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.     

Modeling NMR chemical shift: A survey of density functional theory approaches for calculating tensor properties

The NMR chemical shift, a six-parameter tensor property, is highly sensitive to the position of the atoms in a molecule. To extract structural parameters from chemical shifts, one must rely on theoretical models. Therefore, a high quality group of shift tensors that serve as benchmarks to test the validity of these models is warranted and necessary to highlight existing computational limitations. Here, a set of 102 13C chemical-shift tensors measured in single crystals, from a series of aromatic and saccharide molecules for which neutron diffraction data are available, is used to survey models based on the density functional (DFT) and Hartree-Fock (HF) theories. The quality of the models is assessed by their least-squares linear regression parameters. It is observed that in general DFT outperforms restricted HF theory. For instance, Becke's three-parameter exchange method and mpw1pw91 generally provide the best predicted shieldings for this group of tensors. However, this performance is not universal, as none of the DFT functionals can predict the saccharide tensors better than HF theory. Both the orientations of the principal axis system and the magnitude of the shielding were compared using the chemical-shift distance to evaluate the quality of the calculated individual tensor components in units of ppm. Systematic shortcomings in the prediction of the principal components were observed, but the theory predicts the corresponding isotropic value more accurately. This is because these systematic errors cancel, thereby indicating that the theoretical assessment of shielding predictions based on the isotropic shift should be avoided.     

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.     

Zero-point vibrational effects on proton shieldings: functional-group contributions from ab initio calculations.

We investigate the effects of zero-point vibrational motion on the nuclear magnetic shielding constants of a large number of organic molecules. The vibrational corrections include anharmonic contributions from the potential energy surface and harmonic contributions from the curvature of the property surface. Particular attention is paid to vibrational corrections to hydrogen shielding constants where we show that vibrational corrections may be substantial, ranging from about +0.50 to -0.70 ppm, and thus demonstrating that ignoring these effects may give errors in the chemical shifts by more than 1 ppm in certain extreme cases. These effects can therefore not be neglected when comparing calculated results with experiment, not even for the chemical shifts. However, we also demonstrate that the vibrational corrections to the hydrogen shieldings are to a large extent transferable from one molecule to another. We have tabulated functional vibrational corrections to the hydrogen shieldings, based on results for more than 35 molecules. Unfortunately, no similar transferability has been observed for the vibrational corrections to shielding constants of other nuclei such as carbon, nitrogen, or oxygen.     

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.     

Analyzing Discrepancies in Chemical-Shift Predictions of Solid Pyridinium Fumarates

Highly accurate chemical-shift predictions in molecular solids are behind the success and rapid development of NMR crystallography. However, unusually large errors of predicted hydrogen and carbon chemical shifts are sometimes reported. An understanding of these deviations is crucial for the reliability of NMR crystallography. Here, recently reported large deviations of predicted hydrogen and carbon chemical shifts of a series of solid pyridinium fumarates are thoroughly analyzed. The influence of the geometry optimization protocol and of the computational level of NMR calculations on the accuracy of predicted chemical shifts is investigated. Periodic calculations with GGA, meta-GGA and hybrid functionals are employed. Furthermore, molecular corrections at the coupled-cluster singles-and-doubles (CCSD) level are calculated. The effect of nuclear delocalization on the structure and NMR shielding is also investigated. The geometry optimization with a computationally demanding hybrid functional leads to a substantial improvement in proton chemical-shift predictions.     

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.     

DFT-GIAO calculations of 19F NMR chemical shifts for perfluoro compounds

The (19)F NMR shieldings for 53 kinds of perfluoro compounds were calculated by the B3LYP-GIAO method using the 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311++G(d,p), 6-311G(2d,2p), 6-311++G(2d,2p), 6-311++G(2df,2p), 6-311++G(3d,2p), and 6-311++G(3df,2p) basis sets. The diffuse functions markedly reduce the difference between the calculated and experimental chemical shifts. The calculations using the 6-31++G(d,p) basis set give the chemical shifts within 10 ppm deviations from experimental values except for the fluorine nuclei attached to an oxygen atom, a four- and a six-coordinated sulfur atom, and FC(CF(3))(2) attached to a sulfur atom.     

