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.     

Four‐component relativistic DFT calculations of 77Se NMR chemical shifts: A gateway to a reliable computational scheme for the medium‐sized organoselenium molecules

A versatile high‐accuracy computational scheme for the ⁷⁷Se nuclear magnetic resonance (NMR) chemical shifts of the medium‐sized organoselenium compounds is suggested within a framework of a full four‐component relativistic density functional theory (DFT). The main accuracy factors (DFT functionals, relativistic geometry, vibrational corrections, and solvent effects) are addressed. The best result is achieved with NMR‐oriented KT2 functional of Keal–Tozer characterized by a fairly small error of only 30 ppm for the span of about 1700 ppm (<2%). © 2015 Wiley Periodicals, Inc.     

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.     

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.     

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.     

Stereochemical behavior of geminal and vicinal 77Se–13C spin–spin coupling constants studied at the SOPPA(CC2) level taking into account relativistic corrections

A systematic theoretical study of geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants in the series of the open‐chain selenides and selenium‐containing heterocycles revealed that relativistic effects play an essential role in the selenium–carbon coupling mechanism, especially when the coupling pathway includes a triple bond, contributing to about 10–15% of their total values and noticeably improving the agreement of the calculated couplings with experiment. Both geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants show marked stereochemical behavior as documented by their calculated dihedral angle dependence that could be used as a practical guide in stereochemical studies of organoselenium compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

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 © 2014 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.     

Study of stereospecificity of 1H, 13C, 15N and 77Se shielding constants in the configurational isomers of the selenophene-2-carbaldehyde azine by NMR spectroscopy and MP2-GIAO calculations

In the (1)H and (13)C NMR spectra of selenophene-2-carbaldehyde azine, the (1)H-5, (13)C-3 and (13)C-5 signals of the selenophene ring are shifted to higher frequencies, whereas those of the (1)H-1, (13)C-1, (13)C-2 and (13)C-4 are shifted to lower frequencies on going from the EE to ZZ isomer or from the E moiety to the Z moiety of EZ isomer. The (15)N chemical shift is significantly larger in the EE isomer relative to the ZZ isomer and in the E moiety relative to the Z moiety of EZ isomer. A very pronounced difference (60-65 mg/g) between the (77)Se resonance positions is revealed in the studied azine isomers, the (77)Se peak being shifted to higher frequencies in the ZZ isomer and in the Z moiety of EZ isomer. The trends in the changes of the measured chemical shifts are reasonably reproduced by the GIAO calculations at the MP2 level of the (1)H, (13)C, (15)N and (77)Se shielding constants in the energy-favorable conformation with the syn orientation of both selenophene rings relative to the C = N groups. The NBO analysis suggests that such an arrangement of the selenophene rings may take place because of a higher energy of some intramolecular interactions.     

Normal halogen dependence of 13C 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 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.     

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.     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. 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.     

Quasirelativistic study of 125Te nuclear magnetic shielding constants and chemical shifts

Calculations for ¹²⁵Te magnetic shielding constants and chemical shifts were carried out using a quasirelativistic Hamiltonian including the spin‐free relativistic, one‐ and two‐electron spin–orbit, and relativistic magnetic interaction terms. For the tellurium‐containing series Te(CH₃)₂, TeH₂, TeF₆, Te(CH₃)₄, and Te(CH₃)₂Cl₂, the relativistic effects amounted to as much as 1300 ppm and were very important for qualitatively reproducing the absolute value of the ¹²⁵Te shielding constants obtained experimentally. On the other hand, for the ¹²⁵Te chemical shifts the relativistic effects were less important, because they cancelled each other between the sample and reference compounds. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1502–1508, 2001     

Nonempirical calculations of the one‐bond 29Si–13C spin–spin coupling constants taking into account relativistic and solvent corrections

The computational study of the one‐bond ²⁹Si–¹³C spin–spin coupling constants has been performed at the second‐order polarization propagator approximation (SOPPA) level in the series of 60 diverse silanes with a special focus on the main factors affecting the accuracy of the calculation including the level of theory, the quality of the basis set, and the contribution of solvent and relativistic effects. Among three SOPPA‐based methods, SOPPA(MP2), SOPPA(CC2), and SOPPA(CCSD), the best result was achieved with SOPPA(CCSD) when used in combination with Sauer's basis set aug‐cc‐pVTZ‐J characterized by the mean absolute error of calculated coupling constants against the experiment of ca 2 Hz in the range of ca 200 Hz. The SOPPA(CCSD)/aug‐cc‐pVTZ‐J method is recommended as the most accurate and effective computational scheme for the calculation of ¹J(Si,C). The slightly less accurate but essentially more economical SOPPA(MP2)/aug‐cc‐pVTZ‐J and/or SOPPA(CC2)/aug‐cc‐pVTZ‐J methods are recommended for larger molecular systems. It was shown that solvent and relativistic corrections do not play a major role in the computation of the total values of ¹J(Si,C); however, taking them into account noticeably improves agreement with the experiment. The rovibrational corrections are estimated to be of about 1 Hz or 1–1.5% of the total value of ¹J(Si,C). Copyright © 2014 John Wiley & Sons, Ltd.     

A survey of wave function effects on theoretical calculation of gas phase F NMR chemical shifts using factorial design

The wave functions for calculating gas phase ¹⁹F chemical shifts were optimally selected using the factorial design as a multivariate technique. The effects of electron correlation, triple-ξ valance shell, diffuse function, and polarization function on calculated ¹⁹F chemical shifts were discussed. It is shown that of the four factors, electron correlation and the polarization functions affect the results significantly. B3LYP/6-31 + G(df,p) wave functions have been proposed as the best and the most efficient level of theory for calculating ¹⁹F chemical shifts. An additional series of fluoro compounds were used as a test set and their predicted ¹⁹F chemical shifts values confirmed the validity of the approaches.     

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.     

Ab Initio calculation of 19F NMR chemical shielding for alkaline‐earth‐metal fluorides

Gauge‐independent atomic orbital (GIAO) method at Hartree‐Fock (HF) and density functional theory (DFT) levels, respectively, was employed to calculate ¹⁹F NMR chemical shieldings of solid state alkaline‐earth‐metal fluorides MF₂ (M = Mg, Ca, Sr, Ba). The results show that, although the calculated ¹⁹F chemical shieldings tend to be larger than the experimental values, they have a fairly good linear relationship with the observed ones. The calculated results based on different combinations of basis sets show that the B3LYP (a hybrid of DFT with HF) predictions are greatly superior to the HF predictions. When a basis set of metal atom with effective core potential (ECP) has well representation of valence wavefunction, especially wavefunction of d component, and proper definition of core electron number, it can be applied to obtain ¹⁹F chemical shielding which is close to that of all‐electron calculation. The variation of ¹⁹F chemical shielding of alkaline‐earth‐metal fluorides correlates well with the lattice factor A/R².