The many-electron Schrödinger equation for atoms and molecules still remains analytically insoluble after over 90 years of investigation. This has not deterred scientists from developing a large variety of elegant techniques and approximations to workaround this issue and make many-particle quantum calculations computationally tractable. This thesis presents an all-particle treatment of three-particle systems which represent the simplest, most complex, many-particle systems including electron correlation and nuclear motion effects; meaning they provide a close-up view of fundamental particle interaction. Fully-Correlated (FC) energies and wavefunctions are calculated to high accuracy (mJ mol−1 or better for energies); and the central theme of this work is to use the wavefunctions to study fundamental quantum chemical physics. Nuclear motion has not received the same attention as electronic structure theory and this complicated coupling of electron and nuclear motions is studied in this work with the use of intracule and centre of mass particle densities where it is found nuclear motion exhibits strong correlation. A highly accurate Hartree-Fock implementation is presented which uses a Laguerre polynomial basis set. This method is used to accurately calculate electron correlation energies using the Löwdin definition and Coulomb holes by comparing with our FC data. Additionally the critical nuclear charge to bind two electrons within the HF methodology is calculated. A modification to Pekeris' series solution method is implemented to accurately model excited states of three-particle systems, and adapted to include the effects of nuclear motion along with three Non-Linear variational Parameters (NLPs) to aid convergence. This implementation is shown to produce high accuracy results for singlet and triplet atomic excited S states and the critical nuclear charge to bind two electrons in both spin states is investigated. Geometrical properties of three-particle systems are studied using a variety of particle densities and by determining the bound state stability at the lowest continuum threshold as a function of mass. This enables us to better ascertain what is meant when we define a system as an atom or a molecule.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:751887 |
| Date | January 2018 |
| Creators | Baskerville, Adam |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/77136/ |
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