Theoretical study on spin alignments in ferromagnetic heterospin chains with competing exchange interactions: a generalized ferrimagnetic system containing organic biradicals in the singlet ground state

Spin alignments in heterospin chains are examined from numerical calculations of model spin Hamiltonians. The Hamiltonians of the heterospin chains mimic an open-shell molecular assemblage composed of an organic biradical in a singlet (S = 0) ground state and a doublet (S = 1/2) monoradical, which are coupled by intermolecular ferromagnetic exchange interactions. It is found from numerical calculations of the spin Hamiltonians that the spin value S2 of the ground-state singlet biradical embedded in the exchange-coupled assemblage deviates from zero and contributes to the bulk magnetization. The alternating chain is found to have two kinds of ground spin states, a high- and a low-spin state. All the spins are parallel to each other in the high-spin state, which is characterized by the spin correlation function of (S(i).S(j)) = 0.25. On the other hand, the spin alignment in the low-spin state is found to be dependent on the topology of the intermolecular exchange interactions. The energy preference of the two states depends on the relative amplitude of the exchange interactions in the chain. The intermolecular ferromagnetic couplings are competing in the ground-state singlet biradical with the intramolecular antiferromagnetic interaction. The appearance of the two kinds of ground states is attributed to a quantum spin frustration effect inherent in the triangular motif of the competing interactions. Magnetic properties of a zigzag chain complex composed of a nitronyl nitroxide biradical with a singlet ground state and Cu(hfac)2 are examined on the basis of the theoretical calculations. The vanishing magnetic moments, or the product of susceptibility and temperature chiT, at low temperatures observed for the complex are consistent with those of the low-spin state predicted in the theoretical calculations.     

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.     

Triradical cation of p-phenylenediamine having two nitroxide radical groups: spin alignment mediated by delocalized spin

The cationic state of a p-phenylenediamine (PDA) molecule having two nitroxide radical groups was prepared and characterized using electrochemical, electron spin resonance (ESR) spectroscopic, and absorption spectroscopic methods. The delocalized intervalence state of the p-phenylendiamine (PDA) moiety was detected in the cationic state. From the pulsed ESR measurements, it was confirmed that the delocalized spin induces parallel spin alignment between the localized two nitroxide groups which are magnetically weakly coupled in the neutral state. It was found that the resulting high-spin alignment does not seriously affect the delocalized intervalence state of the PDA radical cation.     

Maximum Spin Polarization in Chromium Dimer Cations as Demonstrated by X‐ray Magnetic Circular Dichroism Spectroscopy

X‐ray magnetic circular dichroism spectroscopy has been used to characterize the electronic structure and magnetic moment of Cr₂⁺. Our results indicate that the removal of a single electron from the 4sσ_g bonding orbital of Cr₂ drastically changes the preferred coupling of the 3d electronic spins. While the neutral molecule has a zero‐spin ground state with a very short bond length, the molecular cation exhibits a ferromagnetically coupled ground state with the highest possible spin of S=11/2, and almost twice the bond length of the neutral molecule. This spin configuration can be interpreted as a result of indirect exchange coupling between the 3d electrons of the two atoms that is mediated by the single 4s electron through a strong intraatomic 3d‐4s exchange interaction. Our finding allows an estimate of the relative energies of two states that are often discussed as ground‐state candidates, the ferromagnetically coupled ¹²Σ and the low‐spin ²Σ state.     

High resolution NMR study of T1 magnetic relaxation dispersion. II. Influence of spin-spin couplings on the longitudinal spin relaxation dispersion in multispin systems

Effects of scalar spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of coupled multispin systems were analyzed. Taking spin systems of increasing complexity we demonstrated pronounced influence of the intramolecular spin-spin couplings on the NMRD of protons. First, at low magnetic fields where there is strong coupling of spins the apparent relaxation times of the coupled spins become equal. Second, there are new features, which appear at the positions of the nuclear spin level anticrossings. Finally, in coupled spin systems there can be a coherent contribution to the relaxation kinetics present at low magnetic fields. All these peculiarities caused by spin-spin interactions are superimposed on the features in NMRD, which are conditioned by changes of the motional regime. Neglecting the effects of couplings may lead to misinterpretation of the NMRD curves and significant errors in determining the correlation times of molecular motion. Experimental results presented are in good agreement with theoretical calculations.     

