Probe Beam Dichroism and Birefringence in Stimulated Raman Scattering in Polyatomic Molecules.

Dichroism and birefringence in Stimulated Raman Scattering (SRS) in polyatomic molecules were studied theoretically. General expressions describing the change of the polarization matrix of the probe laser beam transmitted through initially isotropic molecular sample excited by the pump laser beam have been derived. Arbitrary polarization states and propagation directions of the incoming pump and probe beams were considered. The expressions were written in terms of spherical tensor operators that allowed for separation of the field polarization tensor and the molecular part containing three scalar values of nonlinear optical susceptibility χ K p u 3 ${{\chi }_{{K}_{pu}}^{\left(3\right)}}$ with K p u ${{K}_{pu}}$ =0,1,2. The geometry of almost collinear propagation of the pump and probe beams through the molecular sample was considered in greater details. It was shown that the dichroism and birefringence refer to the nonlinear optical susceptibility element χ 2 3 ${{\chi }_{2}^{\left(3\right)}}$ and that their contributions to the SRS signal can be separated experimentally by using an appropriate probe beam polarization analyzer installed in front of the photodetector. Particular cases of the off-resonant SRS and resonant SRS have been considered. The results obtained were expressed in terms of the Stokes polarization parameters of the pump and probe beams.

Two-Photon Excited Fluorescence of NADH-Alcohol Dehydrogenase Complex in a Mixture with Bacterial Enzymes.

Thorough study of composition and fluorescence properties of a commercial reagent of active equine NAD-dependent alcohol dehydrogenase expressed and purified from E. coli has been carried out. Several experimental methods: spectral- and time-resolved two-photon excited fluorescence, sodium dodecyl sulfate-polyacrylamide gel electrophoresis, fast protein liquid chromatography, and mass spectrometry were used for analysis. The reagent under study was found to contain also a number of natural fluorophores: free NAD(P)H, NADH-alcohol dehydrogenase, NADPH-isocitrate dehydrogenase, and pyridoxal 5-phosphate-serine hydroxymethyltransferase complexes. The results obtained demonstrated the potential and limitations of popular optical methods as FLIM for separation of fluorescence signals from free and protein-bound forms of NADH, NADPH, and FAD that are essential coenzymes in redox reactions in all living cells. In particular, NADH-alcohol dehydrogenase and NADPH-isocitrate dehydrogenase complexes could not be optically separated in our experimental conditions although fast protein liquid chromatography and mass spectrometry analysis undoubtedly indicated the presence of both enzymes in the molecular sample used. Also, the results of fluorescence, fast protein liquid chromatography, and mass spectrometry analysis revealed a significant contribution of the enzyme-bound coenzyme pyridoxal 5-phosphate to the fluorescence signal that could be separated from enzyme-bound NADH by using bandpass filters, but could effectively mask contribution from enzyme-bound FAD because the fluorescence spectra of the species practically overlapped. It was shown that enzyme-bound pyridoxal 5-phosphate fluorescence can be separated from enzyme-bound NAD(P)H and FAD through analysis of short fluorescence decay times of about tens of picoseconds. However, this analysis was found to be effective only at relatively high number of peak photon counts in recorded fluorescence signals. The results obtained in this study can be used for interpretation of fluorescence signals from a mixture of enzyme-bound fluorophores and should be taken into consideration when determining the intracellular NADH/FAD ratio using FLIM.

Machine Learning Assisted Classification of Cell Lines and Cell States on Quantitative Phase Images.

In this report, we present implementation and validation of machine-learning classifiers for distinguishing between cell types (HeLa, A549, 3T3 cell lines) and states (live, necrosis, apoptosis) based on the analysis of optical parameters derived from cell phase images. Validation of the developed classifier shows the accuracy for distinguishing between the three cell types of about 93% and between different cell states of the same cell line of about 89%. In the field test of the developed algorithm, we demonstrate successful evaluation of the temporal dynamics of relative amounts of live, apoptotic and necrotic cells after photodynamic treatment at different doses.

Two-Photon Excited Fluorescence Dynamics in Enzyme-Bound NADH: the Heterogeneity of Fluorescence Decay Times and Anisotropic Relaxation.

