Imaging of transition charge densities involving carbon core excitations by all X-ray sum-frequency generation

X-ray diffraction signals from the time-evolving molecular charge density induced by selective core excitation of chemically inequivalent carbon atoms are calculated. A narrowband X-ray pulse selectively excites the carbon K-edge of the -CH ₃ or -CH ₂ F groups in fluoroethane (CH ₃ -CH ₂ F). Each excitation creates a distinct core coherence which depends on the character of the electronic transition. Direct propagation of the reduced single-electron density matrix, using real-time time-dependent density functional theory, provides the time-evolving charge density following interactions with external fields. The interplay between partially filled valence molecular orbitals upon core excitation induces characteristic femtosecond charge migration which depends on the core-valence coherence, and is monitored by the sum-frequency generation diffraction signal. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.