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

Simulation of depth-dose curves and water equivalent ratios of energetic proton beams in cortical bone

We have determined the depth-dose curve, penetration range, and water equivalent ratio for proton beams of clinical energies in cortical bone by means of a detailed and accurate simulation that combines molecular dynamics and Monte Carlo techniques. The fundamental input quantities (stopping power and energy loss straggling) for the simulation were obtained from a reliable electronic excitation spectrum of the condensed-phase target, which takes into account the organic and mineral phases that form it. Our simulations with these inputs, which are in excellent agreement with the scarce data available for a cortical bone target, deviate from simulations performed using other stopping quantities, such as those provided by the International Commission on Radiation Units and Measurements in its widely used Report No. 49 [M. J. Berger et al., Stopping powers and ranges for protons and alpha particles, International Commission on Radiation Units and Measurements, Bethesda, Maryland, 1993]. The results of this paper emphasize the importance of an accurate determination of the stopping quantities of cortical bone to advance towards the millimetric precision for the proton penetration ranges and deposited dose needed in radiotherapy.

Many-body screening effects in liquid water

The screening arising from many-body excitations is a crucial quantity for describing absorption and inelastic X-ray scattering (IXS) of materials. Similarly, the electron screening plays a critical role in state-of-the-art approaches for determining the fundamental band gap. However, ab initio studies of the screening in liquid water have remained limited. Here, we use a combined analysis based on the Bethe-Salpeter equation and time-dependent density functional theory. We first show that absorption spectra at near-edge energies are insufficient to assess the accuracy by which the screening is described. Next, when the energy range under scrutiny is extended, we instead find that the IXS spectra are highly sensitive and allow for the selection of the optimal theoretical scheme. This leads to good agreement with experiment over a large range of transferred energies and momenta, and enables establishing the elusive fundamental band gap of liquid water at 9.3 eV.

Sub-keV corrections to binary encounter cross section models for electron ionization of liquid water with application to the Geant4-DNA Monte Carlo code

INTRODUCTION

The electron ionization cross section of water is one of the most important input in Monte Carlo studies of cellular radiobiological effects. Analytical cross section models of the binary-encounter type have the potential of reducing simulation time and facilitate application to a variety of biological materials (other than water). The Binary-Encounter-Bethe (BEB) and Binary-Encounter-Dipole (BED) models of NIST are perhaps the most popular of such models giving reliable results for atoms and molecules in the gas-phase over a wide energy range. However, the use of such models to sub-keV electron energies in liquid water raises concerns due to the neglect of condensed phase effects that leads to a significant overestimation when compared to medium-specific dielectric models.

PURPOSE

To modify the BEB and BED models towards better agreement with the recommended low-energy dielectric model of Geant4-DNA (Option 4). To implement the new modifications to the existing BEB model of the Option 6 physics constructor of Geant4-DNA and re-evaluate fundamental transport quantities for sub-keV electrons.

METHODS

In analogy to a Yukawa potential a simple, yet physically-motivated, modification of the Burgess correction term is proposed to account for the reduction of the Coulomb interaction due to the polarizability of the target. The magnitude of the correction is guided by the dielectric-based ionization cross section implemented in Option 4.

RESULTS

Differential, total and stopping ionization cross sections for low-energy electrons in liquid water are presented. When combined with the Vriens correction (which is not included in Option 6), the proposed modification to the BEB and BED models brings the ionization and stopping cross sections in much better agreement against those used in the Option 4 dielectric model of Geant4-DNA, with up to 30% and 10% deviation, respectively. Implementation of the new correction to the Option 6 constructor of Geant4-DNA and re-evaluation of fundamental transport quantities, such as electron penetration ranges and dose-point-kernels, reduced the discrepancies from Option 4 at sub-keV energies from 20 to 100% (or more) to well below 10% in most cases.

CONCLUSIONS

A simple modification to the BEB and BED analytic models was found to improve their performance for sub-keV electrons in liquid water medium. Implementation of the new modification to the Option 6 constructor of Geant4-DNA significantly improved the agreement with the recommended low-energy Option 4 constructor for a variety of fundamental quantities related to electron transport.

Intercomparison of nanodosimetric distributions in nitrogen simulated with Geant4 and PTra track structure codes

To facilitate the use of Geant4-DNA for radiation transport simulations in micro- and nanodosimeters, which are physically operated with tissue-equivalent gases such as nitrogen (and propane), this work aims to extend the cross section data available in Geant4-DNA to include those of nitrogen for electron energies ranging from 1 MeV down to the ionisation threshold. To achieve this, interaction cross section data for nitrogen that have been used with the in-house PTB PTra track structure code have been implemented in the current state-of-the-art Geant4-DNA simulation toolkit. An intercomparison has been performed between the two codes to validate this implementation. To quantify the agreement between the cross section models for nitrogen adopted in PTra and those implemented in Geant4-DNA, the simulation results of both codes were analysed using three physical parameters describing the ionisation cluster size distribution (ICSD): mean ionisation cluster size, variance of the cluster size and the probability to obtain a single ionisation within the target. Statistical analysis of the results indicates that the interaction cross section models for nitrogen used in PTra (elastic scattering, impact ionisations and electronic excitations) have been successfully implemented in Geant4-DNA. In addition, simulated ICSDs were compared to those measured with the Jet Counter nanodosimeter for energies between 100 and 2000 eV. For greater energies, the ICRP data for LET and particle range were used as a reference. The modified Geant4-DNA code and data successfully passed all these benchmarks fulfilling the requirement for their public release in the next version of the Geant4 toolkit.

