Density-functional computation of 53Cr NMR chemical shifts

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts

Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.

Systematic Evaluation of Modern Density Functional Methods for the Computation of NMR Shifts of 3d Transition-Metal Nuclei

A wide range of density functionals from all rungs of Jacob's ladder have been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 × ⁴⁹Ti, 10 × ⁵¹V, 10 × ⁵³Cr, 11 × ⁵⁵Mn, 9 × ⁵⁷Fe, 9 × ⁵⁹Co, and 9 × ⁶¹Ni shift values, as well as a diverse range of electronic structure characteristics. The overall 39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs (including their current-density-functional─CDFT─versions), nine global hybrids, four range-separated hybrids, eight local hybrids, and two double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled-cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d-nuclei set are in the range between 4 and 5%. Strikingly, the overall best-performing functionals are the recently implemented CDFT versions of two meta-GGAs, namely cM06-L (4.0%) and cVSXC (4.3%), followed by cLH14t-calPBE (4.9%), B3LYP (5.0%), and cLH07t-SVWN (5.1%), i.e., the previously best-performing global hybrid and two local hybrids. A number of further functionals achieve aggregate deviations in the range 5-6%. Range-separated hybrids offer no particular advantage over global hybrids. Due to the overall poor performance of Hartree-Fock theory for all systems except the titanium complexes, MP2 and double-hybrid functionals are unsuitable for these 3d-nucleus shifts and provide large errors. Global hybrid functionals with larger EXX admixtures, such as BHLYP or M06-2X, also perform poorly, and some other highly parametrized global hybrids also are unsuitable. For many functionals depending on local kinetic energy τ, their CDFT variants perform much better than their "non-CDFT" versions. This holds notably also for the above-mentioned M06-L and VSXC, while the effect is small for τ-dependent local hybrids and can even be somewhat detrimental to the agreement with experiment for a few other cases. The separation between well-performing and more poorly performing functionals is mainly determined by their results for the most critical nuclei ⁵⁵Mn, ⁵⁷Fe, and ⁵⁹Co. Here either moderate exact-exchange admixtures or CDFT versions of meta-GGAs are beneficial for the accuracy. The overall deviations of the better-performing global or local hybrids are then typically dominated by the ⁵³Cr shifts, where triplet instabilities appear to disfavor exact-exchange admixture. Further detailed analyses help to pinpoint specific nuclei and specific types of complexes that are challenges for a given functional.

Recent progress in solid-state nuclear magnetic resonance of half-integer spin low-γ quadrupolar nuclei applied to inorganic materials

An overview is presented of recent progress in the solid-state nuclear magnetic resonance (NMR) observation of low-γ nuclei, with a focus on applications to inorganic materials. The technological and methodological advances in the last 20 years, which have underpinned the increased accessibility of low-γ nuclei for study by solid-state NMR techniques, are summarised, including improvements in hardware, pulse sequences and associated computational methods (e.g., first principles calculations and spectral simulation). Some of the key initial observations from inorganic materials of these nuclei are highlighted along with some recent (most within the last 10 years) illustrations of their application to such materials. A summary of other recent reviews of the study of low-γ nuclei by solid-state NMR is provided so that a comprehensive understanding of what has been achieved to date is available.

Approaching Dissolved Species in Ammonoacidic GaN Crystal Growth: A Combined Solution NMR and Computational Study

Solutions of gallium trihalides GaX₃ (X=F, Cl, Br, I) and their ammoniates in liquid ammonia were studied at ambient temperature under autogenous pressure by multinuclear (⁷¹ Ga, ³⁵ Cl, ⁸¹ Br) NMR spectroscopy. To unravel the role of pH, the analyses were done both in absence and in presence of ammonium halides, which are employed as mineralizers during ammonoacidic gallium nitride crystal growth. While gallium trifluoride and its ammoniate were found to be too sparingly soluble to give rise to a NMR signal, the spectra of solutions of the heavier halides reveal the presence of a single gallium-containing species in all cases. DFT calculations and molecular dynamics simulations suggest the identification of this species as consisting of a [Ga(NH₃ )₆ ]³⁺ cation and up to six surrounding halide anions, resulting in an overall trend towards negative complex charge. Quantitative ⁷¹ Ga NMR studies on saturated solutions of GaCl₃ containing various amounts of additional NH₄ Cl revealed a near linear increase of GaCl₃ solubility with mineralizer concentration of about 0.023 mol GaCl₃ per mol NH₄ Cl at room temperature. These findings reflect the importance of Coulombic shielding for the inhibition of oligomerization and precipitation processes and help to rationalize both the low solubility of gallium halides in neutral ammonia solution and, in turn, the proliferating effect of the mineralizer during ammonoacidic gallium nitride formation.

