Values Of Exchange Integrals Research Articles

Issues on DFT+U calculations of organic diradicals.

The diradical state is an important electronic state for understanding molecular functions and should be elucidated for the in silico design of functional molecules and their application to molecular devices. The density functional theory calculation with plane-wave basis and correction of the on-site Coulomb parameter U (DFT+U/plane-wave calculation) is a good candidate of high-throughput calculations of diradical-band interactions. However, it has not been investigated in detail to what extent the DFT+U/plane-wave calculation can be used to calculate organic diradicals with a high degree of accuracy. In the present study, using typical organic diradical molecules (bisphenalenyl molecules) as model systems, the discrepancy in the optimum U values between the two electronic states (open-shell singlet and triplet) that compose the diradical state is detected. The calculated results show that the reason for this U value discrepancy is the difference in electronic delocalisation due to π-conjugation between the open-shell singlet and triplet states, and that the effect of U discrepancy becomes large as diradical character decreases. This indicates that it is necessary to investigate the U value discrepancy with reference to the calculated results by more accurate methods or to experimental values when calculating organic diradicals with low diradical character. For this investigation, the local magnetic moments, unpaired beta electron numbers, and effective magnetic exchange integral values can be used as reference values. For the effective magnetic exchange integral values, the effects of U discrepancy are partially cancelled out. However, because the effects may not be completely offset, care should be taken when using the effective magnetic exchange integral value as a reference. Furthermore, a comparison of DFT+U and hybrid-DFT calculations shows that the DFT+U underestimates the HOMO-LUMO gap of bisphenalenyls, although a qualitative discussion of the gap is possible.

Surface magnetic properties of a ternary nanocomposite and its ecotoxicological properties in Daphnia magna

A ternary magnetic nanohybrid, composed of maghemite, titanium dioxide (anatase phase), and graphene oxide as synthetized by co-precipitation method and initially applied with success to arsenic removal from contaminated synthetic effluent, has its main magnetic properties (the thermal dependence of the coercive field, the saturation magnetization, and the effective anisotropy constant values) systematically studied using a modified Kneller’s and modified Bloch’s laws applied to magnetization data. Besides values of exchange integral and spin wave stiffness constant equal to 2.7 meV and 949 meV Å2 respectively calculated, the Fe-oxide nanoparticles have ca. 11% of Fe spin in canted configuration, a result that also agreed with the description of the in-field Mössbauer spectrum. A magnetization saturation value of 47.5 emu g −1 (size of 19.6 nm) at 300 K and the Bloch’s exponent of 3/2 have suggested that the ternary nanocomposite behaves like a 3D material. In order to check the impact of this ternary nanocomposite, acute toxicity tests were performed on Daphnia Magna water fleas neonates for a 24-hour exposure period due to (i) the fast metabolism of daphnids and (ii) the fact that the nanocomposite precipitates within one day at concentrations of interest for nanoremediation. Post-exposure effects were also studied after the first offspring hatched (2 weeks). A lethal concentration LC50 value of 0.55 mg mL−1 was found for this experiment. Analysis of morphological changes showed toxicity with little significant difference between exposed and negative control individuals. The reproductive rate test was dose dependent.

Study the bias field in bilayer film by computer simulation

Computer modeling of two-layer system from antiferromagnetic and ferromagnetic films is carried out. The Ising model is used. Wolf ′s cluster algorithm is used for calculations. Phase transition temperatures are determined. A state with an ordered antiferromagnetic film and a disordered ferromagnetic film is selected for examination. Dependence the ferromagnetic film magnetization on parameters of antiferromagnetic film is determined. Computer simulation of ferromagnetic film behavior in external magnetic field is performed. The value of the anti-ferromagnetic bias field is determined from the comparison these two experiments. The dependence of the bias field on the exchange integral value at the film boundary is determined.

Study of the equilibrium critical behavior of thin granular membranes by Monte Carlo methods

Simulation of thin granular films and twolayer structures is carried out by Monte Carlo methods. Temperature dependence of equilibrium macroscopic characteristics of granular films such as magnetization, energy, heat capacity, and magnetic susceptibility are calcu-lated for different linear sizes of granules. Influence of exchange integral values for inter-action between granules in film and interlayer interaction in twolayer structure is studied.

