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.

Relativistic heavy atom effect on the 31 P NMR parameters of phosphine chalcogenides. Part 1. Chemical shifts.

Four-component density functional theory calculations of 31 P NMR chemical shifts have been performed for the representative series of 56 phosphine chalcogenides in order to investigate an influence of different functional groups on the heavy atom relativistic effect on the NMR chemical shifts of light phosphorous atoms (Heavy Atom on Light Atom effect). The validity of the 4-component density functional theory approach used for the wide-scale calculations of the phosphorous chemical shifts in a wide series of phosphine chalcogenides has been confirmed on a small series of 5 representative compounds with the aid of high-quality coupled cluster singles and doubles calculations taking into account solvent, vibrational, and the relativistic corrections in comparison with the experiment.

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.

First example of the correlated calculation of the one-bond tellurium-carbon spin-spin coupling constants: Relativistic effects, vibrational corrections, and solvent effects.

This work reports on the comprehensive calculation of the NMR one-bond spin-spin coupling constants (SSCCs) involving carbon and tellurium, (1) J((125) Te,(13) C), in four representative compounds: Te(CH3 )2 , Te(CF3 )2 , Te(CCH)2 , and tellurophene. A high-level computational treatment of (1) J((125) Te,(13) C) included calculations at the SOPPA level taking into account relativistic effects evaluated at the 4-component RPA and DFT levels of theory, vibrational corrections, and solvent effects. The consistency of different computational approaches including the level of theory of the geometry optimization of tellurium-containing compounds, basis sets, and methods used for obtainig spin-spin coupling values have also been discussed in view of reproducing the experimental values of the tellurium-carbon SSCCs. Relativistic corrections were found to play a major role in the calculation of (1) J((125) Te,(13) C) reaching as much as almost 50% of the total value of (1) J((125) Te,(13) C) while relativistic geometrical effects are of minor importance. The vibrational and solvent corrections account for accordingly about 3-6% and 0-4% of the total value. It is shown that taking into account relativistic corrections, vibrational corrections and solvent effects at the DFT level essentially improves the agreement of the non-relativistic theoretical SOPPA results with experiment. © 2016 Wiley Periodicals, Inc.

Indirect relativistic bridge and substituent effects from the 'heavy' environment on the one-bond and two-bond (13)C-(1)H spin-spin coupling constants.

Indirect relativistic bridge effect (IRBE) and indirect relativistic substituent effect (IRSE) induced by the 'heavy' environment of the IV-th, V-th and VI-th main group elements on the one-bond and geminal (13)C-(1)H spin-spin coupling constants are observed, and spin-orbit parts of these two effects were interpreted in terms of the third-order Rayleigh-Schrödinger perturbation theory. Both effects, IRBE and IRSE, rapidly increase with the total atomic charge of the substituents at the coupled carbon. The accumulation of IRSE for geminal coupling constants is not linear with respect to the number of substituents in contrast to the one-bond couplings where IRSE is an essentially additive quantity.

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

A versatile high-accuracy computational scheme for the (77) Se 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%).

MP2 calculation of (77) Se 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 (77) Se 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 (77) Se 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 (77) Se 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 (77) Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%.

Relativistic environmental effects in (29)Si NMR chemical shifts of halosilanes: light nucleus, heavy environment.

Relativistic calculations of (29)Si NMR shielding constants (chemical shifts) in the series of halosilanes SiX(n)H(4-n) (X = F, Cl, Br and I) are performed within a full four-component relativistic Dirac's scheme using relativistic Dyall's basis sets. Three different theoretical levels are tested in the computation of (29)Si NMR chemical shifts in comparison with experiment: namely, four-component relativistic GIAO-DFT, four-component relativistic GIAO-RPA, and a hybrid scheme of a nonrelativistic GIAO-MP2 with taking into account relativistic corrections using the four-component relativistic GIAO-RPA. The DFT results give larger relativistic effects as compared to the RPA data which might be rationalized in terms of the manifestation of correlation effects taken into account at the DFT level and not accounted for at the uncorrelated RPA level. Taking into account solvent effects slightly improves agreement with experiment, however, being not a matter of principle. Generally, relativistic pure nonempirical wave function methods perform much better as compared to relativistic DFT methods when benchmarked to experiment.

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 (77)Se-(13)C 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 (77)Se-(13)C 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.

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 (31)P 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 (31)P 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 (31)P NMR chemical shifts within the 1-2-ppm error. Relativistic corrections to (31)P 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 (31)P NMR chemical shifts characterized by a mean absolute error of ca 9 ppm in the range of 550 ppm.

Relativistic effects in the one-bond spin-spin coupling constants involving selenium.

One-bond spin-spin coupling constants involving selenium of seven different types, (1) J(Se,X), X = (1) H, (13) C, (15) N, (19) F, (29) Si, (31) P, and (77) Se, were calculated in the series of 14 representative compounds at the SOPPA(CCSD) level taking into account relativistic corrections evaluated both at the RPA and DFT levels of theory in comparison with experiment. Relativistic corrections were found to play a major role in the calculation of (1) J(Se,X) reaching as much as almost 170% of the total value of (1) J(Se,Se) and up to 60-70% for the rest of (1) J(Se,X). Scalar relativistic effects (Darwin and mass-velocity corrections) by far dominate over spin-orbit coupling in the total relativistic effects for all (1) J(Se,X). Taking into account relativistic corrections at both random phase approximation and density functional theory levels essentially improves the agreement of theoretical results with experiment. The most 'relativistic' (1) J(Se,Se) demonstrates a marked Karplus-type dihedral angle dependence with respect to the mutual orientation of the selenium lone pairs providing a powerful tool for stereochemical analysis of selenoorganic compounds.

