The parity-adapted basis set in the formulation of the photofragment angular momentum polarization problem: the role of the Coriolis interaction

We present a theoretical framework for calculating the recoil-angle dependence of the photofragment angular momentum polarization taking into account both radial and Coriolis nonadiabatic interactions in the diatomic/linear photodissociating molecules. The parity-adapted representation of the total molecular wave function has been used throughout the paper. The obtained full quantum-mechanical expressions for the photofragment state multipoles have been simplified by using the semiclassical approximation in the high-J limit and then analyzed for the cases of direct photodissociation and slow predissociation in terms of the anisotropy parameters. In both cases, each anisotropy parameter can be presented as a linear combination of the generalized dynamical functions fK(q,q',q,q') of the rank K representing contribution from different dissociation mechanisms including possible radial and Coriolis nonadiabatic transitions, coherent effects, and the rotation of the recoil axis. In the absence of the Coriolis interactions, the obtained results are equivalent to the earlier published ones. The angle-recoil dependence of the photofragment state multipoles for an arbitrary photolysis reaction is derived. As shown, the polarization of the photofragments in the photolysis of a diatomic or a polyatomic molecule can be described in terms of the anisotropy parameters irrespective of the photodissociation mechanism.     

Photofragment angular momentum distributions in the molecular frame. III. Coherent effects in the photodissociation of polyatomic molecules with circularly polarized light

We extend the a(q) (k)(s) polarization parameter model [T. P. Rakitzis and A. J. Alexander, J. Chem. Phys. 132, 224310 (2010)] to describe the components of the product angular momentum polarization that arise from the one-photon photodissociation of asymmetric top molecules with circularly polarized photolysis light, and provide a general equation for fitting experimental signals. We show that the only polarization parameters that depend on the helicity of the circularly polarized photolysis light are the A(0) (k) and Re[A(1) (k)] (with odd k) and the Im[A(1) (k)] (with even k); in addition, for the unique recoil destination (URD) approximation [for which the photofragment recoil v arises from a unique parent molecule geometry], we show that these parameters arise only as a result the interference between at least two dissociative electronic states. Furthermore, we show that in the breakdown of the URD approximation (for which the photofragment recoil v arises from a distribution of parent molecule geometries), these parameters can also arise for dissociation via a single dissociative electronic state. In both cases, the A(0) (k) and Re[A(1) (k)] parameters (with odd k) are proportional to cosΔφ, and the Im[A(1) (k)] parameters (with even k) are proportional to sinΔφ, where Δφ is the phase shift (or average phase shift) between the interfering paths so that Δφ can be determined directly from the A(q) (k), or from ratios of these A(q) (k) parameters. Therefore, the determination of these A(q) (k) parameters with circularly polarized photolysis light allows the unambiguous measurement of coherent effects in polyatomic-molecule photodissociation.     

Measurement of Br photofragment orientation and alignment from HBr photodissociation: production of highly spin-polarized hydrogen atoms

The orientation and alignment of the (2)P(3/2) and (2)P(1/2) Br photofragments from the photodissociation of HBr is measured at 193 nm in terms of a(q) ((k))(p) parameters, using slice imaging. The A (1)Pi state is excited almost exclusively, and the measured a(q) ((k))(p) parameters and the spin-orbit branching ratio show that the dissociation proceeds predominantly via nonadiabatic transitions to the a (3)Pi and 1 (3)Sigma(+) states. Conservation of angular momentum shows that the electrons of the nascent H atom cofragments (recoiling parallel to the photolysis polarization) are highly spin polarized: about 100% for the Br((2)P(1/2)) channel, and 86% for the Br((2)P(3/2)) channel. A similar analysis is demonstrated for the photodissociation of HCl.     

