Analysis of the spin lattice model for the spin-gapped layered compounds Na(3)Cu(2)SbO(6) and Na(2)Cu(2)TeO(6) on the basis of electronic structure calculations

The spin lattice model for the spin-gapped layered magnetic solids Na3Cu2SbO6 and Na2Cu2TeO6 was examined by evaluating the three spin exchange interactions of their Cu2MO6 (M = Sb, Te) layers in terms of spin dimer analysis based on extended Hückel tight binding calculations and mapping analysis based on first principles density functional theory electronic band structure calculations. For both compounds, our calculations show that the two strongest spin exchange interactions, that is, the Cu-O...O-Cu super-superexchange (J2) and the Cu-O-Cu superexchange (J1) interactions, form alternating chains that interact weakly through the Cu-O-Cu superexchange (J3) interactions. The dominant one of the three spin exchange interactions is J2, and it is antiferromagnetic in agreement with the fact that both of the compounds are spin gapped. For Na3Cu2SbO6 and Na2Cu2TeO6, the superexchange J1 is calculated to be ferromagnetic, hence, leading to the alternating chain model in which antiferromagnetic and ferromagnetic spin exchange interactions alternate. This picture does not agree with the recent experimental analysis, which showed that the temperature-dependent magnetic susceptibilities of both compounds should be described by the alternating chain model in which two antiferromagnetic spin exchange interactions of different strengths alternate.     

Spin dimer analysis of the magnetic structures of Ba3Cr2O8, Ba3Mn2O8, Na4FeO4, and Ba2CoO4 with a three-dimensional network of isolated MO4 (M = Cr, Mn, Fe, Co) tetrahedra

The spin exchange interactions of the magnetic oxides Ba3Cr2O8, Ba3Mn2O8, Na4FeO4, and Ba2CoO4 with a three-dimensional network of isolated MO4 (M = Cr, Mn, Fe, Co) tetrahedra were examined by performing spin dimer analysis on the basis of tight-binding electronic structure calculations. Although the shortest O...O distances between adjacent MO4 tetrahedra are longer than the van der Waals distance, our analysis shows that the super-superexchange interactions between adjacent MO4 tetrahedra are substantial and determine the magnetic structures of these oxides. In agreement with experiment, our analysis predicts a weakly interacting isolated AFM dimer model for both Ba3Cr2O8 and Ba3Mn2O8, the (0.0, 0.5, 0.0) magnetic superstructure for Na4FeO4, the (0.5, 0.0, 0.5) magnetic superstructure for Ba2CoO4, and the presence of magnetic frustration in Ba2CoO4. The comparison of the intra- and interdimer spin exchange interactions of Ba3Cr2O8 and Ba3Mn2O8 indicates that orbital ordering should be present in Ba3Cr2O8.     

Determination of the spin-lattice relevant for the quaternary magnetic oxide Bi4Cu3V2O14 on the basis of tight-binding and density functional calculations

The quaternary magnetic oxide Bi4Cu3V2O14 consists of Cu4O8 triple chains made up of corner-sharing CuO4 square planes. To determine its spin-lattice, the spin exchange interactions of Bi4Cu3V2O14 were evaluated by performing a spin dimer analysis based on tight-binding calculations and a mapping analysis based on first principles density functional theory calculations. Both calculations show that the spin-lattice of Bi4Cu3V2O14 is not an antiferromagnetically coupled diamond chain, which results from an idealized view of the structure of the Cu4O8 triple chain and a neglect of super-superexchange interactions. The correct spin-lattice is an antiferromagnetic chain made up of antiferromagnetic linear trimers coupled through their midpoints via super-superexchange interaction, which predicts that Bi4Cu3V2O14 has an antiferromagnetic spin ground state and has no spin frustration, both in agreement with experiment.     

Investigation of the spin exchange interactions and magnetic Structures of the CrVO4-type transition metal phosphates,sulfates, and vanadates by spin dimer analysis

The CrVO(4)-type magnetic oxides MM'O(4) consist of edge-sharing MO(4) octahedral chains condensed with M'O(4) tetrahedra and exhibit a wide variety of magnetic structures. The magnetic properties of these oxides were examined by studying their spin exchange interactions on the basis of spin dimer analysis. The nature and magnitudes of the intra- and interchain spin exchange interactions depend on the square-to-rectangle distortion in the basal planes of the MO(4) chain and on the difference between the M 3d and O 2p orbital energies. The spiral magnetic structures of beta-CrPO(4) and MnSO(4) originate from the pseudohexagonal arrangement of the MO(4) chains and the frustrated interchain antiferromagnetic interactions.     

