Isotropic-nematic phase transition in athermal solutions of rod-coil diblock copolymers

We present a hybrid method to investigate the isotropic-nematic (I-N) transition in athermal solutions of rod-coil copolymers. This method incorporates the scaled-particle theory for semiflexible chains with two-chain Monte Carlo simulation for the osmotic second virial coefficient and for the angle-dependent excluded volume. We compare the theoretical prediction with Monte Carlo simulations for fused rod-coil copolymers and find good agreement for both the equation of state and the orientational order parameter. The theory is also used to examine the effects of the bond length, the chain length, and the chain composition on orientational ordering in athermal solutions of rod-coil block copolymers. It predicts I-N transition in rod-coil copolymers with fixed rod length but a variable flexible tail in good agreement with experiments.     

How ions affect the structure of water

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.     

Confined water: a Mercedes-Benz model study

We study water that is confined within small geometric spaces. We use the Mercedes-Benz (MB) model of water, in NVT and muVT Monte Carlo computer simulations. For MB water molecules between two planes separated by a distance d, we explore the structures, hydrogen bond networks, and thermodynamics as a function of d, temperature T, and water chemical potential mu. We find that squeezing the planes close enough together leads to a vaporization of waters out of the cavity. This vaporization transition has a corresponding peak in the heat capacity of the water. We also find that, in small pores, hydrogen bonding is not isotropic but, rather, it preferentially forms chains along the axis of the cavity. This may be relevant for fast proton transport in pores. Our simulations show oscillations in the forces between the inert plates, due to water structure, even for plate separations of 5-10 water diameters, consistent with experiments by Israelachvili et al. [Nature 1983, 306, 249]. Finally, we find that confinement affects water's heat capacity, consistent with recent experiments of Tombari et al. on Vycor nanopores [J. Chem. Phys. 2005, 122, 104712].     

Intermolecular hydrogen bonds in hetero-complexes of biologically active aromatic ligands: Monte Carlo simulations results

We report results of the Monte Carlo simulations of systems containing heterodimers of biological active ligands and water molecules. The study was designed to identify the possible formation of intermolecular hydrogen bonds in such systems in order to investigate the molecular mechanisms of hetero-association of aromatic ligands in aqueous solution. The geometry optimization and the calculation of the atomic charges of free ligands were carried out at DFT/B3LYP level of theory. Monte Carlo simulations with Metropolis algorithm were used to determine the low energy conformations of heterodimers in water clusters. The analysis of the Monte Carlo simulation results allows us to describe in detail the hydration properties of all investigated heterodimers and to determine the intermolecular hydrogen bonds between the functional donor–acceptor groups for some of hetero-associates under investigation. In the case of heterodimers without intermolecular hydrogen bonds, the additional stabilization of these hetero-complexes can be explained by the formation the water bridges between donor and acceptor groups of the ligands.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.     

The influence of microhydration on the ionization energy thresholds of uracil and thymine

In the present study the ionization energy thresholds (IET's) of uracil and thymine have been calculated (with the B3LYP, PMP2, and P3 levels of theory using the standard 6-31++G(d,p) basis set) with one to three water molecules placed in the first hydration shell. Then (B3LYP) polarizable continuum model (PCM) calculations were performed with one to three waters of the hydration shell included. Calculations show there is a distinct effect of microhydration on uracil and thymine. For uracil, one added water results in a decrease in the IET of about 0.15 eV. The second and third water molecules cause a further decrease by about 0.07 eV each. For thymine, the first water molecule is seen to decrease the IET by about 0.1 eV, while the second and third water molecules cause a further decrease of less than 0.1 eV each. The changes in IET calculated here for thymine with one to three waters of hydration are smaller than the experimental values determined by Kim et al. (Kim, S. K.; Lee, W.; Herschbach, D. R. J. Phys. Chem. 1996, 100, 7933). Preliminary results presented here indicate that the experimental results may involve keto-enol tautomers of thymine. The results of placing the microhydrated structures of uracil and thymine in a PCM cavity was seen to make very little difference in the IET when compared to the IET of ordinary uracil or thymine in a PCM cavity. The implications are that accurate calculations of the IET's of uracil and thymine can be obtained by simply considering long-range solvation effects.     

