Free Energy Of Crystal Research Articles

Distinct roles of the major binding residues in the cation-binding pocket of the melibiose transporter MelB

Salmonella enterica serovar Typhimurium melibiose permease (MelBSt) is a prototype of the major facilitator superfamily (MFS) transporters, which play important roles in human health and diseases. MelBSt catalyzed the symport of galactosides with either Na+, Li+, or H+, but prefers the coupling with Na+. Previously, we determined the structures of the inward- and outward-facing conformation of MelBSt and the molecular recognition for galactoside and Na+. However, the molecular mechanisms for H+- and Na+-coupled symport still remain poorly understood. In this study, we solved two x-ray crystal structures of MelBSt, the cation-binding site mutants D59C at an unliganded apo-state and D55C at a ligand-bound state, and both structures display the outward-facing conformations virtually identical as published. We determined the energetic contributions of three major Na+-binding residues for the selection of Na+ and H+ by free energy simulations. Transport assays showed that the D55C mutant converted MelBSt to a solely H+-coupled symporter, and together with the free-energy perturbation calculation, Asp59 is affirmed to be the sole protonation site of MelBSt. Unexpectedly, the H+-coupled melibiose transport exhibited poor activities at greater bulky ΔpH and better activities at reversal ΔpH, supporting the novel theory of transmembrane-electrostatically localized protons and the associated membrane potential as the primary driving force for the H+-coupled symport mediated by MelBSt. This integrated study of crystal structure, bioenergetics, and free energy simulations, demonstrated the distinct roles of the major binding residues in the cation-binding pocket of MelBSt.

Strain-induced modification in thermal properties of monolayer 1T-ZrS2 and ZrS2/ZrSe2 heterojunction.

This paper systematically analyzes the phonon dispersion curves of single-layer ZrS2, ZrSe2, and ZrS2/ZrSe2 heterostructures under different strains. The phonon spectra and thermal parameters of the three structures were obtained based on the density functional perturbation theory method. The upper limits of strain that different monolayers and heterojunctions can withstand were studied. The monolayers ZrSe2 and ZrS2 can withstand up to 8% biaxial tensile strain, and the ZrS2/ZrSe2 heterojunction can withstand up to 6% biaxial tensile strain. In addition, the van der Waals force of the heterojunction may cause phonon tearing in the vertical direction. The application of biaxial tensile strain can adjust the thermal properties of the system to a large extent, which is similar to the strain effect in the pristine case. When the temperature rises, the entropy enthalpy of the three structures also gradually increases, the free energy gradually decreases, and the heat capacity of the system gradually increases until it tends to be stable. Taking single-layer ZrS2 as an example, we analyzed the change curve of thermal properties of single-layer ZrS2 under tensile strain. The results show that with the gradual increase of strain, the crystal's entropy, enthalpy, and free energy change differently. In addition, the heat capacity increases slowly under high temperatures. When all systems reach the limit strain, the phonon spectrum appears to have an imaginary frequency, and the thermal properties decrease significantly. This paper uses the first-principle calculation method based on density functional theory, and the PBE exchange-correlation function based on generalized gradient approximation (GGA) is selected for a specific calculation. The density functional perturbation theory (DFPT) calculates the full kinetic matrix. Because the lattice constants of ZrS2 and ZrSe2 are similar and have similar periodicity, the corresponding unit cells are used for structural optimization and property calculation. The Brillouin zone is integrated using the K points generated by the Monkhorst-pack method. For single-layers ZrS2 and ZrSe2, 8 × 8 × 1K-point grid is selected, and for ZrS2/ZrSe2 heterojunction, 8 × 8 × 2K-point grid is selected. A vacuum layer of 30Å was added in the vertical direction to avoid interlayer interaction. The non-conservative pseudopotential method is used to optimize the structure, and the optimization convergence is set as follows: the cutoff energy is set to 700eV, the convergence threshold of the maximum force between atoms is 0.01eV/Å, the convergence threshold of the maximum energy change is set to 1 × 10-9eV, and the convergence threshold of the maximum displacement is 0.001Å.