Interpretation of the magnetic structures of Cu2Te2O5X2 (X = Cl,Br) and Ca3.1Cu0.9RuO6 on the basis of electronic structure considerations: cases for strong super-superexchange interactions involving Cu2+ ions

For super-superexchange interactions between Cu(2+) ions, a qualitative rule was formulated to assess their strengths based on the geometrical parameters of the exchange paths. Spin dimer analysis was carried out for Cu(2)Te(2)O(5)X(2) (X = Cl, Br) and Ca(3.1)Cu(0.9)RuO(6) to evaluate the relative strengths of their superexchange and super-superexchange interactions. The strongest antiferromagnetic interactions in Cu(2)Te(2)O(5)X(2) (X = Cl, Br) are given by the super-superexchange interactions involving the most linear Cu-X.X-Cu paths between tetrahedral clusters Cu(4)O(8)X(4) along the (a +/- b)-directions. The adjacent CuRuO(6) chains of Ca(3.1)Cu(0.9)RuO(6) are antiferromagnetically coupled through the most linear Cu-O.O-Cu paths along the direction perpendicular to the plane of the CuRu zigzag chain. The spin lattices of Cu(2)Te(2)O(5)X(2) and Ca(3.1)Cu(0.9)RuO(6) deduced from our spin dimer analysis are consistent with the available magnetic data. The spin lattice of a magnetic solid should be determined on the basis of appropriate electronic structure considerations.     

Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels

Low-energy excitation energies of a magnetic solid with localized spins are probed by magnetic susceptibility, neutron scattering and Raman scattering measurements, and are analyzed using a spin Hamiltonian with a set of spin exchange parameters. The nature and values of the spin exchange parameters deduced from this analysis depend on what spin exchange paths one includes in the spin Hamiltonian. In this article, we review how spin exchange interactions of magnetic solids with localized spins are described on formal, quantitative and qualitative theoretical levels, investigate antisymmetric and anisotropic interactions for general spin dimers, and discuss the spin exchange interactions and magnetic structures of various extended magnetic solids on the basis of spin dimer analysis. Strongly interacting spin exchange paths of a magnetic solid are determined by the overlap between its magnetic orbitals, so that the strongly interacting spin unit of a magnetic solid does not necessarily have the same geometrical feature as does the arrangement of its magnetic ions or spin-carrying molecules. Therefore, in interpreting results of magnetic susceptibility, inelastic neutron scattering or Raman scattering measurements, it is essential to employ a set of spin exchange parameters chosen on the basis of proper electronic structure considerations. Spin dimer analyses based on extended Hückel tight binding calculations provide a reliable and expedient means to study the relative strengths of superexchange and super-superexchange spin exchange interactions.     

Importance of the O-M-O bridges (M = V5+, Mo6+) for the spin-exchange interactions in the magnetic oxides of Cu2+ ions bridged by MO4 tetrahedra: spin-lattice models of Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28

The spin-lattice models relevant for the magnetic oxides Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28 were determined by evaluating the relative strengths of the spin-exchange interactions between their Cu2+ ions on the basis of spin dimer analysis. Our study shows that the O-M-O bridges (M = V5+, Mo6+) between the magnetic ions Cu2+, provided by the MO4 tetrahedra, are crucial for the spin-exchange interactions and hence for deducing the spin-lattice models needed to interpret the magnetic properties of these oxides. The spin-lattice model of Rb2Cu2(MoO4)3 is not a uniform chain but two interpenetrating spin ladders that interact weakly with geometric spin frustration. The spin-lattice model of BaCu2V2O8 is an alternating chain as expected, but the spin-exchange paths responsible for it differ from those expected. With respect to the strongest spin exchange of BaCu2V2O8, the spin exchange of KBa3Ca4Cu3V7O28 is only slightly weaker, but the strongest spin exchange of Rb2Cu2(MoO4)3 is much weaker. This difference in the spin-exchange strengths is caused by the difference in the bridging modes of the MO4 tetrahedra leading to these spin-exchange interactions.     

