Parallel Tempering Monte Carlo Simulations Research Articles

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping.

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. Inparticular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_{3DCC}^{(1)}≃1.9% and p_{3DCC}^{(2)}≃27.6%. We obtain these results by using parallel tempering MonteCarlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Molecular Understanding of Laccase Adsorption on Charged Self-Assembled Monolayers.

Controlling the orientation of laccase on electrodes is crucial for the achievement of fast direct electron transfer. It is important to find a short pathway between the T1 copper site of laccase and a substrate during the laccase immobilization. In this work, we studied the adsorption orientation and conformation of Trametes versicolor laccase (TvL) on two kinds of charged self-assembled monolayers (SAMs), including NH2-SAM and COOH-SAM, by parallel tempering Monte Carlo and all-atom molecular dynamics simulations. TvL adsorbs on positively and negatively charged surface with "end-on" and "lying" orientation, respectively. On the positively charged surface, T1 copper site of TvL is closer to the surface. The orientation of TvL on positively charged surface is narrower than that on negatively charged surface. Thus, the positively charged surface is more conducive to the immobilization of TvL. The conformational changes of TvL on the charged surfaces are analyzed by RMSD, superimposed structures, dipole moment, gyration radius, and eccentricity. Results show that native structures of TvL are well preserved when it adsorbs on the charged surfaces. This work provides atomistic insight into the mechanism of TvL adsorption on charged surface and is helpful for the design and development of laccase-based electrodes.

Modeling Iron–Gold Nanoparticles Using a Dedicated Semi-Empirical Potential: Application to the Stability of Core–Shell Structures

Core–shell nanoparticles made from iron embedded in gold have a strong potential interest in nanomedicine, the Au shell providing an efficient biocompatible coating for the magnetic Fe core. With the aim of determining theoretically the equilibrium morphologies of Fe–Au nanoparticles in a broad size range and with different compositions, a semiempirical many-body Fe–Au potential was designed combining well-established models for the pure metals and introducing dedicated contributions for the interactions involving mixed elements. The potential was parametrized against various energetic properties involving impurities, intermetallics, and finite clusters obtained using density functional calculations in the generalized gradient approximation. The potential was tested to investigate Fe–Au nanoparticles near equiconcentration containing about 1000–2000 atoms at finite temperature using parallel tempering Monte Carlo simulations initiated from the core–shell structure. The core–shell nanoparticles are found to be thermally stable up to about 800 K, at which point the gold outer layer starts to melt, with the iron core remaining stable up to approximately 1200 K. In contrast, the alternative potential developed by Zhou and co-workers (Zhou, X. Z.; Johnson, R. A.; Wadley, H. N. G. Phys. Rev. B, 2004, 69, 144113) predicts a strong tendency for mixing, the core–shell structure appearing energetically metastable. The two models also predict significantly different vibrational spectra.

Electrostatics-mediated α-chymotrypsin inhibition by functionalized single-walled carbon nanotubes.

The α-chymotrypsin (α-ChT) enzyme is extensively used for studying nanomaterial-induced enzymatic activity inhibition. A recent experimental study reported that carboxylized carbon nanotubes (CNTs) played an important role in regulating the α-ChT activity. In this study, parallel tempering Monte Carlo and molecular dynamics simulations were combined to elucidate the interactions between α-ChT and CNTs in relation to the CNT functional group density. The simulation results indicate that the adsorption and the driving force of α-ChT on different CNTs are contingent on the carboxyl density. Meanwhile, minor secondary structural changes are observed in adsorption processes. It is revealed that α-ChT interacts with pristine CNTs through hydrophobic forces and exhibits a non-competitive characteristic with the active site facing towards the solution; while it binds to carboxylized CNTs with the active pocket through a dominant electrostatic association, which causes enzymatic activity inhibition in a competitive-like mode. These findings are in line with experimental results, and well interpret the activity inhibition of α-ChT at the molecular level. Moreover, this study would shed light on the detailed mechanism of specific recognition and regulation of α-ChT by other functionalized nanomaterials.

High Pressure Structural Transitions in Kr Clathrate-Like Clusters

Classical thermodynamic properties of a size-specific Kr clathrate-like cluster, modeled by an ab initio and a semiempirical Kr–water potential, were computed from parallel-tempering Monte Carlo simulations. The temperature and pressure dependence of the cluster’s heat capacity was studied, and phase diagrams were constructed using a multiple-histogram method. By associating the heat capacity (maxima) and the Pearson correlation coefficient (minima/maxima) values with the phase transitions, attempts were made to identify such changes to particular cluster structures. Various isomers were computed by local optimizations of the interaction enthalpy at a set of randomly selected configurations at each temperature–pressure grid point. Their energy distributions and relative abundances were then employed to assign the observed phase transitions of the cluster. It was found that the structural changes at high pressures are related to Kr clathrate-like cages, such as those of the sI, sII, and sH hydrates, as wel...

