Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes

The application of broken symmetry density functional calculations to homobinuclear and heterobinuclear transition metal complexes produces good estimates of the exchange coupling constants as compared to experimental data. The accuracy of different hybrid density functional theory methods was tested. A discussion is presented of the different methodological approaches that apply when a broken symmetry wave function is used with either Hartree–Fock or density functional calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1391–1400, 1999     

Theoretical study of magnetic coupling interaction in terephthalato‐bridged Ni(II) binuclear systems

The density functional theory combined with broken‐symmetry approach has been successfully extended into the study of the long‐range weak coupling interaction in a binuclear Ni(II) complex bridged by terephthalate dianion. The calculated magnetic coupling constant (?0.27 cm^?1) is well in agreement with the experimental one (?0.33 cm^?1). The relative magnitude of the energies of different spin states has been obtained. The spin delocalization and spin polarization occur between two Ni(II) ions, based on the analysis of the spin density distribution. Weak antiferromagnetic behavior in such a system may result from the competition between spin delocalization and spin polarization where the former is dominant. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Useful parameter describing magnetic interactions in extended bis‐bidentate bridged dimers

A useful parameter describing magnetic coupling interactions has been inspected in transition metal dimers, in which two transition metal ions are bridged by extended bis‐bidentate ligands. This parameter is the square of overlap integral between the spatial parts of magnetic orbitals in the broken symmetry state. The oxalato‐bridged Cu (II) dimers, in which the Cu (II) atom is either in tetrahedral or square pyramid coordination environment, have been calculated with the density functional theory coupling the broken symmetry approach. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

High-spin versus broken symmetry-Effect of DFT spin density representation on the geometries of three diiron (III) model compounds

Unrestricted density functional theory calculations have been conducted on three diiron(III) synthetic model compounds containing antiferromagnetically coupled high-spin (HS) irons for which crystallographic structures and Raman spectral data are available. Three density functionals have been employed: BPW91, PWC, and BOP. The study compares the effects on optimized geometries and harmonic vibrational frequencies of spin-paired (SP) low-spin, HS, and broken symmetry antiferromagnetically coupled singlet representations of the spin density distribution. The geometries around the diiron centers in the HS and broken symmetry (BS) representations are found to be similar, both markedly different from those arising from the SP representation. Small differences between the HS and BS results are seen in bond lengths, angles, Raman frequencies, and spin densities associated with oxo and peroxo bridges between the irons.     

Synthesis and characterization of μ-oxamido copper(Ⅱ)-iron(Ⅱ) heterobinuclear complexes with an antiferromagnetic exchange interaction

Four new u-oxamido heterobinuclear complexes have been synthesized and identified as [Cu(oxap)Fe(L)2]SO4, where oxap denotes the N, N'-bis(2-aminopropyl)oxamido dianion and L represents diaminoethane (en); 1,3-diaminopropane (pn); 1,2-diaminopropane (ap) and 2,9-dimethyl-1,10-phenanthroline (Me2-phen). Based on the elemental analyses, spectroscopic studies, magnetic moments (at room temperature) and molar conductivity measurements, extended oxamido-bridged structures consisting of a copper(Ⅱ) and an iron(Ⅱ) ions, which have a square planar environment and an octahedral environment, respectively, are proposed for these complexes. Complexes [Cu(oxap)Fe(en)2]SO4 (1) and [Cu(oxap)Fe(pn)2]SO4 (2) have been characterized by variable temperature magnetic susceptibility (4.2~300 K) and the observed data were least-squares fitted to the susceptibility equation derived from the spin Hamiltonian including single-ion zero-field interaction for the iron(Ⅱ) ion, H=-2JS1.S2-DSzl2, giving the exchange integrals J=-2     

About the calculation of exchange coupling constants in polynuclear transition metal complexes

The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H. He and CH(2). He units to compare with Hartree-Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data.     

