Broken Symmetry Approach Research Articles

Magnetic Properties of Monomer and Dimer Tetrahedral VO(x) Entities Dispersed on Amorphous Silica-based Materials: Prediction of EPR Parameters from Relativistic DFT Calculations and Broken Symmetry Approach to Exchange Couplings.

Molecular structures of the isolated tetrahedral oxovanadium(IV) and bridged μ-oxo-divanadium(IV) complexes hosted by the clusters mimicking surfaces of amorphous silica-based materials were investigated using density functional theory (DFT) calculations. Principal values of the g and A tensors for the monomer vanadyl species were obtained using the coupled-perturbed DFT level of theory and the spin–orbit mean-field approximation (SOMF). Magnetic exchange interaction for the μ-oxo bridged vanadium(IV) dimer was investigated within the broken symmetry approach. An antiferromagnetic coupling of the individual magnetic moments of the vanadium(IV) centers in the [VO–O–VO]2+ bridges was revealed and discussed in detail. The coupling explains pronounced decrease of the electron paramagnetic resonance signal (EPR) intensity, observed for the reduced VOx/SiO2 samples with the increasing coverage of vanadia, in terms of transformation of the paramagnetic monomer species into the dimers with S = 0 ground state.

W-Knotted Chain {[CuII(dien)]4[WV(CN)8]}5+∞: Synthesis, Crystal Structure, Magnetism, and Theory

The self-assembly of [Cu(II)(dien)(H(2)O)(2)](2+) and [W(V)(CN)(8)](3-) in aqueous solution leads to the formation (H(3)O){[Cu(II)(dien)](4)[W(V)(CN)(8)]}[W(V)(CN)(8)](2)·6.5H(2)O (1). The crystal structure of 1 consists of an unprecedented {[Cu(II)(dien)](4)[W(V)(CN)(8)]}(5+)(∞) chain of (2,8) topology, nonbridging [W(CN)(8)](3-) anions, and crystallization water molecules. The analysis of magnetic behavior of 1 was performed by the density functional theory (DFT) method and magnetic susceptibility measurements. The DFT broken symmetry approach gave two J(CuW) coupling constants: J(ax) = +2.9 cm(-1) assigned to long and strongly bent W-CN-Cu linkage, and the J(eq) = +1.5 cm(-1) assigned to short and less bent W-CN-Cu linkage, located at the axial and the equatorial positions of square pyramidal Cu(II) centers, respectively, in the hexanuclear {W(2)Cu(4)} chain subunit. The dominance of weak-to-moderate ferromagnetic coupling within the chain was confirmed by magnetic calculations. Zero-field susceptibility of the full chain segment {WCu(4)}(n) was calculated by a semiclassical analytical approach assuming that only one W(V) out of five ½ spins of the chain unit WCu(4) is treated as a classical commuting variable. The calculation of the field dependence of the magnetization was performed separately by replacing the same spin with the Ising variable and applying the standard transfer matrix technique. The intermolecular coupling between the chain segments and off-chain [W(CN)(8)](3-) entities was resolved using the mean-field approximation set to be of antiferromagnetic character. The magnetic coupling parameters are compared with those of other low dimensional {Cu(II)-[M(V)(CN)(8)]} systems.

DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)Mn II2(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.

Dissociation curves and binding energies of diatomic transition metal carbides from density functional theory