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.     

Solvation and crystal effects in bilirubin studied by NMR spectroscopy and density functional theory

The open-chain tetrapyrrole compound bilirubin was investigated in chloroform and dimethyl sulfoxide solutions by liquid-state NMR and as solid by (1)H, (13)C, and (15)N magic-angle spinning (MAS) solid-state NMR spectroscopy. Density functional theory (DFT) calculations were performed to interpret the data, using the B3LYP exchange-correlation functional to optimize geometries and to compute NMR chemical shieldings by the gauge-including atomic orbital method. The dependence of geometries and chemical shieldings on the size of the basis sets was investigated for the reference molecules tetramethylsilane, NH(3), and H(2)O, and for bilirubin as a monomer and in clusters consisting of up to six molecules. In order to assess the intrinsic errors of the B3LYP approximation in calculating NMR shieldings, complete basis set estimates were obtained for the nuclear shielding values of the reference molecules. The experimental liquid-state NMR data of bilirubin are well reproduced by a monomeric bilirubin molecule using the 6-311+G(2d,p) basis set for geometry optimization and for calculating chemical shieldings. To simulate the bilirubin crystal, a hexameric model was required. It was constructed from geometry-optimized monomers using information from the X-ray structure of bilirubin to fix the monomeric entities in space and refined by partial optimization. Combining experimental (1)H-(13)C and (1)H-(15)N NMR correlation spectroscopy and density functional theory, almost complete sets of (1)H, (13)C, and (15)N chemical shift assignments were obtained for both liquid and solid states. It is shown that monomeric bilirubin in chloroform solution is formed by 3-vinyl anti conformers, while bilirubin crystals are formed by 3-vinyl syn conformers. This conformational change leads to characteristic differences between the liquid- and solid-state NMR resonances.     

Solid-state NMR spectra and long intradimer bonds in the pi-[TCNE]22- dianion

The principal (13)C chemical-shift values for the pi-[TCNE](2)(2-) dimer anion within an array of counterions have been measured to understand better the electronic structure of these atypical chemical species in several related TCNE-based structures. The structure of pi-[TCNE](2)(2-) is unusual as it contains two very long C-C bond lengths (ca. 2.9 Angstroms) between the two monomeric units and has been found to exist as a singlet state, suggestive of a (1)A(1g) (b(2u)(2)b(1g)(0)) electronic configuration. A systematic study of several oxidation states of [TCNE](n) (n = 0, 1-, 2-) was conducted to determine how the NMR chemical-shift tensor values change as a function of electronic structure and to understand the interactions that lead to spin-pairing of the monomer units. The density functional theory (DFT) calculated nuclear shielding tensors are correlated with the experimentally determined principal chemical-shift values. Such theoretical methods provide information on the tensor magnitudes and orientations of their principal tensor components with respect to the molecular frame. Both theoretical and experimental ethylenic chemical-shielding tensors reveal high sensitivity in the component, delta(perpendicular), lying in the monomer molecular plane and perpendicular to the pi-electron plane. This largest shift dependence on charge density is observed to be about -111 ppm/e(-) for delta(perpendicular). The component in the molecular plane but parallel to the central C=C bond, delta(parallel), exhibits a sensitivity of approximately -43 ppm/e(-). However, the out-of-plane component delta'(perpendicular) shows a minimal dependence of -2.6 ppm/e(-) on the oxidation state (n) of [TCNE](n). These relative values support the claim that it is changes within the ethylenic pi-electrons and not the sigma-electrons that best account for the dramatic variations in bonding and shift tensors in this series of compounds. Concerning the intraion bonding, relatively weak Wiberg bond orders between the two monomeric components of the dimer correlate with the long bonds linking the two [TCNE(*)](-) monomers. The chemical-shift tensors for the cyano group, compared to the ethylene shifts, exhibit a reduced sensitivity on the TCNE oxidation state. The experimental principal chemical-shift components agree (within typical errors) with the calculated quantum mechanical shieldings used to correlate the bonding. The embedded ion model (EIM) was used to investigate the typically large electrostatic lattice potential in these ionic materials. Chemical-shielding principal values calculated with the EIM model differ from experiment by +/-3.82 ppm on average, whereas in the absence of an electrostatic field model, the experimental and theoretical results agree by +/-4.42 ppm, which is only a modest increase in error considering the overall ionic magnitudes associated with the tensor variations. Apparently, the effects of the sizable long-range electrostatic fields cancel when the shifts are computed because of lattice symmetry.     

