Effective Exchange Integrals Research Articles

Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules

Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the MS = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.

Relative stability among intermediate structures in S2 state of CaMn4O5 cluster in PSII by using hybrid-DFT and DLPNO-CC methods and evaluation of magnetic interactions between Mn ions

Full geometry optimization of all S2 intermediates in OEC (oxygen-evolving complex) of PSII (photosystem II) were carried out by using UB3LYP-D3/Def2-TZVP with COSMO solvation effects. Our detail calculations yielded meta-stable structures of six (=3 × 2 (HS (high-spin), IS (intermediate-spin)) intermediates for W1 = W2 = H2O and eight (=4 × 2 (HS, IS)) intermediates for W1 = OH− or W2 = OH−, and were named to H2O and OH models, respectively. In the next step, relative stability among these intermediate structures were investigated by hybrid-DFT and DLPNO-CC methods. UB3LYP methods show that right (R)-opened structures (open-cubane) are more stable than left (L)-opened structures (closed-cubane) by about 3.5 kcal/mol, though decreasing of DFT-weights suppresses such energy gaps. DLPNO-CCSD(T0) methods promote stabilization of (L)-structures and finally reproduce near degeneration or more stable (L)-structure. All pattern of spin configurations in four Mn(III) and Mn(IV) ions were assumed and BS (broken-symmetry) solutions were successfully obtained to find the most stable spin structures. This complete sets of all spin conformations enabled us evaluate sets of effective exchange integrals J as magnetic coupling parameters. The calculated J values for the spin Hamiltonian elucidated one g2 (S = 1/2) and two g4 (S = 5/2) molecular structures in the S2 state in accord with the recent EXAFS results.

Comparison of Effective Exchange Integrals of H-H and H-He-H Chains vs. Single Molecules: A Theoretical Study

The effect of periodic structure on the effective exchange integral (Jab) was investigated using density functional theory calculations with plane-wave basis and approximate spin projection scheme ...

Decomposition of Effective Exchange Integrals of Radical Dimers Using Bond Energy Density Analysis

In this letter, effective exchange integrals of radical dimers obtained by density functional calculations are decomposed into atomic-pair components. The bond energy density analysis, which was originally proposed to evaluate the energy of a chemical bond, was found to be a useful tool to analyze the magnetic interaction of radical dimers.

Ab initio computations of zero-field splitting parameters and effective exchange integrals for single-molecule magnets (Mn12- and Mn11Cr-acetate clusters)

In this study, the zero-field splitting parameters (D, E) and effective exchange integrals (J) for a Mn12/Mn11Cr mixed crystal were evaluated using ab initio molecular orbital (MO) computations based on the hybrid density functional theory (DFT) methods for Mn11Cr∗-acetate cluster (Mn12 and Mn11Cr mixing). In this study, Mn12-acetate, Mn11Cr-acetate, and Mn12−nCrn-acetate clusters were focused on. The zero-field splitting (ZFS) parameters are obtained by UB3LYP methods, i.e. −0.339cm−1 (Mn12-acetate) and −0.351cm−1 (Mn11Cr-acetate). The energy barriers were estimated to be 53.7K and 50.4K, which showed good agreement with previously reported experimental values of 68.8K and 56.8K, respectively. The origin of such anisotropy is assumed to be the eight MnIII ions with d4-electrons in their outer ring subunits, where elongated conformation along the axial direction becomes very important and leads to negative D values. The spin networks in these clusters were discussed by using the effective exchange integral sets. The Js value, as estimated by the UB3LYP method revealed that the J2, J3, and J3′ interactions played important roles in describing the parallel spin ordering in cubane and ring subunits as well as the antiferromagnetic coupling between two subunits. The other interactions, i.e. J1, J1′, J4, and J4′ somewhat disturbed the spin ordering in the Mn12-acetate cluster. The substitution of MnIV by CrIII did not change the spin network. However, the total S value changed after the substitution.

