Ab initio calculations for the neutral and charged O vacancy in sapphire

The energetics, lattice relaxation, and the defect-induced states of st single O vacancy in alpha-Al2O3 are studied by means of supercell total-energy calculations using a first-principles method based on density-functional theory. The supercell model with 120 atoms in a hexagonal lattice is sufficiently large to give realistic results for an isolated single vacancy (square). Self-consistent calculations are performed for each assumed configuration of lattice relaxation involving the nearest-neighbor Al atoms and the next-nearest-neighbor O atoms of the vacancy site. Total-energy data thus accumulated are used to construct an energy hypersurface. A theoretical zero-temperature vacancy formation energy of 5.83 eV is obtained. Our results show a large relaxation of Al (O) atoms away from the vacancy site by about 16% (8%) of the original Al-square (O-square) distances. The relaxation of the neighboring Al atoms has a much weaker energy dependence than the O atoms. The O vacancy introduces a deep and doubly occupied defect level, or an F center in the gap, and three unoccupied defect levels near the conduction band edge, the positions of the latter are sensitive to the degree of relaxation. The defect state wave functions are found to be not so localized, but extend up to the boundary of the supercell. Defect-induced levels are also found in the valence-band region below the O 2s and the O 2p bands. Also investigated is the case of a singly occupied defect level (an F+ center). This is done by reducing both the total number of electrons in the supercell and the background positive charge by one electron in the self-consistent electronic structure calculations. The optical transitions between the occupied and excited states of the: F and F+ centers are also investigated and found to be anisotropic in agreement with optical data.

Structure and properties of microporous titanosilicate determined by first-principles calculations

The structure of EST-10, a member of synthetic microporous titanosilicates, was recently determined by an ingenious combination of experimental and simulational techniques. However, the locations of the alkali atoms in the framework remain elusive and its electronic structure is totally unknown. Based on first-principles local density calculations, the possible locations of the alkali atoms are identified and its electronic structure and bonding fully elucidated. ETS-10 is a semiconductor with a direct band gap of 2.33 eV. The Na atoms are likely to locate inside the seven-member ring pore adjacent to the one-dimensional Ti-O-Ti-O- chain.

Quantum-mechanical calculations of vibrationally resolved cross sections for non-dissociative charge transfer of O3+ with H-2

Charge transfer due to collisions of ground state O3+ (2s(2)2p P-2) ions with molecular hydrogen is investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method, and electronic and vibrational state-selective cross sections along with the corresponding differential cross sections are calculated for projectile energies of 100, 500, 1000 and 5000 eV/u at the orientation angles of 25 degrees,45 degrees and 89 degrees. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations were obtained with the spin-coupled valence-bond approach. The infinite order sudden approximation (IOSA) and the vibrational sudden approximation (VSA) are utilized to deal with the rotation of H-2 and the coupling between the electron and the vibration of H-2. It is found that the distribution of vibrationally resolved cross sections with the vibrational quantum number upsilon' of H-2(+) (upsilon') varies with the increment of the projectile energy; and the electronic and vibrational stateselective differential cross sections show similar behaviors: there is a highest platform within a very small scattering angle, beyond which the differential cross sections decrease as the scattering angle increases and lots of oscillating structures appear, where the scattering angle of the first structure decreases as E-P(-1/2) with the increment of the projectile energy E-P; and the structure and amplitude of the differential cross sections are sensitive to the orientation of molecule H-2, which provides a possibility to identify the orientations of molecule H-2 by the vibrational state-selective differential scattering processes.

Ab initio calculations of differential cross sections for single charge transfer in He-3(2+)+He-4 collisions

The single charge transfer process in He-3(2+)+He-4 collisions is investigated using the quantum-mechanical molecular-orbital close-coupling method, in which the adiabatic potentials and radial couplings are calculated by using the ab initio multireference single- and double-excitation configuration interaction methods. The differential cross sections for the single charge transfer are presented at the laboratorial energies E = 6 keV and 10 keV for the projectile He-3(2+). Comparison with the existing data shows that the present results are better in agreement with the experimental measurements than other calculations in the dominant small angle scattering, which is attributed to the accurate calculations of the adiabatic potentials and the radial couplings.

Time-dependent density-functional calculations for optical spectra of Na-2 and Na-4 clusters

With the frame of the time-dependent local density approximation, an efficient description of the optical response of clusters has been used to study the photo-absorption cross section of Na-2 and Na-4 clusters. It is shown that our calculated results are in good agreement with the experiment. In addition, our calculated spectrum for the Na-4 cluster is in better agreement with experiment than the GW absorption spectrum.

DBHF approach and thermodynamic consistency for nuclear matter calculations

Within the framework of Dirac Brueckner-Hartree-Fock (DBHF) approach, we calculate the energy per nucleon, the pressure, the nucleon self-energy, and the single-nucleon energy in the nuclear matter by adopting two different covariant representations for T-matrix. We mainly investigate the influence of different covariant representations on the satisfiable extent of the Hugenholtz-Van Hove (HVH) theorem in the nuclear medium in the framework of DBHF. By adopting the two different covariant representations of T-matrix, the predicted nucleon self-energy shows a quite different momentum and density dependence. Different covariant representations affect remarkably the satisfiable extent of the HVH theorem. By adopting the complete pseudo-vector representation of the T-matrix, HVH theorem is largely violated, which is in agreement with the result in the non-relativistic Brueckner-Hartree-Fock approach and reflects the importance of ground state correlations for single nucleon properties in nuclear medium, whereas by using the pseudoscalar representation, the ground state correlation cannot be shown. It indicates that the complete pseudo-vector presentation is more feasible than the pseudo-scalar one.

Importance of self-consistency in relativistic continuum random-phase approximation calculations

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

Isospin-dependent pairing interaction from nuclear matter calculations

The isospin dependence of the effective pairing interaction is discussed on the basis of the Bardeen, Cooper, and Schrieffer theory of superfluid asymmetric nuclear matter. It is shown that the energy gap, calculated within the mean field approximation in the range from symmetric nuclear matter to pure neutron matter, is not linearly dependent on the symmetry parameter owing to the nonlinear structure of the gap equation. Moreover, the construction of a zero-range effective pairing interaction compatible with the neutron and proton gaps in homogeneous matter is investigated, along with some recent proposals of isospin dependence tested on the nuclear data table.