Theoretical study of the magnetic exchange coupling behavior substituting Cr(III) with Mo(III) in cyano‐bridged transition metal complexes

Molecular magnetism in a series of cyano‐bridged first and second transition metal complexes has been investigated using density functional theory (DFT) combined with the broken‐symmetry (BS) approach. Several exchange‐correlation (XC) functionals in the ADF package were used to investigate complexes I [?(Me₃tacn)₂(cyclam)NiMo₂(CN)₆]²⁺, II [?(Me₃tacn)₂(cyclam)Ni‐Cr₂(CN)₆]²⁺, III [(Me₃tacn)₆MnMo₆(CN)₁₈]²⁺, and IV [(Me₃tacn)₆MnCr₆(CN)₁₈]²⁺ (Me₃tacn = N,N′,N?‐trimethyl‐1,4,7‐triazacyclononane). For models A (the molded structure of complex I) and B (the modeled structure of complex II), all the XCs given qualitatively reasonable results and predict ferromagnetic coupling character between M (M = Mo^III for A or Cr^III for B) and Ni^II in coincidence with the experimental results (see Tables I and II ). The calculated using Operdew, OPBE, O3LYP, and B3LYP functionals and experimental J values show that substituting Cr^III with Mo^III will enhance the ferromagnetic exchange coupling interactions. But VWN, PW91, PBE, VSXC, and tau‐HCTH functionals have no way to differentiate the relative strength of the intramolecular magnetic exchange coupling interactions of A and B correctly. For models C (the modeled structure of complex III) and D (the modeled structure of complex IV), all the XCs in ADF and B3LYP in Gaussian 03 with several basis sets show that substituting Cr^III with Mo^III will enhance the antiferromagnetic exchange coupling interactions. From the above calculations, the substitution of Cr^III by Mo^III will enhance the magnetic coupling interactions, whether the magnetic coupling interactions are ferro‐ or antiferromagnetic. Moreover, Kahn's model was applied to investigate the above facts. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theoretical studies on electronic structure and magnetic properties of mixed‐valence uteroferrin active site

The electronic structure and magnetic interaction of the active site of pig purple acid phosphatase (PAP, uteroferrin) were investigated using pure DFT (UBLYP) and hybrid DFT methods (UB3LYP and UB2LYP). Uteroferrin catalyzes the hydrolysis of a phosphate ester under acidic conditions and contains a binuclear iron center. The mammalian PAPs are expected to be targets for drug design of osteoporosis. Their active sites are typical examples of the Fe(II)‐Fe(III) mixed‐valence system. We studied double exchange interaction of the mixed‐valence system, using the potential energy difference between the Fe(II)‐Fe(III) and the Fe(III)‐Fe(II) states. The pathway of the antiferromagnetic coupling between Fe(III) and Fe(II) were also discussed by using chemical indices, which are evaluated by the occupation numbers of singly occupied natural orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical Studies on the Spin Exchange Interaction in Copper(II) Complexes Coordinated with Nitronyl Nitroxide

In the recent years, a wide variety of transition metal complexes with the nitronyl radical ligands have been reported1,2. These systems display the various magnetic behaviors (ferro- or antiferro-magnetism) between the unpaired electrons on the radical ligands and on the paramagnetic metal ion center. However, few theoretical studies on the metal-radical complexes were reported and quite few are known about the nature of the exchange coupling interactions. In this work, we are interested i…     

Ferromagnetic interactions in EO-azido-bridged binuclear transition metal(II) systems: Syntheses, crystal structures and magnetostructural correlations

Three new isostructural binuclear transition metal complexes with azido ion and 1,2-bis(3-(pyridin-2-yl)-1H-pyrazol-1-yl)ethane (bppe), formulated as [M 2 (N 3 ) 2 (bppe) 2 ](ClO 4 ) 2 (M = Co, 1; Ni, 2; Cu, 3), were successfully synthesized. They were structurally and magnetically characterized. In 1-3, the double azido ions link two adjacent octahedral metal centers together in the end-to-on mode (EO), with the M-N EO -M angles of 99.41°, 100.24° and 99.80°, respectively. The co-ligand bppe acts as terminal ligand to saturate the remaining coordination sites. The magnetic properties of 1-3 have been investigated in the temperature range of 2-300 K. Fitting of the magnetic susceptibility data revealed the occurrence of the strong ferromagnetic interactions [J = 26.32 cm-1 (1), J = 38.23 cm-1 (2) and J = 139.83 cm-1 (3)]. Density functional theory calculations have been performed on 1-3 to provide a magneto-structural correlation of the ferromagnetic behavior.     

