DFT Studies on the Magnetic Exchange Across the Cyanide Bridge

Heterobimetallic cyanide-bridged FeIII(μ-CN)MII complexes (M = Mn and Cu): synthesis, structure and magnetism

Systematic magneto-structural studies reveal ‘[FeIII(Tp)(CN)2(μ-CN)MnIICl(L1/L2)]′ (both antiferromagnetic) and [FeIII(Tp)(CN)2(μ-CN)CuII(L1/L2)]+′(L1 ferro- and L2 antiferromagnetic).

Modelling spin Hamiltonian parameters of molecular nanomagnets

Molecular nanomagnets encompass a wide range of coordination complexes possessing several potential applications. A formidable challenge in realizing these potential applications lies in controlling the magnetic properties of these clusters. Microscopic spin Hamiltonian (SH) parameters describe the magnetic properties of these clusters, and viable ways to control these SH parameters are highly desirable. Computational tools play a proactive role in this area, where SH parameters such as isotropic exchange interaction (J), anisotropic exchange interaction (Jx, Jy, Jz), double exchange interaction (B), zero-field splitting parameters (D, E) and g-tensors can be computed reliably using X-ray structures. In this feature article, we have attempted to provide a holistic view of the modelling of these SH parameters of molecular magnets. The determination of J includes various class of molecules, from di- and polynuclear Mn complexes to the {3d-Gd}, {Gd-Gd} and {Gd-2p} class of complexes. The estimation of anisotropic exchange coupling includes the exchange between an isotropic metal ion and an orbitally degenerate 3d/4d/5d metal ion. The double-exchange section contains some illustrative examples of mixed valance systems, and the section on the estimation of zfs parameters covers some mononuclear transition metal complexes possessing very large axial zfs parameters. The section on the computation of g-anisotropy exclusively covers studies on mononuclear Dy(III) and Er(III) single-ion magnets. The examples depicted in this article clearly illustrate that computational tools not only aid in interpreting and rationalizing the observed magnetic properties but possess the potential to predict new generation MNMs.

Synthesis and magneto-structural studies on a new family of carbonato bridged 3d–4f complexes featuring a [CoII3LnIII3(CO3)] (Ln = La, Gd, Tb, Dy and Ho) core: slow magnetic relaxation displayed by the cobalt(ii)–dysprosium(iii) analogue

A new series of carbonato-bridged complexes containing a CoII3LnIII3 core have been synthesized.

Prospecting Lighting Applications with Ligand Field Tools and Density Functional Theory: A First-Principles Account of the 4f(7)-4f(6)5d(1) Luminescence of CsMgBr3:Eu(2+)

The most efficient way to provide domestic lighting nowadays is by light-emitting diodes (LEDs) technology combined with phosphors shifting the blue and UV emission toward a desirable sunlight spectrum. A route in the quest for warm-white light goes toward the discovery and tuning of the lanthanide-based phosphors, a difficult task, in experimental and technical respects. A proper theoretical approach, which is also complicated at the conceptual level and in computing efforts, is however a profitable complement, offering valuable structure-property rationale as a guideline in the search of the best materials. The Eu(2+)-based systems are the prototypes for ideal phosphors, exhibiting a wide range of visible light emission. Using the ligand field concepts in conjunction with density functional theory (DFT), conducted in nonroutine manner, we develop a nonempirical procedure to investigate the 4f(7)-4f(6)5d(1) luminescence of Eu(2+) in the environment of arbitrary ligands, applied here on the CsMgBr3:Eu(2+)-doped material. Providing a salient methodology for the extraction of the relevant ligand field and related parameters from DFT calculations and encompassing the bottleneck of handling large matrices in a model Hamiltonian based on the whole set of 33,462 states, we obtained an excellent match with the experimental spectrum, from first-principles, without any fit or adjustment. This proves that the ligand field density functional theory methodology can be used in the assessment of new materials and rational property design.

Intra-molecular magnetic exchange interaction in the tripyridinium bis[tetrachloroferrate(iii)] chloride molecular magnet: a broken symmetry-DFT study

The investigation of magnetic ordering in magnetic molecular conductors is the subject of ongoing research studies in the fields of condensed matter physics, chemistry and material sciences. Following the photo-magnetic behavior already observed in individual (FeCl4)2(py·H)3Cl molecules at room temperature, magnetic ordering is studied in this work. Calculations are performed using spin projected broken symmetry via density functional theory within the scheme of the B3LYP approximation. The value of the intra-molecular magnetic coupling constant is obtained as J = 13.2062 kJ mol(-1). A field dependent magnetization experiment is conducted to validate the magnitude and the sign of the exchange constant. Reasonable consistency of experimental and theoretical results confirms the presence of a positive intra-molecular indirect exchange interaction. This work paves the way for possible introduction of a new molecule in the development of advanced molecular electronic devices.

