Velocity-velocity Correlation Function Research Articles

Revealing the molecular structures of α-Al2O3(0001)-water interface by machine learning based computational vibrational spectroscopy.

Solid-water interfaces are crucial to many physical and chemical processes and are extensively studied using surface-specific sum-frequency generation (SFG) spectroscopy. To establish clear correlations between specific spectral signatures and distinct interfacial water structures, theoretical calculations using molecular dynamics (MD) simulations are required. These MD simulations typically need relatively long trajectories (a few nanoseconds) to achieve reliable SFG response function calculations via the dipole moment-polarizability time correlation function. However, the requirement for long trajectories limits the use of computationally expensive techniques, such as abinitio MD (AIMD) simulations, particularly for complex solid-water interfaces. In this work, we present a pathway for calculating vibrational spectra (IR, Raman, and SFG) of solid-water interfaces using machine learning (ML)-accelerated methods. We employ both the dipole moment-polarizability correlation function and the surface-specific velocity-velocity correlation function approaches to calculate SFG spectra. Our results demonstrate the successful acceleration of AIMD simulations and the calculation of SFG spectra using ML methods. This advancement provides an opportunity to calculate SFG spectra for complicated solid-water systems more rapidly and at a lower computational cost with the aid of ML.

Modeling Vibrational Sum Frequency Generation Spectra of Interfacial Water on a Gold Surface: The Role of the Fermi Resonance.

Studying the hydrogen bonding structure of H2O at the metal-water interface is a highly complex yet fascinating endeavor. The intricate interactions and diverse orientations of water molecules on metal surfaces with varying potentials pose a significant challenge in elucidating the coupling between O-H stretching and H-O-H bending modes. In this study, we employed DFT-MD simulation to explore how the orientation of interfacial water molecules changes with the applied potential on the Au(111) surface. Based on the surface-specific velocity-velocity correlation function (ssVVCF) formula, we calculated vibrational sum frequency generation (VSFG) spectra for the O-H stretches. We found that three assigned peaks (∼3300, ∼3450, and 3650 cm-1) shifted toward lower frequencies as the potential moved toward more negative values. Our results align remarkably well with experimental Raman spectroscopy data. Notably, our VSFG analysis revealed a significant change in the VSFG spectra of the hydrogen-bonded O-H groups (∼3300 cm-1), switching from a negative to a positive sign with decreasing potential. This alteration suggests a substantial change in the orientation of these low-frequency O-H groups owing to their increased interactions with the Au surface. In contrast, the orientations of both the high-frequency O-H groups (∼3450 cm-1) and the dangling O-H groups (∼3650 cm-1) remained unaffected by the applied potentials. Furthermore, our analysis of the decomposed vibrational density of states (VDOS) for the H-O-H bending mode uncovered the coupling between the H-O-H bending and O-H stretching vibrations, known as the Fermi resonance. Our work suggests that the H-O-H bending vibration becomes restricted when water molecules transition from the ″one-H-down″ to the ″two-H-down″ conformation, leading to a redshift in the O-H stretching vibration through the Fermi resonance. By constructing the VSFG and decomposed VDOS spectra, we gained valuable insights into the structural changes that Raman spectra alone cannot fully interpret. Specifically, our analysis revealed the critical role of the Fermi resonance effect in shaping the spectroscopic signature of interfacial water molecules on the Au(111) surface.

