Instantaneous Normal Mode Analysis Research Articles

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

Glass transition is an intensively studied topic but many questions in this regard remain unaddressed. This is an important phenomenon related to the physical and mechanical properties of amorphous polymer materials. In this study, existing and newly performed all-atomistic molecular dynamics (MD) simulations of polycarbonate (PC) and poly-(methyl methacrylate) (PMMA) cooling processes were analyzed to address their glass transitions from a molecular perspective. Additionally, potential energy, radius of gyration, dihedral transition, and end effects were characterized. Further analyses were performed to characterize the individual degrees of freedom (DoFs) by the variance, correlation between two DoFs by the correlation coefficient, and collective motions by instantaneous normal mode (INM) analysis. Various DoFs experienced glass transition at temperatures slightly different from the glass transition temperature T g , presumably owing to their different spatial scales and chemical environments. This suggests that the experimentally observed broad T g may be attributed to a similar hierarchy of motions. Collective motions characterized by INM revealed slightly different behaviors for PC and PMMA. • T g of million-atom atomistic models of PC and PMMA were investigated by MD. • Potential energy, Rg, dihedral transition, end effect across T g were characterized. • Abrupt variance uprises and peaks in correlation showed local DoFs' responses to T g . • Hierarchy of local DoFs' characteristic temperatures possibly widened T g range. • INM showed responses to T g at low mode and differences between PC and PMMA.

Unsupervised Machine Learning Neural Gas Algorithm for Accurate Evaluations of the Hessian Matrix in Molecular Dynamics.

The Hessian matrix of the potential energy of molecular systems is employed not only in geometry optimizations or high-order molecular dynamics integrators but also in many other molecular procedures, such as instantaneous normal mode analysis, force field construction, instanton calculations, and semiclassical initial value representation molecular dynamics, to name a few. Here, we present an algorithm for the calculation of the approximated Hessian in molecular dynamics. The algorithm belongs to the family of unsupervised machine learning methods, and it is based on the neural gas idea, where neurons are molecular configurations whose Hessians are adopted for groups of molecular dynamics configurations with similar geometries. The method is tested on several molecular systems of different dimensionalities both in terms of accuracy and computational time versus calculating the Hessian matrix at each time-step, that is, without any approximation, and other Hessian approximation schemes. Finally, the method is applied to the on-the-fly, full-dimensional simulation of a small synthetic peptide (the 46 atom N-acetyl-l-phenylalaninyl-l-methionine amide) at the level of DFT-B3LYP-D/6-31G* theory, from which the semiclassical vibrational power spectrum is calculated.

Computational Study of Helical and Helix-Hinge-Helix Conformations of an Anti-Microbial Peptide in Solution by Molecular Dynamics and Vibrational Analysis.

Many classical antimicrobial peptides adopt an amphipathic helical structure at a water-membrane interface. Prior studies led to the hypothesis that a hinge near the middle of a helical peptide plays an important role in facilitating peptide-membrane interactions. Here, dynamics and vibrations of a designed hybrid antimicrobial peptide LM7-2 in solution were simulated to investigate its hinge formation. Molecular dynamics simulation results on the basis of the CHARMM36 force field showed that the α-helix LM7-2 bent around two or three residues near the middle of the peptide, stayed in a helix-hinge-helix conformation for a short period of time, and then returned to a helical conformation. High-resolution computational vibrational techniques were applied on the LM7-2 system when it has α-helical and helix-hinge-helix conformations to understand how this structural change affects its inherent vibrations. These studies concentrated on the calculation of frequencies that correspond to backbone amide bands I, II, and III: vibrational modes that are sensitive to changes in the secondary structure of peptides and proteins. To that end, Fourier transforms were applied to thermal fluctuations in C-N-H angles, C-N bond lengths, and C═O bond lengths of each amide group. In addition, instantaneous all-atom normal mode analysis was applied to monitor and detect the characteristic amide bands of each amide group within LM7-2 during the MD simulation. Computational vibrational results indicate that shapes and frequencies of amide bands II and especially III were altered only for amide groups near the hinge. These methods provide high-resolution vibrational information that can complement spectroscopic vibrational studies. They assist in interpreting spectra of similar systems and suggest a marker for the presence of the helix-hinge-helix motif. Moreover, radial distribution functions indicated an increase in the probability of hydrogen bonding between water and a hydrogen atom connected to nitrogen (HN) in such a hinge. The probability of intramolecular hydrogen bond formation between HN and an amide group oxygen atom within LM7-2 was lower around the hinge. No correlation has been found between the presence of a hinge and hydrogen bonds between amide group oxygen atoms and the hydrogen atoms of water molecules. This result suggests a mechanism for hinge formation wherein hydrogen bonds to oxygen atoms of water replace intramolecular hydrogen bonds as the peptide backbone folds.