Metal(II)–ligand molar ratio dependence of enantioseparation of tartaric acid by ligand exchange CE with Cu(II) and Ni(II)–D‐quinic acid systems

Enantioseparation of tartaric acid by ligand exchange CE with a Cu(II)–D ‐quinic acid system was studied. Racemic tartaric acid was enantioseparated by ligand exchange CE using BGEs containing relatively low Cu(II)–D ‐quinic acid molar ratios ranging from 1:1 to 1:3 and high molar ratios ranging from 1:8 to 1:12 but was not enantioseparated using BGEs with medium molar ratios ranging from 1:4 to 1:6. While the migration order of D ‐tartaric acid was prior to L ‐tartaric acid at the lower Cu(II)–D ‐quinic acid molar ratios, the enantiomer migration order was reversed at the higher molar ratios. These results were compared with those for Ni(II)–D ‐quinic acid system. The molar ratio dependence of enantiomer migration order can be attributed to a change in the coordination structure of Cu(II) ion with D ‐quinic acid.     

Theoretical investigations on the superhalogen properties and interaction of PdOn (n = 1–5) species

Density functional calculations on the ground state geometries and stabilities of PdO_n species (n = 1–5) are performed in neutral as well as anionic forms. Calculations reveal that Pd can bind stably with four O atoms indicating the maximum oxidation state of Pd as high as +8. The electron affinities of PdO_n suggest that these species behave as superhalogens for n ≥ 2. The large electron affinities of PdO_n species along with stability of their anions point toward the synthesis of new class of compounds having unusual oxidizing capabilities. This possibility is explored by considering the interaction of PdO₂ superhalogen with Ca atom which forms a stable CaPdO₂ complex. In this complex, PdO₂ unit closely mimics the behavior of O atom when compared with CaO molecule. © 2013 Wiley Periodicals, Inc.     

A density functional study on magnetic exchange interaction between Mn(II) ion and nitronyl nitroxide radical in <Emphasis Type="Italic">trans</Emphasis>-and <Emphasis Type="Italic">cis</Emphasis>-metal-radical complexes

The magneto-structural correlation between a Mn(ll) ion, coordinated in an octahedral environment, and two nitronyl nitroxide radical ligands in trans- and cis-metal-radical complexes is investigated by the broken symmetry (BS) approach within density functional theory (DFT). The dependences of coupling constants J on three structural parameters: (i) bond angle θ (Mn-O-N (nitroxide)); (ii) rotating angle ψ, defined by the nitronyl nitroxide radical plane rotating around the axial Mn-O (nitroxide); (iii) bond distance R (Mn-O (nitroxide)) are directly calculated. Our calculations showed that both trans- and cis-Mn(ll)-radical complexes behave a stronger antiferromagnetic interaction, consistent with experiments. In view of molecular orbital theory, the direct exchanges, including σ-type and π-type exchanges, are responsible for the magnetic exchange pathways. There is a preferable linear correlation between the calculated coupling constants J and the overlap integral squares S b between the local magnetic orbitals at the various rotating angle ψ at the fixed bond angle θ and bond distance R, in both trans- and cis-Mn(ll)-radical complexes.     

1,2,3-三氮杂苯－(水)3复合物多体相互作用

The interaction between 1,2,3-triazine and three water molecules was studied using density functional theory B3LYP method at 6-31-t＋＋G^＊＊ basis set. Various structures for 1,2,3-triazine-（water）n （n= 1, 2, 3） complex were investigated and the different lower energy structures were reported. Many-body analysis was also carded out to obtain relaxation energy and many-body interaction energy （two, three, and four-body）, and the most stable conformer has the basis set superposition error corrected interaction energy of -- 102.61 kJ/mol. The relaxation energy, two- and three-body interactions have significant contribution to the total interaction energy whereas four-body interaction was very small for 1,2,3-triazine-（water）3 complex.     

