and the probability of rotational energy transfer can be seen by inspection of Figure 5 to be small. This is why Black and Powis’o*’’observe an increasing propensity for N = K in the CD3 fragments at the higher rotational states where they are able to resolve the transitions from the individual K states.
-
-
From inspection of the Ah2)moment in Table I, it is observed that especially for the higher K levels within a certain N stack the measured Abz) is very close or equal to the maximum for these (N,K) states. This can be explained from the fact that the high-K levels originate from the initial rotational excitation around the C3 axis in the parent molecule. As the K quantum number is expected to be conserved in the photodissociation, a methyl fragment in a high-K state, e.g., K = A’, has not been rotationally excited from the photodissociation. It means no rotational excitation from zero-point bending or from the curve crossing of the two potentials involved in the dissociation“Jg is induced. The fragment in final state (NX)= (K,K) is dissociated collinear to the C3axis, which was parallel to the direction of the polarization of the photolysis laser. This rotational state will then have the maximum parallel alignment expected.
Conclusion We have determined the alignment moments and population distribution for the CD3 fragment following the 266-nm photodissociation of CD31. These alignment moments are explained in terms of a simple linear dissociation model assuming conservation of K quantum number and conservation of the parent ortho/para ratio upon dissociation. A reanalysis of the rotational populations for the ground vibrational state of the CD3 fragment taking into account this high degree of alignment of the CD3 fragments reveals an energy gap law for rotational energy excitation from the dissociation process. Acknowledgment. We thank Mark Jaska and Mitch Williams for their expert technical assistance in the laboratory and Diana Atwood for help with the figures. M.H.M.J., S.S.,and D.H.P. gratefully acknowledge the Sandia National Laboratories’ Visiting Scientists Program and the National Science Foundation, Grant 8619803, for support. Registry No. CDJ, 865-50-9; CD,,2122-44-3.
Observation of a Parallel Recoil Dlstribution from a Perpendicular Absorption Transition in HCO and DCO Scott H. Kable? Jean-Christophe Loison,$ David W. Neyer, Paul L. Houston,* Department of Chemistry, Cornel1 University, Ithaca. New York 14853- 1301
Itamar Burak, School of Chemistry, Tel Aviv University, Tel Aviv, Israel
and Richard N. Dixon School of Chemistry, The University, Bristol BS8 1 TS, England (Received: February 5. 1991) We report results and calc_ulalionsof the recoil anisotropy of H and CO photofragments following laser dissociation of HCO and DCO radicals. The A-X transition of HCO/DCO is known to lie perpendicular to the molecular plane. Excitation using linearly polarized light, however, gives rise to fragments recoilingparallel to the axis of polarization. The degree of spatial anisotropy was found to depend as expected on the value of K (the projection of J onto the a axis) for the upper electronic state, but also to depend on the initial value of K in the lower state, contrary to normal expectation. The anisotropy parameter, p, was measured for the following K’+ K” transitions: 1 0, j3 = 1.0 0.1; 1 2, j3 = 0.0 f 0.15;0 1, Q branch, @ = 0.25 f 0.15;0 1, R branch, @ = 0.0 f 0.15; and 2 1, j3 = 0.1 f 0.2 These unusual results are explained by examining the detailed mechanism of the Renner-Teller interaction and by calculating the angle of recoil of the H atom with respect to the CO molecule.
-
--
*
-
-
I. Introduction The use of Doppler profile techniques to measure the translational energy distribution of recoiling photofragments has become
widespread as lasers and molecular beam technology have been increasingly applied to molecular photodissociation dynamics.’-’*
‘Current address: Environmental Division, Proctor and Gamble, Egham, Surrey TW20 9NW, England. *Currentaddress: Laboratoire de Photophysique Moliculaire, UniversitE de Paris-Sud, Orsay, France.
(1) Simons, J. P. Gas Kinetics and Energy Transfer; Royal Society of Chemistry: London, 1977; Vol. 2, pp 58-95. (2) Ashfold, M. N. R.; Macpherson, M. T.; Simons, J. P. Top. Curr. Chem. 1979, 86, 1-90.