AbstractThe computational description of the catalytic processes on the surface of transition metals (TMs) requires methods capable of accurate prediction of the bond forming and breaking between the atoms of metal and other elements. In our previous report [Goel and Masunov, J Chem Phys, 129, 214302, 2008], we studied TM hydrides and found that Boese–Martin functional for kinetics (BMK) combined with broken symmetry approach described dissociation process more accurately than multireference wavefunction theory (WFT) methods and some other functionals. Here, we investigate the binding energy, geometry, electronic structure, and potential energy curves for diatomic TM carbides using several exchange‐correlation functionals. The functionals that include explicit dependence on the kinetic energy density (τ‐functionals) are considered, among others. We have found M05‐2x performance to be the best, followed by BMK, when compared with experimental and high level WFT energetics. This agreement deteriorates quickly for other functionals when the fraction of the Hartree–Fock exchange is decreased. Scalar relativistic corrections yield mixed results for bond lengths and bond energies. The natural bond orbital analysis provides useful insight in description of stable spin state over others in these diatomics. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Theoretical Study on the Electronic Configurations and Nature of Chemical Bonds of Dirhodium Tetraacetato Complexes [Rh2(CH3COO)4(L)2] (L = H2O, Free): Broken Symmetry Approach

Abstract The electronic configurations and the nature of chemical bonds of the classical lantern-type dinuclear rhodium(II) tetraacetato complexes [Rh2(CH3COO)4(L)2] (L = H2O, free) have been carefully investigated with broken symmetry (BS) Hartree–Fock (HF), BS density functional theory (DFT), and BS hybrid DFT (HDFT) methods. Several electronic configurations have been proposed for the ground states of the [Rh2(RCOO)4(H2O)2] complexes. In this study, we concluded that those different electronic configurations originate from the position of the axial H2Os, and not along the Rh–Rh length. The BS(U)B3LYP calculation indicates that the stability of the σ and δ orbitals changed when the Rh–OH2 length was 2.35 Å. The natural orbital (NO) analyses and chemical indices clearly indicate that there is a σ-type single bond between the Rh ions, and that the axial H2Os does not affect the overlap.

A DFT Study on the Magnetostructural Property of Ferromagnetic Heteroverdazyl Diradicals with Phenylene Coupler

We have theoretically designed five different m-phenylene coupled high-spin bis-heteroverdazyl diradicals and their analogous p-phenylene coupled low-spin positional isomers. The geometry-based aromaticity index, harmonic oscillator model of aromaticity (HOMA) values for both the couplers (local HOMA), and the whole diradicals (global HOMA) have been calculated for all the diradicals. We also qualitatively relate these HOMA values with the intramolecular magnetic exchange coupling constants (J), calculated using a broken symmetry approach within unrestricted density functional theory framework. Structural aromaticity index HOMA of linkage specific benzene rings in our designed diradical systems shows that the aromatic character depends on the planarity of the molecule and it controls the sign and magnitude of J. The predicted J values are explained on the basis of spin polarization maps, average dihedral angles, and magnetic orbitals. The effect of the spin leakage phenomenon on magnetic exchange coupling constant and that on HOMA values of certain phosphaverdazyl systems has been explicitly discussed. In addition, a similar comparison is made between the calculated exchange coupling constants and corresponding HOMA values. The main novelty of this work stands on the consideration of the aromatic behavior by means of the geometrical index HOMA. We also estimate another aromaticity index, nucleus independent chemical shift (NICS) values for the phenylene coupler in each diradical to measure aromaticity and compare its value with that of HOMA. The ground state stabilities of these diradicals have also been compared.

Electronic and magnetic structure of a triacetylphlorogucinol-bridged [formula omitted]-symmetric trinuclear copper complex: Magnetic characterization, ESR spectroscopy, and DFT calculations

For the trinuclear copper complex [Cu 3(tapg)(H 2bhea) 3](ClO 4) 3 based on the tritopic bridging ligand 2,4,6-triacetylphlorogucinol (H 3tapg) and the capping ligand 2-[bis-(2-hydroxyethyl)amino]ethylamine (H 2bhea) a detailed study on the magnetic and electronic properties is presented. The C 3 -symmetric structure of the molecular assembly is preserved in the solid state structure of the compound which crystallizes in the space group R 3 c with a threefold rotation axis passing through the center of the molecule. Susceptibility measurements show weak ferromagnetic interactions with a coupling constant J = 1.10 ( 4 ) cm - 1 mediated by a spin-polarization mechanism. This is confirmed by DFT calculations according the broken symmetry approach at B3LYP/def2-TZVP level of theory. Extended characterization by ESR spectroscopy both in X- and W-band confirm an exchange-coupled system with axial symmetry with g ⊥ = 2.0633 ( 4 ) , g ‖ = 2.2303 ( 4 ) and an effective axial hyperfine constant A ‖ , eff = 64 G .