Energy Deposition around Swift Carbon-Ion Tracks in Liquid Water

Energetic carbon ions are promising projectiles used for cancer radiotherapy. A thorough knowledge of how the energy of these ions is deposited in biological media (mainly composed of liquid water) is required. This can be attained by means of detailed computer simulations, both macroscopically (relevant for appropriately delivering the dose) and at the nanoscale (important for determining the inflicted radiobiological damage). The energy lost per unit path length (i.e., the so-called stopping power) of carbon ions is here theoretically calculated within the dielectric formalism from the excitation spectrum of liquid water obtained from two complementary approaches (one relying on an optical-data model and the other exclusively on ab initio calculations). In addition, the energy carried at the nanometre scale by the generated secondary electrons around the ion's path is simulated by means of a detailed Monte Carlo code. For this purpose, we use the ion and electron cross sections calculated by means of state-of-the art approaches suited to take into account the condensed-phase nature of the liquid water target. As a result of these simulations, the radial dose around the ion's path is obtained, as well as the distributions of clustered events in nanometric volumes similar to the dimensions of DNA convolutions, contributing to the biological damage for carbon ions in a wide energy range, covering from the plateau to the maximum of the Bragg peak.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Self-consistent dielectric functions of materials: Toward accurate computation of Casimir-van der Waals forces

Research on theoretical calculation of Casimir-van der Waals (vdW) forces is characterized by a great number of inconsistencies and conflicting reports with widely differing results for many known materials, including water, contradicting experimental measurements. Despite its importance for conceptual advances in both fundamental aspects and practical applications, a universal framework for the accurate determination of Casimir-vdW forces is lacking. Here, we propose a universal theoretical platform for computing Casimir-vdW forces, accounting for the electronic dielectric constant, optical bandgap, density, and chemical composition. Using this methodology, we determine the dielectric function for 55 materials, over a wide range of photon energies, covering an extensive list of common metals, organic and inorganic semiconductors, and insulators. Internal consistency of the compiled data is validated using optical sum rules and Kramers-Kronig relations. We demonstrate that the calculated vdW forces based on these data match remarkably well with the experimentally measured vdW forces.

Thermally activated delayed fluorescence: A critical assessment of environmental effects on the singlet-triplet energy gap

The effective design of dyes optimized for thermally activated delayed fluorescence (TADF) requires the precise control of two tiny energies: the singlet-triplet gap, which has to be maintained within thermal energy, and the strength of spin-orbit coupling. A subtle interplay among low-energy excited states having dominant charge-transfer and local character then governs TADF efficiency, making models for environmental effects both crucial and challenging. The main message of this paper is a warning to the community of chemists, physicists, and material scientists working in the field: the adiabatic approximation implicitly imposed to the treatment of fast environmental degrees of freedom in quantum-classical and continuum solvation models leads to uncontrolled results. Several approximation schemes were proposed to mitigate the issue, but we underline that the adiabatic approximation to fast solvation is inadequate and cannot be improved; rather, it must be abandoned in favor of an antiadiabatic approach.

Low-energy constraints on photoelectron spectra measured from liquid water and aqueous solutions

We report on the effects of electron collision and indirect ionization processes, occurring at photoexcitation and electron kinetic energies well below 30 eV, on the photoemission spectra of liquid water. We show that the nascent photoelectron spectrum and, hence, the inferred electron binding energy can only be accurately determined if electron energies are large enough that cross sections for quasi-elastic scattering processes, such as vibrational excitation, are negligible. Otherwise, quasi-elastic scattering leads to strong, down-to-few-meV kinetic energy scattering losses from the direct photoelectron features, which manifest in severely distorted intrinsic photoelectron peak shapes. The associated cross-over point from predominant (known) electronically inelastic to quasi-elastic scattering seems to arise at surprisingly large electron kinetic energies, of approximately 10-14 eV. Concomitantly, we present evidence for the onset of indirect, autoionization phenomena (occurring via superexcited states) within a few eV of the primary and secondary ionization thresholds. These processes are inferred to compete with the direct ionization channels and primarily produce low-energy photoelectrons at photon and electron impact excitation energies below ∼15 eV. Our results highlight that vibrational inelastic electron scattering processes and neutral photoexcitation and autoionization channels become increasingly important when photon and electron kinetic energies are decreased towards the ionization threshold. Correspondingly, we show that for neat water and aqueous solutions, great care must be taken when quantitatively analyzing photoelectron spectra measured too close to the ionization threshold. Such care is essential for the accurate determination of solvent and solute ionization energies as well as photoelectron branching ratios and peak magnitudes.

