Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes

We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.     

DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)Mn2(μ-OAc)2 complexes

The magnetic properties of a series of dinuclear Mn^II systems are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DEF-BS). It is found that there are weak antiferromagnetic interactions in these systems with different bridging ligands. The changing trend of the magnetic coupling constants J indicates that with the electronegativity of the increasing bridging ligands, the antiferromagnetic coupling interaction is weakened. The analyses of the magnetic orbitals and the spin densities show that the weakly antiferromagnetic couplings in these systems are due to the vertical magnetic d orbitals and the weak spin delocalization. These results should be instructive for the design of new molecular magnetic materials.     

Theoretical study on the magnetic exchange behavior of a hetero-double-bridged binuclear copper(II) complex: orbital complementary effect

The mechanism of magnetic exchange interaction in a μ-chloro and μ-methoxy double-bridged copper(II) complex is investigated by calculations based on density functional theory combined with the broken-symmetry approach (DFT-BS). The calculated results reveal that the complex has a strong antiferromagnetic interaction. By the analyses of magnetic orbital interaction and spin distribution, it is found that there exists orbital complementary effect between the two bridging ligands. In addition, to examine the contribution to the magnetic exchange interaction of each bridging ligand, two single-bridged systems have been studied.     

Dramatic variation of magnetic exchange through double end-on azide bridges in a series of ladder-like copper(II) coordination polymers

Three ladder-like coordination polymers, [Cu2(phprpy)2-mu-(N3)2(N3)2], 1; [Cu2(terpy)2-mu-(N3)4Cu2-mu-(N3)2(N3)2], 2; and[Cu2(terpy)2-mu-(N3)2(N3)2Cu3-mu-(N3)4(N3)2], 3, consisting of Cu2+ ions with double end-on azide bridges were synthesized, their crystal structures and magnetic properties were determined, and spin dimer analysis was performed to explain the signs and strengths of their strong spin exchange interactions [phprpy is 4-(3-phenylpropyl)pyridine and terpy is 2,2':6,2'-terpyridine]. Although these compounds have ladder-like arrangements of Cu2+ ions, their magnetic structures are described as isolated dimers for 1 and 2 and as isolated trimers for 3. The predominant spin exchange paths in 1-3 have double end-on azide bridges linking adjacent Cu2+ ions, and the geometrical parameters of these bridging structures are similar. However, the spin dimer of 1 exhibits a strong ferromagnetic coupling; that of 2, a strong antiferromagnetic coupling; and that of 3, a weak ferromagnetic coupling. These findings are well explained by the present spin dimer analysis and show that the nature and geometry of the nonbridging ligands can have a strong influence on the sign and strength of the spin exchange interaction between Cu2+ ions connected by double end-on azide bridges.     

Theoretical study of exchange coupling in 3d-Gd complexes: large magnetocaloric effect systems

Polynuclear 3d transition metal-Gd complexes are good candidates to present large magnetocaloric effect. This effect is favored by the presence of weak ferromagnetic exchange interactions that have been investigated using methods based on Density Functional Theory. The first part of the study is devoted to dinuclear complexes, focusing on the nature and mechanism of such exchange interactions. The presence of two bridging ligands is found more favorable for ferromagnetic coupling than a triple-bridged assembly, especially for complexes with small M-O···O-Gd hinge angles. Our results show the crucial role of the Gd 5d orbitals in the exchange interaction while the 6s orbital seems to have a negligible participation. The analysis of the atomic and orbital spin populations reveals that the presence of spin density in the Gd 5d orbital is mainly due to a spin polarization effect, while a delocalization mechanism from the 3d orbitals of the transition metal can be ruled out. We propose a numerical DFT approach using pseudopotentials to calculate the exchange coupling constants in four polynuclear first-row transition metal-Gd complexes. Despite the complexity of the studied systems, the numerical approach gives coupling constants in excellent agreement with the available experimental data and, in conjunction with exact diagonalization methods (or Monte Carlo simulations), it makes it possible to obtain theoretical estimates of the entropy change due to the magnetization/demagnetization process of the molecule.     

Tailoring the Exchange Interaction in Covalently Linked Basic Carboxylate Clusters through Bridging Ligand Selection

We are reporting new dimeric units of basic carboxylates bearing the {Fe(III)(2)M(II)O} motif for M = Co and Ni, covalently bound through the tetradentate bridging (LL) 2,2'-azopyiridine (azpy) and 2,3-di(2-pyridyl)quinoxaline ligands (dpq). We structurally characterized the hexanuclear clusters, and their magnetic properties have been fully analyzed. DFT calculations have been performed as a supplementary tool. All results evidence a weak antiferromagnetic interaction through the bridging ligands between isolated spin ground states arising from intra-Fe(2)MO core exchange couplings. Together with the pioneer 2,2'-bipyrimidine bridged systems, the new complexes reported constitute a family of complexes where the exchange interaction can be tuned by the selection of the bridging LL type ligand.     