Experimental and theoretical investigations of magnetic properties for two low-dimensional spin systems based on bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickelate monoanion building blocks

Two complexes of [Ni(dmit) 2] − (dmit 2− = 2-thioxo-1,3-dithiole-4,5-dithiolate) with nonmagnetic Schiff base cations, 1-(4-bromobenzylideneamino)pyridinium (4-BrBz-1-APy +; 1) and 1-(3-nitrobenzylideneamino)pyridinium (3-NO 2Bz-1-APy +; 2), have been characterized structurally. Their striking structural feature is the deviation of the [Ni(dmit) 2] − anion from the square-planar environment around the Ni atom with 11.42° and 6.57° dihedral angles (between the mean molecular planes of two dmit 2− ligands) in 1 and 2, respectively. These twists arise from the molecular packing interactions between the superimposed anion and cation. In 1, the magnetic [Ni(dmit) 2] − anions are arranged into a wave-shaped regular spin chain, whose magnetism was well fitted by one-dimensional (1D) Heisenberg uniform linear antiferromagnetic chain with | J/ k B| = 66 K. In 2, 1D ladder-shape [Ni(dmit) 2] − chains are formed through lateral-to-lateral S ⋯ S contacts between the adjacent anions, which are further aligned into a two-dimensional (2D) anion layer via van der Waals forces. Complex 2 shows Curie–Weiss-type paramagnetic behavior with Curie constant C = 0.421 emu K mol −1 and Weiss constant θ = −1.279 K. The broken-symmetry DFT approach was utilized to evaluate the magnetic coupling nature for 1 and 2, the theoretical analyses performed at ubpw91/lanl2dz level and concerned the so-called “weak bonding” regime approaches qualitatively explained the magnetic behaviors of 1 and 2.

Exchange Interactions in Systems with Multiple Magnetic Sites

Nonequivalent magnetic interactions in systems with multiple magnetic centers can be explored through a proper description of exchange coupling. The magnetic exchange coupling constant (J) in systems with two magnetic sites is reliably estimated using Heisenberg-Dirac-van Vleck (HDVV) model through broken symmetry approach (BS) within a density functional theory (DFT) framework. However, in case of systems with multiple magnetic centers, exchange coupling constants, evaluated through state-of-the-art techniques, are often found to be inadequate to produce a correct fingerprint of the nature of magnetic interactions therein. This work suggests a new scheme to estimate exchange coupling constants in such systems. In this strategy, distribution of spins on magnetic sites in the ground state of systems with multiple magnetic centers is computed. On the basis of this spin mapping, exchange coupling constants between specific pairs are estimated through BS-DFT approach while keeping all other paramagnetic atoms magnetically inactive. Nonetheless, the effect of magnetically inert paramagnetic sites is already taken into account by the process of spin mapping, which is further justified through expressing the HDVV Hamiltonian in terms of spin density operators. We employ this technique to hypothetical benchmark systems, H(3)He(3) and H(4)He(4) followed by real molecules, cationic manganese trimer, 1,3,5-benzenetriyltris (N-tert-butyl nitroxide), and a pentanuclear manganese complex. Results are found to be concordant with the already established nature of magnetic interaction in these systems. This strategy is different from the most popular scheme to compute J in systems with multiple magnetic centers in the sense that it avoids the formation of a large matrix out of different spin configurations and thus provides a reliable and computationally economic way to address the magnetic interactions in non isotropic systems with multiple magnetic sites.

