3He NMR: from free gas to its encapsulation in fullerene

The ³He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@C_n), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT‐VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization‐consistent basis sets were used (pcS‐n and aug‐pcS‐n), and an estimate of ³He nuclear magnetic shieldings in the complete basis set limit using a two‐parameter fit was established. Theoretical ³He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. ³He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of ³He confinement within fullerene cages of different size on the ³He chemical shift was determined. Copyright © 2013 John Wiley & Sons, Ltd.     

Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³He used as NMR probe. Three closely related nucleus‐independent chemical shift (NICS) based indexes were calculated for benzene at SCF‐HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF‐HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³He nuclear magnetic isotropic shielding (σ) and its zz‐components (σ_zz) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene‐He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³He NMR measurement for benzene saturated with helium gas or in low temperature matrices.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polarization‐consistent and XZP basis sets and B3LYP and BHandH density functionals

Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization‐consistent pcS‐n and pcJ‐n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. ¹J(CH) and ³J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predicted isotropic shieldings and spin–spin values and experiment was good. The BHandH/pcS‐n methanol shieldings obtained using structures optimized at the same level of theory are approaching the accuracy of the advanced coupled‐cluster‐singles‐doubles‐approximate triples (CCSD(T)) calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

Halogen effect on structure and 13C NMR chemical shift of 3,6‐disubstituted‐N‐alkyl carbazoles

Structures of selected 3,6‐dihalogeno‐N‐alkyl carbazole derivatives were calculated at the B3LYP/6‐311++G(3df,2pd) level of theory, and their ¹³C nuclear magnetic resonance (NMR) isotropic shieldings were predicted using density functional theory (DFT). The model compounds contained 9H, N‐methyl and N‐ethyl derivatives. The relativistic effect of Br and I atoms on nuclear shieldings was modeled using the spin–orbit zeroth‐order regular approximation (ZORA) method. Significant heavy atom shielding effects for the carbon atom directly bonded with Br and I were observed (~?10 and ~?30 ppm while the other carbon shifts were practically unaffected). The decreasing electronegativity of the halogen substituent (F, Cl, Br, and I) was reflected in both nonrelativistic and relativistic NMR results as decreased values of chemical shifts of carbon atoms attached to halogen (C3 and C6) leading to a strong sensitivity to halogen atom type at 3 and 6 positions of the carbazole ring. The predicted NMR data correctly reproduce the available experimental data for unsubstituted N‐alkylcarbazoles. Copyright © 2013 John Wiley & Sons, Ltd.     

Local aromaticity mapping in the vicinity of planar and nonplanar molecules

We report on nucleus-independent magnetic shielding (NICS) scans over the centers of six- and five-membered rings in selected metal phthalocyanines (MPc) and fullerene C60 for more accurate characterization of local aromaticity in these compounds. Detailed tests were conducted on model aromatic molecules including benzene, pyrrole, indole, isoindole, and carbazole and subsequently applied to H₂Pc, ZnPc, Al(OH)Pc, and CuPc. Similar behavior of three selected magnetic probes, Bq, ³He, and ⁷Li⁺, approaching perpendicularly the ring centers, was observed. For better visualization of shielding zone over the centers of aromatic rings, we introduced a simple mathematical procedure: the first and second derivatives of scan curves with respect to magnetic probe position enabled their additional examination. It allowed an easier localization of curve minimum and discrimination between areas in space varying by the magnetic field magnitude and to illustrate local aromaticity of two different kinds of rings in MPc with better resolution. Our results supported earlier reports on very low aromaticity indexes of pyrrole ring incorporated into MPc and significant aromaticity of the central macrocycle. No direct dependence between harmonic oscillator model of aromaticity and NICS was observed. Instead, a correlation between position of scan curve minimum and its magnitude were observed. In addition, the NICS values and ³He chemical shifts in the middle of neutral C60 and C60⁶⁻ anion agreed well with the reported experimental NMR values for He@C60 and He@C60⁶⁻.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Local aromaticity in polyacenes manifested by individual proton and carbon shieldings: DFT mapping of aromaticity

Exponential dependencies between locally calculated geometric and magnetic indexes of aromaticity, harmonic oscillator model of aromaticity (HOMA) and nucleus independent chemical shifts (NICS)(0), NICS(1) and NICS(1)zz, and the number of conjugated benzene rings in linear acenes, from benzene to decacene were observed at B3LYP/6-311+G** level of theory. Correlations between HOMA and NICS indexes showed exponential dependencies and were fitted with simple three-parameter function. Similar correlations between both indexes of aromaticity and proton and carbon nuclear isotropic shieldings of individual acene rings were observed. Contrary to proton data, the predicted ¹³C nuclear isotropic shieldings of carbon atoms belonging to inner rings in polyacenes were less shielded, indicating lower aromaticity and therefore, higher reactivity.     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.     

