Combined ligand field and density functional theory analysis of the magnetic anisotropy in oligonuclear complexes based on Fe(III)-CN-M(II) exchange-coupled pairs

Magnetic anisotropy in cyanide-bridged single-molecule magnets (SMMs) with Fe(III)-CN-M(II) (M = Cu, Ni) exchange-coupled pairs was analyzed using a density functional theory (DFT)-based ligand field model. A pronounced magnetic anisotropy due to exchange was found for linear Fe(III)-CN-M(II) units with fourfold symmetry. This results from spin-orbit coupling of the [Fe(III)(CN)6](3-) unit and was found to be enhanced by a tetragonal field, leading to a (2)E g ground state for Fe(III). In contrast, a trigonal field (e.g., due to tau 2g Jahn-Teller angular distortions) led to a reduction of the magnetic anisotropy. A large enhancement of the anisotropy was found for the Fe(III)-CN-Ni(II) exchange pair if anisotropic exchange combined with a negative zero-field splitting energy of the S = 1 ground state of Ni(II) in tetragonally compressed octahedra, while cancellation of the two anisotropic contributions was predicted for tetragonal elongations. A recently developed DFT approach to Jahn-Teller activity in low-spin hexacyanometalates was used to address the influence of dynamic Jahn-Teller coupling on the magnetic anisotropy. Spin Hamiltonian parameters derived for linear Fe-M subunits were combined using a vector-coupling scheme to yield the spin Hamiltonian for the entire spin cluster. The magnetic properties of published oligonuclear transition-metal complexes with ferromagnetic ground states are discussed qualitatively, and predictive concepts for a systematic search of cyanide-based SMM materials are presented.     

Semiempirical Hamiltonians for spatially confined π-electron systems

A study of π-electron systems confined by impenetrable surfaces is presented. The study results in a nonempirical-based approach to obtain confinement-adapted semiempirical π-Hamiltonians including repulsive terms (PPP or Hubbard). The impenetrable surface confinement of a physical system involves changes in the boundary conditions that the eigenvectors of its differential Hamiltonian operator have to fulfill, while the Hamiltonian itself remains unchanged. However, if this Hamiltonian is written in second quantization language, then confinement only involves changes of the Hamiltonian scalar factors (integrals). Semiempirical Hamiltonian integrals are replaced by parameters; therefore, confinement involves only changes of these parameters. It is shown that confinement changes Coulomb (α_i) and exchange (β_ij), while repulsion (γ_ij) parameters remain unaffected. Next, the influence of confinement upon the electron correlation of (i) π-electron molecular systems, (ii) atoms, and (iii) an electron gas is discussed. The behaviour of the correlation energy vs. the confinement size is found to be different for each type of system. A neat explanation of this variety is given in terms of the Coulomb attractive fields of the systems. Some chemical confinement effects such as an increase in the reactivity of π-electron systems is also outlined. © 1996 John Wiley & Sons, Inc.     

Orbital angular momentum contribution to the magneto-optical behavior of a binuclear cobalt(II) complex

We report magnetic and magnetic circular dichroism investigations of a binuclear Co(II) compound. The Hamiltonian of the system involves an isotropic exchange interaction dealing with the real spins of cobalt(II) ions, spin-orbit coupling, and a low-symmetry crystal field acting within the (4)T(1g) ground manifold of each cobalt ion. It is shown that spin-orbit coupling between this ground term and the low-lying excited ones can be taken into consideration as an effective g factor in the Zeeman part of the Hamiltonian. The value of this g factor is estimated for the averaged experimental values of Racah and cubic ligand field parameters for high-spin cobalt(II). The treatment of the Hamiltonian is performed with the use of a irreducible tensor operator technique. The results of the calculation are in good agreement with experimental observations. Both a large effective g factor for the ground state and a large temperature-independent part of the magnetic susceptibility arise because of a strong orbital contribution to the magnetic behavior of the Co(II) dimer.     

