Emergence of pseudo-time during optimal Monte Carlo sampling and temporal aspects of symmetry breaking and restoration.

We argue that one can associate a pseudo-time with sequences of configurations generated in the course of classical Monte Carlo simulations for a single-minimum bound state if the sampling is optimal. Hereby, the sampling rates can be, under special circumstances, calibrated against the relaxation rate and frequency of motion of an actual physical system. The latter possibility is linked to the optimal sampling regime being a universal crossover separating two distinct suboptimal sampling regimes analogous to the physical phenomena of diffusion and effusion, respectively. Bound states break symmetry; one may thus regard the pseudo-time as a quantity emerging together with the bound state. Conversely, when transport among distinct bound states takes place-thus restoring symmetry-a pseudo-time can no longer be defined. One can still quantify activation barriers if the latter barriers are smooth, but simulation becomes impractically slow and pertains to overdamped transport only. Specially designed Monte Carlo moves that bypass activation barriers-so as to accelerate sampling of the thermodynamics-amount to effusive transport and lead to severe under-sampling of transition-state configurations that separate distinct bound states while destroying the said universality. Implications of the present findings for simulations of glassy liquids are discussed.

Glass Dynamics Deep in the Energy Landscape.

When a liquid is cooled, progress down the energy landscape is arrested near the glass transition temperature Tg. In principle, lower energy states can be accessed by waiting for further equilibration, but the rough energy landscape of glasses quickly leads to kinetics on geologically slow time scales below Tg. Over the past decade, progress has been made probing deeper into the energy landscape via several techniques. By looking at bulk and surface diffusion, using layered deposition that promotes equilibration, imaging glass surfaces with faster dynamics below Tg, and optically exciting glasses, experiments have moved into a regime of ultrastable, low energy glasses that was difficult to access in the past. At the same time, both simulations and energy landscape theory based on a random first order transition (RFOT) have tackled systems that include surfaces, optical excitation, and interfacial dynamics. Here we review some of the recent experimental work, and how energy landscape theory illuminates glassy dynamics well below the glass transition temperature by making direct connections between configurational entropy, energy landscape barriers, and the resulting dynamics.

Photon Activation of Glassy Dynamics: A Mechanism for Photoinduced Fluidization, Aging, and Information Storage in Amorphous Materials.

We discuss the photon activation of structural relaxations in glassy melts and frozen glasses containing molecules that can photoisomerize. The built-in stress following a photoinduced electronic transition lowers the thermal activation barrier for subsequent structural reconfiguration of the glassy matrix. We provide explicit predictions for the barrier distribution and structural relaxation spectrum as functions of the concentration of photoactivated molecules and the fragility of the material. The typical barrier decreases upon photoactivation, while the barrier distribution increases in width with increasing mole fraction of photoactive molecules and fluence, and becomes multimodal. In a frozen glass, the initial effects of photoisomerization locally facilitate the dynamics near the excited chromophores and can lead to complete fluidization at a sufficiently high fluence. Photon activation initially decreases the yield strength of the glass. Depending on the precise time course of illumination, there however emerges a spatial coexistence of softened regions with regions that, after being destabilized by illumination, have reconfigured so that they are now made of ultrastable glass or have crystallized as in a porcelain. This sequence of events, after illumination, can lead to highly stable amorphous solids, potentially approaching the Kauzmann limit. These mechanisms are at the root of optical information storage technologies in amorphous materials.

Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids.

We present a microscopic picture rationalizing the surprisingly steep decrease in the bandgap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons-when the latter are present-or their disordered analogs if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell electronic configurations, the existence of an insulating gap or pseudogap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present, with the possible exception of weakly bonded solids such as rare-gas or ferromagnetic Wigner crystals. As a corollary, a (periodic) elemental solid held together by nonclosed shell interactions and whose primitive unit contains only one atom will ordinarily be a metal, consistent with observation. Consequences of the present picture for Wigner solids are discussed. A simple field theory of the metal-insulator transition is constructed that directly ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition. The order parameter is shown to have at least two components, yet no Goldstone mode arises as a result of the transition.

