On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

Substitution effects in the 15N NMR chemical shifts of heterocyclic azines evaluated at the GIAO‐DFT level

A systematic study of the accuracy factors for the computation of ¹⁵N NMR chemical shifts in comparison with available experiment in the series of 72 diverse heterocyclic azines substituted with a classical series of substituents (CH₃, F, Cl, Br, NH₂, OCH₃, SCH₃, COCH₃, CONH₂, COOH, and CN) providing marked electronic σ‐ and π‐electronic effects and strongly affecting ¹⁵N NMR chemical shifts is performed. The best computational scheme for heterocyclic azines at the DFT level was found to be KT3/pcS‐3//pc‐2 (IEF‐PCM). A vast amount of unknown ¹⁵N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental ¹⁵N NMR chemical shifts are almost totally unknown throughout the series. It was found that substitution effects in the classical series of substituents providing typical σ‐ and π‐electronic effects followed the expected trends, as derived from the correlations of experimental and calculated ¹⁵N NMR chemical shifts with Swain–Lupton's F and R constants.     

On the accuracy of the GIAO‐DFT calculation of 15N NMR chemical shifts of the nitrogen‐containing heterocycles – a gateway to better agreement with experiment at lower computational cost

The main factors affecting the accuracy and computational cost of the gauge‐independent atomic orbital density functional theory (GIAO‐DFT) calculation of ¹⁵N NMR chemical shifts in the representative series of key nitrogen‐containing heterocycles – azoles and azines – have been systematically analyzed. In the calculation of ¹⁵N NMR chemical shifts, the best result has been achieved with the KT3 functional used in combination with Jensen's pcS‐3 basis set (GIAO‐DFT‐KT3/pcS‐3) resulting in the value of mean absolute error as small as 5 ppm for a range exceeding 270 ppm in a benchmark series of 23 compounds with an overall number of 41 different ¹⁵N NMR chemical shifts. Another essential finding is that basically, the application of the locally dense basis set approach is justified in the calculation of ¹⁵N NMR chemical shifts within the 3–4 ppm error that results in a dramatic decrease in computational cost. Based on the present data, we recommend GIAO‐DFT‐KT3/pcS‐3//pc‐2 as one of the most effective locally dense basis set schemes for the calculation of ¹⁵N NMR chemical shifts. Copyright © 2014 John Wiley & Sons, Ltd.     

GIAO‐DFT calculation of 15N NMR chemical shifts of Schiff bases: Accuracy factors and protonation effects

¹⁵N NMR chemical shifts in the representative series of Schiff bases together with their protonated forms have been calculated at the density functional theory level in comparison with available experiment. A number of functionals and basis sets have been tested in terms of a better agreement with experiment. Complimentary to gas phase results, 2 solvation models, namely, a classical Tomasi's polarizable continuum model (PCM) and that in combination with an explicit inclusion of one molecule of solvent into calculation space to form supermolecule 1:1 (SM + PCM), were examined. Best results are achieved with PCM and SM + PCM models resulting in mean absolute errors of calculated ¹⁵N NMR chemical shifts in the whole series of neutral and protonated Schiff bases of accordingly 5.2 and 5.8 ppm as compared with 15.2 ppm in gas phase for the range of about 200 ppm. Noticeable protonation effects (exceeding 100 ppm) in protonated Schiff bases are rationalized in terms of a general natural bond orbital approach.     

On the accuracy factors and computational cost of the GIAO–DFT calculation of 15N NMR chemical shifts of amides

The main factors affecting the accuracy and computational cost of Gauge‐independent Atomic Orbital–density functional theory (GIAO–DFT) calculation of ¹⁵N NMR chemical shifts in the benchmark series of 16 amides are considered. Among those are the choice of the DFT functional and basis set, solvent effects, internal reference conversion factor and applicability of the locally dense basis set (LDBS) scheme. Solvent effects are treated within the polarizable continuum model (PCM) scheme as well as at supermolecular level with solvent molecules considered in explicit way. The best result is found for Keal and Tozer's KT3 functional used in combination with Jensen's pcS‐3 basis set with taking into account solvent effects within the polarizable continuum model. The proposed LDBS scheme implies pcS‐3 on nitrogen and pc‐2 elsewhere in the molecule. The resulting mean average error for the calculated ¹⁵N NMR chemical shifts is about 6 ppm. The application of the LDBS approach tested in a series of 16 amides results in a dramatic decrease in computational cost (more than an order of magnitude in time scale) with insignificant loss of accuracy.     

