Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H₃PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

Structure-directed formation of the dative/covalent bonds in complexes with C70piperidine

The combined experimental-computational study has been performed to investigate the complexes formed between C70 carbon allotrope and piperidine. The results of FT-IR, H-NMR, and C-NMR measurements, together with the calculations based on the DFT approach and molecular dynamics simulations, prove the existence of dative/covalent bonding in C70piperidine complexes. The dative bond forms not only at the region of five- and six-membered rings, observed previously with C60, but also at the region formed of six-membered rings. The structure, i.e., nonplanarity, explains the observed dative bond formation. New findings on the character of interaction of secondary amines with C70 bring new aspects for the rational design of modified fullerenes and their applications in electrocatalysis, spintronics, and energy storage.

Aromaticity Survival in Hydrofullerenes: The Case of C66 H4 with Its π-Aromatic Circuits

The isolated-pentagon rule (IPR) is a determining structural feature that accounts for hollow fullerene stabilization and properties related to C_n (n≥60) cages. The recent characterization of an unprecedented non-IPR hydrofullerene, C_2v C₆₆ H₄ , bearing two heptagons with adjacent fused-pentagon motifs, largely dismisses this feature. Herein, employing DFT calculations, the ¹³ C NMR spectroscopy and aromatic behavior of C_2v C₆₆ H₄ are explored. The results show the presence of three π-aromatic circuits at the bottom boat section of C₆₆ H₄ , indicating the unique features of this hydrofullerene in comparison to those of pristine C₆₀ . In addition, under specific orientations of the external field, certain π-aromatic circuits are enabled, resulting in a more aromatic fullerene than that of C₆₀ , but lower than that of the spherical aromatic C₆₀ ^6- fulleride. Notably, under a field aligned with the saturated carbon atoms, nonaromatic characteristics are exposed. This reveals that spherical-like cages can involve a complex magnetic response that heavily depends on the orientation of the applied field.

Th@C86, Th@C82, Th@C80, and Th@C76: role of thorium encapsulation in determining spherical aromatic and bonding properties on medium-sized endohedral metallofullerenes

Thorium encapsulated metallofullerenes (Th-EMFs) with external C76, C80, C82, and C86 cages have been synthesized, with the 13C-NMR spectrum recorded for Th@C82. Here, we explore computationally the chemical bonding, NMR and spherical aromaticity of Th@C82 and related thorium-encapsulated metallofullerenes. Our results show that these Th-EMFs are new examples of spherical aromatic structures, representing interesting low-symmetry exceptions to the Hirsch 2(N + 1)2 rule of spherical aromaticity. Their electronic structures are based on π-electron counts of 80, 84, 86, and 90, respectively, with a shell structure ranging from S2P6D10F14G18H22I8 to S2P6D10F14G18H22I18, where the partially filled I-shell remains as a frontier orbital. Their behavior is comparable to that of the spherical aromatic alkali-C606- phases, which in addition to the favorable endohedral Th-fullerene bonding account for their particular abundance exhibiting the ability to sustain a long-range shielding cone as a result of the favorable metal-cage bonding. This rationalization of such species as neutral spherical aromatic EMFs suggests the possibility of an extensive series of aromatic fullerenes with nuclearity larger than C60 buckminsterfullerene as stable building blocks towards nanostructured metal-organic materials.

Site-Selectivity of Prato Additions to C70: Experimental and Theoretical Studies of a New Thermodynamic Product at the dd-[5,6]-Junction

Three Prato monoadduct isomers were synthesized and structurally characterized by ¹H, ¹³C NMR spectra and single-crystal X-ray diffraction, and one adduct on the dd-[5,6]-bond was found as the first example of a Prato [5,6]-adduct of C₇₀. To investigate the mechanism in the generation of this dd-[5,6]-adduct, computational studies were employed to show that it was thermodynamically obtained by sigmatropic rearrangement from the presumed initial kinetic product de-[6,6]-adduct.

Noble gas dimers confined inside C70

The potential energy surfaces for the interior rotation of a series of pairs of noble gas atoms encapsulated in the C₇₀ cavity have been explored.

Diastereospecific and Highly Site-Selective Functionalization of C70 Fullerene by a Reaction with Diethyl N-Arylaziridine-2,3-dicarboxylates

The diastereospecific and highly site-selective cycloaddition of N-arylazomethine ylides generated in situ from diethyl N-arylaziridine-2,3-dicarboxylates to C₇₀ fullerene is reported. The reaction provides C₇₀ fulleropyrrolidines in up to hundreds on a milligram scale as α- and β-adducts in a 4:1 ratio with a controlled stereochemical outcome: cis-aziridines give exclusively trans-adducts, and trans-aziridines give only cis-adducts. The ¹H and ¹³C{¹H} NMR spectra for different isomeric adducts were recorded and analyzed to identify some characteristic features, which permit an easy identification of isomeric adducts of this type.

C50Cl10, a planar aromatic fullerene. Computational study of 13C-NMR chemical shift anisotropy patterns and aromatic properties

The structural characterization of D_5h-C₅₀Cl₁₀ as an IPR-violating fullerene provides an interesting case of an oblate structure displaying a planar-aromatic character provided by the face-to-face disposition of two IPR structural motifs, as unraveled by DFT calculations.

