Bond Orientational Order Parameters for Classifying Solid-like Clusters in a Lennard-Jones System near Liquid-Solid Transition and at Solid States.

In this paper, we introduced an order parameter, named the local structure similarity (LSS), to measure the resemblance of a cluster structure in a liquid with respect to a perfect crystal. The LSS is based on a dot product of two bond orientational order complex vectors, with one vector associated with a particle in a liquid and the other vector with a particle in a crystal. The calculation of the LSS should scan the entire space of the Euler angles determined by the two coordinate frames describing individually the liquid and the crystal. The effectiveness of the LSS was examined by solid-like clusters in a Lennard-Jones (LJ) system near its liquid-solid phase transition and at solid states below its melting point, where the thermodynamic states of the LJ system were obtained by simulation annealing. The LSS measure was utilized to scrutinize the fcc-like, hcp-like, and bcc-like clusters classified by criteria based on W4 and W6 order parameters. As indicated by our results, the two ways of classification are consistent for fcc-like and hcp-like clusters, which are in a close resemblance to their crystalline counterparts. However, the classification with positive W6 for bcc-like clusters is inconsistent with the results of the LSS measure, which was confirmed by clusters in a LJ system confined between two parallel slabs of particles in the bcc structure arrangement.

Analysis of local bond-orientational order for liquid gallium at ambient pressure: Two types of cluster structures.

In terms of the local bond-orientational order (LBOO) parameters, a cluster approach to analyze local structures of simple liquids was developed. In this approach, a cluster is defined as a combination of neighboring seeds having at least nb local-orientational bonds and their nearest neighbors, and a cluster ensemble is a collection of clusters with a specified nb and number of seeds ns. This cluster analysis was applied to investigate the microscopic structures of liquid Ga at ambient pressure (AP). The liquid structures studied were generated through ab initio molecular dynamics simulations. By scrutinizing the static structure factors (SSFs) of cluster ensembles with different combinations of nb and ns, we found that liquid Ga at AP contained two types of cluster structures, one characterized by sixfold orientational symmetry and the other showing fourfold orientational symmetry. The SSFs of cluster structures with sixfold orientational symmetry were akin to the SSF of a hard-sphere fluid. On the contrary, the SSFs of cluster structures showing fourfold orientational symmetry behaved similarly as the anomalous SSF of liquid Ga at AP, which is well known for exhibiting a high-q shoulder. The local structures of a highly LBOO cluster whose SSF displayed a high-q shoulder were found to be more similar to the structure of ß-Ga than those of other solid phases of Ga. More generally, the cluster structures showing fourfold orientational symmetry have an inclination to resemble more to ß-Ga.

Local structural effects on orientational relaxation of OH-bond in liquid water over short to intermediate timescales.

By simulating the rigid simple point charge extended model at temperature T = 300 K, the orientational relaxation of the OH-bond in water was investigated over short to intermediate timescales, within which molecules undergo inertial rotation and libration and then enter the rotational diffusion regime. According to the second-cumulant approximation, the orientational time correlation function (TCF) of each axis that is parallel or perpendicular to an OH-bond is related to an effective rotational density of states (DOS), which is determined using the power spectra of angular velocity autocorrelation functions (AVAFs) of the other two axes. In addition, the AVAF power spectrum of an axis was approximated as the rotational stable instantaneous normal mode (INM) spectrum of the axis. As described in a previous study [S. L. Chang, T. M. Wu, and C. Y. Mou, J. Chem. Phys. 121, 3605 (2004)], simulated molecules were classified into subensembles, according to either the local structures or the H-bond configurations of the molecules. For global molecules and the classified subensembles, the simulation results for the first- and second-rank orientational TCFs were compared with the second-cumulant predictions obtained using the effective rotational DOSs and the rotational stable-INM spectra. On short timescales, the OH-bond in water behaves similar to an inertial rotor and its anisotropy is lower than that of a water molecule. For molecules with three or more H-bonds, the OH-bond orientational TCFs are characterized by a recurrence, which is an indication for libration of the OH-bond. The recurrence can generally be described by the second-cumulant prediction obtained using the rotational stable-INM spectra; however, the orientational TCFs after the recurrence switch to a behavior similar to that predicted using the AVAF power spectra. By contrast, the OH-bond orientational TCFs of molecules initially connected with one or two H-bonds decay monotonically or exhibit a weak recurrence, indicating rapid relaxation into the rotational diffusion regime after the initial Gaussian decay. In addition to accurately describing the Gaussian decay, the second-cumulant predictions formulated using the rotational stable-INM spectra and the AVAF power spectra serve as the upper and lower limits, respectively, for the OH-bond orientational TCFs of these molecules after the Gaussian decay.