Spin dimer and classical spin analyses of the ordered magnetic structures of alkali iron pyrophosphates NaFeP(2)O(7) and LiFeP(2)O(7)

The magnetic oxides NaFeP(2)O(7) and LiFeP(2)O(7), made up of FeO(6) octahedra containing high-spin Fe(3+)(d(5)) ions, undergo a three-dimensional antiferromagnetic ordering at low temperatures. The strengths of various Fe-O...O-Fe super-superexchange interactions of NaFeP(2)O(7) and LiFeP(2)O(7) were estimated on the basis of spin dimer analysis to probe the nature of their ordered magnetic structures. It is found that the critical factor governing the strength of a Fe-O...O-Fe super-superexchange interaction is not the Fe...Fe distance but the O...O distance. Using the spin exchange parameters thus obtained, the total spin exchange interaction energies were calculated for various ordered spin arrangements of NaFeP(2)O(7) and LiFeP(2)O(7) on the basis of classical spin analysis to confirm that the observed magnetic structures are the magnetic ground states.     

Spin dimer analysis of the anisotropic spin exchange interactions in the distorted wolframite-type oxides CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4

The distorted wolframite-type oxides CuWO4 and CuMoO4-III have a structure in which CuO4 zigzag chains, made up of cis-edge-sharing CuO6 octahedra, run along the c-direction and hence exhibit low-dimensional magnetic properties. We examined the magnetic structures of these compounds and their isostructural analogue Cu(Mo(0.25)W0.75)O4 on the basis of the spin-orbital interaction energies calculated for their spin dimers. Our study shows that these compounds consist of two-dimensional (2D) magnetic sheets defined by one superexchange (intrachain Cu-O-Cu) and three super-superexchange (interchain Cu-O.O-Cu) paths, the strongly interacting spin units of these 2D magnetic sheets are the two-leg antiferromagnetic (AFM) ladder chains running along the (a + c)-direction, and the spin arrangement between adjacent AFM ladder chains leads to spin frustration. The similarities and differences in the magnetic structures of CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4 were discussed by examining how adjacent AFM ladder chains are coupled via the superexchange paths in the 2D magnetic sheets and how adjacent 2D magnetic sheets are coupled via another superexchange paths along the c-direction. Our study reproduces the experimental finding that the magnetic unit cell is doubled along the a-axis in CuWO(4) and along the c-axis in CuMoO4-III and predicts that the magnetic unit cell should be doubled along the a- and b-axes in Cu(Mo(0.25)W0.75)O4. In the understanding of the strength of a super-superexchange interaction, the importance of the geometrical factors controlling the overlap between the tails of magnetic orbitals was pointed out.     

Comparison of the crystal structures and magnetic properties of the low- and high-temperature forms of AgCuPO4: crystal structure determination, magnetic susceptibility measurements, and spin dimer analysis

The crystal structure of the low-temperature form of AgCuPO4 (i.e., alpha-AgCuPO4) was determined by powder X-ray diffraction and was compared with that of the high-temperature form of AgCuPO4 (i.e., beta-AgCuPO4). The magnetic properties of the two forms were examined by measuring their magnetic susceptibilities and evaluating the relative strengths of their spin-exchange interactions on the basis of spin-dimer analysis. Both forms of AgCuPO4 have layers of Cu2P2O8 alternating with silver-atom double layers; beta-AgCuPO4 has two Cu2P2O8 layers per unit cell, while alpha-AgCuPO4 has one. The coordinate environment of each Cu2+ ion is close to being a distorted square pyramid in alpha-AgCuPO4, but it is close to being a distorted trigonal bipyramid in beta-AgCuPO4. The magnetic susceptibilities of alpha- and beta-AgCuPO4 are well simulated by an antiferromagnetic alternating-chain model, which leads to J/k(B) = -146.1 K and alphaJ/k(B) = -75.8 K for alpha-AgCuPO4, and J/k(B) = -82.6 K and alphaJ/k(B) = -31.7 K for beta-AgCuPO4 (with the convention in which the spin-exchange parameter between two adjacent spin sites is written as 2J). The spin gaps, delta/k(B), obtained from these parameters are 93.7 K for alpha-AgCuPO4 and 62.3 K for beta-AgCuPO4. The strongest spin exchange in both forms of AgCuPO4 comes from a super-superexchange path, and this interaction is stronger for alpha-AgCuPO4 than for beta-AgCuPO4 by a factor of approximately 2, in good agreement with the experiment. Our analysis supports the use of this model for beta-AgCuPO4 and indicates that the spin lattice of alpha-AgCuPO4 would be better described by a two-dimensional net made up of weakly interacting alternating chains.     