Computational study of glycine–(water)3 complex by density functional method

Glycine–(water)₃ complexes have been studied by means of B3LYP density functional method using 6-311++G* basis set. In the complex considered here, the three water molecule are either attached to the carboxylic group or bridge between the amino group and carboxylic group of glycine. Four such complexes are studied. Relaxation energies, two-, three- and four-body interaction energies are obtained by applying many-body analysis to know their role in binding energy of the complex. The results are compared with recent work on glycine–(water)₃ complex with group as proton donor [A. Chaudhari, P.K. Sahu, S.L. Lee, J. Chem. Phys. 120 (2004) 170]. In the most stable structure of glycine–(water)₃ complex, the three water molecules are attached to the carboxylic group of glycine and it is 5.3 kcal/mol lower in energy than that of the most stable structure reported earlier. The three-body term from water–water–water interaction in the most stable in this work and that reported earlier is unique since the distances between the water molecules are almost same. The two-body term from water–water interaction has significant contribution to the total two-body term when the distance between water molecules is less than 3 Å.     

Structural and Magnetic Properties of CoGen− (n=2–11) Clusters: Photoelectron Spectroscopy and Density Functional Calculations

A series of cobalt‐doped germanium clusters, CoGe_n^?/0 (n=2–11), are investigated by using anion photoelectron spectroscopy combined with density functional theory calculations. For both anionic and neutral CoGe_n (n=2–11) clusters, the critical size of the transition from exo‐ to endohedral structures is n=9. Natural population analysis shows that there is electron transfer from the Ge_n framework to the Co atom at n=7–11 for both anionic and neutral CoGe_n clusters. The magnetic moments of the anionic and neutral CoGe_n clusters decrease to the lowest values at n=10 and 11. The transfer of electrons from the Ge_n framework to the Co atom and the minimization of the magnetic moments are related to the evolution of CoGe_n structures from exo‐ to endohedral.     

Theoretical investigation of adenine–BX3 (X=F,Cl) complex

Geometries and binding energies are predicted at B3LYP/6-311+G* level for the adenine–BX₃ (X=F,Cl) systems and four conformers with no imaginary frequencies have been obtained for both adenine–BF₃ and adenine–BCl₃, respectively, and single energy calculations using much larger basis sets (6-311+G(2df,p)) and aug-cc-pVDZ were carried out as well. The most stable conformer is BF₃ or BCl₃ connected to N₃ of adenine and with the stabilization energy of 22.55 or 20.59 kcal/mol at B3LYP/6-311+G* level (BSSE corrected). The analyses for the combining interaction between BX₃ and adenine with natural bond orbital method (NBO) and the atom-in-molecules theory (AIM) have been performed. The results indicate that all the conformers were formed with σ–p type interactions between adenine and BX₃, in which pyridine-type nitrogen or nitrogen atom of amino group offers its lone pair electron to the empty p orbital of boron atom and the concomitances of charge transference from adenine to BX₃ were occurred. Frequency analysis suggested that the stretching vibration of BX₃ underwent a red shift in complexes. Adenine–BF₃ complex was more stable than adenine–BCl₃ although the distance of B–N is shorter in the later.     

以N-N基团为单桥的双核Cu(II)体系磁-结构关联的理论研究

在密度泛函数理论的框架下,应用对称性破损方法,研究了以N-N基团为单桥 的二嗪类双核Cu(II)体系的磁耦合强度及磁-结构关联。计算结果表明,随着旋转 角θ的减小,反铁磁性耦合作用逐渐减小,直至出现铁磁性耦合,与实验得到的趋 势一致。破损态能量随着θ的增大发生逆转,先降低后增大。磁耦合常数J与（ε _1-ε_2)~2的关系受到破损态能量逆转的影响。当θ由65°逐渐增大到140°时, 破损态能量依次降低,J与（ε_1 - ε_2)~2呈线性关系;当θ = 150°时,破损 态能量发生逆转,由降低变为升高,二者不再保持原有线性关系。另外,（ε_1 - ε_2)~2与θ的关系也受到破损态能量逆转的影响。在θ = 65°～140°范围内, J与θ以及（ε_1 - ε_2）~2与θ的图形相似,因此可用（ε_1-ε_2)~2代替J讨 论磁性与结构的关系;θ = 150°时,二者图形不同。破损态能量的逆转对磁耦合 常数J的影响不大,而旋转角θ是影响磁耦合常数的关键因素。