Geminal approach to vibronic models of superconductivity in crystals. I. The Jahn–Teller effect

Electronic geminals constructed as linear combinations of binary products of site functions are used to formulate a vibronic model of superconductivity in crystals that is based upon the approximation of independent correlated electron pairs obtained variationally from an electron‐pair Hamiltonian and the Jahn–Teller effect. The cyclic symmetry of the system is taken into account and the geminals are sorted into doubly degenerate pairs. The Herzberg–Teller expansion of the pair Hamiltonian in terms of vibrational modes leads directly to the Jahn–Teller effect. A contact transformation of the vibronic Hamiltonian containing only linear terms lowers the energy of the system by a second‐order term associated with the Jahn–Teller stabilization energy. A possible model for superconductivity in solids is proposed on the basis of the Jahn–Teller effect. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The origin of transverse anisotropy in axially symmetric single molecule magnets

Single-crystal high-frequency electron paramagnetic resonance spectroscopy has been employed on a truly axial single molecule magnet of formula [Mn(12)O(12)(tBu-CH(2)CO(2))16(CH(3)OH)4].CH(3)OH to investigate the origin of the transverse magnetic anisotropy, a crucial parameter that rules the quantum tunneling of the magnetization. The crystal structure, including the absolute structure of the crystal used for EPR experiments, has been fully determined and found to belong to I4 tetragonal space group. The angular dependence of the resonance fields in the crystallographic ab plane shows the presence of high-order tetragonal anisotropy and strong dependence on the MS sublevels with the second-highest-field transition being angular independent. This was rationalized including competing fourth- and sixth-order transverse parameters in a giant spin Hamiltonian which describes the magnetic anisotropy in the ground S = 10 spin state of the cluster. To establish the origin of these anisotropy terms, the experimental results have been further analyzed using a simplified multispin Hamiltonian which takes into account the exchange interactions and the single ion magnetic anisotropy of the Mn(III) centers. It has been possible to establish magnetostructural correlations with spin Hamiltonian parameters up to the sixth order. Transverse anisotropy in axial single molecule magnets was found to originate from the multispin nature of the system and from the breakdown of the strong exchange approximation. The tilting of the single-ion easy axes of magnetization with respect to the 4-fold molecular axis of the cluster plays the major role in determining the transverse anisotropy. Counterintuitively, the projections of the single ion easy axes on the ab plane correspond to hard axes of magnetization.     

A VB model of transition structure regions of the potential energy surfaces for forbidden and allowed cycloaddition reactions

The MC-SCF potential energy surfaces for the 2 + 2 cycloaddition of two ethylenes, the 4 + 2 cycloaddition of butadiene and ethylene and the 1,3 dipolar cycloaddition of fulminic acid and acetylene are modelled using the coulomb and exchange integrals of Heitler-London VB theory. The VB parameters reproduce the MC-SCF results exactly by virtue of their construction using effective Hamiltonian theory. The origin of the critical points and the magnitude of their activation barriers can thus be rationalized in terms of an analysis along the reaction coordinate, while the nature of the critical points is discussed with respect to normal modes that exclude the reaction coordinate. The computed results provide some understanding of the reason why certain transition structures exist for one cycloaddition and not for others.     

Electron delocalization patterns in models of distorted (D2d) mixed-valence cubanes