Antiferromagnetic interactions in the quarter-filled organic conductor (EDO-TTF)2PF6

The ground state electronic structure of the high-temperature (HT) and the low-temperature (LT) phases of (EDO-TTF)(2)PF(6) is investigated using the embedded cluster approach in combination with the density functional method designed to describe the strong non-dynamic electron correlation. It is found that, in the HT phase, the unpaired electron spins located on pairs of neighbouring EDO-TTF molecules are antiferromagnetically coupled along the stacking direction with the Heisenberg exchange integral J = -655 cm(-1). In the LT phase, the unpaired spins located on the cationic EDO-TTF molecules are coupled antiferromagnetically with J values strongly alternating along the stacking axis of the crystal thus rendering it diamagnetic. The parameters of the extended Hubbard model are evaluated and the conductance properties of the two phases are estimated using these parameters. It is suggested to investigate the charge and spin excitations in the two phases of (EDO-TTF)(2)PF(6) with the use of angle-resolved photoemission spectroscopy.     

Analysis of the spin exchange interactions and the ordered magnetic structures of lithium transition metal phosphates LiMPO4 (M = Mn, Fe, Co, Ni) with the olivine structure

The olivine-type compounds LiMPO4 (M = Mn, Fe, Co, Ni) consist of MO4 layers made up of corner-sharing MO6 octahedra of high-spin M2+ ions. To gain insight into the magnetic properties of these phosphates, their spin exchange interactions were estimated by spin dimer analysis using tight binding calculations and by electronic band structure analysis using first principles density functional theory calculations. Three spin exchange interactions were found to be important for LiMPO4, namely, the intralayer superexchange J1, the intralayer super-superexchange Jb along the b-direction, and the interlayer super-superexchange J2 along the b-direction. The magnetic ground state of LiMPO4 was determined in terms of these spin exchange interactions by calculating the total spin exchange interaction energy under the classical spin approximation. In the spin lattice of LiMPO4, the two-dimensional antiferromagnetic planes defined by the spin exchange J1 are antiferromagnetically coupled by the spin exchange J2, in agreement with available experimental data.     

Effects of Edge Oxidation on the Stability and Half‐Metallicity of Graphene Quantum Dots

A comprehensive first‐principles theoretical study of the electronic properties and half‐metallic nature of zigzag edge‐oxidized graphene quantum dots (GQDs) is carried out by using density functional theory (DFT) with the screened exchange hybrid functional of Heyd, Scuseria and Ernzerhof (HSE06). The oxidation schemes include ‐OH, ‐COOH and ‐COO groups. We identify oxidized GQDs whose opposite spins are localized at the two zigzag edges in an antiferromagnetic‐type configuration, showing a spin‐polarized ground state. Oxidized GQDs are more stable than the corresponding fully hydrogenated GQDs. The partially hydroxylated and carboxylated GQDs with the same size exhibit half‐metallic state under almost the same electric‐field intensity whereas fully oxidized GQDs behave as spin‐selective semiconductors. The electric‐field intensity inducing the half metal increases with the length of the partially oxidized GQDs, ranging from M=4 to 7.     

pi-topology and spin alignment utilizing the excited molecular field: observation of the excited high-spin quartet (S = 3/2) and quintet (S = 2) states on purely organic pi-conjugated spin systems.

As a model system for the photoinduced/photoswitched spin alignment in a purely organic pi-conjugated spin system, 9-[4-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (1a), 9-[3-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (1b), 9,10-bis[4-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (2a), and 9,10-bis[3-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (2b) were designed and synthesized. In these spin systems, 9-phenylanthracene and 9,10-diphenylanthracene were chosen as photo spin couplers and iminonitroxide was chosen as a dangling stable radical. Time-resolved electron spin resonance (TRESR) spectra of the first excited states with resolved fine-structure splittings were observed for 1a and 2a in an EPA or a 2-MTHF rigid glass matrix. Using the spectral simulation based on the eigenfield method, the observed TRESR spectra for 1a and 2a were unambiguously assigned as an excited quartet (S = 3/2) spin state (Q) and an excited quintet (S = 2) spin state (Qu), respectively. The g value and fine-structure splitting for the quartet state of 1a were determined to be g(Q) = 2.0043, D(Q) = 0.0235 cm(-1), and E(Q) = 0.0 cm(-1). The relative populations (polarization) of each M(S)() sublevel in Q were determined to be P(+1/2') = P(-1/2') = 0.5 and P(+3/2') = P(-3/2') = 0.0 with an increasing order of energy in zero magnetic field. The spin Hamiltonian parameters for Qu are g = 2.0043, D = 0.0130 cm(-1), and E = 0.0 cm(-1), and the relative populations in Qu were determined to be P(0') = 0.30, P(-1') = P(+1') = 0.35 and P(-2') = P(+2') = 0.0. These are the first observations of a photoexcited quartet and a quintet high-spin state in pi-conjugated triplet-radical pair systems. In contrast high-spin excited states were not observed for 1b and 2b, the pi-topological isomers of 1a and 2a, showing the role of pi-topology in the spin alignment of the excited states. Since a weak antiferromagnetic exchange interaction was observed in the ground state of 2a, the clear detection of the excited quintet high-spin state shows that the effective exchange coupling between the two dangling radicals through the diphenylanthracene spin coupler has been changed from antiferromagnetic to ferromagnetic upon photoexcitation. Thus, a photoinduced spin alignment utilizing the excited triplet molecular field was realized for the first time in the purely organic pi-conjugated spin system. Furthermore, the mechanism for the generation of dynamic electron spin polarization was investigated for the observed quartet and quintet states, and a plausible mechanism of the enhanced selective intersystem crossing was proposed. Ab initio molecular orbital calculations based on density functional theory were carried out to determine the electronic structures of the excited high-spin states and to understand the mechanism of the spin alignment utilizing the excited molecular field. The role of the spin delocalization and the spin polarization mechanisms were revealed on the photoexcited state.     