The dynamics of polarized fluorescence in NADH in alcohol dehydrogenase (ADH) in buffer solution has been studied using the TCSPC spectroscopy. A global fit procedure was used for determination of the fluorescence parameters from experiment. The interpretation of the results obtained was supported by ab initio calculations of the NADH structure. A theoretical model was developed describing the polarized fluorescence decay in ADH-NADH complexes that considered several interaction scenarios. A comparative analysis of the polarization-insensitive fluorescence decay using multiexponential fitting models has been carried out. As shown, the origin of a significant enhancement of the decay time in the ADH-NADH complex can be attributed to the decrease of nonradiative relaxation rates in the nicotinamide ring in the conditions of the apolar binding site environment. The existence of a single decay time in the ADH-NADH complex in comparison with two decay times observed in free NADH was attributed to a single NADH unfolded conformation in the ADH binding site. Comparison of the experimental data with the theoretical model suggested the existence of an anisotropic relaxation time of about 1 ns that is related with the rotation of fluorescence transition dipole moment due to the rearrangement of the excited state NADH nuclear configuration.

Relaxation dynamics of alkyl derivatives of fluorescein MitoFluo and C8-Fl in solutions with liposomes.

We present results of experimental and theoretical studies of excited state dynamics in two alkyl derivatives of fluorescein, MitoFluo and C8-Fl in solutions with liposomes. The liposomes DOPC and soybeanPC + 20% Cardiolipin (Azo-Cl), modelling cellular and inner mitochondrial membranes, respectively, were used in experiments. Both types of liposomes were shown to reduce significantly the fluorescence quantum yield as compared to that of pure fluorescein derivatives in solutions, while DOPC liposomes also caused a noticeable (ca 10 nm) red shift of fluorescence maximum. The study of fluorescence polarization decay has been carried out where important fluorescence parameters: polarization anisotropy, fluorescence lifetimes, and rotational diffusion times have been determined. It was shown that the isotropic fluorescence decay of C8-Fl in liposome containing solutions was single-exponential and the anisotropic decay was double-exponential for both types of lyposomes. In the case of MitoFluo both isotropic and anisotropic fluorescence decays were fitted satisfactory only with double-exponential functions. The interpretation of the experimental data obtained was supported by ab initio calculations of the structure and excitation properties of MitoFluo and C8-Fl in aqueous solution. The analysis of anisotropic fluorescence decay allowed for isolation of the contributions of fluorescein derivatives free in solution from those embedded in liposomes. Also, the experimental data suggest that MitoFluo interacts with liposomes more effectively than C8-Fl. Basing on the experimental and theoretical results obtained we conclude that free C8-Fl and MitoFluo molecules in solution were mostly in their dimer forms.

Two-Photon Excited Fluorescence Dynamics in NADH in Water-Methanol Solutions: The Role of Conformation States.

The dynamics of polarized fluorescence in reduced nicotinamide adenine dinucleotide (NADH) at 460 nm under two-photon excitation at 720 nm by femtosecond laser pulses in water-methanol solutions has been studied experimentally and theoretically as a function of methanol concentration. A number of fluorescence parameters have been determined from experiment by means of the global fit procedure and then compared with the results reported by other authors. A comprehensive analysis of experimental errors was made. Ab initio calculations of the structure of NADH in water and methanol and of ß-nicotinamide mononucleotide (NMNH) in vacuum have been carried out for clarifying the role of decay time heterogeneity. The main results obtained are as follows. An explanation of the heterogeneity in the measured fluorescence decay times in NADH has been suggested based on the influence of the internal molecular electric field in the nicotinamide ring on nonradiative decay rates. We suggest that different charge distributions in the cis and trans configurations result in different internal electrostatic field distributions that lead to the decay time heterogeneity. A slight but noticeable rise of the fluorescence decay times τ1 and τ2 with methanol concentration was observed and treated as a minor effect of a nonradiative relaxation slowing due to the decrease in solution polarity. Relative concentrations of the folded and unfolded NADH conformations in solutions have been determined using a new method of analysis of the rotational diffusion time τr as a function of methanol concentration on the basis of the Stokes-Einstein-Debye equation. The analysis of the fluorescence anisotropy parameters obtained under linearly and circularly polarized excitation and the parameter Ω has been carried out and resulted in the determination of the two-photon excitation tensor components and suggested the existence of two excitation channels with comparable intensities. These were the longitudinal excitation channel dominated by the diagonal tensor component Szz and the mixed excitation channel dominated by the off-diagonal tensor components |Sxz2 + Syz2|1/2.

