Instantaneous normal mode analysis of supercooled water

We study the potential energy surface (PES) sampled by a liquid modeled via the widely studied extended simple point charge (SPC/E) model for water. We characterize the curvature of the PES by calculating the instantaneous normal mode (INM) spectrum for a wide range of densities and temperatures. We discuss the information contained in the INM density of states, which requires additional processing to be unambiguously associated with the long-time dynamics. For the SPC/E model, we find that the slowing down of the dynamics in the supercooled region-where the ideal mode coupling theory has been used to describe the dynamics-is controlled by the reduction in the number of directions in configuration space that allow a structural change. We find that the fraction f(dw) of the double-well directions in configuration space determines the value of the diffusion constant D, thereby relating a property of the PES to a macroscopic dynamic quantity; specifically, it appears that square root D is approximately linear in f(dw). Our findings are consistent with the hypothesis that, at the mode coupling crossover temperature, dynamical processes based on the free exploration of configuration space vanish, and processes requiring activation dominate. Hence, the reduction of the number of directions allowing free exploration of configuration space is the mechanism of diffusion implicitly implemented in the ideal mode coupling theory. Additionally, we find a direct relationship between the number of basins sampled by the system and the number of free directions. In this picture, diffusion appears to be related to geometrical properties of the PES, and to be entropic in origin.

The lack of a well-defined equilibrium reference configuration has long hindered a comprehensive atomic-level understanding of liquid dynamics and properties. The Instantaneous Normal Mode (INM) approach, which involves diagonalizing the Hessian matrix of potential energy in instantaneous liquid configurations, has emerged as a promising framework in this direction. However, several conceptual challenges remain, particularly related to the approach's inability to capture anharmonic effects. In this study, we present a set of "experimental facts" through a comprehensive INM analysis of simulated systems, including Ar, Xe, N2, CS2, Ga, and Pb, across a wide temperature range from the solid to gas phase. First, we examine the INM density of states (DOS) and compare it to the DOS obtained from the velocity auto-correlation function. We then analyze the temperature dependence of the fraction of unstable modes and the low-frequency slope of the INM DOS in search of potential universal behaviors. Furthermore, we explore the relationship between INMs and other properties of liquids, including the liquid-like to gas-like dynamical crossover and the momentum gap of collective shear waves. In addition, we investigate the INM spectrum at low temperatures as the system approaches the solid phase, revealing a significant fraction of unstable modes even in crystalline solids. Finally, we confirm the existence of a recently discussed cusp-like singularity in the INM eigenvalue spectrum and uncover its complex temperature-dependent behavior, challenging current theoretical models.

The instantaneous normal mode (INM) approach to liquid state dynamics is presented. INM is put in historical context, and the underlying physical ideas, including the importance of the potential energy landscape, are explained. It is shown that INM can be the basis of a general starting point for dynamical calculations in liquids, and the theoretical developments necessary for future development are indicated. New results are given for the general INM formalism, as well as for depolarized light scattering, the “Boson peak” in supercooled liquids, friction on a vibrating bond, nonadiabatic solvent induced transitions of a quantum system coupled to a liquid, and diffusion in supercooled liquids.

Instantaneous normal mode analysis for OKE reduced spectra of liquid and supercooled water: Contributions of low-density and high-density liquids

A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.

The instantaneous normal mode (INM) approach, which extends the normal mode description of collective excitations in solids to liquids, is applied to strongly coupled, three‐dimensional Yukawa liquids. Based on data from Langevin dynamics simulations, we compute the instantaneous normal modes across a wide range of coupling and screening parameters. Yukawa liquids at weak to moderate screening exhibit a pronounced maximum in the INM density of states, which disappears as the coupling decreases or screening becomes stronger. The fraction of unstable modes displays a quasi‐universal behavior, which can be described to a large extent by an effective coupling strength. The relation of the INM approach to the quasi‐localized charge approximation (QLCA) is explored in some detail. In particular, the QLCA dispersion relation can be recovered explicitly from an appropriately weighted mode spectrum.

The formalism of the dynamical theory of diffusion is shown to be strictly analogous to that of the reaction-rate theory in the sense that expressions for the jump rate and related quantities can be written in the same form as the corresponding expressions of rate theory. However, the physical meaning of corresponding quantities is different. For example, the role of the saddle-point configuration in rate theory is taken by a dynamical state in the dynamical theory. The reaction coordinate is shown to measure the extent to which lattice reaction forces barring the jump have been overcome by thermal fluctuations. Geometric considerations indicate that for vacancy diffusion, the factor $\ensuremath{\Delta}K$ should have a lower limit on the order of 0.5 in the fcc lattice and an upper limit of the same order for the bcc lattice. In general, $\ensuremath{\Delta}K$ measures the mass dependence of the rms velocity of the system along the jump direction in configuration space. The mass dependence of the isotope effect for impurity diffusion is developed, and a double-isotope-effect experiment involving the simultaneous diffusion of three solute isotopes is proposed to determine impurity correlation factors.

The vibrational relaxation of the amide I mode of deuterated N-methylacetamide in D2O solution is studied through nonequilibrium simulations using the semiempirical Born-Oppenheimer molecular dynamics (SEBOMD) approach to describe the whole solute-solvent system. Relaxation pathways and lifetimes are determined using the instantaneous normal mode (INM) analysis. The relaxation of the amide I mode is characterized by three different time scales; most of the excess energy (80%) is redistributed through intramolecular vibrational energy redistribution processes, with a smaller contribution (20%) of intermolecular energy flowing into the solvent. The amide II mode is found to contribute modestly (7%) to the relaxation mechanism. The amide I mode and the total vibrational energy decay curves obtained using SEBOMD and INM are in satisfactory agreement with the experimental measurements.

