Abstract
Nonlinear all-X-ray signals that involve large core-atom separation compared to the X-ray wavelengths may not be described by the dipole approximation since they contain additional phase factors. Expressions for the rotationally averaged 2D X-ray photon echo signals from randomly oriented systems that take this position-dependent phase into account for arbitrary ratio between the core separation and the resonant wavelength are presented. Application is made to the Se K-edge of a selenium dipeptide system.
Highlights
Nonlinear spectroscopy has been widely applied to excitonic systems spanning the vibrational[1,2] and electronic[3,4,5] response of chromophores in biological[6,7] and engineered[8] systems
X-ray free electron laser[9] sources strong enough to enable nonlinear processes[10,11] promise to extend these studies to core-excitons in molecules. These short, high-frequency pulses can probe the molecule on the time-scale of the attosecond period of the core-excitation and on the lengthscale of the spatial extent of the resonant core orbital
For homonuclear experiments with variable wave vectors, the spatial phases corresponding to the core positions have to be taken into account
Summary
Nonlinear spectroscopy has been widely applied to excitonic systems spanning the vibrational[1,2] and electronic[3,4,5] response of chromophores in biological[6,7] and engineered[8] systems. We consider experiments that are analogs of optical spectroscopy in molecular aggregates, with the molecular chromophores replaced by atomic core orbitals resonant with the X-ray frequencies of the applied fields They contain terms with transitions resonant with separate cores on a molecule, and phases that depend on the distance between these cores. This has been widely applied to calculate the nonlinear response of systems of vibrational[18] and electronic[4] excitations. Andrews et al first derived expressions for the fourth order isotropic tensor[17] used for calculating the four-wave mixing signal They subsequently considered a “phased” rotational averaging tensor, including an exponential containing a dot product between vectors in the molecular and laboratory frames.[19].
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