Anisotropic relaxation in NADH excited states studied by polarization-modulation pump-probe transient spectroscopy.

We present the results of experimental and theoretical studies of fast anisotropic relaxation and rotational diffusion in the first electron excited state of biological coenzyme NADH in water-ethanol solutions. The experiments have been carried out by means of a novel polarization-modulation transient method and fluorescence polarization spectroscopy. For interpretation of the experimental results a model of the anisotropic relaxation in terms of scalar and vector properties of transition dipole moments has been developed based on the Born-Oppenheimer approximation. This model allows for the description of fast isotropic and anisotropic excited state relaxation under excitation of molecules by ultrafast laser pulses in transient absorption and upconversion experiments. The results obtained suggest that the dynamics of anisotropic rovibronic relaxation in NADH under excitation with 100 fs pump laser pulses can be characterised by a single vibrational relaxation time τv lying in the range of 2-15 ps and a single rotation diffusion time τr lying in the range of 100-450 ps, both depending on ethanol concentration. The dependence of the times τv and τr on the solution polarity (static permittivity) and viscosity has been determined and analyzed. Limiting values of the term P2(cos θ) describing the rotation of the transition dipole moment in the course of vibrational relaxation have been determined from experiments as a function of ethanol concentration and analyzed.

Photodissociation by Circularly Polarized Light Yields Photofragment Alignment in Ozone Arising Solely from Vibronic Interactions.

We present a direct determination of photofragment alignment produced by circularly polarized light in photolysis of a planar polyatomic molecule. This alignment arises via a new mechanism involving coherent excitation of two mutually perpendicular in-plane transition dipole moment components. The alignment is described by a new anisotropy parameter γ_{2}^{'} that was isolated by a unique laser polarization geometry. The determination of the parameter γ_{2}^{'} was realized in ozone photolysis at 266 nm where dc slice images of O(^{1}D_{2}) atomic fragments were acquired. A model developed for interpretation of the photolysis mechanism shows that it can exist only in case of failure of the Born-Oppenheimer approximation when electronic and vibrational (vibronic) interactions have to be taken into account. This finding suggests that determination of the alignment parameter γ_{2}^{'} can be used as a key for direct insight into vibronic interactions in photolysis of polyatomic molecules. The results obtained for ozone photolysis via the Hartley band showed significant γ_{2}^{'} alignment but little recoil speed dependence, consistent with the notion that, as opposed to the situation for derivative coupling, under our experimental conditions, the vibronic contributions to the nonadiabatic dynamics are not dependent on recoil speed.

Two-color two-photon excited fluorescence of indole: determination of wavelength-dependent molecular parameters.

We present a detailed study of two-color two-photon excited fluorescence in indole dissolved in propylene glycol. Femtosecond excitation pulses at effective wavelengths from 268 to 293.33 nm were used to populate the two lowest indole excited states (1)La and (1)Lb and polarized fluorescence was then detected. All seven molecular parameters and the two-photon polarization ratio Ω containing information on two-photon absorption dynamics, molecular lifetime τf, and rotation correlation time τrot have been determined from experiment and analyzed as a function of the excitation wavelength. The analysis of the experimental data has shown that (1)Lb-(1)La inversion occurred under the conditions of our experiment. The two-photon absorption predominantly populated the (1)La state at all excitation wavelengths but in the 287-289 nm area which contained an absorption hump of the (1)Lb state 0-0 origin. The components of the two-photon excitation tensor S were analyzed giving important information on the principal tensor axes and absorption symmetry. The results obtained are in a good agreement with the results reported by other groups. The lifetime τf and the rotation correlation time τrot showed no explicit dependence on the effective excitation wavelength. Their calculated weighted average values were found to be τf = 3.83 ± 0.14 ns and τrot = 0.74 ± 0.06 ns.

Two-color two-photon excited fluorescence of 2-methyl-5-tert-butyl-p-quaterphenyl (DMQ): ab initio calculations and experimental determination of the molecular parameters.

