Vector correlations in photodissociation of polarized polyatomic molecules beyond the axial recoil limit

We present the full quantum mechanical theory of the angular momentum distributions of photofragments produced in photolysis of oriented/aligned parent polyatomic molecules beyond the axial recoil limit. This paper generalizes the results of Underwood and Powis(28,29) to the case of non-axial recoil photodissociation of an arbitrary polyatomic molecule. The spherical tensor approach is used throughout this paper. We show that the recoil angular distribution of the angular momentum polarization of each of the photofragments can be presented in a universal spherical tensor form valid for photolysis in diatomic or polyatomic molecules, irrespective of the reaction mechanism. The angular distribution can be written as an expansion over the Wigner D-functions in terms of the set of the anisotropy-transforming coefficients c(K(i)q(i))(K) (k(d), K(0)) which contain all of the information about the photodissociation dynamics and can be either determined from experiment, or computed from quantum mechanical theory. An important new conservation rule is revealed through the analysis, namely that the component q(i) of the initial reagent polarization rank K(i) and the photofragment polarization rank K onto the photofragment recoil direction k is preserved in any photolysis reaction. Both laboratory and body frame expressions for the recoil angle dependence of the photofragment angular momentum polarization are presented. The parent molecule polarization is shown to lead to new terms in the obtained photofragment angular distributions compared with the isotropic case. In particular, the terms with |q(i)| > 2 can appear which are shown to manifest angular momentum helicity non-conservation in the reaction. The expressions for the coefficients c(K(i)q(i))(K) (k(d), K(0)) have been simplified using the quasiclassical approximation in the high-J limit which allows for introducing the dynamical functions and the rotation factors which describe the decreasing of the photofragment angular momentum orientation and alignment due to the rotation of the molecular axis during photodissociation. In this case, the resultant recoil angle dependence is also presented in a form where the anisotropy of the parent molecular ensemble is expressed in terms of the molecular axis distribution, rather than in terms of the molecular density matrix.     

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.     

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.     

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.     

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.     

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.     

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.     

Further investigation of the photodissociation dynamics of dichlorocarbene near 248 nm

A further investigation of the 248 nm photodissociation of CCl(2), which expands upon our original study of this process [S. K. Shin and P. J. Dagdigian, Phys. Chem. Chem. Phys. 8, 3446 (2006)], is presented. The CCl(2) parent molecule and the CCl photofragment were detected by laser fluorescence excitation in a molecular beam experiment. From the dependence of the CCl(2) signals on the photolysis laser fluence, attenuation cross sections of the 0(0), 1(1), and 2(1) vibrational levels were determined; the cross sections for the excited vibrational levels were found to be significantly smaller than those for the ground vibrational level. The previously observed fragment CCl bimodal rotational state distribution was found to arise from the photolysis of more than one parent molecule. At low CHCl(3) mole fractions in the gas supplied to the pyrolysis beam source, it was concluded that CCl(2) is the photolysis precursor for both low-J and high-J CCl fragments. On the basis of the dependence of the CCl signals on the photolysis laser fluence, ground and vibrationally excited CCl(2), respectively, were assigned as the precursors to these two classes of fragments. The photofragment excitation spectra for low-J and high-J CCl fragments from the photolysis of CCl(2) were recorded in the wavelength range around 248 nm; both were found to be structureless. The 248 nm photodissociation dynamics of CCl(2) is discussed in light of our experimental observations and quantum chemical calculations of the CCl(2) excited electronic states.     

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.     

Photofragment alignment in the photodissociation of I2 from 450 to 510 nm

A combination of velocity map imaging and slicing techniques have been used to measure the product recoil anisotropy and angular momentum polarization for the photodissociation process I2-->I(2P(3/2))+I(2P(3/2)) and I2-->I(2P(3/2)))+I(2P(1/2)) in the 450-510 nm laser wavelength region using linearly polarized photolysis and probe laser light. The former channel is produced predominantly via perpendicular excitation to the 1Piu state, and the latter is predominantly parallel, via the B 3Pi(0u)+ state. In both cases we observe mostly adiabatic dissociation, which produces electronically aligned iodine atoms in the mid /m/=1/2 states with respect to the recoil direction.     

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.     

Orbital alignment in N2O photodissociation. I. Determination of all even rank anisotropy parameters

We present a general method for determination of the photofragment K=4 state multipoles in an ion imaging experiment. These multipoles are important for determining the full density matrix for any photofragment with j(a)> or =2. They are expressed in terms of laboratory frame anisotropy parameters that have distinct physical origins and possess characteristic angular distributions. The explicit expression for the (2+1) resonant multiphoton ionization absorption signal for the case of arbitrarily polarized probe light is derived and a procedure for isolation of the rank-4 state multipoles from all others is shown. This treatment is applied to the case of O((1)D) produced in the 193 nm photodissociation of N2O. The results show nonzero values for all K=4 anisotropy parameters, indicating the complexity of the photodissociation dynamics in this system.     

