Local Noncollinear Spin Analysis

Generalized spin σ-SCF method

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm^-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for Fe^III complexes. On the other hand, for a Ni^II polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.

Extraction of local spin-coupled states by second quantized operators

We present a methodology for analyzing chemical bonds embedded in the electronic wave function of molecules, especially in terms of spin correlations or so-called "local spin." In this paper, based on biorthogonal second quantization, the spin correlation functions of molecules are naturally introduced, which enables us to extract local singlet and local triplet elements from the wave function. We also clarify the relationship between these spin correlations and traditional chemical concepts, i.e., resonance structures. Several chemical reactions, including the intramolecular radical cyclization and the formation of preoxetane, are demonstrated to verify the analysis method numerically.

Modulating the relaxation dynamics of the Na2Mn3 system via an auxiliary anion change

This paper reports two closely related heteropentanuclear manganese complexes, namely, {Na₂Mn₃(opch)₃(μ₄-O)(μ₂-N₃) (μ₂-AcO)(μ₂-MeO)}·6CH₃OH·0.5H₂O (1) and {Na₂Mn₃(opch)₃(μ₄-O)(μ₂-N₃)₂(μ₂-AcO)}·2.5CH₃OH·2H₂O (2), where H₂opch is (E)-N'-(2-hydroxy-3-methoxybenzylidene)pyrazine-2-carbohydrazide. Single-crystal X-ray diffraction analysis reveals that the trigonal bipyramidal skeletons in both complexes are comparable, where a perfect triangular Mn₃ motif occupies the equatorial plane. Magnetic investigations suggest that overall antiferromagnetic coupling is present within the triangles of 1 and 2. However, their dynamic magnetic properties are drastically distinct. Indeed, complexes 1 and 2 show two kinds of dual slow magnetic relaxation processes that correspond to anisotropy barriers (Δ) of 9.2 cm^-1 (11.4 cm^-1 for 2) and 12.8 cm^-1 (30.0 cm^-1 for 2) for the low- and high-frequency domains, respectively. More importantly, a further comparative study of the structure and magnetism indicates that the coordination sphere of these two model complexes with the homologous hydrazone-based coordination sites undergoes an alteration from methoxide-O to azide-N upon a subtle change of the auxiliary anion accompanied by modulating octahedron geometries, leading to a further influence on different relaxation dynamics.

Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings

We analyze the effect of removing self-interaction error on magnetic exchange couplings using the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in the framework of density functional theory (DFT). We compare magnetic exchange couplings obtained from self-interaction-free FLOSIC calculations with the local spin density approximation (LSDA) with several widely used DFT realizations and wave function based methods. To this end, we employ the linear H-He-H model system, six organic radical molecules, and [Cu₂Cl₆]^2- as representatives of different types of magnetic interactions. We show that the simple self-interaction-free version of LSDA improves calculated couplings with respect to LSDA in all cases, even though the nature of the exchange interaction varies across the test set, and in most cases, it yields results comparable to modern hybrids and range-separated approximate functionals.