The complete optical spectrum of liquid water measured by inelastic x-ray scattering

A complete dielectric response model for liquid water: a solution of the Bethe ridge problem

We present a complete yet computationally simple model for the dielectric response function of liquid water over the energy-momentum plane, which, in contrast to earlier models, is consistent with the recent inelastic X-ray scattering spectroscopy data at both zero and finite momentum transfer values. The model follows Ritchie's extended-Drude algorithm and is particularly effective at the region of the Bethe ridge, substantially improving previous models. The present development allows for a more accurate simulation of the inelastic scattering and energy deposition process of low-energy electrons in liquid water and other biomaterials. As an example, we calculate the stopping power of liquid water for electrons over the 0.1-10 keV range where direct experimental measurements are still impractical and the Bethe stopping formula is inaccurate. The new stopping power values are up to 30-40% lower than previous calculations. Within the range of validity of the first Born approximation, the new values are accurate to within the experimental uncertainties (a few percent). At the low end, the introduction of Born corrections raises the uncertainty to perhaps approximately 10%. Thus the present model helps extend the ICRU electron stopping power database for liquid water down to about two orders of magnitude with a comparable level of uncertainty.

The electronic structure of liquid water within density-functional theory

In the last decade, computational studies of liquid water have mostly concentrated on ground-state properties. However, recent spectroscopic measurements have been used to infer the structure of water, and the interpretation of optical and x-ray spectra requires accurate theoretical models of excited electronic states, not only of the ground state. To this end, we investigate the electronic properties of water at ambient conditions using ab initio density-functional theory within the generalized gradient approximation (DFT/GGA), focusing on the unoccupied subspace of Kohn-Sham eigenstates. We generate long (250 ps) classical trajectories for large supercells, up to 256 molecules, from which uncorrelated configurations of water molecules are extracted for use in DFT/GGA calculations of the electronic structure. We find that the density of occupied states of this molecular liquid is well described with 32-molecule supercells using a single k point (k=0) to approximate integration over the first Brillouin zone. However, the description of the unoccupied electronic density of states (u-EDOS) is sensitive to finite size effects. Small, 32-molecule supercell calculations, using the Gamma-point approximation, yield a spuriously isolated state above the Fermi level. Nevertheless, the more accurate u-EDOS of large, 256-molecule supercells may be reproduced using smaller supercells and increased k-point sampling. This indicates that the electronic structure of molecular liquids such as water is relatively insensitive to the long-range disorder in the molecular structure. These results have important implications for efficiently increasing the accuracy of spectral calculations for water and other molecular liquids.

The effect of model approximations on single-collision distributions of low-energy electrons in liquid water

The development of cross sections for the inelastic interaction of low-energy electrons with condensed tissue-like media is best accomplished within the framework of the dielectric theory. In this work we investigate the degree to which various model approximations, used in the above methodology, influence electron single-collision distributions. These distributions are of major importance to Monte Carlo track structure codes, namely, the energy-loss spectrum, the inelastic inverse mean free path, and the ionization efficiency. In particular, we make quantitative assessment of the influence of (1) the optical data set, (2) the dispersion algorithm, and (3) the perturbation and exchange Born corrections. It is shown that, although the shape and position of the energy-loss spectrum remains almost fixed, its peak height may vary by up to a factor of 1.5. Discrepancies in the calculated inelastic inverse mean free path are largely within 20-30% above 100 eV; they increase drastically, though, at lower energies. Exchange and perturbation Born corrections increase gradually below 1 keV leading to a approximately 30 to 40% reduction of the inverse mean free path at 100 eV. The perturbation effect contributes more than the exchange effect to this reduction. Similar to the dispersion situation, the effect of Born corrections at lower energies is also unclear since the models examined disagree strongly below 100 eV. In comparison, the vapor data are higher than the liquid calculations by 20 to 50% as the energy decreases from 1 to 0.1 keV, respectively. The excitation contribution is the main cause of this difference, since the ionization efficiency in the liquid levels off at approximately 90%, whereas the plateau value for the vapor is approximately 70%. It is concluded that electron inelastic distributions for liquid water, although in some respects distinctively different from the vapor phase, have associated uncertainties that are comparable in magnitude to the phase differences. The situation below 100 eV is uncertain.

Optical absorption of water: coulomb effects versus hydrogen bonding

The optical spectrum of water is not well understood. For example, the main absorption peak shifts upwards by 1.3 eV upon condensation, which is contrary to the behavior expected from aggregation-induced broadening of molecular levels. We investigate theoretically the effects of electron-electron and electron-hole correlations, finding that condensation leads to delocalization of the exciton onto nearby hydrogen-bonded molecules. This reduces its binding energy and has a dramatic impact on the line shape. The calculated spectrum is in excellent agreement with experiment.

Imaging density disturbances in water with a 41.3-attosecond time resolution

We show that the momentum flexibility of inelastic x-ray scattering may be exploited to invert its loss function, allowing real time imaging of density disturbances in a medium. We show the disturbance arising from a point source in liquid water, with a resolution of 41.3 attoseconds (4.13 x 10(-17) s) and 1.27 A (1.27 x 10(-8) cm). This result is used to determine the structure of the electron cloud around a photoexcited chromophore in solution, as well as the wake generated in water by a 9 MeV gold ion. We draw an analogy with pump-probe techniques and suggest that energy-loss scattering may be applied more generally to the study of attosecond phenomena.

Monte Carlo simulation of the energy loss of low-energy electrons in liquid water

A Monte Carlo code that performs detailed (i.e. event-by-event) simulation of the transport and energy loss of low-energy electrons (approximately 50-10 000 eV) in water in the liquid phase is presented. The inelastic model for energy loss is based on a semi-empirical dielectric-response function for the valence-shells of the liquid whereas an exchange corrected semi-classical formula was used for K-shell ionization. Following a methodology widely used for the vapour phase, we succeeded in parametrizing the dielectric cross-sections of the liquid in accordance with the Bethe asymptote, thus providing a unified approach for both phases of water and greatly facilitating the computations. Born-corrections at lower energies have been implemented in terms of a second-order perturbation term with a simple Coulomb-field correction and the use of a Mott-type exchange modification. Angular deflections were determined by empirical schemes established from vapour data. Electron tracks generated by the code were used to calculate energy- and interaction-point-kernel distributions at low electron energies in liquid water. The effect of various model assumptions (e.g., dispersion, Born-corrections, phase) on both the single-collision and slowing-down distributions is examined.

Hamaker Constants of Systems Involving Water Obtained from a Dielectric Function That Fulfills the f Sum Rule

Hamaker constants of systems involving liquid water are evaluated, within the full Lifshitz theory, by means of a recently proposed model of the dielectric function of this substance [Dingfelder et al., Radiat. Phys. Chem. 53, 1 (1998)], which has been extended in the present work by including terms corresponding to infrared excitations and microwave relaxation. An important feature of the complete model is that, besides a good fit to experimental data, it satisfies the physical constraint provided by the f sum rule. For symmetrical systems interacting across water, calculated Hamaker constants are generally in good agreement with results obtained using the Ninham-Parsegian representation with the Roth and Lenhoff parameters for water. Copyright 2000 Academic Press.