Abstract
We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.
Highlights
Porphyrins and metalloporphyrins attract a great deal of interest due to their crucial role in biological processes such as respiration and photosynthesis
density functional theory (DFT) can fail in predicting if the ground state has low, intermediate, or high total spin polarization (this failure can be mitigated if we allow spin contamination in the calculations [55])
We investigated heme-like iron centers in graphene and the FeC10 N4 molecule using an exact canonical transformation within the framework of the density matrix renormalization group (DMRG) method
Summary
Porphyrins and metalloporphyrins attract a great deal of interest due to their crucial role in biological processes such as respiration and photosynthesis. As a result of their versatility, these complexes have found a range of exciting applications in spintronics [5,6,7,8,9,10,11,12,13,14], optoelectronics [15, 16], solar cells [17,18,19,20,21,22], and as building blocks of magnetic materials [23,24,25,26,27,28,29] or highly tunable qubits for quantum computing applications [30] These complexes display important correlation physics, such as spin and orbital variants of the Kondo effect in phthalocyanine (FePc) molecules deposited on the (111) surface of noble metals [31,32,33,34,35,36,37,38]. Transition metals can be a source of magnetism [49] to provide another knob for realizing unconventional functionalities
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