Parallel Monte Carlo Simulations Research Articles

Adsorption of cytochrome c on different self-assembled monolayers: The role of surface chemistry and charge density.

In this work, the adsorption behavior of cytochrome c (Cyt-c) on five different self-assembled monolayers (SAMs) (i.e., CH3-SAM, OH-SAM, NH2-SAM, COOH-SAM, and OSO3--SAM) was studied by combined parallel tempering Monte Carlo and molecular dynamics simulations. The results show that Cyt-c binds to the CH3-SAM through a hydrophobic patch (especially Ile81) and undergoes a slight reorientation, while the adsorption on the OH-SAM is relatively weak. Cyt-c cannot stably bind to the lower surface charge density (SCD, 7% protonation) NH2-SAM even under a relatively high ionic strength condition, while a higher SCD of 25% protonation promotes Cyt-c adsorption on the NH2-SAM. The preferred adsorption orientations of Cyt-c on the negatively-charged surfaces are very similar, regardless of the surface chemistry and the SCD. As the SCD increases, more counterions are attracted to the charged surfaces, forming distinct counterion layers. The secondary structure of Cyt-c is well kept when adsorbed on these SAMs except the OSO3--SAM surface. The deactivation of redox properties for Cyt-c adsorbed on the highly negatively-charged surface is due to the confinement of heme reorientation and the farther position of the central iron to the surfaces, as well as the relatively larger conformation change of Cyt-c adsorbed on the OSO3--SAM surface. This work may provide insightful guidance for the design of Cyt-c-based bioelectronic devices and controlled enzyme immobilization.

A photon source model for alpha-emitter radionuclides

Objective. A Monte Carlo virtual source model named PHID (photon from Ion decay) that generates photons emitted in the complex decay chain process of alpha-emitter radionuclides is proposed, typically for use during the simulation of SPECT image acquisition. Approach. Given an alpha-emitter radionuclide, the PHID model extracts from Geant4 databases the photon emission lines from all decaying daughters for both isometric transition and atomic relaxation processes. According to a given time range, abundances and activities in the decay chain are considered thanks to the Bateman equations, taking into account the decay rates and the initial abundances. Main results. PHID is evaluated by comparison with analog Monte Carlo simulation. It generates photons with the correct energy and temporal distribution, avoiding the costly simulation of the complete decay chain thus decreasing the computation time. The exact time gain depends on the simulation setup. As an example, it is 30× faster for simulating 1 MBq of 225Ac in water for 1 section Moreover, for 225Ac, PHID was also compared to a simplified source model with the two main photon emission lines (218 and 440 keV). PHID shows that 2 times more particles are simulated and 60% more counts are detected in the images. Significance. PHID can simulate any alpha-emitter radionuclide available in the Geant4 database. As a limitation, photons emitted from Bremsstrahlung are ignored, but they represent only 0.7% of the photons above 30 keV and are not significant for SPECT imaging. PHID is open-source, available in GATE 10, and eases the investigation of imaging photon emission from alpha emitters.

Simulation Study of Polyethylene Terephthalate Hydrolase Adsorption on Self-Assembled Monolayers.

Polyethylene terephthalate (PET) hydrolase, discovered in Ideonella sakaiensis (IsPETase), is a promising agent for the biodegradation of PET under mild reaction conditions, yet the thermal stability is poor. The efficient immobilization and orientation of IsPETase on different solid substrates are essential for its application. In this work, the combined parallel tempering Monte Carlo simulation with the all-atom molecular dynamics simulation approach was adopted to reveal the adsorption mechanism, orientation, and conformational changes of IsPETase adsorbed on charged self-assembled monolayers (SAMs), including COOH-SAM and NH2-SAM with different surface charge densities (SCDs). The results show that the protein adsorption orientation was determined not only by attraction interactions but also by repulsion interactions. IsPETase is adsorbed on the COOH-SAM surface with an "end-on" orientation, which favors the exposure of the catalyzed triplet to the solution. In addition, the entrance to the catalytic active center is larger on the COOH-SAM surface with a low SCD. This work reveals the controlled orientation and conformational information on IsPETase on charged surfaces at the atomistic level. This study would certainly promote our understanding of the mechanism of IsPETase adsorption and provide theoretical support for the design of substrates for IsPETase immobilization.