Computer simulation of three-layer ferromagnetic nanosystems in magnetic field

A computer modelling of magnetization behavior in ultrathin ferromagnetic films, divided by antiferromagnetic film is carried out. The exchange integral value is different for each ferromagnetic films. One of the films is magnetohard, the second one is magnetosoft. The situation where magnetosoft film has the exchange integral value twice smaller than the value of magnetohard film is investigated. Heisenberg model is used. Calculations are made using Metropolis algorithm. The phase transition temperature is obtained for all three films. The magnetic field was applied along the film plane. The simulation showed that magnetizations of ferromagnetic films first become perpendicular to the direction the staggered magnetization vector in the antiferromagnetic film. With a higher magnetic field value, the magnetization vectors of the ferromagnetic films become mutually perpendicular. Thus, in these multi-layer systems, it is possible to control the orientation of the substances spins, which is an important property for implementing spintronics devices.

Dynamics of Frenkel Excitons in Pentacene.

The dispersion relation for noninteracting excitons and the influence of perturbative corrections are examined in the case of pentacene structure. The values of exchange integrals are determined by nonlinear fits to the experimental dispersion data, obtained by the inelastic electron scattering reported in recent experiments. We obtain theoretical dispersion curves along four different directions in the Brillouin zone which possess the same periodicity as the experimental data. We also show that perturbative corrections are negligible since the exciton gap in the dispersion relation is huge in comparison to the exchange integrals.

One-Dimensional Chain-Type Dicopper Coordination Polymer Linked by 1,4-Di(4-pyridyl)benzene; Synthesis, Crystal Structure, Magnetic Property, and Gas-Adsorption Property

A one-dimensional chain-type dicopper(II) coordination polymer with 1,4-di(4-pyridyl)-benzene (dpybz), [Cu2(O2C-tBu)4(dpybz)] (1), is synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy, and CHN elemental analysis. Single crystal X-ray diffraction confirms that the one-dimensional chains of 1 are assembled with CH···π interactions at the dpybz moieties to form a brick-like porous network structure. Magnetic susceptibility measurement and broken-symmetry density functional theory (BS-DFT) calculations indicate that (i) antiferromagnetic interactions are present between two copper ions through the bridging carboxylate ligands; the observed exchange integral value (J) of 1 is −175.3 cm−1, which is consistent with the DFT-calculated value for 1 (−174.5 cm−1), and (ii) the magnetic interaction between two Cu2 units through the dpybz ligand is negligible. N2 adsorption measurements indicate that the porous structure of 1 is retained even after evacuation of the guest solvents from the pores of 1, and 1 adsorbs N2 molecules into its pores (the Langmuir surface area of 1 is estimated as 538.0 m2/g).

Mechanisms of optical orientation of an individual Mn2+ ion spin in a II–VI quantum dot

We provide a theoretical description of the optical orientation of a single Mn2+ ion spin under quasi-resonant excitation demonstrated experimentally by Goryca et al (2009 Phys. Rev. Lett. 103 087401). We build and analyze a hierarchy of models by starting with the simplest assumptions (transfer of perfectly spin-polarized excitons from Mn-free dot to the other dot containing a single Mn2+ spin, followed by radiative recombination) and subsequently adding more features, such as spin relaxation of electrons and holes. Particular attention is paid to the role of the influx of the dark excitons and the process of biexciton formation, which are shown to contribute significantly to the orientation process in the quasi-resonant excitation case. Analyzed scenarios show how multiple features of the excitonic complexes in magnetically-doped quantum dots, such as the values of exchange integrals, spin relaxation times, etc, lead to a plethora of optical orientation processes, characterized by distinct dependencies on light polarization and laser intensity, and occurring on distinct timescales. Comparison with experimental data shows that the correct description of the optical orientation mechanism requires taking into account Mn2+ spin-flip processes occurring not only when the exciton is already in the orbital ground state of the light-emitting dot, but also those that happen during the exciton transfer from high-energy states to the ground state. Inspired by the experimental results on energy relaxation of electrons and holes in nonmagnetic dots, we focus on the process of biexciton creation allowed by mutual spin-flip of an electron and the Mn2+ spin, and we show that by including it in the model, we obtain good qualitative and quantitative agreement with the experimental data on quasi-resonantly driven Mn2+ spin orientation.