Instantaneous normal mode analysis for intermolecular and intramolecular vibrations of water from atomic point of view.

By exploiting the instantaneous normal mode (INM) analysis for models of flexible molecules, we investigate intermolecular and intramolecular vibrations of water from the atomic point of view. With two flexible SPC/E models, our investigations include three aspects about their INM spectra, which are separated into the unstable, intermolecular, bending, and stretching bands. First, the O- and H-atom contributions in the four INM bands are calculated and their stable INM spectra are compared with the power spectra of the atomic velocity autocorrelation functions. The unstable and intermolecular bands of the flexible models are also compared with those of the SPC/E model of rigid molecules. Second, we formulate the inverse participation ratio (IPR) of the INMs, respectively, for the O- and H-atom and molecule. With the IPRs, the numbers of the three species participated in the INMs are estimated so that the localization characters of the INMs in each band are studied. Further, by the ratio of the IPR of the H atom to that of the O atom, we explore the number of involved OH bond per molecule participated in the INMs. Third, by classifying simulated molecules into subensembles according to the geometry of their local environments or their H-bond configurations, we examine the local-structure effects on the bending and stretching INM bands. All of our results are verified to be insensible to the definition of H-bond. Our conclusions about the intermolecular and intramolecular vibrations in water are given.

Melting behavior of Ag14 cluster: an order parameter by instantaneous normal modes.

This paper studies the melting behavior of Ag(14) cluster employing the instantaneous normal mode (INM) analysis that was previously developed for bimetallic cluster Ag(17)Cu(2). The isothermal Brownian-type molecular dynamics simulation is used to generate atom configurations of Ag(14) at different temperatures up to 1500 K. At each temperature, these atomic configurations are then analyzed by the INM technique. To delve into the melting behavior of Ag(14) cluster which differs from Ag(17)Cu(2) by the occurrence of an anomalous prepeak in the specific heat curve in addition to the typical principal peak, we appeal to examining the order parameter τ(T) defined in the context of the INM method. Two general approaches are proposed to calculate τ(T). In one, τ(T) is defined in terms of the INM vibrational density of states; in another, τ(T) is defined considering the cluster as a rigid body with its rotational motions described by three orthogonal eigenvectors. Our results for Ag(14) by these two methods indicate the mutual agreement of τ(T) calculated and also the consistent interpretation of the melting behavior with the specific heat data. The order parameter τ(T) provides in addition an insightful interpretation between the melting of clusters and the concept of broken symmetry which has been found successful in studies of the melting transition of bulk systems.

Comparative study of cluster Ag17Cu2 by instantaneous normal mode analysis and by isothermal Brownian-type molecular dynamics simulation.

We perform isothermal Brownian-type molecular dynamics simulations to obtain the velocity autocorrelation function and its time Fourier-transformed power spectral density for the metallic cluster Ag(17)Cu(2). The temperature dependences of these dynamical quantities from T = 0 to 1500 K were examined and across this temperature range the cluster melting temperature T(m), which we define to be the principal maximum position of the specific heat is determined. The instantaneous normal mode analysis is then used to dissect the cluster dynamics by calculating the vibrational instantaneous normal mode density of states and hence its frequency integrated value I(j) which is an ensemble average of all vibrational projection operators for the jth atom in the cluster. In addition to comparing the results with simulation data, we look more closely at the entities I(j) of all atoms using the point group symmetry and diagnose their temperature variations. We find that I(j) exhibit features that may be used to deduce T(m), which turns out to agree very well with those inferred from the power spectral density and specific heat.

Revisiting anomalous structures in liquid Ga.

