On the use of the gaussian chain as a monte carlo simulation model for the equilibrium properties of polymer solutions

We have explored the performance of a simulation model for Gaussian chains at different concentrations in a good solvent. The Gaussian statistics for the distances between contiguous beads in the model is directly implemented in the individual moves of a Monte Carlo algorithm. When the results of conformational properties for the Gaussian model are compared with those provided by a freely jointed model in the same conditions, significant differences arise at finite concentrations. The modeled Gaussian chain yields incorrect results for the quadratic average dimensions 〈R²〉 and 〈S²〉 at high concentrations, but correctly reproduces the results for the scaled end-to-end distance distribution function at any concentration, showing the effects of the screening of excluded volume when concentration increases. The reason for the wrong behavior of the simulated Gaussian model comes from a strong distortion of the “bond distance” distribution as a result of the concentration increase. We conclude that this model can only be safely applied to infinitely dilute solutions.     

Electrostatic stability of a large collection of charged anisotropic nanoparticles: a monte carlo study exploiting a hierarchical approach

We have performed Monte Carlo simulations of the self-organization of large collections of charged disks of various electric charges to probe the influence of electrostatic coupling on the structure and the mechanical stability of aqueous dispersions of charged anisotropic nanoparticles in the presence of salt. A hierarchical approach of the long-range Coulombic potential was used to perform such Monte Carlo simulations of a large number of charged species. By analyzing the influence of the net electric charge of the disks on their self-organization, we detected a negative contribution to the mean force potential resulting from their electrostatic coupling. In addition, it has been shown that the same electrostatic coupling restricts the spatial extend of locally ordered microdomains within dilute dispersions of charged anisotropic colloids.     

Freezing phenomena of lennard-jones fluid confined in jungle-gym nanospace: a monte carlo study

We performed grand canonical Monte Carlo simulations for a Lennard-Jones fluid confined in a jungle-gym (JG) nanospace of cubic structure modeled on a specific type of metal organic frameworks (MOFs) to investigate freezing phenomena. Our simulations clarified that the JG nanospace with the pore sizes from 5sigma to 11sigma strongly depresses freezing due to a geometrical hindrance effect, resulting in far lower freezing temperature than the bulk freezing point. The fluid-rod interaction is found to give little effect on the freezing temperature in the larger pore sizes. For smaller pores from 2sigma to 3sigma, on the other hand, a dominant factor is a template effect to enhance the localization of molecules into a specific configuration that matches the locations of potential minima, leading to a variety of molecular configurations. In this range of smaller pore sizes, the solidification temperatures are higher than those of the larger pores mainly due to strong influence of the fluid-rod interaction but are still lower than the bulk freezing temperature. In addition, a unique solid-to-solid transition is observed in a specific size of pore of 2.73sigma, which is caused by structural correlation between adjacent cells. On the basis of these results, a phase diagram in the JG nanospace is drawn.     

Quantum monte carlo study of the retinal minimal model C5H6NH2+

In this work, we study the electronic and geometrical properties of the ground state of the Retinal Minimal Model C₅H₆NH₂⁺ using the variational Monte Carlo (VMC) method by means of the Jastrow antisymmetrized geminal power (JAGP) wavefunction. A full optimization of all wavefunction parameters, including coefficients, and exponents of the atomic basis, has been achieved, giving converged geometries with a compact and correlated wavefunction. The relaxed geometries of the cis and trans isomers present a pronounced bond length alternation pattern characterized by a C?C central double bond slightly shorter than that reported by the CASPT2 structures. The comparison between different basis sets indicates converged values of geometrical parameters, energy differences, and dipole moments even when the smallest wavefunction is used. The compactness of the wavefunction as well as the scalability of VMC optimization algorithms on massively parallel computers opens the way to perform full structural optimizations of conjugated biomolecules of hundreds of electrons by correlated methods like Quantum Monte Carlo. © 2012 Wiley Periodicals, Inc.     