The paper presents experimental and theoretical studies of two-photon excitation dynamics in 2-methyl-5-tert-butyl-p-quaterphenyl (DMQ) dissolved in cyclohexane/paraffin. Experimentally, a two-color two-photon (2C2P) excitation by two femtosecond laser pulses at 800 and 400 nm has been used in combination with the time-resolved detection of polarized molecular fluorescence. The fluorescence decay was found to be two-exponential, resulting in the molecular excited state lifetime of 753 ± 10 ps and the rotational correlation time of 724 ± 45 ps. Control over the excited and fluorescent photons polarization has been used for determination from experiment of seven independent molecular parameters. The experimental data were analyzed on the basis of the recent theoretical approach [Shternin, P. S., Gericke, K.-H., and Vasyutinskii, O. S. Mol. Phys. 2010, 108, 813-825] supported by ab initio computations of the DMQ electronic structure and transition dipole moments. The results obtained imply that the two-photon absorption tensor S is mostly diagonal and that the Szz tensor component onto the molecular long axis gives the major contribution of 93%. However, it was also found that a number of different symmetry two-photon transitions related to the dipole moment components dxdz and dydz are excited in the conditions of our measurements.

Spin-polarized hydrogen Rydberg time-of-flight: experimental measurement of the velocity-dependent H atom spin-polarization.

We have developed a new experimental method allowing direct detection of the velocity dependent spin-polarization of hydrogen atoms produced in photodissociation. The technique, which is a variation on the H atom Rydberg time-of-flight method, employs a double-resonance excitation scheme and experimental geometry that yields the two coherent orientation parameters as a function of recoil speed for scattering perpendicular to the laser propagation direction. The approach, apparatus, and optical layout we employ are described here in detail and demonstrated in application to HBr and DBr photolysis at 213 nm. We also discuss the theoretical foundation for the approach, as well as the resolution and sensitivity we achieve.

Polarization of molecular angular momentum in the chemical reactions Li + HF and F + HD.

The quantum mechanical approach to vector correlation of angular momentum orientation and alignment in chemical reactions [G. Balint-Kurti and O. S. Vasyutinskii, J. Phys. Chem. A 113, 14281 (2009)] is applied to the molecular reagents and products of the Li + HF [L. Gonzalez-Sanchez, O. S. Vasyutinskii, A. Zanchet, C. Sanz-Sanz, and O. Roncero, Phys. Chem. Chem. Phys. 13, 13656 (2011)] and F + HD [D. De Fazio, J. Lucas, V. Aquilanti, and S. Cavalli, Phys. Chem. Chem. Phys. 13, 8571 (2011)] reactions for which accurate scattering information has become recently available through time-dependent and time-independent approaches. Application of the theory to two important particular cases of the reactive collisions has been considered: (i) the influence of the angular momentum polarization of reactants in the entrance channel on the spatial distribution of the products in the exit channel and (ii) angular momentum polarization of the products of the reaction between unpolarized reactants. In the former case, the role of the angular momentum alignment of the reactants is shown to be large, particularly when the angular momentum is perpendicular to the reaction scattering plane. In the latter case, the orientation and alignment of the product angular momentum was found to be significant and strongly dependent on the scattering angle. The calculation also reveals significant differences between the vector correlation properties of the two reactions under study which are due to difference in the reaction mechanisms. In the case of F + HD reaction, the branching ratio between HF and DF production points out interest in the insight gained into the detailed dynamics, when information is available either from exact quantum mechanical calculations or from especially designed experiments. Also, the geometrical arrangement for the experimental determination of the product angular momentum orientation and alignment based on a compact and convenient spherical tensor expression for the intensity of the resonance enhanced multiphoton ionization (REMPI 2 + 1) signal is suggested.

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.

Vector correlation analysis for inelastic and reactive collisions between partners possessing spin and orbital angular momentum.

A general reactive collision of the type A + B --> C + D is considered where both the collision partners (A and B) or the products (C and D) may possess internal, i.e., spin, orbital or rotational, angular momenta. Compact expressions are derived using a rigorous quantum mechanical analysis for the angular momentum anisotropy of either of the products (C or D) arising from an initially polarized distribution of the reactant angular momentum. The angular momentum distribution of the product is expressed in terms of canonical spherical tensors multiplied by anisotropy-transforming coefficients c(K(i)q(k))(K)(K(r),L). These coefficients act as transformation coefficients between the angular momentum anisotropy of the reactants and that of the product. They are independent of scattering angle but depend on the details of the scattering dynamics. The relationship between the coefficients c(K(i)q(k))(K)(K(r),L) and the body-fixed scattering S matrix is given and the methodology for the quantum mechanical calculation of the anisotropy-transforming coefficients is clearly laid out. The anisotropy-transforming coefficients are amenable to direct experimental measurement in a similar manner to vector correlation and alignment parameters in photodissociation processes. A key aspect of the theory is the use of projections of both reactant and product angular momenta onto the product recoil vector direction. An important new conservation rule is revealed through the analysis, namely that if the state multipole for reactant angular momentum distribution has a projection q(k) onto the product recoil vector the state multipoles for the product angular momentum distribution all have this same projection. Expressions are also presented for the distribution of the product angular momentum when its components are evaluated relative to the space-fixed Z-axis. Notes with detailed derivations of all the formulas are available as Supporting Information.

