Parallel Tempering Molecular Dynamics Research Articles

Gold Clusters on Graphene/Graphite—Structure and Energy Landscape

Adopting an advanced microscopic model of the Au–graphite interaction, a systematic study of Au nanoclusters (up to sizes of 11 238 atoms) on graphene and on graphite is carried out to explore their structure and energy landscape. Using parallel tempering molecular dynamics, structural distribution as a function of temperature is calculated in the entire temperature range. Low‐energy structures are identified through a combination of structural optimization and Wulff–Kaischew construction which are then used to explore the energy landscape. The potential energy surface (PES), which is energy as a function of translation and rotation, is calculated for a few Au nanoclusters along specific directions on carbon lattice. Minimum‐energy pathways are identified on the PES indicating a reduced barrier for pathways involving simultaneous rotation and translation. Diffusion simulations of Au233 on graphite show that diffusion mechanism is directly related to the PES, and the information of the cluster pinning events is already present in the PES. Finally, a comparison of various interaction models highlights the importance of reasonably correct Au–C interactions which is crucial for studying the energy landscape and cluster sliding.

Green-Kubo paralell tempering molecular dynamics determination of the thermal conductivity for the wurtzite ZnO: statistical problems of the method

The thermal conductivity for the wurtzite ZnO is determined in the temperature range from 300 to 1100 K by using parallel tempering molecular dynamics within the Green-Kubo approach and a classical Morse-Born-Mayer-Coulomb hybrid interaction potential. Compared to other previous calculations for the thermal conductivity of common crystals within the same Green-Kubo and molecular dynamics approach, the used parallel tempering scheme shows some appealing improvements in the calculation of the time self-correlation of the heat flux vector, although at the price of using a relatively large number of total computational steps. However, in spite of the found improvements for the calculation of the self-correlation of the heat flux vector, some statistical problems on this point remain on the particular application of the method. Finally, even with the presence of a clear statistical noise, the obtained values and temperature trend of the calculated thermal conductivity shows the classical 1/T decaying behavior reported in previous works for wurtzite ZnO and other related semiconductor systems using the alternative Boltzmann transport equation theory.

Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics.

We performed parallel-tempering molecular dynamics simulations to predict the temperature- and size-dependent equilibrium shapes of a series of Cu nanocrystals in the 100- to 200-atom size range. Our study indicates that temperature-dependent, solid-solid shape transitions occur frequently for Cu nanocrystals in this size range. Complementary calculations with electronic density functional theory indicate that vibrational entropy favors nanocrystals with a shape intermediate between a decahedron and an icosahedron. Overall, we find that entropy plays a significant role in determining the shapes Cu nanocrystals, so studies aimed at determining minimum-energy shapes may fail to correctly predict shapes observed at experimental temperatures. We also observe significant shape changes with nanocrystal size - sometimes with changes in a single atom. The information from this study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

Structural classification of Ag and Cu nanocrystals with machine learning.

We use machine learning (ML) to classify the structures of mono-metallic Cu and Ag nanoparticles. Our datasets comprise a broad range of structures - both crystalline and amorphous - derived from parallel-tempering molecular dynamics simulations of nanoparticles in the 100-200 atom size range. We construct nanoparticle features using common neighbor analysis (CNA) signatures, and we utilize principal component analysis to reduce the dimensionality of the CNA feature set. To sort the nanoparticles into structural classes, we employed both K-means clustering and the Gaussian mixture model (GMM). We evaluated the performance of the clustering algorithms through the gap statistic and silhouette score, as well as by analysis of the CNA signatures. For Ag, we found five structural classes, with 14 detailed sub-classes, while for Cu, we found two broad classes (crystalline and amorphous), with the same five classes as for Ag, and 15 detailed sub-classes. Our results demonstrate that these ML methods are effective in identifying and categorizing nanoparticle structures to different levels of complexity, enabling us to classify nanoparticles into distinct and physically relevant structural classes with high accuracy. This capability is important for understanding nanoparticle properties and potential applications.

Charting Nanocluster Structures via Convolutional Neural Networks.

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

Minimum Free-Energy Shapes of Ag Nanocrystals: Vacuum vs Solution.

