The geometric simulation approach operates at an entirely different level of theory from ab initio electronic structure and all-atom empirical-potential methods it does not generate a detailed energy landscape, but rather explores framework geometries that satisfy local steric and bonding geometric requirements. The process of fitting cluster geometries to groups of atoms can also be used as an analysis tool to investigate structural models produced by other methods, particularly reverse Monte Carlo (RMC) modelling based on total scattering data. This makes the method particularly suitable for the investigation of large system sizes and for the rapid exploration of hypothetical conditions of strain and/or extra framework contents in porous frameworks, on its own or as an adjunct to simulations with conventional methods. The method is computationally robust and inexpensive, with results typically being generated in seconds or minutes on a single processor, e.g. Thus the method implements a simple physical model which includes the strongest, most local forces in the system – covalent bonding and steric exclusion – while neglecting all longer ranged interactions. In the course of a ‘geometric relaxation’, the positions of atoms and templates are mutually updated to minimise both deviations from cluster geometry and steric overlap of atomic spheres. Harmonic constraints linking each atom to the corresponding vertex of a template then penalise any deviation from the ideal cluster geometry. The central concept of geometric simulation is to represent the bonding within rigid units, not by a collection of two-, three- and four-body empirical potentials, but by a template or ‘ghost’ representing the ideal bonding geometry of the cluster, either polyhedral or molecular. In a metal–organic framework (MOF), both the organic linker molecules and the coordination polyhedra around metal centres may be treated as rigid clusters, with the potential for flexibility at the interface between them.
In the case of a 3D framework silicate, such as quartz or a siliceous zeolite, the SiO tetrahedra are the relatively rigid clusters, while the Si–O–Si bridge is a more flexible linkage, as indicated by the wide range of Si–O–Si angles observed in different framework silicate structures. Such frameworks are composed of relatively rigid subunits (clusters) connected by relatively flexible linkages that is, the energetic penalty for distortions of the clusters is an order of magnitude greater than the energetic penalty for flexion in the linkage. Template-based geometric simulation is a specialised method for the study of flexible frameworks.
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