On the nature of the spin frustration in the CuO2 ribbon chains of LiCuVO4: crystal structure determination at 1.6 K, magnetic susceptibility analysis, and density functional evaluation of the spin exchange constants

The spin-1/2 Cu(2+) ions of LiCuVO(4) form one-dimensional chains along the b direction, and the spin frustration in LiCuVO(4) is described in terms of the nearest-neighbor ferromagnetic exchange J(1) and the next-nearest-neighbor antiferromagnetic exchange J(2) in these chains. Recently, it has become controversial whether or not J(1) is stronger in magnitude than J(2). To resolve this controversy, we determined the crystal structure of LiCuVO(4) at 1.6 K by neutron diffraction, analyzed the magnetic susceptibility of LiCuVO(4) to deduce the Curie-Weiss temperature θ and the J(2)/J(1) ratio, and finally extracted the spin exchange constants of LiCuVO(4) on the basis of density functional calculations. Our work shows unambiguously that the Curie-Weiss temperature θ of LiCuVO(4) is negative in the range of -20 K, so that J(2) is substantially stronger in magnitude than J(1).     

Synthesis and Characterization of the Crystal Structure and Magnetic Properties of the New Fluorophosphate LiNaCo[PO(4)]F

The new compound LiNaCo[PO(4)]F was synthesized by a solid state reaction route, and its crystal structure was determined by single-crystal X-ray diffraction measurements. The magnetic properties of LiNaCo[PO(4)]F were characterized by magnetic susceptibility, specific heat, and neutron powder diffraction measurements and also by density functional calculations. LiNaCo[PO(4)]F crystallizes with orthorhombic symmetry, space group Pnma, with a = 10.9334(6), b = 6.2934(11), c = 11.3556(10) ?, and Z = 8. The structure consists of edge-sharing CoO(4)F(2) octahedra forming CoFO(3) chains running along the b axis. These chains are interlinked by PO(4) tetrahedra forming a three-dimensional framework with the tunnels and the cavities filled by the well-ordered sodium and lithium atoms, respectively. The magnetic susceptibility follows the Curie-Weiss behavior above 60 K with θ = -21 K. The specific heat and magnetization measurements show that LiNaCo[PO(4)]F undergoes a three-dimensional magnetic ordering at T(mag) = 10.2(5) K. The neutron powder diffraction measurements at 3 K show that the spins in each CoFO(3) chain along the b-direction are ferromagnetically coupled, while these FM chains are antiferromagnetically coupled along the a-direction but have a noncollinear arrangement along the c-direction. The noncollinear spin arrangement implies the presence of spin conflict along the c-direction. The observed magnetic structures are well explained by the spin exchange constants determined from density functional calculations.     

Crystal-packing-induced antiferromagnetic interactions of metallocenes: cyanonickelocenes, -cobaltocenes, and -ferrocenes

The cyano-substituted metallocenes [M(C5H4CN)2] (M=Fe, 1; Co, 2; Ni 3) and [M(C5Me5)(C5H4CN)] (M=Fe, 4; Co, 5; Ni, 6) were synthesized in yields up to 58 % by treating K(C5H4CN) or Tl(C5H4CN) with suitable transition-metal precursors. Cyclic voltammetry indicated that the oxidation and reduction potentials of all the cyanometallocenes were shifted to positive values by up to 0.8 V. Single-crystal X-ray structure analysis showed that 1 had eclipsed ligands, formed planes in the lattice, and--unlike usual metallocenes--lined up in stacks perpendicular to these planes. Powder X-ray studies established that 1 and 2 are isotypic. The 1H and 13C NMR spectra were recorded for all the new compounds. Signal shifts of up to delta=1500 ppm were recorded for the paramagnetic molecules 2 and 3 and were, at a given temperature, strikingly different for solution and solid-state spectra. These results pointed to antiferromagnetic interactions as a consequence of molecular ordering in the lattice, as confirmed by magnetic measurements. The temperature-dependent susceptibilities were reproduced by Heisenberg spin-chain models (H=-J sum n- 1 i=1 SiSi+1), thus yielding J=-28.3 and -10.3 cm(-1) for 2 and 3, respectively, whereas J=-11.8 cm(-1) was obtained for 3 from the Ising spin-chain model. In accordance with molecular orbital (MO) considerations, much spin density was found to be delocalized not only on the cyclopentadienyl ligand but also the cyano substituents. The magnetic interaction was interpreted as a Heitler-London spin exchange and was analyzed based on how the interaction depends on the singly occupied MOs and the shift of parallel metallocenes relative to each other.     

