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

The MP2-F12 method in the Turbomole program package

A detailed description of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method, as implemented in the TURBOMOLE program package, is presented. The TURBOMOLE implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open- and closed-shell species, using unrestricted as well as restricted (open-shell) Hartree-Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the TURBOMOLE implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H-ZSM-5. Various basis sets are used, including the correlation-consistent basis sets specially optimized for explicitly correlated calculations (cc-pVXZ-F12).

Modeling environmental effects on charge density distributions in polar organometallics: validation of embedded cluster models for the methyl lithium crystal

The charge density and its Laplacian at the Li-C and C-H bond critical points and other features of the electron density distribution of the methyl lithium crystal have been compared by density functional methods for (i) the isolated (LiCH(3))(4) tetramer or larger clusters, (ii) for quantum mechanically treated clusters in polarizable continuum model (PCM) surroundings, (iii) for clusters augmented by the periodic electrostatic embedded cluster model (PEECM), and for (iv) the periodic crystal. Comparisons with identical functional and basis sets indicate that both PCM and PEECM embedding of only a tetramer did not fully account for the environmental effect. In contrast, embedding of a full unit cell gave results that were essentially converged to the periodic crystal data. Effects of basis set and exchange correlation functional on the QTAIM bond descriptors are of a comparable order of magnitude as the crystal environmental effects. In this context, embedded cluster computations provide distinct advantages over explicit solid-state calculations with respect to their freedom of the choice of computational and theoretical level. This is demonstrated by embedded MP2 calculations.

Charge distribution near bulk oxygen vacancies in cerium oxides

Understanding the electronic charge distribution around oxygen vacancies in transition metal and rare earth oxides is a scientific challenge of considerable technological importance. We show how significant information about the charge distribution around vacancies in cerium oxide can be gained from a study of high resolution crystal structures of higher order oxides which exhibit ordering of oxygen vacancies. Specifically, we consider the implications of a bond valence sum analysis of Ce₇O₁₂ and Ce₁₁O₂₀. To illuminate our analysis we show alternative representations of the crystal structures in terms of orderly arrays of coordination defects and in terms of fluorite-type modules. We found that in Ce₇O₁₂, the excess charge resulting from removal of an oxygen atom delocalizes among all three triclinic Ce sites closest to the O vacancy. In Ce₁₁O₂₀, the charge localizes on the next nearest neighbour Ce atoms. Our main result is that the charge prefers to distribute itself so that it is farthest away from the O vacancies. This contradicts the standard picture of charge localization which assumes that each of the two excess electrons localizes on one of the cerium ions nearest to the vacancy. This standard picture is assumed in most calculations based on density functional theory (DFT). Based on the known crystal structure of Pr₆O₁₁, we also predict that the charge in Ce₆O₁₁ will be found in the second coordination shell of the O vacancy. We also extend the analysis to the Magnéli phases of titanium and vanadium oxides (M(n)O(₂n₋₁), where M = Ti, V) and consider the problem of metal-insulator transitions (MIT) in these oxides. We found that the bond valence analysis may provide a useful predictive tool in structures where the MIT is accompanied by significant changes in the metal-oxygen bond lengths. Although this review focuses mainly on bulk cerium oxides with some extension to the Magnéli phases of titanium and vanadium, our approach to characterizing electronic properties of oxygen vacancies and the physical insights gained should also be relevant to surface defects and to other rare earth and transition metal oxides.

The direct approach to gravitation and electrostatics method for periodic systems

The direct approach to gravitation and electrostatics (DAGE) algorithm is an accurate, efficient, and flexible method for calculating electrostatic potentials. In this paper, we show that the algorithm can be easily extended to consider systems with many different kinds of periodicities, such as crystal lattices, surfaces, or wires. The accuracy and performance are nearly the same for periodic and aperiodic systems. The electrostatic potential for semiperiodic systems, namely defects in crystal lattices, can be obtained by combining periodic and aperiodic calculations. The method has been applied to an ionic model system mimicking NaCl, and to a corresponding covalent model system.