Photofragment angular momentum distribution beyond the axial recoil approximation: predissociation

We present the quantum mechanical expressions for the angular momentum distribution of the photofragments produced in slow predissociation. The paper is based on our recent theoretical treatment [J. Chem. Phys. 123, 034307 (2005)] of the recoil angle dependence of the photofragment multipole moments which explicitly treat the role of molecular axis rotation on the electronic angular momentum polarization of the fragments. The electronic wave function of the molecule was used in the adiabatic body frame representation. The rigorous expressions for the fragment state multipoles which have been explicitly derived from the scattering wave function formalism have been used for the case of slow predissociation where a molecule lives in the excited quasibound state much longer than a rotation period. Possible radial nonadiabatic interactions were taken into consideration. The optical excitation of a single rotational branch and the broadband incoherent excitation of all possible rotational branches have been analyzed in detail. The angular momentum polarization of the photofragments has been treated in the high-J limit. The polarization of the photofragment angular momenta predicted by the theory depends on photodissociation mechanism and can in many cases be significant.     

Coherent and incoherent orientation and alignment of ICN photoproducts

We report extended measurements of the rotational polarization and correlated angular distribution of CN photofragments from ICN photodissociation, with a particular emphasis on the creation and detection of molecular orientation with circularly-polarized light. Doppler profiles of the nascent photoproducts are measured by Frequency-Modulated (FM) transient absorption, and the resulting high signal-to-noise data are valuable for verifying the form of the angular correlations between the recoil velocity, the photofragment rotational angular momentum, and the space-fixed frame defined by the dissociation polarization. A space-fixed bipolar moment notation can be used for an unambiguous characterization of the maximal set of polarization properties that can be created with one-photon excitation and detected with one-photon Doppler-resolved absorption spectroscopy. Relating the observed polarization moments to the various coherent and incoherent, adiabatic and non-adiabatic mechanisms, that have been derived and verified extensively in the case of diatomic photodissociation to polarized atomic fragments, is not unambiguous in the case of diatomic fragments from triatomic precursors. Constraints among various polarization moments confirmed in the case of diatomic dissociation are not confirmed in this triatomic case, where the perpendicular transitions to non-degenerate A' and A' components of a linear Omega = 1 state are qualitatively different from excitation to degenerate Omega = +/-1 states in a diatomic molecule.     

Determination of the helicity of oriented photofragments

Equations to enable determination of the helicity (angular momentum orientation) of photofragments resulting from single-photon dissociation of an isotropic sample of molecules are presented. The symmetry of the photofragment distribution is illustrated by three-dimensional vector plots of the expectation values of projections of the fragment total angular momentum. Equations describing circular polarization of light in the spherical tensor basis are presented. Methods for the optical measurement of angular momentum orientation are discussed, including determination of the helicity of circularly polarized light by a quarter-wave plate or single Fresnel rhomb.     

Photolysis wavelength dependence of the translational anisotropy and the angular momentum polarization of O2(a 1Deltag) formed from the UV photodissociation of O3

The translational anisotropy and angular momentum polarization of the O(2)(a (1)Delta(g),v = 0;J = 15-27) molecular photofragment produced from the UV photodissociation of O(3) in the range from 270 to 300 nm have been determined using resonance-enhanced multiphoton ionization in conjunction with time-of-flight mass spectrometry. At the shortest photolysis wavelengths used, the fragments exhibit the anisotropic vector correlations expected from a prompt dissociation via the (1)B(2) <--(1)A(1) transition. Deviations from this behavior are observed at longer photolysis wavelengths with, in particular, the angular momentum orientation showing a significant reduction in magnitude. This indicates that the dissociation can no longer be described by a purely impulsive model and a change in geometry of the dissociating molecule is implied. This observation is substantiated by the variation of the translational anisotropy with photolysis wavelength. We also observe that the bipolar moments describing the angular momentum polarization of the odd J states probed are consistently lower in magnitude than those of the even J states and that this variation is observed for all photolysis wavelengths.     

