NMR shielding constants for hydrogen guest molecules in structure II clathrates

Proton NMR shielding constants and chemical shifts for hydrogen guests in small and large cages of structure II clathrates are calculated using density-functional theory and the gauge-invariant atomic-orbital method. Shielding constants are calculated at the B3LYP level with the 6-311++G(d,p) basis set. The calculated chemical shifts are corrected with a linear regression to reproduce the experimental chemical shifts of a set of standard molecules. The calculated chemical shifts of single hydrogen molecules in the small and large structure II cages are 4.94 and 4.84 ppm, respectively, which show that within the error range of the method the H2 guest molecules in the small and large cages cannot be distinguished. Chemical shifts are also calculated for double occupancy of the hydrogen guests in small cages, and double, triple, and quadruple occupancy in large cages. Multiple occupancy changes the chemical shift of the hydrogen guests by approximately 0.2 ppm. The relative effects of other guest molecules and the cage on the chemical shift are studied for the cages with multiple occupancies.     

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.     

Geometric dependence of the B3LYP-predicted magnetic shieldings and chemical shifts

We perform a systematic investigation of how the B3LYP/6-311+G(2d,p) calculated 13C nuclear magnetic shielding constants depend on the 6-31G(d)-optimized geometries for a set of 18 molecules with various chemical environments. For absolute shieldings, the Hartree-Fock (HF)-optimized geometries lead to a mean absolute deviation (MAD) of 5.65 ppm, while the BLYP- and B3LYP-optimized geometries give MADs of 13.07 and 10.14 ppm, respectively. For chemical shifts, the HF, BLYP and B3LYP geometries lead to MADs of 2.36, 5.80, and 4.43 ppm, respectively. We find that the deshielding tendency of B3LYP can be effectively compensated by using the HF-optimized geometries. When we apply the B3LYP//HF protocol to versicolorin A and 5alpha-androstan-3,17-dione, MADs of 1.86 and 1.41 ppm, respectively, are obtained for chemical shifts, in satisfactory agreement with the experiment.     

Computational studies of 13C NMR chemical shifts of saccharides

The (13)C NMR chemical shifts for alpha-D-lyxofuranose, alpha-D-lyxopyranose (1)C(4), alpha-D-lyxopyranose (4)C(1), alpha-D-glucopyranose (4)C(1), and alpha-D-glucofuranose have been studied at ab initio and density-functional theory levels using TZVP quality basis set. The methods were tested by calculating the nuclear magnetic shieldings for tetramethylsilane (TMS) at different levels of theory using large basis sets. Test calculations on the monosaccharides showed B3LYP(TZVP) and BP86(TZVP) to be cost-efficient levels of theory for calculation of NMR chemical shifts of carbohydrates. The accuracy of the molecular structures and chemical shifts calculated at the B3LYP(TZVP) level is comparable to those obtained at the MP2(TZVP) level. Solvent effects were considered by surrounding the saccharides by water molecules and also by employing a continuum solvent model. None of the applied methods to consider solvent effects was successful. The B3LYP(TZVP) and MP2(TZVP)(13)C NMR chemical shift calculations yielded without solvent and rovibrational corrections an average deviation of 5.4 ppm and 5.0 ppm between calculated and measured shifts. A closer agreement between calculated and measured chemical shifts can be obtained by using a reference compound that is structurally reminiscent of saccharides such as neat methanol. An accurate shielding reference for carbohydrates can be constructed by adding an empirical constant shift to the calculated chemical shifts, deduced from comparisons of B3LYP(TZVP) or BP86(TZVP) and measured chemical shifts of monosaccharides. The systematic deviation of about 3 ppm for O(1)H chemical shifts can be designed to hydrogen bonding, whereas solvent effects on the (1)H NMR chemical shifts of C(1)H were found to be small. At the B3LYP(TZVP) level, the barrier for the torsional motion of the hydroxyl group at C(6) in alpha-D-glucofuranose was calculated to 7.5 kcal mol(-1). The torsional displacement was found to introduce large changes of up to 10 ppm to the (13)C NMR chemical shifts yielding uncertainties of about +/-2 ppm in the chemical shifts.     

Quantitative prediction of gas-phase 19F nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via second-order vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are -1.9 and 1.6 ppm, respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Density-functional theory calculations of absolute and relative (19)F nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree-Fock self-consistent-field calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorine-oxygen, fluorine-nitrogen, and fluorine-fluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.     

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.     

MP2 calculation of 77Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second‐order Möller‐Plesset perturbation theory (MP2) calculation of ⁷⁷Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390–466 ppm) dominates over diamagnetic term (192–198 ppm) resulting in a total shielding relativistic correction of about 230–260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70–80 ppm. In the ⁷⁷Se NMR chemical shifts scale, relativistic corrections are about 20–30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of ⁷⁷Se NMR chemical shifts of the medium‐sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of ⁷⁷Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%. Copyright © 2015 John Wiley & Sons, Ltd.     

