Electronic structure of three-dimensional isotropic quantum dots by four-component relativistic coupled cluster methods

Abstract

Quantum dots with three-dimensional isotropic harmonic confining potentials and up to 60 electrons are studied. The Dirac-Coulomb Hamiltonian serves as a framework, so that relativistic effects are included, and electron correlation is treated at a high level by the Fock-space coupled cluster method, with single and double excitations summed to all orders. Large basis sets composed of spherical Gaussian functions are used. Energies of ground and excited states are calculated. The orbital order is 1s, 2p, 3d, 3s, 4f, 4p, 5g, ... , and closed-shell structures appear for 2, 8, 18, 20, 34, 40, and 58 electrons. Relativistic effects are negligible for low strengths of the harmonic potential and increase rapidly for stronger potentials. Breit contributions, coming from the lowest order relativistic correction to the interelectronic repulsion terms, are also studied. Correlation effects are significant for these systems, in particular for weak confining potentials and for small systems, where they constitute up to 6% of the total energies. Their relative weight goes down (although they increase in absolute value) for larger systems or confining potentials. Planned applications to quantum dots with impurities are discussed briefly.

Multireference Nature of Chemistry: The Coupled-Cluster View

“…229 The method has been extensively employed in highly accurate studies of heavy atoms 229À233 and even in a model study of quantum dots. 234 Importantly, Landau et al suggested a mixed-sector variant of the IH-FS-MRCC method (MIH-FS-MRCC), where flexibility in constructing the model space is enhanced by mixing different sectors of the Fock space. 201 This brings relaxation to the lower sectors of the Fock space and adds absent components to the higher-sector wave functions, thus improving the description of the corresponding electronic states.…”

“…Kaldor and co-workers also formulated a relativistic variant of the IH-FS-MRCC method . The method has been extensively employed in highly accurate studies of heavy atoms − and even in a model study of quantum dots . Importantly, Landau et al suggested a mixed-sector variant of the IH-FS-MRCC method (MIH-FS-MRCC), where flexibility in constructing the model space is enhanced by mixing different sectors of the Fock space .…”

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

“…7(a) compares the above expression for a symmetric 3D dot with the values obtained in Ref. [37] by the coupled-cluster method. The present analytical model provides an excellent match with the numerically intensive calculation.…”

Linear and nonlinear optical absorption coefficients of two-electron spherical quantum dot with parabolic potential

“…Confined quantum systems have been one of the most important subjects of investigation. Therefore, due to their fundamental properties and their wide range of technological applications [1], a great deal of theoretical works on these structures has been reported extensively by using different methods like a finite element method [2,3], perturbation [4], density functional [5,6], configuration interaction [7,8], variational [9,10], exact solution [11], quantum genetic algorithm and Hartree-Fock Roothaan method [12] and other methods [13,14]. Understanding of the electronic and optical properties in such structures is important because these properties are strongly affected by the presence of impurity.…”