Relative Role of Physical Mechanisms on Complex Biodamage Induced by Carbon Irradiation

The effective use of swift ion beams in cancer treatment (known as hadrontherapy) as well as appropriate protection in manned space missions rely on the accurate understanding of the energy delivery to cells that damages their genetic information. The key ingredient characterizing the response of a medium to the perturbation induced by charged particles is its electronic excitation spectrum. By using linear-response time-dependent density functional theory, we obtained the energy and momentum transfer excitation spectrum (the energy-loss function, ELF) of liquid water (the main constituent of biological tissues), which was in excellent agreement with experimental data. The inelastic scattering cross sections obtained from this ELF, together with the elastic scattering cross sections derived by considering the condensed phase nature of the medium, were used to perform accurate Monte Carlo simulations of the energy deposited by swift carbon ions in liquid water and carried away by the generated secondary electrons, producing inelastic events such as ionization, excitation, and dissociative electron attachment (DEA). The latter are strongly correlated with cellular death, which is scored in sensitive volumes with the size of two DNA convolutions. The sizes of the clusters of damaging events for a wide range of carbon-ion energies, from those relevant to hadrontherapy up to those for cosmic radiation, predict with unprecedented statistical accuracy the nature and relative magnitude of the main inelastic processes contributing to radiation biodamage, confirming that ionization accounts for the vast majority of complex damage. DEA, typically regarded as a very relevant biodamage mechanism, surprisingly plays a minor role in carbon-ion induced clusters of harmful events.

Excitation and ionisation cross-sections in condensed-phase biomaterials by electrons down to very low energy: application to liquid water and genetic building blocks

A model is presented for computing electron-impact electronic excitation and ionisation cross-sections for arbitrary condensed-phase biomaterials in a wide energy range, showing a general good agreement with the available experimental data.

Ultrafast Dynamics of Water Radiolysis: Hydrated Electron Formation, Solvation, Recombination, and Scavenging

The ultrafast formation, solvation, and geminate recombination of hydrated electrons upon vacuum ultraviolet photoexcitation of liquid water and the static and dynamic scavenging by NO₃^- are investigated using femtosecond time-resolved photoelectron spectroscopy. The solvation time constant for excess electrons is typical of that for liquid water but increases slightly with increasing excitation energy. The electron survival probability for geminate recombination is found to be much lower than the literature values owing to previously unobserved ultrafast geminate recombination in a period of 5 ps. NO₃^- induces the ultrafast (static) scavenging of photoexcited electronic states of liquid water and the dynamic scavenging of detached electrons with a reaction rate that is dependent on the excitation energy. The formation of hydrated electrons at 7.7 eV is ascribed to a H-atom-transfer process, but it is plausible that additional formation channels open at higher energies.

Ink synthesis and inkjet printing of electrostatically stabilized multilayer graphene nanoshells

HYPOTHESIS

Most functional inkjet inks are sterically stabilized nanoparticle dispersions that require a post-printing-process to remove stabilizing materials and gain functionality. This post-process limits material selection and increases fabrication time and complexity for printed devices. By optimizing the electrostatic stability of a carbon nanomaterial dispersed in water or ethylene glycol via pH adjustment, a stable and printable ink should be attainable without a steric stabilizing material and hence the post-process may be avoided.

EXPERIMENTS

The electrostatic stability of multilayer graphene nanoshells (MGNS)-an inexpensive and net carbon-negative nanomaterial-dispersed in water and ethylene glycol was studied by measuring zeta potential as a function of pH and modeling energetic potentials between particles. Requirements for electrical percolation of printed MGNS were analyzed and corroborated with electrical measurements.

FINDINGS

Electrostatic stability improved with increased zeta potential caused by an increased pH. Ionic strength also increased with pH, causing strong destabilization. By increasing zeta potential while minimizing ionic strength, the maximum solid-loading of MGNS in DI water and ethylene glycol was increased up to 20%. For the MGNS solid-loading achieved here, electrical percolation occurs with 20-30 consecutively printed layers producing a resistivity of 30 Ω-cm. The inexpensive, environmentally-friendly MGNS are a promising material for printed, flexible electronics.