A mechanism for reversible mesoscopic aggregation in liquid solutions.

Solutions of proteins and other molecules exhibit puzzling, mesoscopically sized inclusions of a solute-rich liquid, well outside the region of stability of the solute-rich phase. This mesoscopic size is in conflict with existing views on heterophase fluctuations. Here we systematically work out a microscopic mechanism by which a metastable solute-rich phase can readily nucleate in a liquid solution. A requisite component of the mechanism is that the solute form long-lived complexes with itself or other molecules. After nucleated in this non-classical fashion, individual droplets grow until becoming mechanically unstable because of a concomitant drop in the internal pressure, the drop caused by the metastability of the solute-rich phase. The ensemble of the droplets is steady-state. In a freshly prepared solution, the ensemble is predicted to evolve in a way similar to the conventional Ostwald ripening, during which larger droplets grow at the expense of smaller droplets.

Structural Origin of the Midgap Electronic States and the Urbach Tail in Pnictogen-Chalcogenide Glasses.

We determine the electronic density of states for computationally generated bulk samples of amorphous chalcogenide alloys As xSe100- x. The samples were generated using a structure-building algorithm reported recently by us. Several key features of the calculated density of states are in good agreement with experiment: The trend of the mobility gap with arsenic content is reproduced. The sample-to-sample variation in the energies of states near the mobility gap is quantitatively consistent with the width of the Urbach tail in the optical edge observed in experiment. Most importantly, our samples consistently exhibit very deep-lying midgap electronic states that are delocalized significantly more than what would be expected for a deep impurity or defect state; the delocalization is highly anisotropic. These properties are consistent with those of the topological midgap electronic states that have been proposed by Zhugayevych and Lubchenko as an explanation for several puzzling optoelectronic anomalies observed in the chalcogenides, including light-induced midgap absorption and electron spin resonance signal, and anomalous photoluminescence. In a complement to the traditional view of the Urbach states as a generic consequence of disorder in atomic positions, the present results suggest these states can be also thought of as intimate pairs of topological midgap states that cannot recombine because of disorder. Finally, samples with an odd number of electrons exhibit neutral, spin 1/2 midgap states as well as polaron-like configurations that consist of a charge carrier bound to an intimate pair of midgap states; the polaron's identity, electron or hole, depends on the preparation protocol of the sample.

Aging, Jamming, and the Limits of Stability of Amorphous Solids.

Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily far away from equilibrium and require a description of the history of the conditions under which they formed. In this paper we describe how the locality of interactions intrinsic to finite-dimensional systems affects the stability of amorphous solids far off equilibrium. Our analysis encompasses both structural glasses formed by cooling and colloidal assemblies formed by compression. A diagram outlining regions of marginal stability can be adduced which bears some resemblance to the quasi-equilibrium replica meanfield theory phase diagram of hard sphere glasses in high dimensions but is distinct from that construct in that the diagram describes not true phase transitions but kinetic transitions that depend on the preparation protocol. The diagram exhibits two distinct sectors. One sector corresponds to amorphous states with relatively open structures, the other to high density, more closely packed ones. The former transform rapidly owing to there being motions with no free energy barriers; these motions are string-like locally. In the dense region, amorphous systems age via compact activated reconfigurations. The two regimes correspond, in equilibrium, to the collisional or uniform liquid and the so-called landscape regime, respectively. These are separated by a spinodal line of dynamical crossovers. Owing to the rigidity of the surrounding matrix in the landscape, high-density part of the diagram, a sufficiently rapid pressure quench adds compressive energy which also leads to an instability toward string-like motions with near vanishing barriers. Conversely, a dilute collection of rigid particles, such as a colloidal suspension leads, when compressed, to a spatially heterogeneous structure with percolated mechanically stable regions. This jamming corresponds to the onset of activation when the spinodal line is traversed from the low density side. We argue that a stable glass made of sufficiently rigid particles can also be viewed as exhibiting sporadic and localized buckling instabilities that result in local jammed structures. The lines of instability we discuss resemble the Gardner transition of meanfield systems but, in contrast, do not result in true criticality owing to being short-circuited by activated events. The locally marginally stable modes of motion in amorphous solids correspond to secondary relaxation processes in structural glasses. Their relevance to the low temperature anomalies in glasses is also discussed.