We use two variants of replica-exchange molecular dynamics (MD) simulations, parallel tempering MD and partial replica exchange MD, to probe the minimum free-energy shapes of Ag nanocrystals containing 100-200 atoms in a vacuum, ethylene glycol (EG) solvent, and EG solvent with a PVP polymer containing 100 repeat units. Our simulations reveal a shape intermediate between a Dh and an Ih, a Dh-Ih, that has distinct structural signatures and magic sizes. We find several prominent features associated with entropy: pure FCC nanocrystals are less common than FCC crystals containing stacking faults, and crystals with the minimum potential energy are not always preferred over the range of relevant temperatures. The shapes of the nanocrystals in solution are influenced by the chemical identities of the solution-phase molecules. Comparing Ag nanocrystal shapes in EG to those in an EG+PVP solution, we find more icosahedra in EG and more decahedra in EG+PVP across all of the nanocrystal sizes probed in this study. At certain critical sizes, nanocrystal shapes can change dramatically with the addition and removal of a single atom or with a change in temperature at a fixed size. The information in our study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

Structural transformations in Cu, Ag, and Au metal nanoclusters.

Finite-temperature structures of Cu, Ag, and Au metal nanoclusters are calculated in the entire temperature range from 0K to melting using a computational methodology that we proposed recently [M. Settem et al., Nanoscale 14, 939 (2022)]. In this method, Harmonic Superposition Approximation (HSA) and Parallel Tempering Molecular Dynamics (PTMD) are combined in a complementary manner. HSA is accurate at low temperatures and fails at higher temperatures. PTMD, on the other hand, effectively samples the high temperature region and melts. This method is used to study the size- and system-dependent competition between various structural motifs of Cu, Ag, and Au nanoclusters in the size range 1-2nm. Results show that there are mainly three types of structural changes in metal nanoclusters, depending on whether a solid-solid transformation occurs. In the first type, the global minimum is the dominant motif in the entire temperature range. In contrast, when a solid-solid transformation occurs, the global minimum transforms either completely to a different motif or partially, resulting in the co-existence of multiple motifs. Finally, nanocluster structures are analyzed to highlight the system-specific differences across the three metals.

Implementation of the parallel-tempering molecular dynamics method in deMon2k and application to the water hexamer

Implementation of the parallel-tempering molecular dynamics method in deMon2k and application to the water hexamer

Au147 nanoparticles: Ordered or amorphous?

Structural aspects of the Au147 cluster have been investigated through a density functional based tight binding global optimization involving a parallel tempering molecular dynamics scheme with quenching followed by geometries relaxation at the Density Functional Theory (DFT) level. The focus is put on the competition between relaxed ordered regular geometries and disordered (or amorphous) structures. The present work shows that Au147 amorphous geometries are relevant low energy candidates and are likely to contribute in finite temperature dynamics and thermodynamics. The structure of the amorphous-like isomers is discussed from the anisotropy parameters, the atomic coordinations, the radial and pair distribution functions, the IR spectra, and the vibrational DOS. With respect to the regular structures, the amorphous geometries are shown to be characterized by a larger number of surface atoms, a less dense volume with reduced coordination number per atom, a propensity to increase the dimension of flat facets at the surface, and a stronger anisotropy. Moreover, all amorphous clusters have similar IR spectra, almost continuous with active frequencies over the whole spectral range, while symmetric clusters are characterized by a few lines with large intensities.

Melting of the Au20 Gold Cluster: Does Charge Matter?

We investigate the dependence upon the charge of the heat capacities of magic gold cluster Au20 obtained from density functional-based tight binding theory within parallel tempering molecular dynamics and the multiple histogram method. The melting temperatures, determined from the heat capacity curves, are found to be 1102 K for neutral Au20 and only 866 and 826 K for Au20+ and Au20-. Both the canonical and the microcanonical aspects of the transition are discussed. A convex intruder, associated with a negative heat capacity, is evidenced in the microcanonical entropy in the case of the neutral cluster but is absent in the melting processes of the ions. The present work shows that a single charge quantitatively affects the thermal properties of the gold 20mer.

Global optimization of neutral and charged 20- and 55-atom silver and gold clusters at the DFTB level

The global optimization of metallic clusters is an important topic because nanoclusters exhibit structure-dependent properties. In this paper, we present a global optimization study of Ag20, Au20, Ag55 and Au55 in their neutral and charge states (−1, 0, +1) conducted using a Parallel-Tempering Molecular Dynamics algorithm at the DFTB level without pre-screening. For Au20, Ag20 and their ions, the present DFTB low energy structures are in good agreement with previously published calculations and experimental data. In the case of Ag55- and Au55-, the present study is consistent with photo-electron detachment experiments suggesting highly symmetric icosahedral structures for silver and more disordered morphologies for gold. The present results are also compatible with trapped ion electron diffraction experiments and calculations for Ag55+ and Ag55-. We report low-energy isomers of Au55 exhibiting cavities below their external shell. This work quantitatively confirms the relevance of DFTB for structure calculation of noble metal clusters. Furthermore, it also demonstrates the feasibility of global optimization using DFTB, without pre-screening through classical potential, for sizes up to a few tens of atoms and for different charge states.