Macrophase and microphase separations for surfactants adsorbed on solid surfaces: a gauge cell monte carlo study in the lattice model

By combining the gauge cell method and lattice model, we study the surface phase transition and adsorption behaviors of surfactants on a solid surface. Two different cases are considered in this work: macrophase transition and adsorption in a single-phase region. For the case of macrophase transition, where two phases coexist, we investigate the shape and size of the critical nuclei and determine the height of the nucleation barrier. It is found that the nucleation depends on the bulk surfactant concentration. Our simulations show that there exist a critical temperature and critical adsorption energy, below which the transition from low-affinity adsorption to the bilayer structure shows the characteristic of a typical first-order phase transition. Such a surface phase transition in the adsorption isotherm is featured by a hysteresis loop. The hysteresis loop becomes narrower at higher temperature and weaker adsorption energy and finally disappears at the critical value. For the case where no macrophase transition occurs, we study the adsorption isotherm and microphase separation in a single-phase region. The simulation results indicate that the adsorption isotherm in adsorption processes is divided into four regions in a log-log plot, being in agreement with experimental observations. In this work, the four regions are called the low-affinity adsorption region, the hemimicelle region, the morphological transition region, and the plateau region. Simulation results reveal that in the second region the adsorbed monomers aggregate and nucleate hemimicelles, while adsorption in the third region is accompanied by morphological transitions.     

A monte carlo model of network formation by step-growth: Star-shaped structures developed at an isolated crosslink site

A Monte Carlo lattice model of step growth network formation from systems of divalent and multivalent molecules has been used to investigate the manner in which the latter function as nodes when diluted considerably be the former. Star molecules develop in the simulation, giving nodes that have pendent tails and loops. We show how the number and size of tails and loops is rather insensitive to the valency, f, of the nodes, and examine the distribution functions for the numbers of tails and loops present in the systems at the end of the reaction. Topological considerations created by a high number of valencies that might be expected to enhance molecule size are frustrated by the presence of adjacent segments of chains from developing the full structural potential.     

Application of the quasi-variational coupled cluster method to the nonlinear optical properties of model hydrogen systems

We present a pilot application of the recently proposed quasi-variational coupled cluster method to the energies, polarizabilities, and second hyperpolarizabilities of model hydrogen chains. Relative to other single-reference methods of equivalent computational complexity, we demonstrate this method to be highly robust and especially useful when traditional coupled cluster theory fails to perform adequately. In particular, our results indicate it to be a suitable method for the black-box treatment of multiradicals, making it of widespread general interest and applicability.     

The band structure and magnetic properties of some transition-metal phosphides. II. V,Cr, and Mn monophosphides

The band structures and density of states for VP, CrP, and MnP are calculated by an LCAO-TB method. The results allow interpretation of the metallic nature of the materials, the trend in magnetic properties observed, and the bonding in such binary phosphides.     

Fluorescence correlation spectroscopy simulations of photophysical phenomena and molecular interactions: a molecular dynamics/monte carlo approach

Fluorescence correlation spectroscopy (FCS) is being applied increasingly to study diffusion and interactions of fluorescently labeled macromolecules in complex biological systems. Fluctuations in detected fluorescence, deltaF(t), are expressed as time-correlation functions, G(tau), and photon-count histograms, P(k;DeltaT). Here, we developed a generalized simulation approach to compute G(tau) and P(k;DeltaT) for complex systems with arbitrary geometry, photophysics, diffusion, and macromolecular interactions. G(tau) and P(k;DeltaT) were computed from deltaF(t) generated by a Brownian dynamics simulation of single-molecule trajectories followed by a Monte Carlo simulation of fluorophore excitation and detection statistics. Simulations were validated by comparing analytical and simulated G(tau) and P(k;DeltaT) for diffusion of noninteracting fluorophores in a three-dimensional Gaussian excitation and detection volume. Inclusion of photobleaching and triplet-state relaxation produced significant changes in G(tau) and P(k;DeltaT). Simulations of macromolecular interactions and complex diffusion were done, including transient fluorophore binding to an immobile matrix, cross-correlation analysis of interacting fluorophores, and anomalous sub- and superdiffusion. The computational method developed here is generally applicable for simulating FCS measurements on systems complicated by fluorophore interactions or molecular crowding, and experimental protocols for which G(tau) and P(k;DeltaT) cannot be computed analytically.     

Simulation of organic nonelectrolytes in water and tetrachloromethane by the monte carlo method. New data on the thermodynamics of dissolution

Scientific-Research Institute of Physical and Organic Chemistry, Rostov State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 5, pp. 57–68, September–October, 1991.     

Incorporation of inhomogeneous ion diffusion coefficients into kinetic lattice grand canonical monte carlo simulations and application to ion current calculations in a simple model ion channel

To deal with inhomogeneous diffusion coefficients of ions without altering the lattice spacing in the kinetic lattice grand canonical Monte Carlo (KLGCMC) simulation, an algorithm that incorporates diffusion coefficient variation into move probabilities is proposed and implemented into KLGCMC calculations. Using this algorithm, the KLGCMC simulation method is applied to the calculation of ion currents in a simple model ion channel system. Comparisons of ion currents and ion concentrations from these simulations with Poisson-Nernst-Planck (PNP) results show good agreement between the two methods for parameters where the latter method is expected to be accurate.     

