Symmetry Of Atomic Orbitals Research Articles

First-principles definition of ionicity and covalency in molecules and solids.

The notions of ionicity and covalency of chemical bonds, effective atomic charges, and decomposition of the cohesive energy into ionic and covalent terms are fundamental yet elusive. For example, different approaches give different values of atomic charges. Pursuing the goal of formulating a universal approach based on firm physical grounds (first-principles or non-empirical), we develop a formalism based on Wannier functions with atomic orbital symmetry and capable of defining these notions and giving numerically robust results that are in excellent agreement with traditional chemical thinking. Unexpectedly, in diamond-like boron phosphide (BP), we find charges of +0.68 on phosphorus and -0.68 on boron atoms, and this anomaly is explained by the Zintl-Klemm nature of this compound. We present a simple model that includes energies of the highest occupied cationic and lowest unoccupied anionic atomic orbitals, coordination numbers, and strength of interatomic orbital overlap. This model captures the essential physics of bonding and accurately reproduces all our results, including anomalous BP.

Orbital-enhanced warping effect in px,py-derived Rashba spin splitting of monatomic bismuth surface alloy

Spin-split Rashba bands have been exploited to efficiently control the spin degree of freedom of moving electrons, which possesses a great potential in frontier applications of designing spintronic devices and processing spin-based information. Given an intrinsic breaking of inversion symmetry and sizeable spin–orbit interaction, two-dimensional (2D) surface alloys formed by heavy metal elements exhibit a pronounced Rashba-type spin splitting of the surface states. Here, we have revealed the essential role of atomic orbital symmetry in the hexagonally warped Rashba spin-split surface state of the sqrt 3 times sqrt 3 R30^0 BiCu2 monatomic alloy by scanning tunneling spectroscopy (STS) and density functional theory (DFT). From dI/dU spectra and calculated band structures, three hole-like Rashba-split bands hybridized from distinct orbital symmetries have been identified in the unoccupied energy region. Because of the hexagonally deformed Fermi surface, quasi-particle interference (QPI) mappings have resolved scattering channels opened from interband transitions of px,py (mj = 1/2) band. In contrast to the s,pz-derived band, the hexagonal warping is predominately accompanied by substantial out-of-plane spin polarization Sz up to 24% in the dispersion of px,py (mj = 1/2) band with an in-plane orbital symmetry.

Ferromagnetism and temperature-dependent electronic structure of hcp gadolinium

We use a combination of a many-body model analysis with an ``ab initio'' band-structure calculation to derive the temperature-dependent electronic quasiparticle structure of the rare-earth metal gadolinium. As a local-moment system Gd is properly represented by the ferromagnetic (multiband) Kondo-lattice model [$s\text{\ensuremath{-}}f(d\text{\ensuremath{-}}f)$ model]. The single-particle part of the model Hamiltonian is taken from an augmented spherical wave band calculation. The proposed method avoids the double counting of relevant interactions by exploiting an exact limiting case of the model and takes into account the correct symmetry of atomic orbitals. The weakly correlated $5d$ conduction bands become polarized via interband exchange coupling to the localized $4f$ levels with a distinct temperature dependence. This results in a Rudermann-Kittel-Kasuya-Yosida-type mechanism of coupling leading to the ferromagnetism of Gd. We get a self-consistently derived Curie temperature of $294.1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a $T=0$ moment of $7.71{\ensuremath{\mu}}_{\mathrm{B}}$, surprisingly close to the experimental values. The striking temperature dependence of the $5d$ conduction bands provides insight into the origin of the temperature dependence of the photoemission data. The only parameter of the theory (interband exchange coupling $J$) is uniquely fixed by the band calculation.

Real Space Approach to the Electronic Structure of Transition Metals

The role of d symmetry of atomic orbitals in determining the electronic structure of transition metals is discussed by use of a real space expansion of the Green function. Terms which are sensitive to the crystal structures are separated from those corresponding to the path integrals on a Bethe type lattice. On the basis of this discussion a simple method is developed for calculating the electronic structure of transition metals. By use of the method the correspondence between the band theory and atomic interaction models can be established. It is found that the density of states for bcc and fcc are satisfactorily reproduced with the information from the interactions among near neighboring atoms, and that the difference between bcc and fcc arises mostly from three or four atoms interactions, while distant neighbors contribute mostly to the structure insensitive self-energy.