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This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn–Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.
A complete theoretical analysis using first the simple Hückel model followed by more sophisticated multi-reference calculations on a trinuclear Ni(II) complex (Tp#Ni3HHTP), bearing the non-innocent bridging ligand HHTP3−, is carried out. The three semiquinone moieties of HHTP3− couple antiferromagnetically and lead to a single unpaired electron localized on one of the moieties. The calculated exchange coupling integrals together with the zero-field parameters allow, when varied within a certain range, reproducing the experimental data. These results are generalized for two similar other trinuclear complexes containing Ni(II) and Cu(II). The electronic structure of HHTP3− turns out to be independent of both the chemical nature and the geometry of the metal ions. We also establish a direct correlation between the geometrical and the electronic structures of the non-innocent ligand that is consistent with the results of calculations. It allows experimentalists to get insight into the magnetic behavior of this type of complexes by an analysis of their X-ray structure.
In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the $j_{\mathrm{eff}}$ states is key. However, in particular for its structurally simple member Ba$_2$IrO$_4$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-$j_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling and Coulomb interactions, we map out a rich phase diagram and identify a region of effective one-band metal-insulator transition relevant to Ba$_2$IrO$_4$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba$_2$IrO$_4$ and to clarify further the similarities and differences with cuprates.
Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.
This chapter is dedicated to the rationalization of magnetic anisotropy in metal complexes. Analytical derivations allow one to predict the nature and magnitude of both the zero-field-splitting and the anisotropies of magnetic exchange. The first section is devoted to mononuclear complexes. It addresses the effect of spin–orbit coupling (SOC) in two different cases: (i) when the ground state is non-degenerate and a second-order SOC applies. The effect of the SOC can then be modeled by an energy splitting of the MS components of the ground spin state. Illustrations of the power of these analytical derivations for the rationalization of the ZFS of various complexes are presented; (ii) when the ground state is (almost) degenerate, a first-order SOC applies. A more sophisticated model is here derived which rationalizes the obtaining of a giant value of the ZFS in a Ni(II) complex. The second section is devoted to the derivation of multi-spin models for binuclear complexes. We will determine the physical content of both the symmetric and the antisymmetric exchange tensors in the case of two centers with spin S = 1/2. A peculiar derivation concerns the Dzyaloshinskii–Moriya (antisymmetric exchange) interaction in case of a local degeneracy of the orbitals and shows how the first-order SOC can generate giant values of this anisotropy of exchange. In the last subsection, we will show that the usual multi-spin model for spin S = 1 centers is not valid and derive an appropriate model involving a four-rank exchange tensor. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Sujets
NMR
Iridates
First-order spin–orbit coupling
Exchange and superexchange interactions
Covalency
Lanthanide
Complexes de métaux de transition
Décontamination de spin
Actinides
DOTA ligand
Electron paramagnetic resonance
Effective Hamiltonian theory
Spin-orbit coupling
Cooperative effect
Excitation energies
Ab initio calculation
AB-INITIO
Configuration interaction
Effets magnéto-résistifs
Bleaney's model
Magnetic susceptibility
FOS Physical sciences
MOLCAS calculations
Dzyaloshinskii–Moriya interaction
Determinants
Calculs ab initio
Isotropic and anisotropic exchange
Divalent cobalt
Magnetic Susceptibility
Electronic structure
Density functional theory
Calculs ab initio relativistes et corrélés
Crystal field theory
Modeling
Electron g-factor
Double exchange model
Hyperfine structure
Modèle de Bleaney
Metal-insulator transition
Magnetic anisotropy
Dynamical mean field theory
Diagonalisations exactes
High pressure
Heptacoordination
Free radicals
Magnetism
Electron spin
Spin-orbit interactions
Lanthanides
CLUSTERS
Excited states
Dzyaloshinskii-Moriya interaction
Magneto-resistive effects
Actinide
Bleaney
Bleaney's theory
Ligand-field theory
Electronic correlation
Heavy fermions
Coupled cluster calculations
Iridate
Ground states
Correlated relativistic ab initio calculations
Model hamiltonian
Wave functions
Luminescence
Magnétisme dans les systèmes organiques
Dynamical mean-field theory
Imidazolium salt
Ab initio calculations
MECHANISM
Manganites
Déplacements chimiques paramagnétiques
Electron paramagnetism
Crystal field parameters
Magnetism in organic systems
Hamiltonien modèle
Anisotropie magnétique
Magnetic properties
Iodine
Model Hamiltonians
Calcul ab initio
Crystal-field theory and spin Hamiltonians
Perturbation theory
Anderson mechanism
Disordered Systems and Neural Networks cond-matdis-nn
Relativistic corrections
Basis sets
MOLECULAR MAGNETIC-MATERIALS
MACROCYCLIC POLYARYLMETHYL POLYRADICALS
Hyperfine coupling
Finite nucleus effects
Model Hamiltonian derivation
Magnétisme moléculaire
HIGH-SPIN
Binuclear compounds
Configuration interactions
Ionic liquid
Exact diagonalization
Anisotropy