Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

An unusual way of augmenting one-electron basis sets: New aug-pecS-n (n = 1, 2) basis sets for H, C, N, and O atoms for NMR shielding constant calculations that require extra diffuse functions

In this paper, the augmentation of the NMR chemical shift-oriented pecS-n (n = 1, 2) basis sets for H, C, N, and O atoms with diffuse functions was proposed. New aug-pecS-n basis sets were shown to significantly improve the accuracy of the calculated solvent corrections to 1H, 13C, 15N, and 17O NMR shielding constants and these shielding constants of anion systems. The augmentation of the pecS-n (n = 1, 2) basis sets was carried out with the property-energy consistent method using the isotropic dipole polarizability as the target property, which is cardinally different from the usual approach based on the anion energy minimization.

Liquid-Phase NMR of Humic and Fulvic Acids

Present review focuses on the most recent advances in the NMR of the coal-derived humic and fulvic acids, covering exclusively the results of the liquid-phase NMR and leaving apart an overwhelming amount of publications dealing with the solid-state NMR investigations in this field (the latter are comprehensively reviewed elsewhere). Owing to the complexity of humic and fulvic acids together with other coal-derived products, their 1H and 13C NMR spectra consist of a number of overlapping signals belonging to different hydrocarbon types. Comprehensive studies of humic and fulvic acids by means of NMR revealed characteristic functional groups of their composition together with spectral regions in which they resonate. Quantitative 1H and 13C NMR spectra characterize aromatic and saturated carbons spread over many structural moieties, which provides a solid guideline into molecular structure of humic and fulvic acids together with parent coal-derived products. Nowadays, quantitative 13C NMR measurements yield information about a variety of structural parameters such as functional group distribution, aromaticity, degree of condensation of aromatic rings, and medium chain lengths together with many other more specific parameters. The structural NMR studies of the coal-derived products are developing on a background of a marked progress in experimental and computational NMR. Discussed in the present review are the most recent advances in the liquid-state NMR studies of the coal-derived humic and fulvic acids together with their processing products.

Quelling the Geometry Factor Effect in Quantum Chemical Calculations of 13C NMR Chemical Shifts with the Aid of the pecG-n (n = 1, 2) Basis Sets

A root factor for the accuracy of all quantum chemical calculations of nuclear magnetic resonance (NMR) chemical shifts is the quality of the molecular equilibrium geometry used. In turn, this quality depends largely on the basis set employed at the geometry optimization stage. This parameter represents the main subject of the present study, which is a continuation of our recent work, where new pecG-n (n = 1, 2) basis sets for the geometry optimization were introduced. A goal of this study was to compare the performance of our geometry-oriented pecG-n (n = 1, 2) basis sets against the other basis sets in massive calculations of 13C NMR shielding constants/chemical shifts in terms of their efficacy in reducing geometry factor errors. The testing was carried out with both large-sized biologically active natural products and medium-sized compounds with complicated electronic structures. The former were treated using the computation protocol based on the density functional theory (DFT) and considered in the theoretical benchmarking, while the latter were treated using the computational scheme based on the upper-hierarchy coupled cluster (CC) methods and were used in the practical benchmarking involving the comparison with experimental NMR data. Both the theoretical and practical analyses showed that the pecG-1 and pecG-2 basis sets resulted in substantially reduced geometry factor errors in the calculated 13C NMR chemical shifts/shielding constants compared to their commensurate analogs, with the pecG-2 basis set being the best of all the considered basis sets.

The Scope of the Applicability of Non-relativistic DFT Calculations of NMR Chemical Shifts in Pyridine-Metal Complexes for Applied Applications

Heavy metals are toxic, but it is impossible to stop using them. Considering the variety of molecular systems in which they can be present, the multicomponent nature and disorder of the structure of such systems, one of the most effective methods for studying them is NMR spectroscopy. This determines the need to calculate NMR chemical shifts for expected model systems. For elements beyond the third row of the periodic table, corrections for relativistic effects are necessary when calculating NMR parameters. Such corrections may be necessary even for light atoms due to the shielding effect of a neighboring heavy atom. This work examines the extent to which non-relativistic DFT calculations are able to reproduce experimental 15N and 113Cd NMR chemical shift tensors in pyridine-metal coordination complexes. It is shown that while for the calculation of 15N NMR chemical shift tensors there is no real need to consider relativistic corrections, for 113Cd, on the contrary, none of the tested calculation methods could reproduce the experimentally obtained tensor to any extent correctly.

Evidence of extremely short hydrogen bond in the homoconjugated ferrocene-1,1'-diyl-bisphosphinic acid anion: sign change of the H/D isotope effect on the 31P NMR chemical shift

The structure of the two intramolecular hydrogen-bonded motifs within ferrocene-1,1'-diyl-bisphosphinic acid, a cyclic dimer and a homoconjugated anion, has been experimentally revealed by NMR spectroscopy for a solution in a low-freezing polar aprotic CDF3/CDF2Cl medium at 100 K. Structure elucidation was achieved with the help of the H/D isotope effects on the 1H, 2H and, for the first time, 31P NMR chemical shifts. The questions of bridging hydron localization and origins of opposite signs of H/D isotope effects on the 31P NMR chemical shifts in the cyclic dimer and homoconjugated anion have also been addressed by DFT calculations, including numerical solution of the Schrödinger equation for proton and deuteron vibrations in the anharmonic double well potentials.

Computational NMR spectroscopy of 205 Tl

We have investigated the NMR chemical shift of 205 Tl in several thallium compounds, ranging from small covalent Tl(I) and Tl(III) molecules to supramolecular complexes with large organic ligands and some thallium halides. NMR calculations were run at the ZORA relativistic level, with and without spin-orbit coupling using few selected GGA and hybrid functionals, namely BP86, PBE, B3LYP, and PBE0. We also tested solvent effects both at the optimization level and at the NMR calculation step. At the ZORA-SO-PBE0 (COSMO) level of theory we find a very good performance of the computational protocol that allows to discard or retain possible structures/conformations based on the agreement between the calculated chemical shift and the experimental value.

New pecJ-n (n = 1, 2) Basis Sets for Selenium Atom Purposed for the Calculations of NMR Spin-Spin Coupling Constants Involving Selenium

We present new compact pecJ-n (n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

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.

Computational 199 Hg NMR

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin–Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin–spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin–spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z⁺ basis set of quadruple-ζ quality.