Search

The mean atomic kinetic energies of the proton, Ke(H), and of the deuteron, Ke(D), were calculated in moderate and strongly hydrogen bonded (HB) systems, such as the ferro-electric crystals of the KDP type (XH2PO4, X = K, Cs, Rb, Tl), the DKDP (XD2PO4, X = K, Cs, Rb) type, and the X3H(SO4)2 superprotonic conductors (X = K, Rb). All calculations utilized the simulated partial phonon density of states, deduced from density functional theory based first-principle calculations and from empirical lattice dynamics simulations in which the Coulomb, short range, covalent, and van der Waals interactions were accounted for. The presently calculated Ke(H) values for the two systems were found to be in excellent agreement with published values obtained by deep inelastic neutron scattering measurements carried out using the VESUVIO instrument of the Rutherford Laboratory, UK. The Ke(H) values of the M3H(SO4)2 compounds, in which the hydrogen bonds are centro-symmetric, are much lower than those of the KDP type crystals, in direct consistency with the oxygen-oxygen distance ROO, being a measure of the HB strength. [ABSTRACT FROM AUTHOR]

Reflection electron energy loss spectra from some insulating materials (CaCO3, Li2CO3, and SiO2) taken at relatively high incoming electron energies (5-40 keV) are analyzed. Here, one is bulk sensitive and a well-defined onset of inelastic excitations is observed from which one can infer the value of the band gap. An estimate of the band gap was obtained by fitting the spectra with a procedure that includes the recoil shift and recoil broadening affecting these measurements. The width of the elastic peak is directly connected to the mean kinetic energy of the atom in the material (Doppler broadening). The experimentally obtained mean kinetic energies of the O, C, Li, Ca, and Si atoms are compared with the calculated ones, and good agreement is found, especially if the effect of multiple scattering is taken into account. It is demonstrated experimentally that the onset of the inelastic excitation is also affected by Doppler broadening. Aided by this understanding, we can obtain a good fit of the elastic peak and the onset of inelastic excitations. For SiO2, good agreement is obtained with the well-established value of the band gap (8.9 eV) only if it is assumed that the intensity near the edge scales as (E - Egap)1.5. For CaCO3, the band gap obtained here (7 eV) is about 1 eV larger than the previous experimental value, whereas the value for Li2CO3 (7.5 eV) is the first experimental estimate. [ABSTRACT FROM AUTHOR]

• The mean kinetic energy of the proton, Ke(H), in nanoconfined supercooled water between 25 K and 300 K, is calculated semi-empirically. • The results nicely agree with DINS measurements. • The calculation coincides with that of bulk ice, indicating no evidence for the occurrence of the liquid-liquid transition along this T range. • We conclude that Ke(H) in ordinary H 2 O phases and in water nanoconfined in porous silica is nearly constant between 5 K to 295 K and is hence poorly sensitive to phase transitions of a thermodynamic nature in these systems. We calculated the effect of temperature on the mean kinetic energy of the protons, Ke(H), in supercooled water confined in nanoporous silica using a quantum harmonic semi-empirical model. The results are in very good agreement with recently published deep inelastic neutron scattering (DINS) measurements taken at 210 K and 250 K. The calculated T -effect between 5 K and 295 K was found to be practically the same as that previously calculated for bulk H 2 O. We emphasize in this connection that the measurement of the total (isotropic) Ke(H) using the DINS technique cannot be used for distinguishing the liquid-liquid phase transition in super cooled water confined in nanoporous silica. Nonetheless, the possible occurrence of such a transition may be explored by looking for quantum competing effects between the Cartesian components of Ke(H), along and perpendicular to the hydrogen bond direction. [ABSTRACT FROM AUTHOR]

