Dmitry O. Samultsev

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 Jensens 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

Solvent effects in the GIAO-DFT calculations of the 15N NMR chemical shifts of azoles and azines

The calculation of 15N NMR chemical shifts of 27 azoles and azines in 10 different solvents each has been carried out at the gauge including atomic orbitals density functional theory level in gas phase and applying the integral equation formalism polarizable continuum model (IEF‐PCM) and supermolecule solvation models to account for solvent effects. In the calculation of 15N NMR, chemical shifts of the nitrogen‐containing heterocycles dissolved in nonpolar and polar aprotic solvents, taking into account solvent effect is sufficient within the IEF‐PCM scheme, whereas for polar protic solvents with large dielectric constants, the use of supermolecule solvation model is recommended. A good agreement between calculated 460 values of 15N NMR chemical shifts and experiment is found with the IEF‐PCM scheme characterized by MAE of 7.1 ppm in the range of more than 300 ppm (about 2%). The best result is achieved with the supermolecule solvation model performing slightly better (MAE 6.5 ppm). Copyright

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

Theoretical and experimental (15)N 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

Normal halogen dependence of (13) C NMR chemical shifts of halogenomethanes revisited at the four-component relativistic level.

The ‘Normal Halogen Dependence’ of 13C NMR chemical shifts in the series of halogenomethanes is revisited at the four‐component relativistic level. Calculations of 13C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four‐component relativistic theory of Dirac‐Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyalls basis sets of triple‐zeta quality or higher are to be used within the framework of the four‐component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non‐relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright

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 Tozers KT3 functional used in combination with Jensens 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.

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 Tozers KT3 functional used in combination with Dyalls 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.

New relativistic computational schemes for 13C NMR chemical shifts

In С NMR spectra of organic compounds containing heavy halogens an upfield shift is well known to occur for the carbon atom linked to the halogen that may reach several tens and even hundreds of ppm in the case of bromine and iodine atoms. This is a so-called “normal halogen dependence” of chemical shifts reliably established in several studies [1–5], which on the background of the progress in the calculation procedures in NMR [6–9] acquires exclusive importance for practical applications.

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–Luptons F and R constants.

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 Tomasis 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.