Instantaneous Normal Mode Approach to Liquid State Dynamics

Keyes, T.

doi:10.1021/jp963706h

Cited by 338 publications

(316 citation statements)

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“…First, not all of the imaginary frequency modes can be properly called ''unstable,'' since not all correspond to the system being near the top of a barrier, but are associated with the anharmonic shoulder of an otherwise singlewell potential. As predicted by Keyes 35 and demonstrated in the present work and Ref. 34 there is a cutoff imaginary frequency below which all imaginary frequency modes are stable.…”

Section: Instantaneous Normal Modessupporting

confidence: 86%

“…In a recent paper, 35 Keyes has examined the functional form of the imaginary frequency branch of the INM density of states. For a Lennard-Jones system with 3 ϭ1.0 this part of the DOS was found to be well fit by…”

Section: Results For the Inverse-sixth-power Systemmentioning

confidence: 99%

“…To make contact with the recent results of Keyes, 35 we also collected data for a Lennard-Jones system v͑ r ͒ϭ4⑀ ͫͩ r ͪ 12 Ϫ ͩ r ͪ 6 ͬ ͑12͒ and will briefly summarize them here. The potential was shifted in the same manner as for the inverse sixth-power system using a cutoff of r c ϭ2.5 .…”

Section: Results For a Lennard-jones Systemmentioning

confidence: 99%

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The role of localization in glasses and supercooled liquids

Bembenek

Laird

1996

The Journal of Chemical Physics

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Localized excitations ͑tunneling modes, soft harmonic vibrations͒ are believed to play a dominant role in the thermodynamics and transport properties of glasses at low temperature. Using instantaneous normal-mode ͑INM͒ analysis, we explore the role that such localization plays in determining the behavior of such systems in the vicinity of the glass transition. Building on our previous study ͓Phys. Rev. Lett. 74, 936 ͑1995͔͒ we present evidence that the glass transition in two simple model systems is associated with a transition temperature below which all unstable INM's become localized. This localization transition is a possible mechanism for the change in diffusion mechanism from continuous flow to localized hopping that is believed to occur in fragile glass formers at a temperature just above T g .

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Section: Instantaneous Normal Modessupporting

confidence: 86%

Section: Results For the Inverse-sixth-power Systemmentioning

confidence: 99%

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The role of localization in glasses and supercooled liquids

Bembenek

Laird

1996

The Journal of Chemical Physics

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“…41,42,43,44 Proposals to extend such ideas to consider a partition of configuration space in terms of saddle points have been suggested in the context of supercooled liquids and glasses. 3 This approach has much in common with the instantaneous normal mode theory developed by Keyes and coworkers, 45,46,47 where the focus of attention is the spectrum of Hessian eigenvalues for instantaneous configurations. Theoretical contributions based upon the premise of dividing configuration space into saddles have appeared, 48,49,50,51 following the observation that the Hessian index of the stationary points sampled in simulations approaches zero around the critical temperature of modecoupling theory.…”

Section: Introductionmentioning

confidence: 99%

Stationary points and dynamics in high-dimensional systems

Wales¹,

Doye²

2003

The Journal of Chemical Physics

154

167

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We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.

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“…Applications of the method are to be found in the calculation of macroscopic quantities through the knowledge of the density of states (e.g. the diffusion coefficient [1]) and in the interpretation of atomic motion through the inspection of the eigenvectors [2][3][4]. This last method appears to be a unique tool for the interpretation of dynamical features (single molecule or collective) of a disordered system in terms of correlated motions of its constituents.…”

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confidence: 99%

Instantaneous Normal Mode Analysis of Liquid HF

Garberoglio

Vallauri

2000

Phys. Rev. Lett.

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We present an Instantaneous Normal Modes analysis of liquid HF aimed to clarify the origin of peculiar dynamical properties which are supposed to stem from the arrangement of molecules in linear hydrogen-bonded network. The present study shows that this approach is a unique tool for the understanding of the spectral features revealed in the analysis of both single molecule and collective quantities. For the system under investigation we demonstrate the relevance of hydrogen-bonding "stretching" and fast librational motion in the interpretation of these features.PACS numbers: 62.60.+v, 63.20.Pw In recent years the analysis of Instantaneous Normal Modes (INM) of normal and supercooled liquids has given a sound improvement to the understanding of the microscopic processes underlying the dynamical properties of these systems. Applications of the method are to be found in the calculation of macroscopic quantities through the knowledge of the density of states (e.g. the diffusion coefficient [1]) and in the interpretation of atomic motion through the inspection of the eigenvectors [2][3][4]. This last method appears to be a unique tool for the interpretation of dynamical features (single molecule or collective) of a disordered system in terms of correlated motions of its constituents. In particular it is interesting to explore how the presence of locally ordered units is reflected in the time behaviour of, for example, the velocity autocorrelation function (VACF). Attempts in this direction have to be found in the analyses of: i) the correlation function of the projection of the centre of mass (CoM) velocity of water molecules along the directions of the normal coordinates of a cluster of three molecules [5]; ii) the projection of INM eigenvectors onto the totally symmetric displacement coordinates of ZnCl 2− 4 tetrahedral units [2]. Moreover the INM approach has been exploited to describe the dynamical features of molecular liquids (e.g. diatomic Lennard-Jones [6], CS 2 [7]) including hydrogen bonded systems like water [8,3]. On the other hand recent molecular dynamics (MD) simulations of HF have revealed peculiar dynamical features, e.g. a peak at ≃ 50 ps −1 in the spectra of both collective and single molecule correlation functions [9,10]. In the collective longitudinal and transverse current spectra this mode appears to have an optical-like character, since its frequency is found to be independent of the wavevector. For the interpretation of the CoM VACF spectrum this peak has been related to the relative motion of two nearest neighbour molecules [10]. Since nearest neighbours are also hydrogen bonded it is tempting to assign this dynamical feature to hydrogen bonding "stretching". As a matter of fact HF molecules have been demonstrated to form irregular zig-zag chains of different size, being this peculiar clustering favoured by the geometry of the molecule and the strong electrostatic interaction [11]. A dynamical characterisation of these ordered units has not yet been given, so that any assignment of the sp...

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Instantaneous Normal Mode Approach to Liquid State Dynamics

Cited by 338 publications

References 56 publications

The role of localization in glasses and supercooled liquids

The role of localization in glasses and supercooled liquids

Stationary points and dynamics in high-dimensional systems

Instantaneous Normal Mode Analysis of Liquid HF

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