Vibrational Sum-Frequency Generation Spectroscopy in the Energy Representation from Dual-Level Molecular Dynamics Simulations.

We report a cost-effective molecular dynamics approach to calculate sum-frequency generation (SFG) vibrational spectra of molecular species at liquid interfaces in the energy representation formalism that brings together the instantaneous normal mode (INM) analysis at free-energy minima (FEM) and the dual-level free-energy perturbation (FEP) methods. This combined FEP-INM-FEM approach allows analyzing SFG spectra in terms of normal mode contributions at very-high ab initio levels, in contrast to standard time-correlation function (TCF)-based methods, from which it can be considered complementary. It is applied here to the study of the CH3-stretching band of methanol at the air-water interface, which has been thoroughly studied in the literature. The SFG band of acetonitrile in the same conditions has also been calculated with the aim of testing the capability of the method to reproduce small chemical shifts. The suitability of the proposed model is demonstrated by comparing the results with TCF data from QM/MM simulations and with experiments. Analysis of these results provides new insights into the strength and orientational dependence of the SFG signal of symmetric and asymmetric stretching vibrations of CH3 groups, which can be of paramount importance to analyze the spectra of more complex systems.

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

In this paper, we investigated the optical Kerr effect (OKE) reduced spectral density (RSD) of liquid and supercooled water at ambient pressure and focused on the contributions of low-density liquid (LDL) and high-density liquid (HDL), which local structures are characterized with tetrahedral order and disorder, respectively. The water systems were generated by performing molecular dynamics (MD) simulations with TIP4P/2005 force fields, and molecules were classified into LDL and HDL with the microscopic structural descriptor [Nature commun. 3 (2014) 3556.]. The OKE RSD was calculated with a model involving the intrinsic polarizabilities of individual molecules and the dipole-induced-dipole mechanism between them. The instantaneous normal mode (INM) analysis was used to dissect the OKE RSD obtained by MD simulations. By considering water as a mixture of LDL and HDL, the OKE RSD in the linearized INM theory is a sum of three contributions, which are resulted from the two partial liquids individually and a cross correlation associated with both of them, in a formulism similar as that for the static structure factor of a binary mixture. By exploring with two separation schemes on the collective polarizability, where they are complemental to each other, the INM analysis provides an insight into the physical causes for the bands in the OKE RSD of liquid and supercooled water and the relation of each band to the local structures of LDL and HDL.

Pressure response of the THz spectrum of bulk liquid water revealed by intermolecular instantaneous normal mode analysis.

The radial distribution functions of liquid water are known to change significantly their shape upon hydrostatic compression from ambient conditions deep into the kbar pressure regime. It has been shown that despite their eye-catching changes, the fundamental locally tetrahedral fourfold H-bonding pattern that characterizes ambient water is preserved up to about 10 kbar (1 GPa), which is the stability limit of liquid water at 300 K. The observed increase in coordination number comes from pushing water molecules into the first coordination sphere without establishing an H-bond, resulting in roughly two such additional interstitial molecules at 10 kbar. THz spectroscopy has been firmly established as a powerful experimental technique to analyze H-bonding in aqueous solutions given that it directly probes the far-infrared lineshape and thus the prominent H-bond network mode around 180 cm-1. We, therefore, set out to assess pressure effects on the THz response of liquid water at 10 kbar in comparison to the 1 bar (0.1 MPa) reference, both at 300 K, with the aim to trace back the related lineshape changes to the structural level. To this end, we employ the instantaneous normal mode approximation to rigorously separate the H-bonding peak from the large background arising from the pronounced librational tail. By exactly decomposing the total molecular dynamics into hindered translations, hindered rotations, and intramolecular vibrations, we find that the H-bonding peak arises from translation-translation and translation-rotation correlations, which are successively decomposed down to the level of distinct local H-bond environments. Our utmost detailed analysis based on molecular pair classifications unveils that H-bonded double-donor water pairs contribute most to the THz response around 180 cm-1, whereas interstitial waters are negligible. Moreover, short double-donor H-bonds have their peak maximum significantly shifted toward higher frequencies with respect to such long H-bonds. In conjunction with an increasing relative population of these short H-bonds versus the long ones (while the population of other water pair classes is essentially pressure insensitive), this explains not only the blue-shift of the H-bonding peak by about 20-30 cm-1 in total from 1 bar to 10 kbar but also the filling of the shallow local minimum of the THz lineshape located in between the network peak and the red-wing of the librational band at 1 bar. Based on the changing populations as a function of pressure, we are also able to roughly estimate the pressure-dependence of the H-bond network mode and find that its pressure response and thus the blue-shifting are most pronounced at low kbar pressures.