Significance of bending restraints for the stability of helical polymer conformations.

We performed parallel-tempering Monte Carlo simulations to investigate the formation and stability of helical tertiary structures for flexible and semiflexible polymers, employing a generic coarse-grained model. Structural conformations exhibit helical order with tertiary ordering into single helices, multiple helical segments organized into bundles, and disorganized helical arrangements. For both bending-restrained semiflexible and bending-unrestrained flexible helical polymers, the stability of the structural phases is discussed systematically by means of hyperphase diagrams parametrized by suitable order parameters, temperature, and torsion strength. This exploration lends insight into the restricted flexibility of biological polymers such as double-stranded DNA and proteins.

Gyroidal nanoporous carbons - Adsorption and separation properties explored using computer simulations

Adsorption and separation properties of gyroidal nanoporous carbons (GNCs) - a new class of exotic nanocarbon materials are studied for the first time using hyper parallel tempering Monte Carlo Simulation technique. Porous structure of GNC models is evaluated by the method proposed by Bhattacharya and Gubbins. All the studied structures are strictly microporous. Next, mechanisms of Ar adsorption are described basing on the analysis of adsorption isotherms, enthalpy plots, the values of Henry's constants, $\alpha_{s}$ and adsorption potential distribution plots. It is concluded that below pore diameters ca. 0.8 nm, primary micropore filling process dominates. For structures possessing larger micropores, primary and secondary micropore filling mechanism is observed. Finally, the separation properties of GNC toward CO$_2$/CH$_4$, CO$_2$/N$_2$, and CH$_4$/N$_2$ mixtures are discussed and compared with separation properties of Virtual Porous Carbon models. GNCs may be considered as potential adsorbents for gas mixture separation, having separation efficiency similar or even higher than activated carbons with similar diameters of pores.

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here, we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem-an Ising spin glass-on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other computing paradigm affected by noise.

Parallel Tempering Monte Carlo Simulations of Spherical Fixed-Connectivity Model for Polymerized Membranes

We study the first order phase transition of the fixed-connectivity triangulated surface model using the Parallel Tempering Monte Carlo (PTMC) technique on relatively large lattices. From the PTMC results, we find that the transition is considerably stronger than the reported ones predicted by the conventional Metropolis MC (MMC) technique and the flat histogram MC technique. We also confirm that the results of the PTMC on relatively smaller lattices are in good agreement with those known results. This implies that the PTMC is successfully used to simulate the first order phase transitions. The parallel computation in the PTMC is implemented by OpenMP, where the speed of the PTMC on multi-core CPUs is considerably faster than that on the single-core CPUs.

Lattice Monte Carlo Simulations in Search of Zeolite Analogues: Effects of Structure Directing Agents

We use parallel tempering Monte Carlo simulations to search for crystalline states of a lattice model of silica polymerization in the presence of structure directing agents (SDAs). Following previous work where we have discretized continuous space into a body-centered cubic (bcc) lattice, we have modeled tetrahedral molecules (T(OH)4) as corner-sharing tetrahedra on a bcc unit cell. The SDAs were represented as quasi-spherical species with diameters of 6.4 and 10.4 Å to study the effect of SDA size on the resulting crystal structures. Our parallel tempering Monte Carlo simulations produce fully connected crystalline structures finding the emergence of 3D microporous materials with SDAs occupying the pore spaces and 2D layered materials with SDAs occupying the gallery space in between layers. We have found that the strength of SDA–oxygen attraction plays a significant role in directing final micropore structures. For relatively strong attractions (>1.2 kcal/mol SDA–oxygen contacts) we have found only 2D layered materials; for attractions below this cutoff we observed 3D microporous crystals; and for no attraction—modeling the SDA as a quasi-hard sphere—we again found only 2D layered materials. In the space of 3D microporous crystals, we have also found that using larger SDAs or a lower concentration of a given SDA generate crystals with larger rings.

Molecular simulation study of feruloyl esterase adsorption on charged surfaces: effects of surface charge density and ionic strength.

