Ergodicity-breaking transition and high-frequency response in a simple free-energy landscape

We present a simple dynamical model described by a Langevin equation in a piecewise parabolic free-energy landscape, modulated by a temperature-dependent overall curvature. The zero-curvature point marks a transition to a phase with broken ergodicity. The frequency-dependent response near this transition is reminiscent of observations near the glass transition.     

Solvent-coordinate free-energy landscape view of water-mediated ion-pair dissociation

Water-mediated ion-pair dissociation is studied by molecular dynamics simulations of NaCl in water. Multidimensional free-energy analysis clarifies the relation between two essential solvent coordinates: the water coordination number and water-bridge formation. These two are related in a complex way. Both are necessary to describe ion-pair dissociation. The mechanism constructed with both solvent variables clearly shows the individual roles. The water coordination number is critical for starting ion-pair dissociation. Water-bridge formation is also important because it increases the likelihood of ion-pair dissociation by reducing the dissociation free-energy barrier. Additional Ca–Cl and NH₄–Cl calculations show that these conclusions are unaffected by changes in the ion charge and shape. The present results will contribute to future explorations of many other molecular events such as surface water exchange and protein-ligand dissociation because the same mechanism is involved in such events.     

In silico folding of a three helix protein and characterization of its free-energy landscape in an all-atom force field

We report the reproducible first-principles folding of the 40 amino-acid, three-helix headpiece of the HIV accessory protein in a recently developed all-atom free-energy force field. Six of 20 simulations using an adapted basin-hopping method converged to better than 3 A backbone rms deviation to the experimental structure. Using over 60 000 low-energy conformations of this protein, we constructed a decoy tree that completely characterizes its folding funnel.     

Dynamic disorder characteristics of single-molecule pulling experiments on two-dimensional free-energy landscape

The dynamic characteristic of macromolecule is mainly subject to the fluctuation of rate constant and this phenomenon is usually considered as dynamic disorder (DD). In order to detect the DD nature in the bio-molecule system more accurately, here we propose a theoretical framework based on the two-dimensional (2D) free-energy landscape including the pulling coordinate and other slow conformational variables. The generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and the power-law memory kernel are used on this landscape for the research. The transition rate, which depends on both intrinsic barrier height and noise strength ratio, has been analyzed under the condition of external force. The particular discrepancies were investigated between the kinetics of the transitions with and without DD. We find that the discrepancies relied on the barrier height and the noise strength ratio. Taken together, our study illustrates the importance of the DD characteristics, which should be taken into account during the research into the single-molecule pulling experiments.     

Gels and glasses in a single system: evidence for an intricate free-energy landscape of glassy materials

In the free-energy landscape picture of glassy systems, their slow dynamics is due to a complicated free-energy landscape with many local minima. We show that for a colloidal glassy material multiple paths can be taken through the free-energy landscape. The evolution of the nonergodicity parameter shows two distinct master curves that we identify as gels and glasses. We show that for a range of colloid concentrations, the transition to nonergodicity can occur in either direction (gel or glass), accompanied by "hesitations" between the two. Thus, colloidal gels and glasses are merely global free-energy minima in the same free-energy landscape, and the paths leading to these minima can be complicated.     

Computer simulation study of a two-dimensional nematogenic lattice model based on a mapping from elastic free-energy density

Over the last few years, it has been recognized that on can construct, in different ways, a nematogenic lattice model with pairwise additive interactions, which approximately reproduce the elastic free energy density, and where the parameters defining the pair potential are expressed in terms of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess [Z. Naturforsch. A 51 (1996) 1] has been investigated by Monte Carlo simulation, for particle centers of mass associated with both a three- and a two-dimensional lattice. Another approximate procedure for the mapping had also been proposed, and studied by simulation on a three-dimensional lattice (Luckhurst and Romano [Liq. Cryst. 26 (1999) 871]) continuing along this line, we investigate here the 2-dimensional lattice counterpart, by means of Mean Field theory and Monte Carlo simulations. In 2 dimensions, the anisotropic character of these potential models does not preclude the existence of orientational order at finite temperature. The model produces a ground state where particles are aligned in the lattice plane; both Mean Field (MF) predictions and simulation results for the second-rank ordering tensor show a low-temperature régime where the system becomes biaxial, with the main director aligned along a lattice axis; at higher temperature there is a transition to uniaxial order with negative order parameter, and director orthogonal to the lattice plane; this orientational order survives up to temperatures higher than the transition temperature of the 3-dimensional counterpart, possibly at all finite temperatures. MF predictions and simulation results appear to agree qualitatively, but in quantitative terms the MF prediction for the transition temperature is some 56% too high.     

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamic and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the local minima energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.     

