Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming interacting spins lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure, and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard-$U$ energy scale, and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of $U$, and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled $S=1/2$ phenalenyl triangulenes, using multi-configurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions.
Exchange interactions and intermolecular hybridization in a spin-1/2 nanographene dimer
Department of Chemistry, University of Zurich（苏黎世大学化学系）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Universidad del País Vasco UPV/EHU（巴斯克国立大学先进聚合物与材料系：物理、化学与技术）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）；Integrated Systems Laboratory, ETH Zürich（苏黎世联邦理工学院集成系统实验室）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学化学、生物化学与药学系）
Two topological phases in exchange alternating spin-1 nanographene chains
International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术实验室）；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Centro de Física das Universidades do Minho e do Porto, Universidade do Minho（米尼奥与波尔图大学物理中心，米尼奥大学）；NOVA School of Science and Technology (FCT NOVA)（新里斯本科学与技术学院）
Learning Inhomogeneous Heisenberg Hamiltonians in Nanographene Spin Chains
Aalto University（阿尔托大学）；Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技与检测局）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微结构物理研究所）；Technische Universität Dresden（德累斯顿工业大学）
Quantum phase transition in magnetic nanographenes on a lead superconductor
Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学生物与医学工程学院）；East China University of Science & Technology（华东理工大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
Engineering Ferrimagnetic Interactions in Molecular Quantum Systems
Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技研究院）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子科技与卡弗里纳米科学研究所）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微观结构物理研究所）；Center for Advancing Electronics Dresden (cfaed) & Faculty of Chemistry and Food Chemistry, Technische Universität Dresden（德累斯顿工业大学先进电子中心及化学与食品化学学院）；Department of Chemistry, University of Zurich（苏黎世大学化学系）；College of Materials Science and Optoelectronic Technology & Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院及材料科学与工程中心）；Beijing National Laboratory for Molecular Science, CAS Key Laboratory for Organic Solids, Institute of Chemistry, Chinese Academy of Sciences（中国科学院化学研究所有机固体院重点实验室及北京分子科学国家实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学生物化学与药学系化学部）