Density-functional computation of ⁹³Nb NMR chemical shifts

93Nb chemical shifts of [NbX6](-) (X = Cl, F, CO), [NbXCl4](-) (X = O, S), Nb2(OMe)10, Cp*2Nb(κ2-BH4), (Cp*Nb)2(µ-B2H6)2, CpNb(CO)4, and Cp2NbH3 are computed at the GIAO (gauge-including atomic orbitals)-, BPW91- and B3LYP-, and CSGT (continuous set of gauge transformations)-CAM-B3LYP, -ωB97, and -ωB97X levels, using BP86-optimized or experimental (X-ray) geometries. Experimental chemical shifts are best reproduced at the GIAO-BPW91 level when δ(93Nb) values of inorganic complexes are referenced directly relative to [NbCl6](-) and those of organometallic species are first calculated relative to [Nb(CO)6](-). An inadvertent error in the reported δ(93Nb) values of cyclopentadiene borane complexes (H. Brunner et al., J. Organomet. Chem.1992, 436, 313) is corrected. Trends in the observed 93Nb NMR linewidths for anionic niobates [Nb(CO)5](3-), [Nb(CO)5H](2-), and [Nb(CO)5(NH3)](-) are rationalized in terms of computed electric field gradients at the metal.

A solid-state 53Cr NMR study of chromate and dichromate salts

Solid-state (53)Cr NMR spectra of a series of chromate (CrO4(2-)) and dichromate (Cr2O7(2-)) salts have been examined by employing the stepped-frequency quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) experiment and high applied magnetic field strengths, 11.75 and 18.8 T. Cr-53 nuclear quadrupolar coupling constants, CQ(53Cr), ranging from 1.23 to 5.01 MHz for the Cr(4(2-) salts and 7.25 to 8.14 MHz for the Cr2O7(2-) salts have been measured. For the dichromate salts, this corresponds to central transition 53Cr NMR lineshapes of 200-250 kHz at 18.8 T. The use of hyperbolic secant (HS) pulses in combination with the Hahn-echo (HE) or QCPMG experiment results in significant sensitivity enhancements when acquiring 53Cr NMR spectra of magic-angle spinning (MAS) samples, provided the MAS rate is fast with respect to the second-order quadrupolar interaction. For the CrO4(2-) and Cr2O7(2-) salts, the anisotropic chromium magnetic shielding interaction is generally negligible compared to the second-order 53Cr nuclear quadrupolar interaction. No simple correlation between the structure of the CrO4(2-) and Cr2O7(2-) anions and the observed CQ(53Cr) values has been found.

Density-functional computation of (99)Tc NMR chemical shifts

99Tc chemical shifts of TcO4(-), TcH9(2-), TcOF5, TcO2F4(-), TcOCl4(-), Tc2(CO)10, and Tc(CO)3L3(+) (L = CO, MeCN, H2O) are computed using geometries optimized with the gradient-corrected BP86 and hybrid B3P86 density functionals, at the gauge-including atomic orbitals (GIAO), -BPW91 and -B3LYP levels. For this set of compounds, substituent effects on delta(99Tc) are better described with the pure BPW91 functional than with B3LYP, in contrast to most other transition-metal chemical shifts studied so far. A rough, qualitative correlation is found between computed electric-field gradients at the Tc nuclei and the corresponding 99Tc NMR line widths. Thermal and solvation effects on magnetic shielding constants of aqueous TcO4(-), as assessed by averaging these properties over trajectories from Car-Parrinello molecular dynamics simulations, are indicated to be small and comparable to those of MnO4(-). Complexation to aqueous uranyl, UO2(2+), is predicted to affect delta(99Tc) of TcO4(-) only slightly; somewhat larger complexation shifts are obtained for the oxygen nuclei of pertechnetate, suggesting that 17O NMR could be a useful probe for the extent of association between both radionuclides in solution.

Transition metal NMR chemical shifts from optimized effective potentials

Metal shielding constants and chemical shifts are determined for nine transition metal complexes using an uncoupled formalism with orbitals and eigenvalues determined using the Yang-Wu implementation [W. Yang and Q. Wu, Phys. Rev. Lett. 89, 143002 (2002)] of the optimized effective potential approach in density functional theory. Preliminary calculations using generalized gradient approximation functionals quantify the influence of the variables in the optimized effective potential implementation. In particular, a flexible potential expansion is necessary for a precise calculation of these quantities. Hybrid functionals are then considered. Expanding the potential in the primary orbital basis yields chemical shifts that are a notable improvement over conventional hybrid values, and which are a marginal improvement over those obtained using a high-quality generalized gradient approximation. Similar shifts are obtained using a more flexible potential expansion, although care is required to avoid unphysical structure in the exchange-correlation potential.

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.