Iglo calculations of the antisymmetric components of nuclear magnetic shielding tensors

Calculations of the antisymmetric components of ¹³C shielding tensors have been performed in several compounds using the IGLO (individual gauge for localized orbitals) method. The results indicate chemical situations in which the detection of the antisymmetric components should be easier than in the cases analyzed by Iwai and Saika.     

Molecular orbital studies of the NMR hydrogen bond shift

Magnetic shielding constants are calculated for the protons in XOH and XOH…OH₂ (XH, CH₃, NH₂, OH and F) molecules using a slightly extended set of atomic functions modified by gauge factors. These results are used to determine theoretical values for the NMR hydrogen bond shifts in the XOH…OH₂ systems. Such theoretical data are consistent with the few available experimental data. An analysis of the theoretical results reveals that there are three major types of shielding contribution to the NMR hydrogen bond shift; (a) a deshielding change due to the variation of the local currents on the hydrogen bonded proton; (b) a reduction in shielding from currents localized on the oxygen atom of the proton donor; (c) a deshielding contribution from currents induced on the oxygen atom of the proton acceptor. Except for the water dimer, contributions (a), (b) and (c) are of comparable importance for changes in isotropic shielding. For (H₂O)₂ contributions (a) and (c) are somewhat more important than contribution (b). Contribution (c) is almost totally responsible for the changes in the anistropies of the shielding tensors associated with the hydrogen bonded protons. The proton shielding anisotropy changes which occur on hydrogen bond formation are generally much larger than the corresponding variations in the isotropic values of the shielding tensors. This suggests that proton magnetic shielding anisotropies may be more sensitive measures of features of hydrogen bonding than are isotropic proton shielding constants.     

A comparison of the IGLO and LORG methods for the calculations of nuclear magnetic shieldings

The individual gauge for localized orbitals (IGLO) and localized orbital/local origin (LORG) methods for the calculation of chemical shieldings are compared from their theoretical and computational viewpoints. A detailed analysis of the fluorine α-substituent effect in a series of fluoromethanes is given in terms of the IGLO and LORG bond contributions. The performance of both methods is discussed for molecular systems of fairly different sizes.     

Ab initio calculation of magnetic properties by the “direct” IGLO method

A direct method for the ab initio calculation of the magnetic susceptibility and chemical shielding tensors based on the individual gauge for localized molecular orbitals (IGLO) formalism is introduced. “Direct” in this context means we avoid storing the two-electron repulsion integrals in favor of recalculating them whenever necessary. In conjunction with the Direct-SCF package TURBOMOLE Direct IGLO (DIGLO) permits calculation of magnetic second-order properties for large molecules by minimizing peripheral disc storage requirements. The size of the molecules to be treated is limited only by the amount of CPU time available. The performance of DIGLO is demonstrated for some selected examples.     

Theory of 31P Chemical Shifts

Abstract

The IGLO (individual gauge for localized orbitals) method¹, has been applied successfully to organic molecules.² The application to phosphorous compounds is more laborious, mainly since larger basis sets are required. By the IGLO method one obtains the chemical shielding as a sum of contributions of localized orbitals. For ³¹P the dominant contributions come from the K-shell (well transferable), the L-shell (depending somewhat on the bonding situation), the bonds attached to P (large differences between single and multiple bonds), and the lone pair on P (large variations), the contributions of distant bonds and lone pairs being small, but often not negligible. We find good agreement with experiments for those molecules for which experimental data are available (e.g. PH₃, P₂H₄, P₄, CH₃PH₂, OPF₃) and we can make predictions for others (e.g. P₂, P₂H₂, HSiP). The interpretation of the variation of is more complicated than in the case of hydrocarbons, since bond contributions are usually not transferable between different molecules, and it is hard to justify an increment system. An interesting example is the dependence of the ³¹P-shift in RC≡P on R.     