Low-symmetry distortions are present in cubanes such as Fe(4)S(4), but their effects on electron delocalization properties are not well-understood. Mixed-valence cubanes often exhibit experimentally measurable "pair delocalization" of a delocalizable electron. An important question is, what is the role of physical interactions (vibronic, electronic, exchange) and symmetry distortions in determining the electron delocalization pattern? Semiclassical models are used to explore the electron delocalization patterns of S=1/2 tetragonally (D(2d)) distorted mixed-valence cubanes comprising four metal centers with bridging ligands, a single delocalizable "excess" electron, and either closed-shell or open-shell ion cores. Phase diagrams show that distorted S=1/2 ground state cubanes with antiferromagnetic exchange (as found in nature) have delocalization patterns qualitatively similar to those of an S=1/2 model with no Heisenberg exchange, suggesting that exchange is not necessarily a dominant factor in determining electron delocalization properties. The open-shell model reveals two types of pair delocalization for the S=1/2 ground state, with differing dimer subunit spins for compressed and elongated geometries. Previous studies emphasize the importance of exchange interactions for pair delocalization. Here, it is shown that electron exchange is not always necessary for pair delocalization and that it can be achieved with relatively small tetragonal distortions from tetrahedral (T(d)) symmetry. The results contradict those of an earlier theoretical study of distorted Fe(4)S(4) clusters, which concluded that distortions of lower symmetry than D(2d) are necessary to induce a transition to pair delocalization.     

Hamiltonian replica‐permutation method and its applications to an alanine dipeptide and amyloid‐β(29–42) peptides

We propose the Hamiltonian replica‐permutation method (RPM) (or multidimensional RPM) for molecular dynamics and Monte Carlo simulations, in which parameters in the Hamiltonian are permuted among more than two replicas with the Suwa‐Todo algorithm. We apply the Coulomb RPM, which is one of realization of the Hamiltonian RPM, to an alanine dipeptide and to two amyloid‐β(29–42) molecules. The Hamiltonian RPM realizes more efficient sampling than the Hamiltonian replica‐exchange method. We illustrate the protein misfolding funnel of amyloid‐β(29–42) and reveal its dimerization pathways. © 2013 Wiley Periodicals, Inc.     

Potential energy surfaces and dynamics of Ni2+ ion aqueous solution: molecular dynamics simulation of the electronic absorption spectrum

We develop a model effective Hamiltonian for describing the electronic structures of first-row transition metals in aqueous solutions using a quasidegenerate perturbation theory. All the states consisting of 3d(n) electronic configurations are determined by diagonalizing a small effective Hamiltonian matrix, where various intermolecular interaction terms such as the electrostatic, polarization, exchange, charge transfer, and three-body interactions are effectively incorporated. This model Hamiltonian is applied to constructing the ground and triplet excited states potential energy functions of Ni(2+) in aqueous solution, based on the ab initio multiconfiguration quasidegenerate perturbation theory calculations. We perform molecular dynamics simulation calculations for the ground state of Ni(2+) aqueous solution to calculate the electronic absorption spectral shape as well as the ground state properties. Agreement between the simulation and experimental spectra is satisfactory, indicating that the present model can well describe the Ni(2+) excited state potential surfaces in aqueous solution.     

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.     

Critical assessment of electron spin resonance studies on Cu(I)-NO complexes in Cu-ZSM-5 zeolites prepared by solid- and liquid-state ion exchange

Cu(I)-NO adsorption complexes were formed over Cu-ZSM-5 zeolites prepared by (i) solid-state ion exchange of NH(4)-ZSM-5 with CuCl and (ii) liquid-state ion exchange of ZSM-5 with Cu(CH(3)COO)(2). Electron spin resonance spectroscopy revealed the formation of two different Cu(I)-NO species A and B in both systems, whose spin Hamiltonian parameters are comparable with those already reported for the Cu(I)-NO species formed over 66% Cu(II) liquid-state ion-exchanged Cu-ZSM-5 materials. The population of the species A and B differs for the two systems studied. Formation of species B is more favored in the solid-state ion-exchanged Cu-ZSM-5 when compared to the liquid-state exchanged zeolite. The X-, Q- and W-band electron spin resonance spectra recorded at 6 and 77 K reveal the presence of a rigid geometry of the adsorption complexes at 6 K and a dynamic complex structure at higher temperatures such as 77 K. This is indicated by the change in the spin Hamiltonian parameters of the formed Cu(I)-NO species in both the liquid- and solid-state ion-exchanged Cu-ZSM-5 zeolites from 6 to 77 K. Possible models for the motional effects found at elevated temperatures are discussed. The temperature dependence of the electron spin phase memory time measured by two-pulse electron spin-echo experiments indicates, likewise, the onset of a motional process of the adsorbed NO molecules at temperatures above 10 K. The studies support previous assignments where the NO complexes are formed at two different Cu(I) cationic sites in the ZSM-5 framework and highlight that multifrequency electron spin resonance experiments at low temperatures are essential for reliable determination of the spin Hamiltonian parameters of the formed adsorption complexes for further comparison with Cu(I)-NO complex structures predicted by quantum chemical calculations.     