Coordination complexes of 1-(4-[N-tert-butyl-N-aminoxyl]phenyl)-1H-1,2,4-triazole with paramagnetic transition metal dications

1-(4-(N-tert-Butyl-N-aminoxylphenyl))-1H-1,2,4-triazole (NIT-Ph-Triaz) forms isostructural cyclic 2:2 dimeric complexes with M(hfac)(2), M = Mn, Ni, Co, hfac = hexafluoroacetylacetonate. For M = Cu, only a sufficient sample for crystallographic analysis was isolated. For M = Mn, Ni, and Co, the M-NIT exchange is strongly antiferromagnetic. The intradimer exchange coupling between M-NIT units is J/k = +0.53 K for M = Mn, J/k = (-)3.5 K for M = Ni. For M = Co, J/k < 0 K, with the magnetic susceptibility tending toward zero at low temperatures. The exchange behavior is consistent with an intradimer spin polarization mechanism linking M-NIT units through the conjugated pi-system of the radical. Computational modeling of NIT-Ph-Triaz gives Mulliken spin populations in good accord with experimental electron spin resonance hyperfine coupling constants, and is consistent with the presumed radical spin density distribution in the complexes. The results provide useful guidelines to anticipate spin polarization effects in organic pi-radical building blocks in magnetic materials, particularly when qualitative connectivity-based analyses are clouded by nonalternant molecular connectivities.     

同结构GdIIIMII(M=Cu，Ni，Co，Fe，Mn)配合物磁性理论研究

基于DFT-BS方法,在不同泛函方法和基组下计算[CuIIGdIII{pyCO(OEt)py C(OH)(OEt)py}3]2+及3d-Gd异金属配合物的磁耦合常数,结果表明,PBE0/TZVP(Gd为SARC-DKH-TZVP)水平可用于描述其磁学性质。顺磁中心CuII、GdIII与桥联配位氧原子间存在较强的轨道相互作用,其磁轨道主要由GdIII的4fz3、4fz(x2-y2)轨道、CuII的3dx2-y2轨道和桥联配位原子O的p轨道组成。顺磁中心CuII离子以自旋离域作用为主,GdIII离子以自旋极化作用为主,顺磁中心CuII自旋离域作用对桥联氧原子的影响大于顺磁中心GdIII的自旋极化作用。在同结构3d-Gd配合物中,随着MII离子未成对电子的增加,顺磁中心间自旋密度平方差越大,顺磁中心MII和GdIII之间的反铁磁性贡献越大,其磁耦合常数越小。     

Towards understanding of magnetic interactions within a series of tetrathiafulvalene-pi conjugated-verdazyl diradical cation system: a density functional theory study

The intramolecular magnetic exchange coupling constants (J) for a series of tetrathiafulvalene (TTF) and verdazyl diradical cations connected by a range of pi conjugated linkers have been investigated by means of methodology based on unrestricted density functional theory. The magnetic interaction between radicals is transmitted via pi-electron conjugation for all considered compounds. The calculation of J yields strong or medium ferromagnetic coupling interactions (in the range of 56 and 300 K) for diradical cations connected by linkers with an even number of carbon atoms that are able to provide a spin polarization pathway, while antiferromagnetic coupling is predicted when linkers with an odd number of carbon atoms are employed. The topological analysis of spin density distributions have been used to reveal the effects of the spin polarization on both linkers and spin carriers. The absence of heteroatoms that impede the spin polarization pathway, and the existence of a unique spin polarization path instead of several possible competitive routes are factors which contribute to large positive J values favoring ferromagnetic interactions between the two terminal pi-radicals. The magnitude of J depends strongly on the planarity of the molecular structure of the diradical cation since a more effective orbital overlap between the two pi-systems can be achieved. Hence, the dependence of J on the torsion angle (theta) of each spin carrier has been analyzed. In this respect, our findings show that this geometrical distortion reduces largely the calculated J values for ferromagnetic couplings, leading to weak antiferromagnetic interactions for a torsion angle of 90 degrees .     

Influence of multi-atom bridging ligands on the electronic structure and magnetic properties of homodinuclear titanium molecules

The electronic structure and magnetic properties of homodinuclear titanium(III) molecules with bridging ligands from groups 14, 15, and 16 are examined. Single- and multireference methods with triple-zeta plus polarization basis sets are employed. Dynamic electron correlation effects are included via second-order multireference perturbation theory. Isotropic interaction parameters are calculated, and two of the complexes studied are predicted to be ferromagnetic based on multireference second-order perturbation (MRMP2) theory, using the TZVP(fg) basis set. Zero-field splitting parameters are determined using spin-orbit coupling obtained from complete active space (CAS) self-consistent field (SCF) and multiconfigurational quasi-degenerate perturbation theory (MCQDPT) wave functions. Three Breit-Pauli-based spin coupling methods were employed: full Breit-Pauli (HSO2), the partial two-electron method (P2E), and the semiempirical one-electron method (HSO1).     

