The importance of Rydberg orbitals in dissociative ionization of small hydrocarbon molecules in intense laser fields

Abstract

Much of our intuition about strong-field processes is built upon studies of diatomic molecules, which typically have electronic states that are relatively well separated in energy. In polyatomic molecules, however, the electronic states are closer together, leading to more complex interactions. A combined experimental and theoretical investigation of strong-field ionization followed by hydrogen elimination in the hydrocarbon series C₂D₂, C₂D₄ and C₂D₆ reveals that the photofragment angular distributions can only be understood when the field-dressed orbitals rather than the field-free orbitals are considered. Our measured angular distributions and intensity dependence show that these field-dressed orbitals can have strong Rydberg character for certain orientations of the molecule relative to the laser polarization and that they may contribute significantly to the hydrogen elimination dissociative ionization yield. These findings suggest that Rydberg contributions to field-dressed orbitals should be routinely considered when studying polyatomic molecules in intense laser fields.

Figure 1

(a) The two-dimensional slice (P_y ≈ 0) through the three-dimensional momentum distribution obtained from VMI data of C₂D₃ ⁺ photofragments produced in the nω + C₂D₄ → C₂D₄ ⁺ → C₂D₃ ⁺  + D process. The laser polarization, indicated by the arrow, is vertical (0–180°) in all panels. The faint outer ring is mirrored in the D⁺ momentum image, suggesting that those ions are part of the double ionization process (D⁺  + C₂D₃ ⁺). The laser pulses are approximately 5 fs in duration with a central wavelength of 740 nm and a focused peak intensity (I_peak) of approximately 6 × 10¹⁴ W cm⁻². The corresponding focal-volume-averaged intensity, I_avg, (see the Methods section for details) is approximately 2 × 10¹³ W cm⁻². (b) Measured yield as a function of the relative angle between the C₂D₃ ⁺ photofragment and the laser polarization. The yield is obtained for the inner single ionization followed by hydrogen elimination process and excludes the faint outer double ionization process. (c) Calculated angular distribution for the C₂D₃ ⁺ photofragments (see Methods for details) without including FDRC orbitals at a uniform intensity of 9 × 10¹³ W cm⁻². (d) Similar calculations for an intensity of 9 × 10¹³ W cm⁻² but with the ionization from FDRC orbitals included. The ethylene HOMO has π symmetry.

Figure 2

(Left) Experimental C₂D⁺ photofragment angular distributions arising from nω + C₂D₂ → C₂D₂ ⁺ → C₂D⁺  + D. Experimental laser parameters are about 5 fs pulse duration and a central wavelength of 740 nm. The laser polarization is vertical (along the 0–180° direction) in all panels, as indicated by the arrow. (a) Experimental results with I_peak = 4 × 10¹⁵ W cm⁻² and I_avg = 4 × 10¹³ W cm^−2. (b) I_peak = 8 × 10¹⁵ W cm⁻² and I_avg = 7 × 10¹³ W cm⁻². (c) I_peak = 1 × 10¹⁶ W cm⁻² and I_avg = 1 × 10¹⁴ W cm⁻². (Right) Calculated angular distribution for the C₂D⁺ photofragments (see Methods for details). In panel (d) the calculations are done without including FDRC orbitals, at a uniform intensity of 9 × 10¹³ W cm⁻². (e) Similar calculations but with the ionization from FDRC orbitals included, at the same intensity of 9 × 10¹³ W cm⁻². The symmetry of the acetylene HOMO and LUMO are π_u and π_g, respectively.

Figure 3

(a) Measured C₂D₅ ⁺ photofragment angular distribution from the nω + C₂D₆ → C₂D₆ ⁺ → C₂D₅ ⁺ + D process at I_peak = 2 × 10¹⁵ W cm⁻² (I_avg = 2 × 10¹³ W cm⁻²) and a pulse duration of about 5 fs. (b) Measured C₂D₅ ⁺ photofragment angular distribution for the same process and pulse duration but at a higher intensity: I_peak = 7 × 10¹⁵ W cm⁻² and I_avg = 6 × 10¹³ W cm⁻². (c) Calculated C₂D₅ ⁺ angular distribution without including FDRC orbitals, at a uniform intensity of 9 × 10¹³ W cm⁻². (d) Calculated C₂D₅ ⁺ angular distribution once the FDRC orbitals are included, at a uniform intensity of 2 × 10¹⁵ W cm⁻². The laser polarization, indicated by the red arrow in (a), is vertical in all panels. The ethane HOMO has π* symmetry.

Figure 4

Ethylene orbitals for various orientations of the laser polarization, for an intensity of 9 × 10¹³ W cm⁻². The rightmost column shows the case where the laser polarization lies along the C-H bond direction. In this configuration, the field easily shifts electron density in that direction and the ionization rate correspondingly increases.

Figure 5

Schemes for calculating the photofragment angular distributions in C₂D₄ (right) and corresponding results (polar plots, left). The red arrow indicates the direction of the dipole field. The dashed arrows relate the orientation of the molecule to the dipole vector with the angle between the field and the dissociation direction plotted in the polar diagram. (a) Contributions from the hole localized at “nearby” C-H bonds only. The blue vectors indicate the dissociation direction of these H-atoms. (b) The hole delocalizes quickly, allowing all C-H bonds to dissociate with equal probability. The cyan vectors indicate the dissociation direction of the more remote H-atoms (c) Contributions to dissociative ionization yield are weighted partially by their projection to the dipole vector which is indicated by the dark and light green line, respectively (see Eq. (4)). The individual projections are indicated as dotted lines.

Figure 6

Snapshots of the time-dependent hole density in ethylene. The complete animation produced in the calculation is included in the supplemental information.

Figure 7

Intensity-dependent energies of the HOMO (red line) and the FDRC orbitals (green line) in ethane. The laser polarization is along a C-H bond for the most noticeable effect. Δ represents the difference in energy between these orbitals as a function of intensity and is shown by the blue line.

Figure 8

Relevant angles α, between the dipole field and the molecular orientation (in this case the C-C axis), and β, between the dipole field and the C-H dissociation direction.