0022-3654/91/2095-8013$02.50/0
0 1991 American Chemical Society
8014 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
These Doppler-based techniques not only provide a measurement of the recoil velocity but, when the dissociation laser and probe laser are polarized, also convey important information concerning vector properties of the recoiling fragments. In particular, since molecules preferentially absorb light when their transition dipole moments are aligned parallel to the polarization vector of the exciting light, photodissociation may lead to anisotropic photofragment recoil velocities, espesially when dissociation is rapid compared to parent rotation.I3J4 Furthermore, the Doppler profile can also measure the angular alignment of the recoil velocity and a photofragment rotation vector.15-20 Such information provides a clearer insight into the dissociation process than does simple measurement of the magnitude of the velocity and rotation vectois. It has been usual to infer from the recoil velocity anisotropy the direction of the transition dipole moment in a frame of reference fixed to the parent molecule. For example, recoil velocity distributions with a peak parallel to the polarization vector of the dissociating light are usually interpreted to mean that the transition dipole moment is parallel to the dissociating bond. Conversely, a recoil distribution with a peak perpendicular to the polarization vector usually indicates that the dipole moment is perpendicular to the breaking bond. We report here a case where a known perpendicular transition in a triatomic molecule gives rise to a photofragment recoil distribution that is peaked parallel to the polarization vector of the dissociating light. The bent ground and linear first excited electronic states of HCO and DCO are-Renner-Te_ller components of a *II state. Excitation from the X(A’) to the A(A”) state arises from a transition moment that certainly lies perpendicular to the H C O plane. We observe the recoiling photofragments following laser excitation to this state (both H and CO) to be anisotropically distributed, but with velocity vectors parallel to the electric vector of the dissociating light. Since the lifetime of the excited state varies with K’(the projection of J onto the a axis), the results depend as expected on the value of K in the upper A(A”) state. Surprisingly, they also depend on the original value of K in the lower R(A’) state. Ajthough much work on the spectroscopy and dynamics of the A X HCO dissociation has been previously reported,21-32this is the first report
-
(3) Leone, S.R. Adv. Chem. Phys. 1982,50, 255-324. (4) Leone, S.R. Ace. Chem. Res. 1983, 16, 88-95. (5) Crim, F. F. Annu. Rev. Phys. Chem. 1984,35,657-691. (6) Lawley, K. P.,Ed. Advances in Chemical Physics; Wiley: New York, 1985; p 60. (7) Jackson, W. H.; Okabe, H. Adv. Photochem. 1986, 13, 95. (8) Simons, J. P. J . Phys. Chem. 1987, 91, 5378-5387. (9) Houston, P. L. J . Phys. Chem. 1987, 91, 5388-5397.
( I O ) Ashfold, M. N. R.; Baggott, J. E., Eds. Molecular Photodissociation Dynamics; London, Royal Society of Chemistry: London, 1987. (11) Schinke, R. Annu. Rev. Phys. Chem. 1988, 39, 39-68. (12) Hall, G. E.; Houston, P. L. Annu. Rev. Phys. Chem. 1989, 40, 373-405. (13) Zare, R. N.; Herschbach, D. R. Proc. IEEE 1963, S I , 173-182. (14) Zare, R. N. Mol. Photochem. 1972,4, 1-37. (1 5 ) Hall, G. E.; Sivakumar, N.; Houston, P.L.; Burak, 1. Phys. Reo. Lett. 1986, 56, 1671-1674. (16) Dubs, M.; BrlLhlman, U.; Hubcr, J. R. J . Chem. Phys. 1986, 81, 3106-3119. (17) Gericke, K.-H.; Klee, S.;Comes, F.J.; Dixon, R. N. J . Chem. Phys. 1986,85,4463-4479. (18) Docker, M.P.;Hodgson, A.; Simons, J. P. Chem. Phys. Lett. 1986, 128, 264-269. (19) Dixon, R. N. J . Chem. Phys. 1986, 85, 1866-1879. (20) Hall, G. E.;Sivakumar, N.; Chawla, G.; Houston, P.L.; and Burak, 1. J . Chem. Phys. 1988,88. 3682-3691. (21) Ramsay, D. A. J . Chem. Phys. 1953, 21, 960. (22) Herzberg. G.; Ramsay, D. A. Proc. R . Soc. 1955,4233, 34. (23) Johns, J . W . C.; Riddle, S.H.; Ramsay, D. A. Discuss. Faraday Soc. 1963, No. 35, 90. (24) Brown, J. M.; Ramsay, D. A. Can. J . Phys. 1975, 53, 2322. (25) Vasudev, R.;Zare, R. N. J . Chem. Phys. 1982, 76, 5267. (26) Kbnig, R.; Lademann, J. Chem. Phys. Lett. 1983, 91, 152. (27) Stone, B. M.; Noble, M.;Lee, E. K. C. Chem. Phys. Lett. 1985,118, 83.