Broken spin symmetry approach to chemical reactivity and magnetism of graphenium species

The basic problem of weak interaction between odd electrons in graphene and silicene is considered in the framework of the broken spin symmetry approach. This approach exhibits the peculiarities of the odd-electron behavior via both enhanced chemical reactivity and magnetism.

Electronic structures of [n]-cyclacenes (n = 6–12) and short, hydrogen-capped, carbon nanotubes

Density functional (M06-L and B3LYP) and multiconfigurational second-order perturbation (CASPT2) theories are applied to [n]-cyclacenes having n = 6–12 in order to assess their strain energies and the degree of di- or polyradical character inherent in their electronic structures. In the case of density functional theory, a broken symmetry approach must be employed and the sensitivity of the results to choice of functional and broken-symmetry protocol is explored. Viewing the [n]-cyclacenes as monomeric building blocks which may be joined to grow finite length (n,0) single-walled carbon nanotubes, density functional calculations are further employed to explore changes in electronic structure associated with increasing nanotube length. Spin-state energy gaps are predicted to decrease both with increasing cyclacene size and with increasing nanotube length; [n]-cyclacenes with odd values of n are predicted to develop polyradical character for smaller n than is the case for even values n.

Insights into the control of magnetic coupling in the Mn4III complex: from ferromagnetic to antiferromagnetic

Magnetic coupling interactions of a Mn(III)(4) system are investigated by calculations based on density functional theory combined with a broken-symmetry approach (DFT-BS). Three different interactions including ferromagnetic and antiferromagnetic coupling are concomitant in this complex. This magnetic phenomenon of the complex is due to the different bridging angles between the Mn(III) centers in the three different models and the orbital complementarity of the μ-pzbg and μ-OCH(3) bridging ligands, which is proven by the analyses of the molecular orbitals. According to the analyses of the magneto-structural correlation, it is revealed that the magnetic coupling interaction switches from ferromagnetic to antiferromagnetic at the point of the bridging angle Mn-(μ-OCH(3))-Mn = 99°, which is equal to the value in the origin crystal. Significant correlation between the magnetic properties and the component of the d orbitals in these systems shows that the larger contribution of the d(z(2)) orbital corresponds to the larger ferromagnetic coupling interaction. These results should provide a means to control the magnetic coupling of the polynuclear Mn systems, which is instructive for the design of new molecular magnetic materials.

Photoinduced Antiferromagnetic to Ferromagnetic Crossover in Organic Systems

Magnetization reversal is important for different technological applications. Photoinduced magnetization reversal is easier to implement than conventional reversal methods. Here, we theoretically design and investigate the photomagnetic property of azobenzene based diradical systems, where trans isomers convert into corresponding cis forms upon irradiation with light of appropriate wavelength. The coupling constant values have been estimated using the broken symmetry approach in the density functional theory framework. In each case, the trans isomer is found to be antiferromagnetic, while the cis form is ferromagnetic in nature. Therefore, photoinduced magnetic crossover from antiferromagnetic to ferromagnetic regime would be observed. This is a new observation in case of the systems of organic origin. Importance of such systems for photomagnetic switches, sensors, high density data storage, spin valves, and semiconductor spintronic materials have also been discussed with support from density of state analysis, singly occupied molecular orbital-singly occupied molecular orbital energy gaps and spin density plots.

Redox potential of the Rieske iron–sulfur protein: Quantum-chemical and electrostatic study

Quantum-chemical study of structures, energies, and effective partial charge distribution for several models of the Rieske protein redox center is performed in terms of the B3LYP density functional method in combination with the broken symmetry approach using three different atomic basis sets. The structure of the redox complex optimized in vacuum differs markedly from that inside the protein. This means that the protein matrix imposes some stress on the active site resulting in distortion of its structure. The redox potentials calculated for the real active site structure are in a substantially better agreement with the experiment than those calculated for the idealized structure. This shows an important role of the active site distortion in tuning its redox potential. The reference absolute electrode potential of the standard hydrogen electrode is used that accounts for the correction caused by the water surface potential. Electrostatic calculations are performed in the framework of the polarizable solute model. Two dielectric permittivities of the protein are employed: the optical permittivity for calculation of the intraprotein electric field, and the static permittivity for calculation of the dielectric response energy. Only this approach results in a reasonable agreement of the calculated and experimental redox potentials.

