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We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory. Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.

Methyl esters of Kemp's tri-acid and cyclohexanetricarboxylic acid are structurally similar to acrylate polymers, having the same functionalities and stereoregularities as poly(methylmethacrylate) and poly(methylacrylate), respectively. The photochemistry and free radicals from these model systems have been studied using time-resolved electron paramagnetic resonance spectroscopy with laser flash photolysis at 248 nm. Chemically induced electron spin polarization from the triplet mechanism (net emission) is observed. Well-resolved spectra are obtained at all temperatures for the model system radicals, which are determined to be in the slow motion condition, that is, there is no interconversion of chair conformations. The temperature dependence of the spectra is minimal; some hyperfine lines shift as the temperature increases, but without much broadening. Density functional theory calculations are presented and discussed in support of the experimental data.

We succeeded in synthesizing of a whole family of isostructural solvates of the copper(II) hexafluoroacetylacetonate complex with pyrazolyl-substituted nitronyl nitroxide (L): Cu(hfac)2L x 0.Solv. The main feature inherent in nature of Cu(hfac)2L x 0.5 Solv single crystals is their incredible mechanical stability and ability to undergo reversible structural rearrangements with temperature variation, accompanied by anomalies on the mu(eff(T)) dependence. Structural investigation of the complexes over a wide temperature range before and after the structural transition and the ensuing magnetic phase transition showed that the spatial peculiarities of the solvent molecules incorporated into the solid govern the character of the mu(eff(T)) dependence and the temperature region of the magnetic anomaly. Thus, doping of crystals with definite solvent molecules could be used as an efficient method of control over the magnetic anomaly temperature (T(a)). The investigation of this special series of crystals has revealed the relationship between the chemical step and the magnetic properties. It was shown that "mild" modification of T(a) for Cu(hfac)2L x 0.5 Solv required a much smaller structural step than the typical change of one -CH2- fragment in a homologous series in organic chemistry. Quantum-chemical calculations with the use of X-ray diffraction data allowed us to trace the character of changes in the exchange interaction parameters in the range of the phase transition. In the temperature range of the phase transition, the exchange parameter changes substantially. The gradual decrease in the magnetic moment, observed in most experiments during sample cooling to T(a), is the result of the gradual increase in the fraction of the low-temperature phase in the high-temperature phase.

Kemp's triacid (KTA) and cyclohexane tricarboxylic acid (CTA) are small-molecule model systems for acrylic acid polymers, having the same functionalities and stereoregularities as isotactic poly(methacrylic acid) (PMAA) and poly(acrylic acid) (PAA), respectively. As part of an ongoing investigation of radicals produced by photolysis of acrylic polymers, the photochemistry and free radicals from the model systems have been studied using time-resolved EPR spectroscopy as a function of temperature and pH. Radicals are created by direct photolysis of the acids at 248 nm or by sensitized photo-oxidation using quinone triplet states at 308 nm. The two methods of radical production lead to different chemically induced electron spin polarization (CIDEP) patterns in the ensuing radicals, which are simulated and discussed. Well-resolved spectra are obtained at all temperatures for the model system radicals, which are determined to be in the slow motion condition. DFT calculations of the model system radicals are presented and discussed in support of the experimental data.

Heterospin complexes [Cu(SQ)2Py].C7H8, Cu(SQ)2DABCO, and [Cu(SQ)2NIT-mPy].C6H6, where Cu(SQ)2 is bis(3,6-di-tert-butyl-o-benzosemiquinonato)copper(II), DABCO is 1,4-diazabicyclo(2,2,2)octane, and NIT-mPy is the nitronyl nitroxide 2-(pyridin-3-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, have been synthesized. The molecules of these complexes have a specific combination of the intramolecular ferro- and antiferromagnetic exchange interactions between the odd electrons of Cu(II) and SQ ligands, characterized by large exchange coupling parameters |J| approximately 100-300 cm(-1). X-ray and magnetochemical studies of a series of mixed-ligand compounds revealed that an extra ligand (Py, NIT-mPy, or DABCO) coordinated to the metal atom produces a dramatic effect on the magnetic properties of the complex, changing the multiplicity of the ground state. Quantum chemical analysis of magnetostructural correlations showed that the energy of the antiferromagnetic exchange interaction between the odd electrons of the SQ ligands in the Cu(SQ)2 bischelate is extremely sensitive to both the nature of the extra ligand and structural distortions of the coordination unit, arising from extra ligand coordination.

Since the classic work of Roothaan [Rev. Mod. Phys. 32, 179 (1960)], the one-electron energies of a ROHF method are known as ambiguous quantities having no physical meaning. Together with this, it is often assumed in present-day computational studies that Koopmans' theorem is valid in a ROHF method. In this work we analyze the specific dependence of orbital energies on the choice of the basic equations in a ROHF method which are the Euler equations and different forms of the generalized Hartree-Fock equation. We first prove that the one-electron open-shell energies epsilon(m) derived by the Euler equations can be related to the respective ionization potentials I(m) via the modified Koopmans' formula I(m)= -epsilon(m)f(m) where f(m) is an occupation number. As compared to this, neither the closed-shell orbital energies nor the virtual ones derived by the Euler equations can be related to the respective ionization potentials and electron affinities via Koopmans' theorem. Based on this analysis, we derive the new (canonical) form for the Hamiltonian of the Hartree-Fock equation, the eigenvalues of which obey Koopmans' theorem for the whole energy spectrum. A discussion of new orbital energies is presented on the examples of a free N atom and an endohedral N@C(60) (I(h)). The vertical ionization potentials and electron affinities estimated via Koopmans' theorem are compared with the respective observed data and, for completeness, with the respective estimates derived via a DeltaSCF method. The agreement between observed data and their estimates via Koopmans' theorem is qualitative and, in general, appears to possess the same accuracy level as in the closed-shell SCF.