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Modern density-functional methods for the calculation of electronic g-tensors have been implemented within the framework of the deMon code. All relevant perturbation operators are included. Particular emphasis has been placed on accurate yet efficient treatment of the two-electron spin−orbit terms. At an all-electron level, the computationally inexpensive atomic mean-field approximation is shown to provide spin−orbit contributions in excellent agreement with the results obtained using explicit one- and two-electron spin−orbit integrals. Spin−other−orbit contributions account for up to 25−30% of the two-electron terms and may thus be non-negligible. For systems containing heavy atoms we use a pseudopotential treatment, where quasirelativistic pseudopotentials are included in the Kohn−Sham calculation whereas appropriate spin−orbit pseudopotentials are used in the perturbational treatment of the g-tensors. This approach is shown to provide results in good agreement with the all-electron treatment, at moderate computational cost. Due to the atomic nature of both mean-field all-electron and pseudopotential spin−orbit operators used, the two approaches may even be combined in one calculation. The atomic character of the spin−orbit operators may also be used to analyze the contributions of certain atoms to the paramagnetic terms of the g-tensors. The new methods have been applied to a wide variety of species, including small main group systems, aromatic radicals, as well as transition metal complexes.

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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.

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A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.

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of the N-H‚‚‚N hydrogen bonds in the anion [Ct 15 N‚‚‚L‚‚‚ 15 NtC] -(1), L ) H, D, and of the cyclic hydrogenbonded formamidine dimer (HCNHNH 2 ) 2 (2) have been performed using the density functional formalism as a function of the hydrogen bond and molecular geometries. The coupling constants are discussed in comparison with the experimental and calculated constants 1 J 19 F-1 H ≡ J FH and 2 J 19 F-19 F ≡ J FF reported previously as first set of examples of scalar couplings across hydrogen bonds for the hydrogen-bonded clusters of [F(HF) n ] -, n ) 1-4 by Shenderovich, I.