Exchange Interaction in Binuclear Complexes with Rare Earth and Copper Ions: A Many-Body Model Study

We have used a many-body model Hamiltonian to study the nature of the magnetic ground state of hetero-binuclear complexes involving rare-earth and copper ions. We have taken into account all diagonal repulsions involving the rare-earth 4f and 5d orbitals and the copper 3d orbital. Besides, we have included direct exchange interaction, crystal field splitting of the rare-earth atomic levels and spin-orbit interaction in the 4f orbitals. We have identified the inter-orbital $4f$ repulsion, U$_{ff}$ and crystal field parameter, $\Delta_f$ as the key parameters involved in controlling the type of exchange interaction between the rare earth $4f$ and copper 3d spins. We have explored the nature of the ground state in the parameter space of U$_{ff}$, $\Delta_f$, spin-orbit interaction strength $\lambda$ and the $4f$ filling n$_f$. We find that these systems show low-spin or high-spin ground state depending on the filling of the $4f$ levels of the rare-earth ion and ground state spin is critically dependent on U$_{ff}$ and $\Delta_f$. In case of half-filling (Gd(III)) we find a reentrant low-spin state as U$_{ff}$ is increased, for small values of $\Delta_f$, which explains the recently reported apparent anomalous anti-ferromagnetic behaviour of Gd(III)-radical complexes. By varying U$_{ff}$ we also observe a switch over in the ground state spin for other fillings . We have introduced a spin-orbit coupling scheme which goes beyond L-S or j-j coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.Comment: 22 pages, 11 ps figure

Theoretical study of spin interactions in stacked acetylene radical ions

The search for organic ferromagnets has so far focused on radical ions of cyclic conjugated systems which have a doubly degenerate highest-occupied molecular orbital. However, recent theoretical studies on dimers of such systems have shown that the ground state is a singlet and not a triplet as expected. In this paper, we demonstrate that an acetylenic radical ion system possesses a high-spin ground state which is stable with respect to different geometries of packing and substitutions. The stability of the high-spin state is attributed to the degeneracy of the atomic orbitals involved in conjugation. We suggest that these systems are prime candidates for observing organic ferromagnetism

Direct versus kinetic exchange in multiband models for organic ferromagnetism

Multiband Hubbard and Pariser-Parr-Pople calculations have been carried out on mixed donor-acceptor (DA) stacks with doubly degenerate acceptor orbitals and nondegenerate donor orbitals at two-thirds filling. Model exact results for 2, 3, and 4 DA units show that McConnell's prediction of high-spin ground states in these systems is, in general, incorrect. The larger phase space available for the low-spin states leads to their kinetic stabilization in preference to high-spin states. However, for large electron-correlation strengths, the direct exchange dominates over the kinetic exchange resulting in a high-spin ground stat

A theoretical study of spin excitations in [ 2,2 ] -paracyclophane skeleton substituted with two dicarbene units

The different spin states in pseudo-ortho-, pseudo-meta- and pseudo-para-dicarbene substituted [2,2]-paracyclophanes have been studied using a Heisenberg spin model. The ground state is always a quintet in pseudo-ortho and -para isomers and the lowest energy spin excitation is to a triplet state while the pseudo-meta isomer possesses a singlet ground state. The spin densities in the quintet states are provided to enable an estimate of the exchange constants from ESR studies. Our studies confirm the possibility of obtaining high-spin molecules and eventually an organic ferromagnet in one-dimension as proposed by McConnell

Optical and magnetic properties of the exact PPP states of biphenyl

The low-lying singlets and triplets of biphenyl are obtained exactly within the PPP model using the diagrammatic valence bond method. The energy gaps within the singlet manifold as well as the lowest singlet-triplet gap are found to be in good agreement with experimental results. The two weak absorptions between 4·1 and 4·2 eV reported experimentally are attributed to the two states lying below the optical gap that become weakly allowed on breaking electron-hole and inversion symmetries. The observed blue shift of the spectral lines, attributed to a change in dihedral angle, on going from crystalline to solution to vapour phase is also well reproduced within the PPP model. The bond orders show that the ground singlet state is benzenoidal while the dipole excited state as well as the lowest triplet state are quinonoidal and planar. Comparison with the experimental spin densities and the fine structure constants D and E in the triplet state point to slightly weaker correlations than assumed by the PPP model. The introduction of a 1-8 bond to mimic poly(paraphenylene)s gives an optical gap that is in good agreement with experiment

