On the self-consistent implementation of general occupied-orbital dependent exchange-correlation functionals with application to the B05 functional

Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke's real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)].

57Fe NMR spectroscopy of ferrocenes derived from aminoferrocene and 1,1'-diaminoferrocene

Three series of ferrocenes, derived from aminoferrocene Fc-NH2 and 1,1'-diaminoferrocene fc(NH2)2, were studied by 57Fe NMR spectroscopy. A marked decrease in 57Fe magnetic nuclear shielding with respect to ferrocene is observed if the nitrogen atom becomes part of a pi-acceptor linked to one or both cyclopentadienyl rings. In contrast, pi-donor properties of the amino group(s) affect delta57Fe to a much smaller extent. In the case of the fairly rigid structures of 1,3-diaza-2-element-[3]ferrocenophanes, a significant increase of 57Fe nuclear magnetic shielding is observed, in contrast to the corresponding [n]ferrocenophanes with n > 3. Structures of numerous of the ferrocene derivatives have been optimized for the gas phase by calculations (B3LYP/6-311 + G(d,p) level of theory), and 57Fe nuclear magnetic shieldings were calculated using these geometries. There is reasonable agreement in the trends for experimental and calculated data.

Thermal Effects and Vibrational Corrections to Transition Metal NMR Chemical Shifts

Both zero-point and classical thermal effects on the chemical shift of transition metals have been calculated at appropriate levels of density functional theory for a number of complexes of titanium, vanadium, manganese and iron. The zero-point effects were computed by applying a perturbational approach, whereas classical thermal effects were probed by Car-Parrinello molecular dynamics simulations. The systematic investigation shows that both procedures lead to a deshielding of the magnetic shielding constants evaluated at the GIAO-B3 LYP level, which in general also leads to a downfield shift in the relative chemical shifts, delta. The effect is small for the titanium and vanadium complexes, where it is typically on the order of a few dozen ppm, and is larger for the manganese and iron complexes, where it can amount to several hundred ppm. Zero-point corrections are usually smaller than the classical thermal effect. The pronounced downfield shift is due to the sensitivity of the shielding of the metal centre with regard to the metal-ligand bond length, which increase upon vibrational averaging. Both applied methods improve the accuracy of the chemical shifts in some cases, but not in general.

NMR shielding calculations across the periodic table: diamagnetic uranium compounds. 2. Ligand and metal NMR

In this and a previous article (J. Phys. Chem. A 2000, 104, 8244), the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. Two relativistic DFT methods are used, ZORA ("zeroth-order regular approximation") and the quasirelativistic (QR) method. In the given second paper, NMR shieldings and chemical shifts are calculated and discussed for a wide range of compounds. The molecules studied comprise uranyl complexes, [UO(2)L(n)](+/-)(q); UF(6); inorganic UF(6) derivatives, UF(6-n)Cl(n), n = 0-6; and organometallic UF(6) derivatives, UF(6-n)(OCH(3))(n), n = 0-5. Uranyl complexes include [UO(2)F(4)](2-), [UO(2)Cl(4)](2-), [UO(2)(OH)(4)](2-), [UO(2)(CO(3))(3)](4-), and [UO(2)(H(2)O)(5)](2+). For the ligand NMR, moderate (e.g., (19)F NMR chemical shifts in UF(6-n)Cl(n)) to excellent agreement [e.g., (19)F chemical shift tensor in UF(6) or (1)H NMR in UF(6-n)(OCH(3))(n)] has been found between theory and experiment. The methods have been used to calculate the experimentally unknown (235)U NMR chemical shifts. A large chemical shift range of at least 21,000 ppm has been predicted for the (235)U nucleus. ZORA spin-orbit appears to be the most accurate method for predicting actinide metal chemical shifts. Trends in the (235)U NMR chemical shifts of UF(6-n)L(n) molecules are analyzed and explained in terms of the calculated electronic structure. It is argued that the energy separation and interaction between occupied and virtual orbitals with f-character are the determining factors.

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.