A theoretical investigation on the honeycomb potential fluid

A local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive NVT-Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory's reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy, pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local self-consistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.     

Proton ordering in cubic ice and hexagonal ice; a potential new ice phase--XIc

Ordinary water ice forms under ambient conditions and has two polytypes, hexagonal ice (Ih) and cubic ice (Ic). From a careful comparison of proton ordering arrangements in Ih and Ic using periodic density functional theory (DFT) and diffusion Monte Carlo (DMC) approaches, we find that the most stable arrangement of water molecules in cubic ice is isoenergetic with that of the proton ordered form of hexagonal ice (known as ice XI). We denote this potential new polytype of ice XI as XIc and discuss a possible route for preparing ice XIc.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

An improved thermodynamic perturbation theory for Mercedes-Benz water

We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.     

Multiple "time step" Monte Carlo simulations: application to charged systems with Ewald summation

Recently, we have proposed an efficient scheme for Monte Carlo simulations, the multiple "time step" Monte Carlo (MTS-MC) [J. Chem. Phys. 117, 8203 (2002)] based on the separation of the potential interactions into two additive parts. In this paper, the structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of the Ewald summation and the common Metropolis Monte Carlo method. We report a number of observables as a function of CPU time calculated using MC and MTS-MC. The correlation functions indicate that speedups on the order of 4.5-7.5 can be obtained for systems of 108-500 waters for n=10 splitting parameter.     

The density distributions of the counterions and the coions confined in two similarly charged plates

By using the field-theoretic method, we established a unified systematic formulation of a model of counterions and coions confined in two similarly charged plates, and calculated the density distributions of counterions and coions with various coupling parameters by the two methods: Poisson-Boltzmann (PB) approach and the strong coupling (SC) theory, respectively. We also performed Monte Carlo simulations, and obtained the density distributions of counterions and coions with several different coupling parameters. Comparing our theoretical results with those from Monte Carlo simulation, we find that the PB approach is valid when the coupling parameter Xi is smaller than 1, but, as Xi > or = 1, the results by the PB approach deviate from the corresponding Monte Carlo simulation data, and the deviation gets larger with the coupling parameter increasing. This shows that the PB approach is completely invalid when the coupling parameter is equal to 1 or larger than 1. For the latter case, the development trend of the distribution curve calculated by SC theory agrees with that from Monte Carlo simulation as the coupling parameter increases. This demonstrates that the SC theory can give a qualitative available explanation on the density distribution of the counterions in the system in which the coupling parameters are strictly confined.     

Cluster-variation approximation for a network-forming lattice-fluid model

We consider a three-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi et al. by means of Monte Carlo simulations [J. Chem. Phys. 126, 064503 (2007)], with the aim of describing water anomalies. We develop an approximate semianalytical calculation, based on a cluster-variation technique, which turns out to reproduce almost quantitatively different thermodynamic properties and phase transitions determined by the Monte Carlo method. Nevertheless, our calculation points out the existence of two different phases characterized by long-range orientational order, and of critical transitions between them and to a high-temperature orientationally disordered phase. Also, the existence of such critical lines allows us to explain certain "kinks" in the isotherms and isobars determined by the Monte Carlo analysis. The picture of the phase diagram becomes much more complex and richer, though unfortunately less suitable to describe real water.     