UNO DMRG CASCI calculations of effective exchange integrals for m-phenylene-bis-methylene spin clusters

ABSTRACTTheoretical examinations of the ferromagnetic coupling in the m-phenylene-bis-methylene molecule and its oligomer were carried out. These systems are good candidates for exchange-coupled systems to investigate strong electronic correlations. We studied effective exchange integrals (J), which indicated magnetic coupling between interacting spins in these species. First, theoretical calculations based on a broken-symmetry single-reference procedure, i.e. the UHF, UMP2, UMP4, UCCSD(T) and UB3LYP methods, were carried out with a GAUSSIAN program code under an SR wave function. From these results, the J value by the UHF method was largely positive because of the strong ferromagnetic spin polarisation effect. The J value by the UCCSD(T) and UB3LYP methods improved an overestimation problem by correcting the dynamical electronic correlation. Next, magnetic coupling among these spins was studied using the CAS-based method of the symmetry-adapted multireference methods procedure. Thus, the UNO DMRG CASCI (UNO, unrestricted natural orbital; DMRG, density matrix renormalised group; CASCI, complete active space configuration interaction) method was mainly employed with a combination of ORCA and BLOCK program codes. DMRG CASCI calculations in valence electron counting, which included all orbitals to full valence CI, provided the most reliable result, and support the UB3LYP method for extended systems.

Magnetic fluctuations and effective magnetic moments inγ-iron due to electronic structure peculiarities

Applying the local density and dynamical mean field approximations to paramagnetic \gamma-iron we revisit the problem of theoretical description of magnetic properties in a wide temperature range. We show that contrary to \alpha-iron, the frequency dependence of the electronic self-energy has a quasiparticle form for both, t_{2g} and e_g states. In the temperature range T=1200-1500 K, where \gamma-iron exist in nature, this substance can be nevertheless characterized by temperature-dependent effective local moments, which yield relatively narrow peaks in the real part of the local magnetic susceptibility. At the same time, at low temperatures \gamma-iron (which is realized in precipitates) is better described in terms of itinerant picture. In particular, the nesting features of the Fermi surfaces yield maximum of the static magnetic susceptibility at the incommensurate wave vector q_{max} belonging the direction q_X-q_W (q_X=(2\pi/a)(1,0,0),q_W=(2\pi/a)(1,1/2,0), a is a lattice parameter) in agreement with the experimental data. This state is found however to compete closely with the states characterized by magnetic wave vectors along the directions q_X-q_L-q_K, where q_L=(2\pi/a)(1/2,1/2,1/2), q_K=(2\pi/a)(3/4,3/4,0). From the analysis of the uniform magnetic susceptibility we find that contrary to \alpha-iron, the Curie-Weiss law is not fulfilled in a broad temperature range, although the inverse susceptibility is nearly linear in the moderate-temperature region (1200-1500 K). The non-linearity of the inverse uniform magnetic susceptibility in a broader temperature range is due to the density of states peak located close to the Fermi level. The effective exchange integrals in the paramagnetic phase are estimated on the base of momentum dependent susceptibility.

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.

Effective Heisenberg exchange integrals of diluted magnetic semiconductors determined within realistic multi-band tight-binding models

Diluted magnetic semiconductors (DMS) like Ga1−x Mn x As are described by a realistic tight-binding model (TBM) for the (valence) bands of GaAs, by a Zener (J-)term modeling the coupling of the localized Mn-spins to the spins of the valence band electrons, and by an additional potential scattering (V-) term due to the Mn-impurities. We calculate the effective (Heisenberg) exchange interaction between two Mn-moments mediated by the valence electrons. The influence of the number of bands taken into account (6-band or 8-band TBM) and of the potential (impurity) scattering V-term is investigated. We find that for realistic values of the parameters the indirect exchange integrals show a long-range, oscillating (RKKY-like) behavior, if the V-term is neglected, probably leading to spin-glass behavior rather than magnetic order. But by including a V-term of a realistic magnitude the exchange couplings become short ranged and mainly positive allowing for the possibility of ferromagnetic order. Our results are in good agreement with available results of ab initio treatments.

