Water Monte Carlo simulations

Molecular sciences look for explanations of macroscopic properties, e.g., solubility, from the microscopic properties of matter. Statistical mechanics is one of such disciplines, which hnks those two pictures through the probabilistic treatment of particle ensembles. The application of Kirkwood s continuum solvent approach to nondissociating fluids resulted in a variety of simulation techniques. Applications of such techniques to study phase equilibria have been reported widely in literature [1-10]. Although some simple hydrocarbons can nowadays be reasonably well described by molecular modeling (molecular dynamics and Monte Carlo simulations), water and especially water mixtures, still represent challenges for such simulations techniques despite 30 years of active parameterization of appropriate force-fields. This is due to the extremely strong and complicated electrostatic and hydrogen-bond interactions. 

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

The most important molecular interactions of all are those that take place in liquid water. For many years, chemists have worked to model liquid water, using molecular dynamics and Monte Carlo simulations. Until relatively recently, however, all such work was done using effective potentials [4T], designed to reproduce the condensed-phase properties but with no serious claim to represent the tme interactions between a pair of water molecules. 

TIk experimentally determined dipole moment of a water molecule in the gas phase is 1.85 D. The dipole moment of an individual water molecule calculated with any of thv se simple models is significantly higher for example, the SPC dipole moment is 2.27 D and that for TIP4P is 2.18 D. These values are much closer to the effective dipole moment of liquid water, which is approximately 2.6 D. These models are thus all effective pairwise models. The simple water models are usually parametrised by calculating various pmperties using molecular dynamics or Monte Carlo simulations and then modifying the... 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

Jorgensen W L, J Gao and C Ravimohan 1985. Monte Carlo Simulations of Alkanes in Water Hydratior Numbers and the Hydrophobic Effect. Journal of Physical Chemistry 89 3470-3473. 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

Ab initio molecular orbital calculations are being used to study the reactions of anionic nucleophiles with carbonyl compounds in the gas phase. A rich variety of energy surfaces is found as shown here for reactions of hydroxide ion with methyl formate and formaldehyde, chloride ion with formyl and acetyl chloride, and fluoride ion with formyl fluoride. Extension of these investigations to determine the influence of solvation on the energy profiles is also underway the statistical mechanics approach is outlined and illustrated by results from Monte Carlo simulations for the addition of hydroxide ion to formaldehyde in water. 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

Monte Carlo simulation, an iterative technique which derives a range of risk estimates, was incorporated into a trichloroethylene risk assessment using the PBPK model developed by Fisher and Allen (1993). The results of this study (Cronin et al. 1995), which used the kinetics of TCA production and trichloroethylene elimination as the dose metrics relevant to carcinogenic risk, indicated that concentrations of 0.09-1.0 pg/L (men) and 0.29-5.3 pg/L (women) in drinking water correspond to a cancer risk in humans of 1 in 1 million. For inhalation exposure, a similar risk was obtained from intermittent exposure to 0.07-13.3 ppb (men) and 0.16-6.3 ppb (women), or continuous exposure to 0.01-2.6 ppb (men) and 0.03-6.3 ppb (women) (Cronin et al. 1995). 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

Medeiros M, Costas ME (1997) Gibbs ensemble Monte Carlo simulation of the properties of water with a fluctuating charges model. J Chem Phys 107(6) 2012-2019... 

Fig. 5. Probabilities pn of observing n water-oxygen atoms in spherical cavity volumes v. Results from Monte Carlo simulations of SPC water are shown as symbols. The parabolas are predictions using the flat default model in Eq. (11). The center-to-center exclusion distance d (in nanometers) is noted next to the curves. The solute exclusion volume is defined by the distance d of closest approach of water-oxygen atoms to the center of the sphere. (Hummer et al., 1998a)... 

Fig. 2.2. Average electrostatic potential mc at the position of the methane-like Lennard-Jones particle Me as a function of its charge q. mc contains corrections for the finite system size. Results are shown from Monte Carlo simulations using Ewald summation with N = 256 (plus) and N = 128 (cross) as well as GRF calculations with N = 256 water molecules (square). Statistical errors are smaller than the size of the symbols. Also included are linear tits to the data with q < 0 and q > 0 (solid lines). The fit to the tanh-weighted model of two Gaussian distributions is shown with a dashed line. Reproduced with permission of the American Chemical Society...

Fig. 6.11. The error in the free energy measured by several NEW implementations. Results are from Monte Carlo simulations of ion charging in water at 298 K. System 0 consists of a single Lennard-Jones atom with charge of +le and 216 SPC water molecules, and system 1 is the same but with the charge turned off. One work cycle contains 100 nonuniform steps in 7 from 0 to 1 and back. For a detailed description of the simulation, see [43]...

Thirumalai, D. Wallqvist, A. Berne, B.J., Path-integral Monte Carlo simulations of electron localization in water clusters, J. Stat. Phys. 1986, 43, 973-984... 

Bandyopadhyay, P. Ten-No, S. Iwata, S., Ab initio Monte Carlo simulation using multicanonical algorithm temperature dependence of the average structure of water dimer, Mol. Phys. 1999, 96, 349-358... 

Woo, H. J. Dinner, A. R. Roux, B., Grand canonical Monte Carlo simulations of water in protein environments, J. Chem. Phys. 2004,121, 6392-6400. 

G. C. Lie and E. Clementi, Study of the structure of molecular complexes XII Structure of liquid water obtained by Monte Carlo simulation with the Hartree-Fock potential corrected by inclusion of dispersion forces, J. Chem. Phys. 62 2195 (1975). 

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