Ultrafast X-ray scattering offers a structural view of excited-state charge transfer

Abstract

Intramolecular charge transfer and the associated changes in molecular structure in N,N'-dimethylpiperazine are tracked using femtosecond gas-phase X-ray scattering. The molecules are optically excited to the 3p state at 200 nm. Following rapid relaxation to the 3s state, distinct charge-localized and charge-delocalized species related by charge transfer are observed. The experiment determines the molecular structure of the two species, with the redistribution of electron density accounted for by a scattering correction factor. The initially dominant charge-localized state has a weakened carbon-carbon bond and reorients one methyl group compared with the ground state. Subsequent charge transfer to the charge-delocalized state elongates the carbon-carbon bond further, creating an extended 1.634 Å bond, and also reorients the second methyl group. At the same time, the bond lengths between the nitrogen and the ring-carbon atoms contract from an average of 1.505 to 1.465 Å. The experiment determines the overall charge transfer time constant for approaching the equilibrium between charge-localized and charge-delocalized species to 3.0 ps.

Keywords: X-ray scattering; charge transfer; excited state; femtosecond; ultrafast dynamics.

Fig. 1.

A schematic illustration of the experimental setup. The ground-state molecules (DMP) were excited by 200 nm ultraviolet pump pulses, and the transient structures were probed by 9.5 keV X-ray pulses at variable time delays. The scattering signals were recorded on a CSPAD detector. The inset shows the calculated spin density, which gives the difference in density of electrons with spin up and spin down, of the charge-localized DMP (3sL) and charge-delocalized DMP (3sD) in the 3s Rydberg states at isovalues of 0.1 electron/ų.

Scheme 1.

Reaction pathway for Rydberg-excited DMP as determined previously (33).

Fig. 2.

The anisotropic pump-probe scattering patterns. (Top) Computed patterns for TDM parallel (top left, direction of red solid arrow indicated in Bottom Right) and perpendicular (top right, direction of red dashed arrow indicated in Bottom Right) to the optimal TDM direction in the ${\sigma }_h$ plane. (Bottom, Left) Experimental pattern at 10 fs. (Bottom, Right) Direction of TDM illustrated in the mirror plane, with the z-axis aligned with the C₂ symmetry axis of the ground-state DMP molecule.

Fig. 3.

The isotropic component, $\mathrm{\Delta }{I}_{\text{iso}}\left(q,t\right)$ (see Eq. 2), of the experimental percent difference scattering signal as a function of delay time 𝑡 (ps) and the magnitude of the momentum transfer vector 𝑞 (Å⁻¹), with the value of the percent difference indicated by the color bar. Note the change of scale in the time axis at 2 ps.

Fig. 4.

Absolute values of the percent difference isotropic scattering signals $\mathrm{\Delta }{I}_{\text{iso}}\left(q,t\right)$ averaged over three different q ranges. Shown are the experimental data (red circles, blue squares, and black diamonds) with 1$\sigma$ uncertainties and the kinetic fits (solid lines). The lower panel shows the residuals; that is, the difference between the experimental values and the fit.

Fig. 5.

Experimental and calculated percent difference isotropic scattering patterns and molecular structures of DMP in the charge-localized 3sL and the charge-delocalized 3sD conformers. The experimental results (circles and diamonds) are extracted from the kinetics fit with 3$\sigma$ uncertainties and divided by the excitation fraction $\gamma$, determined from the fit. Calculated scattering patterns (solid lines) are for the experimentally determined optimal structural parameters with electronic contributions included. (Inset) Representative geometries of 3sL and 3sD.

Fig. 6.

Calculated percent difference scattering patterns caused by electronic structure changes, assuming 100% excitation. The 3sL (red solid line) and 3sD (blue solid line) curves are the electronic contribution difference between the charge-localized structure in the 3s and electronic ground states and between the charge-delocalized structure in the 3s and electronic ground states, respectively. The black dashed line shows the difference between the 3sD and 3sL curves. The inset shows calculated 3sL and 3sD Rydberg orbitals, respectively, rendered at 0.0005 Å^−3/2 isovalues.

Fig. 7.

Experimentally determined structural parameters for the Rydberg-excited charge-localized (left column) and charge-delocalized (right column) species, compared with computed values for the molecular ion and the molecular ground state. The black curve is the Gaussian function $e^{-\frac{1}{2}{\left(\frac{x-\mu }{\sigma }\right)}^2}$ . Here, $\mu$ is the experimentally determined interatomic distance in the 3s electronic state, averaged over symmetry-equivalent distances as listed in the left legend of each panel, and $\sigma$ is the error as listed in SI Appendix, Table S1 (propagated when there are several symmetry-equivalent distances). The red lines are distances calculated at the DMRG-CASSCF(19,20)/aug-cc-pVDZ level of theory for the ionic localized and ionic delocalized ground states (37). The blue lines are the ground-state structure distances calculated from CCSD/aug-cc-pVDZ reported by Cheng et al. (34). (Full interatomic distances and characteristic angles are given in SI Appendix, Table S1.)