Assessing <i>GW</i> Approaches for Predicting Core Level Binding Energies

Here we present a systematic study on the performance of different <i>GW</i> approaches: <i>G</i>₀<i>W</i>₀, <i>G</i>₀<i>W</i>₀ with linearized quasiparticle equation (lin-<i>G</i>₀<i>W</i>₀), and quasiparticle self-consistent <i>GW</i> (qs<i>GW</i>), in predicting core level binding energies (CLBEs) on a series of representative molecules comparing to Kohn–Sham (KS) orbital energy-based results. KS orbital energies obtained using the PBE functional are 20–30 eV lower in energy than experimental values obtained from X-ray photoemission spectroscopy (XPS), showing that any Koopmans-like interpretation of KS core level orbitals fails dramatically. Results from qs<i>GW</i> lead to CLBEs that are closer to experimental values from XPS, yet too large. For the qs<i>GW</i> method, the mean absolute error is about 2 eV, an order of magnitude better than plain KS PBE orbital energies and quite close to predictions from Δ<i>S</i>CF calculations with the same functional, which are accurate within ∼1 eV. Smaller errors of ∼0.6 eV are found for qs<i>GW</i> CLBE shifts, again similar to those obtained using Δ<i>S</i>CF PBE. The computationally more affordable <i>G</i>₀<i>W</i>₀ approximation leads to results less accurate than qs<i>GW</i>, with an error of ∼9 eV for CLBEs and ∼0.9 eV for their shifts. Interestingly, starting <i>G</i>₀<i>W</i>₀ from PBE0 reduces this error to ∼4 eV with a slight improvement on the shifts as well (∼0.4 eV). The validity of the <i>G</i>₀<i>W</i>₀ results is however questionable since only linearized quasiparticle equation results can be obtained. The present results pave the way to estimate CLBEs in periodic systems where ΔSCF calculations are not straightforward although further improvement is clearly needed

Post-B3LYP Functionals Do Not Improve the Description of Magnetic Coupling in Cu(II) Dinuclear Complexes

The accuracy of post-B3LYP functionals is analyzed using an open-shell database of Cu­(II) dinuclear complexes with well-defined experimental values of the magnetic coupling constants. This database provides a sound open-shell training set to be used to improve the fitting schemes in defining new functionals or when reparametrizing the existing ones. For a large set of representative hybrid exchange-correlation functionals, it is shown that the overall description of moderate-to-strong antiferromagnetic interactions is significantly more accurate than the description of ferromagnetic or weakly antiferromagnetic interactions. In the case of global hybrids, the most reliable ones have 25–40% Fock exchange with SOGGA and PBE0 being the most reliable and M06 the exception. For range-corrected hybrids, the long-range corrected CAM-B3LYP and ωB97XD provide acceptable results, and M11 is comparable but more erratic. It is concluded that the reliability of the calculated values is system- and range-dependent, and this fact introduces a serious warning on the blind use of a single functional to predict magnetic coupling constants. Hence, to extract acceptable magnetostructural correlations, a “standardization” of the method to be used is advised to choose the optimal functional

Spin Adapted versus Broken Symmetry Approaches in the Description of Magnetic Coupling in Heterodinuclear Complexes

The performance of a series of wave function and density functional theory based methods in predicting the magnetic coupling constant of a family of heterodinuclear magnetic complexes has been studied. For the former, the accuracy is similar to other simple cases involving homodinuclear complexes, the main limitation being a sufficient inclusion of dynamical correlation effects. Nevertheless, these series of calculations provide an appropriate benchmark for density functional theory based methods. Here, the usual broken symmetry approach provides a convenient framework to predict the magnetic coupling constants but requires deriving the appropriate mapping. At variance with simple dinuclear complexes, spin projection based techniques cannot recover the corresponding (approximate) spin adapted solution. Present results also show that current implementation of spin flip techniques leads to unphysical results

New Series of Triply Bridged Dinuclear Cu(II) Compounds: Synthesis, Crystal Structure, Magnetic Properties, and Theoretical Study

Five new triply bridged dinuclear Cu(II) compounds have been synthesized, and their magnetic properties have been measured and characterized. The magnetic coupling constants (<i>J</i>) of these compounds plus a previously structurally characterized compound of the same type have been derived by appropriate fitting of the experimentally measured molar susceptibility variation with the temperature. Two of the compounds are ferromagnetically coupled, and three are antiferromagnetically coupled with <i>J</i> values in the [+150, −40] cm^–1 range. The validity of the structural aggregate Addison’s parameter as a qualitative magneto-structural correlation is confirmed. The origin of the magnetic interactions and the magnitude of the magnetic coupling have been analyzed by means of density functional theory-based calculations using a variety of state of the art exchange-correlation potentials. It is shown that the long-range separated LC-ωPBE provides the overall best agreement with experiment for this family as well as for a set of previously reported hetero triply bridged dinuclear Cu(II) compounds, especially for ferromagnetic systems