Direct estimation of an element of order matrix from 1H NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyses require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported. Copyright © 2009 John Wiley & Sons, Ltd.     

High‐spin behavior of molecular crystals and extended π systems

The qualitative rules for the existence of high‐spin ground states in extended systems and molecular crystals are examined here on a firmer theoretical footing. Extended systems have been categorized into three groups, namely, type I, type II, and type III, depending on the type of bonding interactions. The general form of the spin Hamiltonian operators have been written down. The active spaces have been restricted to the minimum size for each of these three types of spin systems. The zeroth‐order state vectors and the Hartree–Fock ground‐state energies have been identified for unit species of each type. The extended system Hamiltonian operators are further truncated in such a way that only the nearest‐neighbor interactions are retained. Expressions have been derived for the energy gap from a molecular orbital approach. The relatively small effects of electron correlation on the energy gaps have been estimated for the type I systems, which belong to the systems of solid‐state physics. In particular, it has been shown that for the type I systems the singlet–triplet gap, and hence the ferromagnetic coupling constant, primarily depends upon the difference of one‐electron kinetic energies and not on the two‐electron exchange integrals. This result agrees with the concept of kinetic exchange that was introduced in the context of a resonating valence‐bond formalism. Type II systems are exemplified by extended systems that can be prepared from conjugated molecules while organic molecular crystals form examples of type III species. For these systems, however, the Coulomb exchange interaction has been shown to dominate the energy gap. A quick review of the Heisenberg spin Hamiltonian for the H₂ molecule is sufficient to point out that the sign of the calculated ferromagnetic coupling constant depends on the method of calculation, the nature of the basis set, and the bond length. This is amply supported by ab initio calculations on this species. Numerical data have also been obtained from computations on m‐phenylene‐coupled nitroxy radicals and stacks of α‐nitronyl nitroxide, but these calculations have been based on a semiempirical quantum chemical methodology (INDO) since some of the species involved are exceedingly large. Computed energy gaps are in good agreement with experimental and other theoretical (AM1, PM3) results. Nevertheless, for the dimer, trimer, tetramer, and pentamer of the type II specimen, the important π orbitals are far from being degenerate. The quantitative results clearly deviate from the criterion of degeneracy that was suggested from qualitative theories for the existence of a high‐spin ground state. Therefore, the criteria for the existence of high spins have been reformulated in terms of the monomer orbitals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 308–324, 2000     

Spin in a Closed‐Shell Organic Molecule on a Metal Substrate Generated by a Sigmatropic Reaction

Inert metal surfaces present more chances of hosting organic intact radicals than other substrates, but large amounts of delocalized electronic states favor charge transfer and thus spin quenching. Lowering the molecule–substrate interaction is a usual strategy to stabilize radicals on surfaces. In some works, thin insulating layers were introduced to provide a controllable degree of electronic decoupling. Recently, retinoid molecules adsorbed on gold have been manipulated with a scanning tunneling microscope (STM) to exhibit a localized spin, but calculations failed to find a radical derivative of the molecule on the surface. Now the formation of a neutral radical spatially localized in a tilted and lifted cyclic end of the molecule is presented. An allene moiety provokes a perpendicular tilt of the cyclic end relative to the rest of the conjugated chain, thus localizing the spin of the dehydrogenated allene in its lifted subpart. DFT calculations and STM manipulations give support to the proposed mechanism.     