Electron Inelastic Mean Free Paths for LiF, CaF2, Al2O3, and Liquid Water from 433 keV down to the Energy Gap

We report new calculations, which include the influence of the band gap and exciton states, of the electron inelastic mean free path (IMFP) for liquid water, LiF, CaF₂, and Al₂O₃ from the band gap to 433 keV. Among compounds, liquid water is the most studied due to its role in radiobiological research, whereas LiF and CaF₂ are the most widely used thermoluminescent dosimeters in environmental monitoring and medical and space dosimetry. Due to its sensitivity, the optically stimulated luminescent dosimeter, Al₂O₃, has recently begun to be used for personnel monitoring. Previous treatments have modified the integration domain to consider the indistinguishability between the incident electron and the ejected one or the bandgap energy for nonconductors but not to accommodate exciton states within the band gap, and no published IMFP data are available for CaF₂. Our calculation was carried out using an electron-beam-solid-state interaction model through the relativistic full Penn algorithm. Integration limits that consider the band gap, the valence band width, and exciton interactions have been used. The results suggest that, at electron energies below 100 eV, the different choices of models for integration limits and the exciton interaction can affect the IMFP by 9-29%. At higher energies, the differences associated with the choice of energy-loss function and other input parameters are around 2.5-7.5%.

Intercomparison of dose enhancement ratio and secondary electron spectra for gold nanoparticles irradiated by X-rays calculated using multiple Monte Carlo simulation codes

PURPOSE

Targeted radiation therapy has seen an increased interest in the past decade. In vitro and in vivo experiments showed enhanced radiation doses due to gold nanoparticles (GNPs) to tumors in mice and demonstrated a high potential for clinical application. However, finding a functionalized molecular formulation for actively targeting GNPs in tumor cells is challenging. Furthermore, the enhanced energy deposition by secondary electrons around GNPs, particularly by short-ranged Auger electrons is difficult to measure. Computational models, such as Monte Carlo (MC) radiation transport codes, have been used to estimate the physical quantities and effects of GNPs. However, as these codes differ from one to another, the reliability of physical and dosimetric quantities needs to be established at cellular and molecular levels, so that the subsequent biological effects can be assessed quantitatively.

METHODS

In this work, irradiation of single GNPs of 50 nm and 100 nm diameter by X-ray spectra generated by 50 and 100 peak kilovoltages was simulated for a defined geometry setup, by applying multiple MC codes in the EURADOS framework.

RESULTS

The mean dose enhancement ratio of the first 10 nm-thick water shell around a 100 nm GNP ranges from 400 for 100 kVp X-rays to 600 for 50 kVp X-rays with large uncertainty factors up to 2.3.

CONCLUSIONS

It is concluded that the absolute dose enhancement effects have large uncertainties and need an inter-code intercomparison for a high quality assurance; relative properties may be a better measure until more experimental data is available to constrain the models.

Mechano-chemical stability and water effect on gas selectivity in mixed-metal zeolitic imidazolate frameworks: a systematic investigation from van der Waals corrected density functional theory

A series of Zn/Cu Zeolitic Imidazolate Frameworks (ZIFs) ZIF-202, -203, and -204 are systematically investigated by Density Functional Theory (DFT) with and without van der Waals (vdW) corrections.

A comparative study on Monte Carlo simulations of electron emission from liquid water

PURPOSE

Liquid water being the major constituent of the human body, is of fundamental importance in radiobiological research. Hence, the knowledge of electron-water interaction physics and particularly the secondary electron yield is essential. However, to date, only very little is known experimentally on the low energy electron interaction with liquid water because of certain practical limitations. The purpose of this study was to gain some useful information about electron emission from water using a Monte Carlo (MC) simulation technique that can numerically model electron transport trajectories in water.

METHODS

In this study, we have performed MC simulations of electron emission from liquid water in the primary energy range of 50 eV-30 keV by using two different codes, i.e., a classical trajectory MC (CMC) code developed in our laboratory and the Geant4-DNA (G4DNA) code. The calculated secondary electron yield and electron backscattering coefficient are compared with experimental results wherever applicable to verify the validity of physical models for the electron-water interaction.

RESULTS

The secondary electron yield vs. primary energy curves calculated using the two codes present the same generic curve shape as that of metals but in rather different absolute values. G4DNA underestimates the secondary electron yield due to the application of one step thermalization model by setting a cutoff energy at 10 eV so that the low energy losses due to phonon excitations are omitted. Our CMC code, using a full energy loss spectrum to model electron inelastic scattering, allows the simulation of individual phonon scattering events for very low energy losses down to 10 meV, which then enables the calculated secondary electron yields much closer to the experimental data and also gives quite reasonable energy distribution curve of secondary electrons.

CONCLUSIONS

It is concluded that full dielectric function data at low energy loss values below 10 eV are recommended for modeling of low energy electrons in liquid water.

Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy

The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.

Absolute Energy Levels of Liquid Water

We determine the ionization potential (IP) and the electron affinity (EA) of liquid water together with the absolute redox level of the standard hydrogen electrode (SHE) by combining advanced electronic-structure calculations, ab initio molecular dynamics simulations, thermodynamic integration, and potential alignment at the water-vacuum interface. The calculated SHE level lies at 4.56 eV below the vacuum level, close to the experimental reference of 4.44 eV inferred by Trasatti. The band edges are determined through a hybrid functional designed to reproduce the band gap achieved with highly accurate GW calculations. Our analysis yields IP = 9.7 eV and EA = 0.8 eV, consistent with both photoemission spectra of liquid water and thermodynamical data for the hydrated electron.

