Four-Component Relativistic Calculations of NMR Shielding Constants of the Transition Metal Complexes-Part 2: Nitrogen-Coordinated Complexes of Cobalt.

Both four-component relativistic and nonrelativistic computations within the GIAO-DFT(PBE0) formalism have been carried out for 15N and 59Co NMR shielding constants and chemical shifts of a number of the nitrogen-coordinated complexes of cobalt. It was found that the total values of the calculated nitrogen chemical shifts of considered cobalt complexes span over a range of more than 580 ppm, varying from -452 to +136 ppm. At that, the relativistic corrections to nitrogen shielding constants and chemical shifts were demonstrated to be substantial, changing accordingly from ca. -19 to +74 ppm and from -68 to +25 ppm. Solvent effects on 15N shielding constants and chemical shifts were shown to have contributions no less important than the relativistic effects, namely from -35 to +63 ppm and from -74 to +23 ppm, respectively. Cobalt shielding constants and chemical shifts were found to vary in the ranges of, accordingly, -20,157 to -11,373 ppm and from +3781 to +13,811. The relativistic effects are of major importance in the cobalt shielding constants, resulting in about 4% for the shielding-type contributions, while solvent corrections to cobalt shielding constants appeared to be of less significance, providing corrections of about 1.4% to the gas phase values.

Four-component relativistic calculations of NMR shielding constants of the transition metal complexes. Part 1: Pentaammines of cobalt, rhodium, and iridium.

The nonrelativistic and four-component fully relativistic calculations of 1 H, 15 N, 59 Co, 103 Rh, and 193 Ir shielding constants of pentaammineaquacomplexes of cobalt(III), rhodium(III), and iridium(III) were carried out at the density functional theory (DFT) level of theory. The noticeable deshielding relativistic corrections were observed for nitrogen shielding constants (chemical shifts), whereas those corrections were found to be negligible for protons. For the transition metals cobalt, rhodium, and iridium, relativistic corrections to their nuclear magnetic resonance (NMR) shielding constants were found to be rather small for cobalt and rhodium (some 5-10%), whereas they are essentially larger for iridium (up to 70%).

The 1 H and 13 C NMR chemical shifts of Strychnos alkaloids revisited at the DFT level.

The density functional theory calculation of 1 H and 13 C NMR chemical shifts in a series of ten 10 classically known Strychnos alkaloids with a strychnine skeleton was performed at the PBE0/pcSseg-2//pcseg-2 level. It was found that calculated 1 H and 13 C NMR chemical shifts provided a markedly good correlation with experiment characterized by a mean absolute error of 0.08 ppm in the range of 7 ppm for protons and 1.67 ppm in the range of 150 ppm for carbons, so that a mean absolute percentage error was as small as ~1% in both cases.

Calculation of 15N NMR Chemical Shifts in a Diversity of Nitrogen-Containing Compounds Using Composite Method Approximation at the DFT, MP2, and CCSD Levels.

Computations of 15N NMR chemical shifts in 93 diverse nitrogen-containing compounds representing almost all known classes are performed at the density functional theory (DFT), second-order Møller-Plesset perturbation theory (MP2), and coupled cluster singles and doubles (CCSD) levels using the composite method approximation (CMA) in comparison with experimental results. It is shown that the CMA-DFT and CMA-CCSD methods provided the best performance characterized by a normalized mean absolute error of 1.1-1.3% as compared to 2.3% for the CMA-MP2 results. Taking into account solvent effects within the conductor-like polarizable continuum model decreased the normalized mean absolute error by 0.4% for the CMA-DFT and by 0.2% for the CMA-CCSD calculations.

Computational Multinuclear NMR of Platinum Complexes: A Relativistic Four-Component Study.

The structures of 16 derivatives of cisplatin and transplatin were optimized at the DFT/dyall.ae2z levels, and their 1H, 15N, and 195Pt NMR chemical shifts were evaluated within the nonrelativistic and four-component relativistic approaches. Reliable correlations of calculated NMR chemical shifts with available experimental data were achieved by taking into account relativistic effects, solvent effects, and vibrational corrections.

DFT computational schemes for 15 N 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 15 N 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 15 N 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 15 N 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.

Calculation of 15N and 31P NMR Chemical Shifts of Azoles, Phospholes, and Phosphazoles: A Gateway to Higher Accuracy at Less Computational Cost.

A number of computational schemes for the calculation of 15N and 31P NMR chemical shifts and shielding constants in a series of azoles, phospholes, and phosphazoles was examined. A very good correlation between calculated at the CCSD(T) level and experimental 15N and 31P NMR chemical shifts was observed. It was found that basically solvent, vibrational, and relativistic corrections are of the same order of magnitude and alternate in sign, being, on average, of about 2-3 ppm in absolute value but, being much larger (up to 14 ppm) in the case of solvent molecules explicitly introduced into computational space. At the DFT level, the performance of nine exchange-correlation functionals including six conventional gradient functionals and three hybrid functionals was studied. The most accurate results were reached with the OLYP and Keal-Tozer's family of functionals, KT1, KT2, and KT3, while the most popular B3LYP and PBE0 functionals showed the most unreliable results. On the basis of these data, we highly recommend OLYP and KT2 functionals for the computation of 15N and 31P NMR chemical shifts at the DFT level in the diverse series of nitrogen- and phosphorus-containing heterocycles. Benchmark calculations of 15N and 31P NMR chemical shifts in a series of larger nitrogen- and phosphorus-containing heterocycles were performed at the DFT level in comparison with experiment and revealed the OLYP functional in combination with the aug-pcS-3/aug-pcS-2 locally dense basis set scheme as the most effective computational scheme.

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

A systematic study of the accuracy factors for the computation of 15 N 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 15 N 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 15 N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental 15 N 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 15 N NMR chemical shifts with Swain-Lupton's F and R constants.

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

15 N 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 15 N 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 15 N 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 15 N 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 15 N 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 15 N NMR chemical shifts of halogenated azines.

Long-range ß- and γ-relativistic effects of halogens in 15 N 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, ß- and γ-relativistic effects are important contributors to the accuracy of the 15 N calculation. Taking into account long-range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of 15 N 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 15 N 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.

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

The 'Normal Halogen Dependence' of 13 C NMR chemical shifts in the series of halogenomethanes is revisited at the four-component relativistic level. Calculations of 13 C 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 Dyall's 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 © 2016 John Wiley & Sons, Ltd.

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 (15)N 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 (15)N 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.

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 sp(2)-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.

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

The calculation of (15)N 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 (15)N 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 (15)N 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).

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 (15)N NMR chemical shifts in the representative series of key nitrogen-containing heterocycles--azoles and azines--have been systematically analyzed. In the calculation of (15)N 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 (15)N NMR chemical shifts. Another essential finding is that basically, the application of the locally dense basis set approach is justified in the calculation of (15)N 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 (15)N NMR chemical shifts.