Dipolar-induced dephasing of triplet electron spins

In this paper, magnetic dipolar-induced spin dephasing is considered for localized electronic triplet spin states in solids. Using a projection operator formalism, expressions are derived to describe the Hahn-echo decay behavior for an ensemble of triplet spins at zero- and low-magnetic field strengths. For triplet states localized on non-axially symmetric molecules (or defects) it is shown that, at zero field, cross-relaxation with rapidly relaxing spins is essential in the dipolar-induced dephasing process; secular spin-spin interactions become important only in the presence of a static magnetic field or hyperfine couplings. The results are used to relate experimental dephasing data previously obtained for photoexcited triplet states of axially- and non-axially symmetric defects in CaO.     

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.     

Confinement effects on dipole-dipole interactions in nanofluids: the role of equilibrium fluctuations

When spin bearing molecules are enclosed in an elongated nanovoid, and each molecule diffuses across the whole volume in times much shorter than the characteristic times of NMR spin dynamics, a time independent average dipolar Hamiltonian emerges which couples the spins in each molecule equally with the spins in any other molecule. Baugh et al. [Science, 134, 1505 (2001)] have observed the remarkable orientation dependent linewidth in such a situation, and offered a convincing interpretation using the techniques of solid state NMR. In the present paper I show that, contrary to previous expectations, the same linewidth can be predicted with liquid NMR techniques, provided that one takes into account equilibrium fluctuations in the estimation of the dipolar field.     

Local Spin Analysis and Chemical Bonding

The electronic structure of main‐group diatomic molecules is discussed in the light of local spin analysis. A deep investigation into the origin of local spins and their coupling is presented. It is shown that the presence of significant local spins in bonded molecules flags deviations from the classical bonding prototypes. For the notorious example of the C₂ molecule, the local spin analysis indicates that its ground state has all ingredients to be categorized as a diradical.     

Ab initio MO analysis of interaction paths between radicals in ferromagnetic organic systems

Interaction path analyses for pi-conjugated organic systems were performed at the ab initio molecular orbital level to examine the relationship between inter-radical interactions and the high-spin stability of the system. It was found that the high-spin stability results from through-bond interactions between radicals, not from through-space interactions, in relation to the stabilization of a low-spin state due to the effects of electron correlation. L(ij)(min) value for estimating the mixing of nonbonding molecular orbitals well predicted the relationship between the through-bond interactions and the high-spin stability. Furthermore, molecular orbital calculations revealed that the all-trans type interaction path between radicals produces long-range exchange interactions, and the additivity of high-spin stability is observed by keeping short-range through-bond interaction paths.     

Electronic structure of the lowest excited triplet state of 5,12-naphthacenequinone

Continuous-wave time-resolved EPR (cw-TREPR) and pulsed electron nuclear double resonance (ENDOR) studies have been carried out to clarify the electronic structure of the lowest excited triplet (Tl) state of 5,12-naphthacenequinone (5,12-NpQ) as well as 1,4-anthraquinone (1,4-AQ) and 6,13-pentacenequinone (6,13-PeQ). The Tl energy level and the D value of the zero-field splitting (ZFS) parameters only slightly decreased with the increasing pi-conjugated system. The Tl states of these linear para-acenequinones were assigned to the pi pi* character. In triplet 5,12-naphthacenequinone, more than 80% of the unpaired electron spins are localized on the naphthalene aromatic sub-system.     

Spin state selective detection of single quantum transitions using multiple quantum coherence: simplifying the analyses of complex NMR spectra

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)-single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.     

Magnetism and bonding in graphene nanodots with H modified interior, edge, and apex

Ab initio density functional theory calculations of hexagonal shaped zigzag edged graphene nanodot molecules, modified by the addition of atomic H to interior and perimeter sites, predict significant changes to the hexagonally sectored spin distribution and chemical bonding of the originals. The redistribution of Kohn-Sham levels at the top of the valence manifold from parent to derivative hint at large changes in the electronic structure. A centrally added H atom creates an occupied level in the middle of the 0.3 eV band gap of the parent molecule and is surrounded by an island of spins. The latter is isolated enough from the perimeter to provide a calibration of the edge spins of the modified parent. Mid-edge addition of a H atom "quenches" the spin on the edge by drawing a p(z)-electron into the C-H bond without reducing the spin on the other edges. Addition of H to an apex carbon atom results in a localized spin freed from the double bond that coexists with the parent spin on the same edge. Saturating the apex double bond by adding two H atoms, returns π-levels shifted in energy and index and parent-like spin patterns on all edges, intact except for small changes on the edges joined at the apex. Taken in unison these results demonstrate how atomic hydrogen and other groups could be used to engineer the magnetism of graphene nanodots.