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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 13 C 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 13 C 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 basis set issue has always been one of the most important factors of accuracy in the quantum chemical calculations of NMR chemical shifts. In a previous paper, we developed new pecS- n ( n = 1, 2) basis sets purposed for the calculations of the NMR chemical shifts of the nuclei of the most popular NMR-active isotopes of 1-2 row elements and successfully approbated these on the DFT calculations of chemical shifts in a limited series of small molecules. In this paper, we demonstrate the performance of the pecS- n ( n = 1, 2) basis sets on the calculations of as much as 713 1 H and 767 13 C chemical shifts of 23 biologically active natural products with complicated stereochemical structures, carried out using the GIAO-DFT(PBE0) approach. We also proposed new alternative contraction schemes for our basis sets characterized by less contraction depth of the p -shell. New contraction coefficients have been optimized with the property-energy consistent (PEC) method. The accuracies of the pecS- n ( n = 1, 2) basis sets of both the original and newly contracted forms were assessed on massive benchmark calculations of proton and carbon chemical shifts of a vast variety of natural products. It was found that less contracted pecS- n ( n = 1, 2) basis sets provide no noticeable improvement in accuracy. These calculations represent the most austere test of our basis sets as applied to routine calculations of the NMR chemical shifts of real-life compounds.

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.

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 1 H and 13 C) 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.

Both four-component relativistic and nonrelativistic computations within the GIAO-DFT(PBE0) formalism have been carried out for 15 N and 59 Co NMR shielding constants and chemical shifts of a number of the nitrogen-coordinated complexes of cobalt. It was found that the total values of the calculated nitrogen chemical shifts of considered cobalt complexes span over a range of more than 580 ppm, varying from -452 to +136 ppm. At that, the relativistic corrections to nitrogen shielding constants and chemical shifts were demonstrated to be substantial, changing accordingly from ca. -19 to +74 ppm and from -68 to +25 ppm. Solvent effects on 15 N shielding constants and chemical shifts were shown to have contributions no less important than the relativistic effects, namely from -35 to +63 ppm and from -74 to +23 ppm, respectively. Cobalt shielding constants and chemical shifts were found to vary in the ranges of, accordingly, -20,157 to -11,373 ppm and from +3781 to +13,811. The relativistic effects are of major importance in the cobalt shielding constants, resulting in about 4% for the shielding-type contributions, while solvent corrections to cobalt shielding constants appeared to be of less significance, providing corrections of about 1.4% to the gas phase values.

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.