Rotationally inelastic collisions of OH X 2 Ar. II. The effect of molecular orientation

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1 JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 2 8 JULY 2000 Rotationally inelastic collisions of OH X 2 Ar. II. The effect of molecular orientation M. C. van Beek and J. J. ter Meulen Department of Molecular and Laser Physics, University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands M. H. Alexander Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland Received 17 February 2000; accepted 13 April 2000 Orientation effects in inelastic collisions of OH(X 2 ) Ar at an energy of 746 cm 1 have been studied in a crossed molecular beam experiment. The OH(X 2 ) radicals were prepared in the v 0, 3 2, J 3 2, f state by hexapole state selection and oriented with their O-end or H-end towards the Ar atom by a static electric field in the collision zone. The orientation-dependent probability density function has been determined by laser induced fluorescence spectroscopy using a narrow band dye laser and the Stark mixing induced P 1 (1) transition. A degree of orientation of cos 0.55 has been obtained. The steric asymmetry factor has been determined for rotational excitation up to the 2, 3 J 9 2 and 1 2, J 5 2 states. Differences up to a factor of 8 in cross section were found between O-end and H-end impact. In general a slight preference for O-end impact was found for low rotational excitation, while a strong preference for H-end impact was found for excitation to high rotational states. The experimental results are compared to quantum scattering calculations on ab initio potential energy surfaces developed by Degli-Esposti and Werner J. Chem. Phys. 93, and Klos et al. J. Chem. Phys. 112, The agreement between experiment and calculations based on the Klos and Chalasinski potential is excellent for transitions to states of A symmetry and good for transitions to states of A symmetry American Institute of Physics. S I. INTRODUCTION In addition to the collision energy and the initial states of the collision partners, the relative orientation is a key factor in determining the outcome of a molecular collision. 1 Hence, in the past three decades considerable effort has been devoted to probing the stereodynamic aspects of reactive collisions, reviews of which can be found in Refs. 2 and 3 and recent examples in Refs. 4 and 5. Although initial orientation also modulates inelastic collisions, this has attracted much less attention. To the best of our knowledge the dependence on molecular orientation of initial and final state-resolved inelastic cross sections was first reported in 1996 for collisions of NO with Ar. 6 Control of molecular orientation by either molecular beam or laser methods is more difficult than selection of the initial state or the collision energy. There exist two different techniques which have been used to align or orient molecules: In one class of methods a laser is used, 7 in the other class a static electric field. In the latter class of experiments two different techniques can be distinguished: brute force orientation 8 and hexapole state selection and orientation. 9 Because of ease compared to laser methods, the absence of Stark induced J mixing, the inherent -doublet state selection, and the high degree of orientation which can be achieved, the hexapole technique is ideally suited for collisions of molecules in 2 electronic states. We use this technique to orient OH(X 2 ) radicals. In a series of experiments we have studied inelastic collisions of OH(X 2 ) radicals The OH radical is of significance in combustion process, 15 atmospheric chemistry, 16 and astrophysics. 17 Recently, interest has focused on the benchmark, four-atom reactions of OH with H 2 and CO. 18 An additional advantage of studying the OH(X 2 ) Ar system is the availability of high quality ab initio potential energy surfaces PES s which can be used in quantum scattering studies for comparison with experimentally determined cross sections. Two sets of PES s are available; the coupled electron pair approximation CEPA PES s of Degli-Esposti and Werner 19 and the more recent unrestricted fourth-order Mo ller Plesset UMP4 PES s of Klos et al. 20 In the preceding paper we reported experiments and quantum scattering calculations for state-to-state inelastic scattering of OH(X 2 ) by Ar at a collision energy of 746 cm 1. 4 In these experiments a single initial fine-structure state was prepared by electrostatic state selection. This permitted the investigation of the influence of the spin orbit manifold and the e/ f symmetry on the magnitude of the inelasticity. More detailed information about the role of the anisotropy of the PES s can be obtained if the relative orientation of the collision partners can be controlled such that collisions of Ar with the H-end or the O-end of the radical can be distinguished. The influence of the molecular orientation on the collision process is quantified by the steric asymmetry factor which is defined as /2000/113(2)/637/10/$ American Institute of Physics

