J. Phys. Chem. 1995,99, 13611-13619
13611
How a Collision Causes Misalignment: Alignment Decay in Acetylene 2’ Joshua B. Halpern* Department of Chemistry, Howard University, Washington, D. C. 20059
Ralf Dopheide and Helmut Zacharias Fakultaet firer Physik, Universitaet Essen, 451 17 Essen, Germany Received: March 9, 1995; In Final Form: June 7, 1995@
The effects of acetylene self-collisions on alignment have been studied in detail. Strongly aligned samples of C2H2 were prepared in several rotational states of the 2l level by stimulated Raman pumping. Laserinduced fluorescence verified the initial degree of alignment and was used to follow its decrease via collisions. Measurements of the initially excited alignment agree well with theoretical calculations of that achievable by stimulated Raman pumping, and the decay can be well modeled by a simple kinetic scheme.
Introduction Although there are literally thousands of papers on energy transfer, only a handful deal with changes in molecular spatial orientation during elastic or inelastic collisions. Such experiments, perforce, start by spatially orientating a group of molecules or selecting those with a particular orientation out of an isotropic sample. Either task is a difficult one. Richard Berstein was well-known for his pioneering work using multipole field electrostatic focusing to form molecular beams of selectively oriented molecules.’ Toennies, another early proponent of electrostatic beam selection and detection, measured cross sections for a few [i,m)-changing collisions of T1F and CsF with several collision partners.2 Recently Loesch has oriented beams of molecules cooled in a supersonic expansion by brute force application of an electrical field.3 Beam-focusing techniques work only for molecules with permanent dipole moments. Another beam method, dynamic cooling in a supersonic expansion spatially aligns symmetric top molecules. Several rotational levels are populated, the range depending on the molecule’s moment of inertia and the beam temperature. This is limiting for alignment decay and transfer measurements where it is advantageous to start in a single state.4 Optical methods of initiating such experiments are also possible, usually involving some type of double-resonance excitation with photons whose energy can range from the microwave5 to the UV.6 An important distinction between optical methods and electrostatic focusing is that the latter operates directly on the molecular framework. The fields exert real torques to spatially orient molecules or to move molecules in undesired quantum states out of the beam while focusing those with the desired characteristics into the reaction region or the detector. On the other hand, optical methods work selectively by exciting only those molecules whose angular momentum vectors happen to be favorably aligned with the exciting light’s polarization. The spatially aligned excited states are populated by optical transitions which start only from a particular group of ground state molecules, or molecules with other than the desired orientation are preferentially removed from the ground state, leaving a spatially aligned sample behind. Microwave rotational transitions are, of course, also only possible for molecules with permanent dipole moments, while IR transitions in molecules lacking a permanent dipole moment @
Abstract published in Advance ACS Abstracts, August 15, 1995.
0022-3654/95/2099- 13611$09.00/0
require a unit quantum change in an asymmetric vibrational mode. Development of narrow band visible-W lasers shifted applications toward studies of collisional misalignment in electronically excited states,6 but such experiments can only be done in molecules which have a stable intermediate electronic state linked by strong transitions to the initial and final levels. Steinfeld’s group has exploited rare coincidences between isolated IR active vibrational-rotational transitions of spherical top molecules ( C h , and S i b ) and COT lasers, monitoring rotational energy transfer with tunable diode lasers.’ Various [i,k) [if&’) transition probabilities have been measured for these spherical tops. One may anticipate that the availability of narrow band tunable optical parametric oscillators will lead to many more collisional dynamics studies in levels which can be reached by IR active transitions. Recently, we demonstrated how stimulated Raman pumping can produce strongly aligned and state-selected acetylene. A single example was given of the alignment collisional decay from the 2l, J = 3, state.8 Shortly thereafter, Sitz and Farrow provided essentially equivalent information for N2 excited by stimulated Raman p ~ m p i n g . Stimulated ~ Raman pumping is the best method of studying energy transfer processes in low lying levels of molecules lacking a permanent dipole moment. It is especially useful since for all practical purposes natural atmospheres are composed of homonuclear diatomics (N2, 0 2 , and H2) leavened with a few symmetric polyatomics. IR transitions are strongly forbidden for the homonuclear diatomics, while most of the polyatomics lack a permanent dipole moment and thus have several IR inactive vibrational modes ( C b , C3H6, C2H2, C02, etc.), the exceptions being H20, NH3, and S02. Within the limits of this restriction, stimulated Raman pumping is a relatively efficient and relatively simple method for populating individual rotational levels in the ground state of homonuclear diatomics and symmetric vibrational modes of polyatomic molecules. Besides their importance in atmospheric dynamics, elastic and inelastic collisions of these types of molecules are interesting because scattering will occur only through higher order and weaker processes rather than the dipole-dipole or dipole-induced dipole interactions which dominate collisions of molecules with a permanent dipole moment. I o Stimulated Raman pumping can excite a strongly aligned or oriented single rotational state in a low lying vibrational level. From that starting point it is straightforward to measure detailed
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0 1995 American Chemical Society
Halpem et al.