Minimalist landscape model of glass relaxation

The relaxation behavior of glass is of great scientific and technological importance. However, prediction of glass relaxation behavior using direct first principles techniques is currently infeasible for realistic laboratory time scales. The enthalpy landscape approach has proven to be successful in overcoming this time scale constraint and providing insights into the fundamental physics governing glass transition and relaxation behavior. However, it is still too computationally intensive to calculate representative enthalpy landscapes for multicomponent glasses of industrial interest. It is thus interesting to consider a simplified enthalpy landscape that captures the essential features of glass relaxation and can be solved analytically. Here, we present the analytical solution for such a “minimalist landscape” model that is complicated enough to capture both primary (α$\alpha$) and secondary (β$\beta$) relaxation processes, yet simple enough to offer a closed-form solution. Using this minimalist landscape, we perform model calculations to illustrate the relative impact of activation barriers and entropy on glass relaxation behavior. The results of our model show that α$\alpha$ and β$\beta$ relaxation processes are largely decoupled, in agreement with recently published experimental results.     

Failure of the work-Hamiltonian connection for free-energy calculations

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial differentialH(x,t)/partial differentialt, which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free-energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.     

Reconstructing the electron in a fractionalized quantum fluid

The low-energy physics of the fractional Hall liquid is described in terms of quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electronlike quasiparticle also exists in the excitation spectrum: the state obtained by the application of an electron creation operator to a fractional quantum Hall ground state has a nonzero overlap with a complex, high energy bound state containing an odd number of composite-fermion quasiparticles. The electron annihilation operator similarly couples to a bound complex of composite-fermion holes. We predict that these bound states can be observed through a conductance resonance in experiments involving a tunneling of an external electron into the fractional quantum Hall liquid. A comment is made on the origin of the breakdown of the Fermi liquid paradigm in the fractional Hall liquid.     

Curvature of the energy landscape and folding of model proteins

We study the geometric properties of the energy landscape of coarse-grained, off-lattice models of polymers by endowing the configuration space with a suitable metric, depending on the potential energy function, such that the dynamical trajectories are the geodesics of the metric. Using numerical simulations, we show that the fluctuations of the curvature clearly mark the folding transition, and that this quantity allows to distinguish between polymers having a proteinlike behavior (i.e., that fold to a unique configuration) and polymers which undergo a hydrophobic collapse but do not have a folding transition. These geometrical properties are defined by the potential energy without requiring any prior knowledge of the native configuration.     

Potential energy landscape and long-time dynamics in a simple model glass

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained by studying small size samples, we describe the dynamics of the systems in multidimensional configurational space by means of a simple model. This considers the configurational space as a connected network of minima where the dynamics proceeds by jumps described by an appropriate master equation. Using this model we are able to reproduce the long-time dynamics and the low temperature regime. We investigate both the equilibrium regime and the off-equilibrium one, finding those typical glassy behaviors usually observed in the experiments such as (i) a stretched exponential relaxation, (ii) a temperature-dependent stretching parameter, (iii) a breakdown of the Stokes-Einstein relation, and (iv) the appearance of a critical temperature below which one observes a deviation from the fluctuation-dissipation relation as a consequence of the lack of equilibrium in the system.     

Anharmonicity and self-similarity of the free energy landscape of protein G

The near-native free-energy landscape of protein G is investigated through 0.4-micros-long atomistic molecular dynamics simulations in an explicit solvent. A theoretical and computational framework is used to assess the time dependence of salient thermodynamical features. While the quasiharmonic character of the free energy is found to degrade in a few ns, the slow modes display a very mild dependence on the trajectory duration. This property originates from a striking self-similarity of the free-energy landscape embodied by the consistency of the principal directions of the local minima, where the system dwells for several ns, and of the virtual jumps connecting them.     

Reconstructing a separable interaction within the relativistic quasipotential approach

Within the relativistic quasipotential approach to quantum field theory, a method is developed according to which a nonlocal separable quasipotential that represents the interaction between two relativistic particles of unequal masses can be reconstructed on the basis of the phase shift and bound-state energies.     

Signatures of dynamical heterogeneity in the structure of glassy free-energy minima

From numerical minimization of a model free-energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation, similar to that of the "local Debye-Waller factor" in simulations of dynamical heterogeneity. Molecular dynamics simulations starting from a particle configuration generated from the density distribution at a glassy free-energy minimum show similar spatial heterogeneity in the degree of localization, implying a direct connection between dynamical heterogeneity and the structure of glassy free-energy minima.     

基于路径积分分子动力学与热力学积分方法的高压氢自由能计算

在相图研究中, 严格计算一个真实系统在特定温度、压强下的自由能是近年来该领域理论方法发展的前沿. 自Mermin提出有限温度密度泛函理论后, 在电子结构层面, 弱关联系统中人们就其在对自由能贡献的描述已相对完善, 但在原子核运动的描述上, 热运动与量子运动的非简谐项却总被忽视. 本文将路径积分分子动力学与热力学积分结合, 对300 GPa下氢晶体Cmca 结构中原子核热涨落与量子涨落对自由能的影响进行了分析. 发现在100 K核量子涨落非简谐项的贡献约为15 meV每原子, 远大于不同结构间静态焓的差别. 该研究提醒人们简谐近似在核量子效应描述中可能存在的不准确性(即使在低温下). 同时, 我们采取的方法 也为人们进行自由能的准确计算提供了一个简单有效的手段.