Automated workflow for accurate scattering function calculation of light water using quantum corrections

Molecular dynamics analysis of incoherent neutron scattering from light water via the Van Hove space–time self-correlation function with a new quantum correction

In principle, given the potential energy function, the values of thermodynamic variables can be computed from statistical mechanics for a system of molecules. In practice for the liquid state, however, two barriers must be overcome. This paper treats the first problem, how to quantum correct the classical mechanical thermodynamic values available from molecular dynamics, Monte Carlo, perturbation, or integral methods in order to compare with experimental quantum reality. A subsequent paper will focus on the second difficulty, the effective computation of free energy and entropy. A simple technique, derived from spectral analysis of the atomic velocity time histories, is presented here for the frequency domain quantum correction of classical thermodynamic values. This technique is based on the approximation that potential anharmonicities mainly affect the lower frequencies in the velocity spectrum where the system behaves essentially classically, while the higher spectral frequencies, where the deviation from classical mechanics is most pronounced, involve sufficiently harmonic atomic motions that harmonic quantum corrections apply. Thus, a harmonic quantum correction can be applied at all frequencies: at low frequencies where it is inaccurate it will be small, while at high frequencies where it is large it will also be relatively accurate. The approach is demonstrated by computation of the energy and constant volume heat capacity for water from classical molecular dynamics followed by quantum correction. The potential used to describe the interactions of the system of water molecules includes internal vibrational degrees of freedom and thus strong quantum effects. Comparison of the quantum corrected theoretical values with experimental measurements shows good agreement. The quantum corrections to classical thermodynamics (which are also derived for free energy and entropy) are shown to be important not only for internal vibrational motion, but also for intermolecular hindered rotational and translational motions in liquid water. They are presumably also important for other strongly associated molecules, including bimolecules, and thus should be included when comparing calculated and measured thermodynamic quantities. The approach illustrated here allows the calculation of thermodynamic quantum corrections for liquids, solutions, and large molecules such as polymers (including proteins and nucleic acids) with full inclusion of both intra- and intermolecular degrees of freedom.

The isobaric heat capacity (Cp) is frequently used as a benchmark property whenever a new model is proposed or when comparing different force fields with classical molecular dynamics (MD) simulations. However, classical MD is not able to capture the quantum effects inherent in fluids and researchers have opted to apply quantum corrections in the post-processing when evaluating this property. Nevertheless, there is no consensus in the literature regarding the magnitude of quantum corrections for water, with reported values differing by up to a factor of 4. This term can account for up to one third of the Cp value and its erroneous prediction can lead to misleading conclusions. Therefore, we investigate different approaches to properly address quantum corrections when predicting Cp using classical MD. To accomplish this, the quantum correction methods proposed by Horn et al. and Berens et al. are considered, both of which use the single quantum harmonic oscillator approach but employ different strategies to address the frequency space. Two flexible polarizable water models are used in the evaluation, iAMOEBA and AMOEBA14. We show that the method of Berens et al. is a more robust approach to obtain the quantum corrections, as it accounts for all the frequency space by employing the vibrational spectra of the corresponding model under evaluation, making this approach a fully model-based method to determine Cp from MD. In addition, its capability of capturing the shift of low-frequency modes with temperature results in improved performance over the method of Horn et al.