Parent-molecule rotational depolarization of photofragment angular momentum distributions: diatomic and polyatomic molecules

We extend the A(q)(k) polarization-parameter model, which describes product angular momentum polarization from one photon photodissociation of polyatomic molecules in the molecular frame [J. Chem. Phys., 2010, 132, 224310], to the case of rotating parent molecules. The depolarization of the A(q)(k) is described by a set of rotational depolarization factors that depend on the angle of rotation of the molecular axis γ. We evaluate these rotational depolarization factors for the case of dissociating diatomic molecules and demonstrate that they are in complete agreement with the results of Kuznetsov and Vasyutinskii [J. Chem. Phys., 2005, 123, 034307] obtained from a fully quantum mechanical approach of the same problem, showing the effective equivalence of the two approaches. We further evaluate the set of rotational depolarization factors for the case of dissociating polyatomic molecules that have three (near) equal moments of inertia, thus extending these calculations to polyatomic systems. This ideal case yields insights for the dissociation of polyatomic molecules of various symmetries when we compare the long lifetime limit with the results obtained for the diatomic case. In particular, in the long lifetime limit the depolarization factors of the A(0)(k) (odd k), Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) for diatomic molecules vanish; in contrast, for polyatomic molecules the depolarization factors for the A(0)(k) (odd k) reduce to a value of 1/3, whereas for the Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) they reduce to 1/5.     

Molecular photofragment orientation in the photodissociation of H2O2 at 193 nm and 248 nm

Angular momentum orientation has been observed in the OH(X(2)Π, v = 0) fragments generated by circularly polarized photodissociation of H(2)O(2) at 193 nm and 248 nm. The magnitude and sign of the orientation are strongly dependent on the OH(X) photofragment rotational state. In addition to conventional laser induced fluorescence methods, Zeeman quantum beat spectroscopy has also been used as a complementary tool to probe the angular momentum orientation parameters. The measured orientation at 193 nm is attributed solely to photodissociation via the ?(1)A state, even though at this wavelength H(2)O(2) is excited near equally to both the ?(1)A and B(1)B electronic states. This observation is confirmed by measurements of the photofragment orientation at 248 nm, where access to the ?(1)A state dominates. Several possible mechanisms are discussed to explain the observed photofragment orientation, and a simple physical model is developed, which includes the effects of the polarization of the parent molecular rotation upon absorption of circularly polarized light. Good agreement between the experimental and simulation results is obtained, lending support to the validity of the model. It is proposed that photofragment orientation arises mainly from the coupling of the parent rotational angular momentum with that induced during photofragmentation.     

The photodissociation dynamics of ozone at 193 nm: an O(1D2) angular momentum polarization study

Polarized laser photolysis, coupled with resonantly enhanced multiphoton ionization detection of O(1D2) and velocity-map ion imaging, has been used to investigate the photodissociation dynamics of ozone at 193 nm. The use of multiple pump and probe laser polarization geometries and probe transitions has enabled a comprehensive characterization of the angular momentum polarization of the O(1D2) photofragments, in addition to providing high-resolution information about their speed and angular distributions. Images obtained at the probe laser wavelength of around 205 nm indicate dissociation primarily via the Hartley band, involving absorption to, and diabatic dissociation on, the B 1B2(3 1A1) potential energy surface. Rather different O(1D2) speed and electronic angular momentum spatial distributions are observed at 193 nm, suggesting that the dominant excitation at these photon energies is to a state of different symmetry from that giving rise to the Hartley band and also indicating the participation of at least one other state in the dissociation process. Evidence for a contribution from absorption into the tail of the Hartley band at 193 nm is also presented. A particularly surprising result is the observation of nonzero, albeit small values for all three rank K = 1 orientation moments of the angular momentum distribution. The polarization results obtained at 193 and 205 nm, together with those observed previously at longer wavelengths, are interpreted using an analysis of the long range quadrupole-quadrupole interaction between the O(1D2) and O2(1Deltag) species.     

