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

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.

Nuclear quadrupole moment of 197Au from high-accuracy atomic calculations.

The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment Q from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussians) are employed. Energy splittings of the 2D5/2 and 2D3/2 levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with Q up to 10(-5) a.u., whereas the latter display significant nonlinearity even at Q=10(-8) a.u. Larger Q values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between Q values derived from 2D5/2 and 2D3/2 data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of Q(197Au) is 521(7) mb. It is lower than the muonic 547(16) mb and agrees within error bounds with the recent value of 510(15) mb obtained from molecular calculations.

High-accuracy calculation of nuclear quadrupole moments of atomic halogens.

Electric field gradients at the nuclei of halogen atoms are calculated using a finite field approach. The four-component Dirac-Coulomb Hamiltonian serves as the framework, all electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the Gaunt term, the main part of the Breit interaction, is included. Large basis sets (e.g., 28s24p21d9f4g2h Gaussian-type functions for I) are used. Combined with experimental nuclear quadrupole coupling constants, accurate estimates of the nuclear quadrupole moments are obtained. The calculated values are Q(35Cl)=-81.1(1.2) mb, Q(79Br)=302(5) mb, and Q(127I)=-680(10) mb. Currently accepted reference values [Pyykko, Mol. Phys. 99, 1617 (2001)] are -81.65(80), 313(3), and -710(10) mb, respectively. Our values are lower for the heavier halogens, corroborating the recent work of van Stralen and Visscher [Mol. Phys. 101, 2115 (2003)], who obtained Q(127I)=-696(12) mb in a series of molecular calculations.