Systematic enumeration of two-dimensional layered aluminophosphates with [Al₃P₄O₁₆]^3- stoichiometry

In this paper, we provide a systematic method to generate the sheets of two-dimensional layered aluminophosphates with Al₃P₄O^3-₁₆ stoichiometry. Our approach adopts the divide-and-conquer algorithm to reduce the degree of combination explosion caused by simple enumeration. We use Coordination Sequences to identify the same topological meshes in order to get the distinct sheets. We relax the generated sheets using Genetic Algorithm, then minimize the energies of the sheets to choose the lower energy sheets which may be synthesized. This approach can generate systemically more than 4,000 distinct sheets by the computer. Some sheets have been synthesized, while some new hypothetical sheets resemble lower energy as the known 2D Al₃P₄O^3-₁₆ compounds. We further discuss the structural features of 2D Al₃P₄O^3-₁₆ nets.