Kable et al. of anisotropy in the recoil velocity distribution of the photofragments. The results are explained by examining the dstailed Renner-Teller mechanism for crossing from the bound A-state surface to the unbound X-state surface and by calculating the recoil angle of the H atom with respect to the CO axis. 11. Experimental Section
A synopsis of this experiment is as follows: acetaldehyde was photolyzed in a supersonic free-jet e~pansion.~’The ensuing HCO/DCO radicals were cooled to about 70 K in the expansion and then dissociated by a second laser. The dissociation fragments ( H and CO) were detected 50-100 ns later by laser induced fluorescence (LIF) in the vacuum ultraviolet region with subDoppler resolution. A. heparation of HCO/DCO.The preparation of jet-cooled HCO and DCO from the 308-nm photolysis of C H 3 C H 0 or CD3CD0 has been described in detail previou~ly.~’Briefly, a mixture of 25% acetaldehyde in He was expanded into a vacuum chamber using a Newport pulsed beam valve. Immediately after exiting the nozzle orifice, the acetaldehyde molecules were photolyzed by a 308-nm laser (Lambda Physik EMG150ES). The photolysis products (including HCO/DCO) continue to cool in the expansion. About 10 mm downstream, where the local temperature was about 70 K, the H C O or DCO was dissociated by a second laser in the range 5 W 5 7 0 nm (Lambda Physik EMGlO2 pumped FL2002e dye laser). The linear polarization of the dissociation laser could be rotated by a half-wave plate. B. Detection of CO. Detection of C O molecules by vacuum UV-LIF has been described p r e v i o ~ s l y . ~Briefly, ~ an excimer laser operating at 308 nm (Lambda Physik LPX205i) simultaneously pumped two dye lasers (Lambda Physik FL2002e) operating at frequencies wI and w2. The light was spatially and temporally overlapped and then focused into a heat pipe containing Mg vapor held at 750-800 OC. When one laser (frequency ol) was tuned to a two-photon resonance in Mg at 430.88 nm, resonance-enhanced four-wave mixing occurred in the heat pipe giving rise to vacuum ultraviolet radiation with frequency 2wl + w2. This vacuum UV radiation was tunable with w2. Etalons installed in both dye lasers provided a vacuum UV line width of approximately 0.15 cm-I. The vacuum UV radiation excited CO molecules via the A-X transition; ensuing A-X fluorescence was imaged (f/ 1.5 with a 1.5 in. MgFz lens) onto a solar-blind photomultiplier tube (EMR 5426). The signal was processed with a SR250 boxcar module and gated integrator and stored on a PDP- 11 computer. The data were transferred to an IBM PS-I1 computer for further processing. C. Detection of H Atoms. H atoms from the dissociation of HCO were detected by LIF at 121.56 nm. Radiation at this wavelength was generated by frequency tripling in Kr.35 A 150-mm cell containing 200-250 Torr of Kr and 600-800 Torr of Ar was attached to one of the arms of the vacuum chamber such that the exit window was about 25 mm from the free-jet expansion. The cell was equipped with a quartz entrance window and a LiF exit window. The 365-nm light from an excimerpumped dye laser (one of those used for CO detection above) was focused into the cell by using a 100 mm focal length lens. The light was not recollimated after exiting the cell. The Kr and Ar pressures and the location of the lens were optimized by monitoring the 121.56-nm light through a 0.25-m Minuteman vacuum UV (28) Dixon, R. N. Mol. Phys. 1985, 54, 333. (29) Rumbles, G.; Valentini, J. J.; Stone, B. M.; Lee, E. K. C. J . Phys. Chem. 1989, 93, 1303. (30) Kable, S . H.; Loison, J.-C.; Houston, P. L.; Burak, 1. J. Chem. Phys. 1990, 92, 6332. (31) Loison, J.-C.; Kable, S. H.; Houston, P. L.; Burak, I. J . Chem. Phys.,
in ntecc ... r-
(32) Rumbles, G.; Lee, E. K. C.; Valentini, J. J. J . Chem. Soc., Faraday Tram. 1990, 86, 3837. (33) Horowitz, A.; Kershner, C. J.; Calvert, J. G. J. Phys. Chem. 1982, 86, 3094. (34) Trentelman, K. A.; Kable, S. H.; Moss, D. B.; Houston, P. L. J . Chem. Phys. 1989, 91, 7498. (35) Wallenstein, R. Opt. Commun. 1980, 33, 119.