Unusual magnetic properties of mixed-valence system: multiconfigurational method theoretical study on Mn2+ cation

The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets (CASSCF/ANO-s), CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets (CASPT2/ANO-s) levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 A calculated at the CASPT2/ANO-s level of theory and 214.4 cm-1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J(-71.2 cm-1) and the double-exchange constant B(647.7 cm-1) are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12Sigmag+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d-3d for Cr2, Mn2+, and Mn2.     

Self-assembly of a Mn9 nanoscopic mixed-valent cluster: synthesis, crystal structure, and magnetic behavior

A rare Mn9 micro3-oxo-centered mixed-valent cluster [Mn9O7(O2CPh)11(thmn)(py)2 (H2O)3] (1) is prepared by assembling an oxo-centered MnIIMnIII2 triangle, [Mn3O(O2CPh)6(py)2(H2O)].0.5MeCN, as the secondary building unit in the presence of a tripodal alcohol, 1,1,1-tris(hydroxymethyl)nitromethane (H3thmn), as the capping ligand. Complex 1 was formed along with a minor byproduct, [Mn6O2(O2CPh)10(MeCN)4] (2). Complex 1 was characterized by X-ray single-crystal structure analysis and was crystallized in a monoclinic system, space group P2(1)/n, a=16.214(6) A, b=25.874(10) A, c=26.497(10) A, and beta=94.214(7) degrees. The Manganese-oxo-carboxylate core in 1 looks like a funnel. Variable-temperature magnetic studies down to 2 K reveal the existence of dominant ferromagnetic interaction within the cluster. Alternating current susceptibility data of the cluster show strong frequency dependence of both the real and imaginary parts of susceptibility chi' and chi' below 5 K. Moreover, the calculated relaxation time, tau0=1.2x10(-7) s, and the energy barrier, DeltaE=25 K, are consistent with the single-molecule magnetic behavior of 1.     

Calculation of the entropy and free energy from monte carlo simulations of a peptide stretched by an external force

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy, S, and free energy, F, from a trajectory generated by any simulation technique. HSMC was applied initially to fluids (argon and water) and later to peptides and self-avoiding walks on a lattice. In this paper we make a step further and apply it to a model of decaglycine (at T = 300 K) in vacuum with constant bond lengths where external stretching forces are exerted at the end points; the changes in S and F are calculated as the forces are increased. The molecule is placed initially in a helical structure, which is changed to an extended structure after a short simulation time due to the exerted forces. This study has relevance to problems in polymers (e.g., rubber elasticity) and to the analysis of experiments where individual molecules are stretched by atomic force microscopy (AFM), for example. The results for S and F are accurate and are significantly better than those obtained by the quasi-harmonic approximation and the local states method. However, the molecule is quite stiff due to the strong bond angle potentials and the extensions are small even for relatively large forces. Correspondingly, as the force is increased the decrease in the entropy is relatively small while the potential energy is enhanced significantly. Still, differences, TDeltaS, for different forces are obtained with very good accuracy of approximately 0.2 kcal/mol.     

Methods for the calculation of occupied volumes in glassy polymers: The lattice integration and the monte carlo methods

A new model for characterizing the free volume of a glassy polymer—gas systems is proposed. An improved method for the calculation of occupied volume per monomer unit was developed within the limits of this model. The model assumptions, error estimates and algorithm efficiencies are described. Using the example of polyvinyltrimethylsilane, it is shown that linear dependences of logarithms of the diffusion and the permeability coefficients on specific accessible volume for inert gases exist.     

Hydration structure around a non-electrolyte molecule as revealed by monte carlo calculation: have you seen the “iceberg”?

Monte Carlo calculations have been carried out for pure water and an infinitely dilute aqueous solution of methanol at 298.15 K at ordinary density by the Metropolis method in NTV ensemble. The hydration structure around methanol revealed by a graphic display technique indicates a structure-forming effect near the hydrophobic group.     