29Si NMR Shielding Tensors in Triphenylsilanes – 29Si Solid State NMR Experiments and DFT‐IGLO Calculations

²⁹Si NMR shielding tensors of a series of triphenylsilanes Ph₃SiR with R = Ph, Me, F, Cl, Br, OH, OMe, SH, NH₂, SiPh₃, C≡CPh were determined from ²⁹Si CP/MAS spectra recorded at low spinning rates. In addition the principal components of the shielding tensor were calculated employing the DFT‐IGLO method. For most silanes experimental and calculated values are in good accordance. Larger differences were observed for systems with hydrogen bridge forming substituents and the halides bromide and chloride. In some of the spectra the shielding information interfered with residual dipolar couplings. The different contributions of the various substituents to the principal components of the shielding tensor and the orientation of the tensor within the molecules are discussed and compared for the compounds under investigation.     

31P MAS-NMR an Phosphoroxidsulfiden — experimentelle Bestimmung und quantenchemische Berechnung der Tensoren der chemischen Verschiebung

³¹P MAS-NMR of Phosphorus Oxide Sulfides — Experimental Determination and Quantumchemical Calculation of Chemical Shift Tensors By high resolution solid state ³¹P MAS NMR and analysis of spinning sidebands the principal values of the chemical shift tensors in the series P₄O₆S_n with n = 0–4 have been determined. The orientations of the corresponding principal axes within the molecules have been derived. All magnetic shielding tensors show axial symmetry within the limits of experimental error. Thus the orientation of the shielding tensor within the molecules can be deduced indirectly. This information is usually not accessible for polycrystalline samples. The principal values of the tensor of the trivalent phosphorus atoms in P₄O₆S seem to deviate considerably from those of the other compounds with respect to anisotropy and axiality. The reason is a dynamic effect: the rotation of the molecule about the PS bond. All experimental results are confirmed by ab-initio calculations using the IGLO method.     

Paramagnetic contributions to the NMR shielding constants of 1H and 17O in water by triple perturbation theory

Triple perturbation theory is applied to evaluate the paramagnetic contributions to the NMR shielding constants of proton and oxygen in the water molecule, starting from SCF wavefunctions ofincreasing accuracy. The results computed assuming the gauge of the vector potential on the center of mass are quite for ¹H and ¹⁷O. Only the xx component of the paramagnetic shielding of ¹⁷O diverges significantly from the coupled Hartree-Fock estimate.     

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]     

Nuclear shielding calculations on the primary structure of the gellan polysaccharide

Ab initio, GIAO and IGLO, nuclear shielding calculations are performed on each of the four pyranose ring residues of the tetrasaccharide repeating unit in a single chain of the gellan polysaccharide, [→ 3)- -Glcp-(1 → 4)-β- -GlcpA-(1 → 4)-β- -Glcp-(1 → 4)-- -Rhap(1 _n. The results provide an insight into the effects of the changing primary molecular electronic structure on the calculated ¹³C, ¹⁷O and ¹H shieldings. In particular, the observed trends in the calculated isotropic (σⁱ) shielding values are rationalised withi the framework of the localised molecular orbital shielding contributions and Mulliken population analyses (MPA).     

High-resoluttin 29Si NMR in solid silicates: Correlations between shielding tensor and Si-O bond length

²⁹Si NMR spectra of polycrystalline Ca₆[Si₂O₇¦(OH)₆] and [(CH₃)₄N] ₈Si₈O₂₀·69H₂O were measured using the cross polarization double-resonance technique. Observed shielding tensors are related to the known Si-O bond systems. The arrangement of the four Si-O bonds in the SiO₄ tetrahedra is reflected by the ²⁹Si shielding tensor. The most shielded direction corresponds to the shortest Si-O bond.     