Theoretical investigation of the solid-liquid phase transition in protonated water clusters.

Protonated water clusters have received a lot of attention as they offer tools to bridge the gap between molecular and bulk scales of water. However, their properties are still not fully understood and deserve further theoretical and experimental investigations. In this work, we simulate the caloric curves of protonated water clusters (H2O)nH+ (n = 20-23). These curves, which have recently been measured experimentally, are characteristic of the phase changes occurring in the aggregates with respect to temperature. The present simulations are achieved by combining parallel-tempering molecular dynamics and the self-consistent-charge density-functional based tight-binding approach and are focused on a restricted size range around (H2O)21H+ which presents singular properties. The shape of the experimental caloric curves and their size dependence are satisfactorily reproduced by the simulations which allows us to further provide a description of the phase transition in terms of structural modifications, dynamics of water molecules and proton mobility. Similar to the experiments, we observe that (H2O)21H+ exhibits a sharper phase transition than the neighbouring size clusters, which can be traced back to both structural and dynamic peculiarities.

Structural Characterization of Sulfur-Containing Water Clusters Using a Density-Functional Based Tight-Binding Approach.

A global optimization search of low-energy isomers is carried out to investigate the structural and stability properties of sulfur-containing water clusters, including both (H2O)nSO42- and (H2O)nH2SO4 aggregates. The systematic optimization algorithm involves a combination of parallel-tempering molecular dynamics and periodic gradient-driven quenches with energy and energy-gradient calculations performed using the Self-Consistent-Charge Density-Functional based Tight-Binding (SCC-DFTB) scheme. Comparisons with new MP2 and DFT calculations on the smallest systems and previous ab initio investigations of the literature show that the SCC-DFTB approach provides a fairly accurate description of both neutral and ionic species, comparable to that of DFT. Structural and stability features of larger sulfur-containing clusters, with up to 20 water molecules, are also determined using the SCC-DFTB scheme. The interest of this work is 2-fold: (i) the benchmark on small species demonstrates the ability of SCC-DFTB to describe complex potential energy landscapes involving hydrogen-bonds and proton transfers; (ii) it opens the way to the study of large clusters that can hardly be performed within ab initio approaches.

Structures and Free Energy Landscapes of the A53T Mutant-Type α-Synuclein Protein and Impact of A53T Mutation on the Structures of the Wild-Type α-Synuclein Protein with Dynamics

The A53T genetic missense mutation of the wild-type α-synuclein (αS) protein was initially identified in Greek and Italian families with familial Parkinson's disease. Detailed understanding of the structures and the changes induced in the wild-type αS structure by the A53T mutation, as well as establishing the direct relationships between the rapid conformational changes and free energy landscapes of these intrinsically disordered fibrillogenic proteins, helps to enhance our fundamental knowledge and to gain insights into the pathogenic mechanism of Parkinson's disease. We employed extensive parallel tempering molecular dynamics simulations along with thermodynamic calculations to determine the secondary and tertiary structural properties as well as the conformational free energy surfaces of the wild-type and A53T mutant-type αS proteins in an aqueous solution medium using both implicit and explicit water models. The confined aqueous volume effect in the simulations of disordered proteins using an explicit model for water is addressed for a model disordered protein. We also assessed the stabilities of the residual secondary structure component interconversions in αS based on free energy calculations at the atomic level with dynamics using our recently developed theoretical strategy. To the best of our knowledge, this study presents the first detailed comparison of the structural properties linked directly to the conformational free energy landscapes of the monomeric wild-type and A53T mutant-type α-synuclein proteins in an aqueous solution environment. Results demonstrate that the β-sheet structure is significantly more altered than the helical structure upon A53T mutation of the monomeric wild-type αS protein in aqueous solution. The β-sheet content close to the mutation site in the N-terminal region is more abundant while the non-amyloid-β component (NAC) and C-terminal regions show a decrease in β-sheet abundance upon A53T mutation. Obtained results utilizing our new theoretical strategy show that the residual secondary structure conversion stabilities resulting in α-helix formation are not significantly affected by the mutation. Interestingly, the residual secondary structure conversion stabilities show that secondary structure conversions resulting in β-sheet formation are influenced by the A53T mutation and the most stable residual transition yielding β-sheet occurs directly from the coil structure. Long-range interactions detected between the NAC region and the N- or C-terminal regions of the wild-type αS disappear upon A53T mutation. The A53T mutant-type αS structures are thermodynamically more stable than those of the wild-type αS protein structures in aqueous solution. Overall, the higher propensity of the A53T mutant-type αS protein to aggregate in comparison to the wild-type αS protein is related to the increased β-sheet formation and lack of strong intramolecular long-range interactions in the N-terminal region in comparison to its wild-type form. The specific residual secondary structure component stabilities reported herein provide information helpful for designing and synthesizing small organic molecules that can block the β-sheet forming residues, which are reactive toward aggregation.

