From mathematical models to quantum chemistry in cluster science : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Chemistry at Massey University, Albany, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesThe structures and stabilities of hollow gold clusters are investigated by means of density functional theory (DFT) as topological duals of carbon fullerenes. Fullerenes can be constructed by taking a graphene sheet and wrapping it around a sphere, which requires the introduction of exactly 12 pentagons. In the dual case, a (111) face-centred cubic (fcc) gold sheet can be deformed in the same way, introducing 12 vertices of degree five, to create hollow gold nano-cages. This one-to-one relationship follows trivially from Euler’s polyhedral formula and there are as many golden dual fullerene isomers as there are carbon fullerenes. Photoelectron spectra of the clusters are simulated and compared to experimental results to investigate the possibility of detecting other dual fullerene isomers. The stability of the hollow gold cages is compared to compact structures and a clear energy convergence towards the (111) fcc sheet of gold is observed. The relationship between the Lennard-Jones (LJ) and sticky-hard-sphere (SHS) potential is investigated by means of geometry optimisations starting from the SHS clusters. It is shown that the number of non-isomorphic structures resulting from this procedure depends strongly on the exponents of the LJ potential. Not all LJ minima, that have been discovered in previous work, can be retrieved this way and the mapping from the SHS to the LJ structures is therefore non-injective and non-surjective. The number of missing structures is small and they correspond to energetically unfavourable minima on the energy landscape. The optimisations are also carried out for an extended Lennard-Jones potential derived from coupled-cluster calculations for the xenon dimer, and, although the shape of the potential is not too different from a regular (6,12)-LJ potential, the number of minima increases substantially. Gregory-Newton clusters, which are clusters where 12 spheres surround and touch a central sphere, are obtained from the complete set of SHS clusters. All 737 structures result in an icosahedron, when optimised with a (6,12)-LJ potential. Furthermore, the contact graphs, consisting only of atoms from the outer shell of the clusters, are all edge-induced sub-graphs of the icosahedral graph. For higher LJ exponents the symmetry of the potential energy surface breaks away from the icosahedral motif towards the SHS landscape, which does not support a perfect icosahedron for energetic reasons. This symmetry breaking is mainly governed by the shape of the potential in the repulsive region, with the long-range attractive region having little influence

From sticky-hard-sphere to Lennard-Jones-type clusters.

A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.epsr

Hume–Rothery Phase-Inspired Metal-Rich Molecules: Cluster Expansion of [Ni(ZnMe)₆(ZnCp*)₂] by Face Capping with Ni⁰(η⁶‑toluene) and Ni^I(η⁵‑Cp*)

The novel all-hydrocarbon ligand-stabilized binuclear clusters of metal–core composition Ni₂Zn₇E, [(η⁵-Cp*)­Ni₂(ZnMe)₆(ZnCp*)­(ECp*)] (<b>1-Zn</b>, E = Zn; <b>1-Ga</b>, E = Ga) and [(η⁶-toluene)­Ni₂(ZnCp*)₂(ZnMe)₆] (<b>2</b>; Cp* = pentamethylcyclopentadienyl), were obtained via Ga/Zn and Al/Zn exchange reactions using the starting compounds [Ni₂(ECp*)₃(η²-C₂H₄)₂] (E = Al/Ga) and an excess of ZnMe₂ (Me = CH₃). Compounds <b>1-Zn</b> and <b>1-Ga</b> are very closely related and differ only by one Zn or Ga atom in the group 12/13 metal shell (Zn/Ga) around the two Ni centers. Accordingly, <b>1-Zn</b> is EPR-active and <b>1-Ga</b> is EPR-silent. The compounds were derived as a crystalline product mixture. All new compounds were characterized by ¹H and ¹³C NMR and electron paramagnetic resonance (EPR) spectroscopy, mass spectrometric analysis using liquid-injection field desorption ionization, and elemental analysis, and their molecular structures were determined by single-crystal X-ray diffraction studies. In addition, the electronic structure has been investigated by DFT and QTAIM calculations, which suggest that there is a Ni1–Ni2 binding interaction. Similar to Zn-rich intermetallic phases of the Hume–Rothery type, the transition metals (here Ni) are distributed in a matrix of Zn atoms to yield highly Zn-coordinated environments. The organic residues, ancillary ligands (Me, Cp*, and toluene), can be viewed as the “protecting” shell of the 10-metal-atom core structures. The soft and flexible binding properties of Cp* and transferability of Me substituents between groups 12 and 13 are essential for the success of this precedence-less type of cluster formation reaction