Theoretical and experimental study of 15N NMR protonation shifts

A combined theoretical and experimental study revealed that the nature of the upfield (shielding) protonation effect in ¹⁵N NMR originates in the change of the contribution of the sp²‐hybridized nitrogen lone pair on protonation resulting in a marked shielding of nitrogen of about 100 ppm. On the contrary, for amine‐type nitrogen, protonation of the nitrogen lone pair results in the deshielding protonation effect of about 25 ppm, so that the total deshielding protonation effect of about 10 ppm is due to the interplay of the contributions of adjacent natural bond orbitals. A versatile computational scheme for the calculation of ¹⁵N NMR chemical shifts of protonated nitrogen species and their neutral precursors is proposed at the density functional theory level taking into account solvent effects within the supermolecule solvation model. Copyright © 2015 John Wiley & Sons, Ltd.     

Towards the versatile DFT and MP2 computational schemes for 31P NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the calculation of ³¹P NMR chemical shifts in the representative series of organophosphorous compounds are examined at the density functional theory (DFT) and second‐order Møller–Plesset perturbation theory (MP2) levels. At the DFT level, the best functionals for the calculation of ³¹P NMR chemical shifts are those of Keal and Tozer, KT2 and KT3. Both at the DFT and MP2 levels, the most reliable basis sets are those of Jensen, pcS‐2 or larger, and those of Pople, 6‐311G(d,p) or larger. The reliable basis sets of Dunning's family are those of at least penta‐zeta quality that precludes their practical consideration. An encouraging finding is that basically, the locally dense basis set approach resulting in a dramatic decrease in computational cost is justified in the calculation of ³¹P NMR chemical shifts within the 1–2‐ppm error. Relativistic corrections to ³¹P NMR absolute shielding constants are of major importance reaching about 20–30 ppm (ca 7%) improving (not worsening!) the agreement of calculation with experiment. Further better agreement with the experiment by 1–2 ppm can be obtained by taking into account solvent effects within the integral equation formalism polarizable continuum model solvation scheme. We recommend the GIAO‐DFT‐KT2/pcS‐3//pcS‐2 scheme with relativistic corrections and solvent effects taken into account as the most versatile computational scheme for the calculation of ³¹P NMR chemical shifts characterized by a mean absolute error of ca 9 ppm in the range of 550 ppm. Copyright © 2014 John Wiley & Sons, Ltd.     

Structural and solvent effects on the 13C and 15N NMR chemical shifts of indoloquinoline alkaloids: experimental and DFT study

Indoloquinoline alkaloids represent an important class of antimalarial, antibacterial and antiviral compounds. They have been shown to bind to DNA via intercalation preferentially at GC-rich sequences containing nonalternating CC sites. The stability of complexes formed with biological macromolecules depends on noncovalent binding. In the present study, the ability of indoloquinolines to form intermolecular interactions with solvents was investigated by using NMR spectroscopy and density functional theory (DFT) (B3LYP/6-31G**) calculations. NMR data measured for indoloquinoline bases and the corresponding hydrochlorides are discussed in relation to the structure. DFT calculations of shielding constants in vacuo and in solution allowed the investigation of the influence of the environment on the NMR parameters. Calculations incorporating solvent effects indicated significant changes in the anisotropy of the electron distribution, reflected in the span of the chemical shielding tensor (Omega = sigma11 - sigma33). Solvent effects on the span of the 13C and 15N shielding tensor depended on the type of atom and the data indicated a significant influence of solute-solvent interactions.     