2 638 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 van Beek, ter Meulen, and Alexander FIG. 1. Artist s impression of experimental setup with orientation field. S HO Ar OH Ar 100%, 1 HO Ar OH Ar where HO Ar and OH Ar represent the cross sections when the OH radical is directed with the O-end or the H-end towards the Ar atom, respectively. The steric factor varies between 100 and 100%. A positive factor implies that the cross section is larger for collisions at the O-end of the radical while a negative factor indicates that rotational excitation at the H-end is preferred. Stolte and co-workers were the first to report the quantitative determination of the effect of molecular orientation on state-to-state inelastic cross sections of neutral open-shell molecules. 6,21 These authors investigated transitions of NO out of the ground rotational state 2 1/2, J 1 2 to states with J up to 33 2 in collisions with Ar. They found steric asymmetries between 28% and 49%. Remarkably, the steric asymmetry alternates in sign with J even or odd for 2 J There have been several quantum scattering calculations of these NO Ar steric factors, based on ab initio PES s. 6,21,22 The calculations predict the general trends quite well, although, in general, the calculated magnitude of the steric asymmetry is too large. Although the ground electronic states of OH and NO are both 2, because of its much larger rotational constant, the rotational levels of the OH radical are described in intermediate Hund s case coupling, and hence behave quite differently in inelastic collisions. 23 Because transitions between the two spin orbit manifolds are much more probable for collisions of OH with Ar, as compared to NO, we are able to study the effect of orientation on these processes, which has, of yet, not been possible for NO. Several years ago we first reported the investigation of orientation effects in collisions of OH with He, normal-h 2, para-h 2, and Ar. 12 However, due to the limited signal to noise ratio, transitions to only the lowest rotational states could be investigated. Further, no comparison was made with theoretically calculated steric factors. In the present article we describe and compare new experiments and scattering calculations on inelastic collisions of oriented OH(X 2 ) with Ar. The experiments are performed at a higher collision energy. In addition, the sensitivity of the experimental setup has been improved by a factor of 4, which allows for a more accurate determination of the steric asymmetry for transitions to an increased number of rotational states. The layout of this article will be as follows: In the next section the experimental setup will be described with a particular emphasis on the methods used to determine the degree of orientation. The quantum scattering calculations will be described in Sec. III. In Sec. IV the experimental and theoretical results will be presented and compared. Conclusions will be drawn in the last section. Throughout this article we use the notation, J, to refer to different OH states. Here, represents the projection of the J vector on the internuclear axis and is used to label the spin orbit manifolds, J represents the total angular momentum without nuclear spin and the symmetry index e or f designates the lower and upper -doublet substate, respectively. The quantum labels, J, are used to denote the states after the collision. An exception is made in the discussion in Sec. II D on laser-induced fluorescence LIF spectroscopy, where J denotes the angular momentum of the excited electronic state. For the labeling of the LIF transitions the nomenclature of Dieke and Crosswhite 24 will be used. II. EXPERIMENT A. Experimental setup The experimental setup Fig. 1 is identical to the one which has been used for the measurements of the state-tostate cross sections, 14 but with the addition of an orienting field in the collision zone. Since most of the setup has been described in detail in the previous papers, we will concentrate here only on the methods used to orient the molecules and to probe the degree of orientation. The measurements have been carried out in a pulsed crossed molecular beam experiment. The OH beam is produced by an electrical discharge in H 2 O seeded in Ar at the beginning of the expansion. After the cooling due to the expansion followed by the electrostatic state selection more

3 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 Collisions of OH(X 2 ) Ar. II 639 TABLE I. Experimental steric asymmetries for rotational excitation of OH(X 2 3/2,J 3 2, f ) in collisions with Ar at a collision energy of cm 1. a Final state Steric asymmetry J Single hexapole Double hexapole 3/2 5/2 e f /2 e f /2 e f /2 1/2 e f /2 e b f /2 f a Although the results with the double hexapole are believed to be more reliable, the results with the single hexapole are incorporated to indicate the effect of initial population in excited rotational states. b Transitions for scattering into the 1 2, 2 3, e and 1 2, 5 2, e levels cannot be separately resolved. Accordingly, the tabulated steric asymmetry is the combined steric asymmetry for the 2, 3 3 2, f 1 3 2, 2, e and 2, 3 3 2, f 1 5 2, 2, e transitions. then 93.2% of the OH radicals are in the initial v 0, 3 2, J 3 2, f state. Two electrostatic state selectors have been used. The first consists of one hexapole, the second of two hexapoles along with a beam stop and diaphragm. After passage through the single hexapole the ratio of OH populations in the M J 3 2 and M J 1 2 states is 2.6; after passage through the double hexapole this ratio is enhanced to Table I of the preceding paper lists the initial populations of all OH rotational states. B. Orientation After state selection the OH radicals are oriented by a static electric field in the collision zone. The theory of hexapole state selection and orientation of OH has been described in detail by Schreel and ter Meulen 12 and Hain and Curtiss 25 and will not be repeated here. Only some relevant results will be presented. The hexapole electric field state selector focuses the upper f -doublet level of the OH molecule. 26 When the molecule enters the static field E, this state will evolve into a linear combination of the field-free e and f -doublet states, namely, 6,12,22 JM J E M J E JM J e M J E JM J f, where the real coefficients and are given by solution of a 2 2 Stark mixing Hamiltonian, and 12 2 M J E 2 M J E 1. 