Stability of the high-spin ground state in alternant π\pi-conjugated organic molecules

Alternant quantum cell models with unequal numbers of atoms on the two sublattices have been predicted to have a high-spin ground state. In this paper, we examine the stability of this high-spin ground state with respect to breaking the alternancy symmetry and distortion of the backbone conjugation. We find that in the Pariser-Parr-Pople (PPP) models and the Hubbard models with weak correlations, the ground state continues to be the high-spin state, even when alternancy symmetry is broken by introducing large site-energy differences. In the Hubbard model, for strong correlation strengths, the ground state switches from a high-spin to a low-spin state when large site-energy differences are introduced. The bond-order calculations in all these models shows that the low-spin state is susceptible to dimerization of the backbone. In the distorted chains, the low-spin state stabilizes to a greater extent leading to low-spin ground states at least in ‘‘soft’’ lattices. However, experience with one-dimensional systems suggests that the lattice distortion could occur unconditionally leading to low-spin ground state in infinitely long polymers. Thus, realization of organic ferromagnetics via high-spin polymers could be elusive

Stability of the high-spin ground state in alternant π-conjugated organic molecules

Alternant quantum cell models with unequal numbers of atoms on the two sublattices have been predicted to have a high-spin ground state. In this paper, we examine the stability of this high-spin ground state with respect to breaking the alternancy symmetry and distortion of the backbone conjugation. We find that in the Pariser-Parr-Pople (PPP) models and the Hubbard models with weak correlations, the ground state continues to be the high-spin state, even when alternancy symmetry is broken by introducing large site-energy differences. In the Hubbard model, for strong correlation strengths, the ground state switches from a high-spin to a low-spin state when large site-energy differences are introduced. The bond-order calculations in all these models shows that the low-spin state is susceptible to dimerization of the backbone. In the distorted chains, the low-spin state stabilizes to a greater extent leading to low-spin ground states at least in "soft" lattices. However, experience with one-dimensional systems suggests that the lattice distortion could occur unconditionally leading to low-spin ground state in infinitely long polymers. Thus, realization of organic ferromagnetics via high-spin polymers could be elusive

Theoretical studies of the spin states of macrocyclic aza-amido binuclear copper (II) complexes

The spin and charge excitation gaps and charge and spin density distributions have been studied in macrocyclic binuclear aza-amido copper (II) complexes employing a model Hamiltonian. The spin gaps depend on the σ-orbital occupancies, and for small gaps, the exchange integral between the σ orbitals of the bridging oxygen atoms, KOO, which is sensitive to geometry, determines the low-lying spin excitations. The singlet—singlet gaps also depend upon the σ-orbital occupancy but are weakly dependent upon KOO

Diagrammatic valence bond studies on hemocyanin

The Diagrammatic Valence Bond studies on the active sites of hemocyanin, consisting of two Cu(I) ions and an oxygen molecule, are performed to find out the stable geometrical pattern and electronic structure. Different parameters used in this theoretical approach are taken from existing literature on high T-c superconductors. Attempts have been made to find out the differences in electronic structure of [Cu2O2](+2) and [Cu2O2N4](+2) as it is observed that coordination of nitrogen ligand do affect electronic structure i.e. spin excitation gaps and charge and spin density distribution. A comparison of our results with earlier theoretical results are also presented

Diagrammatic valence bond studies on hemocyanin

The Diagrammatic Valence Bond studies on the active sites of hemocyanin, consisting of two Cu(I) ions and an oxygen molecule, are performed to find out the stable geometrical pattern and electronic structure. Different parameters used in this theoretical approach are taken from existing literature on high Tc superconductors. Attempts have been made to find out the differences in electronic structure of [Cu2O2]+2 and [Cu2O2N4]+2 as it is observed that coordination of nitrogen ligand do affect electronic structure i.e. spin excitation gaps and charge and spin density distribution. A comparison of our results with earlier theoretical results are also presented