An Empirical Proton NMR Shielding Equation for Alkenes Based on Ab Initio Calculations

Nuclei of hydrogen atoms located over a carbon-carbon double bond in the presence of a strong magnetic field experience a perturbed magnetic field caused primarily by the magnetic anisotropy of the bond. However, the commonly used theoretical model for predicting the shielding effect of an alkene double bond on hydrogen nuclei is sometimes inconsistent with the observed proton NMR chemical shifts in structures that have covalently bonded hydrogens located over a carbon-carbon double bond. We have used the ab initio gauge including atomic orbital (GIAO) method to calculate isotropic shielding values and to determine the proton NMR shielding increments for a simple model system: methane held at various positions over ethene. These shielding increments calculated for one proton of methane have been mapped as a function of their position in Cartesian coordinates relative to the center of ethene. A mathematical function has been fit to this three-dimensional shielding increment surface at each of four distances from the face of the ethene molecule. Additionally, a single mathematical equation has been developed for predicting the shielding caused by the carbon-carbon double bond in ethene. In contrast to the traditionally employed shielding model, our results predict deshielding for protons within 3 Å above the center of a carbon-carbon double bond, consistent with experimental observations in several molecular systems. The NMR shielding increments predicted by this equation are compared to observed shielding increments in some test alkenes.     

Estimation of the contribution of vibronic interaction to the isotope effect on the nuclear magnetic shielding constant of a hydrogen bridge

A nonadiabatic correction to the H/D isotope effect on the constant of electronic magnetic shielding of a nucleus was estimated within the framework of the first-order perturbation theory. The procedure consists in the ab initio calculation of frequencies and relative intensities in the vibronic spectrum for H and D forms of a molecule taking into account only the transitions allowed in the magnetic-dipole approximation. With the elementary assumptions (case of Herzberg vibronic interaction), the semiquantitative estimation of adiabatic (geometrical) and nonadiabatic contributions to the H/D isotope effect on the ¹⁵N shielding constant of a complex with the HF-pyridine hydrogen bond was carried out. These two contributions to the isotope effect are comparable in the order of magnitude, at least for unsaturated molecules with low-lying excited electronic states. A correct solution to the problem requires ab initio calculation that is not based on the Born-Oppenheimer approximation.     

Proton chemical shifts in NMR: Part 17. Chemical shifts in alkenes and anisotropic and steric effects of the double bond

The ¹H NMR spectra of a number of alkenes of known geometry were recorded in CDCl₃ solution and assigned, namely ethylene, propene, 4-methylcyclohexene, 1,4-dimethylcyclohexene, methylene cyclohexane (in CFCl₃–CD₂Cl₂ at 153 K), 5-methylene-2-norbornene, camphene, bicyclopentadiene, styrene and 9-vinylanthracene. These results together with literature data for other alkenes, i.e. 1,3- and 1,4-cyclohexadiene, norbornene, norbornadiene, bicyclo[2.2.2]oct-2-ene and α- and β-pinene, and other data allowed the determination of the olefinic shielding in these molecules. The shielding was analysed in terms of the magnetic anisotropy and steric effects of the double bond together with a model (CHARGE7) for the calculation of the two- and three-bond electronic effects. For the aromatic alkenes ring current and π-electron effects were included. This analysis showed that the double bond shielding arises from both anisotropic and steric effects. The anisotropy is due to the perpendicular term only with a value of Δχ(CC) of −12.1 × 10⁻⁶cm³mol⁻¹. There is also a steric deshielding term of 82.5/r⁶ (r in Å). The shielding along the π-axis changes sign from shielding at long range (>2.5 Å) to deshielding at short range (<2 Å). The model gives the first comprehensive calculation of the shielding of the alkene group. For the data set considered (172 proton chemical shifts) ranging from δ=0.48 to 8.39, the r.m.s. error of observed vs calculated shifts was 0.11 ppm. Copyright © 2001 John Wiley & Sons, Ltd.     

