Thermal and vibrationalstate selected rates of the CH4+Cl↔HCl+CH3 reaction J. Chem. Phys. 103, 9642 (1995); 10.1063/1.470731Core extraction for measuring statetostate differential cross sections of bimolecular reactionsThe mechanism for the reaction of atomic chlorine with vibrationally excited methane is investigated by measurement of correlated state and scattering distributions using the method of core extraction ͑see preceding paper͒. Laser photolysis of molecular chlorine creates monoenergetic chlorine atoms ͑Ͼ98% Cl 2 P 3/2 ͒ that react with vibrationally excited methane molecules prepared by linearly polarized infrared laser excitation. The resulting HCl product population distributions are determined by ͑2ϩ1͒ resonance-enhanced multiphoton ionization ͑REMPI͒, and the differential cross section for each product rovibrational state is measured by core extraction. Approximately 30% of the product is formed in HCl(ϭ1,J) with a cold rotational distribution; the remaining population is formed in HCl(ϭ0,J) and is more rotationally excited. We observe a rich variation of the scattered flux that is dependent on the internal-energy state of the product. The HCl͑ϭ1͒ product is sharply forward scattered for low J and becomes nearly equally forward-backward scattered for high J; the HCl(ϭ0,J) product is back and side scattered. The reactions of Cl with C-H stretch-excited methane ͑CH 4 ͒ and C-H stretch-excited CHD 3 are found to have similar angular and internal-state distributions. Observation of the spatial anisotropy of the HCl͑ϭ0, Jϭ3͒ product shows that significant vibrational excitation of the methyl fragment does not occur. The measured spatial anisotropy is most consistent with a model in which backscattered HCl͑ϭ0, Jϭ3͒ is formed in coincidence with slight methyl vibrational excitation and the forward-scattered HCl͑ϭ0, Jϭ3͒ is formed in coincidence with no methyl excitation. The approach of the attacking chlorine atom with respect to the C-H stretch direction can be varied by rotating the plane of polarization of the infrared excitation. A marked steric effect is observed in which Cl atoms approaching perpendicular to the C-H stretch preferentially yield forward-scattered HCl͑ϭ1͒ product. On the other hand, the reaction is weakly dependent on the rotational quantum state of CH 4 ( 3 ϭ1,J), and on the rotational polarization. The data are consistent with a model that has a widely open ''cone of acceptance'' in which the impact parameter controls the internal-state and scattering distributions of the HCl product.

In this article we present a new approach to the already popular methods of ion imaging and velocity mapping. The novelty of this approach is that the speed and angular distributions are measured directly from the images without the need of inverse Abel transformation as in the conventional approaches. This is achieved by using delayed pulsed extraction of the ions following photodissociation and positioning of the nascent products. Delayed pulsed extraction causes a sufficient velocity spread in the ion cloud such that the time width of the ion packet at the detector is on the order of 500 ns. By using a narrow detector time gate (<40 ns) we are able to image only the center slice of the ion packet. The result is equivalent to that obtained by conventional methods using the inverse Abel transform, however, the artificial noise introduced by this transform is eliminated. The energy resolution of the new approach is at least comparable to that achieved with the velocity mapping technique.

Photolysis of a molecule typically yields open-shell photofragments having angular momenta. A procedure is described for the measurement of the photofragment angular momentum distribution in terms of polarization parameters aq(k)(p) which are expressed in the molecular frame and which may be related to the transition dipole matrix elements. The index (p) indicates either a parallel transition (∥), a perpendicular transition (⊥), or a mixed transition (∥,⊥) having both parallel and perpendicular character. This procedure has the advantage that it decouples the angular momentum distributions in the molecular frame from the photofragment angular distributions in the laboratory frame, which gives new insight into the photodissociation dynamics. For cases in which k⩽2 and with linearly polarized photolysis light, the photofragment angular momentum distribution arising from pure parallel transitions can be described with only one parameter, a0(2)(∥); photofragment angular momentum distributions arising from pure perpendicular transitions require only two parameters, a0(2)(⊥) and a2(2)(⊥); photofragment angular momentum distributions arising from mixed transitions, having both parallel and perpendicular character, can be described with five parameters: the two (coherent) interference terms Im[a1(1)(∥,⊥)] and Re[a1(2)(∥,⊥)] in addition to the three incoherent terms mentioned above. We describe procedures for the measurement of the complete angular momentum distribution of state-selected photofragments using laser detection (such as REMPI) and some form of laboratory velocity selection (such as time-of-flight mass spectrometry, Doppler spectroscopy, or ion imaging). The laser-detection probability of a single photofragment is presented in the form I=1+f[θε,Θ,Φ,β,aq(k)(p)], where θε is the angle between the recoil direction and the photolysis polarization, Θ and Φ are the spherical polar angles describing the orientation of the probe polarization about the recoil direction, and β is the spatial anisotropy parameter. The physical significance of the aq(k)(p) is discussed; in particular, the a0(k)(∥) and a0(k)(⊥) describe the photofragment m-state distribution along the recoil direction; the a2(k)(⊥) describe how broken cylindrical symmetry in the parent molecule is reflected in the photofragment angular momentum distribution in a plane perpendicular to the recoil direction; and the a1(k)(∥,⊥) are related to the asymptotic phase difference associated with the interfering channels, and are thus sensitive to the shapes of the dissociative surfaces.