Structures of the E46K Mutant-Type α-Synuclein Protein and Impact of E46K Mutation on the Structures of the Wild-Type α-Synuclein Protein

The E46K genetic missense mutation of the wild-type α-synuclein protein was recently identified in a family of Spanish origin with hereditary Parkinson's disease. Detailed understanding of the structures of the monomeric E46K mutant-type α-synuclein protein as well as the impact of the E46K missense mutation on the conformations and free energy landscapes of the wild-type α-synuclein are required for gaining insights into the pathogenic mechanism of Parkinson's disease. In this study, we use extensive parallel tempering molecular dynamics simulations along with thermodynamic calculations to assess the secondary and tertiary structural properties as well as the conformational preferences of the monomeric wild-type and E46K mutant-type α-synuclein proteins in an aqueous solution environment. We also present the residual secondary structure component conversion stabilities with dynamics using a theoretical strategy, which we most recently developed. To the best of our knowledge, this study presents the first detailed comparison of the structural and thermodynamic properties of the wild-type and E46K mutant-type α-synuclein proteins in an aqueous solution environment at the atomic level with dynamics. We find that the E46K mutation results not only in local but also in long-range changes in the structural properties of the wild-type α-synuclein protein. The mutation site shows a significant decrease in helical content as well as a large increase in β-sheet structure formation upon E46K mutation. In addition, the β-sheet content of the C-terminal region increases significantly in the E46K mutant-type αS in comparison to the wild-type αS. Our theoretical strategy developed to assess the thermodynamic preference of secondary structure transitions indicates that this shift in secondary structure is the result of a decrease in the thermodynamic preference of turn to helix conversions while the coil to β-sheet preference increases for these residues. Long-range intramolecular protein interactions of the C-terminal with the N-terminal and NAC regions increase upon E46K mutation, resulting in more compact structures for the E46K mutant-type rather than wild-type αS. However, the E46K mutant-type αS structures are less stable than the wild-type αS. Overall, our results show that the E46K mutant-type αS has a higher propensity to aggregate than the wild-type αS and that the N-terminal and C-terminal regions are reactive toward fibrillization and aggregation upon E46K mutation and we explain the associated reasons based on the structural properties herein. Small molecules or drugs that can block the specific residues forming abundant β-sheet structure, which we report here, might help to reduce the reactivity of these intrinsically disordered fibrillogenic proteins toward aggregation and their toxicity.

The protein amide 1HN chemical shift temperature coefficient reflects thermal expansion of the N–H···O=C hydrogen bond

The protein amide (1)H(N) chemical shift temperature coefficient can be determined with high accuracy by recording spectra at different temperatures, but the physical mechanism responsible for this temperature dependence is not well understood. In this work, we find that this coefficient strongly correlates with the temperature coefficient of the through-hydrogen-bond coupling, (3h)J(NC'), based on NMR measurements of protein GB3. Parallel tempering molecular dynamics simulation suggests that the hydrogen bond distance variation at different temperatures/replicas is largely responsible for the (1)H(N) chemical shift temperature dependence, from which an empirical equation is proposed to predict the hydrogen bond thermal expansion coefficient, revealing responses of individual hydrogen bonds to temperature changes. Different expansion patterns have been observed for various networks formed by β strands.

Electronic effects on the melting of small gallium clusters

Motivated by experimental reports of higher-than-bulk melting temperatures in small gallium clusters, we perform first-principles molecular dynamics simulations of Ga(20) and Ga(20)(+) using parallel tempering in the microcanonical ensemble. The respective specific heat (C(V)) curves, obtained using the multiple histogram method, exhibit a broad peak centered at approximately 740 and 610 K--well above the melting temperature of bulk gallium (303 K) and in reasonable agreement with experimental data for Ga(20)(+). Assessment of atomic mobility confirms the transition from solid-like to liquid-like states near the C(V) peak temperature. Parallel tempering molecular dynamics simulations yield low-energy isomers that are ~0.1 eV lower in energy than previously reported ground state structures, indicative of an energy landscape with multiple, competing low-energy morphologies. Electronic structure analysis shows no evidence of covalent bonding, yet both the neutral and charged clusters exhibit greater-than-bulk melting temperatures.