Breakdown of phonon band theory in MgO

We present a series of detailed images of the distribution of kinetic energy among frequencies and wave vectors in the bulk of an MgO crystal as it is heated slowly until it melts. These spectra, which are Fourier transforms of mass-weighted velocity-velocity correlation functions calculated from accurate molecular dynamics (MD) simulations, provide a valuable perspective on the growth of thermal disorder in ionic crystals. We use them to explain why the most striking and rapidly progressing departures from a band structure occur among longitudinal optical (LO) modes, which would be the least active modes at low temperature (T) if phonons did not interact. The degradation of the LO band begins, at low T, as an anomalously large broadening of modes near the center of the Brillouin zone (BZ), which gradually spreads towards the BZ boundary. The LO band all but vanishes before the crystal melts, and transverse optical (TO) modes' spectral peaks become so broad that the TO branches no longer appear band-like. Acoustic bands remain relatively well defined until melting of the crystal manifests in the spectra as their sudden disappearance. We argue that, even at high T, the long wavelength acoustic (LWA) phonons of an ionic crystal can remain partially immune to disorder generated by its LO phonons; whereas, even at low T, its LO phonons can be strongly affected by LWA phonons. This is because LO displacements average out in much less than the period of an LWA phonon; whereas during each period of an LO phonon, an LWA phonon appears as a quasistatic perturbation of the crystal, which warps the LO mode's intrinsic electric field. LO phonons are highly sensitive to acoustic warping of their intrinsic fields because their frequencies depend strongly on them: They cause the large frequency difference between LO and TO bands known as . We calculate vibrational spectra from MD trajectories using a method that we show to be classically exact and therefore applicable, with equal validity, to any solid or liquid in any thermal or nonthermal state. By demonstrating its power and generality, we show that it has become possible to go far beyond the reach of perturbation theories and mean-field theories in the study of vibrations in materials. Published by the American Physical Society 2024

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings.

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

Impact of intermolecular vibrational coupling effects on the sum-frequency generation spectra of the water/air interface

ABSTRACTWe have examined the impact of intermolecular vibrational coupling effects of the O-H stretch modes, as obtained by the surface-specific velocity-velocity correlation function approach, on the simulated sum-frequency generation spectra of the water/air interface. Our study shows that the inclusion of intermolecular coupling effects within the first three water layers, i.e. from the water/air interface up to a distance of 6 Å towards the bulk, is essential to reproduce the experimental SFG spectra. In particular, we find that these intermolecular vibrational contributions to the SFG spectra of the water/air interface are dominated by the coupling between the SFG active interfacial and SFG inactive bulk water molecules. Moreover, we find that most of the intermolecular vibrational contributions to the spectra originate from the coupling between double-donor water molecules only, whereas the remaining contributions originate mainly from the coupling between single-donor and double-donor water molecules.

Proposal for an analog Schwarzschild black hole in condensates of light

By etching a hole in the mirrors or by placing a scatterer in the center of a cavity, we can create a sink for light. In a Bose-Einstein condensate of photons this sink results in the creation of a so-called radial vortex, which is a two-dimensional analogue of a Schwarzschild black hole. We theoretically investigate the Hawking radiation and the associated greybody factor of this Schwarzschild black hole. In particular, we determine the density-density and velocity-velocity correlation functions of the Hawking radiation, which can be measured by observing the spatial correlations in the fluctuations in the light emitted by the cavity.

Sum Frequency Generation Spectra from Velocity-Velocity Correlation Functions.

We developed an expression for the calculation of the sum frequency generation spectra (SFG) of water interfaces that is based on the projection of the atomic velocities on the local normal modes. Our approach permits one to obtain the SFG signal from suitable velocity-velocity correlation functions, reducing the computational cost to that of the accumulation of a molecular dynamics trajectory, and therefore cutting the overhead costs associated with the explicit calculation of the dipole moment and polarizability tensor. Our method permits to interpret the peaks in the spectrum in terms of local modes, also including the bending region. The results for the water-air interface, obtained using ab initio molecular dynamics simulations, are discussed in connection to recent phase resolved experimental data.

Spatiotemporal velocity-velocity correlation function in fully developed turbulence.

Turbulence is a ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is, from the Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the functional space and time dependence of the velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the Navier-Stokes equation with stochastic forcing. This prediction, which goes beyond Kolmogorov theory, is the analytical fixed point solution of nonperturbative renormalization group flow equations, which are exact in the limit of large wave numbers. This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.

