C. L. Tian

The spin and orbital moment of Fen (n = 2–20) clusters

Complementary to the recent experimental finding that the orbital magnetic moment is strongly quenched in small Fe clusters [M. Niemeyer, K. Hirsch, V. Zamudio-Bayer, A. Langenberg, M. Vogel, M. Kossick, C. Ebrecht, K. Egashira, A. Terasaki, T. Möller, B. v. Issendorff, and J. T. Lau, Phys. Rev. Lett. 108, 057201 (2012)], we provide the theoretical understanding of the spin and orbital moments as well as the electronic properties of neutral and cation Fen clusters (n = 2-20) by taking into account the effects of strong electronic correlation, spin-orbit coupling, and noncollinearity of inter-atomic magnetization. The generalized gradient approximation (GGA)+U method is used and its effluence on the magnetic moment is emphasized. We find that without inclusion of the Coulomb interaction U, the spin (orbital) moments have an average value between 2.69 and 3.50 μB/atom (0.04 and 0.08 μB/atom). With inclusion of U, the magnetic value is between 2.75 and 3.80 μB/atom (0.10 and 0.30 μB/atom), which provide an excellent agreement with the experimental measurements. Our results confirm that the spin moments are less quenched, while the orbital moments are strongly quenched in small Fe clusters. Both GGA and GGA+U functionals always yield collinear magnetic ground-state solutions for the fully relaxed Fe structures. Geometrical evolution, as a function of cluster size, illustrates that the icosahedral morphology competes with the hexagonal-antiprism morphology for large Fe clusters. In addition, the calculated trends of ionization potentials, electron affinities, fragment energies, and polarizabilities generally agree with respective experimental observations.

Density functional calculations for structural, electronic, and magnetic properties of gadolinium-oxide clusters

Gadolinium-oxide clusters in various sizes and stoichiometries have been systematically studied by employing the density functional theory with the generalized gradient approximation. The clusters in bulk stoichiometry are relatively more stable and their binding energies increase with the increasing size. Stoichiometric (Gd2O3)n clusters of n = 1–3 prefer cage-like structures, whereas the clusters of n = 4–30 prefer compact structures layered by wedge-like units and exhibit a rough feature toward the bulk-like arrangement with small disorders of atomic positions. The polyhedral-cages analogous to carbon-fullerenes are stable isomers yet not the minimum energy configurations. Their stabilities can be improved by embedding one oxygen atom or a suitable cage to form core-shell configurations. The mostly favored antiferromagnetic couplings between adjacent Gd atoms are nearly degenerated in energy with their ferromagnetic couplings, resulting in super-paramagnetic characters of gadolinium-oxide clusters. The...

Ab initio calculations of many-body interactions for compressed solid argon

An investigation on many-body effects of solid argon at high pressure was conducted based on a many-body expansion of interaction energy. The three- and four-body terms in the expansion were calculated using the coupled-cluster method with single, double, and noniterative triple theory and incremental method, in which the configurations of argon trimers and tetramers were chosen as the same as those in the actual lattice. The four-body interactions in compressed solid argon were estimated for the first time, and the three-body interaction ab initio calculations were extended to a small distance. It shows that the four-body contribution is repulsive at high densities and effectively cancels the three-body lattice energy. The dimer potential plus three-body interaction can well reproduce the measurements of equation of state at pressure approximately lower than ∼60 GPa, when including the four-body effects extends the agreement up to the maximum experimental pressure of 114 GPa.

Electronic structural and magnetic properties of Mn5Ge3 clusters.

Theoretical understanding of the stability, ferromagnetism, and spin polarization of Mn5Ge3 clusters has been performed by using the density functional theory with generalized gradient approximation for exchange and correlation. The magnetic moments and magnetic anisotropy energy (MAE) have been calculated for both bulk and clusters, and the enhanced magnetic moment as well as the enlarged MAE have been identified in clusters. The most attractive achievement is that Mn5Ge3 clusters show a fine half-metallic character with large energy scales. The present results may have important implications for potential applications of small Mn5Ge3 clusters as both emerging spintronics and next-generation data-storage technologies.

Five- and six-body effects on equation of state of solid 4He

The interaction energies of hcp and fcc helium are calculated by using a many-body expansion and cluster approach. The two- to six-body contributions are evaluated based on numerical solution of the Schrodinger equation for N-atomic clusters in the frame of the Born–Oppenheimer approximation. The convergence of the many-body expansion and its truncation position are discussed for the molar volume from 8.4 to 1.744 cm3 mol−1. It indicates that the five-body interactions become manifest at volume smaller than 3.0 cm3 mol−1, providing negative correction to the potential energy; while the six-body interactions emerge at volume smaller than 2.3 cm3 mol−1, with positive correction. With the use of the Einstein approximation for the zero-point contribution, the calculated 0 K equation of state is given up to 180 GPa and compared with measurements.