Microphysics of liquid complex plasmas in equilibrium and non-equilibrium systems

The dynamic evolution of the microscopic structure of solid and liquid phases of complex plasmas is studied experimentally and by means of molecular dynamics (MD) simulations. In small finite systems, the cooperative motion can be described in terms of discrete modes. These modes are studied with different experimental approaches. Using diffuse scattered laser light, applying laser tweezer forces to individual particles, and periodic laser pulses, the excitation of modes is investigated. The instantaneous normal mode analysis of experimental data from two-dimensional liquid clusters gives access to the local dynamics of the liquid phase. Our investigations shed light on the role of compressional and shear modes as well as the determination of diffusion constants and melting temperatures in finite systems. Special attention is paid to hydrodynamic situations with a stationary inhomogeneous dust flow. MD simulations allow to study the collective motion in the shell of nearest neighbors, which can be linked to smooth and sudden changes of the macroscopic flow. Finally, the observed micro-motion in all situations above allows to shed light on the preference of shear-like over compressional motion in terms of a minimized potential energy and a dynamic incompressibility.

Understanding the connection between conformational changes of peptides and equilibrium thermal fluctuations.

Despite the increasing evidence that conformational transitions in peptides and proteins are driven by specific vibrational energy pathways along the molecule, the current experimental techniques of analysis do as yet not allow to study these biophysical processes in terms of anisotropic energy flows. Computational methods offer a complementary approach to obtain a more detailed understanding of the vibrational and conformational dynamics of these systems. Accordingly, in this work we investigate jointly the vibrational energy distribution and the conformational dynamics of trialanine peptide in water solution at room temperature by applying the Instantaneous Normal Mode analysis to the results derived from equilibrium molecular dynamics simulations. It is shown that conformational changes in trialanine are triggered by the vibrational energy accumulated in the low-frequency modes of the molecule, and that excitation is caused exclusively by thermal fluctuations of the solute-solvent system, thus excluding the possibility of an intramolecular vibrational energy redistribution process.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode.

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

Vibrational energy relaxation of the amide I mode of N-methylacetamide in D₂O studied through Born-Oppenheimer molecular dynamics.

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.

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.

Order parameter by instantaneous normal mode analysis for melting behaviour of cluster Ag17Cu2

We perform isothermal Brownian-type molecular dynamics simulations with the Gupta potential for bimetallic cluster Ag17Cu2 from T=0 to 1500K, across the temperature range associated with the melting behaviour determined by the specific heat of the cluster. We also use the instantaneous normal mode (INM) analysis to dissect dynamics of the cluster. In terms of the projected density of states of the vibrational INMs, we propose a new order parameter that specifically describes the melting behaviour of the cluster. The calculated result of our order parameter is consistent with the information inferred from the specific heat data.

Instantaneous normal mode analysis of the vibrational relaxation of the amide I mode of alanine dipeptide in water

Nonequilibrium Molecular Dynamics (MD) simulations coupled to instantaneous normal modes (INMs) analysis are used to study the vibrational relaxation of the acetyl and amino-end amide I modes of the alanine dipeptide (AlaD) molecule dissolved in water (D2O). The INMs are assigned in terms of the equilibrium normal modes using the Effective Atomic Min-Cost algorithm as adapted to make use of the outputs of standard MD packages, a method which is well suited for the description of flexible molecules. The relaxation energy curves of both amide I modes show multiexponential decays, in good agreement with the experimental findings. It is found that ~85%-90% of the energy relaxes through intramolecular vibrational redistribution. The main relaxation pathways are also identified. The rate at which energy is transferred into the solvent is similar for the acetyl-end and amino-end amide I modes. The conformational changes occurring during relaxation are investigated, showing that the populations of the alpha and beta region conformers are altered by energy transfer in such a way that it takes 15 ps for the equilibrium conformational populations to be recovered after the initial excitation of the AlaD molecule.

Analyzing the liquid state of two-dimensional dust clusters: The instantaneous normal mode approach

The liquid state and the freezing transition of finite two-dimensional dust systems are studied using the instantaneous normal mode (INM) analysis. This technique measures the instantaneous unstable modes of a cluster configuration and relates them to the liquid properties of the system. Here, the INM analysis has been applied to experiments on laser-heated dust clusters. From the experiments, diffusion constants and melting temperatures for clusters of different size have been derived. The INM diffusion constants have been compared to those derived from other standard approaches. The scatter of the diffusion constant retrieved by the INM is smaller than that retrieved by other methods, allowing a more reliable determination of melting temperatures. Moreover, the behavior of double-well and escape modes, which reflect certain topological properties of unstable modes, correlates very well with the behavior of the diffusion constant. Further, the dynamic nature of the unstable modes has been determined as mostly shearlike. Finally, the INM results on the experiments are checked against those from Langevin simulations.