GIAO,DFT, AIM and NBO analysis of the N?H···O intramolecular hydrogen‐bond influence on the 1J(N,H) coupling constant in push–pull diaminoenones

In the series of diaminoenones, large high‐frequency shifts of the ¹H NMR of the N? H group in the cis‐position relative to the carbonyl group suggests strong N? H···O intramolecular hydrogen bonding comprising a six‐membered chelate ring. The N? H···O hydrogen bond causes an increase of the ¹J(N,H) coupling constant by 2–4 Hz and high‐frequency shift of the ¹⁵N signal by 9–10 ppm despite of the lengthening of the relevant N? H bond. These experimental trends are substantiated by gauge‐independent atomic orbital and density functional theory calculations of the shielding and coupling constants in the 3,3‐bis(isopropylamino)‐1‐(aryl)prop‐2‐en‐1‐one (12) for conformations with the Z‐ and E‐orientations of the carbonyl group relative to the N? H group. The effects of the N? H···O hydrogen‐bond on the NMR parameters are analyzed with the atoms‐in‐molecules (AIM) and natural bond orbital (NBO) methods. The AIM method indicates a weakening of the N? H···O hydrogen bond as compared with that of 1,1‐di(pyrrol‐2‐yl)‐2‐formylethene (13) where N? H···O hydrogen bridge establishes a seven‐membered chelate ring, and the corresponding ¹J(N,H) coupling constant decreases. The NBO method reveals that the LP(O) →σ*_{N? H} hyperconjugative interaction is weakened on going from the six‐membered chelate ring to the seven‐membered one due to a more bent hydrogen bond in the former case. A dominating effect of the N? H bond rehybridization, owing to an electrostatic term in the hydrogen bonding, seems to provide an increase of the ¹J(N,H) value as a consequence of the N? H···O hydrogen bonding in the studied diaminoenones. Copyright © 2010 John Wiley & Sons, Ltd.     

Density Functional Calculations of the Anisotropic Effects of Borazine and 1,3,2,4‐Diazadiboretidine

On the basis of the nucleus‐independent chemical shift (NICS) concept, the anisotropic effects of two inorganic rings, namely, borazine and planar 1,3,2,4‐diazadiboretidine, are quantitatively calculated and visualized as isochemical shielding surfaces (ICSSs). Dissection of magnetic shielding values along the three Cartesian axes into contributions from σ and π bonds by the natural chemical shielding–natural bond orbital (NCS–NBO) method revealed that their appearance is not a simple reflection of the extent of (anti)aromaticity.     

Comparative analysis of 13C shielding constants stereospecificity in the silicon and germanium derivatives of acetylenic aldehyde and ketone oximes based on the 13C NMR spectroscopy and GIAO calculations

In the acetylenic aldehyde oximes with substituents containing silicon and germanium, the ¹³C NMR signal of the C‐2 carbon of triple bond is shifted by 3.5 ppm to lower frequency and that of the C‐3 carbon is moved by 7 ppm to higher frequency on going from E to Z isomer. A greater low‐frequency effect of 5.5 ppm on the C‐2 carbon signal and a greater high‐frequency effect of 11 ppm on the C‐3 carbon signal are observed in the analogous acetylenic ketone oximes. The carbon chemical shift of the C?N bond is larger by 4 ppm in E isomer relative to Z isomer for the aldehyde and ketone oximes. The ²⁹Si chemical shifts in the silicon containing acetylenic aldehyde and ketone oximes are almost the same for the diverse isomers. The trends in changes of the measured chemical shifts are well reproduced by the gauge‐including atomic orbital (GIAO) calculations of the ¹³C and ²⁹Si shielding constants. Copyright © 2009 John Wiley & Sons, Ltd.     

77Se shielding tensors of diphenyl diselenide, comparison of the results from CP/MAS NMR spectroscopy and IGLO calculations

The cross-polarization/magic-angle-spinning (CP/MAS) ⁷⁷SeNMR experiment of Ph-Se-Se-Ph affords two signal series with isotropic chemical shifts at δ_iso = 425 and 350. IGLO calculations allow to assign the ⁷⁷Se signals and to predict the orientation of the shielding tensors. The different chemical shifts can be explained by different torsion angles Se-Se-C^ipso-C^ortho which produce different β effects of the phenyl rings upon the respective next but one selenium atom. Received: 24 April 1996 / Accepted: 15 May 1996