Theoretical calculations of effective exchange integrals by spin projected and unprojected broken-symmetry methods. I. Cluster models of K2NiF4-type solids

Electronic Structure and Magneto-Structural Correlations Study of Cu2UL Trinuclear Schiff Base Complexes: A 3d-5f-3d Case

The magnetic properties of trinuclear Schiff base complexes M₂AnLⁱ (M^II = Zn, Cu; An^IV = Th, U; Lⁱ = Schiff base; i = 1-4, 6, 7, 9), exhibiting the [M(μ-O)₂]₂U core structure with adjacent M1···U and M2···U and next-adjacent M1···M2 interactions, featuring 3d-5f-3d subsystems, have been investigated theoretically using relativistic ZORA/B3LYP computations combined with the broken symmetry (BS) approach. Bond order and natural population analyses reveal that the covalent contribution to the bonding within the Cu-O-U coordination is important thus favoring superexchange coupling between the transition metal and the uranium magnetic centers. The calculated coupling constants J_CuU between the Cu and U atoms, agree with the observed shift from the antiferromagnetic (AF) character of the L^1,2,3,4 complexes to the ferromagnetic (ferro) of the L^6,7,9 ones. The structural parameters, i.e., the Cu···U distances and the Cu-O-U angles, as well as the electronic factors driving the magnetic couplings are discussed. The analyses are supported by the study of the mixed ZnCuULⁱ and Cu₂ThLⁱ systems, where in the first complex the Cu^II (3d⁹) ion is replaced by the diamagnetic Zn^II (3d¹⁰) one, whereas in the second complex the U^IV (5f²) paramagnetic center is replaced by the diamagnetic Th^IV (5f⁰) one.

Theoretical Investigation of the Electronic Structure and Magnetic Properties of Oxo-Bridged Uranyl(V) Dinuclear and Trinuclear Complexes

The uranyl(V) complexes [UO₂(dbm)₂K(18C6)]₂ (dbm = dibenzoylmethanate) and [UO₂(L)]₃(L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate), exhibiting diamond-shaped U₂O₂ and triangular-shaped U₃O₃ cores respectively with 5f¹-5f¹ and 5f¹-5f¹-5f¹ configurations, have been investigated using relativistic density functional theory (DFT). The bond order and QTAIM analyses reveal that the covalent contribution to the bonding within the oxo cores is slightly more important for U₃O₃ than for U₂O₂, in line with the shorter U-O distances existing in the trinuclear complex in comparison to those in the binuclear complex. Using the broken symmetry (BS) approach combined with the B3LYP functional for the calculation of the magnetic exchange coupling constants (J) between the magnetic centers, the antiferromagnetic (AF) character of these complexes was confirmed, the estimated J values being respectively equal to -24.1 and -7.2 cm^-1 for the dioxo and trioxo species. It was found that the magnetic exchange is more sensitive to small variations of the core geometry of the dioxo species in comparison to the trioxo species. Although the robust AF exchange coupling within the U_xO_x cores is generally maintained when small variations of the UOU angle are applied, a weak ferromagnetic character appears in the dioxo species when this angle is higher than 114°, its value for the actual structure being equal to 105.9°. The electronic factors driving the magnetic coupling are discussed.

Electronic Structure and Magnetic Properties of Dioxo-Bridged Diuranium Complexes with Diamond-Core Structural Motifs: A Relativistic DFT Study

Electronic structures and magnetic properties of the binuclear bis(μ-oxo) U(IV)/U(IV) K2[{(((nP,Me)ArO)3tacn)U(IV)}2(μ-O)2] and U(V)/U(V) [{(((nP,Me)ArO)3tacn)U(V)}2(μ-O)2] (tacn = triazacyclononane, nP = neopentyl) complexes, exhibiting [U(μ-O)2U] diamond-core structural motifs, have been investigated computationally using scalar relativistic Density Functional Theory (DFT) combined with the Broken Symmetry (BS) approach for their magnetic properties. Using the B3LYP hybrid functional, the BS ground state of the pentavalent [U(V)(μ-O)2U(V)] 5f(1)-5f(1) complex has been found of lower energy than the high spin (HS) triplet state, thus confirming the antiferromagnetic character in agreement with experimental magnetic susceptibility measurements. The nonmagnetic character observed for the tetravalent K2[U(IV)(μ-O)2U(IV)] 5f(2)-5f(2) species is also predicted by our DFT calculations, which led practically to the same energy for the HS and BS states. As reported for related dioxo diuranium(V) systems, superexchange is likely to be responsible for the antiferromagnetic coupling through the π-network orbital pathway within the (μ-O)2 bridge, the dissymmetrical structure of the U2O2 core playing a determining role. In the case of the U(IV) species, our computations indicate that the K(+) counterions are likely to play a role for the observed magnetic property. Finally, the MO analysis, in conjunction with NPA and QTAIM analyses, clarify the electronic structures of the studied complexes. In particular, the fact that the experimentally attempted chemical oxidation of the U(V) species does not lead straightforwardly to binuclear complexes U(VI) is clarified by the MO analysis.