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.

Instantaneous Normal Mode Analysis of Melting of Finite Dust Clusters

The experimental melting transition of finite two-dimensional dust clusters in a dusty plasma is analyzed using the method of instantaneous normal modes. In the experiment, dust clusters are heated in a thermodynamic equilibrium from a solid to a liquid state using a four-axis laser manipulation system. The fluid properties of the dust cluster, such as the diffusion constant, are measured from the instantaneous normal mode analysis. Thereby, the phase transition of these finite clusters is approached from the liquid phase. From the diffusion constants, unique melting temperatures have been assigned to dust clusters of various sizes that very well reflect their dynamical stability properties.

A theoretical study of the sum frequency vibrational spectroscopy of the carbon tetrachloride/water interface

Theoretical approximations to the sum frequency vibrational spectroscopy (SFVS) of the carbon tetrachloride/water interface are constructed using the quantum-corrected time correlation functions (TCF) to aid in interpretation of experimental data and to predict novel vibrational modes. Instantaneous normal mode (INM) methods are used to characterize the observed modes leading to the TCF signal, thus providing molecular resolution of the vibrational lineshapes. Detailed comparisons of the theoretical signals are made with those obtained experimentally and show excellent agreement for the spectral peaks in the O–H stretching region of water. An intermolecular mode, unique to the interface, at 848 cm−1 is also identifiable, similar to the one seen for the water/vapor interface. INM analysis reveals the resonance is due to a wagging mode (hindered rotation) that was previously identified (Perry et al 2005 J. Chem. Phys. 123 144705) as localized on a single water molecule with both hydrogens displaced normal to the interface—generally it is found that the symmetry breaking at the interface leads to hindered translations and rotations at hydrophilic/hydrophobic interfaces that assume finite vibrational frequencies due to anchoring at the aqueous interface. Additionally, examination of the real and imaginary parts of the theoretical SFVS spectra reveal the spectroscopic species attributed the resonances and possible subspecies in the O–H region; these results are consistent with extant experimental data and associated analysis.

Instantaneous Normal Mode Analysis of a Series of Model Molten Salts

A combination of analytical theory and molecular dynamics simulation was previously used to investigate how the dynamics of a fused salt are affected by the distributions of mass and charge in its component ions. These studies are now extended by using instantaneous normal mode analysis to explore how changes in ionic structure affect translational and rotational dynamics at different frequencies. The results indicate that the details of the charge distribution are important in coupling translational and rotational motion in ionic liquids. The observations are broadly consistent with the predictions of the charge lever moment formalism, and provide insight on the nature of dynamics in fused salts.

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.

Core-softened fluids, water-like anomalies, and the liquid-liquid critical points

Molecular dynamics simulations are used to examine the relationship between water-like anomalies and the liquid-liquid critical point in a family of model fluids with multi-Gaussian, core-softened pair interactions. The core-softened pair interactions have two length scales, such that the longer length scale associated with a shallow, attractive well is kept constant while the shorter length scale associated with the repulsive shoulder is varied from an inflection point to a minimum of progressively increasing depth. The maximum depth of the shoulder well is chosen so that the resulting potential reproduces the oxygen-oxygen radial distribution function of the ST4 model of water. As the shoulder well depth increases, the pressure required to form the high density liquid decreases and the temperature up to which the high-density liquid is stable increases, resulting in the shift of the liquid-liquid critical point to much lower pressures and higher temperatures. To understand the entropic effects associated with the changes in the interaction potential, the pair correlation entropy is computed to show that the excess entropy anomaly diminishes when the shoulder well depth increases. Excess entropy scaling of diffusivity in this class of fluids is demonstrated, showing that decreasing strength of the excess entropy anomaly with increasing shoulder depth results in the progressive loss of water-like thermodynamic, structural and transport anomalies. Instantaneous normal mode analysis was used to index the overall curvature distribution of the fluid and the fraction of imaginary frequency modes was shown to correlate well with the anomalous behavior of the diffusivity and the pair correlation entropy. The results suggest in the case of core-softened potentials, in addition to the presence of two length scales, energetic, and entropic effects associated with local minima and curvatures of the pair interaction play an important role in determining the presence of water-like anomalies and the liquid-liquid phase transition.