3 We note that this definition of and corresponds with the definition by de Lange et al., 21,27 but differs from that of Alexander and Stolte. 22 The orientation as a function of the electric field is given by 12 2 FIG. 2. Calculated Stark shift of OH and measured LIF scan over the P 1 (1) and P 1 (1) transitions. From the separation of the peaks the Stark shift and hence the value of the orienting field can be determined. The area under the peaks yields the population of the different M J states. M J cos M J E 2 M J E M J E J J 1. 4 Expressions for M J (E) and M J (E) can be found in Ref. 12. The orientation field is produced by four parallel stainless steel rods 2 mm in diameter and separated by 17 mm, which are set pairwise at a voltage of 12 kv or 12 kv. By changing the polarity of the rods, the OH radicals can be oriented with the H or O-end towards the Ar atoms. In the presence of this electric field the zero-field -doublet states are Stark mixed and shifted. This mixing allows for additional, field induced, spectroscopic transitions which can be used to probe the degree of orientation. 27 The stray fields of the hexapole and the orienting field are large enough to maintain the orientation of OH, hence, a guiding field is not needed. To determine the orientation probability density function, both the electric field at the collision zone and the distribution over the M J states has to be known. Both have been determined by saturated LIF using the OH A 2 (v 0) X 2 (v 0) transition at 308 nm with a narrow band dye laser system. The 616 nm narrow band radiation was generated by a cw ring dye laser Spectra Physics 380 operating on a mixture of DCM and Rhodamine 6G and pumped by an Argon-ion laser Spectra Physics The output is amplified by a pulsed dye amplifier Lambda Physik LPD 3000 which operates on Sulforhodamine 640 and is pumped by a Nd:YAG Spectra Physics GCR 190 laser and subsequently frequency doubled in a KDP crystal. The resulting pulsed 10 Hz 308 nm radiation has a bandwidth of 100 MHz and an energy of a few mj per pulse. The frequency of this laser system was scanned over the P 1 (1) and P 1 (1) transitions to probe the population of the 3 2, 3 2,e, M J and 2, 3 3 2, f, M J states, respectively. The observed spectrum is shown in Fig. 2. The P 1 (1) transition probes the lower -doublet states and is parity allowed in zero electric field, while the P 1 (1) transition probes the upper -doublet components and is parity forbidden in zero field. This measurement was performed using the single hexapole.

4 640 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 van Beek, ter Meulen, and Alexander As can be seen from Fig. 2, transitions from the different -doublet states as well as from different M J states are clearly visible. Although the hyperfine effects in the electronic ground state cannot be resolved, the hyperfine splitting of the excited electronic state can easily be seen. From the separation of the lines, the Stark shift, and, hence, the electric field can be calculated. At the applied voltage of 12 kv the electric field in the center is found to be E orient kv/cm. For the observed electric field, the mixing parameters are 1/ , 3/ , 1/ , and 3/ From these parameters the average orientation of the OH radical can be calculated to be cos 1/ and cos 3/ , where is the angle between the orientational field and the internuclear axis. The ratio between the population of the 2, 3 3 2, f, M J 3 2 and 3 2, 3 2, f, M J 1 2 states has been determined from the area under the peaks in Fig. 2 to be Weighted for the different population of the M J states, the overall average orientation in the experiment with the single hexapole is given by cos To check these measurements we have also measured the fluorescence signal from the P 1 (1) and P 1 (1) transitions with a normal pulsed dye laser. 14 The bandwidth of this laser is 0.3 cm 1, which is wide enough to probe both lines simultaneously. For these measurements the laser beam had a well defined linear polarization. Since, after passage through the hexapole, the population of the e state is much lower than the population of the f state, the contribution of the P 1 (1) line can be neglected. The laser power was kept high enough to saturate the P 1 (1) transition. The population of the M J 1 2 and M J 3 2 states was determined by rotating the polarization of the laser with respect to the electric field axis. When the polarization is parallel to the electric field, only M J 0 transitions can be made, which couple the M J 1 2 states in the ground state with the M J 1 2 states in the electronically excited state, resulting in 50% excitation of the population of the M J 1 2 states. When the polarization is perpendicular to the electric field, however, only M J 1 transitions are allowed, which couple the M J 3 2 and M J 1 2 states in the ground state to the M J 1 2 states in the excited state, resulting in a 33 3% 1 excitation of the total ground state population. For both polarizations the M J states in the excited state are equally populated, resulting in an isotropic fluorescence. From the LIF signal at perpendicular (I ) and parallel (I ) polarizations the population ratio of the M J states can be calculated FIG. 3. Measured fluorescence signal from the field induced P 1 (1) transition as a function of the voltage on the rods and the calculated strength of the P 1 (1) transition dashed line. The degree of parity mixing and orientation as a function of the orientational electric field are plotted with solid lines. The limiting values in an infinite electric