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.
Analytical expressions through the binomial coefficients and recursive relations are derived for the expansion coefficients of overlap integrals in terms of a product of well-known auxiliary functions A and B . These formulas are especially k k useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the computer results is satisfactory for the values of quantum numbers up to 50 and for the arbitrary values of screening constants of atomic orbitals and internuclear distances.
The electronic structure of Quantum Dot (QD), GaAs/Al x Ga 1-x As , has been investigated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. One-electron system with an on-center impurity is considered by assuming a spherically symmetric confining potential of finite depth. The ground and excited state energies of one-electron QD were calculated depending on the dot radius and stoichiometric ratio. Expectation values of energy were determined by using the HFR method along with Slater-Type Orbitals (STOs) and QGA was used for the wavefunctions optimization. In addition, the effect of the size of the basis set on the energy of QD was investigated. We also calculated the binding energy for a dot with finite confining potential. We found that the impurity binding energy increases for the finite potential well when the dot radius decreases. For the finite potential well, the binding energy reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. Whereas in previous study, in Ref. 40, for the infinite potential well, we found that the impurity binding energy increases as the dot radius decreases.
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