All-atomistic molecular dynamics study of the glass transition of amorphous polymers

Specific features of nonlinear systems determined by the energy interaction of their coordinates are considered. To assess these features, the potential energy surfaces are considered, on which the system dynamics is presented using the trajectories of motion of an image point. The specific features of these trajectories are determined by the topological characteristics of the potential energy surface in the configuration space (local surface curvatures). Unlike linear systems, nonlinear systems are characterized by the presence on the energy surface of additional extremal curvatures and characteristic points: in addition to elliptic points, parabolic and hyperbolic points appear, which determine the character of geodetic lines near these extrema and points. The specific features of the geodetic lines determine the character of free and forced vibrations in the system, its dynamic features, and the presence of nonlinear effects in the system.

In this paper, we present a new 3D reconstruction approach based on local surface curvature analysis. Its integration can make a normal active stereoscopic system intelligent, and capable to produce directly optimized 3D model. The iterative 3D reconstruction process begins with a sparse and regular point pattern. Based on the reconstructed 3D point cloud, the local surface curvature around each 3D point is estimated. Those 3D points located in flat areas are removed from the 3D model, and a new pattern is created to project more points onto the object where there is high surface curvature. The 3D model is thus refined progressively during the acquisition process, and finally an optimized 3D model is obtained. Our numerous experiments showed that compared to the 3D models generated by commercial system, the loss of morphological quality is negligible, and the gain by the simplification of the model is considerable.KeywordsGaussian CurvatureCamera CalibrationPattern PointMesh SimplificationLocal Surface CurvatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Low-wavenumber vibrational dynamics are studied for liquid formamide (FA) and N-methylformamide (NMF) by the methods of molecular dynamics (MD) and instantaneous normal mode (INM) analysis. The dipole-induced dipole (DID) mechanism is employed for calculating polarizability tensors, the correlation function of which determines Raman spectral profiles and optical Kerr effect (OKE) responses. It is shown that the calculated Raman spectra and OKE responses are in reasonable agreement with those observed in previous studies. The main features of these optical signals are explained by simple librations of the unperturbed molecular polarizability (UMP) tensors, which are considerably anisotropic, although the intensities of the librational components are enhanced to some extent by intermolecular interactions, especially in the case of liquid NMF. The DID term gives rise to smaller intensities in a lower wavenumber region than the UMP term. It is suggested that these features of the optical signals may be regarded as characteristic of strongly interacting liquids with substantial anisotropy in molecular polarizability tensors. It is also shown that the marked difference between the Raman spectra of liquid FA and NMF in the low-wavenumber region arises from a difference in the librations of these molecules around the longer in-plane molecular axis of inertia. The difference is related to the dimensionality of hydrogen bonding in the liquids: two-dimensional in liquid FA and one-dimensional in liquid NMF.

We present an approach to integrate a preprocessing step of the region of interest (ROI) localization into 3-D scanners (laser or stereoscopic). The definite objective is to make the 3-D scanner intelligent enough to localize rapidly in the scene, during the preprocessing phase, the regions with high surface curvature, so that precise scanning will be done only in these regions instead of in the whole scene. In this way, the scanning time can be largely reduced, and the results contain only pertinent data. To test its feasibility and efficiency, we simulated the preprocessing process under an active stereoscopic system composed of two cameras and a video projector. The ROI localization is done in an iterative way. First, the video projector projects a regular point pattern in the scene, and then the pattern is modified iteratively according to the local surface curvature of each reconstructed 3-D point. Finally, the last pattern is used to determine the ROI. Our experiments showed that with this approach, the system is capable to localize all types of objects, including small objects with small depth.

We perform molecular dynamics simulations of a binary mixture of water and trehalose with the TIP4P/Ice water model. We analyze the slow dynamics of trehalose molecules in the mildly supercooled region for concentrations of 3.66 and 18.57 wt. %. We previously studied the dynamics of water in the same mixtures. Supercooled TIP4P/Ice water solvating trehalose molecules was found to follow the Mode Coupling Theory (MCT) and to undergo a transition from a fragile to a strong behavior for both concentrations. Here, we show that also the dynamics of trehalose molecules follows the MCT and displays a fragile to strong crossover (FSC). The results show that trehalose in binary mixtures with water shares with it the dynamical behavior typical of glass forming liquids. Moreover, the FSC for trehalose structural relaxation times is found to occur at temperatures close to those previously obtained for water in the same solutions, showing that the dynamics of the solute is strongly coupled to that of the solvent. We also perform a MCT test showing that the trehalose dynamics obeys the MCT time-temperature superposition principle and that the exponents derived from the theory and the ones obtained from fitting procedure of the relaxation times are comparable, confirming that trehalose molecules in supercooled water solutions follow the MCT of glassy dynamics. Moreover, as predicted by the theory, trehalose particles have MCT parameters comparable to those of water in the same mixtures. This is an important result, given that MCT was originally formulated for monoatomic particles.

In this paper the geometric formulation of the single layer perceptron weight optimization problem previously described by Coetzee et al. (1993, 1996) is combined with results from other researchers on nonconvex set projections to describe sufficient conditions for uniqueness of weight solutions. It is shown that the perceptron data surface is pseudoconvex and has infinite folding, allowing for the specification of a region of desired vectors having unique projections purely in terms of the local curvature of the data surface. No information is therefore required regarding the global curvature or size of the data surface. These results in principle allow for a posteriori evaluation of whether a weight solution is unique or globally optimal, and for a priori scaling of desired vector values to ensure uniqueness, through analysis of the input data. The practical applicability of these results from a numerical perspective is evaluated on some carefully chosen examples.