Molecular dynamics simulation theory

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

For any even vaguely realistic atomically constituted membrane it is unlikely that any theory will become available in the near future which will properly or reasonably describe the dynamic properties of the membrane, the fluids near it, and their passage, or selective passage, through it. Nevertheless, one should continue trying with simple models and simple theories [39-43], which show the way forward and can, as usual, be tested by the virtually exact results of molecular dynamics simulation. 

This section provides an alternative measurement for a material parameter the one in the ensemble averaged sense to pave the way for usage of continuum theory from a hope that useful engineering predictions can be made. More details can be found in Ref. [15]. In fact, macroscopic flow equations developed from molecular dynamics simulations agree well with the continuum mechanics prediction (for instance. Ref. [16]). 

The theory was very similar to that described earlier, but was simplified in view of the complexity of the problem. A number of reaction intermediates were considered explicitly, and the corresponding signals were calculated by molecular dynamics simulation. Kinetic equations governing the reaction sequence were established and were solved numerically. The main simplification of the theory is that, when calculating A5[r, r], the lower limit of the Fourier integral was shifted from 0 to a small value q. The authors wrote [59]... 

Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. 

Termath, V., Sauer, J., 1997, Ab Initio Molecular Dynamics Simulation of H502+ and H703+ Gas Phase Clusters Based on Density Functional Theory , Mol. Phys., 91, 963. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

Lamoureux G, Roux B (2003) Modeling induced polarization with classical Drude oscillators theory and molecular dynamics simulation algorithm. J Chem Phys 119(6) 3025-3039... 

Lu ZY, Zhang YK (2008) Interfacing ab initio quantum mechanical method with classical Drude os-illator polarizable model for molecular dynamics simulation of chemical reactions. J Chem Theory Comput 4(8) 1237-1248... 

David B. Graves and Cameron F. Abrams, Molecular Dynamics Simulations if Ion-Surface Interactions with Applications to Plasma Processing Christian M. Lastoskie and Keith E. Gubbins, Characterization of Porous Materials Using Molecular Theory and Simulation... 

Parchment et al. [271] have provided more recent calculations on the 3-hydroxypyrazole equilibrium at the ab initio level. They noted that tautomer 9, which was not considered by Karelson et al. [268], is the lowest-energy tautomer in the gas phase at levels of theory (including AMI) up to MP4/6-31G //HF/3-21G [271], Although 8 is the dominant tautomer observed experimentally in aqueous solution, in the gas phase 8 is predicted to be nearly 9 kcal/mol less stable than 9 at the MP4 level [271], Using a DO model with an unphysically small cavity radius of 2.5 A, Parchment et al. [271] were able to reproduce at the ab initio level the AMI-DO prediction of Karelson et al. [268], namely that 8 is the most stable tautomer in aqueous solution. With this cavity, though, 8 is predicted to be better solvated than 9 by -22.2 kcal/mol [271], This result is inconsistent with molecular dynamics simulations with explicit aqueous solvation [271], and with PCM and SCME calculations with more reasonable cavities [271] these predict that 8 is only about 3 kcal/mol better solvated than 9. In summary, the most complete models used by Parchment et al. do not lead to agreement with experiment... 

To circumvent this problem avoiding such inefficient exploration of the configurational space, several methods have emerged. Two particularly useful approaches are the Umbrella Sampling and the Statistical Perturbation Theory. Both methods can be used either with Monte Carlo or with Molecular Dynamics simulations. 

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