Relativistic Effects for NMR Shielding Constants in Transition Metal Oxides Using the Zeroth-Order Regular Approximation

Abstract

Relativistic effects for NMR shielding constants have been calculated using the zero order regular approximation (ZORA) for relativistic effects. Isotropic NMR shielding constants were obtained using density functional theory with gauge including atomic orbitals (GIAO) in a spin-free formalism for the metal nuclei in transition metal oxides MO4 n - (M = Cr, Mn, Fe, Mo, Tc, Ru, W, Re, Os) and carbonyl complexes M(CO)6 (M = Cr, Mo, W). The ZORA isotropic shieldings are compared with results from an extended version of the relativistic method employing the Pauli Hamiltonian developed earlier by Schreckenbach and Ziegler. Comparison between ZORA and Pauli shieldings, employing the restrictions necessary for the Pauli approachfrozen cores, restricted basis sets in the core regionshow the ZORA shieldings to be significantly different from Pauli ones, but the chemical shifts of the metal oxides with respect to the carbonyl complexes do not differ much. However, extending the ZORA calculations (no frozen core, extended basis sets) gives significant changes, proving the limitation to frozen cores and restricted basis sets of the Pauli method to be unwarranted. Comparison to experiment shows that the errors of the most precise ZORA chemical shifts are ca. 10% (in the order of a few 100 ppm) for both the light and heavy transition metals. Error sources may be, apart from deficiencies of the density functional, the neglect of spin−orbit coupling and the neglect of solvent effects.

95Mo nuclear magnetic resonance parameters of molybdenum hexacarbonyl from density functional theory: appraisal of computational and geometrical parameters

“…[26][27][28]30 Most of them use a relativistic approach of shielding calculations. 26,28,30 Schreckenbach and Ziegler used a quasi-relativistic method employing a Pauli-type Hamiltonian to compute 17 O and metal CS parameters of some [MO 4 ] nÀ (M = Cr, Mo, W, Mn, Tc, Re, Ru, Os) complexes and group 6 hexacarbonyls. Later, Baerends et al published a study using the twocomponent relativistic method, ZORA, that enables the use of all-electron basis sets and thus improves the computed isotropic shielding values for the same TM series.…”

Density functional theory investigation of3dtransition metal NMR shielding tensors in diamagnetic systems using the gauge-including projector augmented-wave method

“…Calculation of the NMR shielding tensor can be separated into two steps: The self consistent field (SCF) procedure which at least leads to the unperturbed Kohn-Sham (KS) eigenvalues and orbitals, and the linear response of these orbitals due to the presence of the magnetic field. Thus, two kinds of relativistic effects are distinguished when calculating the shielding parameters: [85] The indirect term which is associated to the energy and shape modifications of the unperturbed KS orbitals induced by a relativistic SCF procedure, [13] and the direct relativistic effects associated to the use of a relativistic field-dependant Hamiltonian which yields additional terms in the shielding tensor expressions. [86][87][88] Moreover, these terms can be separated in scalar and spin-orbit coupling parts, depending on the level of approximation used.…”

Perturbational and ECP Calculation of Relativistic Effects in NMR Shielding and Spin–Spin Coupling

“…The "passive" perturbations do not contain I or B 0 , and affect the NMR parameters through relativistic modification of the wave function only. Bouten et al [24] earlier referred to exactly the same classification with their "direct" and "indirect" effects, respectively. The SO-I effect on either r or J is an example of a passive effect, where the I-and B 0 -independent part of the SO interaction induces spin polarisation to the closed-shell reference state, and the magnetic perturbations take the NR form.…”

“…Ref. [24] extended the method with the active SR effects on r. HAHA effects and, hence, r in the absolute sense are incompletely recovered by the frozen core method, whereas the situation is better for the relative chemical shifts.…”

“…Leading-order, O(a 4 ), relativistic contributions to the nuclear magnetic shielding tensor r. a First-order terms, AEAae The results of Ref [24]. point to the HAHA character.…”