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

The constrained space orbital variation analysis for periodic ab initio calculations

The constrained space orbital variation (CSOV) method for the analysis of the interaction energy has been implemented in the periodic ab initio CRYSTAL03 code. The method allows for the partition of the energy of two interacting chemical entities, represented in turn by periodic models, into contributions which account for electrostatic effects, mutual polarization and charge transfer. The implementation permits one to carry out the analysis both at the Hartree-Fock and density functional theory levels, where in the latter the most popular exchange-correlation functionals can be used. As an illustrating example, the analysis of the interaction between CO and the MgO (001) surface has been considered. As expected by the almost fully ionic character of the support, our periodic CSOV results, in general agree with those previously obtained using the embedded cluster approach, showing the reliability of the present implementation.Ministerio de Educación y Ciencia de España MAT2005-1872Secretaría de la Educación Pública (SEP)-Consejo Nacional de Ciencia y Tecnología (CONACYT). Gobierno de México SEP-2004-CO1-4698

Infrared and Raman spectroscopic features of the self-interstitial defect in diamond from exact-exchange hybrid DFT calculations

International audienceQuantum-mechanical calculations are performed to investigate the structural, electronic, and infrared (IR) and Raman spectroscopic features of one of the most common radiation-induced defects in diamond: the “dumb-bell” 〈100〉 split self-interstitial. A periodic super-cell approach is used in combination with all-electron basis sets and hybrid functionals of density-functional-theory (DFT), which include a fraction of exact non-local exchange and are known to provide a correct description of the electronic spin localization at the defect, at variance with simpler formulations of the DFT. The effects of both defect concentration and spin state are explicitly addressed. Geometrical constraints are found to prevent the formation of a double bond between the two three-fold coordinated carbon atoms. In contrast, two unpaired electrons are fully localized on each of the carbon atoms involved in the defect. The open-shell singlet state is slightly more stable than the triplet (the energy difference being just 30 meV, as the unpaired electrons occupy orthogonal orbitals) while the closed-shell solution is less stable by about 1.55 eV. The formation energy of the defect from pristine diamond is about 12 eV. The Raman spectrum presents only two peaks of low intensity at wave-numbers higher than the pristine diamond peak (characterized by normal modes extremely localized on the defect), whose positions strongly depend on defect concentration as they blue shift up to 1550 and 1927 cm−1 at infinite defect dilution. The first of these peaks, also IR active, is characterized by a very high IR intensity, and might then be related to the strong experimental feature of the IR spectrum occurring at 1570 cm−1. A second very intense IR peak appears at about 500 cm−1, which, despite being originated from a “wagging” motion of the self-interstitial defect, exhibits a more collective, less localized character

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