Extensive inelastic-neutron-scattering experiments have been carried out on single crystals of $^{4}\mathrm{He}$ in the bcc and low-density hcp phases. The results of our present and previous measurements have established the over-all characteristics of the scattering function $S(Q,\ensuremath{\omega})$ for a wide range of energy and momentum transfers. The general features of the scattering function can be described as showing well-defined, sharp, elementary excitations at energy transfers $\ensuremath{\hbar}\ensuremath{\omega}l1.0$ meV, and single-particle excitations for scattering vectors $|Q|g3.0$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and $\ensuremath{\hbar}\ensuremath{\omega}g5.0$ meV. The changes in the structure of the scattering function to accommodate these two different excitations occur in an ill-defined transition region, wherein the spectral response of the sharp excitation gradually becomes more distorted and merges with the multiexcitation response at the higher energies. In the low-energy regime, the scattering cross section for sharp excitations observed in the [$0\overline{1}1$] zone for the bcc phase is found to be unusual in that the effective Debye-Waller factor constructed from the data via the Ambegaokar, Conway, and Baym sum rule displays oscillations. The data for the lowest transverse branch ${T}_{1}$, however, do not show oscillations. In our previous work, this anomalous cross section appeared to be associated with an energy transfer of \ensuremath{\sim} 1.4 meV, and a concomittant distortion in the Gaussian-like spectral response. The present results show that this is not the case. The unexpected behavior of the cross section was observed for sharp, symmetric excitations whose energy distribution has no extraordinary contribution near 1.4 meV. The measurements in the hcp phase show that these anomalous features of the scattering function are similar in both phases. The high-resolution measurements on the sharp excitations at small wave vector were used to construct a self-consistent set of elastic constants. These elastic constants are considerably more accurate than those from previous measurements. They suggest that the dispersion of the ${T}_{1}$ mode in the [011] direction need not be anomalous, in contrast to recent theoretical results. Finally, at high energy and momentum transfers, single-particle excitations are observed in both phases. Their dispersion relation is isotropic, and is the same in both phases within the accuracy of the measurements. The profiles of these excitations are very similar to those recently observed by Woods and Cowley in the superfluid phase.

Vibrational spectrum and entropy in simulation of melting

In contrast to the detailed understanding of inorganic materials, researchers lack a comprehensive view of how the properties of bulk organic materials arise from their individual components. For conjugated polymers to eventually serve as low cost semiconductor layers in electronic devices, researchers need to better understand their functionality. For organics, traditional materials science measurements tend to destroy the species of interest, especially at low concentrations. However, fluorescence continues to be a remarkably flexible, relatively noninvasive tool for probing the properties of individual molecules and allows researchers to carry out a broad range of experiments based on a relatively simple concept. In addition, the sensitivity of single-molecule spectroscopy allows researchers to see the properties of an individual component that would be masked in the bulk phase. In this Account, we examine several photophysical properties of different conjugated polymers using single-molecule spectroscopy. In these experiments, we probed the relationship between the conformation of single conjugated polymer chains and the distance scale and efficiency of energy transfer within the polymer. Recent studies used polarization anisotropy measurements on single polymer chains to study chain folding following spin-casting from solution. This Account summarizes the effects of monomer regioregularity and backbone rigidity, by comparing a regiorandom phenylene vinylene (MEH-PPV) with both a regiorandom and regioregular thiophene (P3HT). Synthesis of novel polymers allowed us to explore the role of different conformation-directing inclusions in a PPV backbone. We showed that these inclusions control the conformation of individual chains and that molecular dynamics can predict these structural effects. In situ solvent vapor annealing studies explored the dynamics of polymer chains as well as the effect of solvent evaporation on the structural equilibrium of the polymer. We observed that a slower rate of solvent evaporation results in a narrow population of highly ordered polymer chains. These highly ordered single chains serve as a model system to probe the effect of conformation on energy transfer following excitation in single MEH-PPV polymer chains in two distinct experiments. In the first, we correlated the anisotropy of the fluorescence emission of individual chains with the anisotropy of their fluorescence excitation. Using this data, we derived a model for energy transfer in a conjugated polymer, simulating chromophores along a chain, coupled via Förster energy transfer. In the second experiment, super-resolution measurements demonstrated the ability of single-molecule spectroscopy to directly visualize energy transfer along a polymer chain embedded in a model device environment. A capacitive device allowed for controlled localization of hole polarons onto the polymer chain. These positive charges subsequently quenched local excitations, providing insight into the range of energy transfer in these single polymer molecules. As researchers continue to characterize conjugated polymer films and develop methods for creating multichain systems, single-molecule techniques will provide a greater understanding of how polymer morphology influences interchain interactions and will lead to a richer description of the electronic properties of bulk conjugated polymer films.

