NMR shielding tensors from auxiliary density functional theory

The working equations for the calculation of NMR shielding tensors in the framework of auxiliary density functional theory are derived. It is shown that in this approach the numerical integration over gauge-including atomic orbitals can be avoided without the loss of accuracy. New integral recurrence relations for the required analytic electric-field-type integrals are derived. The computational performance of the resulting formalism permits shielding tensor calculations of systems with more than 1000 atoms and 15,000 basis functions.     

A density functional study of chemical reactions

Density functional theory (DFT ) was used to study reactions involving small molecules. Relative energies of isomers and transition structures of diazene, formaldehyde, and methylenimine were determined using various DFT functionals and results were compared with MP 2 and MP 4 calculations. DFT reaction barriers were found to be consistently lower. For some reactions, such as OH + H₂→ H₂O + H, gradient-corrected functionals predict very low or nonexistent barriers. The hybrid Hartree–Fock–DFT adiabatic connection method (ACM ) often provides much better results in such cases. The performance of several density functionals, including ACM , was tested in calculations on over 100 atomization, hydrogenation, bond dissociation, and isodesmic reactions. The ACM functional provides consistently better geometries and reaction energetics than does any other functional studied. In cases where both HF and gradient-corrected DFT methods underestimate bond distances, the ACM geometries may be inferior to those predicted by gradient-corrected DFT methods. © 1995 John Wiley & Sons, Inc.     

A density functional study of the 13C NMR chemical shifts in functionalized single-walled carbon nanotubes

The 13C NMR chemical shifts for functionalized (7,0), (8,0), (9,0), and (10,0) single-walled carbon nanotubes (SWNTs) have been studied computationally using gauge-including projector-augmented plane-wave (GIPAW) density functional theory (DFT). The functional groups NH, NCH3, NCH2OH, and CH2NHCH2 have been considered, and different sites where covalent addition or substitution may occur have been examined. The shifts of the carbons directly attached to the group are sensitive to the bond which has been functionalized and may, therefore, be used to identify whether the group has reacted with a parallel or a diagonal C-C bond. The addition of NH to a parallel bond renders the functionalized carbons formally sp3-hybridized, yielding shifts of around 44 ppm, independent of the SWNT radius. Reaction with a diagonal bond retains the formal sp2 hybridization of the substituted carbons, and their shifts are slightly lower or higher than those of the unsubstituted carbon atoms. The calculated 1H NMR shifts of protons in the functional groups are also dependent upon the SWNT-group interaction. Upon decreasing the degree of functionalization for the systems where the group is added to a parallel bond, the average chemical shift of the unfunctionalized carbons approaches that of the pristine tube. At the same time, the shifts of the functionalized carbons remain independent upon the degree of functionalization. For the SWNTs where N-R attaches to a parallel bond, the average shift of the sp2 carbons was found to be insensitive to the substituent R. Moreover, the shifts of the functionalized sp3 carbons, as well as of the carbons within the group itself, are independent of the SWNT radius. The results indicate that a wealth of knowledge may be obtained from the 13C NMR of functionalized SWNTs.     

103Rh NMR chemical shifts in organometallic complexes: a combined experimental and density functional study

Experimental 103Rh NMR chemical shifts of mono- and binuclear rhodium(I) complexes containing s- or as-hydroindacenide and indacenediide bridging ligands with different ancillary ligands (1,5-cyclooctadiene, ethylene, carbonyl) are presented. A protocol, based on density functional theory calculations, was established to determine 103Rh NMR shielding constants in order to rationalise the effects of electronic and structural variations on the spectroscopic signal, and to gain insight into the efficiency of this computational method when applied to organometallic systems. Scalar and spin-orbit relativistic effects based on the ZORA (zeroth order regular approximation) level have been taken into account and discussed. A good agreement was found for model compounds over a wide range of chemical shifts of rhodium (approximately 10,000 ppm). This allowed us to discuss the experimental and calculated delta(103Rh) in larger complexes and to relate it to their electronic structure.     