Assessment of enveloping distribution sampling to calculate relative free enthalpies of binding for eight netropsin-DNA duplex complexes in aqueous solution

The performance of enveloping distribution sampling (EDS) simulations to estimate free enthalpy differences associated with seven alchemical transformations of A-T into G-C base pairs at the netropsin binding site in the minor groove of a 13-base pair DNA duplex in aqueous solution is evaluated. It is demonstrated that sufficient sampling can be achieved with a two-state EDS Hamiltonian even for large perturbations such as the simultaneous transformation of up to three A-T into three G-C base pairs. The two parameters required to define the EDS reference state Hamiltonian are obtained automatically using a modified version of a scheme presented in earlier work. The sensitivity of the configurational sampling to a variation of these parameters is investigated in detail. Although for relatively small perturbations, that is, one base pair, the free enthalpy estimate depends only weakly on the EDS parameters, the sensitivity is stronger for the largest perturbation. Yet, EDS offers various convenient measures to evaluate the degree of sampling and thus the reliability of the free enthalpy estimate and appears to be an efficient alternative to the conventional thermodynamic integration methodology to obtain free energy differences for molecular systems.     

Analysis of the rotational spectrum of methylene (CH2) in its vibronic ground state with an Euler expansion of the Hamiltonian

We present an analysis of a global, field-free data set of the methylene radical CH2 in its X 3B1 vibronic ground state by means of a novel Euler expansion of the Hamiltonian. The data set comprises pure rotational transitions up to 2 THz obtained with microwave accuracies of 30-500 kHz as well as nu2 ground-state combination differences and pure rotational data obtained with infrared accuracies of 0.001-0.010 cm(-1). Highly accurate spectroscopic parameters have been determined. These include rotational, spin-spin, spin-rotation, and electron-spin-nuclear-spin coupling terms along with several centrifugal distortion corrections. The spectroscopic model has been tested and improved by recording newly three weak DeltaN not equalDeltaJ fine-structure components of the N(KaKc)=2(12)-3(03) and 5(05)-4(14) transitions near 434, 454, and 581 GHz. These lines were rather close to the predictions. Overall weighted root mean squares of 1.28 and 0.83 were achieved for fits in which the Euler expansion was used only for the rotational part of the Hamiltonian or for the rotational and spin-spin terms of the Hamiltonian, respectively. The resulting spectroscopic parameters allow for precise frequency predictions of astrophysically important rotational transitions of methylene.     

The magnetic properties of trinuclear Fe(III) substituted carboxylate clusters

The new Fe(III) complexes with isosceles or equilateral configurations showed atypical magnetic behaviour with a magnetic susceptibility which does not obey the Curie-Weiss law. The experimental data were fitted by using the Heisenberg-Dirac-van Vleck model with a spin Hamiltonian containing different exchange parameters in the case of isosceles configuration. A more elaborate Hamiltonian, taking into account the perturbation arising from a biquadratic exchange interaction was used in the case of equilateral configurations.     