Introduction Group IV alloy semiconductor material is anticipated to be used for the miniaturized thermoelectric (TE) energy harvester, because it has high TE properties, which is called ZT (= S 2 σTκ -1), is related to the Seebeck coefficient S, the electrical conductivity σ, the thermal conductivity κ, and the temperature T. In the previous study, it was indicated the drastically low thermal conductivity in group IV alloy is mainly caused by the mass disorder scattering of phonon [1]. The low thermal conductivity of group IV alloy was reproduced by our molecular dynamics (MD) simulations [2]. In classical MD simulation, it was considered the difference of the atomic mass and the interatomic potentials. Both mass and potential disorder scattering of phonon is deeply linked with the decreasing thermal conductivity. In this study, we quantitatively investigated which disorder is more affected to thermal conductivity in the group IV alloys whose atomic mass and interatomic potentials were varied independently by MD simulations to clarify. Simulation Procedure The models in MD simulation were 28Si x 73Si(1−x), 28Si x 119Si(1−x), 28Si x 28Ge(1−x), 28Si x 28Sn(1−x), 28Si x 73Ge(1−x), and 28Si x 119Sn(1−x) wire with periodic boundary condition. The initial model length and the one side width of square were 30ai and 4ai Å, respectively. The employed interatomic potential is the Stillinger-Weber (SW) potential, which is defined by the sum of two- and three-body potential energy terms that depend on local geometric positions. This potential was optimized to reproduce the lattice constant and the phonon frequencies in the group IV alloy [2]. The thermal conductivity was calculated by equilibrium MD method. The phonon related properties were conducted from the Fourier analysis. Results and Discussion Fig. 1 shows 28Si concentration dependences of thermal conductivities. Red lines represent results of 28Si x 73Si(1−x) and 28Si x 119Si(1−x) alloys, purple lines represent results of 28Si x 28Ge(1−x) and 28Si x 28Sn(1−x) alloys, blue lines represent results of 28Si x 73Ge(1−x), and orange lines represent calculation results from the research of Khatami et al. [1]. Fig. 2 shows the phonon dispersion of 28Si0.5 73Si0.5, 28Si0.5 28Ge0.5, and 28Si0.5 73Ge0.5 alloys. The changing of the thermal conductivities and the phonon dispersion is caused by mass and potential disorders. The amount of the changing by potential disorder is smaller than that of mass disorder. Fig. 3 shows frequency spectra of vibration density of states (VDOS) and phonon lifetimes in 28Si0.5 73Si0.5, 28Si0.5 28Ge0.5, and 28Si0.5 73Ge0.5 alloys. The VDOS D(ω) is closely related to the phonon lifetime due to alloying τalloy, which is defined as τalloy -1(ω) = (π/6)V 0Γalloy D(ω)ω 2, where V 0 is volume per atom, Γalloy is scattering strength due to the mass and potential disorders, and ω is phonon frequencies. The phonon lifetime in 28Si0.5 28Ge0.5 is almost ten times than that of 28Si0.5 73Si0.5 and 28Si0.5 73Ge0.5. The thermal conductivity is defined as κ(ω) = (1/3)C(ω)v 2(ω)τall(ω), and the phonon lifetime is defined as τall -1(ω) = τpure -1(ω) + τalloy -1(ω) = τpure -1(ω) + τmass -1(ω) + τforce -1(ω), where C is heat capacity, v is phonon velocity, τpure is phonon lifetime in pure crystal, τmass is mass disorder phonon lifetime, and τforce is potential disorder phonon lifetime [1]. When we assumed Cv 2 = 100, τpure = 1, τmass = 1/100, and τforce = 1/10, the thermal conductivity scattered by only potential disorder is 9.09, that scattered by only mass disorder is 0.99, and that scattered by both mass and potential disorder is 0.90. This tendency is agree to the results of MD calculation. The mass disorder is dominant factor for the changing of the thermal and phonon properties. Moreover, the potential disorder is ignorable in phonon and thermal calculation by MD method. Acknowledgements This study was partially supported by the Japan Science and Technology Agency’s (JST) CREST program (JPMJCR15Q7) and the Japan Society for the Promotion of Science (JSAP) through a Grant-in-Aid for JSPS Fellows (15J07583).

A method for calculating the vibrational densities of states of crystalline materials by use of molecular dynamics (MD) is presented. It consists mainly of starting the calculation with all atoms at rest in their equilibrium positions, except one which is given an initial velocity; the time evolution of this velocity is Fourier transformed to give the local vibrational density of states, and the procedure repeated for nonequivalent atoms in the lattice. It is shown with examples that the vibrational densities of states are unbiased and show very low noise and that calculations with this method require much fewer MD steps than those performed using standard random initializations.