15N NMR study of substituted 2-(phenylamino)-5-phenyl-1,3,4-oxadiazoles

Substituted 2-(phenylamino)-5-phenyl-1,3,4-oxadiazoles were studied by 15N NMR spectroscopy. All signals were assigned on the basis of HMQC and HMBC experiments. Chemical shifts values were correlated with empirical Hammett parameters as well as with calculated electron densities and chemical shieldings.     

Accurate prediction of proton chemical shifts. II. Peptide analogues

Proton chemical shifts of eight cyclic amide molecules were measured in DMSO and D2O solutions. The magnetic shieldings of the corresponding aliphatic, aromatic, and amide protons were calculated by Hartree-Fock and DFT, using the 6-311G**, 6-311++G**, and TZVP basis sets. For aliphatic protons, all of these methods reproduce the experimental values in DMSO solutions excellently after linear regression. The Hartree-Fock method tends to give slightly better agreement than DFT. The best performance is given by the HF/6-311G** method, with an rms deviation of 0.068 ppm. The deviations from experimental chemical shifts in D2O solutions are only slightly larger than those in DMSO solutions. This suggests that we can use the calculated gas phase proton chemical shifts directly to predict experimental data in various solvents, including water. For amide protons, which exchange with water and form hydrogen bonds with DMSO, only modest agreement is obtained, as expected. The present studies confirm that the GIAO approach can reach high accuracy for the relative chemical shifts of aliphatic and aromatic protons at a low cost. Such calculations may provide constraints for the conformational analysis of proteins and other macromolecules.     

13C nuclear magnetic resonance spectra of ethers and glycols

The ¹³C NMR spectra of 21 linear and branched ethers together with the corresponding alcohols have been determined in an attempt to correlate the shieldings in both series. It has been found that the shielding of a carbon in an acyclic ether can be given by the summation of additive shift parameters for substituents and correction parameters for the substitution patterns based on the shielding of the parent alcohol. On examination of solvent-induced shifts for α- and β-carbons in ethers and alcohols, significant ones have been noted in carbon tetrachloride→dimethylsulfoxide and carbon tetrachloride→trifluoroacetic acid. No appreciable concentration-dependent shifts of the shieldings have been observed in both ethers and alcohols. For the shieldings of α-carbons in acyclic glycols, it has been noticed that the observed and predicted values are in accord in 1,3-, 1,4- and 1,5-glycols but deviate in 1,2-glycols. The latter has been examined in a polycyclic system, where the deviations ( > 3·5ppm) in a cis (gauche) 1,2-glycol are larger than those (<2·5 ppm) in a trans (anti-parallel) 1,2-glycol.     