Flux growth of vanadyl pyrophosphate, (VO)(2)P(2)O(7), and spin dimer analysis of the spin exchange interactions of (VO)(2)P(2)O(7) and vanadyl hydrogen phosphate,VO(HPO(4)).0.5H(2)O

Large transparent blue crystals of vanadyl pyrophosphate, (VO)(2)P(2)O(7), were grown from a phosphorus pentoxide flux, and the single-crystal X-ray structure of (VO)(2)P(2)O(7) was determined with high precision. On the basis of spin dimer analysis, we examined the spin exchange interactions of (VO)(2)P(2)O(7) and its precursor VO(HPO(4)).0.5H(2)O. Our analysis of (VO)(2)P(2)O(7) using two high-precision crystal structures shows unambiguously that the V3-V4 chain has a larger spin gap than does the V1-V2 chain and that the super-superexchange (V-O...O-V) interaction is stronger than the superexchange (V-O-V) interaction in the V3-V4 chain while the opposite is true in the V1-V2 chain. Our analysis of VO(HPO(4)).0.5H(2)O reveals that the superexchange interaction must dominate over the super-superexchange interaction, in disagreement with the conclusion from a powder neutron scattering study of VO(DPO(4)).0.5D(2)O.     

Density functional analysis of the spin exchange interactions and charge order patterns in the layered magnetic oxides YBaM2O5 (M = Mn, Fe, Co)

The spin and charge order phenomena of the layered magnetic oxides YBaM(2)O(5) (M = Mn, Fe, Co) were analyzed on the basis of density functional calculations. We evaluated the spin exchange interactions of YBaM(2)O(5) by performing energy-mapping analysis based on density functional calculations to find why they undergo a three-dimensional magnetic ordering at high temperature. We estimated the relative stabilities of the checkerboard and stripe charge order patterns of YBaM(2)O(5) (M = Mn, Fe, Co) by optimizing their structures with density functional calculations to probe if the nature of the charge order pattern depends on whether their transition-metal ions are Jahn-Teller active.     

Theoretical investigation of the magnetic interactions of Ni9 complexes

On the basis of density-functional theory (DFT) calculations, a theoretical analysis of the exchange interactions in Ni9L2(O2CMe)8{(2-py)2CO2}4, was performed, where L is a bridging ligand, OH- (1) or N3- (2). Each magnetic interaction between the Ni spin centers is analyzed for 1 and 2 in terms of exchange integrals (J values), orbital overlap integrals (T values) and natural orbitals. It was found that a J3 interaction, which is a magnetic interaction via the bridging ligand orbitals, mainly controls the whole magnetic properties, and the dominant interaction is a sigma-type orbital interaction between Ni dz2 orbitals. Further investigations on the magnetostructural correlations are performed on the J3 interactions using simplest Ni-L-Ni models. These models reproduced the magnetic interactions qualitatively well not only for the Ni9 complexes but also for other inorganic complexes. Strong correlations have been found between the magnetic orbital overlaps (T values) and the Ni-L-Ni angle. These results revealed that the difference of the magnetic properties between OH- and N3- is caused by the orbital overlap integral (T values) of the sigma-type J3 interaction pathway. The magnetic interactions are also discussed from a Hubbard model by evaluating the transfer integral (t) and on-site Coulomb integrals (U), in relation to the Heisenberg picture.     