ROY Crystallization on Poly(ethylene) Fibers, a Model for Bed Net Crystallography.

Many long-lasting insecticidal bed nets for protection against disease vectors consist of poly(ethylene) fibers in which insecticide is incorporated during manufacture. Insecticide molecules diffuse from within the supersaturated polymers to surfaces where they become bioavailable to insects and often crystallize, a process known as blooming. Recent studies revealed that contact insecticides can be highly polymorphic. Moreover, insecticidal activity is polymorph-dependent, with forms having a higher crystal free energy yielding faster insect knockdown and mortality. Consequently, the crystallographic characterization of insecticide crystals that form on fibers is critical to understanding net function and improving net performance. Structural characterization of insecticide crystals on bed net fiber surfaces, let alone their polymorphs, has been elusive owing to the minute size of the crystals, however. Using the highly polymorphous compound ROY (5-methyl-2-[(2-nitrophenyl)-amino]thiophene-3-carbonitrile) as a proxy for insecticide crystallization, we investigated blooming and crystal formation on the surface of extruded poly(ethylene) fibers containing ROY. The blooming rates, tracked from the time of extrusion, were determined by UV-vis spectroscopy after successive washes. Six crystalline polymorphs (of the 13 known) were observed on poly(ethylene) fiber surfaces, and they were identified and characterized by Raman microscopy, scanning electron microscopy, and 3D electron diffraction. These observations reveal that the crystallization and phase behavior of polymorphs forming on poly(ethylene) fibers is complex and dynamic. The characterization of blooming and microcrystals underscores the importance of bed net crystallography for the optimization of bed net performance.

Tethered hard spheres: A bridge between the fluid and solid phases.

The thermodynamics of hard spheres tethered to a Face-Centered Cubic (FCC) lattice is investigated using event-driven molecular-dynamics. The particle-particle and the particle-tether collision rates are related to the phase space geometry and are used to study the FCC and fluid states. In tethered systems, the entropy can be determined by at least two routes: (i) through integration of the tether collision rates with the tether length rT or (ii) through integration of the particle-particle collision rates with the hard-sphere diameter σ (or, equivalently, the density). If the entropy were an entirely analytic function of rT and σ, these two methods for calculating the entropy should lead to the same results; however, a non-analytic region exists as an extension of the solid-fluid phase transition of the untethered hard-sphere system, and integration paths that cross this region will lead to values for the entropy that depend on the particular path chosen. The difference between the calculated entropies appears to be related to the communal entropy, and the location of the non-analytic region appears to be related to conditions where the regions of phase space associated with the FCC configuration become separated from those associated with the disordered fluid. The non-analytic region is finite in extent, vanishing below rT/a ≈ 0.55, where a is the lattice spacing, and there are many continuous paths that connect the fluid and solid phases that can be used to determine the crystal free energy with respect to the fluid.

Free energy calculation of crystalline solids using normalizing flows

Taking advantage of the advances in generative deep learning, particularly normalizing flow, a framework, called Boltzmann generator, has recently been proposed to generate equilibrium atomic configurations from the canonical ensemble and determining the associated free energy. In this work, we revisit Boltzmann generator to motivate the construction of the loss function from the statistical mechanical point of view and to cast the training of the normalizing flow model in a purely unsupervised manner that does not require any sample of the atomic configurations from the equilibrium ensemble. We further show that the normalizing flow framework furnishes a reference thermodynamic system, very close to the real thermodynamic system under consideration, that is suitable for the well-established free energy perturbation methods to determine accurate free energy of solids. We then apply the normalizing flow to two problems: temperature-dependent Gibbs free energy of perfect crystal and formation free energy of monovacancy defect in a model system of diamond cubic Si. The results obtained from the normalizing flow are shown to be in good agreement with that obtained from independent well-established free energy methods.

