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.     

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.     

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.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XIII. Accuracy of the calculation of 15N NMR chemical shifts of azines with account taken of solvation effects

Effects of solvation on the accuracy of the calculation of ¹⁵N chemical shifts in the azine series have been analyzed at the DFT/GIAO level of theory. The best results are obtained with the use of the Keal-Tozer KT2 functional in combination with the Dunning aug-cc-pVTZ basis set with inclusion of solvent effects according to the Tomasi polarizable continuum model (PCM). If specific solvation is strong, additional consideration of solvent effects in the supermolecule approximation is necessary with explicit inclusion of solvent molecules.     

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.     

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.     

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.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: VIII. Solvation effects on 15N NMR chemical shifts of nitrogen-containing heterocycles

Effect of solvation on the accuracy of DFT quantum-chemical calculations of ¹⁵N NMR chemical shifts of pyrrole, N-methylpyrrole, and pyridine was studied. The use of continuum model is sufficient to obtain consistent theoretical σ_N values for weakly polar aprotic solvents, whereas solvation effects in strongly polar and protic solvents should be taken into account in the explicit form.     

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.     

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.     

Calculation of <Superscript>15</Superscript>N NMR chemical shifts of amines in the framework of the density functional theory

The ¹⁵N NMR magnetic shielding constants (followed by recalculation into chemical shifts) in a representative series of amines were calculated in the framework of the density functional theory. The results were compared with experiment. The accuracy factors of this calculation (functional, basis set, solvent effects, and multistandard) were studied. Taking into account all the above factors leads to a noticeable decrease in the average absolute error in the calculation of the ¹⁵N NMR chemical shifts (from 13 to 4 ppm) in a range of their changing in the studies series of compounds of ～60 ppm (which is 6—7% in relative units).     

An ab initio study of solvent polarity and hydrogen bonding effects on the nitrogen NMR shieldings of N,N‐dimethylacetamidine

Density functional theory combined with the polarizable continuum model (PCM) and continuous set of gauge transformations method is applied to investigate the effects of solvent polarity on the nitrogen NMR shieldings of N, N‐dimethylacetamidine. Hydrogen bonding effects on shielding are likewise calculated using a supermolecule approach, where the imino group of the solute is hydrogen bonded with solvent. Theoretical results are compared with published experimental data. The PCM shielding calculations utilizing PCM‐optimized solute geometries yield results comparable to those obtained with the supermolecule approach. Geometry optimization of the solute appears to be more important in PCM shielding calculations than in the supermolecule approach. The large solvent shifts observed in water can only be reproduced when the N·H distance used in the calculation indicates full proton transfer from water to the imino nitrogen of the solute. Copyright © 2002 John Wiley & Sons, Ltd.     

A joint theoretical and experimental investigation on the 13C and 1H NMR chemical shifts of coumarin derivatives

¹H and ¹³C NMR chemical shifts of coumarin derivatives have been determined using first principles approaches with and without accounting for the effects of the solvent and compared to experiment in order to assess their reliability. Good linear relationships are obtained between theory and experiment, which allows correcting the calculated values for systematic errors. This is particularly the case when using the PCM scheme to model the solvent effects because the δ values larger than 150 ppm are more difficult to reproduce. The final accuracy of the method amounts to about 1 ppm for ¹³C and 0.05 ppm for ¹H.     

A Computational Understanding of Solvent Effect on the Structure,Electronic, Thermochemical,and Spectroscopic Properties of Ni(η2‐C6H4)(H2PCH2CH2PH2) Complex

Here we report the density functional calculations of the molecular parameters including the energy, geometries, electric dipole moments, vibrational IR frequencies, and ¹H and ¹³C NMR chemical shifts of Ni(η²‐C₆H₄ )(H₂PCH₂CH₂PH₂ ) (a benzyne complex). Based on the polarizable continuum model (PCM ), the effect of polarity of the solvent on these parameters was explored. The wavenumbers of υ(C1–C2 ) as well as the ¹H and ¹³C NMR chemical shift values of complex in various solvents were calculated and correlated with the Kirkwood–Bauer–Magat equation (KBM ), the solvent acceptor numbers (ANs ), and the linear solvation energy relationship (LSER ). The bonding interaction between the benzyne and Ni(H₂PCH₂CH₂PH₂ ) fragment was analyzed by means of the energy decomposition analysis (EDA ). The character of the Ni–C bonds of the molecules was analyzed by natural bond orbital (NBO ) analysis. Also, Monte Carlo simulations were used for the calculation of the total energy and solvation free energy of the complex in water.     