The role of the Coriolis interaction on vector correlations in molecular predissociation: excitation of isolated rotational lines.

We present the full quantum mechanical expressions for the polarization differential cross sections of the photofragments produced in slow predissociation of a parent molecule via isolated rotational branches. Both radial and Coriolis nonadiabatic interactions between the molecular potential energy surfaces have been taken into account. The expressions describe the recoil angle distribution of the photofragments and the distributions of the photofragment angular momentum polarization (orientation and alignment) in terms of the anisotropy parameters of the ranks K=0,1,2. The explicit expressions for the anisotropy parameters are presented and analyzed which contain contributions from different possible photolysis mechanisms including incoherent, or coherent optical excitation of the parent molecule followed by the radial, or Coriolis nonadiabatic transitions to the dissociative states. The obtained expression for the zeroth-rank anisotropy parameter beta is valid for any molecule and for an arbitrary value of the molecular total angular momentum J. The expressions for the orientation (K=1) and alignment (K=2) anisotropy parameters are given in the high-J limit in terms of the generalized dynamical functions which were analyzed for the case of photolysis of linear/diatomic molecules. As shown, the Coriolis nonadiabatic interaction results in several new photolysis mechanisms which can play an important role in the predissociation dynamics.

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 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.

Non-invasive and isotope-selective laser-induced fluorescence spectroscopy of nitric oxide in exhaled air.

The detection of nitric oxide (NO) is of considerable medical interest. NO is involved in a multitude of mammal physiological processes, and various non-invasive concentration determination methods for NO have been developed during the last few years. Regarding time resolved metabolism behavior the quantitative determination of the (15)N(16)O-isotopologue in combination with (15)N-labeled drugs and amino acids is a central interest of current medical research. We apply laser-induced fluorescence (LIF) spectroscopy for isotope-selective detection of NO in various biological environments with a theoretical detection limit below 0.1 parts per trillion (ppt). Electronic excitation of the AX-transition in the UV provides fluorescence around 247 nm from [Formula: see text]. For an online measurement of human exhaled air, a respiratory mask has been constructed and integrated into our system. This paper gives an overview of the applied LIF device for non-invasive detection of NO originated from exhaled human air. The main advantages of this device compared to established methods are as follows: high sensitivity for NO concentrations in the ppt region, a high time resolution of 20 ms and isotopic selectivity to distinguish between (14)NO and (15)NO. Visualizations of single-exhalation profiles and long-time online measurements including the determination of absolute NO concentrations are presented and the influence of quenching gases present during the experiment is discussed. To our knowledge, we present for the first time time-resolved (15)NO online profiles of exhaled human air.

S(1D2) atomic orbital polarization in the photodissociation of OCS at 193 nm: Construction of the complete density matrix.

The absolute velocity-dependent alignment and orientation for S(1D2) atoms from the photodissociation of OCS at 193 nm were measured using the dc slice imaging method. Three main peaks ascribed to specific groups of high rotational levels of CO in the vibrational ground state were found, with rotationally resolved rings in a fourth slow region ascribed to weak signals associated with excited vibrational states of CO. The observed speed-dependent beta and polarization parameters support the interpretation that there are two main dissociation processes: a simultaneous two-surface (A' and A") excitation and the initial single-surface (A') excitation followed by the nonadiabatic crossing to ground state. At 193 nm photodissociation, the nonadiabatic dissociation process is strongly enhanced relative to longer wavelengths. The angle- and speed-dependent S(1D2) density matrix can be constructed including the higher order (K = 3,4) contributions for the circularly polarized dissociation light. This was explicitly done for selected energies and angles. It was found in one case that the density matrix is sensitively affected by the rank 4 terms, suggesting that the higher order contributions should not be overlooked for an accurate picture of the dissociation dynamics in this system.