Quasi-Restricted Orbital Treatment for the Density Functional Theory Calculations of the Spin–Orbit Term of Zero-Field Splitting Tensors

Zero-field splitting parameters within exact two-component theory and modern density functional theory using seminumerical integration

An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin-dipole contribution and the response equations of the spin-orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn-Sham equations for the spin-orbit perturbation term. Second, the spin-orbit perturbation is formulated within relativistic exact two-component theory and the screened nuclear spin-orbit (SNSO) approximation. The accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. In addition, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin-orbit mean field Ansatz.

Isostructural M(ii) complexes (M = Mn, Fe, Co) with field-induced slow magnetic relaxation for Mn and Co complexes

We herein report the synthetic, structural, theoretical, and magnetic studies on three isostructural complexes, [M(L)2(CH3OH)2] (M = Mn (Mn), Fe (Fe), and Co (Co); HL = 2,6-bis(pyrazole-1-yl)pyridine-4-carboxylic acid). From single crystal X-ray crystallography, it is found that the complexes crystallized in the same space group (C2/c) and had seven-coordinate pentagonal bipyramidal structures. From direct current (dc) and alternating current (ac) magnetic susceptibility measurements, Mn and Co were found to undergo field-induced slow magnetic relaxation with two relaxation pathways. To elucidate the origin of the slow magnetic relaxation phenomena of Mn, electron paramagnetic resonance (EPR) measurements and theoretical calculations were performed. The EPR measurements were performed on polycrystalline powder samples, and the following parameters were obtained by simulating the EPR data: giso = 2.00 and small zero field splitting parameter D = -0.13 cm-1. To the best of our knowledge, this is the first example of a seven-coordinate mononuclear Mn(ii) complex undergoing slow magnetic relaxation.

Thermally activated delayed fluorescence processes for Cu(i) complexes in solid-state: a computational study using quantitative prediction

The photophysical properties of four representative Cu(i) complex crystals have been investigated using the combination of an optimally tuned one- and two-dimensional range-separated hybrid functional with the polarizable continuum model, and the thermal vibration correlation function (TVCF) approach. The calculated excited singlet-triplet energy gap, radiative rates and lifetimes match the experimentally available data perfectly. At 300 K, the reverse intersystem crossing (RISC) proceeds at a rate of k dir. RISC ≈ 106-8 s-1, which is 4-5 orders of magnitude larger than the mean phosphorescence rate, k P ≈ 102-3 s-1. At the same time, the ISC rate k dir. ISC ≈ 109 s-1 is again 2 orders of magnitude larger than the fluorescence rate k F ≈ 107 s-1. In the case of k dir. RISC ≫ k F and k dir. RISC ≫ k P, thermally activated delayed fluorescence should occur. Vibronic spin-orbit coupling can remarkably enhance the ISC rates by the vital "promoting" modes, which can provide crucial pathways to decay. This can be helpful for designing novel excellent TADF Cu(i) complex materials.

Analyses of sizable ZFS and magnetic tensors of high spin metallocomplexes

The fictitious spin-1/2 Hamiltonian approach is the putative method to analyze the fine-structure/hyperfine ESR spectra of high spin metallocomplexes having sizable zerofield splitting (ZFS), thus giving salient principal g-values far from around g = 2 without explicitly providing their ZFS parameters in most cases. Indeed, the significant departure of the g-values from g = 2 is indicative of the occurrence of their high spin states, but naturally they never agree with true g-values acquired by quantum chemical calculations such as sophisticated DFT or ab initio MO calculations. In this work, we propose facile approaches to determine the magnetic tensors of high spin metallocomplexes having sizable ZFS, instead of performing advanced high-field/high-frequency ESR spectroscopy. We have revisited analytical expressions for the relationship between effective g-values and true principal g-values for high spins. The useful analytical formulas for the g^eff-g^true relationships are given for S's up to 7/2. The genuine Zeeman perturbation formalism gives the exact solutions for S = 3/2, and for higher S's it is much more accurate than the pseudo-Zeeman perturbation approach documented so far (A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Metal Ions, 1970; J. R. Pilbrow, J. Magn. Reson., 1978, 31, 479; F. Trandafir et al., Appl. Magn. Reson., 2007, 31, 553; M. Fittipaldi et al., J. Phys. Chem. B, 2008, 112, 3859), in which the E(S_x² - S_y²) term is putatively treated to the second order. To show the usefulness of the present approach, we exploit Fe^III(Cl)OEP (S = 5/2) (OEP: 2,3,7,8,12,13,17,18-octaethylporphyrin) and Co^IIOEP (S = 3/2) well magnetically diluted in the diamagnetic host crystal lattice of Ni^IIOEP. The advantage of single-crystal ESR spectroscopy lies in the fact that the molecular information on the principal axes of the magnetic tensors is crucial in comparing with reliable theoretical results. In high spin states of metallocomplexes with sizable ZFS in pseudo-octahedral symmetry, their fine-structure ESR transitions for the principal z-axis orientation appear in the lower field far from g = 2 at the X-band, disagreeing with the putative intuitive picture obtained using relevant ESR spectroscopy. A Re^III,IV dinuclear complex in a mixed valence state exemplifies the cases, whose fine-structure/hyperfine ESR spectra of the neat crystals have been analyzed in their principal-axis system. The DFT-based/ab initio MO calculations of the magnetic tensors for all the high spin entities in this work were carried out.

ESR analyses of picket fence MnII and 6th ligand coordinated FeIII porphyrins (S = 5/2) and a CoII(hfac) complex (S = 3/2) with sizable ZFS parameters revisited: a full spin Hamiltonian approach and quantum chemical calculations

The conventional X-band ESR spectra are fully reanalyzed by a full spin Hamiltonian approach.

Behaviour of DFT-based approaches to the spin–orbit term of zero-field splitting tensors: a case study of metallocomplexes, MIII(acac)3 (M = V, Cr, Mn, Fe and Mo)

Zero-field splitting tensors of M^III(acac)₃ complexes are calculated using ab initio and DFT methods.