Amorphous chalcogenides as random octahedrally bonded solids: I. Implications for the first sharp diffraction peak, photodarkening, and Boson peak.

We develop a computationally efficient algorithm for generating high-quality structures for amorphous materials exhibiting distorted octahedral coordination. The computationally costly step of equilibrating the simulated melt is relegated to a much more efficient procedure, viz., generation of a random close-packed structure, which is subsequently used to generate parent structures for octahedrally bonded amorphous solids. The sites of the so-obtained lattice are populated by atoms and vacancies according to the desired stoichiometry while allowing one to control the number of homo-nuclear and hetero-nuclear bonds and, hence, effects of the mixing entropy. The resulting parent structure is geometrically optimized using quantum-chemical force fields; by varying the extent of geometric optimization of the parent structure, one can partially control the degree of octahedrality in local coordination and the strength of secondary bonding. The present methodology is applied to the archetypal chalcogenide alloys AsxSe1-x. We find that local coordination in these alloys interpolates between octahedral and tetrahedral bonding but in a non-obvious way; it exhibits bonding motifs that are not characteristic of either extreme. We consistently recover the first sharp diffraction peak (FSDP) in our structures and argue that the corresponding mid-range order stems from the charge density wave formed by regions housing covalent and weak, secondary interactions. The number of secondary interactions is determined by a delicate interplay between octahedrality and tetrahedrality in the covalent bonding; many of these interactions are homonuclear. The present results are consistent with the experimentally observed dependence of the FSDP on arsenic content, pressure, and temperature and its correlation with photodarkening and the Boson peak. They also suggest that the position of the FSDP can be used to infer the effective particle size relevant for the configurational equilibration in covalently bonded glassy liquids, where the identification of the effective rigid molecular unit is ambiguous.

The chemical bond as an emergent phenomenon.

We first argue that the covalent bond and the various closed-shell interactions can be thought of as symmetry broken versions of one and the same interaction, viz., the multi-center bond. We use specially chosen molecular units to show that the symmetry breaking is controlled by density and electronegativity variation. We show that the bond order changes with bond deformation but in a step-like fashion, regions of near constancy separated by electronic localization transitions. These will often cause displacive transitions as well so that the bond strength, order, and length are established self-consistently. We further argue on the inherent relation of the covalent, closed-shell, and multi-center interactions with ionic and metallic bonding. All of these interactions can be viewed as distinct sectors on a phase diagram with density and electronegativity variation as control variables; the ionic and covalent/secondary sectors are associated with on-site and bond-order charge density wave, respectively, the metallic sector with an electronic fluid. While displaying a contiguity at low densities, the metallic and ionic interactions represent distinct phases separated by discontinuous transitions at sufficiently high densities. Multi-center interactions emerge as a hybrid of the metallic and ionic bond that results from spatial coexistence of delocalized and localized electrons. In the present description, the issue of the stability of a compound is that of the mutual miscibility of electronic fluids with distinct degrees of electron localization, supra-atomic ordering in complex inorganic compounds coming about naturally. The notions of electronic localization advanced hereby suggest a high throughput, automated procedure for screening candidate compounds and structures with regard to stability, without the need for computationally costly geometric optimization.

Lack of Dependence of the Sizes of the Mesoscopic Protein Clusters on Electrostatics.