MG-63 and FetMSC Cell Response on Atomic Layer Deposited TiO2 Nanolayers Prepared Using Titanium Tetrachloride and Tetraisopropoxide

Titanium oxide nanocoatings were synthesized on the surface of monocrystalline silicon and ultra-fine-grained titanium by atomic layer deposition (ALD) using titanium tetrachloride (TiCl4) and titanium tetraisopropoxide (TTIP). The morphology of the samples was studied by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The structure and composition were studied by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), contact angle measurements, and energy-dispersive spectroscopy (EDS). The cytological response of osteosarcoma MG-63 and human fetal mesenchymal stem cells (FetMSCs) were studied by analyzing their morphology, viability, and alkaline phosphatase activity with and without the use of medium-induced differentiation in the osteogenic direction. A significant influence of the precursor type and ALD temperature on the crystal structure, morphology, composition, and surface free energy of TiO2 nanocoatings was found. The biocompatibility of amorphous non-stoichiometric and partially crystalline stoichiometric TiO2 coatings was compared. Both types of cells showed faster adhesion and improved spreading on the surface for the samples from TTIP compared to those from TiCl4 at the early stages of cultivation (2 h) due to the difference in composition and higher surface free energy. No cytotoxic effect was found on both types of coatings, nor was there a noticeable difference in cell differentiation. All ALD coatings provided excellent biocompatibility and osteoconductive properties.

Harnessing Deep Learning for Optimization of Lennard-Jones Parameters for the Polarizable Classical Drude Oscillator Force Field.

The outcomes of computational chemistry and biology research, including drug design, are significantly influenced by the underlying force field (FF) used in molecular simulations. While improved FF accuracy may be achieved via inclusion of explicit treatment of electronic polarization, such an extension must be accompanied by optimization of van der Waals (vdW) interactions, in the context of the Lennard-Jones (LJ) formalism in the present study. This is particularly challenging due to the extensive nature of chemical space combined with the correlated nature of LJ parameters. To address this challenge, a deep learning (DL)-based parametrization framework is developed, allowing for sampling of wide ranges of LJ parameters targeting experimental condensed phase thermodynamic properties. The present work utilizes this framework to develop the LJ parameters for atoms associated with four distinct groups covering 10 different atom types. Final parameter selection was facilitated by quantum mechanical data on rare-gas interactions with the training set molecules. The chosen parameters were then validated through experimental hydration free energies and condensed phase thermodynamic properties of validation set molecules to confirm transferability. The ultimate outcome of utilizing this framework is a set of LJ parameters in the context of the polarizable Drude FF, which demonstrated improvement in the reproduction of both experimental pure solvent and crystal properties and hydration free energies of the molecules compared to the additive CHARMM General FF (CGenFF) including the ability of the Drude FF to accurately reproduce both experimental pure solvent properties and hydration free energies. The study also shows how correlations between difference in the reproduction of condensed phase data between model compounds may be used to direct the selection of new atom types and training set molecules during FF development.

Structural Insights into the Highly Solvating System of Axitinib via Binary and Ternary Solvates

Axitinib is a well-known model in crystal engineering, exhibiting a high tendency to form various solvates, and more than 70 kinds of solvates have been reported. Therefore, it is a challenge to elucidate the effect of solvents on the crystallization of Axitinib and develop the polymorph or solvate landscape of Axitinib. Here, we illustrate an uncommon and complicated solvation behavior of Axitinib from the structural analysis and theoretical characterization. The structures of two new ternary solvates and five binary solvates are reported for the first time. Experimental and theoretical calculation and studies on phase transition are performed to rationalize and understand the formation of solvates and the transformation of polymorphisms. Crystal structure analysis and molecular properties reveal that shape, size, the hydrogen bond donor of the solvents, and the chance to lower crystal free energy are the main factors to drive solvates. Three sets of isostructural binary solvate are distinguished and calculated quantitatively to prove that the intermolecular interactions, strong hydrogen bond donor, CH−π, and orientation force control the classification results of binary solvates. Stability of solvates is found to be associated with the intermolecular interaction energies of solvent molecules with surrounding molecules. The polymorphic behavior of the desolventized product is attributed to the two-dimensional isostructurality between form IV and solvate.

