Topological Analysis with Bond-Valence Maps

Topological Analysis with Bond-Valence Maps 

As with VT, identifying conduction pathways with bond valence maps provides accurate predictions for ionic conductors (both crystalline and amorphous) with a percolation mechanism of conductivity, but is less successful when modeling proton conductors. 

Static First-Principles Calculations and Molecular Dynamics Modeling 

The behavior of atoms in condensed matter is ultimately defined by the cooperative interaction of nuclei and electrons. If it was possible to accurately describe this interaction for a material on length and time scales that are studied experimentally in a laboratory or are used in practice, any physical property could be predicted ab initio given just its chemical composition (see also Chapter 5). Unfortunately, a many-body Schrodinger equation is not analytically solvable for any system of acceptable size. The most successful approach to treating many-body problems is the density functional theory (DFT) developed by Kohn et al. [103, 104]. The DFT reduces many-particic electron-electron interactions to a single electron potential expressed 

Despite the rapid development of both computing hardware and numerical 

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Topological Analysis with Bond-Valence Maps... 

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