Theory of quantum transport in molecular-scale structures : English

Alotaibi, Turki and Lambert, Colin (2022) Theory of quantum transport in molecular-scale structures : English. PhD thesis, Lancaster University.

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Abstract

Molecular electronics is a flexible approach to studying nanoscale thermoelectricity and helping the discovery of new low-cost and environmentally friendly organic thermoelectric materials. This thesis introduces the theoretical tools used to support this process, starting in chapters 2 and 3, respectively. I have addressed the fundamental equations and techniques that support my work, such as the Schrodinger equation, density functional theory (DFT), and the SIESTA programme, which implements DFT and solves the underlying equations. I also explain single particle transport theory, which is based on the Hamiltonian and Green's functions, and provide some illustrations of how it may be employed. Chapter 4 is the first results chapter in this thesis, in which the three endohedral metallofullerenes (EMFs) Sc3N@C80, Sc3C2@C80 and Er3N@C80 are studied and compared with C60. I commenced my investigation by displaying the wave function plots of the molecules under investigation. I examined the charge transfer between metallic moieties and the cage employing three different methods: Mulliken population, Hirshfeld, and Voronoi. The charge transfer analyses were performed on a gold substrate and in the gas phase. The counterpoise approach was utilised to determine the most energy-favourable orientation for metallic moieties like Sc3N@C80, Sc3C2@C80 and Er3N@C80 to settle within the Ih-cage. I have shown how rotation angles θ,Φ,α and β about different axes play an important role in the conductance and Seebeck coefficient fluctuations. I investigated how the total energy varies with the angle of rotation, both in presence and absence of the gold substrate. There are an infinite number of inequivalent orientations of the metallic moieties comparative to their fullerene cage. Therefore, for each of the four axes, I considerd one mode of rotation in the gas phase and three modes of rotation on a substrate. I used DFT to determine the optimum distances between EMFs and the metallic electrodes. In chapter 5, I address the parameters that I investigated in Chapter 4 to enhance my simulations. Then I demonstrated how standard deviations in the Seebeck coefficient σ_S of EMF-based junctions are associated to the geometric standard deviation σ and charge inhomogeneity σ_q, exhibiting a fascinating structure-function relation. I compared EMF molecules to C60 and identified that σ_q,σ_S are the highest for Sc3C2@C80, and the lowest for C60, whereas the other EMFs follow the order Sc3C2@C80 >Sc3N@C80 > Er3N@C80 > C60. A significant value of σ_S indicates that a molecule could exhibit a wide range of Seebeck coefficients, and if the orientations corresponding to the large range can be isolated and controlled, the molecule has the potential to exhibit high-performance thermoelectricity. Large values of σ_S are associated with a broad Seebeck coefficient distribution, with both positive and negative signs. Ffor the EMFs explored here, this shows that they are bi-thermoelectric materials. Furthermore, molecules with high charge inhomogeneity reveal rare examples of high thermopower, suggesting that such molecules have the potential to produce high-performance thermoelectricity if these rare junction configurations can be isolated and controlled.