Photodissociation of laboratory oriented molecules: Revealing molecular frame properties of nonaxial recoil

We report the photodissociation of laboratory oriented OCS molecules. A molecular beam of OCS molecules is hexapole state-selected and spatially oriented in the electric field of a velocity map imaging lens. The oriented OCS molecules are dissociated at 230 nm with the linear polarization set at 45 degrees to the orientation direction of the OCS molecules. The CO(nu=0,J) photofragments are quantum state-selectively ionized by the same 230 nm pulse and the angular distribution is measured using the velocity map imaging technique. The observed CO(nu=0,J) images are strongly asymmetric and the degree of asymmetry varies with the CO rotational state J. From the observed asymmetry in the laboratory frame we can directly extract the molecular frame angles between the final photofragment recoil velocity and the permanent dipole moment and the transition dipole moment. The data for CO fragments with high rotational excitation reveal that the dissociation dynamics is highly nonaxial, even though conventional wisdom suggests that the nearly limiting beta parameter results from fast axial recoil dynamics. From our data we can extract the relative contribution of parallel and perpendicular transitions at 230 nm excitation.     

REMPI-TOF studies of the translational anisotropy and the polarization of the O ((1)D2) photofragment angular momentum following ozone photolysis at 298 nm

The translational anisotropy and the polarization of the electronic angular momentum of the O ((1)D2) fragment produced from the 298 nm photodissociation of ozone have been determined using resonance enhanced multiphoton ionization (REMPI) in conjunction with time-of-flight mass spectrometry (TOFMS). The translational anisotropy parameter beta, which is necessarily averaged over the O2 co-fragment rotational distribution, is measured to be 1.08 +/- 0.04. This is consistent with that expected for the (1)B2 <-- (1)A1 transition within an impulsive model if the tangential velocity associated with the zero point motion of the bend is constricted to opening the bond angle. Molecular frame polarization parameters of rank up to k = 4 have been extracted for the O ((1)D2) fragment and the calculated m(J) populations show a strong preference for the absolute value(m(J)) = 1 states. A small coherence term is also observed, a manifestation of the nuclear geometry of the dissociating molecule and the existence of possible non-adiabatic processes in the exit channel. The orientation associated with the mapping of the photon helicity onto the O ((1)D2) electronic angular momentum distribution was observed to have been quenched. However, the parameter gamma1', which describes the contribution to the orientation from a coherent superposition of a parallel and perpendicular excitation where the photofragment angular momentum lies perpendicular to both the recoil velocity and to the transition dipole moment, was determined to be -0.06.     

Atomic polarization in the photodissociation of diatomic molecules

The angular momentum polarization of atomic photofragments provides a detailed insight into the dynamics of the photodissociation process. In this article, the origins of electronic angular momentum polarization are introduced and experimental and theoretical methods for the measurement or calculation of atomic orientation and alignment parameters described. Many diatomic photodissociation systems are surveyed, in order to provide an overview both of the historical development of the field and of the most state-of-the-art contemporary studies.     

Velocity-map imaging study of the photodissociation of acetaldehyde

Velocity-map imaging studies are reported for the photodissociation of acetaldehyde over a range of photolysis wavelengths (317.5-282.5 nm). Images are obtained for both the HCO and CH3 fragments. The mean rotational energy of both fragments increases with photodissociation energy, with a lesser degree of excitation in the CH3 fragment. The CH3 images demonstrate that the CH3 fragments are rotationally aligned with respect to the recoil direction and this is interpreted, and well modeled, on the basis of a propensity for forming CH3 fragments with M approximately K, where M is the projection of the rotational angular momentum along the recoil direction. The origin of the CH3 rotation is conserved motion from the torsional and methyl-rocking modes of the parent molecule. Nonstatistical vibrational distributions for the CH3 fragment are obtained at higher energies.     