The Journal of Physical Chemistry, Vo1. 95, No. 21, 1991 8015
Parallel Recoil from Perpendicular Absorption Parallel
Perpendicular
TABLE I: Experimental Measurements of the Anisotropy Parameter, 8, for Various Transitions in HCO rad DCO
HCO/DCO trans K’+ Kff 0
--
1 (Qline)
1-2 261 0
-
+
cm-l
H from HCO
1 (R line) 1 6 0
0
b: nm 562.99 562.50 540.36 543.50 565.20
12441 12456 13208 13 208 12394
/3 obsd
* *
0.25 0.15 0.0 f 0.15 0.7 0.15 0.0 f 0.2 0.1 0.2
CO from DCO 1 (Q line) 1 (R line)
0 l+O 1-2 2el
547.45 547.04 565.45 567.30 549.00
12943 12 956 12385 12385 12890
0.25 f 0.25 0.0 0.2 1.0 0.1 0.0 i 0.2 0.15 & 0.2
*
Excitation wavelength for HCO/DCO dissociation. Calculated by using AHmnion = 5300 cm-I. c J transitions can only be resolved for K’for 0. light is aligned parallel or perpendicular to the probe direction. The difference is most marked in Figure IC, where the exciting 0. The Doppler profiles were transition is K’- K” = 1 simulated by assuming that the H atom velocity distribution was consistent with the measured C O internal energy distributiod6 and by allowing the anisotropy parameter j3 to vary.” There are four features of these Doppler profiles that deserve special attention: (i) The simulated Doppler profiles that best fit these data require an anisotropy parameter B that is between 0.0 and +0.7. The largest anisotropy is observed in Figure IC, where the value of j3 that characterizes the data is 0.7 f 0.1. This indicates that the fragments have a propensity to recoil parallel to the direction of the polarization vector even though the absorption step favors selection of molecules that are initially aligned perpendicular to this direction. (ii) j3 is also sensitive to the choice of K’level prepared by the laser. This observation is not entirely surprising since it has been reported p r e v i o ~ s l y *that ~ ~states ~ ~ with different values of K’and J’have markedly different lifetimes ranging from T = 20 ps for K‘ = 0 to 70 fs for K‘ = 3. (iii) The data in Figure la,b show results for dissociation of HCO from almost the samestate; Le., (O,ll,O), K’= 0, J’= 1-4 for Figure l a and (O,ll,O), K’= 0 but J’= 7-10 for Figure Ib. Despite the near equivalence of these prepared states, it is apparent that the states prepared via the R-branch transition produce isotropically recoiling fragment, whereas those prepared via the Q-branch transition produce a somewhat anisotropic spatial distribution of fragments. This may be due either to the difference in the J’state prepared or to the difference in selection rule, AJ = 0 vs AJ = 1. These effects are examined in detail in the Discussion. (iv) The data in Figure lc,d are perhaps the most surprising. In this case the prepared states are nominally identical, vis. (0,12,0), K’ = 1, It is only the exciting transition that is different: 1 0 in Figure IC, 1 2 in Figure Id. The recoil anisotropy, however, is quite different for the two different excitation cases: j3 = 0.7 for excitation via the 1 0 transition and j3 Z= 0 for the 1 2 transition. This behavior has been confirmed by observing the 1 0 and 1 2 transitions of the (0,14,0) transition. It has been shown previously3’ that the upper state lifetime (700 fs) is independent of the transition chosen. This marked difference in dynamics must therefore arise because of some important feature of the excitation transition. We were able to measure only a single transition terminating 1 band (Figure le). The recoil distribution in K’= 2, the 2
-
Doppler Shift (cm-’)
Figure 1. Doppler profiles of the H fragment from the dissociation of
HCO. The left column gives the profile obtained when the polarization vector of the dissociating light is parallel to the probe direction,while the right column gives the result when it is perpendicular. The center of each profile has been omitted due to interference of slow-moving H atoms from other sources (see text). (a) Profiles obtained when the HCO transition was (0,11,0) (O,O,O) and the rotational transition was K ‘ c K” = 0 1 with AJ = 0 (Q branch). The data are fit by a simulated profile using /3 = 0.25. (b) Profiles obtained when the HCO transition was (0,11,0) (O,O,O) and the rotational transition was K’+ K” = 0 I with AJ = 1 (R branch). The data are fit by a simulated profile using /3 = 0.0. (c) Profiles obtained when the HCO transition was (0,12,0) (O,O,O) and K‘- K” = 1 0. The data are fit by a simulated profile using 6 = 0.7. (d) Profiles obtained when the HCO transition was (0,12,0) (O,O,O) and K ’ c K”= 1 2. The data are fit by a simulated profile using @ = 0.0 (e) Profiles obtained when the HCO transition was (O,II,O) (O,O,O) and K’+ K” = 2 1. The data arc fit by a simulated profile using @ = 0. I . +
+
-
-
+
-
-
-
+
-
monochromator located a t the opposite arm of the vacuum chamber. A solar-blind PMT (same as above) was attached to the exit slit of the monochromator. Fluorescence from H atoms formed in the dissociation of HCO was detected by a PMT placed on the side of the chamber, as above, but without the collection optics, which absorbed too much of the 121.56-nm fluorescence. To demonstrate that observed fluorescence at this wavelength originated only from H atoms produced in the dissociation of HCO, we measured a photofragment excitation (PHOFEX) spectrum of HCO using the H atom fragment. (See ref 31 for a more complete description of PHOFEX spectroscopy.) The spectrum was found to be identical with that obtained by using the CO phot~fragment.~~.” We are therefore confident that the H atoms detected here originate from the dissociation of HCO radicals. 111. Results
H C O and DCO radicals were excited via the A-8transition in the range 500-570 nm. Doppler profiles of the H fragment from the dissociation of H C O and the CO fragment from DCO have been measured. These profiles have been analyzed as a function of the relative alignment between the probe direction and the polarization axis of the dissociating light and as a function of the particular transition in the parent HCO/DCO molecule. A. H Fragments from HCO. Figure 1 shows H atom Doppler profiles for a variety of exciting transitions in the HCO. In all (O,O,O) for cases the vibronic transition is either (0,12,0) (O,O,O) for those with K’ transitions with K’odd or (0,11,0) even. The two columns of Figure I demonstrate the difference in Doppler profile when the polarization vector of the dissociating
-
-
-
-- -
-
-
-
(36)Kable, S.H.;Loison, J. C.; Neyer, D. W.; Goldfield, E. M.;Houston, P.L.;Burak, I. To be submitted for publication.
