INVESTIGATION OF ELECTRONIC STRUCTURE OF A QUANTUM DOT USING SLATER-TYPE ORBITALS AND QUANTUM GENETIC ALGORITHM

In this study, electronic properties of a low-dimensional quantum mechanical structure have been investigated by using Genetic Algorithm (GA). One- and two-electron Quantum Dot (QD) systems with an on-center impurity are considerable by assuming the confining potential to be infinitely deep and spherically symmetric. Linear combinations of Slater-Type Orbitals (STOs) were used for the description of the single electron wave functions. The parameters of the wave function of the system were used as individuals in a generation, and the corresponding energy expectation values were used for objective functions. The energy expectation values were determined by using the Hartree-Fock-Roothaan (HFR) method. The orbital exponent ζi's and the expansion coefficient ci's of the STOs were determined by genetic algorithm. The obtained results were compared with the exact result and found to be in a good agreement with the literature.

ANTIFERROMAGNETIC PHASE OF WIGNER ELECTRON CRYSTAL

The ground state energies of the 3-dimensional antiferromagnetic Wigner crystal corresponding to sc, bcc, fcc, diamond and perovskite structures are computed and the structural stability is analyzed. It is found that the bcc structure has the lowest energy. The possibility of the antiferromagnetic phase of the Wigner crystal having cubic or spherical surface as the region of occupation is analyzed. The effect of correlation is suitably taken into account. This still lowers the ground state energy. The calculations are done for the whole range of the density parameter r s from 1 to 200. The low density region favorable for Wigner crystallization is found to be above r s =10. The structure dependent Wannier function is approximated by orthonormalized Gaussian and it is employed in the calculation. The orbital exponent of the Gaussian is used as a variational parameter. The calculations are also done for the non-uniform positive background case.

Orbital exponent optimization for molecular self-consistent-field wave functions including the polarization function

We have applied the analytical energy gradient method with respect to the orbital exponents for molecular self-consistent-field wave functions including the polarization functions. The gradients for Gaussian-type functions in Huzinaga–Dunning's double zeta basis set with and without polarization functions were compared for some hydrides of the first-row elements. The changes in the gradients caused by the polarization functions were observed. It was found that the polarization functions on hydrogen play a role in reducing the gradients produced in the absence of these functions. Although optimization of the exponents gives results depending on the molecules, the total energies as well as the dipole moments are insensitive to the exponent values. We could confirm that the exponents for Gaussian functions in the standard double zeta plus polarization basis set work adequately by coupling with the variational parameters for the simple hydrides even if they have gradients in the molecules. Keywords: orbital exponent, Gaussian-type functions, analytical energy gradient, molecular SCF wave function, polarization function.

A molecular orbital study of the conformation (inversion and rotational barriers) and electronic properties of sulfamide

Abinitio calculations have been used to study the conformational potential surface of sulfamide, by considering the S—N bond rotations and the nitrogen inversion processes. The lowest energy conformation (b) is found for a cis–trans arrangement of the amino groups, although conformations with cis–cis (a), trans–trans (c), and near staggered (c′) arrangements lie close in energy. Nitrogen inversion barriers are very low, and consequently one may expect forms b and c′ to be the only ones present in the gas phase. Conformer a is very polar, its dipole moment being twice that of b, so it may be favored in condensed media or in polar-solvent solutions. The relative stability of the different isomers is governed by interactions between the amino protons and between the nitrogen lone pairs. Our results show that d–π backbonding, involving the d orbitals on sulfur, is responsible for the multiple bond character of the S—O linkage, but is very small in the S—N interactions. The role of the sulfur d-orbital exponent, when a 6-31G* basis is used, is analyzed on a series of model compounds containing SII, SIV, and SVI. Although the inclusion of d functions on sulfur is crucial to describing correctly the bonding in sulfamide, the results obtained do not change appreciably if a second set of d functions is centered on sulfur. Nevertheless, only when polarization functions are also included for first-row atoms is the description of the system reliable. Keywords: sulfamide, inversion and rotational barriers, sulfur d-functions.