Search for Stable Structures of Adsorbed Molecules on Material Surfaces by Bayesian Optimization

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Titanium dioxide (TiO2) is one of the most technologically promising oxides with a broad range of catalytic and photocatalytic activities, and first-principles simulations of molecular adsorption onto TiO2 surface have been extensively performed. Our group experimentally reported that the formation of an amorphous structure on the TiO2 surface enhances its catalytic activity, and is investigating the origin of high activity for amorphous surface. From the theoretical point of view, searching for stable adsorption sites on an amorphous surface model based on first-principles calculations need much high computational cost due to many adsorption sites in a large supercell. In this study, to efficiently explore stable adsorption sites on an amorphous surface, we applied Bayesian optimization, a global search method for black-box optimization, and found the most stable adsorption site of a water molecule.First-principles calculations are performed with SIESTA code [1] with localized basis, using the generalized gradient approximation (GGA) for the exchange-correlation energy functional. The amorphous surface models of TiO2 are generated by quenching a (101) surface model of anatase-type TiO2 crystal containing 162 atoms with first-principles molecular dynamics simulation. Fig. 1 shows one of TiO2 surface models.The adsorption energy of a molecule adsorbate is defined asEads=Etot (surf+mol)-(Etot surf+Etot mol )Etot (surf+mol) is the total energy of the surface with a molecule adsorbate, Etot surf is the total energy of the clean surface, and Etot mol is the energy of a molecular in a vacuum.Bayesian optimization is adopted for searching the lowest energy site with fixing TiO2 surface configurations. A Gaussian kernel and an Expected Improvement (EI) for the acquisition function are used.Absorption energies were calculated on mesh points in the six-dimension space of the atomic positions of the oxygen (x, y, z) and rotational angles. First, we performed Bayesian optimization in the six-dimension space of the position and the angle, but this did not work well due to the discontinuity of the potential surface. Thus, we performed Bayesian optimization in the structural-descriptor space. We adopted the smooth overlap of atomic positions (SOAP) and the radial distribution function (RDF) as structural descriptors. The lowest energy sites were much efficiently found in the descriptor space, and we achieved high search efficiency. Figure 1