Study of the critical behavior of antiferromagnetic thin films by computer modeling

In article the study of the surface phase changes in the thin films described by the antiferromagnetic Ising model, by computer modeling is executed. The Metropolis algorithm is used. Modeling is executed at various values of exchange integrals relation on a surface and in bulk of films RS. The difference of exchange integral between the surface spins and the first subsurface layer RSB from volume value is considered. The limiting cases of the value RSB are considered. Two order parameters are used. The first order parameter defines an antiferromagnetic order in the bulk of system. It is calculated as chess magnetization of the spins located not on a surface. Its value is equal to the difference of magnet moments for two sublattices. For study of the surface phase transition, the second order parameter is entered. It is calculated as chess magnetization of the spins located on the free surface. For definition of transition temperature, bulk and surface Binder’s cummulants are used. The computer experiment for various values of film thickness from 4 to 12 layers is made. The relation of exchange integrals changed from 0.5 to 2.0. Temperatures of bulk and surface phase transition are identical at all relations of exchange integrals. Transition temperature grows at increase in the exchange integrals relation RS. Growth rate of transition temperature depends on thickness of a film and velue RSB. The difference of exchange integral between the surface layer and the first subsurface layer leads to more rapid growth of the transition temperature. For all values of exchange integrals there is a cross point for temperature curves at any thickness of a film.

Dinuclear Metallacycles with Single M–X–M Bridges (X = Cl–, Br–; M = Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II)): Strong Antiferromagnetic Superexchange Interactions

A series of monochloride-bridged, dinuclear metallacycles of the general formula [M2(μ-Cl)(μ-L)2](ClO4)3 have been prepared using the third-generation, ditopic bis(pyrazolyl)methane ligands L = m-bis[bis(1-pyrazolyl)methyl]benzene (Lm), M = Cu(II), Zn(II), and L = m-bis[bis(3,5-dimethyl-1-pyrazolyl)methyl]benzene (Lm*), M = Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II). These complexes were synthesized from the direct reactions of M(ClO4)2·6H2O, MCl2, and the ligand, Lm or Lm*, in the appropriate stoichiometric amounts. Three analogous complexes of the formula [M2(μ-Cl)(μ-L)2](BF4)3, L = Lm, M = Cu(II), and L = Lm*, M = Co(II), Cu(II), were prepared from the reaction of [M2(μ-F)(μ-L)2](BF4)3 and (CH3)3SiCl. The bromide-bridged complex [Cu2(μ-Br)(μ-Lm*)2](ClO4)3 was prepared by the first method. Three acyclic complexes, [Co2(μ-Lm)μ-Cl4], [Co2(μ-Lm*)Cl4], and [Co2(μ-Lm*)Br4], were also prepared. The structures of all [M2(μ-X)(μ-L)2]3+ (X = Cl-, Br-) complexes have two ditopic bis(pyrazolyl)methane ligands bridging two metals in a metallacyclic arrangement. The fifth coordination site of the distorted trigonal bipyramidal metal centers is filled by a bridging halide ligand that has an unusual linear or nearly linear M-X-M angle. The NMR spectra of [Zn2(μ-Cl)(μ-Lm*)2](ClO4)3 and especially [Cd2(μ-Cl)(μ-Lm*)2](ClO4)3 demonstrate that the metallacycle structure is maintained in solution. Solid state magnetic susceptibility data for the copper(II) compounds show very strong antiferromagnetic exchange interactions, with -J values of 536 cm-1 for [Cu2(μ-Cl)(μ-Lm)2](ClO4)3·xCH3CN, 720 cm-1 for [Cu2(μ-Cl)(μ-Lm*)2](ClO4)3, and 945 cm-1 for [Cu2(μ-Br)(μ-Lm*)2](ClO4)3·2CH3CN. Smaller but still substantial antiferromagnetic interactions are observed with other first row transition metals, with -J values of 98 cm-1 for [Ni2(μ-Cl)(μ-Lm*)2](ClO4)3, 55 cm-1 for [Co2(μ-Cl)(μ-Lm*)2](ClO4)3, and 34 cm-1 for [Fe2(μ-Cl)(μ-Lm*)2](ClO4)3. EPR spectra of [Cu2(μ-Cl)(μ-Lm*)2](BF4)3 confirm the dz2 ground state of copper(II). In addition, the sign of the zero-field splitting parameter D was determined to be positive for [Cu2(μ-F)(μ-Lm*)2](BF4)3. Electronic spectra of the copper(II) complexes as well as Mössbauer spectra of the iron(II) complexes were also studied in relation with the EPR spectra and magnetic properties, respectively. Density functional theory calculations were performed using ORCA, and exchange integral values were obtained that parallel but are slightly higher than the experimental values by about 30%.

