3He NMR studies on helium–pyrrole,helium–indole,and helium–carbazole systems: a new tool for following chemistry of heterocyclic compounds

The ³He nuclear magnetic shieldings were calculated for free helium atom and He–pyrrole, He–indole, and He–carbazole complexes. Several levels of theory, including Hartree–Fock (HF), Second‐order Møller‐Plesset Perturbation Theory (MP2), and Density Functional Theory (DFT) (VSXC, M062X, APFD, BHandHLYP, and mPW1PW91), combined with polarization‐consistent pcS‐2 and aug‐pcS‐2 basis sets were employed. Gauge‐including atomic orbital (GIAO) calculated ³He nuclear magnetic shieldings reproduced accurately previously reported theoretical values for helium gas. ³He nuclear magnetic shieldings and energy changes as result of single helium atom approaching to the five‐membered ring of pyrrole, indole, and carbazole were tested. It was observed that ³He NMR parameters of single helium atom, calculated at various levels of theory (HF, MP2, and DFT) are sensitive to the presence of heteroatomic rings. The helium atom was insensitive to the studied molecules at distances above 5 Å. Our results, obtained with BHandHLYP method, predicted fairly accurately the He–pyrrole plane separation of 3.15 Å (close to 3.24 Å, calculated by MP2) and yielded a sizable ³He NMR chemical shift (about ?1.5 ppm). The changes of calculated nucleus‐independent chemical shifts (NICS) with the distance above the rings showed a very similar pattern to helium‐3 NMR chemical shift. The ring currents above the five‐membered rings were seen by helium magnetic probe to about 5 Å above the ring planes verified by the calculated NICS index. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

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.     

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.     

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

Phosphorus mononitride: A difficult case for theory

Phosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero-point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree-Fock, density functional theory (DFT), or even the coupled-cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug-cc-pVXZ basis sets with the size from double-ζ to sextuple-ζ, as well as Jensen's aug-pc-n, aug-pcJ-n, and aug-pcSseg-n basis sets, where n = 1-4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three- or two-parameter formulas. The ³¹P NMR shieldings estimated with the aug-cc-pVXZ and aug-cc-pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree-Fock self-consistent field (HF-SCF) NMR parameters evinced similar behavior as the coupled-cluster data. The only smooth convergence was achieved using the aug-cc-pCVXZ basis sets that include core-valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF-SCF and CCSD levels that provide ³¹P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.     

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.     

Disruptive influence of the host cage C60 on the guest He–H+ bond and bonding in H3+

Although a helium atom prefers to stay at the centre of a fullerene (C₆₀) cage and a proton binds with one of the carbon atoms from inside, DFT(MN15)/cc-pVTZ and DLPNO-MP2/def2-TZVP calculations show that the helium atom and the proton in HeH⁺ prefer to stay away from the centre of the cage, weakening the He–H⁺ covalent bond considerably. Both the helium atom and the proton exhibit noncovalent interactions with the carbon atoms of two pentagons at the opposite ends of the fullerene cage. Our calculations also show that a linear arrangement of H₃⁺ (inside C₆₀), pointing towards the centres of two pentagons opposite to each other, with the proton breaking away from H_2, is energetically more favored over the equilateral triangle geometry of free H₃⁺.     

B24N24 nanocages: a GIAO density functional theory study of 14N and 11B nuclear magnetic shielding and electric field gradient tensors

Abstract  

Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed.     

129Xe and 131Xe nuclear magnetic dipole moments from gas phase NMR spectra

³He, ¹²⁹Xe and ¹³¹Xe NMR measurements of resonance frequencies in the magnetic field B₀ = 11.7586 T in different gas phase mixtures have been reported. Precise radiofrequency values were extrapolated to the zero gas pressure limit. These results combined with new quantum chemical values of helium and xenon nuclear magnetic shielding constants were used to determine new accurate nuclear magnetic moments of ¹²⁹Xe and ¹³¹Xe in terms of that of the ³He nucleus. They are as follows: μ(¹²⁹Xe) = ?0.7779607(158)μ_N and μ(¹³¹Xe) = +0.6918451(70)μ_N. By this means, the new ‘helium method’ for estimations of nuclear dipole moments was successfully tested. Gas phase NMR spectra demonstrate the weak intermolecular interactions observed on the ³He and ¹²⁹Xe and ¹³¹Xe shielding in the gaseous mixtures with Xe, CO₂ and SF₆. Copyright © 2015 John Wiley & Sons, Ltd.     