Theoretical advances in the dissolution studies of mineral–water interfaces

This article presents theoretical advances in computational modeling of dissolution at mineral–water interfaces with specific emphasis on silicates. Two different Monte Carlo methods have been developed that target equilibrium properties and kinetics in silicate–water dissolution. The equilibrium properties are explored using the combined reactive Monte Carlo and configurational bias Monte Carlo (RxMC-CBMC) method. The new RxMC-CBMC method is designed to affordably simulate the three-dimensional structure of the mineral with explicit water molecules. The kinetics of the overall dissolution process is studied using a stochastic kinetic Monte Carlo method that utilizes rate constants obtained from accurate ab initio calculations. Both these methods provide important complementary perspective of the complex dynamics involving chemical and physical interactions at the mineral–water interface. The results are compared to experimental and previous computational data available in the literature.     

Protonated clathrate cages enclosing neutral water molecules: (H+)(H2O)21 and (H+)(H2O)28

This paper describes a systematic study on the clathrate structure of (H+)(H2O)21 using tandem mass spectrometry, vibrational predissociation spectroscopy, Monte Carlo simulations, and density functional theory calculations. We produced (H+)(H2O)n from a continuous corona-discharged supersonic expansion and observed three anomalies simultaneously at the cluster temperature near 150 K, including (1) the peak at n=21 is more intense than its neighboring ions in the mass spectrum, (2) the size-dependent dissociation fractions show a distinct drop for the 21-mer, and (3) the infrared spectrum of (H+)(H2O)21 exhibits only a single feature at 3699 cm(-1), corresponding to the free-OH stretching of three-coordinated water molecules. Interestingly, the anomalies appear or disappear together with cluster temperature, indicating close correlation of these three observations. The observations, together with Monte Carlo simulations and density functional theory calculations, corroborate the notion for the formation of a distorted pentagonal dodecahedral (5(12)) cage with a H2O molecule in the cage and a H3O+ ion on the surface for this "magic number" water cluster ion. The dodecahedral cage melts at higher temperatures, as evidenced by the emergence of a free-OH stretching feature at 3717 cm(-1) for the two-coordinated water in (H+)(H2O)21 produced in a warmer molecular beam. Extension of this study to larger clusters strongly suggests that the experimentally observed isomer of (H+)(H2O)28 is most likely to consist of a distorted protonated pentakaidecahedral (5(12)6(3)) cage enclosing two neutral water molecules.     

Influence of microhydration on the ionization energy thresholds of thymine: comparisons of theoretical calculations with experimental values

In the present study the ionization energy thresholds (IETs) of thymine, and thymine keto-enol tautomers, have been calculated (with the B3LYP, and P3 levels of theory using the standard 6-31++G(d,p) basis set) with 1-3 water molecules placed in the first hydration shell. Calculations show there is a distinct effect of microhydration on the IET of thymine. The first water molecule is seen to decrease the IET by about 0.1 eV, whereas the second and third water molecules cause a further decrease of less than 0.1 eV each. The changes in IET calculated here for thymine with 1-3 waters of hydration are smaller than the experimental values determined by Kim et al. (J. Phys. Chem. 1996, 100, 7933). Therefore calculations have been performed on the microhydrated keto-enol tautomers of thymine. The calculated results on the keto-enol tautomers are seen to be in better agreement with the experimental results. However, the keto-enol thymine tautomers are considerably higher in energy than the canonical form of thymine, and there is presently no good evidence that these thymine tautomers are actually present in a supersonic jet-cooled experiment.     

Density distributions in the water shell of myoglobin

Two different approaches were used to explain the distribution of water coordinates in the crystallographically invisible part of the unit cell. Monte Carlo calculations were done starting from different initial water structures. Extended Monte Carlo calculations using equal initial structures were also used to obtain two further water structures. The differences between the Monte Carlo water structures were used to calculate the mean-square displacements of the water molecules. Monte Carlo calculations starting from different structures lead to a mean-square displacement of 0.58 Ų, whereas extended Monte Carlo moves using the same initial structure only show a mean-square displacement of 0.17 Ų. The mean-square displacement of 0.58 Ų can be used to explain the experimental data. © 1996 John Wiley & Sons, Inc.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.     

Dissociation energy of the water dimer from quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.