+
(37) B is defined by the equation: I(8) a 1 pP2(cos e), where 8 is the angle of the recoil velocity with respect to the polarization vector of the dissociating light.
8016 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
Parallel
Kable et al. Z
Perpendicular
I " ' I " ' " ' I
X
-0.4
-0.2
0.0
0.2
0.4
-0.4
-0.2
0.0
0.2
04
Doppler Shift (cm-')
-
Figure 3. Axis system for HCO. The coordinates xy,z are fixed to the HCO molecule with z along the a axis and with the dipole moment along x. The coordinates X,Y,Z define the laboratory frame, with the polarization vector of the dissociating light along Z. Z lies in the x,z plane at an angle fl to z . The angle $I describes the u axis rotation of HCO of the the x,z plane.
-
Figure 2. Doppler profiles of the CO fragment from the dissociation of DCO. The exciting DCO transition was (0,14,0) (O,O,O) and K'K" = 1 0. All profiles are consistent with B = 1.0 and v I J.
energy for the reaction HCO H + CO. From our data we estimate MImm = 5300 f 200 cm-', in good agreement with the value of 5492 f 67 cm-' obtained by Chuang, Foltz, and Moore.38
here was almost isotropic; the data fit /3 = 0.1 f 0.2. Anisotropy parameters, 6, measured from the H atom recoil data are summarized in Table I. It should be noted that H atoms were also found from the original photolysis of acetaldehyde. These "background" H atoms were jet cooled along with the other original photolysis products and had a translational energy distribution (and hence a Doppler profile) that was much narrower than for nascent H from HCO. In general this 'background" signal was subtracted out with the gated electronics by firing the visible photolysis laser at 5 Hz (half the repetition rate of the rest of the experiment). In the very center of the Doppler profiles in Figure la-e, however, the background signal was too strong to be subtracted accurately. These Doppler profiles are therefore missing this central portion. B. CO from DCO. Doppler profiles of CO fragments from the dissociation of DCO were measured. DCO is preferable to HCO in this case since the heavier mass of the deuterium ensures a faster recoil for the sibling C O and hence better resolution in the Doppler profile. Data were measured for each K'- K" transition, as previously, i.e. 0 1 (Q and R), 1 0, 1 2 and 2 1. An example of the mast unusual 1 0 excitation is shown in Figure 2. A molecular fragment can possess other vector properties not possible in an atom. In the dissociation of a triatomic molecule from a state of low rotational angular momentum, conservation of angular momentum requires that the recoil velocity vector must be perpendicular to the diatom's rotation vector. Such a v-J vector correlation gives rise to different shapes for the P/R and Q lines of the C0.19920 Figure 2 shows Doppler profiles obtained with four variations of excitation/probe conditions: parallel vs perpendicular alignment of the polarization and probe directions and P- vs Q-branch probing transitions. A single value of /3 and a correlation with v I J characterizes all four Doppler profiles. The only varying parameter was the slightly different translational energy brought about by sampling slightly different CO internal energies: Q(31)vs P(27). The values of @ determined from data such as those in Figure 2 are summarized in Table I. It can be noticed from the data in Table I that the anisotropy parameters are slightly different for the H fragment and the CO fragment. In general, /3 is slightly smaller in magnitude for the H fragment. This may arise because of the substantially higher velocity of the H (about 15 times faster than the CO from DCO). The large velocity may cause some of the H atoms to undergo a collision in the 100 ns before they are probed. The effect of such collisions would be to reduce slightly the value of /3. The CO fragments, however, remain essentially collision-free. The slightly higher /3 for the CO is probably close to the true anisotropy parameter of the dissociation. The H and CO Doppler profiles, in addition to determining @ and demonstrating that v IJ, provide an estimate of the available
