SWKB Quantization Rules for Bound States in Quantum Wells

In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix formulation of the Bohr-Sommerfield quantization rule has been applied to the study of bound states in one dimension quantum wells. Here we study these potentials in the frame work of supersymmetric WKB (SWKB) quantization approximation and find that SWKB quantization rule is superior to the modified Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.Comment: 8 page

Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds

Symmetry can dramatically reduce the computational cost (running time and memory allocation) of Self-Consistent-Field ab initio calculations for crystalline systems. Crucial for running time is use of symmetry in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the SACO (Symmetry Adapted Crystalline Orbital) basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. We here illustrate the effectiveness of this scheme, following recent advancements in the CRYSTAL code, concerning memory allocation and direct basis set transformation. Quantitative examples are given for large unit cell systems, such as zeolites (all-silica faujasite and silicalite MFI) and garnets (pyrope). It is shown that the full SCF of 3D systems containing up to 576 atoms and 11136 Atomic Orbitals in the cell can be run with a hybrid functional on a single core PC with 500 MB RAM in about 8 h. © 2014 Science China Press and Springer-Verlag Berlin Heidelberg

Electronic structure, dielectric properties and infrared vibrational spectrum of fayalite: An ab initio simulation with an all-electron Gaussian basis set and the B3LYP functional

The electronic structure, the static and high frequency dielectric tensors, and the infrared (IR) spectrum of fayalite Fe2SiO4, the Fe-rich end-member of olivine solid solutions, are explored at an ab initio quantum mechanical level, by using an all-electron Gaussian type basis set, the B3LYP hybrid DFT functional, and the CRYSTAL09 code. Mulliken population analysis and spin density maps illustrate the electronic structure, characterized by a nearly pure d6, high-spin configuration of the transition metal atom. The full set of IR wavenumbers and intensities is computed. The availability of highly accurate synchrotron radiation data (Suto et al., Astron Astrophys 2002, 389, 568) permits a very accurate comparison between simulated and measured quantities, in primis wavenumbers (ν) and oscillator strengths (f). The mean absolute difference ∆v is as small as 4 cm−1, and the maximum absolute difference |Δνmax| never exceeds 12 cm−1, whereas the summed absolute difference ΔF between fexp and fcalc is around 10%. Modes not detected in the experiment turn out to be (i) characterized by low computed intensity, or (ii) very close to a large intense peak. Computed and experimental IR reflectance curves are in striking agreement also. The nature of the vibrational modes is investigated by means of isotopic substitutions, which clarify the participation of the various atomic species to each mode

The IR vibrational properties of six members of the garnet family: A quantum mechanical ab initio study

The IR vibrational properties and the corresponding reflectance spectra of the six most common members of the garnet family (pyrope Mg3Al2Si3O12, almandine Fe3Al2Si3O12, spessartine Mn3Al2Si3O12, grossular Ca3Al2Si3O12, uvarovite Ca3Cr2Si3O12, and andradite Ca3Fe2Si3O12) were simulated at the ab initio level with the CRYSTAL09 code by using a large all-electron Gaussian-type basis set and the B3LYP hybrid functional. The 17 IR active F1u transverse optical (TO) and longitudinal optical (LO) frequencies, the oscillator strengths, the high frequency and static dielectric constants, and the reflectance spectrum were computed. The agreement with experiments for the TO and LO peaks is always excellent, the mean absolute difference for the whole set of data (overall 178 peaks) being 5 cm−1. Oscillator strengths, calculated from the mass-weighted effective Born charges, are found in semi-quantitative agreement with the experimental data. The reflectance spectra, simulated through the classical dispersion relation, reproduce the experimental curves extremely well. The availability of the full set of simulated frequencies and intensities, obtained by using uniform computational tools (computer code, variational basis sets, density functional), permits the establishment of correlations between IR wavenumbers and structural features suggested, but only partially documented, in the past

Combining the Hybrid Functional Method with Dynamical Mean-Field Theory

We present a new method to compute the electronic structure of correlated materials combining the hybrid functional method with the dynamical mean-field theory. As a test example of the method we study cerium sesquioxide, a strongly correlated Mott-band insulator. The hybrid functional part improves the magnitude of the pd-band gap which is underestimated in the standard approximations to density functional theory while the dynamical mean-field theory part splits the 4f-electron spectra into a lower and an upper Hubbard band.Comment: 5 pages, 2 figures, replaced with revised version, published in Europhys. Let

Exceptionally low shear modulus in a prototypical imidazole-based metal-organic framework.

Using Brillouin scattering, we measured the single-crystal elastic constants (C(ij)'s) of a prototypical metal-organic framework (MOF): zeolitic imidazolate framework (ZIF)-8 [Zn(2-methylimidazolate)(2)], which adopts a zeolitic sodalite topology and exhibits large porosity. Its C(ij)'s under ambient conditions are (in GPa) C(11)=9.522(7), C(12)=6.865(14), and C(44)=0.967(4). Tensorial analysis of the C(ij)'s reveals the complete picture of the anisotropic elasticity in cubic ZIF-8. We show that ZIF-8 has a remarkably low shear modulus G(min) < or approximately 1 GPa, which is the lowest yet reported for a single-crystalline extended solid. Using ab initio calculations, we demonstrate that ZIF-8's C(ij)'s can be reliably predicted, and its elastic deformation mechanism is linked to the pliant ZnN(4) tetrahedra. Our results shed new light on the role of elastic constants in establishing the structural stability of MOF materials and thus their suitability for practical applications