Computer simulation image convention

Fig. 2. (a) Periodic images surrounding the simulation box. Interactions are computed with respect to the nearest image which is indicated by the circle, (b) Violation of the minimum image convention resulting from the interaction of QM particle with point charge 1. 

Fock molecular orbital (HF-MO), Generalized Valence Bond (GVB) [49,50] and the Complete Active Space Self-consistent Filed (CASSCF) [50,51], and full Cl methods. [51] Density Functional Theory (DFT) calculations [52-54] are also incorporated into AIMD. One way to perform liquid-state AIMD simulations, is presented in the paper by Hedman and Laaksonen, [55], who simulated liquid water using a parallel computer. Each molecule and its neighbors, kept in the Verlet neighborlists, were treated as clusters and calculated simultaneously on different processors by invoking the standard periodic boundary conditions and minimum image convention. 

Smith, W., The minimum image convention in non-cubic MD cell, CCP5 Infotmation Quarterly for Computer Simulation of Condensed Phases, 30 35, Infomial Newsletter, Daresbury Laboratory, England, 1989. 

Periodic boundary conditions refer to the simulation of structures consisting of a periodic lattice of identical subunits. Periodic boundaries help simulate bulk-material, solvent, and crystalline systems. Ideally, a periodic system infinitely replicates in all dimensions to form a periodic lattice. However, in practice, all periodic boundary algorithms imply a cutoff criterion for computational efficiency (Figure 1.1). In these cutoff schemes, each atom interacts with the nearest images of other N - I atoms (minimum-image convention) or only with the explicit images contained in a sphere... 

For the computation of the free energy Ap in Eq. (6.29) with the theory of energy representation, 200-ps QM/MM simulation was carried out to constract the energy distribution functions p(e) in the solution system, while 400-ps simulation was devoted for the distributions po(e) and Xoi O in the pure solvent system. In the constmction of these distribution functions the solvent molecules of which mass centers were within a sphere Q. of radius 11 A were considered, where the center of the sphere was placed at the mass center of the solute. In the computation of S/j. in Eq. (6.29), our simulations were conducted over 300 ps to yield the energy distribution functions defined in Eqs. (6.31) and (6.32), where all the solvent molecules are involved with the minimum image convention. 

With respect to single layer systems (conventional, ImRe, Promote and dry developable resists), we expect that computer programs that can simulate latent image formation and development processes will become of great importance in the near future. A better understanding of the mechanism which underlies the dissolution or etching of resist layers in a developer or plasma respectively is also crucial in order to achieve the ultimate resolution of single layer photoresists. In this respect, well chosen and perfectly defined polymers are required. 

The advantages of the approach include very fast computation, avoid the difficulty of taking into account the effects of accessories, seams and styles on drape in conventional drape simulation and, if sufficient drape images are stored in the database, the predicted image can be very close to the actual once. A disadvantage is that only limited styles and changeable features dimensions can be allowed in the approach. 

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