DFT and TD-DFT studies of electronic structures and one-electron excitation states of a cyanide-bridged molecular square complex

The electronic structures and physical properties of [Co₂Fe₂(CN)₆(tp*)₂(dtbbpy)₄](PF₆)₂·2MeOH are investigated by DFT and TD-DFT calculations.

A new series of cyanide-bridged heterobimetallic FeIII–FeIII/MnIII/CuII one-dimensional complexes: synthesis, crystal structures, and magnetic properties

Four new cyanide-bridged Fe^III–Fe^III/Mn^III/Cu^II one-dimensional complexes have been assembled using K[Fe(bpdBrb)(CN)₂]·2H₂O (1) as building blocks, and structurally characterized and magnetically investigated.

Can anisotropic exchange be reliably calculated using density functional methods? A case study on trinuclear Mn(III)-M(III)-Mn(III) (M=Fe, Ru, and Os) cyanometalate single-molecule magnets

Density functional studies have been performed on a set of trinuclear single-molecule magnets (SMMs) of general formula [{Mn2(5-Br salen)2(MeOH)2}M(CN)6](NEt4) (M=Fe(III) (1), Ru(III) (2) and Os(III) (3); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminato anion). We have computed the orbital-dependent exchange interaction for all three complexes for the first time using DFT and complete active space self-consistent field (CASSCF) methods. DFT calculations yield the anisotropic exchange as J(ξξ)=3.5 cm(-1) for 1; J(ξξ)=12.1 cm(-1), J(ζζ)=-6.9 cm(-1) and J(ηη)=-14 cm(-1) for 2; and J(ξξ)=23.7 cm(-1) and J(ζζ) =-11.1 cm(-1) for 3. The computed values are in agreement with the experimental report, and this suggests that the established methodology can be used to compute the anisotropic exchange in larger clusters. Our calculations reiterate the fact that the exchange is described by a three-axis anisotropic exchange for complexes 2 and 3 as evidenced by the experiments. A stronger exchange coupling as we move down the periodic table from 3d to 5d is reproduced by our calculations, and the origin of this enhancement in the exchange interaction has been probed by using molecular orbital analysis. The electronic origin of different types of exchange observed in this series is found to be related to the energy difference between possible degenerate pairs and the nature of orbital interactions. By computing the exchange interaction, the single-ion anisotropy of Mn(III) and zero-field splitting of the S=9/2 ground state of complexes 1-3 using CASSCF and/or DFT methods, we have attempted to shed light on the issue of anisotropic exchange and the barrier height for the magnetisation reversal in SMMs. Comprehensive magneto-structural correlations have been developed to offer clues on how to further enhance the barrier height in this class of SMMs.

Enhancing the magnetic coupling of oxalato-bridged Re(IV)2M(II) (M=Mn, Co, Ni, and Cu) trinuclear complexes via peripheral halide ligand effects

Four heterotrinuclear Re(IV)(2)M(II) compounds of general formula (NBu(4))(2)[{Re(IV)Br(4)(μ-ox)}(2)M(II)(Him)(2)] [NBu(4)(+) = tetra-n-butylammonium cation, ox = oxalate, Him = imidazole; M = Mn (1), Co (2), Ni (3), and Cu (4)] have been synthesized by using the novel mononuclear complex [Re(IV)Br(4)(ox)](2-) as a ligand toward divalent first-row transition metal ions in the presence of imidazole. Compounds 1-4 are isostructural complexes whose structure contains discrete trinuclear [{Re(IV)Br(4)(μ-ox)}(2)M(II)(Him)(2)](2-) anions and bulky NBu(4)(+) cations. The Re and M atoms are six-coordinated: four peripheral bromo and two oxalate-oxygens (at Re), and two cis-coordinated imidazole molecules and four oxygen atoms from two oxalate ligands (at M), build distorted octahedral surroundings. Two peripheral [ReBr(4)(ox)](2-) units act as bidentate ligands through the oxalate group toward the central [M(II)(Him)(2)] fragment affording the trinuclear entities. The values of the intramolecular Re···M separation are 5.62(1) (1), 5.51(1) (2), 5.46(1) (3), and 5.55(1) Å (4). Magnetic susceptibility measurements on polycrystalline samples of 1-4 in the temperature range of 1.9-300 K show the occurrence of intramolecular antiferro- [J = -1.1 cm(-1) (1)] and ferromagnetic interactions [J = +3.9 (2), +19.7 (3), and +14.4 cm(-1) (4)], the Hamiltonian being defined as Ĥ = -J [Ŝ(M)(Ŝ(Re1) + Ŝ(Re2))]. The larger spin delocalization on the oxalato bridge in 1-4 when compared to the trinuclear Re(IV)(2)M(II) complexes with chloro instead of bromo as peripheral ligands (1'-4') accounts for the strengthening of the magnetic interactions in 1-4 [J = -0.35 (1'), +14.2 (3'), and +7.7 cm(-1) (4')]. An incipient frequency dependence of the out-of-phase ac signals of 3 at very low temperatures is reminiscent of a system with slow relaxation of the magnetization, a phenomenon characteristic of single-molecule magnet behavior.

