Roman Reviakine

Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators

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.

Density functional calculations of NMR shielding tensors for paramagnetic systems with arbitrary spin multiplicity: Validation on 3d metallocenes

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.

Calculation of zero-field splitting parameters: Comparison of a two-component noncolinear spin-density-functional method and a one-component perturbational approach

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.

Validation study of meta-GGA functionals and of a model exchange–correlation potential in density functional calculations of EPR parameters

We report the first implementation of the DFT calculation of electronic g-tensors and hyperfine coupling constants using meta-GGA exchange–correlation functionals (both Laplacian and kinetic-energy-density dependent) and statistical average of orbital model exchange–correlation potentials (SAOP). The g-tensors for a set of eleven small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using two meta-GGA functionals (FT98 and PKZB), SAOP, as well as the BP86 GGA, and B3PW91 and BHPW91 hybrid functionals. The same functionals have been compared in the calculation of hyperfine coupling constants for thirteen small main group radicals and twelve 3d transition metal compounds. The results for main group radicals are satisfactory, both with the newly validated and previously tested functionals. In contrast, the accurate evaluation of the EPR parameters for 3d transition metal complexes remains a challenge for “pure” density functional theory: the new functionals (potentials) do not improve the results compared to GGA functionals, whereas hybrid functionals tend to provide superior results. SAOP leads to large spin contamination for a number of transition metal complexes. This has been traced back to the orbital-energy dependence of the potential.