Structure,energy spectra and magnetic properties of poly(m-aniline)s

The energy spectra and magnetic properties of a large class of one-dimensional poly(m-aniline)s (PMA) and further model polymers are investigated theoretically. The band structure of those PMA's which are aza-analogs of the alternant non-classical (non-Kekulé) hydrocarbons (polymers) is characterized by a wide gap in which there is a narrow half-filled band (HFB). The different contributions to the effective spin exchange between the unpaired electrons in the HFB: Coulomb (Hund), kinetic and indirect exchange interactions are calculated. While it has been shown earlier that PMA exhibits a net spin exchange of ferromagnetic nature, this approach enables a detailed understanding of the influence of substituents on the nitrogen centers and changes in the aromatic bridging unit. The ferromagnetic nature of the spin coupling in the singly bridged PMA models therebye prevails independent of the structural changes. The HFB width of those PMA's which are derivatives (aza-analogs) of ladder-type non-alternant hydrocarbons is very large and the Wannier functions are delocalized. For this group of polymers the delocalized, non-magnetic state is favored and, therefore, they may be good candidates for testing electrical conduction.     

DFT studies on the magnetic exchange across the cyanide bridge

Exchange coupling across the cyanide bridge in a series of novel cyanometalate complexes with CuII-NC-MIII (M = Cr and low-spin Mn, Fe) fragments has been studied using the broken-symmetry DFT approach and an empirical model, which allows us to relate the exchange coupling constant with sigma-, pi-, and pi*-type spin densities of the CN- bridging ligand. Ferromagnetic exchange is found to be dominated by pi-delocalization via the CN- pi pathway, whereas spin polarization with participation of sigma orbitals (in examples, where the dz2 orbital of MIII is empty) and pi* orbitals of CN- yields negative spin occupations in these orbitals, and reduces the CuII-MIII exchange coupling constant. When the dz2 orbital of MIII is singly occupied, an additional positive spin density appears in the sigma(CN) orbital and leads to an increase of the ferromagnetic Cu-NC-M exchange constant. For low-spin [MIII(CN)6]3- complexes, the dz2 orbital occupancy results in high-spin metastable excited states, and this offers interesting aspects for applications in the area of molecular photomagnetism. The DFT values of the exchange coupling parameters resulting from different occupations of the t2g orbitals of low-spin (t2g5) FeIII are used to discuss the effect of spin-orbit coupling on the isotropic and anisotropic exchange coupling in linear Cu-NC-Fe pairs.     

Characterization of the crystal and magnetic structures of the mixed-anion coordination polymer Cu(HCO2)(NO3)(pyz) {pyz = Pyrazine} by X-ray diffraction, ac magnetic susceptibility, dc magnetization, muon-spin relaxation, and spin dimer analysis

The mixed-anion coordination polymer Cu(HCO2)(NO3)(pyz) was synthesized, its crystal structure was determined by X-ray diffraction, and its magnetic structure was characterized by ac susceptibility, dc magnetization, muon-spin relaxation, and spin dimer analysis. The crystal structure consists of five-coordinate Cu2+ ions that are connected through syn-anti bridging mu-HCO2- and mu-pyz ligands to form a highly corrugated two-dimensional layered network. Bulk magnetic measurements show a broad maximum in chi(T) at 6.6 K. The HCO2- and pyz ligands mediate ferromagnetic and antiferromagnetic spin exchange interactions between adjacent Cu2+ ions with the spin exchange parameters J/kB = 8.17 and -5.4 K, respectively (H = -JSigmaSi x Sj). The muon-spin relaxation data show a transition to a long-range magnetic ordering below TN = 3.66(3) K. For T < TN, the M(H) and chi'ac measurements provide evidence for a field-induced spin-flop transition at 15.2 kOe. That Cu(HCO2)(NO3)(pyz) undergoes a long-range magnetic ordering is an unexpected result because the one-dimensional Cu(NO3)2(pyz) and three-dimensional Cu(HCO2)2(pyz) compounds display linear chain antiferromagnetism with no long-range magnetic ordering down to 2 K.     

