Relativistic effects on the shielding of SnH2XY and PbH2XY (X, Y = F, Cl, Br and I) heavy atom–containing molecules

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

The LRESC-Loc Model to Analyze Magnetic Shieldings with Localized Molecular Orbitals

The leading electronic mechanisms of relativistic effects in the NMR magnetic shieldings of heavy-atom (HA) containing molecules are well described by the linear response with elimination of small components model (LRESC). We show here first results from a new version of the LRESC model written in terms of localized molecular orbitals (LMOs) which is coined as LRESC-Loc. Those LMOs resemble "chemist's orbitals", representing lone-pairs, atomic cores, and bonds. The whole set of relativistic effects are expressed in terms of non-ligand-dependent and ligand-dependent contributions. We show the electronic origin of trends and behavior of different mechanisms in molecular systems which contain heavy elements that belong to any of the IB to VIIA groups of the periodic table. The SO mechanism has a well-defined dependence with the LPs (LPσ and LPπ) when the HAs have them, but the non-SO mechanisms mostly depend on other LMOs. In addition we propose here that the SO mechanism can be used to characterize interactions involving LPs and the non-SO mechanisms to characterize covalent and close-shell interactions. All our main results are in accord with previous findings, though we are now able to analyze them in a different manner.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications

An accurate quantum chemical (QC) modeling of ⁷⁷ Se and ¹²⁵ Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of ⁷⁷ Se and ¹²⁵ Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of ⁷⁷ Se and ¹²⁵ Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Performance of the LRESC Model on top of DFT Functionals for Relativistic NMR Shielding Calculations

The linear response within the elimination of the small component model (LRESC) is an insightful and computationally efficient method for including relativistic effects on molecular properties like the nuclear magnetic shielding constants, spin-rotation constant, g-tensor, and electric field gradient of heavy atom containing molecules with atoms belonging up to the sixth row of the periodic table. One of its main advantages is its capacity to analyze the electronic origin of the different relativistic correcting terms. Until now, it was always applied on top of Hartree-Fock ground-state wave functions (LRESC/HF) to calculate and analyze NMR shieldings. In this work, we show the performance of the LRESC formalism on top of some density functional theory (DFT) functionals to compute tin shielding constants in SnX₄ (X = H, F, Cl, Br, I) molecular systems. We analyze the performance of each LRESC/DFT scheme on reproducing the electronic mechanisms of the shieldings, taking as a benchmark the results of relativistic calculations at the RPA level of approach (4c/RPA). As in previous works, we divide the LRESC relativistic correcting terms into two groups: core-dependent and ligand-dependent contributions. It is shown here that core-dependent corrections are well-reproduced for the selected DFT functionals, but some differences arise in the ligand-dependent ones. We focus on the performance of different functionals, including the same electron correlation part but containing different amounts of HF exchange. The best results are obtained for the BHandHLYP functional (50% of HF exchange) and the worst for BLYP (0%). When the percentage of HF exchange increases, ligand-dependent contributions are better described, and the final LRESC/DFT results are closer to those obtained with LRESC/HF and 4c/RPA methods. The spin-orbit correction to the shielding constant is one of the main ligand-dependent contributions (there are two more) with total value depending on the amount of HF exchange included in the functional. When the amount of HF exchange decreases, the spin-orbit contribution becomes larger, overestimating the shielding constant even when nonrelativisitc DFT values are much smaller than the nonrelativistic HF ones, as it happens for the heaviest molecular system studied here (SnI₄).

Calculation of 15N NMR chemical shifts: Recent advances and perspectives

Recent advances in computation of ¹⁵N NMR chemical shifts are reviewed, concentrating mainly on practical aspects of computational protocols and accuracy factors. The review includes the discussion of the level of theory, the choice of density functionals and basis sets together with taking into account solvent effects, rovibrational corrections and relativistic effects. Computational aspects of ¹⁵N NMR are illustrated for the series of neutral and protonated open-chain nitrogen-containing compounds and nitrogen heterocycles, coordination and intermolecular complexes.