field are indicated by the horizontal dashed lines. The vertical dotted line indicates our value of the orienting field. n 3/2 3I 2I. 5 n 1/2 2I In the experiments with the single hexapole this population ratio has been determined to be , which is in good agreement with the ratio of determined from the spectrum in Fig. 2. The power of this laser was then attenuated by a factor of 10 4 to avoid saturation of the P 1 (1) transition. Since the polarization of the laser was perpendicular to the electric field only M J 1 transitions can be made. Under these conditions the strength of the transitions probing the M J 1 2 states is 1 3 of the strength of the transitions probing the M J 3 2 lines. Furthermore, for each M J state the LIF signal is proportional to the amount of negative 2 parity, given by M and the number of molecules in the J M J state, given by n M J. Hence, the total LIF signal of the P 1 (1) transition is proportional to I 4n 1 1/2 2 1/2 E 4n 3 3/2 2 3/2 E. 6 In order to check the calibration of the orienting electric field, the LIF signal of the P 1 (1) transition has been measured as a function of the voltage on the rods. The strength of this transition has then been calculated as a function of the electric field. In the calculation the relative population of the M J states as determined from the polarization measurements has been used. From Fig. 3 we see that the agreement between the calculations and the measurements is very good, which validates our determination of the electric field. This method of determining the degree of orientation is an extension of the technique proposed by de Lange et al. 27 for determining the orientation of the NO(X 2 1/2,J 2) 1 radical. 2 In Fig. 3 we also show the degree of parity mixing 1/2 and 2 3/2 and the degree of orientation cos 1/2 and cos 3/2 as a function of the electric field. At an electric field of 7.5 kv/cm the degree of mixing is still modest, while the degree of orientation is nearly maximal. This has the advantage that the degree of orientation is not very sensitive to the exact value of the electric field. For higher rotational states the mixing is even smaller because of the increasing -doublet splitting. This implies, notably, that the parity quantum labels e/ f can still be used to label all rotationally excited states. Because the voltage and geometry of the orienting field are unchanged in the experiments with the single and the double hexapole, we conclude that the strength of the orienting field remains 7.5 kv/cm in the experiments with the double hexapole. Using the polarization dependence of the P 1 (1) transition the population ratio between the M J 3 2

5 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 Collisions of OH(X 2 ) Ar. II 641 FIG. 4. Steric asymmetries for transitions to the 2, 3 J 2, 5 e( ) and 3 2, J 9 2, e( ) states as a function of the diameter of the detection laser beam. FIG. 5. Steric asymmetries for transitions to the 3 2, J 5 2, e( ) and 2, 3 J 2, 9 e( ) states as a function of the orientation field strength. and M J 1 2 states was determined to be With this ratio the overall average degree of orientation in the double hexapole experiment can be calculated to be cos 1/ This is very close to the maximum value of 0.6 which can be reached only in an infinitely high electric field, and when just the M J 3 2 state is populated. C. Collisions The Ar beam is produced in a differentially pumped chamber. The collision energy has been determined to be cm Single collision conditions are ensured by keeping the population decrease of the initial state below 7.5%. As has been shown in the preceding paper, 14 the fluxto-density transformation can be neglected under our experimental conditions. The independence of the steric asymmetry factors of the flux-to-density transformation has been checked by measuring the steric asymmetry for transitions to the 3 2, 2, 5 e and 3 2, 9 2, e states as a function of the detection area by changing the diameter of the laser beam from 1 to 8 mm Fig. 4. No differences outside the error bars have been found. A possible error in the interpretation of the steric asymmetry factors could be made if the degree of orientation is changed by reorientation before the collision; as the Ar approaches the OH molecule the intramolecular electric field might decouple the OH J-vector from the orienting field. 28 To investigate the possibility of this effect, the steric asymmetries for transitions to the 2, 3 5 2, e and 3 9 2, 2, e states have been measured as a function of the orienting field between 2 and 10.5 kv/cm. Between 4 and 10.5 kv/cm the degree of orientation does not change appreciably, and only the strength of the coupling between the J-vector and the orienting field is altered. The results are presented in Fig. 5. From this figure it can be seen that within the error bars the steric asymmetry does not change for field strengths lying between 4 and 10.5 kv/cm. This indicates that reorientation does not significantly affect our experiments. At 2 kv/cm the steric asymmetries become smaller. This is due to a decrease of the degree of orientation at this low electric field see also Fig. 3. D. LIF detection and data reduction The population of the OH rotational states has been probed by saturated LIF using the A 2 (v 0) X 2 (v 0) transition near 308 nm. For the interpretation of the LIF signals, the exact relation between the population and the fluorescence yield has to be known. For the determination of steric effects this relation is not important, because it only depends on the rotational state and not on the orientation, hence, from the definition of the steric asymmetry Eq. 1 all proportionality factors