Massey Documents by Type

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Pushing the limits of the periodic table — A review on atomic relativistic electronic structure theory and calculations for the superheavy elements
(Elsevier B.V., 2023-10-13) Smits OR; Indelicato P; Nazarewicz W; Piibeleht M; Schwerdtfeger P; Schwenk A
We review the progress in atomic structure theory with a focus on superheavy elements and their predicted ground state configurations important for an element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is essential to correctly solve the Dirac equation in strong Coulomb fields, and to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Zcrit≈170, where levels such as the 1s shell dive into the negative energy continuum (Enκ<−mec2). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.
Numerical investigations of the Dirac equation and bound state quantum electrodynamics in atoms : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand
(Massey University, 2022) Piibeleht, Morten
This thesis addresses, from a computational perspective, several open questions in relativistic atomic structure theory, which is the theoretical description of atoms based on the Dirac equation and quantum electrodynamics (QED). The first part of this thesis investigates several fundamental problems of the Dirac equation with the help of a novel numerical solver based on the one-dimensional finite element (FEM) basis set. Significant effort is made to validate and benchmark the solver, which is reliably able to converge to accurate results at numerical floating-point precision, including when nuclear potentials derived from nuclear models with finite spacial extent (as opposed to a point nucleus) are used. The solver is then applied to the Dirac equation in the challenging high nuclear charge regime where the Dirac equation exhibits several mathematical difficulties. In particular, the problem of the 1s bound state diving into the sea of negative energy continuum states is studied and the diving resonance state is numerically traced and analysed. As a type of workaround, a modified version of the Dirac equation where the negative energy plane-wave states are projected out of the Hilbert space is also solved and studied in the high nuclear charge regime. The second part of the thesis involves expanding the QED self-energy treatment in the atomic structure software GRASP. The configuration interaction (CI) portion of the code is significantly refactored to allow for the implementation of new additional effective operators that provide a more modern multi-electron treatment of QED self-energy effects. The implementation is tested by evaluating the QED and other post-Dirac-Coulomb corrections for the ground states of the beryllium-like isoelectronic sequence, which was also discovered to exhibit an interesting ground state configuration transition at high nuclear charge.
A relativistic treatment of atoms and molecules : from relativity to electroweak interaction : a thesis submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy in Theoretical Physics at Massey University, Auckland, New Zealand
(Massey University, 2009) Thierfelder, Christian
Relativistic quantum chemistry is the relativistic formulation of quantum mechanics applied to many-electron systems, that is to atoms, molecules and solids. It combines the principles of special relativity, which are obeyed by any fundamental physical theory, with the basic rules of quantum mechanics. By construction, it represents the most fundamental theory of all molecular sciences, which describes matter by the action, interaction and motion of the elementary particles. This science is of vital importance to physicists, chemists, material scientists, and biologists with a molecular view of the world A full relativistic treatment of atoms and molecules which includes the quantization of the electromagnetic field is currently one of the most challenging tasks in electronic structure theory. Therefore, relativistic effects in atoms and molecules were studied computationally. A combination of wave function and density functional based methods within a correct relativistic framework proved necessary to achieve accurate results of various atomic and molecular properties. The first part of this thesis deals with investigations in atomic systems including quantum electrodynamic effects in the ionization potentials of a large number of elements K-shell and L-shell ionizations potentials for 268Mt were calculated and static dipole polarizabilities of the neutral group 14 elements were investigated. The second part concentrates on molecular systems including superheavy element monohydrides up to 120H+). In particular, the chemical bonding of the superheavy elements 119 and 120 are investigated for the first time. Electric field gradients of a number of gold and copper compounds were also calculated and the nuclear quadrupole moment of gold and copper determined in good agreement with experiment. Finally, the parity violation energy difference in the chiral molecule bromochlorofluoromethane (CHFCIBr) was investigated by relativistic coupled-cluster theory to provide benchmark results for all future investigations in this field.

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