Systematic Study of Ti-Distribution in Titanosilicate *BEA Zeolites via Symmetry-Adapted Enumeration

The high performance of titanosilicate zeolites in various industrial oxidation reactions is highly affected by the distribution of Ti atoms in their frameworks. Because of their structural complexity, previous theoretical studies mainly focus on the preferential location of single Ti atoms within the unit cells of titanosilicate zeolites. When multiple Ti atoms are required, conventional approaches consider only symmetrically related T sites to reduce the computation complexity. Such symmetry-constrained approaches obviously overlooked many possible configurations. Herein, we conduct a systematic study on the distribution of two Ti atoms in the unit cell of titanosilicate zeolite *BEA. Different from conventional symmetry-constrained approaches, we introduce two Ti atoms simultaneously without any constraint and adopt a symmetry-adapted algorithm to enumerate all possible configurations for double-Ti introduction. We generate a total of 273 distinct configurations and analyze the Ti-distribution via Boltzmann statistics. We find that many of the configurations overlooked by conventional symmetry-constrained approaches indeed exhibit more feasible energies, which may lead to different Ti-distributions. Our study indicates the necessity of unconstrained introduction of Ti atoms when multiple-Ti atoms are considered for calculations.