cancel. The only constraint is that the linear polarization of the laser, which is well defined in these experiments, must be perpendicular to the orienting field in order to detect all final M J states, when a rotational state is probed with a P-branch transition. The steric asymmetry factors have been determined for transitions up to rotational states of J 9 2 in the 3 2 manifold and J 5 2 in the 1 2 manifold. For transitions to higher rotational states the cross sections become too small to obtain a reasonable signal to noise ratio. Because the Q 2 (2) and the Q 2 (3) transitions coincide within the linewidth of the laser the 2, 1 3 2, e and 1 5 2, 2, e states can not be probed separately. Relative cross sections are determined by measuring the population of a final state with and without collisions. The laser frequency is fixed at the peak of a transition and the delay of the Ar beam is altered between 0 maximal collision signal and 10 ms no collisions every 128 shots. Subtraction of the average population measurements with and without collisions yields the relative state-to-state cross section. The steric dependence is determined by first measuring the relative cross section with the H-end directed towards the Ar 1000 shots, then with the O-end towards the Ar atom 2000 shots and finally with the H-end towards the Ar again 1000 shots. In this way a first-order correction for fluctuations in the setup is obtained. Each steric factor has been measured 6 18 times. Since the error bars of the different measurement series are comparable, the steric asymmetries are averaged over the different measurements without weighting factors. The final error bar is calculated from the spread of the measurement series. III. THEORY The formalism to describe the scattering of an atom and a diatomic molecule in a 2 electronic state has been de-

6 642 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 van Beek, ter Meulen, and Alexander scribed in detail in a number of earlier publications. 19,29 33 We encourage the reader to consult these papers for more details. In particular, we shall not reproduce here the discussion of the two PES s, V sum and V dif, which describe the interaction of a spherical atom with a diatomic molecule in a 2 electronic state. As mentioned in the Introduction, the rotational levels of the OH radical in its electronic ground state are best described in intermediate Hund s case coupling, so the is no longer a good quantum number. The wave functions are then written as JM J F i J A Fi JM J. J The expansion coefficients A Fi in Eq. 7 are obtained by diagonalization of the rotational Hamiltonian of the isolated OH molecule. 34 The mixed states are denoted F 1 and F 2 in terms of increasing energy. 35 In what follows we will still use the notation 3 2 and 1 2 to designate the F 1 and F 2 spin orbit manifolds, with the understanding that the states so-labeled correspond to the intermediate coupling states of Eq. 7. Experimentally, one observes the scattering of an oriented beam into a particular final spin orbit, rotational, -doublet level. The differential cross section associated with this process is given by the square of the corresponding scattering amplitude, which is a linear combination, comparable to Eq. 2, of the amplitudes for scattering out of the e and f -doublet levels, namely, f JMJ E J M J kˆ 2 1/2 M J f JMJ e J M J kˆ M J f JMJ f J M J kˆ. Here kˆ denotes the direction of the final collision wave vector. The direction of the initial wave vector kˆ, which is also the direction of the initial relative velocity vector, defines the axis of M J quantization in the so-called collision frame. The M J -dependent scattering amplitudes in Eq. 8 can be determined from the fundamental scattering S-matrix elements. 22,33 The differential cross section for inelastic scattering of the oriented beam is then given by d JMJ E J M J kˆ /d 1 k 2 f JMJ E J M J kˆ 2. 9 As discussed by Alexander and Stolte, 22 the differential cross sections of Eq. 9 are unchanged when the initial and final projection quantum numbers M J and M J are both changed in sign, so that calculations need be done only for M J positive. The expression for the orientation-dependent integral cross sections is obtained by multiplying by the sine of the scattering angle and integrating over all angles. The total integral cross sections for either O-end or H-end orientation, which we designate HO Ar or OH Ar are then obtained by 7 8 summing over M J 1 2 and M J 3 2, which are both present in the beam, and weighting by the experimentally determined relative populations of the two M J -states. To simulate the distribution of collision energies in the experiment (E col 746 cm 1,FWHM 320 cm 1 ), calculations were carried out at E col 746 cm 1, as well as E col 486 and 906 cm 1, which corresponds to the FWHM points. Energy-averaged integral cross sections are then obtained as OH Ar 1 4 OH Ar OH Ar OH Ar 906, 10 and similarly for HO Ar. The steric asymmetry is then defined as in Eq. 1. The scattering S-matrices, with which one determines the scattering amplitudes, were obtained by a standard, close-coupled treatment of the collision dynamics. 