Protein-rich clusters of steady submicron size and narrow size distribution exist in protein solutions in apparent violation of the classical laws of phase equilibrium. Even though they contain a minor fraction of the total protein, evidence suggests that they may serve as essential precursors for the nucleation of ordered solids such as crystals, sickle-cell hemoglobin polymers, and amyloid fibrils. The cluster formation mechanism remains elusive. We use the highly basic protein lysozyme at nearly neutral and lower pH as a model and explore the response of the cluster population to the electrostatic forces, which govern numerous biophysical phenomena, including crystallization and fibrillization. We tune the strength of intermolecular electrostatic forces by varying the solution ionic strength I and pH and find that despite the weaker repulsion at higher I and pH, the cluster size remains constant. Cluster responses to the presence of urea and ethanol demonstrate that cluster formation is controlled by hydrophobic interactions between the peptide backbones, exposed to the solvent after partial protein unfolding that may lead to transient protein oligomers. These findings reveal that the mechanism of the mesoscopic clusters is fundamentally different from those underlying the two main classes of ordered protein solid phases, crystals and amyloid fibrils, and partial unfolding of the protein chain may play a significant role.

Pressure in the Landau-Ginzburg functional: Pascal's law, nucleation in fluid mixtures, a meanfield theory of amphiphilic action, and interface wetting in glassy liquids.

We set up the problem of finding the transition state for phase nucleation in multi-component fluid mixtures, within the Landau-Ginzburg density functional. We establish an expression for the coordinate-dependent local pressure that applies to mixtures, arbitrary geometries, and certain non-equilibrium configurations. The expression allows one to explicitly evaluate the pressure in spherical geometry, à la van der Waals. Pascal's law is recovered within the Landau-Ginzburg density functional theory, formally analogously to how conservation of energy is recovered in the Lagrangian formulation of mechanics. We establish proper boundary conditions for certain singular functional forms of the bulk free energy density that allow one to obtain droplet solutions with thick walls in essentially closed form. The hydrodynamic modes responsible for mixing near the interface are explicitly identified in the treatment; the composition at the interface is found to depend only weakly on the droplet size. Next we develop a Landau-Ginzburg treatment of the effects of amphiphiles on the surface tension; the amphiphilic action is seen as a violation of Pascal's law. We explicitly obtain the binding potential for the detergent at the interface and the dependence of the down-renormalization of the surface tension on the activity of the detergent. Finally, we argue that the renormalization of the activation barrier for escape from long-lived structures in glassy liquids can be viewed as an action of uniformly seeded, randomly oriented amphiphilic molecules on the interface separating two dissimilar aperiodic structures. This renormalization is also considered as a "wetting" of the interface. The resulting conclusions are consistent with the random first order transition theory.

Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids.

We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant--which is enhanced by adding polar molecules to the system--the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid, respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the random first order transition theory.

On the mechanism of activated transport in glassy liquids.

We explore several potential issues that have been raised over the years regarding the "entropic droplet" scenario of activated transport in liquids, due to Wolynes and co-workers, with the aim of clarifying the status of various approximations of the random first-order transition theory (RFOT) of the structural glass transition. In doing so, we estimate the mismatch penalty between alternative aperiodic structures, above the glass transition; the penalty is equal to the typical magnitude of free energy fluctuations in the liquid. The resulting expressions for the activation barrier and the cooperativity length contain exclusively bulk, static properties; in their simplest form they contain only the bulk modulus and the configurational entropy per unit volume. The expressions are universal in that they do not depend explicitly on the molecular detail. The predicted values for the barrier and cooperativity length and, in particular, the temperature dependence of the barrier are in satisfactory agreement with observation. We thus confirm that the entropic droplet picture is indeed not only internally consistent but is also fully constructive, consistent with the apparent success of its many quantitative predictions. A simple view of a glassy liquid as a locally metastable, degenerate pattern of frozen-in stress emerges in the present description. Finally, we derive testable relationships between the bulk modulus and several characteristics of glassy liquids and peculiarities in low-temperature glasses.

Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: the comparative role of configurational entropy and elasticity.

We compute the temperature-dependent barrier for α-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition (RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes (Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 2990), which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko (J. Chem. Phys. 2013, 138, 12A534), which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance--a kinetic quantity--from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. (Science 2005, 310, 1797) procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.

Molecular binoculars: how to spatially resolve environmental fluctuations by following two or more single-molecule spectral trails at a time.