Highlights • The Cartesian components of the partial vibrational density of states (p VDOS) of the protons and oxygen atom in light ice (Ih) are simulated for the first time by first principle modeling based on density functional theory (DFT). • The directional p VDOS are utilized for calculating the Cartesian components of the atomic kinetic energies, Ke(H) and Ke(O), along and perpendicular to the hydrogen bonds (HBs) in light ice (Ih). • The DFT method is found to yield better agreement with deep inelastic neutron scattering (DINS) measurements compared to semi empirical calculations. • The kinetic energy fractions shared by the proton in each mode of motion of H2O along and normal to the HBs in ice Ih are also resolved for the first time. • The present study emphasizes the potential of a p VDOS analysis as a powerful theoretical tool for studying nuclear energies, and in particular, resolving possible competing (CQEs) and nuclear (NQEs) quantum effects in HBs containing systems, e.g. as in ordinary H2O phases and in nanoconfined water. Abstract The partial vibrational density of states (p VDOS) of ice Ih, as simulated by first principle modeling based on density functional theory (DFT), is utilized for computing the Cartesian components of the proton and oxygen quantum kinetic energies, Ke(H) and Ke(O) respectively, along and perpendicular to the hydrogen bonds. The DFT method was found to yield better agreement with deep inelastic neutron scattering (DINS) measurements than the semi empirical (SE) calculations. The advantage of using the DFT method is to enable us to resolve the external and internal phonon bands of the Cartesian projections of the p VDOS, and hence those of the lattice and vibrational components of Ke(H). We show that a p VDOS analysis is a valuable tool in testing scattering results of complex systems and suggest its potential to explore competing quantum effects, e.g. on Ke(H) across phase transitions in water. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

The strong anisotropy of the proton mean kinetic energy, Ke(H), in a single crystal of KH 2 PO 4 (KDP), measured by deep inelastic neutron scattering (DINS), is compared with that calculated for its Cs analogue, CsH 2 PO 4 (CDP) in the ferroelectric (FE) and paraelectric (PE) phases. Empirical lattice dynamics (LD) calculations were used to simulate the partial vibrational density of states shared by the protons (H-VDOS), from which Ke(H) values were deduced. Good agreement was found between the measured and calculated Ke(H) values of the two samples despite the different hydrogen bond dynamics. However, the directional components of Ke(H) in the two samples were quite different. In both cases, the Ke(H) tensor is nearly an ellipsoid of rotation: in KDP the shape is oblate around the major axis while being prolate in CDP. By resolving the directional Ke(H) values of the two non-equivalent protons of CDP, a possible signature of competing quantum effects is indicated. [ABSTRACT FROM AUTHOR]

The proton mean kinetic energy Ke(H) in various systems was calculated between 5 and 320 K using a semi-empirical (SE) approach. The SE calculation relies on the harmonic approximation and decoupling between the various modes, where the input data of the internal and external frequencies were taken from inelastic neutron scattering (INS) and IR/Raman experiments. The studied systems included ordinary H2O phases, water of crystallisation in sulphate salts, adsorbed water and water confined in various samples of pore dimensions less than 20 Å. These included some zeolites, periodic mesoporous organosilicas (PMOs), beryl, Bikitaite and single- and double-wall carbon nanotubes. All SE calculated Ke(H) values were close to that of pure ice/liquid water, for which a good agreement was found with the deep inelastic neutron scattering (DINS) measurements. However, for water in Beryl at 5 K and ice in carbon nanotubes, at 170 K, large deviations from DINS results were found. Some insight into this problem may be gained by comparing those deviations with recently studied anharmonic systems involving proton double well potentials: Rb3H(SO4)2and KH2PO4, where an excellent agreement was obtained between SE calculations and DINS measurements. [ABSTRACT FROM AUTHOR]

High resolution electron compton scattering (ECS) is being used to study the atomic momentum distributions and hence the zero-point kinetic energies (ZPKE) of the scattering atoms. Such studies have shown that the scattering is from a single atom of the scattering sample. For an electron beam with a well defined incident energy, the scattered electron energy at any angle from each atomic species is Doppler broadened. The broadening reflects the atomic momentum distribution contributed by both the internal and external motions of the molecular system. By measuring the Doppler broadening of the scattered electron lines it was possible to determine the kinetic energy of the scattering atom including that of its zero-point motion. Thus, the atomic kinetic energies in gases such as H 2 , D 2 , HD, CH 4 and in H 2 O, D 2 O and NH 3 were measured and compared with those calculated semi-empirically using the measured optical infra red (IR) and Raman frequencies of the internal vibrations of the molecules. In general, good agreement between the measured and calculated values was found. Electron scattering was also used to study the ratio of e-scattering intensities from the H- and O-atoms in water (H 2 O), where some anomalies were reported to exist. [ABSTRACT FROM AUTHOR]