Molecular structure of free canonical 2′-deoxyribonucleosides: a density functional study

The molecular structure of isolated canonical 2′-deoxyrinobucleosides was calculated using the density functional theory. It was demonstrated that the geometry of the base unit (BU) is almost unchanged compared to free nucleobases. Only slight out-of-plane deformation of the pyrimidine ring in deoxy-cytidine is observed. The conformation of the furanose ring strongly depends on the nature and orientation of the nucleobase. All nucleosides possess different conformations of this ring. Significant influence of the steric repulsion between the nucleobase and the sugar unit (SU) on puckering of the furanose ring and variation of the C–O and glycosyl bond lengths was demonstrated. The C(3′)-endo conformer of the furanose ring is more stable at the anti-orientation BU with respect to SU. An opposite trend is observed for the syn-orientation which is additionally stabilized by an intramolecular hydrogen bond with participation of the C(5′)OH group.     

A study of NMR chemical shielding in 5-coordinate phosphorus compounds (phosphoranes)

Calculations of the phosphorus NMR chemical shielding in 5-coordinate phosphorus compounds have been carried out using the gauge-including-atomic-orbital (GIAO) 6-311+G(nd,p) basis set at both scaled density functional theory (sDFT) and estimated infinite order Møller–Plesset (EMPI) approaches. Results are generally in accord with previous studies on 3-coordinate phosphorus compounds but fail badly for compounds containing multiple chlorine atoms and indicate a need for a relativistic treatment of these species. We observe that some compounds with reported experimental ³¹P NMR chemical shifts far downfield of the calculated values are in fact in the range known from experiment and calculation to be in that expected for phosphonium ions; the reported structures need to be reconsidered.     

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.     

Predicting 9Be nuclear magnetic resonance chemical shielding tensors utilizing density functional theory

The structures of a series of beryllium containing complexes have been optimized at the B3LYP/6-31G(d) level and their (9)Be magnetic shielding values have been determined using B3LYP/6-311G+g(2d,p) and the gauge-including atomic orbital (GIAO) method. The calculated chemical shifts are in excellent agreement with experimental values. The performance of a variety of NMR methods (SGO, IGAIM, CSGT) were also examined but were found to be inferior to the GIAO method at the chosen level of theory employed. The theoretical method has been utilized to predict the beryllium chemical shifts of structurally characterized complexes for which no measured (9)Be NMR spectrum exists, and to investigate a literature complex with an unusual (9)Be NMR chemical shift. A new standard for beryllium NMR in nonaqueous solvents has been suggested.     

A theoretical study of 31P NMR chemical shielding models for concentrated phosphoric acid solution

Calculations on the hydrates, dimer, and trimer of phosphoric acid were carried out in an effort to obtain a viable model of the phosphorus NMR chemical shielding in 85% phosphoric acid solution. The theoretical approaches used the gauge-including-atomic-orbital (GIAO) 6-311+G(nd,p) basis set at both scaled density functional theory (sB3LYP) and estimated infinite order M?ller-Plesset (EMPI) approaches and with the aug-cc-pvtz basis in the sB3LYP approach. Shieldings and hydrogen bonding stabilization energies are similar in the three approaches and indicate that the faster sB3LYP/6-311+G(nd,p) approach can be used with larger systems. The changes in shielding compared to the isolated species are small and suggest that the undissociated acid dihydrate could serve as a model entity for modeling the phosphorus shielding in concentrated phosphoric acid solution.     

Continuous symmetry analysis of NMR chemical shielding anisotropy

Molecular symmetry is a key parameter which dictates the NMR chemical shielding anisotropy (CSA). Whereas correlations between specific geometrical features of molecules and the CSA are known, the quantitative correlation with symmetry--a global structural feature--has been unknown. Here we demonstrate a CSA/symmetry quantitative relation for the first time: We study how continuous deviation from exact symmetry around a nucleus affects its shielding. To achieve this we employed the continuous symmetry measures methodology, which allows one to quantify the degree of content of a given symmetry. The model case we use for this purpose is a population of distorted SiH(4) structures, for which we follow the (29)Si CSA as a function of the degree of tetrahedral symmetry and of square-planar symmetry. Quantitative correlations between the degree of these symmetries and the NMR shielding parameters emerge.     

