Extraction of geometrical structure of ethylene molecules by laser-induced electron diffraction combined with ab initio scattering calculations

We measured angle-resolved high-energy electron spectra emitted from ${\mathrm{C}}_2{\mathrm{H}}_4$ in an intense laser field, extracted field-free electron-ion elastic scattering differential cross sections (DCSs) according to quantitative rescattering theory, and obtained molecular contrast factors (MCFs) subtracting the incoherent sum of DCSs of all the atoms in the molecule. Comparing the results with ab initio scattering calculations and employing least-squares fitting, we have extracted the C-C and C-H bond lengths of the molecule with $\sim 5\%$ uncertainty. This approach opens the way to retrieve the structure of hydrocarbon molecules, potentially at high temporal resolution, employing low collision energies where electron scattering is sensitive to the hydrogen atoms; and where the independent atom model calculations may fail to reproduce the experimentally extracted MCF.

Figure 1

A PAD of ${\mathrm{C}}_2{\mathrm{H}}_4$ measured in a 1650-nm laser field. The red circle corresponds to the rescattering electrons with a collision momentum of 3.2 a.u.

Figure 2

DCSs of field-free electron-ion elastic scattering extracted from the spectrum shown in Fig. 1 for $p_r=2.0$ a.u. and 2.5 a.u. The (green) solid line is the sum of theoretical atomic DCSs.

Figure 3

MCFs derived from the experimental DCSs shown in Fig. 2. Theoretical MCFs are also shown for $e^{-}\text{−}{\mathrm{C}}_2{\mathrm{H}}_4^{+}$ scattering (blue solid line) and IAM (green dashed line).

Figure 4

Residual sum of squares between the experimental and theoretical MCFs for $p_r=2.5$ a.u. as a function of the bond lengths.