Synthesis, crystal structure, magnetic properties, and electronic structure of the new ternary vanadate CuMnVO4

A new magnetic oxide, CuMnVO4, was prepared, and its crystal structure was determined by single-crystal X-ray diffraction. The magnetic properties of CuMnVO4 were characterized by magnetic susceptibility and specific heat measurements, and the spin exchange interactions of CuMnVO4 were analyzed on the basis of spin-polarized electronic band structure calculations. CuMnVO4 contains MnO4 chains made up of edge-sharing MnO6 octahedra containing high-spin Mn2+ cations. Our work shows that CuMnVO4 undergoes a three-dimensional antiferromagnetic transition at approximately 20 K. Both the intrachain and interchain spin exchanges are antiferromagnetic, and the interchain spin exchange is not negligible compared to the intrachain spin exchange.     

Magnetic exchange couplings in the single-molecule magnet of Mn(12)-Ac

Four types of isotropic exchange interactions of Mn(12)-Ac are obtained by using the classical Monte Carlo simulations. The equilibrium susceptibilities are well reproduced in the temperature range between 10 and 100 K. The calculated effective spin at 0.1 K coincides with the ground-state spin. Our results show that J(1) and J(2) are strong antiferromagnetic, but the magnitude of J(2) is much smaller than that of J(1). Both J(3) and J(4) favor weakly antiferromagnetic couplings. The effects of the exchange couplings on the magnetic properties and ground-state spin are investigated too. The magnetic susceptibilities below 100 K depend more on J(2) rather than on the stronger J(1). The weak exchange couplings J(3) and J(4) have significant frustration effects on the ground-state configuration.     

Density functional theory analysis of the interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in Ca3CoMO6 (M = Co, Rh, Ir)

In the isostructural oxides Ca(3)CoMO(6) (M = Co, Rh, Ir), the CoMO(6) chains made up of face-sharing CoO(6) trigonal prisms and MO(6) octahedra are separated by Ca atoms. We analyzed the magnetic and electronic properties of these oxides on the basis of density functional theory calculations including on-site repulsion and spin-orbit coupling, and examined the essential one-electron pictures hidden behind results of these calculations. Our analysis reveals an intimate interplay between Jahn-Teller instability, uniaxial magnetism, spin arrangement, metal-metal interaction, and spin-orbit coupling in governing the magnetic and electronic properties of these oxides. These oxides undergo a Jahn-Teller distortion, but their distortions are weak, so that their trigonal-prism Co(n+) (n = 2, 3) ions still give rise to strong easy-axis anisotropy along the chain direction. As for the d-state split pattern of these ions, the electronic and magnetic properties of Ca(3)CoMO(6) (M = Co, Rh, Ir) are consistent with d(0) < (d(2), d(-2)) < (d(1), d(-1)) but not with (d(2), d(-2)) < d(0) < (d(1), d(-1)). The trigonal-prism Co(3+) ion in Ca(3)Co(2)O(6) has the L = 2 configuration (d(0))(1)(d(2), d(-2))(3)(d(1), d(-1))(2) because of the metal-metal interaction between adjacent Co(3+) ions in each Co(2)O(6) chain, which is mediated by their z(2) orbitals, and the spin-orbit coupling of the trigonal-prism Co(3+) ion. The spins in each CoMO(6) chain of Ca(3)CoMO(6) prefer the ferromagnetic arrangement for M = Co and Rh but the antiferromagnetic arrangement for M = Ir. The octahedral M(4+) ion of Ca(3)CoMO(6) has the (1a)(1)(1e)(4) configuration for M = Rh but the (1a)(2)(1e)(3) configuration for M = Ir, which arises from the difference in the spin-orbit coupling of the M(4+) ions and the Co···M metal-metal interactions.     

Molecular tailoring and prediction of strongly ferromagnetically coupled trimethylenemethane-based nitroxide diradicals

We have investigated the magnetic properties of four recently synthesized stable TMM-type nitroxide diradicals. Four new diradicals are proposed by tailoring one of the species in such a way that both conjugation and planarity increase. As a remarkable consequence, the intramolecular ferromagnetic exchange interaction was found to be quite high in the proposed radicals. The calculated coupling constants were in the range of +102 to +140 cm-1. The MO and spin density analysis are provided to interpret the exchange interactions. We observed the existence of intramolecular pi-pi-interactions for the species 2. This slightly increased the J value by shortening the length of the spacer between the two spin sources.