Band gap engineering of SnS2 nanosheets by anion–anion codoping for visible-light photocatalysis

SnS2 nanosheets with three atom thickness have previously been synthesized and it has been shown that visible light absorption and hydrogen evolution through photocatalytic water splitting are restricted. In the present study, we have systematically investigated the electronic structures of anionic monodoped (N and P) and codoped (N–N, N–P, and P–P) SnS2 nanosheets for the design of efficient water redox photocatalysts by adopting first principles calculations with the hybrid HSE06 functional. The results show that the defect formation energies of both the anionic monodoped and all the codoped systems decrease monotonically with the decrease of the chemical potential of S. The P–P codoped SnS2 nanosheets are not only more favorable than other codoped systems under an S-poor condition, but they also reduce the band gap without introducing unoccupied impurity states above the Fermi level. Interestingly, although the P–P(ii) codoped system gives a band gap reduction, this system is only suitable for oxygen production and not for hydrogen evolution, which indicates that it may serve as a Z-scheme photocatalyst for water splitting. The P–P(i) codoped system may be a potential candidate for photocatalytic water splitting to generate hydrogen because of the appropriate band gap and band edge positions, which overcome the disadvantage that the pure SnS2 nanosheet is not beneficial for hydrogen production. More importantly, the result of optical absorption spectral analysis shows that the P–P(i) codoped SnS2 nanosheet absorbs a longer wavelength of the visible light spectrum as compared to the pristine SnS2 nanosheet. The P–P(I) codoped system with a lower doping concentration also has an absorption shift towards the visible light region.

Magnetic moment and magnetic anisotropy of Ge3Mn5 thinfilms on Ge(111) substrate: A density functional study

Magnetism and magnetic anisotropy energy (MAE) of the Ge3Mn5 bulk, free-standing surface, and Ge3Mn5(001)|Ge(111) thinfilms and superlattice have been systemically investigated by using the relativistic first-principles electronic structure calculations. For Ge3Mn5 adlayers on Ge(111) substrates within Mn1 termination, the direction of magnetization undergoes a transition from in-plane at 1 monolayer (ML) thickness (MAE = -0.50 meV/ML) to out-of-plane beginning at 3 ML thickness (nearly invariant MAE = 0.16 meV/ML). The surficial/interfacial MAE is extracted to be 1.23/-0.54 meV for Mn1-termination; the corresponding value is 0.19/1.03 meV for Mn2/Ge-termination; the interior MAE is averaged to be 0.09 meV per ML. For various Ge3Mn5 systems, the in-plane lattice expansion and/or interlayer distance contraction would enhance the out-of-plane MAE. Our theoretical magnetic moments and MAEs fit well with the experimental measurements. Finally, the origination of MAE is elucidated under the framework of second-order perturbation with the electronic structure analyses.

[TM13@Bi20]− clusters in three-shell icosahedral matryoshka structure: being as superatoms

Using the density functional theory (DFT) method, the 33-atom intermetalloid [TM13@Bi20]− clusters (TM = 3d, 4d), which are composed of Bi20 pentagonal dodecahedra surrounding TM12 icosahedra with a single TM atom at the center, have been systematically examined to explore the possibility of clusters being as superatoms. The results show that most TM13 clusters can be attractively encapsulated into Bi20 cage to form a stable core–shell configuration, exhibiting an interesting progression of thermal stability along the 3d and 4d periods. Taking into account the structural stability (binding energy, embedding energy, and core–shell interaction) as well as the chemical stability (HOMO–LUMO gap), we proposed that [TM13@Bi20]− clusters with Ti and Mn doping in 3d series (Zr and Ag doping in 4d series) are specially stable and to be the protyle superatoms. For such systems, the molecular orbital shapes and energy alignments are in analogy with the atomic patterns, coinciding the general characters of superatomic orbitals. The closed core superatomic shell together with the partially-filled valence superatomic shell configuration leads to magnetic moment in stable [TM13@Bi20]−, e.g., [Mn13@Bi20]− cluster with the half-filled subshell can be assigned as a magnetic superatom owning to its modest HOMO–LUMO gap of 0.37 eV and large magnetic moment of 36 μB. The exchange-splitting in TM-3d states is found to be the driving force for the improvement of exchange-splitting of superatomic states.

Density functional theory calculations for magnetic properties of Co3W systems

Cheaper permanent magnetic nanostructures with magnetic properties equivalent to those of noble-metal or rare-earth nanomagnets have been experimentally developed for their potential applications in ultrahigh storage densities in magnetic memory. To date, their intrinsic magnetic properties are not well understood under the micro-level of local atomic arrangements and electronic structures. In this work, we performed theoretical investigations on the Co3W bulk, the clean surface, nanoclusters, and the Co|Co3W bilayers and superlattices for their geometrical structures, magnetic moments, and magnetic anisotropy energies (MAEs). We found that the Co3W nanostructures we constructed are stable and have the local minima in the energetic landscape, whose stabilities increase with increasing proportion of W and cluster size. The Co and W atoms in clusters are antiferromagnetically coupled, and their local magnetic moments decrease with increasing proportion of W. The breakdown of the Hunds third rule in W atoms observed in experiment can be interpreted as the competition between the intra-atomic spin-orbit coupling in W atoms and interatomic Co-W hybridizations. The highest MAE of about a few tens of meV is obtained in small cluster sizes, whereas it is an order of magnitude reduction in large cluster sizes. The magnetic systems of Co3W clean surface, Co|Co3W bilayer and superlattice can present large MAEs, and their easy-axes of magnetization are perpendicular to the (001) surface. Our calculated MAEs are of the same order of magnitude as that of the experimental measurements, and the electronic origin is revealed through the second-order perturbation method.

MANY-BODY INTERACTIONS AMONG HELIUM ATOMS AND EQUATION OF STATE OF DENSE HELIUM AT HIGH DENSITIES AND TEMPERATURES

Based on ab initio self-consistent-field technique and atomic cluster method, the various many-body interactions among atoms in dense helium have been computed. By this way, the static high pressure measurements are perfectly explained. A new simple formula for calculation the total energy is proposed by directly combining the two-body potential with the atomic potential. Over a large volume and temperature range of 7.5~1.74 cm3/mol and 2000~21000K, the equation of state (EOS) of helium is given.