Micromagnetic simulation of the influence of grain boundary on cerium substituted Nd-Fe-B magnets

A three-dimensional finite element model was performed to study the magnetization reversal of (CexNd1-x)2Fe14B nanocomposite permanent magnets. The influences of volume fraction, width and performance parameters of the grain boundary (GB) composition on the coercivity were analyzed by the method of micromagnetic simulation. The calculation results indicate that the structure and chemistry of GB phase play important roles in Nd2Fe14B-based magnets. An abnormal increase in the value of coercivity is found to be connected with the GB phase, approximately when the percentage of doped cerium is between 20% and 30%. While the coercivity decreases directly with the increase in cerium content instead of being abnormal when there is no GB phase in magnets at all or the value of magnetocrystalline anisotropy or exchange integral is too large.

Synthesis, structure and properties of nickel-iron-tungsten alloy electrodeposits - Part II: Effect of microstructure on hardness, electrical and magnetic properties

Nanostructured nickel-iron-tungsten alloys were produced by electrodeposition from an ammoniacal citrate bath. The tungsten content of the alloy ranged from 0.8 wt.% to 11 wt.%, and the crystal grain size of the FCC phase of the solid solution of iron and tungsten in nickel was between 14 nm and 3.3 nm. The amorphous phase content of the alloy increases with decreasing crystal grain size. As the amorphous phase content increases, the magnetization, electrical conductivity and hardness of the alloy decrease. Annealing the alloy to crystallization temperature results in structural relaxation during which the alloy undergoes short-range ordering in conjunction with decreases in the density of chaotically distributed dislocations and internal microstrain level, which increases the exchange integral value, the electronic density of states at the Fermi level, the mean free path of electrons, the ordering and the mean size of cluster in the sliding plane and results in more uniform orientation of dipole moments of certain nanoparticles. These changes: a) increase the mobility of magnetic domain walls, facilitate the orientation of domains in the external magnetic field and cause an increase in magnetization; b) cause a decrease in electrical resistance, and c) impede the sliding of grain boundaries and increase the hardness of the alloy. Annealing the alloys at temperatures above 400?C results in amorphous phase crystallization and larger crystal grains of the FCC phase, along with a decrease in the density of chaotically distributed dislocations and a decrease in internal microstrain level. The formation of larger crystal grains reduces the hardness of the alloy, decreases its specific electrical resistance and impedes both the orientation of certain magnetic domains and the shift of walls of already oriented domains, thus inducing a decrease in magnetization. The heat released during the milling of Ni87.3Fe11.3W1.4 alloy with FCC-phase crystal grains 8.8 nm in average size causes amorphous phase crystallization, FCC crystal grain growth and an increase in magnetization. Alloys with relatively high tungsten content (11 wt. %) have an inhomogeneous composition, a high proportion of the amorphous phase and FCC crystal grains with an average size of 3.3 nm. This microstructure results in magnetic domains that have different and relatively low thermal stabilities and relatively low degrees of magnetization.

Bio-relevant cobalt(II) complexes with compartmental polyquinoline ligand: Synthesis, crystal structures and biological activities

Three new Co(II) complexes, [Co4(L)2(μ3-CrO4)2](ClO4)2·2CH3CN (1), [Co2(L)(μ2-na)(H2O)](ClO4)2 (2) and [Co2(L)(μ2-ba)](ClO4)2·0.5CH3CN (3) (Hna=nicotinic acid, Hba=benzoic acid, HL=N,N,N′,N′-tetrakis (2-quinolylmethyl)-1,3-diaminopropan-2-ol), have been synthesized and characterized by various physicochemical techniques. The Co(II) centers are connected by endogenous alkoxy bridge from L− and various extrinsic auxiliary linkers, some of which display coordination number asymmetry (5, 6-coordinated for 1 and 2; 5, 5-coordinated for 3). It is worth mentioning that complex 1 contains two rare reported μ3-η1, η1, η1-CrO42− moieties. Susceptibility data of three complexes indicated intramolecular antiferromagnetic coupling of high-spin Co(II) atoms with exchange integral values (J) −14.94cm−1, −11.26cm−1 and −13.66cm−1 for 1, 2 and 3, respectively. Interaction of compounds with calf thymus DNA (CT-DNA) have been investigated by absorption spectral titration, ethidium bromide (EB) displacement assay and viscosity measurement, which revealed that compounds bound to CT-DNA with a moderate intercalative mode, accompanied the affinities order: 1>2≈3. Three complexes exhibit oxidative cleavage of pBR322 plasmid DNA including a reliance on H2O2 as the activator. Compound 1 demonstrates an increased DNA cleavage activity as compared with 2 and 3, which could degrade super coiled DNA (SC DNA) into nicked coiled DNA (NC DNA) in lower concentration (5μM). Moreover, all compounds could quench the intrinsic fluorescence of bovine serum albumin (BSA) in a static quenching process. Complex 1 also shows higher anticancer activity than cisplatin with lower IC50 value of incubation for both 24h and 48h.