A Computational Study on 3‐Azonia‐, 3‐Phosphonia‐, and 3‐Arsoniaspiro[2.2]pentanes and Related Three‐Membered Heterocycles

A theoretical study at the ab initio MP2/6‐311++G(d,p) level of theory is carried out to characterize several heterocyclic spiro[2.2]pentane cations with N, P, and As as spiro atoms. The strain and relative stability of the spiropentanes are obtained through isodesmic reactions. Nucleus‐independent chemical shifts (NICS) and 3D NICS isosurfaces show σ‐aromatic characteristics, similar to those found in cyclopropane. The interaction with the Cl^? anion, which results in four different stationary structures, is studied and characterized by means of the atoms in molecules methodology, and Cl ??? pnicogen, Cl ??? H, and Cl ??? C interactions are found. The most stable structure in all cases corresponds to opening of one of the three‐membered rings, due to the attack of the Cl atom, and C?Cl bond formation. Furthermore, the reaction with the 3‐boranuidaspiro[2.2]pentane anion results in the formation of a new compound through cleavage of one ring of both reactants.     

Poly[aqua­(μ3‐benzene‐1,2‐dicarboxyl­ato)(μ2‐hydroxo)indium(III)]

In the title compound, [In(C₈H₄O₄)(OH)(H₂O)]_n, the coordination of the In^III ion is composed of six O atoms from three dianionic benzene‐1,2‐dicarboxylate ligands, two hydroxyl groups and one coordinated water mol­ecule in a distorted octa­hedral geometry. The In³⁺ ions are linked by the hydroxyl groups to form zigzag In–OH–In chains, which are further bridged by the benzene‐1,2‐dicarboxylic acid ligands to generate a two‐dimensional layered structure featuring three types of rings (six‐, 14‐ and 20‐membered). Hydrogen bonds between the water mol­ecule and a carboxyl­ate O atom, and between the hydroxyl group and a carboxyl­ate O atom, are observed within the layers. In the crystal packing, there are π–­π stacking inter­actions between the benzene rings of adjacent layers, with a centroid‐to‐centroid distance of 3.668 (3) Å and a dihedral angle of 4.8 (2)°.     

Cyclotridecanone 2,4‐dinitrophenylhydrazone

In cyclotridecanone 2,4‐dinitrophenylhydrazone, C₁₉H₂₈N₄O₄, the 13‐membered carbocycle exists in the triangular [337] conformation. The 2,4‐dinitrophenylhydrazone group is almost perpendicular to the 13‐membered ring, with a dihedral angle of 82.66 (2)° between the mean planes. The dinitrophenylhydrazone rings are packed parallel to each other and separated by 3.28 (1) Å. The NH group forms an intramolecular hydrogen bond to a nitro O atom, and there is a weaker C—H...O interaction between a cyclotridecane CH group and a symmetry‐related 4‐nitro O atom, with a C...O distance of 3.436 (2) Å and a 150° angle about the H atom. The structure, in combination with additional evidence, indicates that [337] is the preferred conformation of cyclotridecane and other simple 13‐membered rings.     

PbCa2[Al8O15] with a novel three‐dimensional aluminate anion

The asymmetric unit of the title compound, lead(II) dicalcium octaaluminate, contains one Pb, one Ca, four Al and eight O atoms, with the Pb atom and one O atom situated on mirror planes. Three Al atoms exhibit slightly distorted tetrahedral coordinations with a mean Al—O bond length of 1.76 Å. The fourth Al atom is in a considerably distorted trigonal–bipyramidal coordination with a mean Al—O bond length of 1.89 Å. One AlO₄ tetrahedron forms infinite chains parallel to [100] via corner‐sharing. These chains are linked by parallel chains of edge‐sharing AlO₅ trigonal bipyramids into layers A of six‐membered double rings extending parallel to (010). The second layer B is made up of the remaining two AlO₄ tetrahedra. These tetrahedra share corners, resulting in likewise six‐membered double rings. Finally, the parallel layers A and B are linked into a three‐dimensional framework by common corners. Charge compensation is achieved by the Pb²⁺ and Ca²⁺ cations, which are situated in the cavities of the anionic framework, and which are surrounded by seven and six O atoms, respectively, both within highly irregular coordination polyhedra.     

Highly accurate relativistic universal Gaussian basis set for Dirac–Fock–Breit calculations

Ion mobilities of H₂O⁺ drifting in helium are calculated and compared with experiment. These calculations employ global potential energy surfaces of the H₂O⁺–He complex, which in the present case were calculated ab initio at the unrestricted MP2 level of theory using a basis set of aug‐cc‐pVTZ quality, and treating the ion as a rigid body. Details are presented of the general characteristics of both the ground and first‐excited electronic states of the complex. Although only the ground‐state surface was used for the mobility calculations, the ab initio determination of the ground state necessitated the inclusion of the first‐excited state owing to the presence of a crossing between the two. This crossing is also described. Mobilities calculated from the global surfaces are in good agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

1H NMR spectra. Part 29§: proton chemical shifts and couplings in esters—the conformational analysis of methyl γ‐butyrolactones