15N and 13C NMR chemical shifts of 6‐(fluoro,chloro, bromo,and iodo)purine 2′‐deoxynucleosides: measurements and calculations

The ¹⁵N and ¹³C chemical shifts of 6‐(fluoro, chloro, bromo, and iodo)purine 2′‐deoxynucleoside derivatives in deuterated chloroform were measured. The ¹⁵N chemical shifts were determined by the ¹H? ¹⁵N HMBC method, and complete ¹⁵N chemical‐shift assignments were made with the aid of density functional theory (DFT) calculations. Inclusion of solvation effects significantly improved the precision of the calculations of ¹⁵N chemical shifts. Halogen‐substitution effects on the ¹⁵N and ¹³C chemical shifts of purine rings are discussed in the context of DFT results. The experimental coupling constants for ¹⁹F interacting with ¹⁵N and ¹³C of the 6‐fluoropurine 2‐deoxynuleoside are compared with those from DFT calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

GIAO DFT 13C/15N chemical shifts in regioisomeric structure determination of fused pyrazoles

The combined use of two‐dimensional NMR correlation experiments and gauge including atomic orbital density functional theory in ¹³C NMR chemical shift (CS) calculations allowed reliable and simple structural determination of regioisomeric heterocyclic systems that originate from the reactions of acylquinolinones with substituted hydrazines. Moreover, the results of differential analysis between the calculated ¹⁵N NMR CSs for hypothetical structures and the experimental data of the title azaheterocyclic systems were even more advantageous with respect to ¹³C because there was no need for correlational analysis: structures of the regioisomeric compounds could be determined just by direct comparison. Copyright © 2010 John Wiley & Sons, Ltd.     

Theoretical and experimental 15N NMR study of enamine–imine tautomerism of 4‐trifluoromethyl[b]benzo‐1,4‐diazepine system

The tautomeric structure of 4‐trifluoromethyl[b]benzo‐1,4‐diazepine system in solution has been evaluated by means of the calculation of ¹⁵N NMR chemical shifts of individual tautomers in comparison with the averaged experimental shifts to show that the enamine–imine equilibrium is entirely shifted toward the imine form. The adequacy of the theoretical level used for the computation of ¹⁵N NMR chemical shifts in this case has been verified based on the benchmark calculations in the series of the push–pull and captodative enamines together with related azomethynes, which demonstrated a good to excellent agreement with experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

DFT computational schemes for 15N NMR chemical shifts of the condensed nitrogen-containing heterocycles

A systematic density functional theory (DFT) study of the accuracy factors (functionals, basis sets, and solvent effects) for the computation of ¹⁵N NMR chemical shifts has been performed in the series of condensed nitrogen-containing heterocycles. The behavior of the most representative functionals was examined based on the benchmark calculations of ¹⁵N NMR chemical shifts in the reference set of compounds. It was found that the best agreement with experiment was achieved with OLYP functional in combination with aug-pcS-3(N)//pc-2 locally dense basis set scheme providing mean absolute error of 5.2 ppm in the range of about 300 ppm. Taking into account solvent effects was performed within a general Tomasi's polarizable continuum model scheme. It was also found that computationally demanding supermolecular solvation model computations essentially improved some “difficult” cases, as was illustrated with phenanthroline dissolved in methanol. Based on the performed calculations, some 200 unknown ¹⁵N NMR chemical shifts were predicted with a high level of confidence for about 50 real-life condensed nitrogen-containing heterocycles, which could serve as a practical guide in structural elucidation of this class of compounds.     

A study of the 15N NMR chemical shifts in substituted anilines and phenylhydrazines, and their derivatives

The analysis of (15)N chemical shift data from over a hundred anilines, N-methyl anilines, N,N-dimethyl anilines and phenylhydrazines with substituents in the phenyl ring leads to an empirical equation, delta(cal) = deltaon + Deltao + Deltam + Deltap, for calculating (15)N NMR chemical shifts of the amino group. This equation is based on a linear regression analysis using eighteen substituent parameters and leads to good conformity with the expected data.     