Pre-Nucleation Clusters Predict Crystal Structures in Models of Chiral Molecules.

Kinetics can play an important role in the crystallization of molecules and can give rise to polymorphism, the tendency of molecules to form more than one crystal structure. Current computational methods of crystal structure prediction, however, focus almost exclusively on identifying the thermodynamically stable polymorph. Kinetic factors of nucleation and growth are often neglected because the underlying microscopic processes can be complex and accurate rate calculations are numerically cumbersome. In this work, we use molecular dynamics computer simulations to study simple molecular models that reproduce the crystallization behavior of real chiral molecules, including the formation of enantiopure and racemic crystals, as well as polymorphism. A significant fraction of these molecules forms crystals that do not have the lowest free energy. We demonstrate that at high supersaturation crystal formation can be accurately predicted by considering the similarities between oligomeric species in solution and molecular motifs in the crystal structure. For the case of racemic mixtures, we even find that knowledge of crystal free energies is not necessary and kinetic considerations are sufficient to determine if the system will undergo spontaneous chiral separation. Our results suggest conceptually simple ways of improving current crystal structure prediction methods.

Direct determination of Lennard-Jones crystal surface free energy by a computational cleavage method

The surface free energy of solids, γ, plays a crucial role in all physical and chemical processes involving material surfaces. For the first time, we obtained γ directly from molecular dynamics simulations using a crystal cleavage method. The approach was successfully realized in a Lennard-Jones system by inserting two movable external walls, each consisting of a single crystal layer, into a bulk crystal to create flat, defect-free surfaces. The cleavage technique designed allowed us to calculate the surface free energy according to its definition and avoid surface premelting. The temperature dependence of γ was determined for the (100) and (110) crystal planes along the whole sublimation line and its metastable extension, up to T = 1.02 · Tm, where Tm is the melting point. Good agreement with indirect values of γ(T) was found. The proposed computational cleavage method can be applied to other solids of interest, providing valuable insight into the understanding of chemical and physical surface processes, and demonstrates the successful import of the cleavage method, traditionally used in technical preparation and study of crystal surfaces, into a modern atomistic simulation.

Bottom-up coarse-grain modeling of plasticity and nanoscale shear bands in α-RDX.

Computationally inexpensive particle-based coarse-grained (CG) models are essential for use in molecular dynamics (MD) simulations of mesoscopically slow cooperative phenomena, such as plastic deformations in solids. Molecular crystals possessing complex symmetry present enormous practical challenges for particle-based coarse-graining at molecularly resolved scales, when each molecule is in a single-site representation, and beyond. Presently, there is no published pairwise non-bonded single-site CG potential that is able to predict the space group and structure of a molecular crystal. In this paper, we present a successful coarse-graining at a molecular level from first principles of an energetic crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX) in the alpha phase, using the force-matching-based multiscale coarse-graining (MSCG/FM) approach. The new MSCG/FM model, which implements an optimal pair decomposition of the crystal Helmholtz free energy potential in molecular center-of-mass coordinates, was obtained by force-matching atomistic MD simulations of liquid, amorphous, and crystalline states and in a wide range of pressures (up to 20GPa). The MSCG/FM potentials for different pressures underwent top-down optimization to fine-tune the mechanical and thermodynamic properties, followed by consolidation into a transferable density-dependent model referred to as RDX-TC-DD (RDX True-Crystal Density-Dependent). The RDX-TC-DD model predicts accurately the crystal structure of α-RDX at room conditions and reproduces the atomistic reference system under isothermal (300K) hydrostatic compression up to 20GPa, in particular, the Pbca symmetry of α-RDX in the elastic regime. The RDX-TC-DD model was then used to simulate the plastic response of uniaxially ([100]) compressed α-RDX resulting in nanoscale shear banding, a key mechanism for plastic deformation and defect-free detonation initiation proposed for many molecular crystalline explosives. Additionally, a comparative analysis of the effect of core-softening of the RDX-TC-DD potential and the degree of molecular rigidity in the all-atom treatment suggests a stress-induced short-range softening of the effective intermolecular interaction as a fundamental cause of plastic instability in α-RDX. The reported RDX-TC-DD model and overall workflow to develop it open up possibilities to perform high quality simulation studies of molecular energetic materials under thermal and mechanical stimuli, including extreme conditions.