The Chemical Shift Baseline for High‐Pressure NMR Spectra of Proteins

High‐pressure (HP) NMR spectroscopy is an important method for detecting rare functional states of proteins by analyzing the pressure response of chemical shifts. However, for the analysis of the shifts it is mandatory to understand the origin of the observed pressure dependence. Here we present experimental HP NMR data on the ¹⁵N‐enriched peptide bond model, N‐methylacetamide (NMA), in water, combined with quantum‐chemical computations of the magnetic parameters using a pressure‐sensitive solvation model. Theoretical analysis of NMA and the experimentally used internal reference standard 4,4‐dimethyl‐4‐silapentane‐1‐sulfonic (DSS) reveal that a substantial part of observed shifts can be attributed to purely solvent‐induced electronic polarization of the backbone. DSS is only marginally responsive to pressure changes and is therefore a reliable sensor for variations in the local magnetic field caused by pressure‐induced changes of the magnetic susceptibility of the solvent.     

Influence of Solvent Polarity and Hydrogen Bonding on the Electronic Transition of Coumarin 120: A TDDFT Study

The characteristics of the electronic transition energy of Coumarin 120 (C120) and its H‐bonded complexes in various solvents have been examined by time‐dependent density functional theory (TDDFT) in combination with a polarizable continuum solvent model (PCM). Molecular structures of C120 and its H‐bonded complexes are optimized with the B3LYP method in PCM solution, and the dihedral angle H14? N13? C7? H15 is dependent on solvent polarity and the type of H‐bond. A linear correlation of the absorption maximum of C120 with the solvent polarity function is revealed with the PCM model for all solvents except DMSO. The experimental absorption maximum of C120 in nine solvents is well described by a PCM–TDDFT scheme augmented with explicit inclusion of a few H‐bonded solvent molecules, and quantitative agreement between our calculated results and experimental measurements is obtained with an average error of less than 2 nm. H‐bonding at three different sites shifts the absorption wavelength of C120 either to the blue or to the red, that is, a significant role is played by solvent molecules in the first solvation shell in determining the electronic transition energy of C120. The dependence on the H‐bonding site and solvent polarity is examined by using the Kamlet–Taft equation for solvatochromism.     

Solvent‐directed Regioselective Benzylation of Adenine: Characterization of N9‐benzyladenine and N3‐benzyladenine

The preferred sites for the benzylation of adenine under basic conditions were proven to be the N9 and N3 positions. Formation of the N9‐benzyladenine product is favored in polar aprotic solvents, such as DMSO, whereas the proportion of N3‐benzyladenine formed increases as the proportion of polar protic solvents, such as water, increases. X‐ray crystal structures were obtained for both N9‐benzyladenine and N3‐benzyladenine. ¹H‐¹³C HMBC NMR spectroscopy revealed diagnostic correlations used to assign the ¹H and ¹³C NMR chemical shifts confirming that the solution structures in three different solvents were the same as the isolated crystals. ¹³C NMR assignment for N9‐benzyladenine, N3‐benzyladenine, and N7‐benzyladenine was confirmed by computation using ADF.     

Computational NMR Spectroscopy of Transition‐Metal/Nitroimidazole Complexes: Theoretical Investigation of Potential Radiosensitizers

The computed chemical shifts of transition‐metal complexes with dimetridazole (= 1,2‐dimethyl‐5‐nitro‐1H‐imidazole; 1 ), a prototypical nitro‐imidazole‐based radiosensitizer, are reported at the GIAO‐BP86 and ‐B3LYP levels for BP86/ECP1‐optimized geometries. These complexes comprise [MCl₂( 1 )₂] (M = Zn, Pd, Pt), [RuCl₂(DMSO)₂( 1 )₂], and [Rh₂(O₂CMe)₄( 1 )₂]. Available δ(¹H) and δ(¹⁵N) values, and Δδ(¹H) and Δδ(¹⁵N) coordination shifts are well‐reproduced theoretically, provided solvation and relativistic effects are taken into account by means of a polarizable continuum model and suitable methods including spin–orbit (SO) coupling, respectively. These effects are particularly important for the metal‐coordinated N‐atom, where the contributions from solvation and relativity can affect δ(¹⁵N) and Δδ(¹⁵N) values up to 10–20 ppm. The ¹⁹⁵Pt chemical shifts of cis‐ and trans‐[PtCl₂( 1 )₂] are well‐reproduced using the zero‐order regular approximation including SO coupling (ZORA‐SO). Predictions are reported for ⁹⁹Ru and ¹⁰³Rh chemical shifts, which suggest that these metal centers could be used as additional, sensitive NMR probes in their complexes with nitro‐imidazoles.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XIV. Solvation effects in calculations of chemical shifts in 13C NMR spectra of chlorine-containing compounds

Analysis of precision factors in calculations of ¹³C NMR chemical shifts in the series of saturated and unsaturated organochlorine compounds was performed in the framework of the method of electron density functional theory GIAO-DFT-KT3/pcS-2 in the gas phase and with accounting for solvent effect by the polarized continuum model IEF-PCM. The accounting for solvation effects in calculations of ¹³C NMR chemical shifts within the framework of the IEF-PCM model is not fundamental for organochlorine compounds, yet it considerably improves the precision of calculations up to 2.5 ppm.