Comparison of state-to-state differential cross sections for methane in the ground vibrational state to methane with one quantum of asymmetric stretch excitation probes the effect of C-H stretch excitation on the reaction of atomic chlorine with methane. We previously reported state-to-state differential cross sections and HCl product state population distributions for the vibrationally excited reaction. Here we report analogous measurements of the reaction for methane in the vibrational ground state. Photolysis of molecular chlorine produces chlorine atoms that react with methane molecules at 0.16 eV collision energy. Calibrated resonanceenhanced multiphoton ionization (REMPI) determines the product state distributions, and the core-extraction technique measures the angular scattering distribution. The product HCl(V)0) is formed with a cold rotationalstate distribution and is strongly back scattered. The product state and angular scattering distributions for the ground-state reaction are consistent with a line-of-centers model in which the cone of acceptance is only narrowly open. The rotational-state distributions and comparisons to thermal rate data indicate that the C-H-Cl angle must be constrained in the transition-state region. One quantum of C-H asymmetric stretch vibrational excitation enhances the rate of reaction at a collision energy of 0.16 eV by a factor of 30 ( 15 ((2σ). The behavior of the ground-state reaction is in marked contrast to our earlier results for the reaction of chlorine atoms with C-H stretch-excited methane, for which the state-to-state angular scattering distributions were consistent with a widely open cone of acceptance. By using the approximation that hard-sphere scattering describes the relation between impact parameter and scattering angle, we can transform the measured stateto-state differential cross section into the distribution of impact parameters that lead to reaction, which forms what we call a b map. This b map pictorially shows that the ground-state reaction occurs only for head-on collisions (with small impact parameters), whereas C-H stretch vibrational excitation allows reactivity to spread to the periphery of the methane molecule. The data indicate that the mechanism of vibrational enhancement is opening of the cone of acceptance and lessening the necessity for collinearity of the C-H-Cl angle in the transition-state region.

We describe a method we call core extraction for measuring the speed distributions of products from photoinitiated bimolecular reactions for the purpose of determining state-to-state differential cross sections. Core extraction is demonstrated by determination of the state-to-state differential cross section for the reaction ClϩCH 4 ͑ 3 ϭ1͒→HCl͑ϭ1, Jϭ1͒ϩCH 3. The method of core extraction measures three-dimensional projections of the velocity distribution using a time-of-flight mass spectrometer equipped with a mask to reject off-axis scattered products. This three-dimensional projection is then converted to a state-to-state differential cross section via simple transformations. Competition between instrumental resolution and signal in core extraction is discussed, and the behavior of our system is checked with simple velocity distributions that result from photodissociation of Cl 2. Core extraction is compared with other methods for the measurement of state-resolved differential cross sections.

Maxwell's equations in isotropic optically active media. In particular, the effective optical rotation path length, near index matching, is equal to the Goos-Hänchen shift 9 of the evanescent wave. The limits of this polarimeter, when using a continuous-wave laser locked to a stable high-finesse cavity, should match sensitivity measurements for linear birefringence (3x10 -13 rad) 10 , which is several orders of magnitude more sensitive than current chiral detection limits 7 , transforming the power of chiral sensing in many fields.

Photolysis of Cl 2 initiates the title reaction at a sharply defined collision energy of 0.24Ϯ0.03 eV. Nascent product rotational state distributions for HCl ͑vϭ0͒ are determined using resonance enhanced multiphoton ionization ͑REMPI͒, center-of-mass scattering distributions are measured by the core-extraction technique, and the average internal energy of the C 2 H 5 product is deduced from the dependence of the core-extracted signal on the photolysis polarization. The HCl product has little rotational excitation, but the scattering distribution is nearly isotropic. Although seemingly contradictory, both of these features can be accounted for by using the simple line-of-centers model presented to explain earlier results for the ClϩCH 4 reaction. In contrast to the ClϩCH 4 reaction, the data suggest that the ClϩC 2 H 6 reaction proceeds through a loosely constrained transition-state geometry. The reactions of atomic chlorine with ethane, C 2 H 6 , and perdeuteroethane, C 2 D 6 , yield virtually identical results. These findings, along with the low energy deposited by the reaction into the ethyl product ͑200Ϯ120 cm Ϫ1 ͒, demonstrate that the alkyl fragment acts largely as a spectator in this hydrogen abstraction reaction.

We observed directional dynamics in the photodissociation of an oriented molecule. When a laser dissociated hexapole-oriented carbonyl sulfide molecules, the three-dimensional recoil of carbon monoxide fragments, which we measured with ion imaging, was strongly asymmetric. We obtained a microscopic view of molecular bond breaking that revealed both the sign and the magnitude of the deflection angle of the fragment in the molecular frame. This experimental approach can be applied to study and control the three-dimensional dynamics of photoinitiated reactions of fixed molecules or molecules oriented by emerging techniques.