Thermodynamic stability of hard sphere crystals in dimensions 3 through 10.

Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.

Approximation of correlation functions in phase‐field crystal model by machine learning approach

Two different phase‐field crystal (PFC) free excess energy expansions have been analyzed with respect to the order of a truncation term and to the accuracy of a pair correlation functions fitting. The coefficients of the correlation function in PFC model was found for the aluminum crystal based on the molecular dynamics data. A machine learning (ML) approach has been utilized to construct a neural network (NN) for the PFC approximation of correlation functions. The effective iteratomic potentials of the embedded atom model were used as an input data for NN training. Obtained NN predicts the coefficients of the correlation functions with the potentials data as input. Predictions were studied and verified with respect to the properties of NN and parameters of ML.

Homogeneous Nucleation of Hydroxyapatite, Ca5OH(PO4)3, at 37 °C

Precipitation of the calcium phosphate hydroxyapatite, Ca5OH(PO4)3, is studied by simple mixing of reagent solutions and measurement of light scattering (turbidimetry) at six different wavelengths from 300 to 800 nm. Measured turbidities are analyzed using Mie’s theory of light scattering from small particles. Results are interpreted in terms of classical theory of homogeneous nucleation, and from this the surface free energy of crystals is determined. The low value thus found is explained as the effect of protonation of the strongly basic anions hydroxide and phosphate at the crystal surface. Relatively large particles registered by turbidimetry are shown to be not monocrystals, but aggregates of nanocrystals.

Large-Scale Free Energy Calculations on a Computational Metal–Organic Frameworks Database: Toward Synthetic Likelihood Predictions

Metal–organic frameworks (MOFs) have captivated the research community because of their modular crystal structure that can be tailored to suit diverse applications. However, identifying ideal MOFs for an application of choice is difficult because of the millions (or more) of possible MOFs one could consider. Although computational screening of MOF databases has provided a fast way to evaluate MOF performance, experimental validation of the predicted “exceptional” MOFs is uncommon because of the uncertainty of the synthetic likelihood of computationally constructed MOFs, hence hindering material discovery. Aiming to leverage the perspective provided by large data sets, we calculated the free energies of each MOF in a topologically diverse database of 8500 frameworks and evaluated to what extent the descriptors of MOF thermodynamic stability “discriminate” previously synthesized MOFs. Upon defining a relative free energy, ΔLMFFL, that corrects for some force field artifacts specific to MOF nodes, we found that previously synthesized MOFs in our database clustered in a region below ΔLMFFL = 4.4 kJ/mol per atom. This suggests that a MOF below this ΔLMFFL threshold may have a higher probability of being synthesized, although other factors may ultimately impair synthetic accessibility. For instance, when isomorphism occurs, multiple isomorphs may reside under the ΔLMFFL threshold and relative stability among isomorphs comes into play. From 32 isomorphic MOF series we examined in detail, we found the synthesized isomorph was the one with the lowest free energy in 80% of cases, and in 20% of cases to be within 1 kJ/mol of the latter. These findings indicate that for a MOF to be synthetically accessible a “low” crystal free energy is necessary, albeit in some cases it may not be sufficient because of the role of other factors not considered here (e.g., solvents, modulators, and kinetics).

Dynamic particularities of the coefficients determination in the crystal Rb2ZnCl4 free energy decomposition according to the polarization by the harmonic analysis method

The values of the energy expansion coefficients in a series of polarization even powers on the base of study of the Rb2ZnCl4 crystal repolarization dynamics according to the theory of Landau-Devonshire are determined. The comparison of experimental results in the dynamics with theoretical concepts of the Landau-Devonshire theory describing dependencies in static is obtained.

