Exchange Interactions and Intermolecular Hybridization in a Spin-1/2 Nanographene Dimer.

Phenalenyl is a radical nanographene with a triangular shape hosting an unpaired electron with spin S = 1/2. The open-shell nature of the phenalenyl is expected to be retained in covalently bonded networks. As a first step, we report synthesis of the phenalenyl dimer by combining in-solution synthesis and on-surface activation and its characterization on Au(111) and on a NaCl decoupling layer by means of inelastic electron tunneling spectroscopy (IETS). IETS shows inelastic steps that are identified as singlet-triplet excitation arising from interphenalenyl exchange. Spin excitation energies with and without the NaCl decoupling layer are 48 and 41 meV, respectively, indicating significant renormalization due to exchange with Au(111) electrons. Furthermore, third-neighbor hopping-induced interphenalenyl hybridization is fundamental to explaining the position-dependent bias asymmetry of the inelastic steps and activation of kinetic interphenalenyl exchange. Our results pave the way for bottom-up synthesis of S = 1/2 spin-lattices with large exchange interactions.

Smart local orbitals for efficient calculations within density functional theory and beyond.

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.