Distributed computing, quantum dynamics

MacKerell AD, Jr, M Feig, CL Brooks III (2004a) Extending the treatment of backbone energetics in protein force fields Limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J. Comput. Chem. 25 (11) 1400-1415... 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

The classical description is quite different from the quantum. In classical dynamics we describe the coordinates and momenta simultaneously as a function of time and can follow the path of the system as it goes from reactants to products during the collision. These paths, called trajectories, provide a fnotion picture of collision process. The results of any real collision can be represented by computing a large number of trajectories to obtain distribution of post-collisions properties of interest (e.g. energy or angular distribution). In fact, the trajectory calculation means the transformation of one distribution function (reagent distribution, pre-collision) into another (product distribution, post-collision), which is determined by PE function. 

Classical and semiclassical moment expressions. The expressions for the spectral moments can be made classical by substituting the classical distribution function, g(R) = exp (— V(R)/kT), for the quantum expressions. Wigner-Kirkwood corrections are known which account to lowest order for the static quantum corrections, Eq. 5.44 [177, 292]. For the second and higher moments, dynamic quantum corrections must also be made [177]. As was mentioned in the previous Chapter, such semiclassical corrections are useful in supplementing quantum computations of the spectral moments at large separations where the quantum effects are small the computational effort of quantum calculations, which is substantial at large separations, may thus be avoided. 

Here, the integration over X was performed in Eq. (63) to define W%a (X, ) which is the integrated value of the combination of the spectral density function with the time independent operator. This spectral density function contains the quantum equilibrium structure of the system. (X, t) is the time evolved matrix element of the number operator for the product state B. Thus, to calculate the rate, one samples initial configurations from the quantum equilibrium distribution, and then computes the evolution of the number operator for product state B. The QCL evolution of the species operator is accomplished using one of the algorithms discussed in Sec. 3.2. Alternative approaches to the dynamics may also be used such as the further approximations to the QCLE discussed in Sec. 4. 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

Our ability to understand the structure and properties of water in all its forms has been dramatically enhanced by the use of computer simulation. Early studies of the liquid used simple representations of the potential surface. These were often three or four point-charge distributions, adjusted to fit dipole and quadrupole moments, embedded in a simple spherical nonelectrostatic interaction. The simulations used classical Monte Carlo (MC) or molecular dynamic (MD) calculations, and the water molecules were assumed to be rigid. Recently, more advanced calculations have been based on quantum simulations, the introduction of intramolecular degrees of freedom, and accurate potential surfaces. As one side benefit... 

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