Intramolecular ferromagnetic coupling in bis-oxoverdazyl and bis-thioxoverdazyl diradicals with polyacene spacers

We predict the intramolecular exchange coupling constant (J) for 10 different oxo- and thioxo-verdazyl-based hi-spin ground-state diradicals with linear polyacene couplers of varying length using the broken symmetry approach in an unrestricted DFT framework. The magnetic characteristics of these systems are explained using the spin-density distribution, and an analysis is made by “magnetic” orbitals. The nuclear independent chemical shift (NICS) values have been calculated for the diradicals. The average NICS(1) (1 A above the ring surface) value per benzenoid ring increases as the size of the coupler increases. So-called ΔNICS(1) values [the difference among average NICS(1) per benzenoid ring in the coupler and the NICS(1) of the linear polyacene molecule] are correlated with J values. Bond orders and hyperfine coupling constants have also been evaluated and analyzed for the diradicals.

Broken symmetry approach and chemical susceptibility of carbon nanotubes

Constituting a part of odd electrons that are excluded from the covalent bonding, effectively unpaired electrons are posed by the singlet instability of the single-determinant broken spin-symmetry unrestricted Hartree–Fock (UBS HF) SCF solution. The correct determination of the total number of effectively unpaired electrons ND and its fraction on each NDÀ atom is well provided by the UBS HF solution. The NDÀ value is offered to be a quantifier of atomic chemical susceptibility (or equivalently, reactivity) thus highlighting targets that are the most favorable for addition reactions of any type. The approach is illustrated for two families involving fragments of arm-chair (n,n) and zigzag (m,0) single-walled nanotubes different by the length and end structure. Short and long tubes as well as tubes with capped end and open end, in the latter case, both hydrogen terminated and empty, are considered. Algorithms of the quantitative description of any length tubes are suggested. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Trinuclear Terpyridine Frustrated Spin System with a MnIV3O4 Core: Synthesis, Physical Characterization, and Quantum Chemical Modeling of Its Magnetic Properties

The trinuclear oxo bridged manganese cluster, [Mn(IV)(3)O(4)(terpy)(terpyO(2))(2)(H(2)O)](S(2)O(8))(2) (5) (terpy = 2,2':2'',6'-terpyridine and terpyO(2) = 2,2':2'',6'-terpyridine 1,1''-dioxide), was isolated in an acidic aqueous medium from the reaction of MnSO(4), terpy, and oxone as chemical oxidant. The terpyO(2) ligands were generated in situ during the synthesis by partial oxidation of terpy. The complex crystallizes in the monoclinic space group P21/n with a = 14.251(5) A, b = 15.245(5) A, c = 24.672(5) A, alpha = 90.000(5) degrees, beta = 92.045(5) degrees, gamma = 90.000(5) degrees, and Z = 4. The triangular {Mn(IV)(3)O(4)}(4+) core observed in this complex is built up of a basal Mn(mu-O)(2)Mn unit where each Mn ion is linked to an apical Mn ion via mono(mu-O) bridges. The facial coordination of the two tridentate terpyO(2) ligands to the Mn(mu-O)(2)Mn unit allows the formation of the triangular core. 5 is also the first structurally characterized Mn complex with polypyridinyl N-oxide ligands. The variable-temperature magnetic susceptibility data for this complex, in the range of 10-300 K, are consistent with an S = 1/2 ground state and were fit using the spin Hamiltonian H(eff) with S(1) = S(2) = S(3) = 3/2, J(a) = -37 (+/-0.5) and J(b) = -53 (+/-1) cm(-1), where J(a) and J(b) are exchange constants through the mono-mu-oxo and the di-mu-oxo bridges, respectively. The doublet ground spin state of 5 is confirmed by EPR spectroscopic measurements. Density functional theory (DFT) calculations based on the broken symmetry approach reproduce the magnetic properties of 5 very well (calculated values: J(a) = -39.4 and J(b) = -55.9 cm(-1)), thus confirming the capability of this quantum chemical method for predicting the magnetic behavior of clusters involving more than two metal ions. The nature of the ground spin state of the magnetic {Mn(IV)(3)O(4)}(4+) core and the role of ancillary ligands on the magnitude of J are also discussed.