Potential nonadiabatic reactions: ring-opening 4,6-dimethylidenebicyclo[3.1.0]hex-2-ene derivatives to aromatic reactive intermediates

Potential singlet-triplet surface crossings for the ring opening of 4,6-dimethylidenebicyclo[3.1.0]hex-2-ene derivatives were explored using density functional theory (DFT) and complete active space self-consistent field (CASSCF) methods. Since these ring openings involve relatively high energy species that lead to relatively stable aromatic species, a good scenario for potential nonadiabatic events, we posited that the reaction paths of these ring openings might come close to or cross excited state surfaces. At the DFT level of theory, all reaction paths exhibited characteristics suggestive of singlet-triplet intersections along their paths. 6-Methylidenebicyclo[3.1.0]hex-3-en-2-one and a closely related derivative (4-methylidenebicyclo[3.1.0]hex-2-en-6-one) were explored at the CASSCF level of theory; CASSCF results were qualitatively similar to DFT results and yielded spin-orbit couplings of 1.1-1.4 cm(-1) at the singlet-triplet crossing points.

Spin states in polynuclear clusters: the [Fe2O2] core of the methane monooxygenase active site

The ability to provide a correct description of different spin states of mono- and polynuclear transition metal complexes is essential for a detailed investigation of reactions that are catalyzed by such complexes. We study the energetics of different total and local spin states of a dinuclear oxygen-bridged iron(IV) model for the intermediate Q of the hydroxylase component of methane monooxygenase by means of spin-unrestricted Kohn-Sham density functional theory. Because it is known that the spin state total energies depend systematically on the density functional, and that this dependence is intimately connected to the exact exchange admixture of present-day hybdrid functionals, we compare total energies, local and total spin values, and Heisenberg coupling constants calculated with the established functionals BP86 and B3LYP as well as with a modified B3LYP version with an exact exchange admixture ranging from 0 to 24%. It is found that exact exchange enhances local spin polarization. As the exact exchange admixture increases, the high-spin state is energetically favored, although the Broken-Symmetry state always is the ground state. Instead of the strict linear variation of the energy splittings observed for mononuclear complexes, a slightly nonlinear dependence is found. The Heisenberg coupling constants J(Fe1Fe2) --evaluated according to three different proposals from the literature -- are found to vary from -129 to -494 cm(-1) accordingly. The experimental finding that intermediate Q has an antiferromagnetic ground state is thus confirmed.

A DFT Study of the Ground State Multiplicities of Linear vs Angular Polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.

Theoretical calculations of effective exchange integrals by spin projected and unprojected broken-symmetry methods. III. Cluster models of three-dimensional KNiF3 solid

Previously, we have performed the spin-polarized hybrid-density functional theory (HUDFT) calculations for elucidating magnetic properties of the two-dimensional (2D) K2NiF4 and K2CuF4 solids. In Part I, it has been concluded that the half-and-half-(HH-) type HUDFT method is one of the best calculation methods for these species. On the other hand, in Part II, we have demonstrated that potential curves for cluster models of K2CuF4 and KCuF3 are reasonably calculated by the HH-type HUDFT method under the approximate spin projection, and the lattice distortion resulted by Jahn-Teller effect is expressed as the second-order polynomial. In this study, we pay attention to the three-dimensional (3D) magnetic interactions in KNiF3. Our effective exchange integral Jab schemes for 3D cluster models such as KNi8F12 (4) with and without point charges have provided the reasonable Jab values (-30.24-34.48 cm(-1)), in comparison with the experimental one (-30.58 cm(-1)). The 3D magnetic interactions have been investigated from viewpoints of the Mulliken spin density and charge density populations, the natural orbital analysis, and chemical indices. Point charges located in positions of fluorine anion adjacent to cluster model have reproduced Jab values well. Roles of potassium as counter cation in KNiF3 solid were also investigated. It was concluded that potassium has a role of stabilizing the 3D magnetic structures. Finally, the mutual relationships between broken-symmetry and symmetry-adapted approaches are discussed on the basis of chemical indices.