Probing ionization potential, electron affinity and self-energy effect on the spectral shape and exciton binding energy of quantum liquid water with self-consistent many-body perturbation theory and the Bethe-Salpeter equation

An accurate theoretical prediction of ionization potential (IP) and electron affinity (EA) is key in understanding complex photochemical processes in aqueous environments. There have been numerous efforts in literature to accurately predict IP and EA of liquid water, however with often conflicting results depending on the level of theory and the underlying water structures. In a recent study based on hybrid-non-self-consistent many-body perturbation theory (MBPT) Gaiduk et al (2018 Nat. Commun. 9 247) predicted an IP of 10.2 eV and EA of 0.2 eV, resulting in an electronic band gap (i.e. electronic gap (IP-EA) as measured by photoelectron spectroscopy) of about 10 eV, redefining the widely cited experimental gap of 8.7 eV in literature. In the present work, we show that GW self-consistency and an implicit vertex correction in MBPT considerably affect recently reported EA values by Gaiduk et al (2018 Nat. Commun. 9 247) by about 1 eV. Furthermore, the choice of pseudo-potential is critical for an accurate determination of the absolute band positions. Consequently, the self-consistent GW approach with an implicit vertex correction based on projector augmented wave (PAW) method on top of quantum water structures predicts an IP of 10.2, an EA of 1.1, a fundamental gap of 9.1 eV and an exciton binding (Eb) energy of 0.9 eV for the first absorption band of liquid water via the Bethe-Salpeter equation (BSE). Only within such a self-consistent approach a simultanously accurate prediction of IP, EA, Eg, Eb is possible.

Simple and universal model for electron-impact ionization of complex biomolecules

We present a simple and universal approach to calculate the total ionization cross section (TICS) for electron impact ionization in DNA bases and other biomaterials in the condensed phase. Evaluating the electron impact TICS plays a vital role in ion-beam radiobiology simulation at the cellular level, as secondary electrons are the main cause of DNA damage in particle cancer therapy. Our method is based on extending the dielectric formalism. The calculated results agree well with experimental data and show a good comparison with other theoretical calculations. This method only requires information of the chemical composition and density and an estimate of the mean binding energy to produce reasonably accurate TICS of complex biomolecules. Because of its simplicity and great predictive effectiveness, this method could be helpful in situations where the experimental TICS data are absent or scarce, such as in particle cancer therapy.

Low-energy electron inelastic mean free paths for liquid water

We improve the Mermin-Penn algorithm (MPA) for determining the energy loss function (ELF) within the dielectric formalism. The present algorithm is applicable not only to real metals, but also to materials that have an energy gap in the excitation spectrum. Applying the improved MPA to liquid water, we show that the present algorithm is able to address the ELF overestimation at the energy gap, and the calculated results are in good agreement with experimental data.

Mechanistic DNA damage simulations in Geant4-DNA part 1: A parameter study in a simplified geometry

Mechanistic modelling of DNA damage in Monte Carlo simulations is highly sensitive to the parameters that define DNA damage. In this work, we use a simple testing geometry to investigate how different choices of physics models and damage model parameters can change the estimation of DNA damage in a mechanistic DNA damage simulation built in Geant4-DNA. The choice of physics model can lead to variations by up to a factor of two in the yield of physically induced strand breaks, and the parameters that determine scavenging, and physical and chemical single strand break induction can have even larger consequences. Using low energy electrons as primary particles, a variety of parameters are tested in this geometry in order to arrive at a parameter set consistent with past simulation studies. We find that the modelling of scavenging can play an important role in determining results, and speculate that high-scavenging regimes, where only chemical radicals within 1 nm of DNA are simulated, could provide a good means of testing mechanistic DNA simulations.

A review on data and predictions of water dielectric spectra for calculations of van der Waals surface forces

Van der Waals forces are one of the important components of intermolecular, colloidal and surface forces governing many phenomena and processes. The latest examples include the colloidal interactions between hydrophobic colloids and interfaces in ambient (non-degassed) water in which dissolved gases and nanobubbles are shown to affect the van der Waals attractions significantly. The advanced computation of van der Waals forces in aqueous systems by the Lifshitz theory requires reliable data for water dielectric spectra. In this paper we review the available predictions of water dielectric spectra for calculating colloidal and surface van der Waals forces. Specifically, the available experimental data for the real and imaginary parts of the complex dielectric function of liquid water in the microwave, IR and UV regions and various corresponding predictions of the water spectra are critically reviewed. The data in the UV region are critical, but the available predictions are still based on the outdated data obtained in 1974 (for frequency only up to 25.5eV). We also reviewed and analysed the experimental data obtained for the UV region in 2000 (for frequency up to 50eV) and 2015 (for frequency up to 100eV). The 1974 and 2000 data require extrapolations to higher frequencies needed for calculating the van der Waals forces but remain inaccurate. Our analysis shows that the latest data of 2015 do not require the extrapolation and can be used to reliably calculate van der Waals forces. The most recent water dielectric spectra gives the (non-retarded) Hamaker constant, A=5.20×10^-20J, for foam films of liquid water. This review provides the most updated and reliable water dielectric spectra to compute van der Waals forces in aqueous systems.