The surrounding conditions, such as surface charge density and ionic strength, play an important role in enzyme adsorption. The adsorption of a nonmodular type-A feruloyl esterase from Aspergillus niger (AnFaeA) on charged surfaces was investigated by parallel tempering Monte Carlo (PTMC) and all-atom molecular dynamics (AAMD) simulations at different surface charge densities (±0.05 and ±0.16 C·m(-2)) and ionic strengths (0.007 and 0.154 M). The adsorption energy, orientation, and conformational changes were analyzed. Simulation results show that whether AnFaeA can adsorb onto a charged surface is mainly controlled by electrostatic interactions between AnFaeA and the charged surface. The electrostatic interactions between AnFaeA and charged surfaces are weakened when the ionic strength increases. The positively charged surface at low surface charge density and high ionic strength conditions can maximize the utilization of the immobilized AnFaeA. The counterion layer plays a key role in the adsorption of AnFaeA on the negatively charged COOH-SAM. The native conformation of AnFaeA is well preserved under all of these conditions. The results of this work can be used for the controlled immobilization of AnFaeA.

Coarse-graining and phase behavior of model star polymer–colloid mixtures in solvents of varying quality

We study the effective interactions and phase behavior of star polymer-colloid mixtures through theory and Monte Carlo simulations. We extend previous theoretical approaches for calculating the effective star-colloid pair potential to take into account attractive contributions, which become significant at worsening solvent conditions. In order to assess the validity of our simulation and theory, we compute the effective interactions via virtual move parallel tempering Monte Carlo simulations using a microscopic bead-spring model for the star polymer and achieve excellent agreement. Finally, we perform grand canonical Monte Carlo simulations of the coarse-grained systems to study the effect of solvent quality on the phase behavior.

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k={1/21/21/2}. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions, and second- and third-nearest neighbor exchange, we use standard mean-field theory (SMFT) to identify an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in SMFT are responsible for the selection of one particular partially ordered phase, e.g., the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a four-component vector order parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature.

Computational investigations of the thermodynamic properties of size-selected water and Ar-water clusters: high-pressure transitions.

Classical parallel-tempering Monte Carlo simulations in the isothermal-isobaric ensemble were carried out for the (H2O)20 and Ar(H2O)20 clusters, over a wide range of temperatures (30-1000 K) and pressures (3 kPa-10 GPa) in order to study their thermodynamic properties and structural changes. The TIP4P/ice water model is employed for the water-water interactions, while both semiempirical and ab initio-based potentials are used to model the interaction between the rare-gas atoms and the water molecules. Temperature-pressure phase diagrams for these cluster systems were constructed by employing a two-dimensional multiple-histogram method. Structural changes were detected by analyzing the heat capacity landscape and the Pearson correlation coefficient profile for the interaction energy and volume. Those at high pressure correspond to solid-to-solid transitions and are found to be related to clathrate-like cages around the Ar atom. It is also shown that the formation and thermodynamic stability of such structures are determined by the intermolecular interaction between the rare-gas atoms and the host water molecules.

Phase transitions in free water nanoparticles. Theoretical modeling of [H2O]48 and [H2O]118

Classical parallel-tempering Monte Carlo simulations of [H2O]48 and [H2O]118 have been performed in the isothermal-isobaric ensemble and a two-dimensional multiple-histogram method has been used to calculate the heat capacity of the two clusters. A semiempirical procedure is proposed for the inclusion of quantum effects and transformed heat capacity profiles are compared with state-of-the-art experimental data [C. Hock et al., Phys. Rev. Lett., 2009, 103, 073401]. A very good agreement is achieved. A detailed analysis of the simulation data is provided to gain an insight into the nature of the phase change which takes place in the two clusters at T ≈ 100 K.

Adsorption of hydrophobin on different self-assembled monolayers: the role of the hydrophobic dipole and the electric dipole.

In this work, the adsorptions of hydrophobin (HFBI) on four different self-assembled monolayers (SAMs) (i.e., CH3-SAM, OH-SAM, COOH-SAM, and NH2-SAM) were investigated by parallel tempering Monte Carlo and molecular dynamics simulations. Simulation results indicate that the orientation of HFBI adsorbed on neutral surfaces is dominated by a hydrophobic dipole. HFBI adsorbs on the hydrophobic CH3-SAM through its hydrophobic patch and adopts a nearly vertical hydrophobic dipole relative to the surface, while it is nearly horizontal when adsorbed on the hydrophilic OH-SAM. For charged SAM surfaces, HFBI adopts a nearly vertical electric dipole relative to the surface. HFBI has the narrowest orientation distribution on the CH3-SAM, and thus can form an ordered monolayer and reverse the wettability of the surface. For HFBI adsorption on charged SAMs, the adsorption strength weakens as the surface charge density increases. Compared with those on other SAMs, a larger area of the hydrophobic patch is exposed to the solution when HFBI adsorbs on the NH2-SAM. This leads to an increase of the hydrophobicity of the surface, which is consistent with the experimental results. The binding of HFBI to the CH3-SAM is mainly through hydrophobic interactions, while it is mediated through a hydration water layer near the surface for the OH-SAM. For the charged SAM surfaces, the adsorption is mainly induced by electrostatic interactions between the charged surfaces and the oppositely charged residues. The effect of a hydrophobic dipole on protein adsorption onto hydrophobic surfaces is similar to that of an electric dipole for charged surfaces. Therefore, the hydrophobic dipole may be applied to predict the probable orientations of protein adsorbed on hydrophobic surfaces.