Spin-orbit effects on the (119)Sn magnetic-shielding tensor in solids: a ZORA/DFT investigation

Periodic-boundary and cluster calculations of the magnetic-shielding tensors of (119)Sn sites in various co-ordination and stereochemical environments are reported. The results indicate a significant difference between the predicted NMR chemical shifts for tin(ii) sites that exhibit stereochemically-active lone pairs and tin(iv) sites that do not have stereochemically-active lone pairs. The predicted magnetic shieldings determined either with the cluster model treated with the ZORA/Scalar Hamiltonian or with the GIPAW formalism are dependent on the oxidation state and the co-ordination geometry of the tin atom. The inclusion of relativistic effects at the spin-orbit level removes systematic differences in computed magnetic-shielding parameters between tin sites of differing stereochemistries, and brings computed NMR shielding parameters into significant agreement with experimentally-determined chemical-shift principal values. Slight improvement in agreement with experiment is noted in calculations using hybrid exchange-correlation functionals.

Theoretical analysis of NMR shieldings of group-11 metal halides on MX (M = Cu, Ag, Au; X = H, F, Cl, Br, I) molecular systems, and the appearance of quasi instabilities on AuF

Accurate calculations of nuclear magnetic shieldings of group-11 metal halides, σ(M; MX) (M = Cu, Ag, Au; X = H, F, Cl, Br, I), were performed with relativistic and nonrelativistic theoretical schemes in order to learn more about the importance of the involved electronic mechanisms that underlie such shieldings. We applied state of the art schemes: polarization propagators at a random phase level of approach (PP-RPA); spin-free Hamiltonian (SF); linear response elimination of small component (LRESC) and density functional theory (DFT) with two different functionals: B3LYP and PBE0. The results from DFT calculations are not close to those from the relativistic polarization propagator calculations at the RPA level of approach (RelPP-RPA), in line with previous results. The spin-orbit (SO) contribution to a shielding constant is important only for MF molecules (M = Cu, Ag, Au). Different electronic mechanisms are considered within the LRESC method, bunched into two groups: core- and ligand-dependent. For the analysed shieldings the core-dependent electronic mechanisms are the most important ones; the ligand-dependent being only important for MF molecules. An out of range value for σ(Au) is found in AuF. It was previously reported in the literature, either originated in the large fluorine electronegativity together with large spin-orbit coupling contributions; or, due to Fermi-contact contributions. We argue here that such an unexpected large value is an artifact originated in the appearance of quasi instabilities, and show how to handle this apparent problem.

Relativistic and electron-correlation effects on the nuclear magnetic resonance shieldings of molecules containing tin and lead atoms

The reference values for NMR magnetic shieldings, σ(ref), are of the highest importance when theoretical analysis of chemical shifts are envisaged. The fact that the nonrelativistically valid relationship among spin-rotation constants and magnetic shieldings is not any longer valid for heavy atoms requires that the search for σ(ref) for such atoms needs new strategies to follow. We present here results of σ(ref) that were obtained by applying our own simple procedure which mixes accurate experimental chemical shifts (δ) and theoretical magnetic shieldings (σ). We calculated σ(Sn) and σ(Pb) in a family of heavy-halogen-containing molecules. We found out that σ(ref)[Sn;Sn(CH3)4] in gas phase should be close to 3864.11 ± 20.05 ppm (0.5%). For Pb atom, σ(ref)[Pb;Pb(CH3)4] should be close to 14475.1 ± 500.7 ppm. Such theoretical values correspond to calculations with the relativistic polarization propagator method, RelPPA, at the RPA level of approach. They are closer to experimental values as compared to those obtained applying few different functionals such as PBE0, B3LYP, BLYP, BP86, KT2, and KT3 of the density functional theory, DFT. We studied tin and lead shieldings of the XY(4-n)Z(n) (X = Sn, Pb; Y, Z = H, F, Cl, Br, I) and PbH(4-n)I(n) (n = 0, 1, 2, 3, 4) family of compounds with four-component functionals as implemented in the DIRAC code. For these systems results of calculations with RelPPA-RPA are more reliable than DFT ones. We argue about why those DFT functionals must be modified in order to obtain more accurate results of NMR magnetic shieldings within the relativistic regime: first, there is a dependence among both electron-correlation and relativistic effects that should be introduced in some way in the functionals; and second, the DIRAC code uses standard nonrelativistic functionals and the functionals B3LYP and PBE0 were parametrized only with data taken from light elements. It can explain why they are not able to properly introduce relativistic effects on nuclear magnetic shieldings. We finally show that in the analysis of magnetic shieldings for the family of compounds mentioned above, one must consider the newest and so-called heavy-atom effect on vicinal heavy atoms, HAVHA. Such effects are among the most important relativistic effects in these kind of compounds.

Relativistic calculations of magnetic resonance parameters: background and some recent developments

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.