Endohedral and external through-space shieldings of the fullerenes c50, c60, c60(-6), c70, and c70(-6)-visualization of (anti)aromaticity and their effects on the chemical shifts of encapsulated nuclei

Endohedral and external through-space NMR shieldings (TSNMRS) and the magnetic susceptibilities of the fullerene carbon cages of C50, C60, C60(-6), C70, and C70(-6) were assessed by ab initio molecular orbital calculations. Employing the nucleus-independent chemical shift (NICS) concept, these TSNMRS were visualized as isochemical shielding surfaces (ICSS) and were applied to quantitatively estimate either the aromaticity or the anti-aromaticity on the fullerene surface pertaining to the five- or six-membered ring moieties and the shielding of any nuclei enclosed within the carbon cages. Differences between the NICSs calculated at the center of the fullerene carbon cages and the experimental chemical shifts of encapsulated NMR-active nuclei as well as experimental shieldings observed for different encapsulated nuclei were able to be understood readily for the first time.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³C and ¹H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.     

B<Subscript>24</Subscript>N<Subscript>24</Subscript> nanocages: a GIAO density functional theory study of <Superscript>14</Superscript>N and <Superscript>11</Superscript>B nuclear magnetic shielding and electric field gradient tensors

Abstract  Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed. Graphical abstract        

Electronic Communication between S=1/2 Spins in Negatively‐charged Double‐caged Fullerene C60 Derivative Bonded by Two Single Bonds and Pyrrolizidine Bridge

Radical anion salt {cryptand[2.2.2] (K⁺)}₂(bispheroid)^2??3.5C₆H₄Cl₂ ( 1 ) of the double‐caged fullerene C₆₀ derivative, in which fullerene cages are linked by a cyclobutane bridging cycle and additionally by a pyrrolizidine moiety, was obtained. Each fullerene cage in this derivative accepts one electron on reduction, thus forming the (bispheroid)^2? dianions with two interacting S=1/2 spins on the neighboring cages. Low‐temperature magnetic measurements reveal a singlet ground state of the bispheroid dianions whereas triplet contributions prevail at increased temperature. An estimated exchange interaction between two spins J/k_B=?78 K in 1 indicates strong magnetic coupling between them, nearly two times higher than that (J/k_B=?44.7 K) in previously studied (C₆₀^?)₂ dimers linked via a cyclobutane bridge only. The enhancement of magnetic coupling in 1 can be explained by a shorter distance between the fullerene cages and, possibly, an additional channel for the magnetic exchange provided by a pyrrolizidine bridge. Quantum‐chemical calculations of the lowest electronic state of the dianions by means of multi‐configuration quasi‐degenerate perturbation theory support the experimental findings.     

83Kr nuclear magnetic moment in terms of that of 3He

High resolution NMR spectroscopy was applied to precisely determine the ⁸³Kr nuclear magnetic dipole moment on the basis of new results available for nuclear magnetic shielding in krypton and helium‐3 atoms. Small amounts of ³He as the solutes and ⁸³Kr as the buffer gas were observed in ³He and ⁸³Kr NMR spectra at the constant external field, B₀ = 11.7578 T. In each case, the resonance frequencies (ν^He and ν^Kr) were linearly dependent on the density of gaseous solvent. The extrapolation of experimental points to the zero density of gaseous krypton allowed for the evaluation of both resonance frequencies free from intermolecular interactions. By combining these measurements with the recommended ⁸³Kr chemical shielding value, the nuclear magnetic moment could be determined with much better precision than ever before, μ(⁸³Kr) = ?0.9707297(32)μ_N, with the improvement due to the greater accuracy of the spectral data. Copyright © 2014 John Wiley & Sons, Ltd.     

Computer simulation of trifluoromethane properties with ab initio force field

Intermolecular interaction potentials of the trifluoromethane dimer in 15 orientations have been calculated using the Hartree‐Fock (HF) self‐consistent theory and the second‐order Møller‐Plesset (MP2) perturbation theory. Single point energies at important geometries were also calibrated by the coupled cluster with single and double and perturbative triple excitation [CCSD(T)] calculations. We have employed Pople's medium size basis sets [up to 6‐311++G(3df,3pd)] and Dunning's correlation consistent basis sets (up to aug‐cc‐pVQZ). Basis set limit potential values were obtained through well‐studied extrapolation methods. The calculated MP2 potential data were employed to parameterize a 5‐site force field for molecular simulations. We performed molecular dynamics simulations using the constructed ab initio force field and compared the simulation results with experiments. Quantitative agreements for the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011