Crystal structure and magnetic properties of a linear tetranuclear CoII cluster

Polynuclear complexes are an important class of inorganic functional materials and are of interest particularly for their applications in molecular magnets. Multidentate chelating ligands play an important role in the design and syntheses of polynuclear metal clusters. A novel linear tetranuclear Co^II cluster, namely bis{μ₃‐(E)‐2‐[(2‐oxidobenzylidene)amino]phenolato}bis{μ₂‐(E)‐2‐[(2‐oxidobenzylidene)amino]phenolato}bis(1,10‐phenanthroline)tetracobalt(II), [Co₄(C₁₄H₁₁NO₂)₄(C₁₂H₈N₂)₂], was prepared under solvothermal conditions through a mixed‐ligand synthetic strategy. The structure was determined by X‐ray single‐crystal diffraction and bulk purity was confirmed by powder X‐ray diffraction. The complex molecule has a centrosymmetric tetranuclear chain‐like structure and the four Co^II ions are located in two different coordination environments. The Co^II ions at the ends of the chain are in a slightly distorted octahedral geometry, while the two inner Co^II ions are in five‐coordinate distorted trigonal bipyramidal environments. A magnetic study reveals ferromagnetic Co^II…Co^II exchange interactions for the complex.     

Electronic and magnetic properties of early transition-metal substituted iron-cyclopentadienyl sandwich molecular wires: parity-dependent half-metallicity

Electronic and magnetic properties of early transition metals (V, Ti, Sc)-Fe(k)Cp(k + 1) sandwich molecular wires (SMWs) are investigated by means of ab initio calculations. It is found that all SMWs favor a ferromagnetic ground state. Significantly, V-Fe(k)Cp(k + 1) SMWs are either half-metallic or semiconducting, dependent upon the parity (even or odd) of the number (k) of Fe atoms in the unit cell of SMWs. This parity oscillation of conductive properties results from the combined effects of the band-folding and gap-opening at the Brillouin-zone boundary of one-dimensional materials. In contrast, Sc-Fe(k)Cp(k + 1) and Ti-Fe(k)Cp(k + 1) SMWs are always semiconducting. Our work may open up the way toward half metal/semiconductor heterostructures with perfect atomic interface.     

Towards graphite: magnetic properties of large polybenzenoid hydrocarbons

The geometries of four different series of D(6h)-symmetric polybenzenoid hydrocarbons (PBH) up to and including C(222)H(42) have been optimized at the B3LYP/6-31G(d) level of theory. Excluding C(48)H(24) and C(138)H(42), which have D(3d) minima due to 1,5 H...H repulsions between adjacent perimeter rings, optimized geometries are planar D(6h) minima. Nucleus Independent Chemical Shifts (NICS), at the same level, indicate the presence of individual aromatic rings, which correspond to Clar's qualitative sextets rule (Clar, E. TheAromatic Sextet; Wiley: London, 1972). NICS and the Clar valence electron topologies agree perfectly in the molecule plane; however, the NICS values computed in parallel planes further away from the molecular surface converge, indicating the presence of a uniform magnetic shielding field. For each series, PBH total NICS values (i.e., the sum of NICS values for all rings in the PBH) correlate linearly with the number of carbon atoms, indicating constant magnetic field development within a series. The C-C lengths depend on their proximity to the more olefinic rich molecular perimeters. However, the large PBH (> or =C(48)H(24)) internal C-C distances converge to approximately 1.426 A. In agreement with Clar's rule, HF/6-31G(d)//B3LYP/6-31G(d) vertical ionization potentials and B3LYP/6-31G(d) HOMO-LUMO gaps are largest within the "fully benzenoid" series, where all carbon atoms are members of a single sextet. The largest members of the four series studied are predicted to exhibit semiconducting properties.     

Use of monte carlo modeling to aid interpretation and quantification of the low energy-loss electron yield at low primary energies

Experimental low-loss electron (LLE) yields were measured as a function of loss energy for a range of elemental standards using a high-vacuum scanning electron microscope operating at 5 keV primary beam energy with losses from 0 to 1 keV. The resulting LLE yield curves were compared with Monte Carlo simulations of the LLE yield in the particular beam/sample/detector geometry employed in the experiment to investigate the possibility of modeling the LLE yield for a series of elements. Monte Carlo simulations were performed using both the Joy and Luo [Joy, D.C. & Luo, S., Scanning 11(4), 176988 (2005)] to assess the influence of the more recent stopping power data on the simulation results. Further simulations have been conducted to explore the influence of sample/detector geometry on the LLE signal in the case of layered samples consisting of a thin C overlayer on an elemental substrate. Experimental LLE data were collected from a range of elemental samples coated with a thin C overlayer, and comparisons with Monte Carlo simulations were used to establish the overlayer thickness.