EPR Spectroscopy of Mercury-Organic Compounds with Nitroxide Radicals

Intramolecular electron spin exchange as a function of temperature, solvent viscosity and polarity has been studied by X-band electron paramagnetic resonance (EPR) spectroscopy for two nitroxide biradicals containing mercury-organic groups in the bridge connecting two 1-oxyl-2,2,6,6-tetramethylpiperidine-3,4-ene-nitroxide rings, R. The temperature dependence of the isotropic hyperfine splitting (hfs) constant a N and the exchange integral value |J/a| of the biradicals were measured from EPR spectra and subsequently analyzed comparing to a N and a Hg hfs constants of ClHgR radical dissolved in the same solvents. In all cases, the interaction of solvent molecules (SM) with >N–O fragments of nitroxide rings led to a slight decrease in a values with increasing temperature. The |J/a| value varied slightly with temperature T changes. The changes of |J/a| are much less comparing to those with variation of the solvent polarity. The interaction between SM and Hg atoms inside the bridge is observed and discussed.

Effect of the applied magnetic field and the layer thickness on the magnon properties in bilayers Co/Pt and symmetrical trilayer Pt/Co/Pt

We have studied the elementary magnetic excitations and their dynamics in multilayer Co(t Co)/Pt(t Pt) and Pt(t Pt)/Co(t Co)/Pt(t Pt) under an applied magnetic field. The Heisenberg hamiltonian used takes into account the magneto-crystalline and surface anisotropies, the exchange and dipolar interactions. The calculated excitation spectrum εN(k) presents a structure with two sub-bands corresponding to the magnons of surface and volume respectively. The existence of a gap of creating these magnons is also highlighted. The lifetimes deduced from these gaps are in good agreement with the results of previous studies. The thermal evolution of the magnetization mz indicates that the system undergoes a dimensional crossover 3D–2D when the temperature increases. The calculated and measured magnetizations are compared and they are in good agreement. The exchange integral and critical temperature values deduced from these adjustments are in very good agreement with the results of previous works.

DFT calculations of effective exchange integrals at the complete basis set limit on oxo-vanadium ring complex

A new scheme for calculations of effective exchange integral (J) values at the complete basis set (CBS) limit is proposed based on an extrapolation method of the total energy and an approximate spin projection (AP) method. By using the scheme, the J values between oxo-vanadium units in a (VO)7 ring complex at the CBS limit are calculated with several hybrid density functional theory (DFT) functional sets that are BHandHLYP, B3LYP and CAM-B3LYP. The calculated results indicate that the J values at the CBS limit with BHandHLYP reproduces the experimental result well. In addition, some basis sets such as Dunning’s correlation-consistent polarized valence, Pople series and def2 series are also examined to elucidate which basis function reproduces the J values at the CBS limit. The results indicate that the basis sets that are larger than 6-31+G∗ level are at least required to reproduce the J values of the (VO)7 complex at the CBS limit.