Optical control of ground-state atomic orbital alignment: Cl(2P3/2) atoms from HCl(v=2,J=1) photodissociation

H(35)Cl(v=0,J=0) molecules in a supersonic expansion were excited to the H(35)Cl(v=2,J=1,M=0) state with linearly polarized laser pulses at about 1.7 microm. These rotationally aligned J=1 molecules were then selectively photodissociated with a linearly polarized laser pulse at 220 nm after a time delay, and the velocity-dependent alignment of the (35)Cl((2)P(32)) photofragments was measured using 2+1 REMPI and time-of-flight mass spectrometry. The (35)Cl((2)P(32)) atoms are aligned by two mechanisms: (1) the time-dependent transfer of rotational polarization of the H(35)Cl(v=2,J=1,M=0) molecule to the (35)Cl((2)P(32)) nuclear spin [which is conserved during the photodissociation and thus contributes to the total (35)Cl((2)P(32)) photofragment atomic polarization] and (2) the alignment of the (35)Cl((2)P(32)) electronic polarization resulting from the photoexcitation and dissociation process. The total alignment of the (35)Cl((2)P(32)) photofragments from these two mechanisms was found to vary as a function of time delay between the excitation and the photolysis laser pulses, in agreement with theoretical predictions. We show that the alignment of the ground-state (35)Cl((2)P(32)) atoms, with respect to the photodissociation recoil direction, can be controlled optically. Potential applications include the study of alignment-dependent collision effects.     

Vector and scalar correlations in the photodissociation of NCCN

The CN photofragments from the photodissociation of NCCN at 193 nm have been measured by high-resolution transient absorption spectroscopy. Doppler-broadened profiles of isolated rotational lines in the 2-0 and 3–1 vibrational bands of the CN A---X transition were observed under collisionless conditions with a tunable, single-frequency Ti:sapphire ring laser. Analysis of the Dopple profiles reveals a vector correlation between the translation and rotation of CN photoproducts, with the angular momentum of the high rotational states increasingly perpendicular to the recoil velocity. After correction for vector correlations, the laboratory-frame scalar speed distribution of state-selected photoproducts can be determined. The mean squared laboratory velocity is directly related to the average internal energy of coincident CN fragments. The wings of the Doppler profiles indicate that the available energy for a pair of ground state CN photoproducts following 193 nm dissociation of NCCN at 295 K is 5300±150 cm⁻¹, which includes the average vibrational energy of the parent molecules selected by the photolysis laser. Phase space theory with an optimized available energy of 5300 cm⁻¹ produces laboratory speed distributions that are in qualitatively reasonable agreement with the kinetic energy measurements, but overestimate the total internal energy of the photofragments. The measurements are good enough to warrant comparison with more sophisticated models of unimolecular decomposition.     

Speed dependent rotational angular momentum polarization of the O2 (a 1Deltag) fragment following ozone photolysis in the wavelength range 248-265 nm

The translational anisotropy and rotational angular momentum polarization of a selection of rotational states of the O2 (a 1Deltag; v=0) photofragment formed from ozone photolysis at 248, 260, and 265 nm have been determined using the technique of resonance enhanced multiphoton ionization in combination with time of flight mass spectrometry. At 248 nm, the dissociation is well described as impulsive in nature with all rotational states exhibiting similarly large, near-limiting values for the bipolar moments describing their angular momentum alignment and orientation. At 265 nm, however, the angular momentum polarization parameters determined for consecutive odd and even rotational states exhibit clear differences. Studies at the intermediate wavelength of 260 nm strongly suggest that such a difference in the angular momentum polarization is speed dependent and this proposal is consistent with the angular momentum polarization parameters extracted and reported previously for longer photolysis wavelengths [G. Hancock et al., Phys. Chem. Chem. Phys. 5, 5386 (2003); S. J. Horrocks et al., J. Chem. Phys. 126, 044308 (2007)]. The alternation of angular momentum polarization for successive odd and even J states may be a consequence of the different mechanisms leading to the formation of the two O2 (a 1Deltag) Lambda doublets. Specifically, the involvement of out of plane parent rotational motion is proposed as the origin for the observed depolarization for the Delta- relative to the Delta+ state.     