Structure and Thermodynamics of Li+Arn Clusters beyond the Second Solvation Shell

Small Li+Arn clusters are employed in this work as model systems to study microsolvation. Although first and second solvation shells are expected to be the most relevant ones for this type of atomic solvents, it is also interesting to explore larger clusters in order to identify the influence of external atoms on structural and thermodynamic properties. In this work, we perform a global geometry optimization for Li+Arn clusters (with n = 41–100) and parallel tempering Monte Carlo (PTMC) simulations for some selected sizes. The results show that global minimum structures of large clusters always have 6 argon atoms in the first solvation shell while maintaining the number of 14 or 16 argon atoms in the second one. By contrast, third and fourth solvation shells vary significantly the number of argon atoms with the cluster size, and other shells can hardly be assigned due to the reduced influence of Li+ on the external argon atoms for large clusters. In turn, PTMC calculations show that the melting of the most external solvation shells of large microsolvation clusters occurs at T∼50K, which is independent of cluster size. Structural transitions can be observed between quasi-degenerated structures at low temperatures. Moreover, the present results highlight the fluxional character of the external solvation shells of these large Li+Arn clusters, which may be seen as typical “snowball” structures.

Efficiently Differentiating Agonists and Competitive Antagonists for Weak Allosteric Protein-Ligand Interactions with Linear Response Theory.

What makes an agonist and a competitive antagonist? In this work, we aim to answer this question by performing parallel tempering Monte Carlo simulations on the serotonin type 3A (5-HT3A) receptor. We use linear response theory to predict conformational changes in the 5-HT3A receptor active site after weak perturbations are applied to its allosteric binding sites. A covariance tensor is built from conformational sampling of its apo state, and a harmonic approximation allows us to substitute the calculation of ligand-induced forces with the binding site's displacement vector. Remarkably, our study demonstrates the feasibility of effectively discerning between agonists and competitive antagonists for multiple ligands, requiring computationally expensive calculations only once per protein.

Simulation insights into the lipase adsorption on zeolitic imidazolate framework-8

Zeolitic imidazolate frameworks (ZIFs) have recently emerged as immobilization matrices for biomolecules, most notably enzymes. Understanding the key factors that dominate the enzyme's catalytic activity on/in ZIFs is crucial for the development of new immobilization matrices. In this work, a combination of the parallel tempering Monte Carlo simulation and all-atom molecular dynamics simulation is performed to study the orientation and conformation of the Candida rugose lipase (CRL) adsorbed on oppositely charged and neutral ZIF-8 (i.e., ZIF-8-COOH, ZIF-8-NH2, and ZIF-8-neutral) surfaces. The results show that CRL could adsorb on all ZIF-8 surfaces, with an ordered orientation obtained on charged ZIF-8 surfaces. ZIF-8-NH2 is a good candidate for CRL immobilization since it can maximize the catalytic activity of CRL. The native conformation of CRL is well preserved on all three surfaces due to the partially water-containing surface of ZIF-8. The results could provide theoretical support for the application of porous materials in enzyme immobilization.