Synthesis, structure, and magnetic characterization of a C3-symmetric Mn(III)3Cr(III) assembly: molecular recognition between a trinuclear Mn(III) triplesalen complex and a fac-triscyano Cr(III) complex

The reaction of the tris(tetradentate) triplesalen ligand H(6)talen(t-Bu(2)), which provides three salen-like coordination environments bridged in a meta-phenylene arrangement by a phloroglucinol backbone, with Mn(II) salts under aerobic conditions, affords, in situ, the trinuclear Mn(III) triplesalen complex [(talen(t-Bu(2))){Mn(III)(solv)(n)}(3)](3+). This species then reacts with [(Me(3)tacn)Cr(CN)(3)] to form the tetranuclear complex [{(talen(t-Bu(2)))Mn(III)(3)}{(Me(3)tacn)Cr(CN)(3)}](3+) ([Mn(III)(3)Cr(III)](3+)). The regular ligand folding observed in the trinuclear triplesalen complex preorganizes the three metal ions for the reaction with three facially coordinated nitrogen atoms of [(Me(3)tacn)Cr(CN)(3)]. [{(talen(t-Bu(2)))(Mn(III)(MeOH))(3)}{(Me(3)tacn)Cr(CN)(3)}](ClO(4))(3) (1) was characterized by infrared spectroscopy, elemental analysis, mass spectrometry, electron absorption spectroscopy, and magnetic measurements. The molecular structure was established for the acetate-substituted derivative [{(talen(t-Bu(2)))(Mn(III)(MeOH))(2)(Mn(III)(OAc))}{(Me(3)tacn)Cr(CN)(3)}](ClO(4))(2) (2) by single-crystal X-ray diffraction. Variable-temperature-variable-field and mu(eff) versus T magnetic data have been analyzed in detail by full-matrix diagonalization of the appropriate spin-Hamiltonian, consisting of isotropic exchange, zero-field splitting, and Zeeman interaction components. Satisfactory reproduction of the experimental data has been obtained for the parameters J(Mn-Cr) = -0.12 +/- 0.04 cm(-1), J(Mn-Mn) = -0.70 +/- 0.03 cm(-1), and D(Mn) = -3.0 +/- 0.4 cm(-1). These generate a triply degenerate pseudo S(t) = 7/2 spin manifold, which cannot be appropriately described by a giant spin model and which exhibits a weak easy-axis magnetic anisotropy. This is corroborated by the onset of a frequency-dependent chi'' signal at low temperatures, demonstrating a slow relaxation of the magnetization indicative of 1 being a single-molecule magnet. Comparing the properties to those of the heptanuclear analogue [{(talen(t-Bu(2)))Mn(III)(3)}(2){Cr(III)(CN)(6)}](3+) ([Mn(III)(6)Cr(III)](3+)) formed by the reaction of 2 equiv of [(talen(t-Bu(2))){Mn(III)(solv)(n)}(3)](3+) with 1 equiv of [Cr(CN)(6)](3-) [Glaser, T.; Heidemeier, M.; Weyhermüller, T.; Hoffmann, R.-D.; Rupp, H.; Müller, P. Angew. Chem. Int. Ed., 2006, 45, 6033-6037] demonstrates a lower driving force for formation, a strongly reduced J(Mn-Cr) exchange, a slightly reduced J(Mn-Mn) exchange, and a significantly longer Mn-N(N[triple bond]C) bond length in [Mn(III)(3)Cr(III)](3+). Taking into account magneto-structural correlations establishes a supramolecular interaction between the two [(talen(t-Bu(2)))Mn(III)(3)](3+) subunits in [Mn(III)(6)Cr(III)](3+) responsible for the structural distortion and the short Mn-N(N[triple bond]C) distance which results in a strong J(Mn-Cr) exchange and thus [Mn(III)(6)Cr(III)](3+) being a single-molecule magnet with a relatively high effective anisotropy barrier of 25.4 K.

