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.

Structural and Crystallographic Information from 61Ni Solid-State NMR Spectroscopy: Diamagnetic Nickel Compounds

Despite the significance of nickel compounds, NMR spectroscopy of the active nickel isotope ⁶¹Ni remains a largely unexplored field. While nickel(0) compounds have been studied by ⁶¹Ni NMR in solution, solid-state experiments have been limited to Knight shift studies of nickel metal and nickel intermetallics. In conjunction with an NMR study of their ligands and ⁶¹Ni relativistic computations, the first ⁶¹Ni solid-state NMR (SSNMR) spectra of diamagnetic compounds are reported here. Specifically, bis(1,5-cyclooctadiene)nickel(0) [Ni(cod)₂], tetrakis(triphenylphosphite)nickel(0) [Ni[P(OPh)₃]₄], and tetrakis(triphenylphosphine)nickel(0) [Ni(PPh₃)₄] were studied. ⁶¹Ni SSNMR spectra of Ni(cod)₂ were used to determine its isotropic chemical shift (δ_iso = 965 ± 10 ppm), span (Ω = 1700 ± 50 ppm), skew (κ = -0.15 ± 0.05), quadrupolar coupling constant (C_Q = 2.0 ± 0.3 MHz), quadrupolar asymmetry parameter (η = 0.5 ± 0.2), and the relative orientation of the chemical shift and electric field gradient tensors. A solution study of Ni(cod)₂ in C₆D₆ yielded a narrow ⁶¹Ni signal, and the temperature dependence of δ_iso(⁶¹Ni) was assessed (δ_iso being 936.5 ppm at 295 K). The solution is proposed as a secondary chemical shift reference for ⁶¹Ni NMR in lieu of the extremely toxic Ni(CO)₄ primary reference. For Ni[P(OPh)₃]₄, ⁶¹Ni SSNMR was used to infer the presence of two distinct crystallographic sites and establish ranges for δ_iso in the solid state, as well as an upper bound for C_Q (3.5 MHz for both sites). For Ni(PPh₃)₄, line shape fitting provided a δ_iso value of 515 ± 10 ppm, Ω of 50 ± 50 ppm, κ of 0.5 ± 0.5, C_Q of 0.05 ± 0.01 MHz, and η of 0.0 ± 0.2. The study of Ni(PPh₃)₄, in particular, demonstrates the utility of ⁶¹Ni SSNMR given the lack of a previously reported crystal structure and transient nature of Ni(PPh₃)₄ in solution.

Decameric uracil complexes around Li+

Electrospray ionization (ESI) in combination with mass spectrometry (MS) experiments were carried out to study decameric uracil complexes cationized with Li(+) ion. A previous study has shown that, under specific experimental conditions, a particularly intense peak of the decamer U(10)Li(+) is formed, which was referred to as an indication for so-called 'magic number' cluster. In order to gain more insight on the structure of this decameric complex, here, we report experimental studies concerning the kinetics of the fragmentation. In accordance with the new experimental data, structural models were constructed and fully optimized using ab initio and density functional theory quantum chemistry calculations. The theoretical study allowed us to propose a stable gas-phase structure which is compatible with all experimental findings.