An experimental setup for proton irradiation of a murine leg model for radiobiological studies

Background The purpose of this study was to introduce an experimental radiobiological setup used for in vivo irradiation of a mouse leg target in multiple positions along a proton beam path to investigate normal tissue- and tumor models with varying linear energy transfer (LET). We describe the dosimetric characterizations and an acute- and late-effect assay for normal tissue damage. Methods The experimental setup consists of a water phantom that allows the right hind leg of three to five mice to be irradiated at the same time. Absolute dosimetry using a thimble (Semiflex) and a plane parallel (Advanced Markus) ionization chamber and Monte Carlo simulations using Geant4 and SHIELD-HIT12A were applied for dosimetric validation of positioning along the spread-out Bragg peak (SOBP) and at the distal edge and dose fall-off. The mice were irradiated in the center of the SOBP delivered by a pencil beam scanning system. The SOBP was 2.8 cm wide, centered at 6.9 cm depth, with planned physical single doses from 22 to 46 Gy. The biological endpoint was acute skin damage and radiation-induced late damage (RILD) assessed in the mouse leg. Results The dose–response curves illustrate the percentage of mice exhibiting acute skin damage, and at a later point, RILD as a function of physical doses (Gy). Each dose–response curve represents a specific severity score of each assay, demonstrating a higher ED50 (50% responders) as the score increases. Moreover, the results reveal the reversible nature of acute skin damage as a function of time and the irreversible nature of RILD as time progresses. Conclusions We want to encourage researchers to report all experimental details of their radiobiological setups, including experimental protocols and model descriptions, to facilitate transparency and reproducibility. Based on this study, more experiments are being performed to explore all possibilities this radiobiological experimental setup permits.

Nuclear data generation & implementation for analog Monte Carlo simulation

Nuclear data is in constant evolution as more experimental data is gathered, computational capabilities increase, and evaluators verify its validity by means of stochastic and deterministic simulations. The focus here is on the analog Monte Carlo simulation of nuclear reactions that produce more than two particles in the outgoing channel, which needs specific considerations to ensure the correlations between the particles and thus the conservation of energy and of translational and angular momenta. It is possible to adapt nuclear data and its exploitation to implement realistic reactions from the phenomenological point of view (as opposed to the historical need of variance reduction techniques), which increases computation time but allows the expansion of the transport codes capabilities. Simulation anomalies were found concerning the kinematical calculations of photon energies emitted from neutron-induced inelastic scattering (n,n’γ), as well as concerning the photon multiplicity of 155Gd(n,γ) due to the presence of a rotational band in 156Gd. Recommendations are given for potential solutions for both anomalies.

TriMem: A parallelized hybrid Monte Carlo software for efficient simulations of lipid membranes.

Lipid membranes are integral building blocks of living cells and perform a multitude of biological functions. Currently, molecular simulations of cellular-scale membrane remodeling processes at atomic resolution are extremely difficult, due to their size, complexity, and the large times-scales on which these processes occur. Instead, elastic membrane models are used to simulate membrane shapes and transitions between them and to infer their properties and functions. Unfortunately, an efficiently parallelized open-source simulation code to do so has been lacking. Here, we present TriMem, a parallel hybrid Monte Carlo simulation engine for triangulated lipid membranes. The kernels are efficiently coded in C++ and wrapped with Python for ease-of-use. The parallel implementation of the energy and gradient calculations and of Monte Carlo flip moves of edges in the triangulated membrane enable us to simulate large and highly curved membrane structures. For validation, we reproduce phase diagrams of vesicles with varying surface-to-volume ratios and area difference. We also compute the density of states to verify correct Boltzmann sampling. The software can be used to tackle a range of large-scale membrane remodeling processes as a step toward cell-scale simulations. Additionally, extensive documentation make the software accessible to the broad biophysics and computational cell biology communities.

Finite-temperature stability of hydrocarbons: Fullerenes vs flakes

The effects of a finite temperature on the equilibrium structures of hydrocarbon molecules are computationally explored as a function of size and relative chemical composition in hydrogen and carbon. Using parallel tempering Monte Carlo simulations employing a reactive force field, we find that in addition to the phases already known for pure carbon, namely, cages, flakes, rings, and branched structures, strong changes due to temperature and the addition of little amounts of hydrogen are reported. Both entropy and the addition of moderate amounts of hydrogen favor planar structures such as nanoribbons over fullerenes. Accurate phase diagrams are proposed, highlighting the possible presence of multiple phase changes at finite size and composition. Astrophysical implications are also discussed.