13612 J. Phys. Chem., Vol. 99, No. 37, 1995 rates for collisional decay and transfer of rotational angular as well as how collisions change a molecule’s spatial orientation. Thus, one can test the predictions of collisional energy transfer theories about state to state scattering and their assumptions of how the spatial orientation changes during a collision. While we relied on laser-induced fluorescence (LIF) for alignment detection and Sitz and Farrow on multiphoton ionization, IR absorption or emission could be used to characterize the alignment or orientation of molecules such as COZ and H20, which lack bound electronic states. In optical experiments spatial molecular anisotropy is almost always described by multipole moments AJk). The elements of order 0, 1, and 2 are called, respectively, the population, orientation, and alignment. Confusion exists because sometimes alignment (orientation) refers to the sum of the even (odd) moments, as opposed to just the element of order 2 (1). The point is moot in this experiment. The experimental geometry suppressed the contribution from A0(4),the highest order moment excited by stimulated Raman pumping, to well below the experimental error. The orientation measures the direction in which the ensemble angular momentum vector points,
while the alignment measures to what degree the axis of rotation is parallel = 2) or perpendicular (A&*) = -1) to the laboratory z axis, often established by the polarization of an exciting laser beam.
The final state population, o(JfMf), is proportional to the stimulated Raman pumping cross section and formally equals the two photon transition probabilities calculated by Lin et al.I3 (T
= L$‘ML“[(2Ji
+ 1)(2Jf + 1)]”2(-1)M1fM-K1-k X
Above, AJ = 2 for S band excitation. The polarization of the laser in the laboratory frame determines AM, where as usual, AM = 0 for the linearly polarized light used to produce aligned samples. Kband Kfare set by the choice of initial and final vibrational levels. For the 201 transitions used in this study they are both 0, and thus Ak is also 0. The factors L+&nand Mkcn are fixed by the excitation geometry for a particular molecule. The moments, &(k), of the various rotational states in the 2’ level, either originally excited or transferred to by collision, can be determined from the intensity of LIF signals, using formulas given by Greene and Zare:I4 Zfl = SC
A,’k’~(kd,ka,k,O:R)b‘k’(Ji)h(kd,ka,k,Ji,Je,Jf) (4)
kdkd
C is the detection efficiency, S is the rotational line strength, and the are the moments we are seeking. Given the cylindrical symmetry imposed by stimulated Raman pumping, we only need to determine the A o ( ~rather ) than all elements Geometric relationships between the various laser beams determine ~(k,,k,,k,O;Q), which is a tabulated polarization tensor.
Stimulated Raman Pumping Lasers Polarization’
t Probe Laser Polarizations
Figure 1. Spatial relationship between the various laser beams and their polarizations. The Raman pumping beams (532 and 594 nm) were combined, and their polarization was held parallel to the z axis. The polarization of the counterpropagating probe beam at 242 nm could be rotated in a KD*P crystal. Fluorescence was detected perpendicular to the laser beams, without regard to polarization.
The b(k)(Ji)are angular momentum operator reduced matrix is a rotational angular momentum elements and h(b,ka,k,Ji,Je,Jf) coupling term that is the product of a Wigner 3-J and a 6-5 symbol with some multiplicity factors. The various A o ( ~can ) be determined using specific detection geometries. In a particularly simple way is best measured when the Raman pumping and LIF exciting lasers are linearly polarized and counterpropagating with an unpolarized detector placed at right angles. As indicated in Figure 1, LIF signals need to be measured when the polarization of the laser is rotated to be both parallel and perpendicular to that of the Raman pumping beams. The alignment is then directly related to the degree of polarization P = (41 - L)/(Zt L).Formally, the polarization induced by stimulated Raman pumping includes a small hexadecapole component, Ao(4),but, as mentioned above, the contribution is vanishingly small for a colinear geometry and certainly much smaller than our experimental error. There have been relatively few papers on loss of alignment through collision, which we choose to call misalignment, and alignment transfer in inelastic collisions. Results on molecules lacking a permanent dipole moment are even rarer, and there is disagreement in even the few papers which have appeared. Our first result for acetylene 2l, J = 3, measured the alignment decay to be roughly 40% of the total inelastic transfer rate and about half of the rotational scattering cross section.8 In Sitz and Farrow’s two examples of nitrogen alignment decay, Y = 1, J = 6, and J = 14, the rate for the lower rotational level was a bit slower than that for rotational energy transfer. For the higher angular momentum state, the alignment decay rate was much slower, perhaps even beyond their limits of measurement. The earlier experiments which bear most strongly on these two are McCaffery’s studies of orientation relaxation from fluorescence induced by CW laser excitation of 1215-’7and Li2,185’9which favored a selection rule [Am[ = 0, and the more relaxed conclusion of Mattheus et al. of a I h l