In terms of an interatomic pair potential, which well characterizes the dynamic properties of liquid Ga, we investigate again the origin of the well known high-q shoulder in the static structure factor of the liquid. Similar to the results of Gong's simulation at high temperature, dimers with extremely short bond lengths are indeed found in our model just above the melting point, but our results indicate that it is unlikely for the high-q shoulder to be produced by these dimers. Instead, based on our model, the high-q shoulder is resulted from some medium-range order, which is related to the structures beyond the first shell of the radial distribution function, caused by Friedel oscillations within a nanoscale range.

Multifractality of instantaneous normal modes at mobility edges.

In terms of the multifractal analysis, we investigate the characteristics of the instantaneous normal modes (INMs) at two mobility edges (MEs) of a simple fluid, where the locations of the MEs in the INM spectrum were identified in a previous work [B. J. Huang and T. M. Wu, Phys. Rev. E 79, 041105 (2009)]. The mass exponents and the singularity spectrum of the INMs are obtained by the box-size and system-size scalings under the typical average. The INM eigenvectors at a ME exhibit a multifractal nature and the multifractal INMs at each ME yield the same results in generalized fractal dimensions and singularity spectrum. Our results indicate that the singularity spectrum of the multifractal INMs agrees well with that of the Anderson model at the critical disorder. This good agreement provides numerical evidence for the universal multifractality at the localization-delocalization transition. For the multifractal INMs, the probability density function and the spatial correlation function of the squared vibrational amplitudes are also calculated. The relation between the probability density function and the singularity spectrum is examined numerically, so are the relations between the critical exponents of the spatial correlation function and the mass exponents of the multifractal INMs.

Localization-delocalization transition in Hessian matrices of topologically disordered systems.

Using the level-spacing (LS) statistics, we have investigated the localization-delocalization transitions (LDTs) in Hessian matrices of a simple fluid with short-ranged interactions. The model fluid is a prototype of topologically disordered systems and its Hessian matrices are recognized as an ensemble of Euclidean random matrices with elements subject to several kinds of constraints. Two LDTs in the Hessian matrices are found, with one in the positive-eigenvalue branch and the other in the negative-eigenvalue one. The locations and the critical exponents of the two LDTs are estimated by the finite-size scaling for the second moments of the nearest-neighbor LS distributions. Within numerical errors, the two estimated critical exponents are almost coincident with each other and close to that of the Anderson model (AM) in three dimensions. The nearest-neighbor LS distribution at each LDT is examined to be in a good agreement with that of the AM at the critical disorder. We conclude that the LDTs in the Hessian matrices of topologically disordered systems exhibit the critical behaviors of orthogonal universality class.

Hard-sphere perturbation theory for a model of liquid Ga.

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.

Mechanism for singular behavior in vibrational spectra of topologically disordered systems: short-range attractions.

At low-enough fluid densities, we have found some naive singular behavior, like the van Hove singularities in the phonon spectra of lattices, appearing in the instantaneous normal mode spectra of the Lennard-Jones (LJ) 2n-n fluids, which serve as a prototype of topologically disordered systems. The singular behavior cannot be predicted by the mean-field theory, but interpreted by the perturbed binary modes of some special pairs, called the mutual nearest neighbor pairs, at separations corresponding to the extreme binary frequencies, which are solely determined by the attractive part of the LJ 2n-n pair potential. By reducing the range of attraction in the pair potential under the conditions of the same particle diameter and well depth, the tendency for the appearance of the singular behavior shifts to higher fluid densities. From this study, we conclude that pair potential with a short-range attraction can be a mechanism to produce a counterpart of the van Hove singularity in the vibrational spectra of disordered systems without a reference lattice.

Instantaneous normal mode analysis of orientational motions in liquid water: local structural effects.

We have investigated the effects of local structures on the orientational motions in liquid water in terms of the instantaneous normal mode (INM) analysis. The local structures of a molecule in liquid water are characterized by two different kinds of index: the asphericity parameter of its Voronoi polyhedron and the numbers of the H bonds donated and accepted by the molecule. According to the two kinds of index, the molecules in the simulated water are classified into subensembles, for which the rotational contributions to the INM spectrum are calculated. Our results indicate that by increasing the asphericity, the rotational contribution has a shift toward the high-frequency end in the real spectrum and a decrease in the fraction of the imaginary modes. Furthermore, we find that this shift essentially relies on the number of the donated H bonds of a molecule, but has almost nothing to do with that of the accepted H bonds. The local structural effects resulting from the geometry of water molecule are also discussed.