Highlights: [•] The proton kinetic energy in H2O was calculated between 5 and 673 K. [•] Input data were taken from IR, Raman and inelastic neutron frequencies. [•] A continuous behavior of the proton kinetic energy between 5 and 673 K was obtained. [ABSTRACT FROM AUTHOR]

[Display omitted] • The Normal Mode Analysis (NMA) of C- 60 and H 2 O in H 2 O@C 60 has been performed using DFT. • The internal frequencies of isolated H 2 O are altered by less than 1% when inserted into the C 60 fullerene. • The ZPKe(H) of the hydrogen bonds free encapsulated H 2 O assumes a value which resemble that of ice. • In contrast to anomalous Ke(H) values reported by DINS for other H 2 O confining systems, H 2 O@C 60 does not reveal a confinement effect on Ke(H). Using a density functional theory approach with the B3LYP and PBE0 functionals and the 6-G31(d,p) basic set, we simulate the partial vibrational spectra of isolated H 2 O and C 60 molecules, of a periodic H 2 O structure (ice XI) and of a single H 2 O molecule encaged in a buckyball (H 2 O@C 60). A very significant result of the H 2 O@C 60 calculation is that the C-atoms of the hosting fullerene lattice (which for pure C 60 are subjected to a vibrational frequency spectrum that terminates at ∼ 1600 cm−1) were found to participate in the high frequency modes at ∼ 3800 cm−1 of the H 2 O guest, indicating a coupling between the modes of the two sub systems. The effect of temperature between 5 and 300 K on the atomic kinetic energies, Ke(X) (X = C,O,H) were also deduced. The calculated Ke(C) in C 60 using B3LYP was found to be in better agreement with experiment than that of PBE0. Surprisingly, the zero point Ke(H) in the hydrogen bonds (HBs) free H 2 O@C 60 , as well as its T-dependence, were found to be nearly the same as those of the HBs containing condensed bulks of H 2 O, namely ice and liquid water. This result is at variance with that of other H 2 O confining systems measured using deep inelastic neutron scattering, where anomalous Ke(H) values were generically observed. An attempt to understand this behavior is made in view of the observed coupling between the caged H 2 O modes and those of the C 60 host. [ABSTRACT FROM AUTHOR]

We calculated the proton kinetic energies Ke(H) of ice under high pressures up to 63 GPa by assuming the harmonic approximation. The input measured optical frequencies of vibration, libration, and translation of ice VII versus pressure as well as the H2O geometry and the distances ROH necessary for calculating Ke(H) (at 298 K) were taken from the literature. The resulting Ke(H) values were found to decrease gradually with increasing pressure, approaching the region where the H-atom is symmetrically hydrogen bonded between two oxygens in the OH-O system. Interestingly, the Ke(H) results were found to be consistent with those of other materials such as Rb3H(PO4)2 and KH2PO4 having similar ROH and ROO distances in the OH-O system. Similar calculations were also carried out for D2O. [ABSTRACT FROM AUTHOR]

• The T-effect of the Oxygen kinetic energy, Ke(O), in silica hydrogel was DFT computed up to 325 K. • The results are higher by up to 40% than those measured by deep inelastic neutron scattering (DINS). • Subtraction of the SiO 2 contribution to the DINS values, results in negative Ke(O) of H 2 O. • This result is challenging as there is a need for more experiments to understand the huge deviation. The effect of temperature on the mean kinetic energy of Oxygen, Ke(O), in silica hydrogel (constituting of water confined in a silica Xerogel matrix) was computed between 5 and 325 K. The results are higher by up to 40% than those deduced from a recent deep inelastic neutron scattering (DINS) measurement. Note that when the mean kinetic energy of Hydrogen Ke(H) was computed using the same method a good agreement was obtained with the DINS measurement. This seems to indicate that the measured Ke(O) values are strongly underestimated due to the DINS method of analysis of the n-scattering intensities as discussed in the text. [ABSTRACT FROM AUTHOR]