Formation of Spherical Aromatic Endohedral Metallic Fullerenes. Evaluation of Magnetic Properties of M@C28 (M = Ti, Zr, and Hf) from DFT calculations

The small C₂₈ cage has been shown experimentally to encapsulate titanium, zirconium, and hafnium (M), among other elements. Here, we explore computationally its magnetic response properties accounting for both global and local shielding tensors. Our results exhibit a continuous shielding region for M@C₂₈ for an orientation-averaged applied field thereby differing from that observed for the hollow C₂₈ structure. Moreover, under a specific orientation of the applied field a long-ranged shielding cone is obtained supporting the spherical aromatic behavior expected by the 2(N + 1)² Hirsch rule for M@C₂₈, standing for its particular abundance. The comparison between the hollow and endohedral C₂₈ fullerenes exhibits a characteristic long-range behavior at the outside region of the structure. The particular shape of the local chemical shift anisotropy tensor at a representative carbon atom exhibits inherent patterns as a consequence of the spherical aromatic behavior. This shows the capabilities from NMR experiments to account for the nonaromatic → aromatic variation. We envisage that the current approach will be beneficial in comparative studies of aromatic and electronic structure properties, to gain a deeper understanding of the geometrical and electronic structure situation in other endohedral species beyond that available from the information provided by routine NMR measurements.

Limitations in the description of conformational preferences of C-disaccharides: The (1 → 3)-C-mannobiose case

Conformational preferences of two C-glycosyl analogues of Manp-(1 → 3)-Manp, were studied using a combined method of theoretical and experimental chemistry. Molecular dynamics was utilized to provide conformational behavior along C-glycosidic bonds of methyl 3-deoxy-3-C-[(α-d-mannopyranosyl)methyl]-α-d- and l-mannopyranosides. The OPLS2005 and Glycam06 force fields were used. Simulations were performed with explicit water (TIP3P) and methanol. Results were compared with a complete conformational scan at the MM4 level with the dielectric constant corresponding to methanol. In order to verify predicted conformational preferences, vicinal ³J_HH NMR coupling constants were calculated by the Karplus equation on simulated potential energy surfaces (PES). A set of new parameters for the Karplus equation was also designed. Predicted ³J_HH were compared with experimental data. We also used reverse methodology, in which the ³J_HH coupling constants were calculated at the DFT level for each family of (ϕ, ψ)-conformers separately and then experimental values were decomposed onto calculated ³J_HH couplings in order to obtain experimentally derived populations of conformers. As an alternative method of evaluation of preferred conformers, analysis of sensitive ¹³C chemical shifts was introduced. We were able to thoroughly discuss several fundamental issues in predictions of preferred conformers of C-saccharides, such as the solvent effect, reliability of the force field, character of empirical Karplus equation or applicability of NMR parameters in predictions of conformational preferences in general.

The Effect of Molecular Conformation on the Accuracy of Theoretical (1)H and (13)C Chemical Shifts Calculated by Ab Initio Methods for Metabolic Mixture Analysis

NMR spectroscopy is a powerful method for analyzing metabolic mixtures. The information obtained from an NMR spectrum is in the form of physical parameters, such as chemical shifts, and construction of databases for many metabolites will be useful for data interpretation. To increase the accuracy of theoretical chemical shifts for development of a database for a variety of metabolites, the effects of sets of conformations (structural ensembles) and the levels of theory on computations of theoretical chemical shifts were systematically investigated for a set of 29 small molecules in the present study. For each of the 29 compounds, 101 structures were generated by classical molecular dynamics at 298.15 K, and then theoretical chemical shifts for 164 (1)H and 123 (13)C atoms were calculated by ab initio quantum chemical methods. Six levels of theory were used by pairing Hartree-Fock, B3LYP (density functional theory), or second order Møller-Plesset perturbation with 6-31G or aug-cc-pVDZ basis set. The six average fluctuations in the (1)H chemical shift were ±0.63, ± 0.59, ± 0.70, ± 0.62, ± 0.75, and ±0.66 ppm for the structural ensembles, and the six average errors were ±0.34, ± 0.27, ± 0.32, ± 0.25, ± 0.32, and ±0.25 ppm. The results showed that chemical shift fluctuations with changes in the conformation because of molecular motion were larger than the differences between computed and experimental chemical shifts for all six levels of theory. In conclusion, selection of an appropriate structural ensemble should be performed before theoretical chemical shift calculations for development of an accurate database for a variety of metabolites.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

Nuclear spin circular dichroism in fullerenes: a computational study

Chemically different carbons in C₇₀ give distinct signals in nuclear spin circular dichroism spectroscopy, a novel candidate for high-resolution identification of chemical compounds.

Modeling 21Ne NMR parameters for carbon nanosystems

The potential of nuclear magnetic resonance (NMR) technique in probing the structure of porous systems including carbon nanostructures filled with inert gases is analysed theoretically using accurate calculations of neon ((21) Ne) nuclear magnetic shieldings. The CBS estimates of (21) Ne NMR parameters were performed for single atom, its dimer and neon interacting with acetylene, ethylene and 1,3-cyclopentadiene. Several levels of theory including restricted Hartree-Fock (RHF), Møller-Plesset perturbation theory to the second order (MP2), density functional theory (DFT) with van Voorhis and Scuseria's t-dependent gradient-corrected correlation functional (VSXC), coupled cluster with single and doubles excitations (CCSD), with single, doubles and triples included in a perturbative way (CCSD(T)) and single, doubles and tripes excitations (CCSDT) combined with polarization-consistent aug-pcS-n series of basis sets were employed. The impact of neon confinement inside selected fullerene cages used as an NMR probe was studied at the RHF/pcS-2 level of theory. A sensitivity of neon probe to the proximity of multiple CC bonds in C2 H2 , C2 H4 , C5 H6 and inside C28 , C30 , C32 , C34 and C60 fullerenes was predicted from (21) Ne NMR parameters' changes. Copyright © 2013 John Wiley & Sons, Ltd.