IV. Discussion: Calculation of Translational Anisotropy W-e consider here the dissociation of HCO after excitation to the A(2A") state. This state is bound within the Born-Oppenheimer approximation, and dissociation proceeds via vibronic coupling to the ground X(2A') state. These two states are the components of a single 211state of linear HCO, and the dynamical transition between them takes place near linearity through Renner-Teller-coupling. We first note that the transition moment p for the A X electronic transition is perpendicular to the molecular plane of bent HCO, whereas for a nonrotating HCO the recoil velocities v of the H and CO fragments would take place in this plane. Consequently, if rotation could be ignored on the time scale of the dissociation, the translational anisotropy would correspond to 6 = -1. This is not in accord with our observation. However, the bands in the electronic spectrum of HCO show resolved K, structure, so that rotation cannot be ignored. J structure is only resolved for K,,' = 0. We will therefore first consider a model in which the a axis rotation is quantized, but rotation about the b and c axes is neglected. Section IVC below will consider how this end-over-end rotation might affect the results. In view of the linear equilibrium geometry of the excited state, we introduce a body-fixed frame x,y,z for which the third Eulerian angle y in the space-fixed frame X,Y,Z is zero, and z coincides with the a axis of HCO, as shown in Figure 3. The electric vector of the excitation field along 2 then lies in the x,z plane. A. Vibronic Wavefunctions. Then let @J be the polar angle in x,y,z for the H C O bending coordinate s and, following earlier authors, let Be be the angle about z conjugate to the electronic orbital angular momentum. The essence of the vibronic coupling is that the total wavefunction must include a linear combination of two products of electronic and nuclear functions. These can be expressed directly either in terms of the above angles (the linear or by referring the electronic functions molecule to the instantaneous nuclear plane in terms of the electronic angle ae = Be - 9 (the bent molecule approach, in which case the . ~ ' the present functions are real with A' or A" ~ y m m e t r y ) . ~ ~For purpose, the second choice is more revealing. We also make the usual Renner-Teller assumptions that A and K, are good quantum numbers to zero order. Then for each vibronic level
+
-
- - - .-
-
+".K
=w
e ? % )
X;,K(Sd)
+ lWe*%)
XE,K(W
(1 1
where (38) Chuang, M. C.; Foltz, M. F.; Moore, C. B. J . Chem. Phys. 1987,87, 3855-3864. (39) Pople, J. A.; Longuet-Higgens, L. C. Mol. Phys. 1958, I , 372. (40) Jungen, Ch.; Merer, A. J . Mol. Phys. 1980, 40. 1. (41) Barrow, T.; Dixon, R.N.; Duxbury, G. Mol. Phys. 1974,27, 1217.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8017
Parallel Recoil from Perpendicular Absorption We,ae= ) r - l ’ z W e )cos (AaJ
(2)
W , , a J = r-~~z!he(re) sin (kc)
(3)
and x : , ~ ( s ,=~ )( 2 W 2 ~ ; , K ( s )exp(iK4)
(4)
X;,K(S,4) = (2*)-”2u:.K(s) exp(iK4)
(5)
except that for a K = 0 level there is either a xs term (Z+level) or a x* term (Z-level) but not both. Each level with K # 0 is doubly degenerate, and K is a signed quantum number in the above equations. It will prove convenient to transform eqs. 4 and 5 to the equivalent real basis in terms of cos (K4) and sin (K4). The total wavefunction is then
= T-’$C(~C) [u:,K(s) COS (ha,)COS (K4) - u;,K(s) sin (ha,) sin (&)I (6)
K+ levels but sin (K4) for the K- levels. Consequently, even though u;,(s) has a much larger magnitude in eqs 6 and 7 than u&(s), the latter term dominates the dissociation; its small amplitude implies a small crossing probability. This change of angular distribution on surface hopping is brought about by the need for a transient exchange of angular momentum between the electrons and nuclei, as illustrated in an earlier time-dependent wave packet study of this process [Figure 4 of ref 281. Consequently, excitation with nuclear wave function x”,(s,~$) and dissociation with xtx+(s,#) involves a phase change around the z axis. On this basis we can now calculate the recoil anisotropy parameter @ = 5(Pz(v.Z)),which in this case is related to the angular distribution of v in the body fixed frame x,y,z, i.e. to Pz(v’z), through the spherical harmonic addition theorem:
j3 = 5 [ ( 4 i ” ( 0 , 4 ) )
+ (~o(j3w2z(~,~) + q-,(e,m
+ZK
(1 1)
where ’ a‘ is a rotation matrix element and C,, is a spherical harmonic. In eq 11, the averaging over j3 needs to include the sin2 (8) weighting factor from eq 8, and the matrix elements of 6 , K = ~ - l v u r ex ) C,, are determined by using the wavefunctions (6) and (9) for [ U ; , ~ ( S ) cos (Aa,) sin (K4) + ut,&) sin (Aa,) cos (K4)] (7) K+ levels and (7) and (10) for K- levels. The first term in the sum of eq 11 is independent of K’and depends only on the angle which functions are respectively symmetric and antisymmetric 8 between the final recoil velocity v and the z axis. We evaluate to reflection in the x,z plane. this angle below. The second term in (1 1) is Kcdependent and Within the framework of this model, transition probabilities proportional to (cos 24). For all values of K’ # 1 this expectation are related to the component of the electronic transition moment value is zero and there is no contribution to j3 from anisotropy operator resolved along the Z axis, that is to about the z axis. For K’ = 1, however, (cos 24) = +OS for the 1+ levels, and -0.5 for the 1- levels. P f = P&e) cos (4)sin (8) = For a purely bending trajectory on the excited state surface, P,(re)[cOs (a,)cos (4) - sin (4 sin (4)l sin (8) (8) the angle B will be 90° for the surface hop a t linearity. The contours of the ground-state surface42suggest that the trajectory j3 being the second Eulerian angle. However, as a consequence will finally lead to dissociation with B between 60° and 100’. We of the restriction so far to a zero-order Renner-Teller model, there have performed classical trajectory calculations on the -BBH are no nonzero matrix elements of (8) _betwe_eneither of the t ~ r f a c starting e ~ ~ on the common linear seam between the? and wavefunctions (6) or (7). The observed A X bands of HCO A surfaces at coordinates and momenta consistent with the A-state come about because eqs 6 and 7 are no longer accurate at the bent vibrational level. The results, which will be reported in more detail ground-state geometry (HCO angle = 125’). In particular, A el~ewhere,)~ indicate that the most probable value for B is 100’ is no longer a good quantum number and hybridhation at the carbon atom mixes 2Z+character (A = 0) into the X [ ~ ( r , , a , ) ] with a distribution characterized by a fwhm of So. The first three columns of Table I1 present calculations made component of the zIIstate (A = 1). Furthermore, the energy by using eq 11 for the distribution of B values determined above. difference between the two Born-Oppenheimer curves is so great For each K subband these include the sum over K+’ P’ and at this large value of s that the amplitude of u:,~,,(s) is negligible K-’ K-”,except for 1’ O+ where only one upper component compared with that of u::~,,(s) (note that the trend is in the is accessible. The different anisotropy for K’= 1 with K” = 0 opposite sense for the excited state). The transitions are thus or 2 is thus readily explained. induced through the first-order perturbations to the ground-state C. Effect of End-Over-End Rotation. End-over-end rotation wavefunctions: of the H C O has so far been neglected on the ground that there $;J)’’= (2rz)-1~~~~~”(r,,s)u;,f’(s) cos (K4) (9) is no resolved J structure except for K’ = 0, but the level widths are not very much greater than the rotational energy separations. and Parent molecule rotation will degrade the recoil anisotropy through &(#” = ( 2 r 2 ) - 1 ~ ~ ~ ~ ) ” ( r Csinr ~(K4) ) ~ ~ , K(10) f ’ ( ~ ) two effects. First, the body-fixed frame will rotate in space in the interval between excitation and dissociation. Second, the The transition probabilities c,an now be evaluated by using eqs dynamics of the dissociation may be altered by the imparting of 9 and 10 for the leveltof the X(2A’) ground state, eqs 6 and 7 tangential velocities to the departing fragments, as well as through for the levels of the A(2A”) excited state, and the transition Coriolis or centrifugal forces. It is already known that dissociation operator of eq 8. This leads to the correct AK = f l selection from K’ = 0 is mediated through both these latter processes.25 rule, with the additional rule that Kif P’but Kif +/+ P”. In a fully quantum treatment, the first effect arises from the Thus, in general the transitions are doubly degenerate except when dephasing of the P, Q, and R transitions, which are initially one or other K value is zero, where the allowed subbands are I + coherently excited. A semiclassical treatment of the rotation is O+ and 0- I-. equivalent to this dephasing provided that these transitions remain B. Dissociation Mechanism. We have already noted above that unresolved. Let p be an angle through which the body-fixed z for a vertical excitation of HCO at the ground-state geometry, axis rotates between excitation and dissociation. Then, with equal , is much less than that of u : , ~(s), , in the amplitude of U : , ~ (s) probability of rotation about the x or y axes, eq 11 can be extended accordance with the 2Af’ Born-Oppenheimer character of the semiclassically to give excited state. Thus, the anisotropy of excitation to the states of P = 5[(dZ,(P))(d2,(P))(Czo(B,4))+ eqs, 6 and 7 is given in the body-fixed frame by the sin (K4) factor for the K+ levels, and cos (K4) for the K- levels, which are the ( ~ ~ ~ ( +0 C~~4- )~ ( B ,(12) ~))I terms associated with +:(r,,a,). However, following this excitation The average rotation angle p will be a function of the rotational to the upper state, dissociation proceeds on the ground-state potential surface after a surface hop near linearity. Hence the out-going nuclear wavefunction is given by u;,&) (i.e., the (42) Bowman, J. M.; Bittman, J. S.;Harding, L. B. J . Chem. Phys. 1986, multiplier of g(r,,a,)), which is associated with cos (Kd) for the 85, 911.
or
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8018 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
Kable et al.