Nonempirical calculations of the one-bond (29)Si-(13)C spin-spin coupling constants taking into account relativistic and solvent corrections.

The computational study of the one-bond (29)Si-(13)C 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 (1)J(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 (1)J(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 (1)J(Si,C).

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 (77)Se-(13)C 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 (1)J(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 (1)J(Se,C). Solvent effects in the values of (1)J(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 (1)J(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 (77)Se-(13)C 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.

First example of a high-level correlated calculation of the indirect spin-spin coupling constants involving tellurium: tellurophene and divinyl telluride.

This paper documents the very first example of a high-level correlated calculation of spin-spin coupling constants involving tellurium taking into account relativistic effects, vibrational corrections and solvent effects for medium sized organotellurium molecules. The (125)Te-(1)H spin-spin coupling constants of tellurophene and divinyl telluride were calculated at the SOPPA and DFT levels, in good agreement with experimental data. A new full-electron basis set, av3z-J, for tellurium derived from the "relativistic" Dyall's basis set, dyall.av3z, and specifically optimized for the correlated calculations of spin-spin coupling constants involving tellurium was developed. The SOPPA method shows a much better performance compared to DFT, if relativistic effects calculated within the ZORA scheme are taken into account. Vibrational and solvent corrections are next to negligible, while conformational averaging is of prime importance in the calculation of (125)Te-(1)H spin-spin couplings. Based on the performed calculations at the SOPPA(CCSD) level, a marked stereospecificity of geminal and vicinal (125)Te-(1)H spin-spin coupling constants originating in the orientational lone pair effect of tellurium has been established, which opens a new guideline in organotellurium stereochemistry.

One-bond 29Si-1H spin-spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations, relativistic effects, and vibrational corrections.

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one-bond (29)Si-(1)H spin-spin coupling constants in the series of halosilanes SiH(n)X(4-n) (X = F, Cl, Br, I), both at the non-relativistic and full four-parameter Dirac's relativistic levels taking into account vibrational corrections. At the non-relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results.

Open-chain unsaturated selanyl sulfides: stereochemical structure and stereochemical behavior of their 77Se-1H spin-spin coupling constants.

Stereochemical structure of nine Z-2-(vinylsulfanyl)ethenylselanyl organyl sulfides has been investigated by means of experimental measurements and second-order polarization propagator approach calculations of their (1)H-(1)H, (13)C-(1)H, and (77)Se-(1)H spin-spin coupling constants together with a theoretical conformational analysis performed at the MP2/6-311G** level. All nine compounds were shown to adopt the preferable skewed s-cis conformation of their terminal vinylsulfanyl group, whereas the favorable rotational conformations with respect to the internal rotations around the C-S and C-Se bonds of the internal ethenyl group are both skewed s-trans. Stereochemical trends of (77)Se-(1)H spin-spin coupling constants originating in the geometry of their coupling pathways and the selenium lone pair effect were rationalized in terms of the natural J-coupling analysis within the framework of the natural bond orbital approach.

Structural trends of 29Si-1H spin-spin coupling constants across double bond.

The calculations of geminal and vicinal (29)Si-(1)H spin-spin coupling constants across double bond in 15 alkenylmethylsilanes and alkenylchlorosilanes were carried out at the second-order polarization propagator approach level in a good agreement with experiment. Two structural trends, namely, (i) the geometry of the coupling pathway and (ii) the effect of the electrowithdrawing substituent, have been interpreted in terms of the natural J-coupling analysis within the framework of the natural bond orbital approach. Thus, the marked difference between cisoidal and transoidal (29)Si-(1)H spin-spin coupling constants across double bond was accounted for the delocalization contributions including bonding and antibonding Si-C and C-H orbitals, whereas the chlorine effect was explained in terms of the steric contributions including bonding Si-Cl orbitals.

Stereochemical behavior of (2) J(Se,H) and (3)J(Se,H) spin-spin coupling constants across sp(3) carbons: a theoretical scrutiny.

A theoretical study of geminal and vicinal (77)Se-(1)H coupling constants in the benchmark dimethyl and diethyl selenides has been performed at the SOPPA level followed by the NJC analysis within the NBO approach to reveal their stereochemical behavior in respect with the three main structural factors, namely, (i) the dihedral angle dependences, (ii) the bond angle dependences and (iii) the lone pair effects. It has been demonstrated that both geminal and vicinal couplings provide a unique stereospecificity in respect with the orientational lone pair effect together with the geometry of a coupling pathway, which is of prime importance for the stereochemical studies of organoselenium compounds.

Resonance assignments of diastereotopic CH(2) protons in the anomeric side chain of selenoglycosides by means of (2) J(Se,H) spin-spin coupling constants.

Unambiguous resonance assignments of diastereotopic CH(2) protons in the anomeric side chain of nine alkyl- and aralkylselenoglycosides have been carried out on the basis of experimental CPMG-HSQMBC measurements and theoretical second order polarization propagator approach (SOPPA) calculations of geminal (77) Se-(1) H spin-spin coupling constants involving diastereotopic pro-R and pro-S protons. Theoretical conformational analyses have been performed at the MP2/6-311G** level. The conformational space of each of the selenoglycosides under study could be adequately described as a mixture of six interconverting conformers with the molar fractions depending on the nature of the side chain substituent at the selenium atom. The good agreement observed between measured and the weighted conformational averaged values of the calculated coupling constants provides a basis for reliable diastereotopic assignments in this type of carbohydrate structures.