Abstract
We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information through the transition charge densities (off-diagonal elements of the charge-density operator). Simulations are presented for the nonadiabatic harpooning process in the excited state of sodium fluoride.
Highlights
X-ray diffraction1–3 has been used for over a century to probe the structure of crystals and has been extended to diffuse scattering from liquids, probing nearest-neighbor distances, and serves as inspiration for the conceptually similar electron diffraction technique.4,5 Timeresolved X-ray diffraction (TRXD) can track the structural changes that characterize phase transitions and chemical reactions and has been actively pursued to create movies of elementary molecular events.5–18 Free electron lasers generate extremely bright and ultrafast X-ray pulses
We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei
That makes it possible to push diffraction to the single-molecule limit,19–24 eliminating the need for time-consuming crystal preparation. Their femtosecond timescale opens up the possibility of tracking ultrafast electronic dynamics, while their brightness may permit even weak signals, such as inelastic scattering from transient electronic coherences, to be measured
Summary
X-ray diffraction has been used for over a century to probe the structure of crystals and has been extended to diffuse scattering from liquids, probing nearest-neighbor distances, and serves as inspiration for the conceptually similar electron diffraction technique. Timeresolved X-ray diffraction (TRXD) can track the structural changes that characterize phase transitions and chemical reactions and has been actively pursued to create movies of elementary molecular events. Free electron lasers generate extremely bright and ultrafast X-ray pulses. That makes it possible to push diffraction to the single-molecule limit, eliminating the need for time-consuming crystal preparation Their femtosecond timescale opens up the possibility of tracking ultrafast electronic dynamics, while their brightness may permit even weak signals, such as inelastic scattering from transient electronic coherences, to be measured.. The charge-density matrix elements of each molecule only differ by the spatial phase factor associated with the location of the molecule and we may drop the subscript a on r We apply these results to a molecular model consisting of two electronic states e, g, and a single active nuclear coordinate R (Fig. 1). Where fa(q) is the atomic charge density of the ath atom in the molecule and /aðqÞ is its phase factor This widely used expression approximates term (i) in Eq (6) but does not account for inelastic scattering events and contributions due to electronic coherences. Our theory explicitly separates inelasticities, which are described by transition charge densities r^ijðqÞ (i 61⁄4 j) that interfere with ground and excited state terms r^iiðqÞ
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