Observation of Magnetic Bistability in Polymorphs of the [Ni(dmit)2]− Complexes

Four ion-pair complexes of [Ni(dmit)(2)](-) with [NO(2)bzql](+) have been obtained, which belong to two kinds of polymorph forms, [NO(2)bzql][Ni(dmit)(2)] (1alpha and 1beta) and [NO(2)bzql][Ni(dmit)(2)].CH(3)COCH(3) (2alpha and 2beta) (where dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate and [NO(2)bzql](+) = 1-(4-nitrobenzyl)quinolinium). Though 1alpha, 2alpha, and 2beta all show anionic dimerization structures at room temperature, they have different anionic and cationic arrangement fashions, which give rise to different magnetic behaviors for these polymorphs or pseudo-polymorphs. Compounds 1alpha, 1beta, and 2alpha exhibit magnetic bistabilities. In particular, 1alpha has a hysteretic loop at approximately 55 K, while 2beta does not display a spin transition in the 2-300 K range. On the basis of the crystal structure data of 2alpha in high- and low-temperature phases, the magnetic coupling feature within the [Ni(dmit)(2)](-) spin dimer was explored with the broken-symmetry approach at the UBPW91/LANL2DZ level; combined with the experimental data and theoretical analyses, the relationship between the magnetic coupling nature and the stacking pattern of [Ni(dmit)(2)](-) anions as well as the origin of the phase interconversion are discussed.

Theoretical Investigation on Triagonal Symmetry Copper Trimers: Magneto-Structural Correlation and Spin Frustration

The mechanisms of the magnetic coupling interactions for two trigonal-bipyramid trinuclear Cu(II) complexes Cu3(mu3-X)2(mu-pz)3X3 (X = Cl and Br, respectively) and three trigonal trinuclear Cu(II) complexes Cu3(mu3-X)(mu-pz)3Cl3 (X = Cl, Br, and O) are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DFT-BS). The research on the magneto-structural correlation reveals that the magnetic coupling interaction is sensitive to the Cu-(mu3-X)-Cu angle. With the Cu-(mu3-X)-Cu angle changing from 76 to 120 degrees, the magnetic coupling interaction is switched from ferromagnetic to antiferromagnetic. According to the analysis of the molecular orbitals and the variation of the spin-state energies versus the ratio of the magnetic coupling constants, it is found that there exists spin frustration phenomenon in these complexes.

Broken Symmetry Approach to Density Functional Calculation of Magnetic Anisotropy or Zero Field Splittings for Multinuclear Complexes with Antiferromagnetic Coupling

Antiferromagnetic coupling in multinuclear transition metal complexes usually leads to electronic ground states that cannot be described by a single Slater determinant and that are therefore difficult to describe by Kohn-Sham density functional methods. Density functional calculations in such cases are usually converged to broken symmetry solutions which break spin and, in many cases, also spatial symmetry. While a procedure exists to extract isotropic Heisenberg (exchange) coupling constants from such calculations, no such approach is yet established for the calculation of magnetic anisotropy energies or zero field splitting parameters. This work proposes such a procedure. The broken symmetry solutions are not only used to extract the exchange couplings but also single-ion D tensors which are then used to construct a (phenomenological) spin Hamiltonian, from which the magnetic anisotropy and the zero-field energy levels can be computed. The procedure is demonstrated for a bi- and a trinuclear Mn(III) model compound.