Minimum image method

The Spherical Cutoff and Minimum Image Methods. Two commonly used and easily implemented approximations are the so-called spherical cutoff (SC) and minimum image (MI) methods. Both involve a simple... 

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. 

The commonly employed methods are known in the literature as periodic boundary condition (PBC) and minimum imaging. " Essentially, the way to remove surfaces is to allow the atoms near opposite surfaces to interact as if they were near neighbors, that is, to create a flat torus in d + 1 dimensions, where d is the dimension of a space. A pictorial representation of minimum imaging can be found in Figure 12. In this section, we discuss the application of these boundary conditions for a simulation cell of arbitrary shape. 

A slightly more sophisticated method is the so-called minimum-image (MI) convention, in which all interactions between the central particle and its nearest image of all other particles are included. This is a significant improvement over a SC, since the central particle and its interacting particles constitute an electroneutral entity. The MI convention has frequently been appUed to simulate simple electrolytes and, to some extent, weakly asymmetric electrolytes. However, it suffers from the same principal deficiencies as a SC, and the MI convention becomes insufficient for higWy asymmetric electrolytes. 

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