Theoretical studies of electronic structures, magnetic properties and electron conductivities of one-dimensional Nin (n = 3, 5, 7) complexes

Electronic structures, magnetic properties and electron conductivities of linearly aligned one-dimensional (1-D) Ni(II)3, Ni(II)5 and Ni(II)7 complexes, i.e. [Ni3(dpa)4NCS2], [Ni5(tpda)4X2] (X = Cl, CN, N3, NCS) and [Ni7(teptra)4Cl2], are systematically investigated by the broken-symmetry B3LYP calculations and simulations based on an elastic scattering Green's function theory. Calculated spin densities appear only at terminal Ni ions, while inner Ni ions are the closed-shell. The calculated effective exchange integrals (J(ab)) values reproduce well the experimental results that indicate anti-ferromagnetic (AF) interactions between two terminal Ni ions. Natural orbitals and their occupation numbers show that a change in the weak AF couplings by axial ligands in penta-nickel complexes originates in σ-type orbitals. Simulated electron conductivities of [Ni3(dpa)4NCS2] and [Ni5(tpda)4NCS2] semi-quantitatively correspond to the experimental results. By the analyses, it is elucidated that electrons are mainly transmitted by σ-type orbitals, but the bonds between Au and axial ligands are also dominant factors for conductivity.

Conditions of ferromagnetic ordering in a model with Anderson-Hubbard centers: effective Hamiltonian approach

A model of strongly correlated electron system in which magnetic impurity levels are hybridized with conduction band has been considered. The effective Hamiltonian has been constructed for the case of strong Coulomb correlation on basis of configurational representation of Hamiltonian with Hubbard X-operators describing the localized spin subsystem. Criteria for the ferromagnetic ordering stabilization have been found in partial case of partially filled band for arbitrary temperatures and Curie temperature has been calculated. For the partial case of weak effective exchange the formula for the Curie temperature reproducing the well-established results has been calculated analytically. The electron concentration region favorable for ferromagnetic ordering is determined by hybridization through effective exchange integral.

Structure and reactivity of the mixed‐valence CaMn4O5(H2O)4 and CaMn4O4(OH)(H2O)4 clusters at oxygen evolution complex of photosystem II. Hybrid DFT (UB3LYP and UBHandHLYP) calculations

AbstractVery recently Umena et al. have determined the X‐ray diffraction (XRD) structure of the CaMn4O5 cluster in the oxygen evolution complex (OEC) of photosystem II (PSII) refined to 1.9 Å resolution. We have performed theoretical attempts to elucidate possible electronic and spin states of their new XRD structure of the CaMn4O5 cluster. For the purpose, hybrid density functional theory (UB3LYP and UBHandHLYP) calculations have been performed for the mixed‐valence (MV) CaMn(III)4‐ω(IV)ωO5(H2O)4 (1) and CaMn(III)4‐ω(IV)ωO4(OH)(H2O)4 (2) clusters as active catalytic site for water splitting reaction in OEC of PSII. Full geometry optimizations of 1a (ω = 2) and 2a (ω = 2) have been performed to elucidate scope and limitation of the cluster models. Both charge and spin fluctuated structures (48 UB3LYP solutions) have been considered for the MV 1a (ω = 2). Total energies obtained by these calculations have elucidated quasi‐degenerated electronic and spin states that are characterized by charge and spin density populations. The energy levels revealed by hybrid DFT are analyzed on the basis of the Heisenberg spin Hamiltonian model, providing the effective exchange integrals between manganese ions at a uniform or MV structure. The spin projections for hybrid DFT solutions are performed using the effective exchange integrals. The charge fluctuation model is introduced to analyze relative stabilities among MV structures of 1a and 2a. These computational results for 1a and 2a have explored several characteristic electronic properties of the species that are used for theoretical elucidation of possible mechanisms of water splitting reaction. Orbital and spin correlation diagrams are derived for the OO bond formation and oxygen evolution in the reaction. Implications of the computational results are also discussed in relation to available experiments and theoretical results by other groups. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Theoretical studies of d– d and d–π– d magnetic interactions in (EDT-TTFVO) 2FeBr 4 crystals