Vibrational density of states of TiO2 nanoparticles

The quantum harmonic model and the two-phase thermodynamics method (2PT) are widely used to obtain quantum corrected properties such as isobaric heat capacities or molar entropies. 2PT heat capacities were calculated inconsistently in the literature. For water the classical heat capacity was also considered, but for organic liquids it was omitted. We reanalyzed the performance of different quantum corrections on the heat capacities of common organic solvents against experimental data. We have pointed out serious flaws in previous 2PT studies. The vibrational density of states was calculated incorrectly causing 39 % relative error in diffusion coefficients and 45 % error in the 2PT heat capacities. The wrong conversion of isobaric isochoric heat capacity also caused about 40 % error but in the other direction. We have introduced the concept of anharmonic correction (AC) which is simply the deviation of the classical heat capacity from that of the harmonic oscillator model. This anharmonic contribution is around +30-40 J/mol/K for water depending on the water model and -8-10 J/mol/K for hydrocarbons and halocarbons. AC is unrealistically large, +40 J/K/mol for alcohols and amines indicating some deficiency of the OPLS force field. The accuracy of the computations was also assessed with the determination of the self-diffusion coefficients.

An embedded ring approach to the vibrational dynamics of low-dimensional amorphous solids with applications to graphitic carbon materials

A very useful formula for interpolating the thermal neutron scattering law in temperature intervals is derived by separating the scattering law into two factors, strongly and weakly dependent on temperature. The strong temperature dependence of the scattering law is characterized by Debye-Waller factors, which are found to increase almost linearly with temperature for most moderators. The Debye-Waller factor is approximated by a linear function of temperature with the proportional constant determined so as to give the exact scattering laws at the boundaries of the temperature interval. Our formula is applied to two typical moderators (graphite and light water) to demonstrate its effectiveness and accuracy. It is shown that interpolated values of the scattering law are accurate within experimental errors in the practical range of momentum and energy transfers of neutrons.

A very useful formula for interpolating the thermal neutron scattering law in temperature intervals is derived by separating the scattering law into two factors, strongly and weakly dependent on temperature. The strong temperature dependence of the scattering law is characterized by Debye-Waller factors, which are found to increase almost linearly with temperature for most moderators. The Debye-Waller factor is approximated by a linear function of temperature with the proportional constant determined so as to give the exact scattering laws at the boundaries of the temperature interval. Our formula is applied to two typical moderators (graphite and light water) to demonstrate its effectiveness and accuracy. It is shown that interpolated values of the scattering law are accurate within experimental errors in the practical range of momentum and energy transfers of neutrons.

A molecular dynamics study on vibration spectra of a-SiO 2 surface

The vibrational lifetime of solute molecules is predicted to be slower at interfaces; however, ultrafast measurements show that this behavior can vary dramatically depending on interfacial structure and vibrational coupling pathways. Surprisingly, the nitrile stretch of SCN- exhibits unexpectedly rapid vibrational energy relaxation at aqueous (D2O) alumina interfaces, while there is no appreciable difference in relaxation in bulk and interfacial H2O. For interfacial D2O, the CN stretch lifetime is nearly three times shorter than in bulk D2O (T1 ∼ 22ps). Ab initio simulations reveal an increased vibrational density of states (VDOS) at the low frequency OD stretch region compared to bulk D2O, enhancing overlap between SCN- and D2O vibrational modes. Additional factors-including stronger transition dipole-transition dipole coupling arising from reduced dielectric screening and increased orientational ordering of interfacial molecules-further accelerate vibrational relaxation at the interface. To directly probe how interfacial VDOS varies with surface structure, we employed the CN stretch lifetime of SCN- as a reporter of the O-D VDOS at two model alumina surfaces: Al2O3(0001)/D2O and Al2O3(112¯0)/D2O. IR pump-vibrational sum frequency generation (vSFG) probe measurements show a shorter vibrational lifetime at the Al2O3(0001)/D2O interface (7.1ps) compared to the Al2O3(112¯0)/D2O interface (8.7ps). Molecular dynamics simulations support these findings, showing that the low-frequency O-D stretch VDOS at the Al2O3(0001)/D2O interface is approximately ∼1.2 times higher than at the Al2O3(112¯0)/D2O surface. The higher VDOS provides more available accepting states for vibrational energy transfer, thus shortening the vibrational lifetime. Together, these results demonstrate that vibrational lifetimes of interfacial solutes provide a powerful experimental probe of interfacial VDOS and solute-solvent coupling. This approach offers new insight into vibrational relaxation pathways and the microscopic origins of energy dissipation in the bulk and at interfaces.