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We have investigated nonlinear processes in small molecules by x-ray photoelectron spectroscopy using the Linac Coherent Light Source free electron laser, and by simulations. The main focus of the experiments was the formation of the two-site double core-hole (tsDCH) states in the molecules CO2, N2O and N-2. These experiments are described in detail and the results are compared with simulations of the photoelectron spectra. The double core-hole states, and in particular the tsDCH states, have been predicted to be highly sensitive to the chemical environment. The theory behind this chemical sensitivity is validated by the experiments. Furthermore, our simulations of the relative integrated intensities of the peaks associated with the nonlinear processes show that this type of simulation, in combination with experimental data, provides a useful tool for estimating the duration of ultra-short x-ray pulses

Double core-hole formation in small molecules at the LCLS free electron laser