NMR shielding constants in hydrogen molecule isotopomers

We analyze the NMR shielding constants in three isotopomers of the hydrogen molecule: H₂, HD and D₂. The results obtained within the Born?COppenheimer approximation using the coupled-cluster singles-and-doubles model are very close to the previous theoretical values. In particular, the isotope shifts computed using significantly larger basis sets agree with the earlier literature results, confirming the disagreement of these calculations with the available experimental data. To examine the accuracy of the computed isotope shifts, we analyze in addition the relativistic corrections and estimate the role of the adiabatic and nonadiabatic effects. The relativistic corrections appear to be negligible; on the other hand, the changes in the shielding constants due to the adiabatic and nonadiabatic effects may account for the discrepancies between the computed and experimental isotope shifts.     

Long-range shielding by cyclopropyl groups in 10-spirocyclopropyl-9,10-dihydroanthracenes

The peri protons in a series of 10-spiroclopropyl-9,10-dihydroanthracenes have been shown to have shifts consistent with large (0.43-0.55 ppm) long-range shielding effects exerted by neighboring cyclopropyl groups. The shieldings are expected to be sensitive to variations in preferred conformation and, since the range of observed shifts for the five compounds studied is relatively small, it is concluded that all exhibit similar conformational preference.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: II. Influence of medium, relativistic effects, and vibrational corrections on phosphorus magnetic shielding constants in the simplest phosphines and phosphine chalcogenides

The influence of solvent nature, relativistic effects, and vibrational corrections on the accuracy of calculation of ³¹P chemical shifts of the simplest phosphines, phosphine oxides, phosphine sulfides, and phosphine selenides was studied. Consideration of the above factors at the stage of both geometry optimization and calculation of magnetic shielding constants was found to appreciably improve the accuracy of calculation of ³¹P NMR chemical shifts in the series of phosphines and phosphine chalcogenides.     

Non-empirical calculations of the nuclear magnetic resonance spectra of imidazole and hydrated imidazole

The magnetic shielding constants of the ¹H, ¹³C and ¹⁵N nuclei of imidazole are calculated for the isolated and hydrated molecules. The results show that the hydrogen bonds produce not only large variations of the chemical shifts for the nitrogen nuclei and the NH proton which are directly involved in the intermolecular bonding, but also measurable shifts for the carbon nuclei. The calculated shielding constants and their variation with hydration are discussed in relation to experimental results concerning imidazole, the 5-membered ring of the purine bases and the imidazole ring of histidine. The calculated values of the spin-spin coupling constants confirm that it is possible to study the tautomeric equilibrium of the imidazole ring from the measurement of these coupling constants and that spin-spin coupling constants are not very sensitive to solvent effects.     

Thermal effects and vibrational corrections to transition metal NMR chemical shifts

Both zero-point and classical thermal effects on the chemical shift of transition metals have been calculated at appropriate levels of density functional theory for a number of complexes of titanium, vanadium, manganese and iron. The zero-point effects were computed by applying a perturbational approach, whereas classical thermal effects were probed by Car-Parrinello molecular dynamics simulations. The systematic investigation shows that both procedures lead to a deshielding of the magnetic shielding constants evaluated at the GIAO-B3 LYP level, which in general also leads to a downfield shift in the relative chemical shifts, delta. The effect is small for the titanium and vanadium complexes, where it is typically on the order of a few dozen ppm, and is larger for the manganese and iron complexes, where it can amount to several hundred ppm. Zero-point corrections are usually smaller than the classical thermal effect. The pronounced downfield shift is due to the sensitivity of the shielding of the metal centre with regard to the metal-ligand bond length, which increase upon vibrational averaging. Both applied methods improve the accuracy of the chemical shifts in some cases, but not in general.     

31P NMR chemical shifts in hypervalent oxyphosphoranes and polymeric orthophosphates

We report the first quantum chemical investigation of the solid- and solution-state 31P NMR chemical shifts in models for phosphoryl transfer enzyme reaction intermediates and in polymeric inorganic phosphates. The 31P NMR chemical shifts of five- and six-coordinate oxyphosphoranes containing a variety of substitutions at phosphorus, as well as four-coordinate polymeric orthophosphates and four-coordinate phosphonates, are predicted with a slope of 1.00 and an R2= 0.993 (N = 34), corresponding to a 3.8 ppm (or 2.1%) error over the entire 178.3 ppm experimental chemical shift range, using Hartree-Fock methods. For the oxyphosphoranes, we used either experimental crystallographic structures or, when these were not available, fully geometry optimized molecular structures. For the four-coordinate phosphonates we used X-ray structures together with charge field perturbation, to represent lattice interactions. For the three-dimensional orthophosphates (BPO4, AlPO4, GaPO4 we again used X-ray structures, but for these inorganic systems we employed a self-consistent charge field perturbation approach on large clusters, to deduce peripheral atom charges. For pentaoxyphosphoranes, the solvent effect on 31P NMR chemical shieldings was found to be very small (<0.5 ppm). The 31P NMR chemical shielding tensors in the pentaoxyphosphoranes were in most cases found to be close to axially symmetric and were dominated by changes in the shielding tensor components in the equatorial plane (sigma22 and sigma33). The isotropic shifts were highly correlated (R2= 0.923) with phosphorus natural bonding orbital charges, with the larger charges being associated with shorter axial P-O bond lengths and, hence, more shielding. Overall, these results should facilitate the use of 31P NMR techniques in investigating the structures of more complex systems, such as phosphoryl transfer enzymes, as well as in investigating other, complex oxide structures.     