The ¹H NMR spectra of 35 cyclic and acyclic esters are analysed to give the ¹H chemical shifts and couplings. The substituent chemical shifts of the ester group were analysed using three‐bond (γ) effects for near protons and the electric field, magnetic anisotropy and steric effect of the ester group for more distant protons. The electric field is calculated from the partial atomic charges on the O?C = O atoms, and the asymmetric magnetic anisotropy of the carbonyl group acts at the midpoint of the C = O bond. The values of the anisotropies Δχ_parl and Δχ_perp were for the aliphatic esters 10.35 and ?18.84 and for the conjugated esters 7.33 and ?15.75 (×10^?6 ų/molecule). The oxygen steric coefficients found were 104.4 (aliphatic C = O), 45.5 (aromatic C = O) and 16.0 (C–O) (×10^?6 Å⁶/molecule). After parameterisation, the overall RMS error for the data set of 280 entries was 0.079 ppm. The strongly coupled ¹H NMR spectra of the 2‐methyl, 3‐methyl and 4‐methyl γ‐butyrolactones were analysed and the methyl conformational equilibrium obtained from the observed couplings. The observed versus calculated density functional theory (DFT) ΔG(ax‐eq) was 1.0 (1.01), 0.34 (0.54) and 0.65 (0.71) kcal/mol res. The shielding effect of a methyl cis to a proton in the five‐membered lactone rings is ?0.40 ±0.05 ppm and deshielding trans effect 0.12 ±0.05 ppm, which is common to both five and six membered rings. The cis/trans isomerism in the vinyl esters methyl acrylate, crotonate and methacrylate and methyl furoate was examined using the ¹H chemical shifts. The calculated shifts of both the cis and trans isomers were in good agreement with the observed shifts. Copyright © 2012 John Wiley & Sons, Ltd.     

A pentaerythritol‐derived spirodi­phospho­nate

The title spirodi­phospho­nate, 3,9‐di­methyl‐2,4,8,10‐tetraoxa‐3λ⁵,9λ⁵‐diphospha­spiro­[5.5]­un­decane‐3,9‐dione, C₇H₁₄O₆P₂, a polymer additive, has crystallographic symmetry 2. At 100 K, its six‐membered rings have chair conformations, with endocyclic torsion‐angle magnitudes in the range 51.87 (8)–58.93 (9)°. The P=O distance is 1.4749 (8) Å, while the P—C(methyl) distance is 1.7691 (12) Å.     

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 (²¹Ne) nuclear magnetic shieldings. The CBS estimates of ²¹Ne 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 C₂H₂, C₂H₄, C₅H₆ and inside C₂₈, C₃₀, C₃₂, C₃₄ and C₆₀ fullerenes was predicted from ²¹Ne NMR parameters' changes. Copyright © 2013 John Wiley & Sons, Ltd.     

The theoretical study of aromaticity in N-heteroatom compounds

In this article, we used nucleus-independent chemical shifts (NICS), aromatic stabilization energies (ASE), and magnetic susceptibility isotropic, calculated with (density functional theory) B3LYP levels at the 6-311+G (d, p) basis set, to evaluate the aromaticity of a set of 12 six-member planar π-electron aromatic systems: mono- and multi-substituted benzenes by nitrogen atoms. NICS were calculated at the center of the rings, 0.5 Å and 1 Å above the molecular plane, and in order to reflect the π-electron effects, we compare the values of NICS(0.5). The result statistically revealed significant correlations among the above three criteria. The comparison result was obtained as benzene > mono-nitrogen benzene > di-nitrogen benzene > tri-nitrogen benzene > tetra-nitrogen benzene > penta-nitrogen benzene.     

(2‐Aminoethanethiolato‐N,S)bis(ethylenediamine‐N,N′)cobalt(III) dinitrate

In the title compound, [Co(C₂H₆NS)(C₂H₈N₂)₂](NO₃)₂, the Co^III atom has a slightly distorted octahedral geometry, coordinated by one 2‐amino­ethane­thiol­ate and two ethyl­enedi­amine ligands. The three five‐membered chelate rings adopt a gauche conformation with the unfavoured (lel)₂(ob) form, which is ascribed to hydrogen bonds between the amine groups in the complex cation and the nitrate counter‐anions [N?O 2.900 (3)–3.378 (3) Å].     

7‐Phenyl‐1‐oxa‐4‐thiaspiro[4.5]decan‐7‐ol stereoisomers

The stereoisomers of 7‐phenyl‐1‐oxa‐4‐thia­spiro­[4.5]­decan‐7‐ol, C₁₄H₁₈O₂S, have the same stereochemistry at the C atom bearing an OH group, i.e. axial OH and equatorial phenyl groups. However, the acetal S and O atoms are axial and equatorial, respectively, in one isomer and reversed in the second. Furthermore, the crystals of one isomer are composed of hydrogen‐bonded mol­ecules involving the hydroxyl H atom and the O atom of the five‐membered heterocyclic ring, with an O?O distance of 2.962 (3) Å, forming a polymeric chain along the b axis. The asymmetric unit of the other isomer is composed of two mol­ecules, wherein hydroxyl H atoms and the O atoms of the five‐membered heterocyclic rings display intramolecular O—H?O hydrogen bonds with O?O separations of 2.820 (2) and 2.834 (2) Å.