We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations. To this end, we estimate the combined probability distribution for the frequencies of a set of chromophores contained within the same sample. The present setup introduces a new length scale, i.e., the interchromophore distance, which breaks the aforementioned scale invariance and enables one to determine independently the concentration of the environmental fluctuations and their coupling to the chromophores, by monitoring the time after which spectral diffusion of distinct chromophores becomes uncorrelated. We illustrate these results with structural excitations in low temperature glasses.

Microscopic calculation of the free energy cost for activated transport in glass-forming liquids.

Activated transport in liquids--supercooled liquids in particular--occurs via mutual nucleation of alternative, aperiodic minima of the free energy. Xia and Wolynes [Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000)] have made a general argument that at temperatures near the ideal glass transition, the surface penalty for this kind of nucleation is largely determined by the temperature and the logarithm of the size of the vibrational fluctuation of rigid molecular units about the local minimum. Here, we independently show how to estimate this surface tension and, hence, the activation barrier for the activated transport for several actual liquids, using their structure factors and knowledge of the finite-frequency elastic constants. In this estimate, the activation free energy, while depending on the configurational entropy, also depends on the elastic modulus as in the "shoving" models. The resulting estimates are however consistent with the estimate provided by Xia and Wolynes' argument near the glass transition and, in addition, reflect the barrier softening effects predicted earlier for fragile substances.

Ostwald-like ripening of the anomalous mesoscopic clusters in protein solutions.

Metastable clusters of mesoscopic dimensions composed of protein-rich liquid exist in protein solutions, both in the homogeneous region of the solution phase diagram and in the region supersaturated with respect to an ordered solid phase, such as crystals; in the latter region they are crucial nucleation sites for ordered solids. We monitor, using three optical techniques, the long-term evolution of the clusters in lysozyme solutions at conditions where no condensed phases, liquid or solid, are stable or present as long-lived metastable domains. We show that cluster formation is a reversible process and that the clusters are in near equilibrium with the solution, up to a capillary correction. In contrast to classical phase transformations, the solution concentration at cluster-solution equilibrium is close to its initial value; this is akin to chemical reaction equilibria and demonstrates the complex chemical composition of the clusters. However, similar to classical phase transformations, en route to full equilibration, the average cluster size grows with time following a universal law t(0.26±0.03), independent of the cluster volume fraction; the cluster size distribution is scale-invariant at all stages of cluster evolution. Despite the correspondence of these behaviors to the Lifshitz-Slyozov-Wagner (LSW) theory predictions, the cluster sizes are about 10× smaller than the LSW prediction, likely due to the complex cluster composition. The observed cluster evolution helps us to understand nucleation mysteries, such as nucleation rates lower by orders of magnitude than classical theory predictions, nucleation rate variable under steady conditions, and others.

Anisotropy of the Coulomb interaction between folded proteins: consequences for mesoscopic aggregation of lysozyme.

Toward quantitative description of protein aggregation, we develop a computationally efficient method to evaluate the potential of mean force between two folded protein molecules that allows for complete sampling of their mutual orientation. Our model is valid at moderate ionic strengths and accounts for the actual charge distribution on the surface of the molecules, the dielectric discontinuity at the protein-solvent interface, and the possibility of protonation or deprotonation of surface residues induced by the electric field due to the other protein molecule. We apply the model to the protein lysozyme, whose solutions exhibit both mesoscopic clusters of protein-rich liquid and liquid-liquid separation; the former requires that protein form complexes with typical lifetimes of approximately milliseconds. We find the electrostatic repulsion is typically lower than the prediction of the Derjaguin-Landau-Verwey-Overbeek theory. The Coulomb interaction in the lowest-energy docking configuration is nonrepulsive, despite the high positive charge on the molecules. Typical docking configurations barely involve protonation or deprotonation of surface residues. The obtained potential of mean force between folded lysozyme molecules is consistent with the location of the liquid-liquid coexistence, but produces dimers that are too short-lived for clusters to exist, suggesting lysozyme undergoes conformational changes during cluster formation.