Nuclear magnetic shielding constants of liquid water: insights from hybrid quantum mechanics/molecular mechanics models

We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in accurate calculations of nuclear magnetic shielding constants: (i) the model includes electron correlation effects, (ii) the model uses gauge-including atomic orbitals to give gauge-origin independent results, and (iii) the effect of the environment is treated self-consistently using a discrete reaction-field methodology. The authors present sample calculations of the isotropic nuclear magnetic shielding constants of liquid water based on a large number of solute-solvent configurations derived from molecular dynamics simulations employing potentials which treat solvent polarization either explicitly or implicitly. For both the (17)O and (1)H isotropic shielding constants the best predicted results compare fairly well with the experimental data, i.e., they reproduce the experimental solvent shifts to within 4 ppm for the (17)O shielding and 1 ppm for the (1)H shielding.     

Relativistic effect of iodine in <Superscript>13</Superscript>C NMR chemical shifts of iodomethanes from quantum chemical calculations within the framework of the full four-component relativistic Dirac—Coulomb scheme

¹³C NMR shielding constants (chemical shifts) of iodomethanes were calculated within the framework of the full four-component relativistic Dirac—Coulomb scheme. As the number of iodine atoms in the molecule increases, the relativistic counterpart of the ¹³C NMR chemical shift increases from a few tens to several hundreds of ppm. Calculations of ¹³C NMR chemical shifts of organoiodine compounds should be performed at the relativistic level using relativistic Dyall’s basis sets dyall.vXz and dyall.xvXz (x = a, c, ac, ae; X = 2, 3, 4) of at least triple-zeta quality or at the correlated non-relativistic level taking into account relativistic corrections. Solvent effects are not of prime importance; however, taking into account the solvent corrections causes the mean absolute error of determination of the ¹³C NMR chemical shifts to decrease by 1—2 ppm.     

Nuclear motion effects on the C, F and H shielding in methyl fluoride

The ¹⁹F , ¹³C and ¹H shielding in methyl fluoride and its deuterated isotopomers has been calculated from ab initio shielding surfaces for selected temperatures. In each case it is the stretching which contributes most to the nuclear motion corrections which total −9.425 ppm for the ¹⁹F shielding, −4.558 ppm for the ¹³C shielding and −0.601 ppm for the proton shielding. However, some second-order stretching and bending contributions are significant. The deuterium induced isotope shifts are substantial and should be easily measurable. There is a predicted nonadditivity in the ¹⁹F and ¹³C isotope shifts which can be traced to two of the bending contributions.     

A solid state 13C NMR, crystallographic, and quantum chemical investigation of chemical shifts and hydrogen bonding in histidine dipeptides

We report the first solid-state NMR, crystallographic, and quantum chemical investigation of the origins of the 13C NMR chemical shifts of the imidazole group in histidine-containing dipeptides. The chemical shift ranges for Cgamma and Cdelta2 seen in eight crystalline dipeptides were very large (12.7-13.8 ppm); the shifts were highly correlated (R2= 0.90) and were dominated by ring tautomer effects and intermolecular interactions. A similar correlation was found in proteins, but only for buried residues. The imidazole 13C NMR chemical shifts were predicted with an overall rms error of 1.6-1.9 ppm over a 26 ppm range, by using quantum chemical methods. Incorporation of hydrogen bond partner molecules was found to be essential in order to reproduce the chemical shifts seen experimentally. Using AIM (atoms in molecules) theory we found that essentially all interactions were of a closed shell nature and the hydrogen bond critical point properties were highly correlated with the N...H...O (average R2= 0.93) and Nepsilon2...H...N (average R2= 0.98) hydrogen bond lengths. For Cepsilon1, the 13C chemical shifts were also highly correlated with each of these properties (at the Nepsilon2 site), indicating the dominance of intermolecular interactions for Cepsilon1. These results open up the way to analyzing 13C NMR chemical shifts, tautomer states (from Cdelta2, Cepsilon1 shifts), and hydrogen bond properties (from Cepsilon1 shifts) of histidine residue in proteins and should be applicable to imidazole-containing drug molecules bound to proteins, as well.     

Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics

The influence of nuclear delocalisation on NMR chemical shifts in molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory calculations of shielding tensors. Nuclear quantum effects are shown to explain previously observed systematic deviations in correlations between calculated and experimental chemical shifts, with particularly large PIMD‐induced changes (up to 23 ppm) observed for carbon atoms in methyl groups. The PIMD approach also enables isotope substitution effects on chemical shifts and J couplings to be predicted in excellent agreement with experiment for both isolated molecules and molecular crystals. An approach based on convoluting calculated shielding or coupling surfaces with probability distributions of selected bond distances and valence angles obtained from PIMD simulations is used to calculate isotope effects.     

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.