The effective exchange integrals ( J(HB)) of the Heisenberg spin model have been evaluated by using the ab initio MO and based on Hartree–Fock (HF) and density functional theory (DFT) for organic magnetic metals, the (EDT-TTFVO) 2FeBr 4 crystal based on the X-ray crystallographic structures at 113 K. In order to study the magnetic properties, we proposed some of the pairs, where the direct ( d– d) and indirect ( d–π– d) magnetic couplings between Fe(III) d-spins ( S = 5/2) without/with π-dimer spins ( S = 1/2) were calculated, respectively. The effective exchange integrals were evaluated by using UB3LYP method, and principal J values were 0.5, −0.1 and 0.4 K. From these results, it is found that there were three dimensional spin arrangements of Fe(III) d-spins. The Quantum Monte Carlo (QMC) simulations had been carried out with our calculated J values to evaluate the magnetic susceptibility for this molecular crystal, reproducing the experimental tendency.

Symmetry and broken symmetry in molecular orbital description of unstable molecules IV: comparison between single- and multi-reference computational results for antiaromtic molecules

First principle calculations of the effective exchange integrals (J) in the Heisenberg model for diradical species are presented for both symmetry-adapted multi-reference (MR) and single-reference broken-symmetry (BS) methods. The Mukherjee-type state-specific MR coupled cluster singles and doubles (MkCCSD) method with several different reference orbitals including BS natural orbitals is used to calculate the singlet–triplet energy gaps (S–T energy gap or 2J) and diradical characters for the antiaromatic molecules [a cyclopropenyl anion (CPA), b cyclobutadiene (CBD), and c cyclopentadienyl cation (CPC)], the cyclobutadiene derivatives with polar substitutents [d aminocyclobutadiene (ACBD), e formylcyclobutadiene (FCBD), and f 1-amino-2-formyl-cyclobutadiene (AFCBD)] and finally the cyclobutadine derivatives with radical substitutents [g 1,2-bis(methylene)cyclobutadiene (1,2-BMCBD) and h 1,3-bis(methylene)cyclobutadiene (1,3-BMCBD)]. For the BS methods, the spin-unrestricted Hartree–Fock based CCSD (UHF-CCSD), the CCD with the spin-unrestricted Brueckner determinant (UBD), and BS density functional theory (UDFT) computations are performed. Comparison between MkCCSD and the UHF-CCSD results indicates that spin-contamination of UHF-CCSD solutions still remains. In comparison with UHF-CCSD, the UBD results show that spin-contamination involved in BS solutions is greatly suppressed. To eliminate the spin contamination, an approximate spin-projection (AP) scheme is applied to the BS solutions. The AP procedure with the use of the expectation value of the total-spin operator corresponding to UHF-CCSD and UBD results yields good agreement with the MkCCSD results. As for the AP correction of the UDFT methods, three different computational schemes for predicting the expectation value of the total-spin operator are examined. Systematic comparisons between these methods are presented for the S–T energy gaps (2J). Implications of the present computational results have been discussed in relation to the design of magnetic oligomers and polymers.

Comment on “Two-Spinon and Four-Spinon Continuum in a Frustrated Ferromagnetic Spin-1/2Chain”

We show that LiVCuO4 should be described by strongly ferromagnetically coupled Heisenberg antiferromagnetic chains (HAC) in sharp contrast with the effective exchange integrals Ji given in Enderle et al., Phys. Rev. Lett. vol. 104, 237207 (2010), and the main issues of that work, namely, (i) LiVCuO4 is well described by two weakly ferromagnetically coupled interpenetrating Heisenberg antiferromagnetic spin-1/2 chains, (ii) the extracted exchange integrals J1, J2 agree with a previous spin-wave description (Enderle et al., Euphys. Lett. vol. 70, 237 (2005)), (iii) the spectral density of inelastic neutron scattering (INS) above 10 meV is ascribed to a 4-spinon continuum. Applying exact diagonalization and DMRG methods to fit their INS and magnetization M(H) data, supported by two independent microscopic methods (5-band Hubbard model and LSDA+U calculations), we demonstrate that LiCuVO4 exhibits strong inchain frustration with alpha =-J2/J1 < 1, i.e. strong coupling of the HAC at odds with (i). An alternative phenomenological set in accord with various experimental results is proposed. In view of the recent possible discovery of quantum-spin nematics and Bose condensation of two-magnon bound states (M. Zhitomirsky et al. arXiv:1003.4096v2 (2010), L. Svistov et al. ibid. 1005.5668v2 (2010)) in LiCuVO4 precise knowledge of the main J-values is of key importance.