Chiral effects in amino acid adsorption on Au(111): A comparison of cysteine, homocysteine and methionine

A combined classical/quantum methodology is used to examine chiral effects upon adsorption of three sulfur-containing amino acids on the Au(111) surface: cysteine, homocysteine and methionine. Parallel tempering Monte Carlo simulations were employed to broadly examine the configurational space of monomers, dimers and trimers of the molecules on the gold surface. Density functional theory was applied to promising structural targets in order to incorporate higher order electronic structure effects in a study of relative stabilities of the various molecular states upon adsorption. As the precursors of chiral structure formation, like and unlike dimers were investigated at some length, with consideration given to the mode of sorption (chemisorption of physisorption) and the existence of zwitterionic states. We found that neutral (non-zwitterionic) molecules adsorbed weakly on the highly-coordinated Au(111) surfaces. As a consequence, pair configurations in dimers were insufficiently constrained to lead to differential stabilities of homochiral and heterochiral dimers. Whereas neutral molecule interactions were non-discriminating, strong chiral discrimination was found in zwitterionic amino acids. The zwitterionic forms of the larger molecules equilibrated closer to the surface, and the stronger molecule–molecule and molecule–surface interactions were such that homochiral dimers were stable whereas heterochiral dimers were not.

20206 Parallel Tempering Monte Carlo法による膜モデルのシミュレーション

The Parallel Tempering Monte Carlo (PTMC) simulations are performed for the fixed-connectivity model for membranes using Open MP parallelization. The results are compared with those obtained by the canonical Metropolis and Flat Histogram MC techniques. The numerical results of the PTMC technique are in good agreement with those obtained by the conventional MC techniques. This implies that the PTMC technique can successfully simulate the first order phase transition of the model. Moreover, the speed of the PTMC technique is three times faster than that of the Metropolis MC technique on 6 cores PC.

Thermal phase transitions in a honeycomb lattice gas with three-body interactions

We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of 9/16, 5/8, and 3/4 that were identified in a previous study of a related quantum model. In particular, both the 9/16 and the 5/8 phase exhibit an extensive ground-state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the 9/16 phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the 5/8 phase. We find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the 5/8 phase, which we obtain via an exact mapping of the ground-state manifold to a hard-core dimer model on an embedded honeycomb superlattice.

Multiscale Simulations of Protein G B1 Adsorbed on Charged Self-Assembled Monolayers

The orientation of an antibody plays an important role in the development of immunosensors. Protein G is an antibody binding protein, which specifically targets the Fc fragment of an antibody. In this work, the orientation of prototypical and mutated protein G B1 adsorbed on positively and negatively charged self-assembled monolayers was studied by parallel tempering Monte Carlo and all-atom molecular dynamics simulations. Both methods present generally similar orientation distributions of protein G B1 for each kind of surface. The root-mean-square deviation, DSSP, gyration radius, eccentricity, dipole moment, and superimposed structures of protein G B1 were analyzed. Moreover, the orientation of binding antibody was also predicted in this work. Simulation results show that with the same orientation trends, the mutant exhibits narrower orientation distributions than does the prototype, which was mainly caused by the stronger dipole of the mutant. Both kinds of proteins adsorbed on charged surfaces were induced by the competition of electrostatic interaction and vdW interaction; the electrostatic interaction energy dominated the adsorption behavior. The protein adsorption was also largely affected by the distribution of charged residues within the proteins. Thus, the prototype could adsorb on a negatively charged surface, although it keeps a net charge of -4 e. The mutant has imperfect opposite orientation when it adsorbed on oppositely charged surfaces. For the mutant on a carboxyl-functionalized self-assembled monolayer (COOH-SAM), the orientation was the same as that inferred by experiments. While for the mutant on amine-functionalized self-assembled monolayer (NH2-SAM), the orientation was induced by the competition between attractive interactions (led by ASP40 and GLU56) and repulsive interactions (led by LYS10); thus, the perfect opposite orientation could not be obtained. On both surfaces, the adsorbed protein could retain its native conformation. The desired orientation of protein G B1, which would increase the efficiency of binding antibodies, could be obtained on a negatively charged surface adsorbed with the prototype. Further, we deduced that with the packing density of 12,076 protein G B1 domain per μm(2), the efficiency of the binding IgG would be maximized. The simulation results could be applied to control the orientation of protein G B1 in experiments and to provide a better understanding to maximize the efficiency of antibody binding.