Derivation of the spin Hamiltonians for Fe in MgO

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non-magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In the first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effects of spin–orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both the undistorted and Jahn–Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed.

Platinum–tin/carbon catalysts for ethanol oxidation: Influence of Sn content on the electroactivity and structural characteristics

Carbon-supported Pt–Sn catalysts commonly contain Pt–Sn alloy and/or Pt–Sn bimetallic systems (Sn oxides). Nevertheless, the origin of the promotion effect due to the presence of Sn in the Pt–Sn/C catalyst towards ethanol oxidation in acid media is still under debate and some contradictions. Herein, a series of Ptx–Sny/C catalysts with different atomic ratios are synthesized by a deposition process using formic acid as the reducing agent. Catalysts structure and chemical compositions are investigated by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) and their relationship with catalytic behavior towards ethanol electro-oxidation was established. Geometric structural changes are producing by highest Sn content (Pt1–Sn1/C) promoted the interaction of Pt and Sn forming a solid solution of Pt–Sn alloy phase, whereas, the intermediate and lowest Sn content (Pt2–Sn1/C and Pt3–Sn1/C, respectively) promoted the electronic structure modifications of Pt by Sn addition without the formation of a solid solution. The amount of Sn added affects the physical and chemical characteristics of the bimetallic catalysts as well as reducing the amount of Pt in the catalyst composition and maintaining the electrocatalytic activities at the anode. However, the influence of the Sn oxidation state in Pt–Sn/C catalysts surfaces and the alloy formation between Pt and Sn as well as with the atomic ratio on their catalytic activity towards ethanol oxidation appears minimal. Similar methodologies applied for synthesis of Ptx–Sny/C catalysts with a small change show differences with the results obtained, thus highlighting the importance of the conditions of the preparation method.

Double Hybrid Functionals and the Π-System Bond Length Alternation Challenge: Rivaling Accuracy of Post-HF Methods

Predicting accurate bond length alternations (BLAs) in long conjugated oligomers has been a significant challenge for electronic-structure methods for many decades, made particularly important by the close relationships between BLA and the rich optoelectronic properties of π-delocalized systems. Here, we test the accuracy of recently developed, and increasingly popular, double hybrid (DH) functionals, positioned at the top of Jacobs Ladder of DFT methods of increasing sophistication, computational cost, and accuracy, due to incorporation of MP2 correlation energy. Our test systems comprise oligomeric series of polyacetylene, polymethineimine, and polysilaacetylene up to six units long. MP2 calculations reveal a pronounced shift in BLAs between the 6-31G(d) basis set used in many studies of BLA to date and the larger cc-pVTZ basis set, but only modest shifts between cc-pVTZ and aug-cc-pVQZ results. We hence perform new reference CCSD(T)/cc-pVTZ calculations for all three series of oligomers against which we assess the performance of several families of DH functionals based on BLYP, PBE, and TPSS, along with lower-rung relatives including global- and range-separated hybrids. Our results show that DH functionals systematically improve the accuracy of BLAs relative to single hybrid functionals. xDH-PBE0 (N4 scaling using SOS-MP2) emerges as a DH functional rivaling the BLA accuracy of SCS-MP2 (N5 scaling), which was found to offer the best compromise between computational cost and accuracy the last time the BLA accuracy of DFT- and wave function-based methods was systematically investigated. Interestingly, xDH-PBE0 (XYG3), which differs to other DHs in that its MP2 term uses PBE0 (B3LYP) orbitals that are not self-consistent with the DH functional, is an outlier of trends of decreasing average BLA errors with increasing fractions of MP2 correlation and HF exchange.