Molecular Simulation of Statherin Adsorption on Hydroxyapatite (001) Surface

AbstractStatherin (SN) is an important protein that can adsorb on enamel to maintain calcium ions balance and promote biomineralization in the human oral cavity. In this work, parallel tempering Monte Carlo simulation and all‐atom molecular dynamics simulation are combined to study the behavior of SN adsorbed on the hydroxyapatite (HAP) (001) surface. The results indicate that SN can “anchor” on HAP (001) surface by its Asp1 and Sep2 with “head‐on” orientation in NaCl solution and its secondary structure and conformation are changed greatly, which means that SN loses its biological activity. However, SN can maintain its conformation in calcium phosphate solution. Furthermore, SN can adsorb on HAP (001) surface with Sep2 and Sep3 by salt bridge with calcium phosphorus clusters with “lying” orientation. More importantly, Glu26 residue can stabilize the free calcium and phosphorus clusters, which can prevent not only the dissolution of HAP surface, but also the precipitation of calcium phosphate due to the supersaturated state. This work can help to better understand the process of biomineralization and also provides a guidance for the design of dental restoration materials.

Massively parallel FDTD full-band Monte Carlo simulations of electromagnetic THz pulses in p-doped silicon at cryogenic temperatures

In semiconductor samples with a low density of free charge carriers the current response to an intense electromagnetic pulse is weak and can be treated as a perturbation in the finite-difference-time-domain calculation of the electromagnetic field. Up to first order the electric field that drives the particles does not depend on their density and the particles can be simulated independently. This opens the door for massively parallel Monte Carlo simulations that can be processed efficiently on a computer cluster and a large number of particles can be simulated resulting in a very low noise level. By this full-band Monte Carlo finite-difference-time-domain approach the generation of higher harmonics in p-doped silicon at cryogenic temperatures is investigated. It is found that the higher harmonics are mostly due to the warped valence bands, which are discretized on adaptive unstructured tetrahedral grids in the k-space to avoid numerical artifacts.

Convolutional neural network-based common-path optical coherence tomography A-scan boundary-tracking training and validation using a parallel Monte Carlo synthetic dataset.

We present a parallel Monte Carlo (MC) simulation platform for rapidly generating synthetic common-path optical coherence tomography (CP-OCT) A-scan image dataset for image-guided needle insertion. The computation time of the method has been evaluated on different configurations and 100000 A-scan images are generated based on 50 different eye models. The synthetic dataset is used to train an end-to-end convolutional neural network (Ascan-Net) to localize the Descemet's membrane (DM) during the needle insertion. The trained Ascan-Net has been tested on the A-scan images collected from the ex-vivo human and porcine cornea as well as simulated data and shows improved tracking accuracy compared to the result by using the Canny-edge detector.

Machine Learning Force Field Aided Cluster Expansion Approach to Configurationally Disordered Materials: Critical Assessment of Training Set Selection and Size Convergence.

Cluster expansion (CE) is a powerful theoretical tool to study the configuration-dependent properties of substitutionally disordered systems. Typically, a CE model is built by fitting a few tens or hundreds of target quantities calculated by first-principles approaches. To validate the reliability of the model, a convergence test of the cross-validation (CV) score to the training set size is commonly conducted to verify the sufficiency of the training data. However, such a test only confirms the convergence of the predictive capability of the CE model within the training set, and it is unknown whether the convergence of the CV score would lead to robust thermodynamic simulation results such as order-disorder phase transition temperature Tc. In this work, using carbon defective MoC1-x as a model system and aided by the machine-learning force field technique, a training data pool with about 13000 configurations has been efficiently obtained and used to generate different training sets of the same size randomly. By conducting parallel Monte Carlo simulations with the CE models trained with different randomly selected training sets, the uncertainty in calculated Tc can be evaluated at different training set sizes. It is found that the training set size that is sufficient for the CV score to converge still leads to a significant uncertainty in the predicted Tc and that the latter can be considerably reduced by enlarging the training set to that of a few thousand configurations. This work highlights the importance of using a large training set to build the optimal CE model that can achieve robust statistical modeling results and the facility provided by the machine-learning force field approach to efficiently produce adequate training data.

