Model for the dynamics of a water cluster in an x-ray free electron laser beam

A microscopic sample placed into a focused x-ray free electron laser beam will explode due to strong ionization on a femtosecond time scale. The dynamics of this Coulomb explosion has been modeled by Neutze et al. [Nature (London) 406, 752 (2000)] for a protein, using computer simulations. The results suggest that by using ultrashort exposures, structural information may be collected before the sample is destroyed due to radiation damage. In this paper a method is presented to include the effect of screening by free electrons in the sample in a molecular dynamics simulation. The electrons are approximated by a classical gas, and the electron distribution is calculated iteratively from the Poisson-Boltzmann equation. Test simulations of water clusters reveal the details of the explosion dynamics, as well as the evolution of the free electron gas during the beam exposure. We find that inclusion of the electron gas in the model slows down the Coulomb explosion. The hydrogen atoms leave the sample faster than the oxygen atoms, leading to a double layer of positive ions. A considerable electron density is located between these two layers. The fact that the hydrogens are found to explode much faster than the oxygens means that the diffracting part of the sample stays intact somewhat longer than the sample as a whole.

Figure 1

Scheme of iteration for the electrostatic potential.

Figure 2

(Color) Top: isometric plot of the electron distribution at (a) the beginning of the pulse $(-10\mathrm{fs})$, (b) the peak of the pulse, and (c) the end of the pulse $\left(15\mathrm{fs}\right)$ for a water cluster of $100\text{molecules}$. Bottom: snapshots of the atomic structure at $-10$, 0, and $15\mathrm{fs}$. Red: oxygen. White: hydrogen.

Figure 3

Evolution of potential (E-pot) and kinetic (E-kin) energy for the atoms and ions for the two different cluster sizes, with and without electron screening. The pulse has a FWHM of $14.1\mathrm{fs}$ and an intensity of ${10}^{12}\text{photons}∕\text{pulse}∕100\mathrm{nm}$, with the peak at time $t=0\mathrm{fs}$.

Figure 4

Evolution of the change in radius of gyration for the two different cluster sizes of water molecules, with and without electron screening. The figure also shows the change in radius of gyration for the oxygen atoms separately, with screening.

Figure 5

Time evolution of the integrated number of electrons per molecule for the two cluster sizes: photoelectrons, Auger electrons, and their secondary electrons produced through inelastic scattering. The pulse has a FWHM of $14.1\mathrm{fs}$ and an intensity of ${10}^{12}\text{photons}∕\text{pulse}∕100\mathrm{nm}$, with the peak at time $t=0\mathrm{fs}$.

Figure 6

(Color) Top: averaged radial ionic charge density from the center of each cluster of water molecules as a function of time. As the clusters are ionized, the ionic charge density accumulates at first and then decreases as the cluster expands. The ionic expansion is mostly due to hydrogen atoms, which can be seen as a shell propagating ahead of the oxygen ions. The hydrogen atoms are ejected a bit later in the larger cluster, but more violently. Bottom: averaged radial electron charge density from the center of each cluster of water molecules as a function of time. In the smaller cluster the electron density rises to a maximum at $t=0$ after which it decreases slightly as the atoms expand radially. In the larger cluster the electrostatic potential becomes higher, and the hydrogen atoms are pushed out more violently, followed by a spherical wave of electrons.