We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.

The calculation of nuclear shieldings for paramagnetic molecules has been implemented in the ReSpect program, which allows the use of modern density functional methods with accurate treatments of spin-orbit effects for all relevant terms up to order Omicron(alpha4) in the fine structure constant. Compared to previous implementations, the methodology has been extended to compounds of arbitrary spin multiplicity. Effects of zero-field splittings in high-spin systems are approximately accounted for. Validation of the new implementation is carried out for the 13C and 1H NMR signal shifts of the 3d metallocenes 4VCp2, 3CrCp2, 2MnCp2, 6MnCp2, 2CoCp2, and 3NiCp2. Zero-field splitting effects on isotropic shifts tend to be small or negligible. Agreement with experimental isotropic shifts is already good with the BP86 gradient-corrected functional and is further improved by admixture of Hartree-Fock exchange in hybrid functionals. Decomposition of the shieldings confirms the dominant importance of the Fermi-contact shifts, but contributions from spin-orbit dependent terms are frequently also non-negligible. Agreement with 13C NMR shift tensors from solid-state experiments is of similar quality as for isotropic shifts.

Individual molecular orbital (MO) contributions to the magnetic shielding of atoms as well as to the nucleusindependent chemical shifts (NICS) of aromatic compounds can be computed by the widely used gaugeincluding atomic orbital (GIAO) method. Detailed analyses of magnetic shielding MO-NICS contributions provide interpretive insights that complement and extend those given by the localized MO ("dissected NICS", LMO-NICS) method. Applications to (4n + 2) π-electron systems, ranging from [n] annulenes to D nh S 3 , S 5 , and N 6 H 6 2+ rings as well as to D 2h cyclobutadiene, show the extent to which their diatropic character results from the σ framework and from the π orbitals. The diatropicity of both these contributions decreases with the number of nodes of the wave function around the ring. The highest-energy orbitals can become paratropic. This is generally the case with the σ orbitals, but is found only for "electron-rich" π systems such as sulfur rings. MO-NICS contributions, which can be interpreted using London-Hu ¨ckel theory, correlate with inverse ring size.

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A coupled-perturbed Kohn−Sham treatment for the calculation of hyperfine tensors has been implemented into the MAG-ReSpect program. It treats spin−orbit contributions to hyperfine tensors by a combination of accurate and efficient approximations to the one- and two-electron spin−orbit Hamiltonians:  (a) by the all-electron atomic mean-field approximation, and (b) by spin−orbit pseudopotentials. In contrast to a previous implementation, the code allows the use of hybrid functionals and lifts restrictions in the orbital and auxiliary basis sets that may be employed. Validation calculations have been performed on various transition metal complexes, as well as on a series of small diatomic molecules. In the case of a series of copper(II) complexes, the spin−orbit contributions are large, and their inclusion is essential to achieve agreement with experiment. Calculations with spin−orbit pseudopotentials allow the efficient simultaneous introduction of scalar relativistic and spin−orbit effects in the case of light nuclei in the neighborhood of heavy atoms.

Modern density functional methods have been used to study spin-density distribution, g tensors, as well as Cu and ligand hyperfine tensors for azurin models, for two more blue copper proteins plastocyanin and stellacyanin, and for small model complexes. The aim was to establish a consistent computational protocol that provides a realistic description of the EPR parameters as probes of the spin-density distribution between metal and coordinated ligands in copper proteins. In agreement with earlier conclusions for plastocyanin, hybrid functionals with appreciable exact-exchange admixtures, roughly around 50%, provide the best overall agreement with all parameters. Then the bulk of the spin density is almost equally shared by the copper atom and the sulfur atom of the equatorial cysteine ligand, and the best values are obtained for copper, histidine nitrogen, and cysteine beta-proton hyperfine couplings, as well as for g(parallel). Spin-orbit effects on the EPR parameters may be appreciable and have to be treated carefully to obtain agreement with experiment. Most notably, spin-orbit effects on the (65)Cu hyperfine coupling tensors in blue copper sites are unusually large compared to more regularly coordinated Cu(II) complexes with similar spin density on copper. In addition to the often emphasized high covalency of the Cu-S(Cys) bond, the characteristically small A(parallel) component of blue copper proteins is shown to derive to a large part from a near-cancellation between negative first-order (Fermi contact and dipolar) and unusually large positive second-order (spin-orbital) contributions. The large spin-orbit effects relate to the distorted tetrahedral structures. Square planar dithiolene complexes with similar spin density on copper exhibit much more negative A(parallel) values, as the cancellation between nonrelativistic and spin-orbit contributions is less complete. Calculations on a selenocysteine-substituted variant of azurin have provided further insight into the relations between bonding and EPR parameters.

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Two different sets of approaches for the density-functional calculation of the spin-orbit contributions to zero-field splitting (ZFS) parameters of high-spin systems have been implemented within the same quantum chemistry code ReSpect and have been validated and compared for a series of model systems. The first approach includes spin-orbit coupling variationally in a two-component calculation, using either an all-electron Douglas-Kroll-Hess ansatz or two-component relativistic pseudopotentials. The ZFS parameters are computed directly from energy differences between different relativistic states. Additionally, an approximate second-order perturbation theory approach has been implemented, based on nonrelativistic or scalar relativistic wave functions. For a series of group 16 triplet diatomics and for the octet GdH3 molecules, two-component density functional calculations underestimate the zero-field splitting D systematically by a factor of 2. This may be rationalized readily by the incomplete description of states with absolute value MJ < J by a single-determinantal wave function built from two-component spinors. In the case of two 3d transition metal complexes and for GdH3, the results depend furthermore sensitively on exchange-correlation functional. Results of the alternative one-component approach agree strikingly with the two-component data for systems with small spin-orbit effects and start to deviate from them only for heavier systems with large spin-orbit effects. These results have fundamental implications for the achievable accuracy of one-component density-functional approaches used widely to compute ZFS parameters in the field of molecular magnetism. Possible refinements of both one-and two-component approaches are discussed.