Toward ab initio molecular dynamics modeling for sum-frequency generation spectra; an efficient algorithm based on surface-specific velocity-velocity correlation function.

Interfacial water structures have been studied intensively by probing the O-H stretch mode of water molecules using sum-frequency generation (SFG) spectroscopy. This surface-specific technique is finding increasingly widespread use, and accordingly, computational approaches to calculate SFG spectra using molecular dynamics (MD) trajectories of interfacial water molecules have been developed and employed to correlate specific spectral signatures with distinct interfacial water structures. Such simulations typically require relatively long (several nanoseconds) MD trajectories to allow reliable calculation of the SFG response functions through the dipole moment-polarizability time correlation function. These long trajectories limit the use of computationally expensive MD techniques such as ab initio MD and centroid MD simulations. Here, we present an efficient algorithm determining the SFG response from the surface-specific velocity-velocity correlation function (ssVVCF). This ssVVCF formalism allows us to calculate SFG spectra using a MD trajectory of only ∼100 ps, resulting in the substantial reduction of the computational costs, by almost an order of magnitude. We demonstrate that the O-H stretch SFG spectra at the water-air interface calculated by using the ssVVCF formalism well reproduce those calculated by using the dipole moment-polarizability time correlation function. Furthermore, we applied this ssVVCF technique for computing the SFG spectra from the ab initio MD trajectories with various density functionals. We report that the SFG responses computed from both ab initio MD simulations and MD simulations with an ab initio based force field model do not show a positive feature in its imaginary component at 3100 cm(-1).

Single-particle spectral density of a Bose gas in the two-fluid hydrodynamic regime

In Bose supefluids, the single-particle Green's function can be directly related to the superfluid velocity-velocity correlation function in the hydrodynamic regime. An explicit expression for the single-particle spectral density was originally written down by Hohenberg and Martin in 1965, starting from the two-fluid equations for a superfluid. We give a simple derivation of their results. Using these results, we calculate the relative weights of first and second sound modes in the single-particle spectral density as a function of temperature in a uniform Bose gas. We show that the second sound mode makes a dominant contribution to the single-particle spectrum in relatively high temperature region. We also discuss the possibility of experimental observation of the second sound mode in a Bose gas by photoemission spectroscopy.

Study on the Structure and Spectrum of Water in 1-Ethyl-3-Methylimidazolium Tetrafluoroborate Ionic Liquids

Various 1-ethyl-3-methylimidazolium tetrafluoroborate ([Emim]BF4)/water mixture with varying concentrations were studied by molecular dynamics simulations. The radial distribution function, the power spectrum velocity-velocity correlation function were calculated to reveal the microstructure and the IR spectrum. In both liquids, with the concentration of water in the mixture increase, the rotation bands and the bending bands of water are red shift whereas the O-H stretch bands are blue shift. It was found that the molecular rotation motions become slower as the proportion of water increases and water molecules tend to be isolated from each other in mixtures with more ions than water molecules. It was shown that water molecules tend to be isolated from each other in mixtures with more ions than water molecules in both liquids.

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.

A QUICKSTEP-based quantum mechanics/molecular mechanics approach for silica

Quantum mechanics/molecular mechanics (QM/MM) approaches are currently used to describe several properties of silica-based systems, which are local in nature and require a quantum description of only a small number of atoms around the site of interest, e.g., local chemical reactivity or spectroscopic properties of point defects. We present a QM/MM scheme for silica suitable to be implemented in the general QM/MM framework recently developed for large scale molecular dynamics simulations, within the QUICKSTEP approach to the description of the quantum region. Our scheme has been validated by computing the structural and dynamical properties of an oxygen vacancy in alpha-quartz, a prototypical defect in silica. We have found that good convergence in the Si-Si bond length and formation energy is achieved by using a quantum cluster of only eight atoms in size. We check the suitability of the method for molecular dynamics and evaluate the Si-Si bond frequency from the velocity-velocity correlation function.

