Nuclear Wavefunctions of Dispersion Bound Systems: Endohedral Eigenstates of Endofullerenes

Endohedral fullerenes, or endofullerenes, are supramolecular complexes where a small chemical species, A, is trapped within a cavity encompassed by a fullerene cage, Cn, denoted as A@Cn. Recent advances in the synthesis and characterisation of these species has produced a wealth of experimental spectroscopic data. These measurements unveil information about the nuclear energy levels of the endohedral species, which due to its entrapment has its translational motion quantised that can couple to its other intramolecular normal modes. Theoretical calculation of these nuclear energy levels is broken down into two phases. Firstly, the electronic Schrodinger equation has to be solved in order to generate the Potential Energy Surface (PES). However, as these endofullerenes are bound through non-covalent interactions, they pose challenges to the electronic structure techniques with respect to achieving spectroscopic accuracy. By restricting the fullerene cage motion sufficiently, the dimensionality of the PES is reduced to a computationally tractable size. However, due to the large cost of the electronic structure calculations, the PES has to be approximated by a known functional form, usually Lennard-Jones or be interpolated from sparse training data. Machine learning methods excel at the latter, and can even provide confidence intervals on the interpolation. Once armed with the PES, the second stage of the calculation is to solve the nuclear Schrodinger equation. This can be framed as solving a (generalised) eigenvalue problem, by diagonalising the nuclear Hamiltonian matrix within a specified nuclear basis set. This unveils the endohedral eigenstates --- the nuclear energy levels and associated wavefunctions. Comparison of the energy gaps in the eigenspectrum allows for scrutinisation of the quality of PES and consequently the underlying electronic structure. Access to the wavefunction allows for calculation of various other experimentally observable properties of the endohedral system, as well as plots of the nuclear orbitals. Starting from the highly symmetric He@C60, this thesis investigates its translational energies and makes comparisons with experimental data. This system is studied using a variety of electronic structure methods and Gaussian process regression to generate the PES. Subsequently the effect of changing both the endohedral species and fullerene cage to Ne@C70 is examined, requiring the construction of a new basis set and wavefunction classification. Expansion to an endohedral diatomic, H2 in a variety of fullerene cages is also studied. Finally, a group of these isolated endofullerenes arranged in regular lattices are studied. Cooperative properties that arise due to the extension to a many body system are also explored.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Panchagnula, Kripa

Advisor dc:contributor.advisor

• Thom, Alex

• endofullerenes
• machine learning
• potential energy surfaces
• electronic structure methods
• vibrational states

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/f651c4ec-82c8-4a1e-8608-dbd2a99e16b8/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0009-0004-3952-073X

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/379241