Monte Carlo Electron Track Structure Calculations in Liquid Water Using a New Model Dielectric Response Function

Monte Carlo track structure codes provide valuable information for understanding radiation effects down to the DNA level, where experimental measurements are most difficult or unavailable. It is well recognized that the performance of such codes, especially at low energies and/or subcellular level, critically depends on the reliability of the interaction cross sections that are used as input in the simulation. For biological media such as liquid water, one of the most challenging issues is the role of condensed-phase effects. For inelastic scattering, such effects can be conveniently accounted for through the complex dielectric response function of the media. However, for this function to be useful it must fulfill some important sum rules and have a simple analytic form for arbitrary energy- and momentum-transfer. The Emfietzoglou-Cucinotta-Nikjoo (ECN) model offers a practical, self-consistent and fully analytic parameterization of the dielectric function of liquid water based on the best available experimental data. An important feature of the ECN model is that it includes, in a phenomenological manner, exchange and correlation effects among the screening electrons, thus, going beyond the random-phase approximation implicit in earlier models. In this work, inelastic cross sections beyond the plane wave Born approximation are calculated for low-energy electrons (10 eV-10 keV) based on the ECN model, and used for Monte Carlo track structure simulations of physical quantities relevant to the microdosimetry of low-energy electrons in liquid water. Important new developments in the physics of inelastic scattering are discussed and their effect on electron track structure is investigated by a comparison against simulations (under otherwise identical conditions) using the Born approximation and a simpler form of the dielectric function based on the Oak Ridge National Laboratory model. The results reveal that both the dielectric function and the corrections to the Born approximation may have a sizeable effect on track structure calculations at the nanometer scale (DNA level), where the details of inelastic scattering and the role of low-energy electrons are most critical.

Vacuum ultraviolet spectroscopy of the lowest-lying electronic state in subcritical and supercritical water

The nature and extent of hydrogen bonding in water has been scrutinized for decades, including how it manifests in optical properties. Here we report vacuum ultraviolet absorption spectra for the lowest-lying electronic state of subcritical and supercritical water. For subcritical water, the spectrum redshifts considerably with increasing temperature, demonstrating the gradual breakdown of the hydrogen-bond network. Tuning the density at 381 °C gives insight into the extent of hydrogen bonding in supercritical water. The known gas-phase spectrum, including its vibronic structure, is duplicated in the low-density limit. With increasing density, the spectrum blueshifts and the vibronic structure is quenched as the water monomer becomes electronically perturbed. Fits to the supercritical water spectra demonstrate consistency with dimer/trimer fractions calculated from the water virial equation of state and equilibrium constants. Using the known water dimer interaction potential, we estimate the critical distance between molecules (ca. 4.5 Å) needed to explain the vibronic structure quenching.

The link between hydrogen bonding and the optical properties of water has been debated for many years, but not fully understood. Here, the authors report vacuum ultraviolet absorption spectra for subcritical and supercritical water, providing insight into the electronic structure of water and its relation to hydrogen bonding.

Calculations of Electron Inelastic Mean Free Paths. XI. Data for Liquid Water for Energies from 50 eV to 30 keV

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy-loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm (FPA) that has been used for previous IMFP and electron stopping-power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single-pole approximation (SPA), the relativistic simplified SPA, and the relativistic extended Mermin method. These calculations were made using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP-2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the FPA. The resulting values were in good agreement with results from first-principles calculations and with inelastic X-ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length (EAL). There were large variations in the measured IMFPs and EALs (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs.

Calculation on spectrum of direct DNA damage induced by low-energy electrons including dissociative electron attachment

In this work, direct DNA damage induced by low-energy electrons (sub-keV) is simulated using a Monte Carlo method. The characteristics of the present simulation are to consider the new mechanism of DNA damage due to dissociative electron attachment (DEA) and to allow determining damage to specific bases (i.e., adenine, thymine, guanine, or cytosine). The electron track structure in liquid water is generated, based on the dielectric response model for describing electron inelastic scattering and on a free-parameter theoretical model and the NIST database for calculating electron elastic scattering. Ionization cross sections of DNA bases are used to generate base radicals, and available DEA cross sections of DNA components are applied for determining DNA-strand breaks and base damage induced by sub-ionization electrons. The electron elastic scattering from DNA components is simulated using cross sections from different theoretical calculations. The resulting yields of various strand breaks and base damage in cellular environment are given. Especially, the contributions of sub-ionization electrons to various strand breaks and base damage are quantitatively presented, and the correlation between complex clustered DNA damage and the corresponding damaged bases is explored. This work shows that the contribution of sub-ionization electrons to strand breaks is substantial, up to about 40-70%, and this contribution is mainly focused on single-strand break. In addition, the base damage induced by sub-ionization electrons contributes to about 20-40% of the total base damage, and there is an evident correlation between single-strand break and damaged base pair A-T.

Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach

We have implemented the polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

Electronic Excitation Dynamics in Liquid Water under Proton Irradiation

Molecular behaviour of liquid water under proton irradiation is of great importance to a number of technological and medical applications. The highly energetic proton generates a time-varying field that is highly localized and heterogeneous at the molecular scale, and massive electronic excitations are produced as a result of the field-matter interaction. Using first-principles quantum dynamics simulations, we reveal details of how electrons are dynamically excited through non-equilibrium energy transfer from highly energetic protons in liquid water on the atto/femto-second time scale. Water molecules along the path of the energetic proton undergo ionization at individual molecular level, and the excitation primarily derives from lone pair electrons on the oxygen atom of water molecules. A reduced charge state on the energetic proton in the condensed phase of water results in the strongly suppressed electronic response when compared to water molecules in the gas phase. These molecular-level findings provide important insights into understanding the water radiolysis process under proton irradiation.

Radiation track, DNA damage and response-a review

The purpose of this paper has been to review the current status and progress of the field of radiation biophysics, and draw attention to the fact that physics, in general, and radiation physics in particular, with the aid of mathematical modeling, can help elucidate biological mechanisms and cancer therapies. We hypothesize that concepts of condensed-matter physics along with the new genomic knowledge and technologies and mechanistic mathematical modeling in conjunction with advances in experimental DNA (Deoxyrinonucleic acid molecule) repair and cell signaling have now provided us with unprecedented opportunities in radiation biophysics to address problems in targeted cancer therapy, and genetic risk estimation in humans. Obviously, one is not dealing with 'low-hanging fruit', but it will be a major scientific achievement if it becomes possible to state, in another decade or so, that we can link mechanistically the stages between the initial radiation-induced DNA damage; in particular, at doses of radiation less than 2 Gy and with structural changes in genomic DNA as a precursor to cell inactivation and/or mutations leading to genetic diseases. The paper presents recent development in the physics of radiation track structure contained in the computer code system KURBUC, in particular for low-energy electrons in the condensed phase of water for which we provide a comprehensive discussion of the dielectric response function approach. The state-of-the-art in the simulation of proton and carbon ion tracks in the Bragg peak region is also presented. The paper presents a critical discussion of the models used for elastic scattering, and the validity of the trajectory approach in low-electron transport. Brief discussions of mechanistic and quantitative aspects of microdosimetry, DNA damage and DNA repair are also included as developed by the authors' work.

Technical Note: Improvements in geant4 energy-loss model and the effect on low-energy electron transport in liquid water

PURPOSE

The geant4-DNA physics models are upgraded by a more accurate set of electron cross sections for ionization and excitation in liquid water. The impact of the new developments on low-energy electron transport simulations by the geant4 Monte Carlo toolkit is examined for improving its performance in dosimetry applications at the subcellular and nanometer level.

METHODS

The authors provide an algorithm for an improved implementation of the Emfietzoglou model dielectric response function of liquid water used in the geant4-DNA existing model. The algorithm redistributes the imaginary part of the dielectric function to ensure a physically motivated behavior at the binding energies, while retaining all the advantages of the original formulation, e.g., the analytic properties and the fulfillment of the f-sum-rule. In addition, refinements in the exchange and perturbation corrections to the Born approximation used in the geant4-DNA existing model are also made.

RESULTS

The new ionization and excitation cross sections are significantly different from those of the geant4-DNA existing model. In particular, excitations are strongly enhanced relative to ionizations, resulting in higher W-values and less diffusive dose-point-kernels at sub-keV electron energies.

CONCLUSIONS

An improved energy-loss model for the excitation and ionization of liquid water by low-energy electrons has been implemented in geant4-DNA. The suspiciously low W-values and the unphysical long tail in the dose-point-kernel have been corrected owing to a different partitioning of the dielectric function.

The realization of the dipole (γ, γ) method and its application to determine the absolute optical oscillator strengths of helium

The dipole (γ, γ) method, which is the inelastic x-ray scattering operated at a negligibly small momentum transfer, is proposed and realized to determine the absolute optical oscillator strengths of the vanlence-shell excitations of atoms and molecules. Compared with the conventionally used photoabsorption method, this new method is free from the line saturation effect, which can seriously limit the accuracies of the measured photoabsorption cross sections for discrete transitions with narrow natural linewidths. Furthermore, the Bethe-Born conversion factor of the dipole (γ, γ) method varies much more slowly with the excitation energy than does that of the dipole (e, e) method. Absolute optical oscillator strengths for the excitations of 1s² → 1 snp(n = 3 − 7) of atomic helium have been determined using the high-resolution dipole (γ, γ) method, and the excellent agreement of the present measurements with both those measured by the dipole (e, e) method and the previous theoretical calculations indicates that the dipole (γ, γ) method is a powerful tool to measure the absolute optical oscillator strengths of the valence-shell excitations of atoms and molecules.