Single-ion anisotropy and exchange interactions in the cyano-bridged trimers MnIII2MIII(CN)6 (MIII = Co, Cr, Fe) species incorporating [Mn(5-Brsalen)]+ units: an inelastic neutron scattering and magnetic susceptibility study

The electronic structures of the compounds K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)M(III)(CN)(6)].2H(2)O (M(III) = Co(III), Cr(III), Fe(III)) have been determined by inelastic neutron scattering (INS) and magnetic susceptibility studies, revealing the manganese(III) single-ion anisotropy and exchange interactions that define the low-lying states of the Mn-M(III)-Mn trimeric units. Despite the presence of an antiferromagnetic intertrimer interaction, the experimental evidence supports the classification of both the Cr(III) and Fe(III) compounds as single-molecule magnets. The value of 17(2) cm(-1) established from AC susceptibility measurements for a spin-reversal barrier of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Cr(CN)(6)].2H(2)O may be readily rationalized in terms of the energy level diagram determined directly by INS. AC susceptibility measurements on samples of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Fe(CN)(6)].2H(2)O are contrary to those previously reported, exhibiting but the onset of peaks below temperatures of 1.8 K at oscillating frequencies in the range of 100-800 Hz. INS measurements reveal an anisotropic ferromagnetic manganese(III)-iron(III) exchange interaction, in accordance with theoretical expectations based on the unquenched orbital angular momentum of the [Fe(CN)(6)](3-) anion, giving rise to an M(s) approximately +/-9/2 ground state, isolated by approximately 11.5 cm(-1) from the higher-lying levels. The reported INS and magnetic data should now serve as a benchmark against which theoretical models that aim to inter-relate the electronic and molecular structure of molecular magnets should be tested.

DFT-Based Studies on the Jahn−Teller Effect in 3d Hexacyanometalates with Orbitally Degenerate Ground States

The topology of the ground-state potential energy surface of M(CN)(6) with orbitally degenerate (2)T(2g) (M = Ti(III) (t(2g)(1)), Fe(III) and Mn(II) (both low-spin t(2g)(5))) and (3)T(1g) ground states (M = V(III) (t(2g)(2)), Mn(III) and Cr(II) (both low-spin t(2g)(4))) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the epsilon(g) and tau(2g) octahedral vibrations (Tg[symbol: see text](epsilon(g)+tau(2g)) Jahn-Teller coupling problem (T(g) = (2)T(2g), (3)T(1g))). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t(2g)(1,5) or t(2g)(2,4) ground-state electronic configurations. The results show that coupling to the tau(2g) bending mode is dominant and leads to a stabilization of D(3d) structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)(6)](3-), where the minimum is of D(4h) symmetry. The Jahn-Teller stabilization energies for the D3d minima are found to increase in the order of increasing CN-M pi back-donation (Ti(III) < V(III) < Mn(III) < Fe(III) < Mn(II) < Cr(II)). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D(3d) minima, the effect of configuration interaction and spin-orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn-Teller distortion parameters with structures from X-ray diffraction data. Jahn-Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-), and the (3)T(1g) ground-state splitting of [Mn(CN)(6)](3-), deduced from near-IR spectra. The implications of the pseudo Jahn-Teller coupling due to t(2g)-e(g) orbital mixing via the trigonal modes (tau(2g)) and the effect of the dynamic Jahn-Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-) are also addressed.

Assessment of Density Functional Theory Methods for the Computation of Heats of Formation and Ionization Potentials of Systems Containing Third Row Transition Metals

The performance of several different density functional theory (DFT) methods, including GGA, hybrid-GGA, meta-GGA, and hybrid-meta-GGA methods, have been assessed in terms of their ability to accurately compute both heats of formation and ionization potentials of systems containing third row transition metals. Two different basis sets were used in this study: 6-31G** and TZVP. It is found that the triple-zeta quality TZVP basis set generally produces the best results for both heats of formation and ionization potentials. One important observation made in this study is that the inclusion of exact exchange terms in DFT methods generally results in more consistently accurate results for both heats of formation and ionization potentials of transition metal systems. In general, DFT methods do not yield good ionization potential results for systems containing titanium or zinc. For heats of formation, it is found that the hybrid-meta-GGA functional, TPSS1KCIS, yields the best overall results when combined with the TZVP basis set, while PBE1PBE (hybrid-GGA) gives the best results for the 6-31G** basis. The hybrid-GGA functional, B3LYP, is found to produce the lowest overall errors for ionization potentials when combined with both 6-31G** and TZVP.