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.

Labile electronic and spin states of the CaMn4O5 cluster in the PSII system refined to the 1.9 Å X-ray resolution. UB3LYP computational results

UB3LYP calculations were first performed to elucidate electronic and spin structures of the CaMn4O5 cluster in the oxygen-evolving-complex of the PSII system refined to the 1.9Å X-ray resolution by Kamiya, Shen, and their collaborators. Eight different UB3LYP solutions with axial spin structures were constructed to obtain the energy levels of the cluster on the basis of their X-ray structure. The energy diagrams were analyzed in terms of the Heisenberg model that involves six effective-exchange integrals between manganese ions. Several characteristic features of the electronic states of the cluster are revealed from these theoretical investigations based on the UB3LYP calculations.

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.

MkMRCC, APUCC, APUBD calculations of didehydronated species: comparison among calculated through-bond effective exchange integrals for diradicals

Mukherjee's type of multireference coupled-cluster (MkMRCC), approximate spin-projected spin-unrestricted CC (APUCC), and AP spin-unrestricted Brueckner's (APUBD) methods were applied to didehydronated ethylene, allyl cation, cis-butadiene, and naphthalene. The focus is on descriptions of magnetic properties for these diradical species such as S-T gaps and diradical characters. Several types of orbital sets were examined as reference orbitals for MkMRCC calculations, and it was found that the change of orbital sets do not give significant impacts on computational results for these species. Comparison of MkMRCC results with APUCC and APUBD results show that these two types of methods yield similar results. These results show that the quantum spin corrected UCC and UBD methods can effectively account for both nondynamical and dynamical correlation effects that are covered by the MkMRCC methods. It was also shown that appropriately parameterized hybrid density functional theory (DFT) with AP corrections (APUDFT) calculations yielded very accurate data that qualitatively agree with those of MRCC and APUBD methods. This hierarchy of methods, MRCC, APUCC, and APUDFT, is expected to constitute a series of standard ab initio approaches towards radical systems, among which we could choose one of them, depending on the size of the systems and the required accuracy.

Theoretical study of electronic structures of [(H2O)3(O-)Mn(μ-oxo)2Mn(OH2)4]q+ (q = 2 or 3) with Mn–O bond

Molecular geometries and electronic structures of manganese binuclear complexes, [(H(2)O)(3)(O-)Mn(bis-mu-oxo-O(2))Mn(OH(2))(4)](q+) (q = 2 or 3), which are model complexes of the S(3) state in the Kok cycle of OEC, were examined using hybrid density functional theory and broken symmetry method. The complexes of q = 2 and 3, which have a Mn-O bond, correspond to those derived from Mn(2)(II,III) and Mn(2)(III,III) at the S(0) state of the Kok cycle. The conformers with the Mn-O bond axial to the Mn(2)O(2) core are lower in energy than those with the equatorial Mn-O bond. The equatorial Mn-O bonds are assigned as Mn(III)-O*(-) and Mn(IV)-O*(-) for M(2)(II,III) and M(2)(III,III) series, respectively. The axial Mn-O bonds are Mn(IV)=O(2-) for M(2)(II,III) and Mn(IV)-O*(-) for Mn(2)(III,III). The characters of Mn-O orbitals are pi-orbitals composed of d-p interactions. The conformer with the axial Mn(IV)=O(2-) derived from M(2)(II,III) at S(0) is thermochemically unstable, leading to proton transfer to give two OHs in the complex, while the axial Mn(IV)-O*(-) from Mn(2)(III,III) at S(0) is stable without the proton transfer. The magnetic interactions between two Mn ions and O were also examined by estimations of effective exchange integrals.