TABLE 11: Commrison of Tbeoretiul rad Ex~erimentrlValues of the Recoil Anisotropy Parameter, 19
(e),
(e), no overall rotation
-
K’
subband 0 1 (Q) 0- 1 (R) 1-0 n/aa 1-2
001+ 11 2
2-1
60’ 0.13 0.13 1.25
-1.00 0.13 0.13
(traj)b
90°
60’
0.43 0.43
0.50 0.50 2.00 -1.00 0.50 0.50
0.13 -0.06 1.04
1.85 -1 .oo 0.43 0.43
-0.87 0.08 0.12
overall rotation for 70 K ( traj)b 90° 0.43 -0.20 1.50 -0.93 0.29 0.39
0.50 -0.23 1.62 -0.94 0.34 0.45
p obsd 0.25
0.0 0.7-1
.O
nla 0.0 0.1-0.1 5
OThere are no subbands that can induce a transition to purely 1-. bAverage over angles 6 given by trajectory calculations.
B value, the line width I?, and the range of ground-state J values populated. The expectation values of d#p) have been evaluated by integration over p with an exponential decay, and summation over J, using B = 1.1 cm-’, a Boltzmann distribution over J at T=70K,r=28cm-lforK’= I,andr=76cm-’forK’= 2. The results of these calculations are given in the last three columns of Table II.” For K’ = 1 the average rotation angle ( p ) is about 28O during the dissociation lifetime. This significantly degrades the axial anisotropy in the body-fixed frame ( ( & ( p ) ) = 0.68), but has a lesser effect on the azimuthal anisotropy ( ( ~ 4 ~ ( p )=) 0.85). The shorter lifetime for K’ = 2 causes somewhat less rotational degradation of the anisotropy in this case ((&(P)) = 0.91). The 0 1 subband requires a different treatment, since the P, Q,and R branches are partially resolved. If we completely neglect their overlap, then they cannot interfere, and with the value of l’ = 0.3 cm-’ we obtain (&(p)) = 1.00 for the Q branch but (&&I)) = -0.48 for the P and R branches. This different behavior is in accordance with the usual propensity for the rotation axis to be respectively parallel or perpendicular to the electric vector defining the 2 axis. The results are again given in Table 11. These considerations show that the uniqueness of the value of /3 for the 1 0 subbands is therefore maintained even when allowing for overall rotation at 70 K. Furthermore, the dculated values of /3 show the same pattern of signs and relative magnitudes as observed experimentally. The absolute magnitudes are calculated to be too large when we use the angular distribution from the classical trajectories, but we note that they would be close to +
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(43) The rotational effects also have been calculated by the full quantum method since there are significant quantitative errors in the semiclassical treatment at the low values of J that are relevant at 70 K. These quantum values have been incorporated in Table 11. However,for clarity they are quoted in eq 12 in the equivalent semiclassical notation.
experiment if the mean value of 0 were changed by 10-15O.
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V. Conclusions The transition dipole moment for the A(2A”) 8(2A’) electronic transition of bent HCO is perpendicular to the molecular plane. Thus, prompt dissociation within this plane would be expected to lead to a negative value of the recoil anisotropy parameter @ for either the H or CO products. Experimental measurements, however, of both the H and CO velocity distributions following the dissociation of HCO or DCO indicate that /3 2 0 and that it is particularly large (0.7) for the K’ K” = 1 0 transition. This result is explained by considering the rapid rotation about the top axis in the excited state, which leads, in general, to an isotropic distribution of products about this axis, and to the prediction of a small positive value for 8. The exception to this rule is for excitation in 1 0 subbands, where the most probable plane of dissociation is at right angles to that of excitation. Thus unusual behavior comes about because of the need for the electrons and nuclei to transiently exchange angular momentum in order to facilitate the nonadiabatic crossing at linearity. In all cases, the predicted values of 6 are reduced by end-over-end rotation_. Calcu_lations based on the first-order wave functions for the A and X states reproduce the observed pattern of experimental results.
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+
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Acknowledgment. The experimental work at Cornell University was supported by the National Science Foundation under Grant CHE-8920404, while the trajectory calculations were supported by a grant from the Cornell National Supercomputer Facility. We thank Dr. E. M. Goldfield and Professor G. Ezra for helpful discussions concerning the trajectory calculations. R.N.D. is grateful to the Science and Engineering Research Council for continued financial support. R d ~ t r yNO. HCO,2597-44-6; DCO,24286-05-3; CO,630-08-0; H, 12385-13-6.
