Elucidating the surface electron states of transition metal compounds is of primary importance in main heterogeneous catalytic processes, such as the hydrogen and oxygen evolution reactions.  Key property in all these processes is the position of the energy of the d-band center relative to the Fermi-level of the catalyst; it must be shifted close to the Fermi level to achieve balance between adsorption and desorption of the catalyst and the adsorbate. Often, these processes involve expensive metals such as Ru or Pt, limiting their applicability. The Nickel Phosphide (Ni_xP_y) family has recently emerged as an important catalyst family replacing noble metals; in these systems the surface electronic properties, may be tailored by doping with different transition metals, decreasing size, or by controlling the nanoparticle shape (facet engineering). It is thus crucial to be able to simultaneously monitor the evolution of the morphology as well as the electronic structure of the NP particles while scaling down the size.

In most of these materials, surface electron states are extremely sensitive to local disturbances, such as impurities, surface defects, as well as surface termination. In contrast, 3D topological insulators like Bi₂Se₃, or Bi₂Te₃, exhibit exceptionally robust metallic surface electron states while the bulk interior is insulating. These extraordinary properties, which become dominant by reducing the system size to the nanometers, have been tied to enhancement of the Seebeck effect, i.e., the conversion of heat into electricity, catalytic activity, and electrochemical performance, the latter of these effects has been pursed in this thesis as well. An important question that has eluded however is the presence of the Dirac electrons themselves and to which extend the Dirac electrons penetrate the nanoparticles, controlling thus the overall electronic properties.

In contrast to the TIs, Weyl semimetals (WSMs), another category of topological materials, host protected electron states in the bulk interior. The bulk conduction and valence bands of these systems cross linearly in pairs of conjugate nodal points, the so-called Weyl points, forming characteristic double cones. Remarkably, in specific WSMs, such as the WTe₂ and MoTe₂, known as type-II WSMs, the Weyl cones are strongly tilted, leading to the formation of electron and hole pockets at the Fermi level, strongly influencing their electronic properties. However, energy bands in these systems are shown to disperse in a very tiny region, rendering standard experimental techniques, such as Angle Resolved Photoemission Spectroscopy obsolete in detecting the Weyl bands. 

In this thesis all the issues mentioned for each case, were tackled by employing solid-state nuclear magnetic resonance (ssNMR) spectroscopy under various temperatures and magnetic fields, combined with high-resolution transmission electron microscopy and density functional theory calculations.