Point defects in CaF2 and CeO2 investigated by the periodic electrostatic embedded cluster method

Abstract

A periodic electrostatic embedding scheme is presented that uses the periodic fast multipole method. The convergence of properties with increasing cluster size is examined for cluster models of calcium fluoride. Properties investigated are the electron density, the density of states, the electronic excitation of color centers, and energies of defect formation. The embedded cluster method is applied to CeO(2) and oxygen vacancies in bulk CeO(2) as well as on its (111) surface. Employing the PBE0 functional, vacancy formation energies of 3.0 and 3.3 eV have been obtained for the bulk and the (111) surface, respectively. Formation of subsurface defects requires 3.33 eV (singlet open shell). The localization of the electrons left behind on defect formation in Ce 4f states is discussed. Occupied Ce 4f states are well localized on nearest Ce atoms for surface and subsurface vacancies. Localization apart from the vacancy was obtained for bulk. The total CPU time spent on the embedding part did not exceed 30 s on a single CPU even if 8000 basis functions of the cluster are involved.

Adsorption, Activation, and Dissociation of Oxygen on Doped Oxides

“…[25] We used Ca 34 O 34 cluster models, surrounded by a shell of full-ion effective core potentials on Ca 2+ positions and embedded into a periodic array of point charges. [26] Communications Oxygen Activation Y. Cui …”

Should environmental effects be included when performing QTAIM calculations on actinide systems? A comparison of QTAIM metrics for Cs2UO2Cl4, U(Se2PPh2)4 and Np(Se2PPh2)4 in gas phase, COSMO and PEECM

“…In order to incorporate long range crystal field effects, calculations were performed using the PEECM [27] as implemented in TURBOMOLE 6.5. The PEECM splits the system into two regions; an inner explicit cluster region treated quantum mechanically as described above and an infinite outer embedding region consisting of point charges, which recreates the Madelung potential of the bulk system.…”

“…This study analysed calculations performed in the gas phase, with a polarizable continuum solvent model, with the Periodic Electrostatic Embedded Cluster Method (PEECM) [27] and with periodic boundary conditions; ρ and ∇ 2 ρ did not vary significantly between the methods, though no comparison was made with experiment. Other studies on organic molecules also found only small differences between molecular and periodic boundary condition DFT calculations.…”

Modeling the noble metal/TiO2 (110) interface with hybrid DFT functionals: A periodic electrostatic embedded cluster model study

“…This PEECM approach with hybrid DFT functional has recently been employed to study point defects in CaF 2 and CeO 2 , and with a careful selection of the quantum cluster model, an accurate description of the atomic and electronic structures could be obtained for both the defect-free and defective surfaces. 25 One of the most common point defects observed on the rutile TiO 2 ͑110͒ surface is a bridging oxygen vacancy, which significantly affects the surface chemistry and electronic properties of this material. Experimental observations indicate that removing bridging oxygen atoms from the TiO 2 surface produces a localized state approximately 0.8 eV below the conduction band.…”

“…However, because of the periodicity of adsorbents and defects, often very large unit cells are necessary to minimize the effect of the interaction between adsorbents and defects, which significantly increases the computational resource needs for these studies. Furthermore, various studies [23][24][25] have recently shown that hybrid DFT functionals that contain a certain percentage of Hartree-Fock exchange are essential for the accurate description of the electronic structure of nonmetallic solid materials in general and of oxygen defects in metal oxides in particular. However, periodic DFT calculations with hybrid DFT functionals are still hardly affordable except for very small unit cells.…”