19,29 33 The total wave function of the OH(X 2 ) Ar system is expanded as a sum of products of the molecular electronicrotational wave functions expressed in an intermediate coupling basis, multiplied by functions which describe the orbital motion of the Ar atom with respect to the OH diatomic. The size of the expansion number of channels, as well as the integration parameters and maximum value of the total angular momentum J, were chosen to ensure an accuracy of better than 1% in the calculated orientationdependent cross sections. All scattering calculations were done with our Hibridon 4 code. 36 Calculations were carried out for both the CEPA and UMP4 PES s. As described above, our determination of the orientation-dependent integral cross sections and steric asymmetries proceeds through the calculation of the orientation-dependent differential cross sections, and then integration over all scattering angles. An alternate, equally valid, approach to the determination of the orientationdependent integral cross section has been presented by Snijders and co-workers 6 in which the integral cross sections are given directly in terms of a double sum over the total angular momentum of products of S-matrix elements. IV. RESULTS AND DISCUSSION A. Results The results from the experiments with both the single and the double hexapole are presented in Table I and Fig. 6. For transitions to the 2, 1 e and f and 2, 3 e states the absolute value of the steric asymmetry is larger in the experiments with the double hexapole. This can easily be understood; because the fraction of M J 3 2 in the beam is much higher, the degree of orientation of OH is much higher as well, which results in a larger steric asymmetry. In transitions to the 2, 3 f states the absolute value of the steric asymmetry as measured with the single hexapole appears to be larger. This is probably due to a combination of the small total cross sections for excitation to these states coupled with the residual initial population in these states when the single hexapole is used. 14 This implies that scattering of the initial population out of these states influences the steric asymme-

7 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 Collisions of OH(X 2 ) Ar. II 643 FIG. 6. Comparison of steric asymmetries measured with the single and double hexapole state selectors. The final spin orbit and -doublet state are given at the top of each graph. The final J quantum number is indicated on the abscissa. try. This is consistent with the fact that the error bars for excitation to the 2, 3 2, 9 f state are much larger when the double hexapole is used. The cross section for excitation from the 3 2, 3 2, f to the 2, 3 2, 9 f state is very small, while the cross section for excitation out of the 2, 3 2, 5 f state is much larger. Hence, initial population in the 2, 3 5 2, f state greatly increases the collision induced population transfer into the 2, 3 9 2, f state, which strongly increases the signal to noise ratio. Because of the higher purity of the initial state selection and the larger degree of orientation, we will only discuss the experiments with the double hexapole in the remaining of this article. A clear general trend can be observed: for excitation to low rotational states the steric asymmetry is small and positive, indicating a weak preference for O-end collisions, while for excitation to higher rotational states the steric factor is large and negative, reflecting a strong preference for H-end collisions. As a function of J the steric asymmetry decreases monotonically. This behavior can be understood in a simple classical ball-and-stick model. For high rotational excitation a large torque is required. This torque can more easily be applied from the H-end of the radical, because the H-atom is further away from the center of mass. The largest steric asymmetry 78.1% was found for transitions from the 3 2, 2, 3 f state to the 2, 3 2, 9 e state. This implies that for this transition the inelastic excitation probability is 8 times as large for H-end as opposed to O-end collisions. Strong differences are seen for scattering into different final spin orbit and -doublet states. For spin orbit conserving transitions there is a clear systematic difference between final states of e or f symmetry; for transitions to e states the steric asymmetry is larger in magnitude and more negative closer to 100% than for transitions to the corresponding f states. This is opposite to what one would expect from a simple orbital picture. For the integral cross sections a strong preference is seen for scattering into final e-labeled -doublet levels in spin orbit conserving transitions. 14 This preference for the integral cross sections can be understood by consideration of the PES s. The PES for the OH Ar electronic state of A reflection symmetry is more repulsive than the PES for the state of A reflection symmetry, because, in the former case, two of the three electrons lie in the triatomic plane. As Dagdigian and co-workers have shown, 23,37 this results, by means of quantum interference, in a distinct preference for inelastic transitions to final OH rotational states of A reflection symmetry, which correspond to the e-labeled levels in the 3 2 spin orbit manifold. Since the nonbonding orbitals are located predominantly on the O-atom, one might expect this propensity to be more pronounced for O-end collisions. For fine-structure conserving transitions, this would imply a stronger preference for transitions into e, as opposed to f, final states in O-end, as compared to H-end, collisions. One might, then, expect the steric asymmetry to be lower for f, as opposed to e, final states. This is opposite to what is observed experimentally. Examination of the theoretical cross sections shows that the propensity, predicted by Dagdigian et al., 23,37 towards population of final states of A symmetry is clearly apparent for both O-end and H-end collisions. 