Structures and free energy landscapes of aqueous zinc(II)-bound amyloid-β(1–40) and zinc(II)-bound amyloid-β(1–42) with dynamics

Binding of divalent metal ions with intrinsically disordered fibrillogenic proteins, such as amyloid-β (Aβ), influences the aggregation process and the severity of neurodegenerative diseases. The Aβ monomers and oligomers are the building blocks of the aggregates. In this work, we report the structures and free energy landscapes of the monomeric zinc(II)-bound Aβ40 (Zn:Aβ40) and zinc(II)-bound Aβ42 (Zn:Aβ42) intrinsically disordered fibrillogenic metallopeptides in an aqueous solution by utilizing an approach that employs first principles calculations and parallel tempering molecular dynamics simulations. The structural and thermodynamic properties, including the secondary and tertiary structures and conformational Gibbs free energies of these intrinsically disordered metallopeptide alloforms, are presented. The results show distinct differing characteristics for these metallopeptides. For example, prominent β-sheet formation in the N-terminal region (Asp1, Arg5, and Tyr10) of Zn:Aβ40 is significantly decreased or lacking in Zn:Aβ42. Our findings indicate that blocking multiple reactive residues forming abundant β-sheet structure located in the central hydrophobic core and C-terminal regions of Zn:Aβ42 via antibodies or small organic molecules might help to reduce the aggregation of Zn(II)-bound Aβ42. Furthermore, we find that helix formation increases but β-sheet formation decreases in the C-terminal region upon Zn(II) binding to Aβ. This depressed β-sheet formation in the C-terminal region (Gly33-Gly38) in monomeric Zn:Aβ42 might be linked to the formation of amorphous instead of fibrillar aggregates of Zn:Aβ42.

A study on the structural transition of a single polymer chain by parallel tempering molecular dynamics simulation

The structural transition of a single polymer chain with chain length of 100, 200 and 300 beads was investigated by parallel tempering MD simulation. Our simulation results can capture the structural change from random coil to orientationally ordered structure with decreasing temperature. The clear transition was observed on the curves of radius of gyration and global orientational order parameter P as the function of temperature, which demonstrated structural formation of a single polymer chain. The linear relationships between three components of square radius of gyration Rgx2, Rgy2, Rgz2 and global orientational order P can be obtained under the structurally transformational process. The slope of the linear relationship between x (or y-axis) component Rgx2 (or Rgy2) and P is negative, while that of Rgz2 as the function of P is positive. The absolute value of slope is proportional to the chain length. Once the single polymer chain takes the random coil or ordered configuration, the linear relationship is invalid. The conformational change was also analyzed on microscopic scale. The polymer chain can be treated as the construction of rigid stems connecting by flexible loops. The deviation from exponentially decreased behavior of stem length distribution becomes prominent, indicating a stiffening of the chain arises leading to more and more segments ending up in the trans state with decreasing temperature. The stem length Ntr is about 21 bonds indicating the polymer chain is ordered with the specific fold length. So, the simulation results, which show the prototype of a liquid-crystalline polymer chain, are helpful to understand the crystallization process of crystalline polymers.

Conformational Plasticity in an HIV-1 Antibody Epitope

The structure of a short fragment of the human HIV-1 membrane glycoprotein gp41 has been examined using a combination of parallel tempering molecular dynamics (PTMD) and far UV circular dichroism spectroscopy. The aim is to resolve conflicting reports on the solution state conformational bias in this membrane proximal domain spanning the epitope for the 2F5 monoclonal antibody. We conclude that gp41(659-671) exhibits conformational plasticity in which competing folding propensities are present and can be influenced by local microenvironment. Contrary to previous reports, the 3(10) helix does not emerge as a dominant motif from either simulation or experiment, and this peptide is therefore not a model system for this fold type. Other fold groups such as turn motifs are identifiable at elevated temperatures in the PTMD trajectories and are potentially relevant in antibody binding. Helical populations in pure water are significantly overestimated according to the CHARMM parametrization. However, circular dichroism (CD) data show that helices are promoted in membrane mimetic solvents. As this is a membrane proximal peptide, the helical motif may well have physiological significance.