Internal state distribution of the CF fragment from the 193 nm photodissociation of CFCl and CFBr

The dynamics of the 193 nm photodissociation of the CFCl and CFBr molecules have been investigated in a molecular beam experiment. The CFCl and CFBr parent molecules were generated by pyrolysis of CHFCl2 and CFBr3, respectively, and the CFCl and the CF photofragment were detected by laser fluorescence excitation. The 193 nm attenuation cross section of CFCl was determined from the reduction of the CF photofragment signal as a function of the photolysis laser fluence. The internal state distribution was derived from the analysis of laser fluorescence excitation spectra in the A 2Sigma+-X 2Pi band system. A very low degree of rotational excitation, with essentially equal A' and A" Lambda-doublet populations, and no vibrational excitation were found in the CF photofragment. The energy available to the photofragments is hence predominantly released as translational energy. The CF internal state distribution is consistent with the dissociation of a linear intermediate state. Considerations of CFCl electronic states suggest that a bent Rydberg state is initially excited.     

Photodissociation dynamics of OCS at 248 nm: the S((1)D(2)) atomic angular momentum polarization

The dissociation of OCS has been investigated subsequent to excitation at 248 nm. Speed distributions, speed dependent translational anisotropy parameters, angular momentum alignment, and orientation are reported for the channel leading to S((1)D(2)). In agreement with previous experiments, two product speed regimes have been identified, correlating with differing degrees of rotational excitation in the CO coproducts. The velocity dependence of the translational anisotropy is also shown to be in agreement with previous work. However, contrary to previous interpretations, the speed dependence is shown to primarily reflect the effects of nonaxial recoil and to be consistent with predominant excitation to the 2 (1)A(') electronic state. It is proposed that the associated electronic transition moment is polarized in the molecular plane, at an angle greater than approximately 60 degrees to the initial linear OCS axis. The atomic angular momentum polarization data are interpreted in terms of a simple long-range interaction model to help identify likely surfaces populated during dissociation. Although the model neglects coherence between surfaces, the polarization data are shown to be consistent with the proposed dissociation mechanisms for the two product speed regimes. Large values for the low and high rank in-plane orientation parameters are reported. These are believed to be the first example of a polyatomic system where these effects are found to be of the same order of magnitude as the angular momentum alignment.     

Photodissociation of HI and DI: polarization of atomic photofragments

The complete angular momentum distributions and vector correlation coefficients (orientation and alignment) of ground state I((2)P(32)) and excited state I((2)P(12)) atoms resulting from the photodissociation of HI have been computed as a function of photolysis energy. The orientation and alignment parameters a(Q) ((K))(p) that describe the coherent and incoherent contributions to the angular momentum distributions from the multiple electronic states accessed by parallel and perpendicular transitions are determined using a time-dependent wave packet treatment of the dissociation dynamics. The dynamics are based on potential energy curves and transition dipole moments that have been reported previously [R. J. LeRoy, G. T. Kraemer, and S. Manzhos, J. Chem. Phys. 117, 9353 (2002)] and used to successfully model the scalar (total cross section and branching fraction) and lowest order vector (anisotropy parameter beta) properties of the photodissociation. Predictions of the a(Q) ((K))(p), parameters for the isotopically substituted species DI are reported and contrasted to the analogous HI results. The resulting polarization for the corresponding H/D partners are also determined and demonstrate that both H and D atoms produced can be highly spin polarized. Comparison of these predictions for HI and DI with experimental measurement will provide the most stringent test of the current model for the electronic structure and the interpretation of the dissociation based on noncoupled excited state dynamics.