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.     

Selenium-77 chemical shifts of cyclodiphosphazane selenides

Isomeric cyclodiphosphazane selenides, R(X)P(NBu¹)₂P(Y)R (R=OMe or NMe₂, X=Se, Y=lone pair; R=OMe or NMe₂, X=Y=Se) display large differences (34–122 ppm) in ⁷⁷Se chemical shift. The ⁷⁷Se shifts of these and related amino derivatives are well to low field of the ⁷⁷Se shifts of analogous acyclic phosphorus selenides.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: II. Influence of medium, relativistic effects, and vibrational corrections on phosphorus magnetic shielding constants in the simplest phosphines and phosphine chalcogenides

The influence of solvent nature, relativistic effects, and vibrational corrections on the accuracy of calculation of ³¹P chemical shifts of the simplest phosphines, phosphine oxides, phosphine sulfides, and phosphine selenides was studied. Consideration of the above factors at the stage of both geometry optimization and calculation of magnetic shielding constants was found to appreciably improve the accuracy of calculation of ³¹P NMR chemical shifts in the series of phosphines and phosphine chalcogenides.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: IV. Effect of intermolecular coordination on <Superscript>31</Superscript>P NMR shielding constants and chemical shifts of molecular complexes of phosphorus pentachloride with azoles

Intermolecular coordination effects on the ³¹P NMR spectra of molecular complexes of N-vinylimidazole and 1-allyl-3,5-dimethylpyrazole with phosphorus pentachloride were studied by theoretical and experimental methods. The formation of intermolecular dative N→P bond was shown to be accompanied by upfield shift of the phosphorus resonance signal by more than 200 ppm. Appreciable contribution of relativistic effects to ³¹P NMR chemical shifts was revealed; the spin-orbital contribution to ³¹P shielding constant was estimated at >210 ppm. Consideration of solvent effect was found to be crucial while studying steric structure of molecular complexes of azoles with phosphorus pentachloride and intermolecular coordination effects on 31P NMR chemical shifts.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: VI. Accuracy of DFT calculations of 29Si chemical shifts of four-coordinate silicon compounds

Systematic analysis of factors affecting the accuracy of DFT calculations of ²⁹Si NMR chemical shifts in four-coordinate silicon compounds showed that the best agreement with the experimental values is attained using B1PW91 and PBE0 functionals in combination with the TZP basis set. In calculations of ²⁹Si chemical shifts by quantum-chemical methods particular attention should be given to the contribution of relativistic spin-orbit interaction and conformational equilibrium.     

Correlated ab initio calculations of one-bond 31P?77Se and 31P?125Te spin–spin coupling constants in a series of PSe and PTe systems accounting for relativistic effects (part 2)

Synthetic chalcogen–phosphorus chemistry permanently makes new challenges to computational Nuclear Magnetic Resonance (NMR) spectroscopy, which has proven to be a powerful tool of structural analysis of chalcogen–phosphorus compounds. This paper reports on the calculations of one-bond ³¹P ⁷⁷Se and ³¹P ¹²⁵Te NMR spin–spin coupling constants (SSCCs) in the series of phosphine selenides and tellurides. The applicability of the combined computational approach to the one-bond ³¹P ⁷⁷Se and ³¹P ¹²⁵Te SSCCs, incorporating the composite nonrelativistic scheme, built of high-accuracy correlated SOPPA (CC2) and Coupled Cluster Single and Double (CCSD) methods and the Density Functional Theory (DFT) relativistic corrections (four-component level), was examined against the experiment and another scheme based on the four-component relativistic DFT method. A special J-oriented basis set (acv3z-J) for selenium and tellurium atoms, developed previously by the authors, was used throughout the NMR calculations in this work at the first time. The proposed computational methodologies (combined and ‘pure’) provided a reasonable accuracy for ³¹P ⁷⁷Se and ³¹P ¹²⁵Te SSCCs against experimental data, characterizing by the mean absolute percentage errors of about 4% and 1%, and 12% and 8% for selenium and tellurium species, respectively. The present study reports typical relativistic corrections to ⁷⁷Se ³¹P and ¹²⁵Te ³¹P SSCCs, calculated within the four-component DFT formalism for a broad series of tertiary phosphine selenides and tellurides with different substituents at phosphorus.     

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.     

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.     

Quantum-chemical calculation of NMR chemical shifts of organic molecules: III. Intramolecular coordination effects on the 31P NMR chemical shifts of phosphorylated N-vinylazoles

Theoretical and experimental studies on magnetic shielding of the phosphorus nucleus in trichloro-[2-(1H-pyrazol-1-yl)ethenyl]phosphonium hexachlorophosphate(V) and 1,1,1,1-tetrachloro-1H-1λ⁶-pyrazolo-[1,2-a][1,2,3]diazaphosphol-8-ium-1-ide showed that intramolecular coordination of the phosphorus atom in the chlorophosphonium group to the nitrogen atom in the pyrazole ring leads to upfield shift of the phosphorus signal (to δ_P 170 ppm) and that the contribution of the spin-orbital contribution to the ³¹P chemical shift reaches 15%. Relativistic effects and effects of the medium are determining in the theoretical calculation of ³¹P NMR chemical shifts.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XV. Relativistic calculations of <Superscript>29</Superscript>Si NMR chemical shifts of silanes

Calculations of ²⁹Si NMR chemical shifts of 68 silanes possessing various substituents, in particular, with heavy halogens attached to silicon atom, were carried out applying an efficient calculation scheme of locally dense basis set in the framework of the electron density functional theory utilizing the Keal–Tozer functional combined with relativistic Dyall basis sets on a four-component relativistic level. The main factors of calculation accuracy of silicon chemical shifts were analyzed including the relativistic effects, environmental impact, and vibrational corrections. The mean absolute calculation error for the studied compounds series accounting for all mentioned factors was 14.0 ppm for the nonrelativistic calculation and 6.7 ppm for the four-component relativistic calculation at the range of silicon chemical shifts variation of ~250 ppm.     

