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.     

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.     

由激光诱导荧光方法探测光碎片分子取向的理论研究

采用密度矩阵方法,推导了从激光诱导荧光(LIF)强度中抽出光碎片取向参数的表达式.光碎片的取向由分子态多极矩描述.用于解离母分子和激发碎片分子的激光均为线偏振光,而探测荧光为非偏振光.激光诱导荧光强度是光碎片分子初始态多极矩、线强度因子和解离-激发几何因子的函数.光碎片的取向参数可以由测量荧光偏振比和计算动力学因子而获得.     

Photofragment angular momentum distribution beyond the axial recoil approximation: the role of molecular axis rotation

We present the quantum-mechanical expressions for 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 paper generalizes the result of Siebbeles et al. [J. Chem. Phys. 100, 3610 (1994)] to the case of dissociation of rotating molecules. The electronic wave function of the molecule was used in the adiabatic body-frame representation. The obtained rigorous expressions for the fragment state multipoles have been explicitly derived from the scattering wave-function formalism and then simplified using the quasiclassical approximation in the high-J limit. Possible radial and Coriolis nonadiabatic interactions have been taken into consideration. It is shown that the rotation of the molecular axis is described by a number of rotation factors which depend on the rank of the incident-photon polarization matrix, on the dissociation mechanism, and on the classical angle of rotation of the molecular axis gamma.     

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.     

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.     

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.     

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.     

Molecular polarization and laser photopredissociation in the presence of a magnetic field

The theory of the angular distribution of the photofragment resulting from weak predissociation in a diatomic molecule is worked out in the density matrix formalism. Special attention is given to the relationship between photofragment anisotropy, molecular polarization and fluorescence light polarization. The effect of a steady applied magnetic field is discussed and compared with classical Hanle effect. Application to the case of O₂⁺, b⁴σ_R^? state studied by fast ion beam laser spectroscopy (FIBLAS) is presented. Zeeman effect of the low J levels is observed in good agreement with theory and the angular distribution of the photofragments arising from a few selected Zeeman sublevels offers qualitative experimental confirmation of the theoretically predicted behavior.     

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.     

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.     

A complete quantum mechanical study of chlorine photodissociation

A fully quantum mechanical dynamical calculation on the photodissociation of molecular chlorine is presented. The magnitudes and phases of all the relevant photofragment T-matrices have been calculated, making this study the computational equivalent of a "complete experiment," where all the possible parameters defining an experiment have been determined. The results are used to simulate cross-sections and angular momentum polarization information which may be compared with experimental data. The calculations rigorously confirm the currently accepted mechanism for the UV photodissociation of Cl(2), in which the majority of the products exit on the C(1)Π(1u) state, with non-adiabatic couplings to the A(3)Π(1u) and several other Ω = 1 states, and a small contribution from the B(3)Π state present at longer wavelengths.     

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.     

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).     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

A semi-empirical model for computing radial matrix elements in one-electron atoms and ions

An easily tractable model is proposed to compute radial matrix elements between discrete states of one-electron atoms or ions. Assuming a closed-shell core, polarization effects are included in the model, and core penetration is accounted for empirically. The required inputs for this algorithm are the energies of the involved levels, and the core size and polarisabilities. Ignoring core polarization, the derived Coulomb matrix elements (possibly between levels with non-zero quantum defects) agree with those tabulated elsewhere in the literature. The method is then applied to dipolar and quadrupolar transitions in alkali atoms and singly-ionized alkaline-earth elements; it proves to be in fair agreement with available experimental data. An accuracy test of the method is proposed.     

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.     

库水硼镁石2MgO.3B2O3.15H2O的65-310K间的比热测定及其热力学性质的计算

用真空绝热量热计测定了库水硼镁石2MgO.3B2O3.15H2O在65-310K间的比热.根据Debye-Einsein函数组合式, 计算了0-65K间的比热, 其误差为0.4%.在65-310K范围内, 每隔5K, 计算了熵、焓和自由能函数.     

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.