A method for the determination of speed-dependent semi-classical vector correlations from sliced image anisotropies

Abstract

We present analytical expressions relating the bipolar moment β(Q)(K)(k(1)k(2)) parameters of Dixon to the measured anisotropy parameters of different pump/probe geometry sliced ion images. In the semi-classical limit, when there is no significant coherent contribution from multiple excited states to fragment angular momentum polarization, the anisotropy of the images alone is sufficient to extract the β(Q)(K)(k(1)k(2)) parameters with no need to reference relative image intensities. The analysis of sliced images is advantageous since the anisotropy can be directly obtained from the image at any radius without the need for 3D-deconvolution, which is not applicable for most pump/probe geometries. This method is therefore ideally suited for systems which result in a broad distribution of fragment velocities. The bipolar moment parameters are obtained for NO(2) dissociation at 355 nm using these equations, and are compared to the bipolar moment parameters obtained from a proven iterative fitting technique for crushed ion images. Additionally, the utility of these equations in extracting speed-dependent bipolar moments is demonstrated on the recently investigated NO(3) system.

Primary and Secondary Loss of CO and NO Ligands in the Ultraviolet Photodissociation of the Heteroleptic Co(CO)3NO Complex

“…We analyzed the angular distribution of the higher-kinetic-energy components on the basis of a semiclassical bipolar moment formalism , to determine vector–correlation parameters in our previous study; the anisotropy parameter [β = 2β 0 2 (20)] for the NO ( v = 0, J = 39.5) fragment was determined to be 1.6, which is qualitatively explained as the result of rapid dissociation following the photoabsorption with a parallel-type transition. Several β Q K ( k 1 k 2 ) parameters were determined with the use of the angular distributions measured at the R 12 + Q 22 and P 11 transitions on the basis of the analytical formula of photofragment angular distributions derived by Grubb et al The β 0 0 (22) parameter, , which is related to a correlation between a recoil velocity vector v and the total angular momentum vector of the NO fragment j NO , was determined to be −0.58 ± 0.09, suggesting a perpendicular rotational alignment of the NO fragment to its recoil direction. The obtained value exceeds the physical limit [−0.5 < β 0 0 (22) <1.0] without the error presumably because the measurement was limited in a single pump–probe polarization configuration .…”

355 nm Photodissociation of N2O3 Revealed by Velocity-Mapped Ion Imaging

“…47,48 The method uses the semiclassical bipolar moment scheme developed by Dixon 49 to determine the vector correlations in the photodissociation. Since all of the transitions studied were of mixed Q and P character, the method of Grubb et al 47,48 was modified to use a weighted average of the alignment sensitivity coefficient, h (2) , in the equations. The weighting is based on the relative Honl− London factors for the mixed Q 11 + P 21 (J″) transitions.…”

“…The weighting coefficients were further analyzed using the method of Grubb et al to determine the vector correlations between and among the transition dipole (μ), NO angular momentum ( J ), and NO velocity ( v ). , The method uses the semiclassical bipolar moment scheme developed by Dixon to determine the vector correlations in the photodissociation. Since all of the transitions studied were of mixed Q and P character, the method of Grubb et al , was modified to use a weighted average of the alignment sensitivity coefficient, h (2) , in the equations. The weighting is based on the relative Hönl–London factors for the mixed Q 11 + P 21 ( J ″) transitions.…”

Photodissociation Dynamics and Stereodynamics of Methyl Mercaptan and Dimethyl Sulfide from the Second Absorption Band at 201 and 210 nm

“…Following the methodology originally described by Grub et al 21,22 and further developments by Rodríguez et al, 23,24 the BMs have been calculated from the phenomenological anisotropy parameters extracted out of the CH 3 fragment sliced images. Four bipolar moments have been determined: For continuous speed distributions, like those measured in this work, a possible partial slicing would have the eect of overlapping signals from dierent fragment velocities, dis-torting the photofragment speed and angular distributions.…”

“…(22), which account, respectively, for the µ-v, v-J, µ-J and µ-J-v correlations, where µ is the transition dipole moment, v the fragment recoil direction, and J the total angular momentum of the detected fragment. The interpretation of the four bipolar moments as a function of the CH 3 speed distribution provides information about the excited-state symmetry, couplings, and dissociation time scales and details about forces and torques between the separating fragments.…”