“…Equations (8) and (9) can be used to express Equation (3) explicitly as an average over all orientations of r il [Eq. (10)] weighted by the distribution of Equation (7):…”
Section: General Theorymentioning
confidence: 99%
“…[3]. An experimental ground state structure [9] of the CF 3 I reactant is used, and the structure of the CF 3…”
Electron scattering expressions are presented which are applicable to very general conditions of implementation of anisotropic ultrafast electron diffraction (UED) experiments on the femto- and picosecond time scale. "Magic angle" methods for extracting from the experimental diffraction patterns both the isotropic scalar contribution (population dynamics) and the angular (orientation-dependent) contribution are described. To achieve this result, the molecular scattering intensity is given as an expansion in terms of the moments of the transition-dipole distribution created by the linearly polarized excitation laser pulse. The isotropic component (n=0 moment) depends only on population and scalar internuclear separations, and the higher moments reflect bond angles and evolve in time due to rotational motion of the molecules. This clear analytical separation facilitates assessment of the role of experimental variables in determining the influence of anisotropic orientational distributions of the molecular ensembles on the measured diffraction patterns. Practical procedures to separate the isotropic and anisotropic components of experimental data are evaluated and demonstrated with application to reactions. The influence of vectorial properties (bond angles and rotational dynamics) on the anisotropic component adds a new dimension to UED, arising through the imposition of spatial order on otherwise randomly oriented ensembles.
“…Equations (8) and (9) can be used to express Equation (3) explicitly as an average over all orientations of r il [Eq. (10)] weighted by the distribution of Equation (7):…”
Section: General Theorymentioning
confidence: 99%
“…[3]. An experimental ground state structure [9] of the CF 3 I reactant is used, and the structure of the CF 3…”
Electron scattering expressions are presented which are applicable to very general conditions of implementation of anisotropic ultrafast electron diffraction (UED) experiments on the femto- and picosecond time scale. "Magic angle" methods for extracting from the experimental diffraction patterns both the isotropic scalar contribution (population dynamics) and the angular (orientation-dependent) contribution are described. To achieve this result, the molecular scattering intensity is given as an expansion in terms of the moments of the transition-dipole distribution created by the linearly polarized excitation laser pulse. The isotropic component (n=0 moment) depends only on population and scalar internuclear separations, and the higher moments reflect bond angles and evolve in time due to rotational motion of the molecules. This clear analytical separation facilitates assessment of the role of experimental variables in determining the influence of anisotropic orientational distributions of the molecular ensembles on the measured diffraction patterns. Practical procedures to separate the isotropic and anisotropic components of experimental data are evaluated and demonstrated with application to reactions. The influence of vectorial properties (bond angles and rotational dynamics) on the anisotropic component adds a new dimension to UED, arising through the imposition of spatial order on otherwise randomly oriented ensembles.
“…He found a linear correlation between the shortening of the C-X bond due to CH 3 /CF 3 substitution and the electronegativity of X. To explain this, he used a rather simple electrostatic model [5]. The three fluorine atoms in CF 3 polarize the carbon atom; it carries a high positive net charge.…”
Pseudopotential SCF calculations for YaC-X, Y =H, F; X=H, F, CI, PH 2 , PF 2 and a simple model, simulating the substituents by a homogeneous, electric field, are presented in order to rationalize the substitution effect on the C-X bond.
“…Here, we must account for multiple internuclear separations and two different molecules, CF 3 I and CF 3 . We use the same ground state structure [16] as used by WZ in their calculation for perpendicular laser polarization of diffraction by the unexcited population only. For a complete picture of anisotropic UED, we assume a 10 % excitation yield via a parallel transition dipole (along the CÀI bond) leading to instantaneous loss of the Figure 8.…”
mentioning
confidence: 99%
“…The laser polarization is parallel to k 0 , T = 2958 K, and the transition dipole moment is parallel to the CÀI bond. The structure of CF 3 I is shown, and the structural parameters of Typke et al [16] for CF 3 I were used in the calculations for both CF 3 I and CF 3 . The solid curve is a calculation for the dissociation assuming isotropic distributions and the light dotted curve is a scaled radial distribution of the reactant only, labeled with the atom pair(s) responsible for each peak.…”
The technique of ultrafast electron diffraction allows direct measurement of changes which occur in the molecular structures of isolated molecules upon excitation by femtosecond laser pulses. The vectorial nature of the molecule-radiation interaction also ensures that the orientation of the transient populations created by the laser excitation is not isotropic. Here, we examine the influence on electron diffraction measurements--on the femtosecond and picosecond timescales--of this induced initial anisotropy and subsequent inertial (collision-free) molecular reorientation, accounting for the geometry and dynamics of a laser-induced reaction (dissociation). The orientations of both the residual ground-state population and the excited- or product-state populations evolve in time, with different characteristic rotational dephasing and recurrence times due to differing moments of inertia. This purely orientational evolution imposes a corresponding evolution on the electron scattering pattern, which we show may be similar to evolution due to intrinsic structural changes in the molecule, and thus potentially subject to misinterpretation. The contribution of each internuclear separation is shown to depend on its orientation in the molecular frame relative to the transition dipole for the photoexcitation; thus not only bond lengths, but also bond angles leave a characteristic imprint on the diffraction. Of particular note is the fact that the influence of anisotropy persists at all times, producing distinct differences between the asymptotic "static" diffraction image and the predictions of isotropic diffraction theory.
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