Heuristic overlap-exchange model of noble gas chemical shifts

It is now generally recognized that overlap-exchange interactions are the primary cause of the medium-dependent magnetic shielding (chemical shift) in all noble gases except helium, although the attractive electrostatic-dispersion (van der Waals) interactions play an indirect role in determining the penetration of the interacting species into the repulsive overlap-exchange region. The short-range nature of these overlap-exchange interactions, combined with the fact that they often can be approximated by simple functions of the overlap of the wave functions of the interacting species, suggests a useful semiempirical model of these chemical shifts. In it the total shielding is the sum of shieldings due to pairwise interactions of the noble gas atom with the individual atoms of the medium, with the "atomic" shielding terms either estimated by simple functions of the atomic overlap integrals averaged over their Boltzmann-weighted separations, or determined by fits to experimental data in systems whose complexity makes the former procedure impractical. Results for (129)Xe chemical shifts in the noble gases and in a variety of molecular and condensed systems, including families of n-alkanes, straight-chain alcohols, and the endohedral compounds Xe@C(60) and Xe@C(70) are encouraging for the applicability of the model to systems of technical and biomedical interest.     

Reactivity of haloethanes with hydroxyl radicals: Effects of basis set and correlation energy on reaction energetics

Ab initio calculations on fluoroethane reactions with the hydroxyl radical have been carried out at different levels of theory. The convergence of reaction barriers and reaction enthalpies has been systematically investigated with respect to the size and quality of the basis set and the treatment of correlation energy. The G2 and MP2 barrier heights and reaction enthalpies show the best agreement with the experimental data. The split valence basis sets of triple-zeta quality supplemented by diffuse and polarization functions are necessary to reproduce experimental values for barrier heights and reaction enthalpies at the MP2 level of theory. The full counterpoise correction was used to calculate the basis set superposition error for several standard basis sets, including polarization and diffuse functions. The smallest counterpoise corrections are associated with basis sets that contain polarization and diffuse functions, the diffuse functions being the most effective in reducing BSSE. However, in our case, the uncorrected barrier heights are in better agreement with experimental results than the counterpoise-corrected data. Thus, at the MP2 level of theory, which seems to be dictated for larger electronic systems of chemical interest, the optimal approach is to increase the basis set to the maximum size affordable and to use results without counterpoise corrections for the calculation of reaction barriers. A viable alternative is the use of G2 theory because its results for the barrier heights and reaction enthalpies are in excellent agreement with the experimental data. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1190–1199     

Ab Initio calculation of 19F NMR chemical shielding for alkaline‐earth‐metal fluorides

Gauge‐independent atomic orbital (GIAO) method at Hartree‐Fock (HF) and density functional theory (DFT) levels, respectively, was employed to calculate ¹⁹F NMR chemical shieldings of solid state alkaline‐earth‐metal fluorides MF₂ (M = Mg, Ca, Sr, Ba). The results show that, although the calculated ¹⁹F chemical shieldings tend to be larger than the experimental values, they have a fairly good linear relationship with the observed ones. The calculated results based on different combinations of basis sets show that the B3LYP (a hybrid of DFT with HF) predictions are greatly superior to the HF predictions. When a basis set of metal atom with effective core potential (ECP) has well representation of valence wavefunction, especially wavefunction of d component, and proper definition of core electron number, it can be applied to obtain ¹⁹F chemical shielding which is close to that of all‐electron calculation. The variation of ¹⁹F chemical shielding of alkaline‐earth‐metal fluorides correlates well with the lattice factor A/R².     

Nuclear magnetic resonance shielding constants and chemical shifts in linear 199Hg compounds: a comparison of three relativistic computational methods

We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL(2) (L = Cl, Br, I, CH(3)) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH(3))(2) within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ～2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr(2) and HgI(2) when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ～500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ～100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible.     

Low temperature 13C NMR magnetic resonance in solids 4. Cyclopropane,bicyclo[1.1.0]butane and [1.1.1] propellane

The solid state ¹³C NMR spectra of bicyclo[1.1.0]butane and [1.1.1]propellane have been measured at low temperature. The orientation of the principal axes of the chemical shielding tensor have been determined with ab initio calculations based on the IGLO (Individual Gauge for Localized Orbitals) method when they are not determined by symmetry. Excellent agreement is obtained between the calculated and experimental principal values of the shielding tensor when basis sets containing polarization functions are used. In most cases the agreement is such that the calculated values are within the experimental error.Part 3 of this series: Ref. [7]     

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.