Vector properties of the O(1D2) fragment produced from the photolysis of ozone in the wavelength range of 298 to 320 nm

The speed averaged translational anisotropy and electronic angular momentum polarization of the O(1D2) atomic fragment formed from the photodissociation of ozone in the atmospherically important long wavelength region of the Hartley band (298 to 320 nm) have been measured using resonance enhanced multiphoton ionization time of flight mass spectrometry. The translational anisotropy parameter, beta, is found to decline from 1.1 for photolysis at 300 nm to a minimum value of 0 at 310 nm which is the threshold for production of O(1D2) in conjunction with the O2(a 1Deltag v = 0) molecular cofragment. For photolysis wavelengths greater than 310 nm, O(1D2) is formed from the dissociation of internally excited ozone molecules. The corresponding beta parameters are markedly lower than for atomic fragments produced with the same speed from the photolysis of ground state ozone molecules. This result is consistent with two different pathways contributing to the photolysis of internally excited ozone at the longest wavelengths studied corresponding to initial internal excitation either in the symmetric or asymmetric stretching vibration. In addition, the polarization of the atomic angular momentum has been determined with the incoherent polarization parameters a0(2)(||) and a0(2)(_|) increasing from values of -0.53 and -0.62 at 300 nm to -0.37 and -0.19 at 317 nm, consistent with the increasing contribution from the photolysis of internally excited ozone as the dissociation wavelength lengthens. Evaluation of these alignment parameters allows the populations of the magnetic substrates, mj, to be determined. For example, for a photolysis wavelength of 303 nm the populations of mj = 0, +/- 1, +/- 2 are in the ratio of 0.36: 0.56: 0.08 and this ratio is essentially independent of the photolysis wavelength. The coherent contribution to the atomic polarization is quantified by the Re{a1(2)(||, _|)} and Im{a1(1)(||, _|)} parameters and these are found to vary from -0.21 and 0.21 at 300 nm to -0.04 and 0.24 at 313 nm, respectively.     

Angular distributions and angular momentum alignment of O((3)P(J)) atoms formed in the photolysis of O(2)via the Herzberg continuum

Sliced velocity-map imaging has been used to measure photofragment scattering distributions for the O((3)P(2)) and O((3)P(1)) products of O(2) photolysis following laser excitation into the Herzberg continuum between 205 and 241 nm. The images were analysed to extract the photofragment spatial anisotropy parameter, β, together with the alignment parameters a(∥), a(⊥), a(⊥), and Re[a(∥, ⊥)]. Our alignment measurements bridge the gap between the recent 193 nm measurement of Brouard et al., Phys. Chem. Chem. Phys., 2006, 8, 5549 and those of Alexander et al., J. Chem. Phys., 2003, 118, 10566 at 222 and 237 nm, and extend out to the threshold at 241 nm. Our measured parameters show no strong dependence on photolysis wavelength. Near the threshold we were able to separate the contributions from the O((3)P(2)) + O((3)P(2)) and O((3)P(2)) + O((3)P(1)) channels, and found significantly different photofragment alignments for the two cases.     

Towards the complete experiment: measurement of S((1)D2) polarization in correlation with single rotational states of CO(J) from the photodissociation of oriented OCS(v2 = 1|JlM = 111)

In this paper we report slice imaging polarization experiments on the state-to-state photodissociation at 42,594 cm(-1) of spatially oriented OCS(v(2) = 1|JlM = 111) → CO(J) + S((1)D(2)). Slice images were measured of the three-dimensional recoil distribution of the S((1)D(2)) photofragment for different polarization geometries of the photolysis and probe laser. The high resolution slice images show well separated velocity rings in the S((1)D(2)) velocity distribution. The velocity rings of the S((1)D(2)) photofragment correlate with individual rotational states of the CO(J) cofragment in the J(CO) = 57-65 region. The angular distribution of the S((1)D(2)) velocity rings are extracted and analyzed using two different polarization models. The first model assumes the nonaxial dynamics evolves after excitation to a single potential energy surface of an oriented OCS(v(2) = 1|JlM = 111) molecule. The second model assumes the excitation is to two potential energy surfaces, and the OCS molecule is randomly oriented. In the high J region (J(CO) = 62-65) it appears that both models fit the polarization very well, in the region J(CO) = 57-61 both models seem to fit the data less well. From the molecular frame alignment moments the m-state distribution of S((1)D(2)) is calculated as a function of the CO(J) channel. A comparison is made with the theoretical m-state distribution calculated from the long-range electrostatic dipole-dipole plus quadrupole interaction model. The S((1)D(2)) photofragment velocity distribution shows a very pronounced strong peak for S((1)D(2)) fragments born in coincidence with CO(J = 61).     

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.     

Photodissociation of HBr. 1. Electronic structure, photodissociation dynamics, and vector correlation coefficients

Ab initio potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P(1/2)), and the lowest order anisotropy parameters, beta, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[a1(3) (parallel, perpendicular)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.     

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.     

Two-photon state selection and angular momentum polarization probed by velocity map imaging: application to H atom photofragment angular distributions from the photodissociation of two-photon state selected HCl and HBr

A formalism for calculating the angular momentum polarization of an atom or a molecule following two-photon excitation of a J-selected state is presented. This formalism is used to interpret the H atom photofragment angular distributions from single-photon dissociation of two-photon rovibronically state selected HCl and HBr prepared via a Q-branch transition. By comparison of the angular distributions measured using the velocity map imaging technique with the theoretical model it is shown that single-photon dissociation of two-photon prepared states can be used for pathway identification, allowing for the identification of the virtual state symmetry in the two-photon absorption and/or the symmetry of the dissociative state. It is also shown that under conditions of excitation with circularly polarized light, or for excitation via non-Q-branch transitions with linearly polarized light the angular momentum polarization is independent of the dynamics of the two-photon transition and analytically computable.