Nuclear magnetic resonance shielding constants and chemical shifts in linear 199Hg compounds: a comparison of three relativistic computational methods

We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL(2) (L = Cl, Br, I, CH(3)) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH(3))(2) within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ～2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr(2) and HgI(2) when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ～500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ～100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible.     

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     

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.     

Selenium-77 NMR chemical shifts of five-membered selenium and sulphur heterocycles with CSe,CS,and CO groups

This paper reports the ⁷⁷Se NMR chemical shifts of 1,3-dithiole-, 1,3-thiaselenole- and 1,3-diselenole-2-ones, -thiones and -selones, of the corresponding saturated compounds 1,3-diselenolane-2-one, -thione and -selone, and the 1,3-thiaselenolium tetrafluoroborates, either unsubstituted or substituted by morpholino, ethylthio or ethylseleno groups in the 2-position. The ⁷⁷Se chemical shift values of the ring selenium and the C?Se groups are compared with the ¹³C chemical shift values of neighbouring carbon atoms. The relationships between the ⁷⁷Se chemical shifts of the C?Se groups and the wavelengths of their n→* absorption in the UV-visible spectrum are discussed with respect to the significance of the δE term in the contribution of the paramagnetic screening and the electron density distribution.     

77Se n.m.r. studies of organoselenium compounds: III—substituent effects in 4,4′-disubstituted diphenyl selenides and 4,4′-disubstituted diphenylmethanes studied by 1H, 13C and 77Se spectroscopy

⁷⁷Se N.m.r. spectra of 4,4′-disubstituted diphenyl selenides have been obtained. The chemical shifts could be correlated with substituent constants of the Hammett type or with Swain and Lupton two-parameter equations. No correlations were observed between these ⁷⁷Se shifts and the ¹³C shifts of the CH₂ group of 4,4′-disubstituted diphenylmethanes, the latter shifts showing no correlation with substituent constants. On the other hand linear correlation was observed between the ⁷⁷Se shifts of the 4,4′-disubstituted diphenyl selenides and the ¹H shifts of the CH₂ group of the diphenylmethanes, the ¹³C shifts of their 1-carbons and the ¹⁹F shifts of 4-substituted fluorobenzenes.     

NMR studies of the chalcogen analogues of benzofuran. IV—Proton,carbon-13 and selenium-77 magnetic resonance in nitrobenzo[b]selenophenes

The ¹H, ¹³C and ⁷⁷Se chemical shifts have been measured for mononitrobenzo[ b ]selenophenes. For the homocyclic nuclei, the observed ¹H- and ¹³C-values calculated from the empirical increments of nitrobenzene. Anomalous effects are observed in the 2- and 3-substituted derivatives and the nature of the Se? NO₂ interactions in the former is discussed. ⁷⁷Se chemical shifts of the 4-, 5- and 7-nitro derivatives are approximately correlated with the CNDO calculated electron densities; they also compare well with those of selenoanisoles and other phenyl alkyl selenides. The chemical shifts are also compared with the corresponding values in other heterocycles containing a selenophene moiety.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: I. Phosphines,phosphine oxides,and phosphine sulfides

The accuracy in the calculation of ³¹P NMR chemical shifts in the series of the simplest phosphines, phosphine oxides, and phosphine sulfides was estimated in terms of the Hartree-Fock self-consistent final perturbation theory and density functional theory with different basis sets. The best agreement between the calculated and experimental data was achieved at the DFT/B3LYP/IGLO-III level of theory.     

Relativistic effect on 77Se NMR chemical shifts of various selenium species in the framework of zeroth-order regular approximation

The relativistic effects on absolute magnetic shielding tensors (σ(Se)) are explicitly evaluated for various selenium species (40 species) with the DFT(BLYP)-GIAO method. Calculations are performed under relativistic and nonrelativistic conditions with the Slater-type basis sets in ADF 2010 in the framework of ZORA, employing the optimized structures under nonrelativistic conditions at B3LYP of Gaussian 03. Quadruple zeta all electron with four polarization functions (QZ4Pae) are mainly applied to evaluate σ(Se). Ranges of the effect on diamagnetic (σ(d)(Se)), paramagnetic shielding tensors (σ(p)(Se)), and σ(d+p)(Se) (= σ(d)(Se) + σ(p)(Se)) are -24 to -20 ppm, -115 to -3 ppm, and -136 to -26 ppm, respectively. The spin-orbit terms (σ(so)(Se)) are evaluated to be 92-225 ppm with QZ4Pae, which clarifies the effect on total shielding tensors (σ(t)(Se) = σ(d+p)(Se) + σ(so)(Se)) to be -8 to 152 ppm, at the spin-orbit ZORA level. The calculated σ(t)(Se) values reproduced well the observed values.     

New chiral 1,3-diphosphine ligands for Rh-catalyzed enantioselective hydrogenation: a search for electronic effects

New electron-rich chiral 1,3-diphosphines of the BDPP type were prepared from 1,3-diphenylpropane-1,3-diol by an economically feasible synthetic approach. The σ-donor properties of the phosphines were determined by measurement of J(³¹P–⁷⁷Se) coupling constants in the corresponding phosphine selenides. For comparison related, but electronically different, 1,3-diphosphines were considered. The new diphosphines showed good enantioselectivities as ligands in the Rh-catalyzed enantioselective hydrogenation of benchmark substrates and β-amino acid precursors (up to 98% ee). The electronic effects on the outcome of the enantioselective catalysis have been analyzed.     

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.