Randomly curved runs interrupted by tumbling: A model for bacterial motion

Small bacteria are strongly buffeted by Brownian forces that make completely straight runs impossible. A model for bacterial motion is formulated in which the effects of fluctuational forces and torques on the run phase are taken into account by using coupled Langevin equations. An integrated description of the motion, including runs and tumbles, is then obtained by the use of convolution and Laplace transforms. The properties of the velocity-velocity correlation function, of the mean displacement, and of the two relevant diffusion coefficients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces. For bacteria smaller than E. coli, the integrated diffusion coefficient crosses over from a jump-dominated to a rotational-diffusion-dominated form.

Steady state properties of a driven granular medium

We study a two-dimensional granular system where an external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic collisions between particles. The velocities of the particles in the steady state satisfy the Maxwellian distribution. We measure the density-density correlation and the velocity-velocity correlation functions in the steady state, and find that they are of power-law scaling forms. The locations of collision events are observed to be time correlated, and such a correlation is described by another power-law form. We also find that the dissipated energy obeys a power-law distribution. These results indicate that the system evolves into a critical state where there are neither characteristic spatial nor temporal scales in the correlation functions. A test particle exhibits an anomalous diffusion which is apparently similar to the Richardson law in a three-dimensional turbulent flow.

Numerical experiments on billiards

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of Poincare recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential.

Generalized Stokes-Einstein equation for spherical particle suspensions.

The cooperative diffusion coefficient ${\mathit{D}}_{\mathit{c}}$ for spherical particle suspensions is calculated using a ``mode-coupling'' method which extends previous calculations of ${\mathit{D}}_{\mathit{c}}$ for critical fluids and semidilute polymer solutions. The renormalization of the viscosity in the velocity-velocity correlation function from the solvent to the suspension viscosity leads to a generalized Stokes-Einstein (SE) equation in which the suspension viscosity \ensuremath{\eta} replaces the solvent viscosity ${\mathrm{\ensuremath{\eta}}}_{0}$ and the correlation length \ensuremath{\xi} (related to the osmotic compressibility) replaces the sphere radius R at nonvanishing suspension concentrations. Insertion of the leading order hard sphere virial expansions for \ensuremath{\eta} and the osmotic compressibility into our generalized SE equation gives a virial expansion for ${\mathit{D}}_{\mathit{c}}$ which is consistent with theoretical estimates obtained by alternative methods. These leading order virial expansions are also consistent with experiments on model (``hard sphere'') suspensions. Results are given for the virial expansion of spherical liquid droplets interacting via a contact attractive interaction. Further experiments are required to test the generalized SE equation at higher suspension concentrations.

A Real-Space Approach to Electronic Transport

Using orthogonal polynomials, a novel approach for studying DC and AC conductivity and velocity-velocity correlation function has been developed. The method works in direct space and can treat order or disordered, finite or infinite, and pure or alloy systems with equal ease. Further, it is not computer intensive and allows conductivity calculations as a function of frequency or the location of the Fermi energy in an efficient manner.

Distribution of Turbulent Velocity Fluctuations in a Drag-Reducing Solution

The probability density function of the velocity fluctuations in turbulent pipe flow is directly obtained from the measured velocity-velocity correlation function by calculating the higher order spectral moments of the correlation function. The probability density function is assumed to be the product of a Gaussian and a Lorentzian. The Gaussian represents the distribution of the «active» velocity fluctuations: the velocity fluctuations which are typically rotational and actually participate in the turbulent cascade. The Lorentzian describes the velocity fluctuations that are inactive, i.e., the «quiescent» velocity fluctuations which are nonparticipating in the turbulent cascade but are slightly excited by their turbulent environment

On frequency-dependent and time-dependent diffusivities

The time-dependent diffusivity D(t) is usually defined as the coefficient that appears in the diffusion equation, while the frequency-dependent diffusivity D( omega ) is defined the Fourier transform of the velocity-velocity correlation function. D( omega )/(i omega ), rather than D( omega ), is the Fourier transform of D(t).