Magnetic frustration in the cubic double perovskite Ba2NiIrO6

Hybrid transition metal oxides continue to attract attention due to their multiple degrees of freedom ($e.g.$, lattice, charge, spin, and orbital) and versatile properties. Here we investigate the magnetic and electronic properties of the newly synthesized double perovskite Ba$_2$NiIrO$_6$, using crystal field theory, superexchange model analysis, density functional calculations, and parallel tempering Monte Carlo (PTMC) simulations. Our results indicate that Ba$_2$NiIrO$_6$ has the Ni$^{2+}$ ($t_{2g}^{6}e_{g}^{2}$)-Ir$^{6+}$ ($t_{2g}^{3}$) charge states. The first nearest-neighboring (1NN) Ni$^{2+}$-Ir$^{6+}$ ions prefer a ferromagnetic (FM) coupling as expected from the Goodenough-Kanamori-Anderson rules, which contradicts the experimental antiferromagnetic (AF) order in Ba$_2$NiIrO$_6$. We find that the strong 2NN AF couplings are frustrated in the fcc sublattices, and they play a major role in determining the observed AF ground state. We also prove that the $J_{\rm eff}$ = 3/2 and $J_{\rm eff}$ = 1/2 states induced by spin-orbit coupling, which would be manifested in low-dimensional (e.g., layered) iridates, are however not the case for cubic Ba$_2$NiIrO$_6$. Our PTMC simulations show that when the long-range (2NN and 3NN) AF interactions are included, an AF transition with $T_{\rm N}$ = 66 K would be obtained and it is well comparable with the experimental 51 K. Meanwhile, we propose a possible 2$\times$2$\times$2 noncollinear AF structure for Ba$_2$NiIrO$_6$.

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study.

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.

Stability of skyrmion crystal phase in antiferromagnetic triangular lattice with DMI and single-ion anisotropy

We study a frustrated antiferromagnetic Heisenberg model on a triangular lattice with the Dzyaloshinskii–Moriya interaction (DMI) in the presence of an external magnetic field and focus on the effects of the single-ion anisotropy on the overall phase diagram topology and the skyrmion lattice (SkX) phase stability. Phase diagrams in the temperature-field plane for both easy-axis and easy-plane anisotropy of a varying strength are constructed in the regimes of a moderate and strong DMI by parallel tempering Monte Carlo simulations. For the considered range of parameters the phase diagrams featuring up to four ordered phases are identified. The SkX phase is found to be stabilized within some temperature and field window for sufficiently large DMI and not too strong anisotropy. We demonstrate that both types of the anisotropy can have beneficial effects on the SkX phase stabilization. Namely, in the systems with moderate DMI a small easy-plane anisotropy extends the field window of the SkX phase appearance by shifting its lower bound to smaller values and in the systems with larger DMI a small easy-axis anisotropy shifts the entire field range of the SkX phase stabilization towards smaller values. The Metropolis dynamics is employed to probe the persistence of the SkX phase upon quenching the field to zero or small finite values. It is confirmed that low temperatures, small DMI and small easy-plane anisotropy values support the skyrmions persistence, i.e., increase their lifetime.

