Inherent structures computer simulation

MD simulations of model membrane systems have provided a unique view of lipid interactions at a molecular level of resolution [21], Due to the inherent fluidity and heterogeneity in lipid membranes, computer simulation is an attractive tool. MD simulations allow us to obtain structural, dynamic, and energetic information about model lipid membranes. Comparing calculated structural properties from our simulations to experimental values, such as areas and volumes per lipid, and electron density profiles, allows validation of our models. With molecular resolution, we are able to probe lipid-lipid interactions at a level difficult to achieve experimentally. 

Realistic three-dimensional computer models for water were proposed already more than 30 years ago (16). However, even relatively simple effective water model potentials based on point charges and Leimard-Jones interactions are still very expensive computationally. Significant progress with respect to the models ability to describe water s thermodynamic, structural, and dynamic features accurately has been achieved recently (101-103). However, early studies have shown that water models essentially capture the effects of hydrophobic hydration and interaction on a near quantitative level (81, 82, 104). Recent simulations suggest that the exact size of the solvation entropy of hydrophobic particles is related to the ability of the water models to account for water s thermodynamic anomalous behavior (105-108). Because the hydrophobic interaction is inherently a multibody interaction (105), it has been suggested to compute pair- and higher-order contributions from realistic computer simulations. However, currently it is inconclusive whether three-body effects are cooperative or anticooperative (109). 

Computer simulations for several models (Weber and Stillinger, 1985 Ohmine, 1995) have determined that the elementary transitions between neighboring basins entail shifts of only small local groups of particles. To be precise, the difference between the inherent structures of the two basins involved in a large V-particle system is concentrated on a neighboring set of (9(1) particles the remainder particles experience at most a minor elastic response to the localized repacking (Lacks, 1998). In view of the fact that the number of such localized repacking possibilities is proportional to system size, the number of transition states (saddle points) in the boundary of any basin will be O(V), i.e., an extensive property. So too, then, will be the net kinetic exit rate from any basin at positive temperature. 

Periodic boundary conditions are not always used in computer simulations. Some systems, such as liquid droplets or van der Waals clusters, inherently contain a boundary. Periodic botmdary conditions may also cause difficulties when simulating inhomogeneous systems or systems that are not at equilibrium. In other cases the use of periodic boundary conditions would require a prohibitive number of atoms to be included in the simulation. This particularly arises in the study of the structural and conformational behaviour of macromolecules such as proteins and protein-ligand complexes. The first simulations of such s) tems ignored all solvent molecules due to the limited computational resources then available. This corresponds to the unrealistic situation of simulating an isolated protein in vacuo and then comparing the results with experimental data obtained in solution. Vacuum calculations can lead to significant problems. A vacuum boundary tends to minimise the surface area and so may distort the shape of the system if it is non-spherical. Small molecules may adopt more compact conformations when simulated in vacuo due to favourable intramolecular electrostatic and van der Waals interactions, which would be dampened in the presence of a solvent. 

Similar stndies have been made on ions in liquid ammonia (at 240K). The mean residence times of ammonia molecules in the second solvation shells of the ions stndied are longer than for water molecules 12.7ps compared to 2.6ps for Ag [116], 28.5 ps compared with 6.5ps for Co [117], but shorter in the case of Cu 3.2ps [118] compared with 7.7ps for water [91]. Molecular dynamics computer simulations of solutions of ions in liquid ammonia [119] yielded the self-diffusion coefficients of ammonia molecules, D/10 m s , in the solvation shells of 6.1 and of R 7.4, shorter than the value for ammonia molecules in the bulk liquid, 11.5 1.5. These studies thus indicate that K and R are structure breakers and Ag" and Co are structure makers regarding the inherent structure of liquid anunonia. 

The variety of examples presented here can be seen as good evidence that simulations have become a valuable, partly indispensi-able tool for the study of chemicals in solution. The inclusion of ab initio QM procedures for the calculation of forces in every step of the simulation ensures the necessary accuracy of the simulation results to predict both structural and dynamical data, thus also providing a correct picture of the molecular and supermolecular species formed simultaneously in solution. The recently developed QMCF MD methodology has overcome several of the previous problems of MD simulations, mostly not only because of the possibility to renounce any kind of empirical or fitted solute-solvent potentials, but also because of an improved embedding scheme and the use of actual atom populations for the calculation of Coulombic forces. Besides its universality of application to various chemical compounds it also offers a straightforward way of further improvement and method-inherent quality control by the employment of correlated ab initio methods, although at a price which is not yet affordable with present computational facilities, but should become feasible within a few years. 

As discussed in Chapter 3, with LES, the smallest scale to be resolved is chosen to lie in the inertial sub-range of the energy spectrum, which means the so-called sub-grid scale (SGS) wave numbers are not resolved. As LES can capture transient large-scale flow structures, it has the potential to accurately predict time-dependent macromixing phenomena in the reactors. However, unlike DNS, a SGS model representing interaction of turbulence and chemical reactions will be required in order to predict the effect of operating parameters on say product yields in chemical reactor simulations. These SGS models attempt to represent an inherent loss of SGS information, such as the rate of molecular diffusion, in an LES framework. Use of such SGS models makes the LES approach much less computationally intensive than the DNS approach. DNS... 

Physical properly estimation methods may be classified into six general areas (1) theory and empirical extension of theory, (2) corresponding states, (3) group contributions, (4) computational chemistry, (5) empirical and quantitative structure property relations (QSPR) correlations, and (6) molecular simulation. A quick overview of each class is given below to provide context for the methods and to define the general assumptions, accuracies, and limitations inherent in each. 

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