Heat capacities and volumes of interaction between mixtures of alcohols in water at 298.15 K

The heat capacities and densities of mixtures of aqueous solutions of normal alcohols (methanol to n-butanol) and t-butanol were measured at 298.15 K at low molalities. The results were used to calculate the thermodynamic pair and triplet interaction parameters between solutes for heat capacities and volumes. The pair parameters are approximately a linear function of the total number of carbon atoms of the two solutes. The enthalpic pair and triplet interaction parameters for (ROH + H₂O) are also reported. The temperature dependence of the pair parameters for Gibbs free energies, enthalpies, entropies, heat capacities, and volumes are discussed in terms of structural changes in the aqueous solutions.     

Characterization of spectroscopic of Pr(DBM)3(TPPO)2 containing poly(methyl methacrylate)

The absorption and fluorescence spectra of Pr(DBM)3(TPPO)2 (DBM: dibenzoylmethane, TPPO: triphenylphosphine oxide) containing poly(methyl methacrylate) (PMMA) were measured. The energy levels are assigned and analyzed in terms of the free-ion Hamiltonian model. From the data available in the absorption spectrum, various spectroscopic parameters such as the spherically symmetric part of the free-ion Hamiltonian (E(AVG)), Slater-Condon (F2, F4, F6), spin-orbit interaction (zeta), Judd-Ofelt (omega2, omega4, omega6) parameters and the reduced matrix elements are derived. The radiative properties of Pr(DBM)3(TPPO)2 containing PMMA were also predicted according to the Judd-Ofelt theory. The values of the fluorescence branching ratio and the emission cross section of 3P0 --> 3F2 fluorescence transition revealed that Pr(DBM)3(TPPO)2 containing PMMA is an efficient luminescent material.     

Triplet-triplet energy-transfer coupling: theory and calculation

Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.     

Magnetic excitations in Cu6 and Mn6 hexagons embedded in D3d-symmetric polyoxotungstates

In this article we reconsider the discussion of the magnetic measurements for the two novel polyoxotungstates, (n-BuNH(3))(12)[(CuCl)(6)(AsW(9)O(33))(2)].6H(2)O and (n-BuNH(3))(12)[(MnCl)(6)(SbW(9)O(33))(2)].6H(2)O, which have been synthesized and characterized by Yamase et al. (Inorg.Chem. 2006, 45, 7698). Analysis of the magnetic susceptibility and magnetization for Cu(6)(12+) and Mn(6)(12+) hexagons based on the exact diagonalization of isotropic exchange Hamiltonian shows that the best-fit first-neighbor coupling parameters are J = 35 and 0.55 cm(-1), respectively, while the second-neighbor interactions are very small. These values exceed considerably those obtained by Yamase et al. (J = 8.82 and 0.14 cm(-1)) on the basis of the Kambe-Van Vleck formula that is inappropriate for six-membered rings. We also got perfect fits to the experimental data for the field dependence of magnetization at 1.8 K. The results imply the importance of axial anisotropy, which is shown to be especially pronounced for the Mn(6)(12+) cluster. We discuss also the symmetry assignments of exchange multiplets to the exact SGamma terms (full spin, S, and irreducible representation, Gamma, of the point group) and correlate the results with the selection rules for the anisotropic magnetic contributions. The antisymmetric exchange is shown to appear in orbitally degenerate multiplets as a first-order perturbation and gives rise to an easy axis of magnetization along the C(6) axis. Evaluation of the Zeeman levels shows that the field applied in the plane of the hexagon fully reduces the effect of the antisymmetric exchange.     

A simple method for derivation of the rovibrational Hamiltonian: application to orthogonal radau coordinate systems as special cases

The molecular Hamiltonian of polyatomic molecules has been obtained. A general choice of internal coordinates depending on external parameters was considered. The rovibrational Hamiltonian for this set of coordinate system was derived in general terms as a function of the external parameters a and b. This procedure is also applicable to various kinds of internal coordinates in a straightforward way. The rovibrational Hamiltonian of triatomic molecules is considered as an application of this general formulation. In addition, orthogonal Radau coordinates are considered as cases of this new approach