14 However, this propensity does not translate into a simple explanation of the observed dependence of the steric asymmetries on the -doublet symmetry of the final state. Note, further, that for spin orbit conserving transitions to f states the error bars are larger. This reflects the smaller size of the cross sections for these transitions as well as the residual initial population in these states. Finally, for spin orbit changing transitions the steric asymmetry is found to be smaller closer to 0% for final states of e symmetry compared to states of f symmetry. We do not have a simple physical explanation of this behavior. B. Comparison with theory The results of the calculations based on the CEPA and UMP4 OH(X 2 ) Ar PES s are presented in Table II and Fig. 7. The calculated steric asymmetries are averaged over the experimental energy distribution. However, the initial population of higher rotational states has not been taken into account. Both potentials predict the general trends quite well, although the differences between calculations based on the CEPA and UMP4 PES s are quite large. The quantitative agreement between the experimental results and the steric asymmetries calculated with the UMP4 PES s is significantly better. To quantify the agreement between experiment and theory the squared deviation is defined as 1 n 2 S exp i S calc i / S exp i 2, 11 i where the sum runs over all final states, n is the number of final states (n 11) and S exp i is the experimental error. We find 7.3 for the CEPA-based calculations but only 3.3 for the UMP4-based calculations. As with the integral inelastic

8 644 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 van Beek, ter Meulen, and Alexander TABLE II. Theoretical steric asymmetries for rotational excitation of OH(X 2 3/2,J 3 2, f ) in collisions with Ar at a collision energy of cm 1. The calculations were performed both with the Degli-Esposti and Werner CEPA a potential and the Klos et al. UMP4 b potential. Final state Steric asymmetry J CEPA UMP4 3/2 5/2 e f /2 e f /2 e f /2 1/2 e f /2 e f /2 e f /2 e f /2 e f a Reference 19. b Reference 20. cross sections presented in Ref. 14, the UMP4 ab initio calculations appear to provide a better description of the OH Ar PES s. Consequently, for the remainder of this section we will discuss only the UMP4-based results. In general theory and experiment agree better for spinorbit conserving as compared to spin orbit changing transitions. This may reflect the higher accuracy of the V sum PES which, for collisions of molecules described in intermediate Hund s case coupling, dominates the spin orbit conserving transitions, while the V dif PES dominates the spin orbit changing transitions. 29,23 For the integral unoriented cross sections, we also found better agreement between theory and experiment for spin orbit conserving as compared to spin orbit changing transitions. 14 The largest deviation between the calculated and measured steric asymmetries occurs for the transition to the 2, 1 2, 1 f state, where the experimental value of S is considerably more positive and larger in magnitude than the calculated value. To check for possible errors, the theoretical results for transitions to the 2, 1 2, 1 e and f states were compared for M J 1 2 and 3 2 and for E col 586, 746, and 906 cm 1. In all cases the calculated steric asymmetry for transitions to the f state was considerably more negative than for transitions to the e state. A possible error could be introduced by elastic and inelastic contaminations, because this state has some 0.7% initial population and the cross section for the 2, 3 2, 3 f 2, 1 1 2, f transition is rather small. However, the measured and calculated integral cross sections are in reasonably good agreement for this transition. 14 Remarkably, although the agreement between theory and experiment is quite good for final states of A symmetry ( 2,e 3 and 1 2, f, it is truly excellent for final states of A symmetry 2, 3 f and 2,e. 1 From the experimental point of view one would expect the best agreement for final states of A symmetry in spin orbit changing transitions, because these states have the largest cross sections and are not contaminated due to residual initial populations in the final states. This is opposite to the experimental observation. For spin orbit conserving transitions, however, one would expect the best agreement for final states of A symmetry for the same reasons. Intriguingly, the most recent spectroscopic studies of Lester and co-workers 38 indicate that the UMP4 potential 20 gives a good representation of V dif but a less accurate representation of V sum. On the contrary, the CEPA potential 19 provides a good description of V sum but is less accurate in its representation of V dif. FIG. 7. Comparison of experimental steric asymmetries with quantum scattering calculations based on the CEPA Ref. 19 and the UMP4 Ref. 20 potential energy surfaces. The final spin orbit and -doublet state are given at the top of each graph. The final J quantum number is indicated on the abscissa. C. Comparison with NO Ar De Lange et al. 21 have determined steric asymmetries for rotationally inelastic collisions of NO(X 2 1/2 ) Ar at a collision energy of 475 cm 1. They obtained an average orientation of cos which is considerably lower then in our experiments, due to the lower, M J and J quantum numbers. Because of the small rotational spacing they were able to determine the steric asymmetry for spin orbit manifold conserving transitions for rotational states up to J Steric effects between 28% and 49% have been measured. Little difference has been found between final e and f -doublet states. This is to be expected for a molecule, such as NO, which is well described in Hund s case a. 22,39 For OH, where the rotational levels are best described in intermediate Hund s case coupling, we no longer expect the steric asymmetries to be independent of the e/ f label of the final state.