Free Energy of Classical Molecular Crystals by Thermodynamic Integration from a Harmonic Reference.

We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and models of rigid molecules, and use it to obtain the harmonic free energy of a crystal. The anharmonic correction is then calculated by the conventional thermodynamic integration over temperature in the NVT ensemble. Attention is paid to finite-size errors, tail corrections, thermostat choice, ergodicity, and other sources of inaccuracies. The calculated free energy of ice XIV modeled by the TIP4P/2005 potential agrees with the previously reported value and is by one order more accurate.

A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals

We propose an unconditionally stable numerical scheme for a 2D dynamic [Formula: see text]-tensor model of nematic liquid crystals. This dynamic [Formula: see text]-tensor model is an [Formula: see text]-gradient flow generated by the liquid crystal free energy that contains a cubic term, which is physically relevant but makes the free energy unbounded from below, and for this reason, has been avoided in other numerical studies. The unboundedness of the energy brings significant difficulty in analyzing the model and designing numerical schemes. By using a stabilizing technique, we construct an unconditionally stable scheme, and establish its unique solvability and convergence. Our convergence analysis also leads to, as a byproduct, the well-posedness of the original PDE system for the 2D [Formula: see text]-tensor model. Several numerical examples are presented to validate and demonstrate the effectiveness of the scheme.

UHMW Ziegler–Natta polyethylene: Synthesis, crystallization, and melt behavior

Abstract The fabrication of normal and UHMW PE end-products involves melting and crystallization of the polymer. Therefore, the melt behavior and crystallization of as-synthesized UHMW PE, and NMW PE and E-1-hexene copolymer have been studied using a new nonisothermal crystallization model, Flory's equilibrium theory and ethylene sequence length distribution concept (SLD), Gibbs–Thompson equation, and DSC experiments. By using this approach, the effects of MW, 1-hexene incorporation, ethylene SLD, the level of undercooling θ , and crystal surface free energy D on crystallite stability, relative crystallinity α , instantaneous crystallinity χ , the crystallization kinetic triplet, crystallization entropy, and lamellar thickness distribution (LTD) have been evaluated. Consequently, this study reports insightful new results, interpretations, and explanations regarding the melting and crystallization of the aforementioned polymers. The UHMW PE results significantly differ from the NMW PE and E-1-hexene copolymer ones. Ethylene sequences shorter than the so called minimum crystallizable ethylene sequence length , irrespective of E-1-hexene copolymer MW, can also crystallize. Additionally, the polymer preparation shows that the catalyst coordination environment and symmetry, as well as achiral ethylene versus prochiral α -olefin steric encumbrance and competitive diffusion affect the synthesis of UHMW PE, particularly the corresponding UHMW copolymers.

Harmonically Assisted Methods for Computing the Free Energy of Classical Crystals by Molecular Simulation: A Comparative Study.

Four methods for calculation of the classical free energy of crystalline systems are compared with respect to their efficiency and accuracy. Two of the methods involve thermodynamic integration along an unphysical path (λ integration, λI), and two involve integration in temperature from the low-temperature harmonic limit (T integration, TI). Specifically, the methods considered are (1) Frenkel-Ladd integration from a noninteracting Einstein crystal reference (ECR-λI); (2) conventional integration in temperature (Conv-TI); (3) integration from an interacting quasi-harmonic reference (QHR-λI); and (4) temperature integration using harmonically mapped averaging to evaluate the integrand (HMA-TI). The latter two methods are "harmonically assisted", meaning that they exploit the harmonic nature of the crystal to greatly reduce fluctuations in the relevant averages. This feature allows them to deliver a result of much higher precision for a given computational effort, compared to ECR-λI and Conv-TI, and with no less accuracy. Regarding the harmonically assisted methods, HMA-TI has several advantages over QHR-λI with respect to the simplicity of the integration path (which promotes a more accurate result), ease of implementation, and usefulness of the data recorded along the integration path.