Advances in Computational Radiation Biophysics for Cancer Therapy: Simulating Nano-Scale Damage by Low-Energy Electrons

Computational radiation biophysics is a rapidly growing area that is contributing, alongside new hardware technologies, to ongoing developments in cancer imaging and therapy. Recent advances in theoretical and computational modeling have enabled the simulation of discrete, event-by-event interactions of very low energy (≪ 100 eV) electrons with water in its liquid thermodynamic phase. This represents a significant advance in our ability to investigate the initial stages of radiation induced biological damage at the molecular level. Such studies are important for the development of novel cancer treatment strategies, an example of which is given by microbeam radiation therapy (MRT). Here, new results are shown demonstrating that when excitations and ionizations are resolved down to nano-scales, their distribution extends well outside the primary microbeam path, into regions that are not directly irradiated. This suggests that radiation dose alone is insufficient to fully quantify biological damage. These results also suggest that the radiation cross-fire may be an important clue to understanding the different observed responses of healthy cells and tumor cells to MRT.

Accurate Measurements of Dielectric and Optical Functions of Liquid Water and Liquid Benzene in the VUV Region (1-100 eV) Using Small-Angle Inelastic X-ray Scattering

Using a third-generation synchrotron source (the BL12XU beamline at SPring-8), inelastic X-ray scattering (IXS) spectra of liquid water and liquid benzene were measured at energy losses of 1-100 eV with 0.24 eV resolution for small momentum transfers (q) of 0.23 and 0.32 au with ±0.06 au uncertainty for q. For both liquids, the IXS profiles at these values of q converged well after we corrected for multiple scattering, and these results confirmed the dipole approximation for q ≤ ∼0.3 au. Several dielectric and optical functions [including the optical oscillator strength distribution (OOS), the optical energy-loss function (OLF), the complex dielectric function, the complex index of refraction, and the reflectance] in the vacuum ultraviolet region were derived and tabulated from these small-angle (small q) IXS spectra. These new data were compared with previously obtained results, and this comparison demonstrated the strong reproducibility and accuracy of IXS spectroscopy. For both water and benzene, there was a notable similarity between the OOSs of the liquids and amorphous solids, and there was no evidence of plasmon excitation in the OLF. The static structure factor [S(q)] for q ≤ ∼0.3 au was also deduced and suggests that molecular models that include electron correlation effects can serve as a good approximation for the liquid S(q) values over the full range of q.

Angular and energy distributions of electrons produced in arbitrary biomaterials by proton impact

We present a simple method for obtaining reliable angular and energy distributions of electrons ejected from arbitrary condensed biomaterials by proton impact. Relying on a suitable description of the electronic excitation spectrum and a physically motivated relation between the ion and electron scattering angles, it yields cross sections in rather good agreement with experimental data in a broad range of ejection angles and energies, by only using as input the target composition and density. The versatility and simplicity of the method, which can be also extended to other charged particles, make it especially suited for obtaining ionization data for any complex biomaterial present in realistic cellular environments.

Future development of biologically relevant dosimetry

Proton and ion beams are radiotherapy modalities of increasing importance and interest. Because of the different biological dose response of these radiations as compared with high-energy photon beams, the current approach of treatment prescription is based on the product of the absorbed dose to water and a biological weighting factor, but this is found to be insufficient for providing a generic method to quantify the biological outcome of radiation. It is therefore suggested to define new dosimetric quantities that allow a transparent separation of the physical processes from the biological ones. Given the complexity of the initiation and occurrence of biological processes on various time and length scales, and given that neither microdosimetry nor nanodosimetry on their own can fully describe the biological effects as a function of the distribution of energy deposition or ionization, a multiscale approach is needed to lay the foundation for the aforementioned new physical quantities relating track structure to relative biological effectiveness in proton and ion beam therapy. This article reviews the state-of-the-art microdosimetry, nanodosimetry, track structure simulations, quantification of reactive species, reference radiobiological data, cross-section data and multiscale models of biological response in the context of realizing the new quantities. It also introduces the European metrology project, Biologically Weighted Quantities in Radiotherapy, which aims to investigate the feasibility of establishing a multiscale model as the basis of the new quantities. A tentative generic expression of how the weighting of physical quantities at different length scales could be carried out is presented.

Effective attenuation length of an electron in liquid water between 10 and 600 eV

The absolute values of the effective attenuation length of an electron in liquid water are determined using soft x-ray O1s photoemission spectroscopy of a liquid beam of water without employing any theoretical estimation or computationally obtained value. The effective attenuation length is greater than 1 nm in the entire electron kinetic energy region and exhibits very flat energy dependence in the 10-100 eV region.