Dinuclear Cu(II) complexes of isomeric bis-(3-acetylacetonate)benzene ligands: synthesis, structure, and magnetic properties

Highly versatile coordinating ligands are designed and synthesized with two β-diketonate groups linked at the carbon 3 through a phenyl ring. The rigid aromatic spacer is introduced in the molecules to orient the two acetylacetone units along different angles and coordination vectors. The resulting para, meta, and ortho bis-(3-acetylacetonate)benzene ligands show efficient chelating properties toward Cu(II) ions. In the presence of 2,2'-bipyridine, they promptly react and yield three dimers, 1, 2, and 3, with the bis-acetylacetonate unit in bridging position between two metal centers. X-ray single crystal diffraction shows that the compounds form supramolecular chains in the solid state because of intermolecular interactions. Each of the dinuclear complexes shows a magnetic behavior which is determined by the combination of structural parameters and spin polarization effects. Notably, the para derivative (1) displays a moderate antiferromagnetic coupling (J = -3.3 cm(-1)) along a remarkably long Cu···Cu distance (12.30 ?).     

氢核磁共振谱自旋耦合裂分现象的量子力学解释

Hydrogen nuclear magnetic resonance spectroscopy (¹H-NMR) is an important content in the university course of instrumental analysis and organic structure analysis. The splitting law of spin coupling between hydrogen nuclei is the focus of teaching and learning. Most textbooks explain that the cause of spin coupling splitting is due to the local magnetic field produced by the different spin orientation of other adjacent nuclei (nuclei magnetic dipole-dipole interaction, direct nuclear spin coupling), and a few monograph on Nuclear Magnetic Resonance refers to electron spin polarization mediated nuclear spin coupling (indirect nuclear spin coupling). Here we introduce quantum mechanics for explanation of the splitting law of spin coupling between hydrogen nuclei.     

Evidence for increased exchange interactions with 5d compared to 4d metal ions. Experimental and theoretical insights into the ferromagnetic interactions of a series of trinuclear [{M(CN)8}3-/NiII] compounds (M = MoV or WV)

Two main questions are addressed in this study: (i) What increase of exchange interaction can be expected when replacing a paramagnetic metal ion with a heavier congener located farther down the periodic table (i.e., 3d-4d-5d), and (ii) for a molecular unit with higher coordination numbers, eight in the present case, how is the magnetic information transferred from the metal ion to its ligand set? Qualitative and quantitative investigations on a series of trimetallic cyano-bridged {MoV(CN)8-NiII} and {WV(CN)8-NiII} compounds revealed ferromagnetic interactions but with a strength modulated by the spin organization and their nature. DFT calculations have been used to examine the mechanism and strengths of the exchange coupling, as well as the influence of the local symmetry of the cyanometalate unit on the spin density distribution. Both the experimental and the calculated behaviors underline a noticeable difference between the Mo and the W derivatives (JMoNi = 26.9 cm(-1) and JWNi = 37.3 cm(-1)) that is correlated to the spin density transferred from the metal center to its ligand set. It is also shown that the shape of the {M(CN)8} polyhedron may lead to nonequivalent CN sites and, consequently, to different strengths of the exchange interaction as a result of the position of the bridging ligands.     

The cyano nitronyl nitroxide radical: experimental and theoretical evidence for the fourth case of the McConnell-I mechanism

The nitronyl nitroxide 2-cyano-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide (1) crystallises in the tetragonal P42(1)m space group with a=7.4050(7), c=8.649(1) A. In the crystal the molecules form layers parallel to the ab plane in which they are orthogonal to each other. In the layers there are close contacts, 2.953(2) A, between the NO groups and the bridging carbon atoms of the O-N-C-N-O fragment of neighbouring radicals. The calculated spin density shows a positive population mainly and equally localised on the NO groups and small but significant negative spin densities on the bridging carbon atom and the cyano nitrogen. Absorption spectra show temperature-dependent transitions related to the magnetic behaviour. The temperature dependence of the magnetic susceptibility in the range 2-300 K reveals that couplings between the radicals are antiferromagnetic, and is interpreted by considering a two-dimensional square array of spin S=1/2 antiferromagnetically coupled (J=-10 cm(-1) and g=2.01). This is interpreted as an exchange coupling through close contact between positive and negative spin densities in orthogonal orbitals on oxygen and carbon atoms, respectively.     

混合桥基双核配合物中的轨道互补与反互补效应

在混合桥基的双核体系中,金属中心的磁轨道的线形组合可与相同对称性的桥基最高占据轨道(HOMO'S)相互作用.如果两种桥联配体稳定同一磁轨道组合,则称它们以互补方式起作用;反铁磁偶合就会被加强.反之,如果桥联配体稳定不同的磁轨道组合,则称它们以反互补方式起作用;这将减小反铁磁偶合.本文就互补和反互补效应以及相关的磁学知识做一简要概述.     

Investigation on Magnetic Properties of Exchange Coupled Transition Metal Complexes Ⅱ．Theoretical Model for Trinuclear Complexes

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