9 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 Collisions of OH(X 2 ) Ar. II 645 What is remarkable in the NO Ar experiments is the observation of a marked alternation in the sign of the steric asymmetry, which persists even to large J. This alternation has been reproduced by several calculations based on the two available sets of ab initio PES s, 21,22 although a clear physical explanation is still lacking. In general, however, both sets of calculations predict the magnitude of the NO Ar steric asymmetries to be larger than what is observed. The steric asymmetries found for NO Ar are smaller than for OH Ar. This is probably caused by the higher degree of orientation achievable in OH Ar experiments and the large charge and mass asymmetry in the OH radical, as compared to NO. No evidence is seen here of an alternation of steric asymmetry with J. However, because of the large rotational constant, we can probe only the lowest rotational levels of OH, while the oscillations for NO show up at J 9 2. Finally, the overall agreement between experiment and theory is better for OH Ar. V. CONCLUSIONS In this article we described a straightforward way to determine the degree of orientation of an OH beam using a narrow-band dye laser as well as Stark shifts and parity mixing. The degree of orientation determined by this method agrees well with that determined with a conventional pulsed dye laser. The accuracy of the new method, however, is much higher. Steric asymmetries have been determined for rotational excitation of OH out of the initial 2, 3 3 2, f state. Transitions to final states with J 9 2 and J 5 2 have been probed for spin orbit conserving and changing transitions, respectively. The steric asymmetries of the cross sections show several general trends. For small rotational excitation there is a weak preference for O-end collisions, while for high rotational excitation there is a strong preference for H-end collisions. As a function of J the steric asymmetry becomes increasingly negative. The steric asymmetry strongly depends on the spin orbit and -doublet labels of the final state. For spin orbit manifold conserving transitions the steric asymmetry is more negative closer to 100%, while for spin orbit changing transitions the steric asymmetry is slightly smaller in magnitude closer to 0% for final states of e compared to f symmetry. The data have been compared with quantum scattering calculations based on the Degli-Esposti and Werner CEPA PES s Ref. 19 and the Klos et al. UMP4 PES s Ref. 20. The agreement between the UMP4-based calculations and experiment is considerably better. The agreement is good for final states of A symmetry and excellent for final states of A symmetry. The largest deviation is found for excitation to the 2, 1 1 2, f state. It is intriguing that the present scattering studies indicate that the UMP4 PES s are more accurate, in particular the average potential V sum. In contrast, the most recent spectroscopic studies 38 suggest that the CEPA V sum is more accurate. In comparison with NO Ar, the steric asymmetries for OH Ar are larger and depend strongly on the -doublet symmetry of the final state. The alternation seen in the NO Ar steric asymmetries is not present in collisions of OH with Ar. It is clear, from both spectroscopic experiments, 20,38 as well as the collision experiments described here and in Ref. 14, that it is now possible to determine ab initio PES s for the simple, yet exemplary, OH Ar system which provide a description of the nuclear motion which is almost as accurate as that obtainable from the most sophisticated experiments. The interplay between experiment and theory revealed here and in Refs. 14 and 38 show also how important high-quality theoretical simulations have become in the interpretation of these sophisticated experiments. ACKNOWLEDGMENTS The authors thank Grzegorz Chalasinski and Marsha I. Lester for providing their results prior to publication. Michiel van Beek and Hans ter Meulen also wish to express their gratitude to Eugène van Leeuwen for his expert technical assistance, to Rick Bethlem and Giel Berden for their assistance with the narrow band pulsed dye laser measurements, and to Nico Dam for stimulating discussions. Millard Alexander wishes to thank the U.S. National Science Foundation for support under Grant No. CHE R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity Oxford University Press, Oxford, D. H. Parker and R. B. Bernstein, Annu. Rev. Phys. Chem. 40, H. J. Loesch, Annu. Rev. Phys. Chem. 46, J. Phys. 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10 646 J. Chem. Phys., Vol. 113, No. 2, 8 July 2000 van Beek, ter Meulen, and Alexander 26 J. J. van Leuken, F. H. W. van Amerom, J. Bulthuis, J. G. Snijders, and S. Stolte, J. Phys. Chem. 99, M. J. L. de Lange, J. J. van Leuken, M. M. J. E. Drabbels, J. Bulthuis, J. C. Snijders, and S. Stolte, Chem. Phys. Lett. 294, F. Harren, D. H. Parker, and S. Stolte, Comments At. Mol. Phys. 26, M. H. Alexander, J. Chem. Phys. 76, M. H. Alexander, Chem. Phys. 92, G. C. Corey and M. H. Alexander, J. Chem. Phys. 85, G. C. Corey and M. H. Alexander, J. Chem. Phys. 88, M. H. Alexander, J. Chem. Phys. 111, H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Diatomic Molecules Academic, New York, G. Herzberg, Spectra of Diatomic Molecules Van Nostrand, Princeton, HIBRIDON is a package of programs for the time-independent quantum treatment of inelastic collisions and photodissociation written by M. H. Alexander, D. E. Manolopoulos, H.-J. Werner, and B. Follmeg, with contributions by P. F. Vohralik, D. Lemoine, G. Corey, B. Johnson, T. Orlikowski, W. Kearney, A. Berning, A. Degli-Esposti, C. Rist, and P. Dagdigian. More information and/or a copy of the code can be obtained from the website mha/hibridon. 37 P. J. Dagdigian, in The Chemical Dynamics and Kinetics of Small Radicals, edited by K. Liu and A. Wagner World Scientific, Singapore, R. T. Bonn, M. D. Wheeler, and M. I. Lester, J. Chem. Phys. 112, M. H. Alexander, Faraday Discuss. Chem. Soc. 113,