Robust topological designs for extreme metamaterial micro-structures

We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

PenRed: An extensible and parallel Monte-Carlo framework for radiation transport based on PENELOPE

Monte Carlo methods provide detailed and accurate results for radiation transport simulations. Unfortunately, the high computational cost of these methods limits its usage in real-time applications. Moreover, existing computer codes do not provide a methodology for adapting these kinds of simulations to specific problems without advanced knowledge of the corresponding code system, and this restricts their applicability. To help solve these current limitations, we present PenRed, a general-purpose, stand-alone, extensible and modular framework code based on PENELOPE for parallel Monte Carlo simulations of electron-photon transport through matter. It has been implemented in C++ programming language and takes advantage of modern object-oriented technologies. In addition, PenRed offers the capability to read and process DICOM images as well as to construct and simulate image-based voxelized geometries, so as to facilitate its usage in medical applications. Our framework has been successfully verified against the original PENELOPE Fortran code. Furthermore, the implemented parallelism has been tested showing a significant improvement in the simulation time without any loss in precision of results. Program summaryProgram title: PenRed: Parallel Engine for Radiation Energy Deposition.CPC Library link to program files:https://doi.org/10.17632/rkw6tvtngy.1Licensing provision: GNU Affero General Public License (AGPL).Programming language: C++ standard 2011.Nature of problem: Monte Carlo simulations usually require a huge amount of computation time to achieve low statistical uncertainties. In addition, many applications necessitate particular characteristics or the extraction of specific quantities from the simulation. However, most available Monte Carlo codes do not provide an efficient parallel and truly modular structure which allows users to easily customise their code to suit their needs without an in-depth knowledge of the code system.Solution method: PenRed is a fully parallel, modular and customizable framework for Monte Carlo simulations of the passage of radiation through matter. It is based on the PENELOPE [1] code system, from which inherits its unique physics models and tracking algorithms for charged particles. PenRed has been coded in C++ following an object-oriented programming paradigm restricted to the C++11 standard. Our engine implements parallelism via a double approach: on the one hand, by using standard C++ threads for shared memory, improving the access and usage of the memory, and, on the other hand, via the MPI standard for distributed memory infrastructures. Notice that both kinds of parallelism can be combined together in the same simulation. Moreover, both threads and MPI processes, can be balanced using the builtin load balance system (RUPER-LB [30]) to maximise the performance on heterogeneous infrastructures. In addition, PenRed provides a modular structure with methods designed to easily extend its functionality. Thus, users can create their own independent modules to adapt our engine to their needs without changing the original modules. Furthermore, user extensions will take advantage of the builtin parallelism without any extra effort or knowledge of parallel programming.Additional comments including restrictions and unusual features: PenRed has been compiled in linux systems with g++ of GCC versions 4.8.5, 7.3.1, 8.3.1 and 9; clang version 3.4.2 and intel C++ compiler (icc) version 19.0.5.281. Since it is a C++11-standard compliant code, PenRed should be able to compile with any compiler with C++11 support. In addition, if the code is compiled without MPI support, it does not require any non standard library. To enable MPI capabilities, the user needs to install whatever available MPI implementation, such as openMPI [24] or mpich [25], which can be found in the repositories of any linux distribution. Finally, to provide DICOM processing support, PenRed can be optionally compiled using the dicom toolkit (dcmtk) [32] library. Thus, PenRed has only two optional dependencies, an MPI implementation and the dcmtk library.

Melting of Fe-terephthalate layers on Cu(1 0 0) surface with randomly distributed point defects

In this theoretical work, we study the influence of the concentration and type of randomly distributed point defects on crystalline solid surfaces on the possibility of self-assembly and thermal stability of surface confined metal-organic networks (SMON). As an example, we chose fundamentally different and well-studied SMONs of Fe-terephthalate on Cu(100) surface: cloverleaf and single-row structures. Using parallel tempering Monte Carlo simulation, we have determined the concentration thresholds for various types of defects above which the SMONs self-assembly is unfavorable. It is shown that the SMONs melting temperatures decrease equally with an increase in the surface concentration of point defects, regardless of the SMON type. Maximum decrease in the SMON melting temperature relative to the homogeneous surface reaches 15–23%, depending on the defect type. Melting of a more “rigid” single-row structure formed only by the coordination bonds is found to occur through the first-order phase transition, while the cloverleaf structure, stabilized mainly by weak hydrogen bonds and long-range substrate mediated interactions, is a continuous phase transition.