The calculation of NMR shielding tensors based on density functional theory and the frozen-core approximation

The application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general terms and for the special case of density functional theory (DFT) and “gauge including atomic orbitals” (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations—if the valence space is increased to contain at least the ns, np, (n − 1)p, (n − 1)d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to ⁷⁷Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300–400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. © 1996 John Wiley & Sons, Inc.     

Oxoperoxo vanadium(V) complexes of L-lactic acid: density functional theory study of structure and NMR chemical shifts

Various combinations of density functionals and pseudopotentials with associated valence basis-sets are compared for reproducing the known solid-state structure of [V 2O 2(OO) 2 l-lact 2] (2-) cis . Gas-phase optimizations at the B3LYP/SBKJC level have been found to provide a structure that is close to that seen in the solid state by X-ray diffraction. Although this may result in part from error compensation, this optimized structure allowed satisfactory reproduction of solution multinuclear NMR chemical shifts of the complex in all-electron DFT-IGLO calculations (UDFT-IGLO-PW91 level), suggesting that it is probably close to that found in solution. This combination of approaches has subsequently been used to optimize the structures of the vanadium oxoperoxo complexes [V 2O 3(OO) l-lact 2] (2-) cis , [V 2O 3(OO) l-lact 2] (2-) trans , and [VO(OO)( l-lact)(H 2O)] (-) cis . The (1)H, (13)C, (51)V, and (17)O NMR chemical shifts for these complexes have been calculated and compared with the experimental solution chemical shifts. Excellent agreement is seen with the (13)C chemical shifts, while somewhat inferior agreement is found for (1)H shifts. The (51)V and (17)O chemical shifts of the dioxo vanadium centers are well reproduced, with differences between theoretical and experimental shifts ranging from 22.9 to 35.6 ppm and from 25.1 to 43.7 ppm, respectively. Inferior agreement is found for oxoperoxo vanadium centers, with differences varying from 137.3 to 175.0 ppm for (51)V shifts and from 148.7 to 167.0 ppm for (17)O(oxo) shifts. The larger errors are likely to be due to overestimated peroxo O-O distances. The chosen methodology is able to predict and analyze a number of interesting structural features for vanadium(V) oxoperoxocomplexes of alpha-hydroxycarboxylic acids.     

A 13C NMR study of pyridoxal-5′-phosphate oxime

Pyridoxal-5′-phosphate amino-oxy acetate oxime was titrated in water, over the pH range 4–12, and the changes followed using ¹³C NMR. The results were compared to those of analogous Schiff's bases presented in the literature. The chemical shifts and titration curves of the oxime were appreciably different from those of the Schiff's bases, and the differences are explained as being due to the absence of ketoenamine-enolimine tautomerism in the oxime. The low chemical shift value and the large changes of the oxime azomethine carbon during titration, as compared to the Schiff's bases, are discussed. The high stability of the oximes in water makes them suitable as model compounds for some tautomeric forms of the Iess stable Schiff's bases.     

Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: the density functional models

We present a systematic density functional investigation on the prediction of the 13C, 15N, 17O, and 19F NMR properties of 23 molecules with 21 density functionals. Extensive comparisons are made for both 13C magnetic shieldings and chemical shifts with respect to the gas phase experimental data and the best CCSD(T) results. We find that the OPBE and OPW91 exchange-correlation functionals perform significantly better than some popular functionals such as B3LYP and PBE1PBE, even surpassing, in many cases, the standard wavefunction-based method MP2. Further analysis has been performed to explore the individual role played by various exchange and correlation functionals. We find that the B88 and PBE exchange functionals have a too strong tendency of deshielding, leading to too deshielded magnetic shielding constants; whereas the OPTX exchange functional performs remarkably well. We claim that the main source of error arises from the exchange functional, but correlation functional also makes important contribution. We find that the correlation functionals may be grouped into two classes. class A, such as LYP and B98, leads to deshielded NMR values, deteriorating the overall performance; whereas class B, such as PW91 and PBE, generally increases the absolute shieldings, which complements the exchange functionals, leading to improved results in the calculation of NMR data.     

Polarizability and chemical hardness—A combined study of wave function and density functional theory approach

A flexible model for generating the molecular wave function and electron density for diatomic molecules is developed employing the quadratic anharmonic oscillator and Morse potential. The chemical hardness, Fukui function, and polarizability were calculated using the electron density of the molecules, and the values are found to be reasonably good. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson-Boltzmann) model. Our calculated chemical shifts of (1)H and (13)C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of (15)N, the results do not agree with experimental values as well as (1)H and (13)C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for (13)C(α) atoms in proteins, and using the (1)H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.     

Improved description of nuclear magnetic resonance chemical shielding constants using the M06-L meta-generalized-gradient-approximation density functional

The performance of the M06-L density functional has been tested for four databases of NMR isotropic chemical shielding constants. Comparison with the B3LYP, BLYP, HCTH, KT1, KT2, LSDA, OPBE, OLYP, PBE, TPSS, and VSXC functionals shows that M06-L has improved performance for calculating NMR chemical shielding constants, especially for highly correlated systems. We also found that VSXC and M06-L have encouraging accuracy for calculating (13)C chemical shielding constants, and both functionals perform very well for the chemical shielding constants in the o-benzyne molecule.     

A simple graphical approach to predict local residue conformation using NMR chemical shifts and density functional theory

The dependency of amino acid chemical shifts on φ and ψ torsion angle is, independently, studied using a five‐residue fragment of ubiquitin and ONIOM(DFT:HF) approach. The variation of absolute deviation of ¹³C^α chemical shifts relative to φ dihedral angle is specifically dependent on secondary structure of protein not on amino acid type and fragment sequence. This dependency is observed neither on any of ¹³C^β, and ¹H^α chemical shifts nor on the variation of absolute deviation of ¹³C^α chemical shifts relative to ψ dihedral angle. The ¹³C^α absolute deviation chemical shifts (ADCC) plots are found as a suitable and simple tool to predict secondary structure of protein with no requirement of highly accurate calculations, priori knowledge of protein structure and structural refinement. Comparison of Full‐DFT and ONIOM(DFT:HF) approaches illustrates that the trend of ¹³C^α ADCC plots are independent of computational method but not of basis set valence shell type. © 2016 Wiley Periodicals, Inc.     

Solid-state 17O NMR study of the electric-field-gradient and chemical shielding tensors in polycrystalline amino acids

We have presented a systematic experimental investigation of carboxyl oxygen electric-field-gradient (EFG) and chemical shielding (CS) tensors in crystalline amino acids. Three 17O-enriched amino acids were prepared: L-aspartic acid, L-threonine, and L-tyrosine. Analysis of two-dimensional 17O multiple-quantum magic-angle spinning (MQMAS), MAS, and stationary NMR spectra yields the 17O CS, EFG tensors and the relative orientations between the two tensors for the amino acids. The values of quadrupolar coupling constants (CQ) are found to be in the range of 6.70-7.60 MHz. The values of deltaiso lie in the range of 268-292 ppm, while those of the delta11 and delta22 components vary from 428 to 502 ppm, and from 303 to 338 ppm, respectively. There is a significant correlation between the magnitudes of delta22 components and C--O bond lengths. Since C--O bond length may be related to hydrogen-bonding environments, solid-state 17O NMR has significant potential to provide insights into important aspects of hydrogen bonds in biological systems.