Substituent effects on 15N and 13C NMR chemical shifts of 3-phenylisoxazoles: a theoretical and spectroscopic study

The synthesis and assignment of 15N and 13C NMR signals of the isoxazole ring in a series of para-substituted 3-phenyl derivatives are reported. DFT calculations of 15N and 13C chemical shifts are presented and compared to observed values. Substituent effects are interpreted in terms of the Hammett correlation and calculated bond orders.     

13C and 15N NMR spectra of high‐energy polyazidocyanopyridines

¹³C and ¹⁵N NMR spectra of high‐energy 2,4,6‐triazidopyridine‐3,5‐dicarbonitrile, 2,3,5,6‐tetraazidopyridine‐4‐carbonitrile and 3,4,5,6‐tetraazidopyridine‐2‐carbonitrile are reported. The assignment of signals in the spectra was performed on the basis of density functional theory calculations. The molecular geometries were optimized using the M06‐2X functional with the 6‐311+G(d,p) basis set. The magnetic shielding tensors were calculated by the gauge‐independent atomic orbital method with the Tao–Perdew–Staroverov–Scuseria hybrid functional known as TPSSh. In all the calculations, a polarizable continuum model was used to simulate solvent effects. This approach provided accurate predictions of the ¹³C and ¹⁵N chemical shifts for all the three compounds despite complications arising due to non‐coplanar arrangement of the azido groups in the molecules. It was found that the ¹⁵N chemical shifts of the N_α atoms in the azido groups of 2,4,6‐triazidopyridines correlate with the ¹³C chemical shifts of the carbon atoms attached to these azido groups. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

N7‐ and N9‐substituted purine derivatives: a 15N NMR study

The ¹⁵N NMR chemical shifts of N⁷‐ and N⁹‐substituted purine derivatives were investigated systematically at the natural abundance level of the ¹⁵N isotope. The NMR chemical shifts were determined and assigned using GSQMBC, GHMBC, GHMQC and GHSQC experiments in solution. ¹⁵N cross‐polarization magic angle spinning data were recorded for selected compounds in order to study the principal values of the ¹⁵N chemical shifts. Geometric parameters obtained by using RHF/6–31G** and single‐crystal x‐ray structural analysis were used to calculate the chemical‐shielding constants (GIAO and IGLO) which were then used to assign the nitrogen resonances observed in the solid‐state NMR spectra and to determine the orientation of the principal components of the shift tensors. Copyright © 2002 John Wiley & Sons, Ltd.     

Structure of irradiated polytetrafluoroethylene according to DFT calculations of NMR chemical shifts

Methods of density functional theory were used to calculate ¹H, ¹³C, and ¹⁹F magnetic shielding tensors for C₇F_nH_mO_l model molecules, which can arise as fragments from radiation exposure of polytetrafluoroethylene.     

Empirical and DFT GIAO quantum‐mechanical methods of 13C chemical shifts prediction: competitors or collaborators?

The accuracy of ¹³C chemical shift prediction by both DFT GIAO quantum‐mechanical (QM) and empirical methods was compared using 205 structures for which experimental and QM‐calculated chemical shifts were published in the literature. For these structures, ¹³C chemical shifts were calculated using HOSE code and neural network (NN) algorithms developed within our laboratory. In total, 2531 chemical shifts were analyzed and statistically processed. It has been shown that, in general, QM methods are capable of providing similar but inferior accuracy to the empirical approaches, but quite frequently they give larger mean average error values. For the structural set examined in this work, the following mean absolute errors (MAEs) were found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm and MAE(QM) = 3.29 ppm. A strategy of combined application of both the empirical and DFT GIAO approaches is suggested. The strategy could provide a synergistic effect if the advantages intrinsic to each method are exploited. Copyright © 2010 John Wiley & Sons, Ltd.