Modeling of the magnetic properties of nanomaterials with different crystalline structure

We propose a method for modeling the magnetic properties of nanomaterials with different structures. The method is based on the Ising model and the approximation of the random field interaction. It is shown that in this approximation, the magnetization of the nanocrystal depends only on the number of nearest neighbors of the lattice atoms and the values of exchange integrals between them. This gives a good algorithmic problem of calculating the magnetization of any nano-object, whether it is ultrathin film or nanoparticle of any shape and structure, managing only a rule of selection of nearest neighbors. By setting different values of exchange integrals, it is easy to describe ferromagnets, antiferromagnets, and ferrimagnets in a unified formalism. Having obtained the magnetization curve of the sample it is possible to find the Curie temperature as a function of, for example, the thickness of ultrathin film. Afterwards one can obtain the numerical values for critical exponents of the phase transition "ferromagnet – paramagnet". Good agreement between the results of calculations and the experimental data proves the correctness of the method.

Substituent Effects on Core Structures and Heterogeneous Catalytic Activities of MnIII(μ-O)2MnIV Dimers with 2,2′:6′,2″-Terpyridine Derivative Ligands for Water Oxidation

[(OH(2))(R-terpy)Mn(μ-O)(2)Mn(R-terpy)(OH(2)) ](3+) (R-terpy = 4'-substituted 2,2':6',2″-terpyridine, R = butoxy (BuO), propoxy (PrO), ethoxy (EtO), methoxy (MeO), methyl (Me), methylthio (MeS), chloro (Cl)) have been synthesized as a functional oxygen-evolving complex (OEC) model and characterized by UV-vis and IR spectroscopic, X-ray crystallographic, magnetometric, and electrochemical techniques. The UV-vis spectra of derivatives in water were hardly influenced by the 4'-substituent variation. X-ray crystallographic data showed that Mn centers in the Mn(III)(μ-O)(2)Mn(IV) cores for derivatives with R = H, MeS, Me, EtO, and BuO are crystallographically indistinguishable, whereas the derivatives with R = MeO and PrO gave the significantly distinguishable Mn centers in the cores. The indistinguishable Mn centers could be caused by rapid electron exchange between the Mn centers to result in the delocalized Mn(μ-O)(2)Mn core. The exchange integral values (J = -196 to -178 cm(-1)) for delocalized cores were lower than that (J = -163 to -161 cm(-1)) for localized cores, though the Mn···Mn distances are nearly the same (2.707-2.750 Å). The half wave potential (E(1/2)) of a Mn(III)-Mn(IV)/Mn(IV)-Mn(IV) pair of the derivatives decreased with an increase of the electron-donating ability of the substituted groups for the delocalized core, but it deviated from the correlation for the localized cores. The catalytic activities of the derivatives on mica for heterogeneous water oxidation were remarkably changed by the substituted groups. The second order rate constant (k(2)/mol(-1) s(-1)) for O(2) evolution was indicated to be correlated to E(1/2) of a Mn(III)-Mn(IV)/Mn(IV)-Mn(IV) pair; k(2) increased by a factor of 29 as E(1/2) increased by 28 mV.

Theoretical study of intra- and inter-chain magnetic interactions in [Ni(chxn) 2Br]Br 2

The intra- and the inter-chain magnetic interactions in [Ni(chxn) 2Br]Br 2, which is one of the typical one-dimensional (1-D) MX complexes are examined by using an unrestricted hybrid DFT (UB3LYP) method. Calculated effective exchange integral ( J) value along the 1-D chain is 2 J Intra = −4016 K and is close to an experimental result (−3600 K). On the other hand, a very weak anti-ferromagnetic inter-chain interaction through Br − ions is observed. The value is estimated to be 2 J Inter = −2 to −6 K. In addition to the J values, transfer integral ( t), on-site Coulomb repulsion ( U) and charge transfer energy ( E CT) values along the 1-D chain are also estimated to be 0.46, 2.46 and 0.6 eV, respectively.

Broken-symmetry natural orbital (BSNO)–Mk-MRCC study on the exchange coupling in the binuclear copper(II) compounds

We have investigated the scope and applicability of Mukherjee’s state-specific multireference coupled cluster singles and doubles (Mk-MRCCSD) method on the magnetic interactions in dichloro-, oxo-, and peroxo-bridged binuclear Cu(II) complexes. Several reference orbitals including broken-symmetry natural orbitals (BSNOs) are examined for the Mk-MRCCSD computations. We compare the effective exchange integral ( J) values calculated by Mk-MRCCSD with those calculated by conventional complete active space self-consistent field (CASSCF) and MRMP2. The BS methods with approximate spin-projection (AP) method are also performed for comparison. It is found that the Mk-MRCCSD method can be applicable to the prediction of exchange couplings in binuclear copper(II) containing systems.