We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).

The behavior of a verdazyl-based radical bound to open-shell transition metal ions in the structurally and magnetically characterized [M(hfac)2imvd(o)] (M = Mn, Ni; hfac = (1,1,1,5,5,5)hexafluoroacetylacetonate; imvd(o) = 3-(2'-imidazolyl)-1,5-dimethyl-6-oxoverdazyl) complexes is rationalized using ab initio wave-function-based calculations analysis. The calculated exchange coupling constants J (H = -J(s(M) x s(imvd(o)); J(Mn)(calcd) = -63 cm(-1), J(Ni)(calcd) = 205 cm(-1)) are in excellent agreement with the experimental ones (J(Mn)(exp) = -63 cm(-1), J(Ni)(exp) = 193 cm(-1)). Even though both rings are involved through the binding mode of the imvd(o) radical, the spin density remains essentially localized on the nitrogen-rich ring. The singularity stems from its bidentate coordinating character. The analysis of the correlated wave function suggests that the verdazyl-based radical acts as a pi* donor ligand which allows ligand-to-metal charge transfer and excludes metal-to-ligand charge transfer. This reflects the weak covalent character of the M-imvd(o) pi coordination bond. From a magnetic point of view, the through-space exchange governs the ferromagnetic character in the Ni derivative up to 153 cm(-1) as expected from a description limited to the magnetic orbitals. Nevertheless, the CI expansion displays the participation of excited doublet and quartet states (spin polarization) on the verdazyl moiety which leads to a significant additional ferromagnetic contribution (52 cm(-1)). In the [Mn(hfac)2imvd(o)] analogue, the antiferromagnetic contribution arising from kinetic exchange is only one-third of the observed exchange coupling constant. It is necessary to introduce dynamical correlation effects to quantitatively recover the exchange interaction in this compound. Since the pi* donor and spin-polarized characters of the verdazyl moiety dominate over the negligible polarizability of the imidazole part, it is concluded that the noninnocent nature of the imvd(o) radical is held by the verdazyl ring part.

The origin of magnetic interactions in verdazyl-based radical stackings is examined using ab initio wave function and density functional theory (DFT) calculations. Starting from the reported crystal structure of the 1,1'-bis(verdazyl)ferrocene diradical compound, the singlet-triplet energy difference has been evaluated on the basis of multireference difference dedicated configurations interaction calculations and suggested the innocent role of the ferrocene spacer. Using the underlying pi-dimer verdazyl structures, the J variations and potential energy surfaces of parallel and antiparallel face-to-face arrangements have been studied with respect to the verdazyl-verdazyl separation to evaluate the Coulomb repulsion U and bandwidth W. While coupled-cluster CCSD(T) calculations are suggestive of a weak bond formation in both dimer arrangements (approximately 40 kJ mol(-1)), the DFT approach fails to reproduce the bonding character. The intrinsically delocalized character of the magnetic orbitals favors an S = 0 ground state, but importantly, the S = 1 spin state is also bound. A typical 0.4 A increase (i.e., 10%) of the verdazyl-verdazyl equilibrium distance accompanying a 16 kJ mol(-1) adiabatic energy difference is calculated between the S = 0 and S = 1 states. In this distance separation regime, we finally suggest that either a relative 1.2 A slippage or a approximately 42 degrees relative orientation of the verdazyl rings is likely to give rise to a high-spin S = 1 ground state. These features are symptomatic of a bistable system, and an interpretation of the exchange interaction in verdazyl pi-dimer structures in terms of spin transition is proposed.

The spectrum arising from the (π*)(2) configuration of the chalcogen dimers, namely, the X(2)1, a2, and b0(+) states, is calculated using wave-function theory based methods. Two-component (2c) and four-component (4c) multireference configuration interaction (MRCI) and Fock-space coupled cluster (FSCC) methods are used as well as two-step methods spin-orbit complete active space perturbation theory at 2nd order (SO-CASPT2) and spin-orbit difference dedicated configuration interaction (SO-DDCI). The energy of the X(2)1 state corresponds to the zero-field splitting of the ground state spin triplet. It is described with high accuracy by the 2- and 4-component methods in comparison with experiment, whereas the two-step methods give about 80% of the experimental values. The b0(+) state is well described by 4c-MRCI, SO-CASPT2, and SO-DDCI, but FSCC fails to describe this state and an intermediate Hamiltonian FSCC ansatz is required. The results are readily rationalized by a two-parameter model; Δε, the π* spinor splitting by spin-orbit coupling and K, the exchange integral between the π(1)* and the π(-1)* spinors with, respectively, angular momenta 1 and -1. This model holds for all systems under study with the exception of Po(2).

Look both ways: Coordination bonding of verdazyl radicals to diamagnetic metal ions dramatically modifies the crystal packing of the electronic spin bearers. The face‐to‐face positioning of two radicals leads to a magnetic behavior that is more relevant to a S=0 to S=1 spin‐transition phenomenon than to the usual exchange‐interaction view.

The chemical control of magnetic and conduction properties for organic radicals is mainly based on t, the resonance integral, and U, the on-site repulsion, used in the Hubbard model. A qualitative analysis based on the competition between the kinetic and the Coulomb contribution, and the expression of the magnetic exchange coupling suggests that U should be roughly 800 cm(-1) while the resonance integral |t| should be 200 cm(-1) to reach bifunctionality. Ab initio wavefunction-based calculations allowed us to quantitatively measure those quantities for several organic materials considered as 1D systems starting from their reported crystal structures. The extraction of t and U parameters from the exchange coupling constants between neighbouring radicals allowed us to anticipate a possible metallic behaviour. Finally, the impact of chemical changes in the constitutive units is measured to rationalize the macroscopic behaviour modifications. It is shown that the intriguing regime characterized by simultaneous itinerant and localized electrons might be achieved by molecular engineering.

Keywords: Exchange interactions / Radicals / Ab initio calculations / CopperThe synthesis, structure and magnetic properties of the first thiooxoverdazyl metal complex [Cu(hfac) 2 (Svdpy)] [hfac = (1,1,1,5,5,5)-hexafluoroacetylacetonate; Svdpy = 1,5-dimethyl-3-(2-pyridyl)-6-thiooxoverdazyl] is described. The organic radical acts as a bidentate ligand leading to a six-coordinate metal complex. The fit of the thermal variations of the

Drastisch ist der Einfluss, den das koordinative Binden von Verdazylradikalen an diamagnetische Metallionen auf die Kristallpackung der Träger des Elektronenspins hat. Die Stapelanordnung der beiden Radikale hat ein magnetisches Verhalten zur Folge, das typischer für einen Spinübergang vom Typ S=0→S=1 ist als für die üblicherweise angenommene Austauschwechselwirkung.