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A root factor for the accuracy of all quantum chemical calculations of nuclear magnetic resonance (NMR) chemical shifts is the quality of the molecular equilibrium geometry used. In turn, this quality depends largely on the basis set employed at the geometry optimization stage. This parameter represents the main subject of the present study, which is a continuation of our recent work, where new pecG- n ( n = 1, 2) basis sets for the geometry optimization were introduced. A goal of this study was to compare the performance of our geometry-oriented pecG- n ( n = 1, 2) basis sets against the other basis sets in massive calculations of 13 C NMR shielding constants/chemical shifts in terms of their efficacy in reducing geometry factor errors. The testing was carried out with both large-sized biologically active natural products and medium-sized compounds with complicated electronic structures. The former were treated using the computation protocol based on the density functional theory (DFT) and considered in the theoretical benchmarking, while the latter were treated using the computational scheme based on the upper-hierarchy coupled cluster (CC) methods and were used in the practical benchmarking involving the comparison with experimental NMR data. Both the theoretical and practical analyses showed that the pecG-1 and pecG-2 basis sets resulted in substantially reduced geometry factor errors in the calculated 13 C NMR chemical shifts/shielding constants compared to their commensurate analogs, with the pecG-2 basis set being the best of all the considered basis sets.

The basis of all molecular property quantum chemical calculations is the correct equilibrium geometry. In this paper, new efficient pecG- n ( n = 1, 2) basis sets for the geometry optimization of molecules containing hydrogen and p elements of 2-3 periods are proposed. These basis sets were optimized via the property-energy consistent (PEC) algorithm directed to the minimization of the molecular energy gradient relative to the bond lengths. New basis sets are compact and give equilibrium geometries of very high quality, which is comparable to that provided by considerably larger energy-optimized basis sets. The equilibrium geometries obtained with the pecG- n ( n = 1, 2) basis sets and the other basis sets of diverse quality were tested in the CCSD calculations of different second-order molecular properties, including NMR shielding constants, static polarizabilities, and static magnetizabilities. As a result, new basis sets have demonstrated far superior performance as compared to the other energy-optimized basis sets of the same or close sizes commonly used at the geometry optimization stage.

31P nuclear magnetic resonance (NMR) chemical shifts were shown to be very sensitive to the basis set used at the geometry optimization stage. Commonly used energy-optimized basis sets for a phosphorus atom containing only one polarization d-function were shown to be unable to provide correct equilibrium geometries for the calculations of phosphorus chemical shifts. The use of basis sets with at least two polarization d-functions on a phosphorus atom is strongly recommended. In this paper, an idea of creating the basis sets purposed for the geometry optimization that provide the least possible error coming from the geometry factor of accuracy in the resultant NMR shielding constants is proposed. The property-energy consisted algorithm with the target function in the form of the molecular energy gradient relative to P-P bond lengths was applied to create new geometry-oriented pecG-n (n = 1, 2) basis sets for a phosphorus atom. New basis sets have demonstrated by far superior performance as compared to the other commonly used energy-optimized basis sets in massive calculations of 31P NMR chemical shifts carried out at the gauge-including atomic orbital-coupled cluster singles and doubles/pecS-2 level of the theory by taking into account solvent, vibrational, and relativistic corrections., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The basis set issue has always been one of the most important factors of accuracy in the quantum chemical calculations of NMR chemical shifts. In a previous paper, we developed new pecS- n ( n = 1, 2) basis sets purposed for the calculations of the NMR chemical shifts of the nuclei of the most popular NMR-active isotopes of 1-2 row elements and successfully approbated these on the DFT calculations of chemical shifts in a limited series of small molecules. In this paper, we demonstrate the performance of the pecS- n ( n = 1, 2) basis sets on the calculations of as much as 713 1 H and 767 13 C chemical shifts of 23 biologically active natural products with complicated stereochemical structures, carried out using the GIAO-DFT(PBE0) approach. We also proposed new alternative contraction schemes for our basis sets characterized by less contraction depth of the p -shell. New contraction coefficients have been optimized with the property-energy consistent (PEC) method. The accuracies of the pecS- n ( n = 1, 2) basis sets of both the original and newly contracted forms were assessed on massive benchmark calculations of proton and carbon chemical shifts of a vast variety of natural products. It was found that less contracted pecS- n ( n = 1, 2) basis sets provide no noticeable improvement in accuracy. These calculations represent the most austere test of our basis sets as applied to routine calculations of the NMR chemical shifts of real-life compounds.

The basis sets that are used in the quantum chemical calculations of 31 P NMR chemical shifts have always been one of the most important factors of accuracy. Regardless of what high-quality approach is employed, using basis sets of insufficient flexibility in the important angular regions may give poor results and lead to misassignments of the signals in the 31 P NMR spectra. In this work, it was found that the existing nonrelativistic basis sets for phosphorus atom of double- and triple- ζ quality, specialized for the 31 P NMR chemical shifts calculations, are essentially undersaturated in the d -angular space that occurred to play a significant role in the overall accuracy of these calculations. This problem has been thoroughly investigated, and new pecS- n ( n = 1, 2) basis sets for phosphorus chemical shifts calculations were proposed. The exponents and contraction coefficients for the pecS- n basis sets were generated with the property-energy consistent method that has been introduced in our earlier paper, and has been proven useful in the creation of efficient property-oriented basis sets. New basis sets were optimized using the GIAO-DFT method with the B97-2 functional. Extensive benchmark calculations showed that the pecS-1 and pecS-2 basis sets provide very good accuracy, characterized by the corrected mean absolute percentage errors against the experiment of about 7.03 and 4.42 ppm, respectively. In particular, the accuracy of 31 P NMR chemical shifts calculations achieved with the pecS-2 basis set is one of the most favorable accuracies for today. We believe that our new pecS- n ( n = 1, 2) basis sets for phosphorus atom will prove useful in modern large-scale quantum chemical calculations of 31 P NMR chemical shifts.

We present new compact pecJ- n ( n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1 H and 13 C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant ( J ). In general, it has been shown that the nonrelativistic J -oriented and σ-oriented basis sets, artificially saturated in the tight s -region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications., (© 2022 John Wiley & Sons Ltd.)

In this paper, we presented new J -oriented basis sets, pecJ- n ( n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin-spin coupling constants involving these nuclei. The pecJ- n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin-spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z + basis set of quadruple-ζ quality.

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations.

This paper presents a new method of generating property-energy consistent (PEC) basis sets that can be applied to any arbitrary molecular property. The PEC method generates a basis set that is optimized for the molecular property under interest, providing the least possible total molecular energy. The main algorithm of the PEC approach involves Monte Carlo simulations to generate random exponents in the predetermined range. In this work, the PEC method is introduced in the example of generation of new pecJ-n (n = 1, 2) basis sets suited for high-quality correlated calculations of indirect nuclear spin-spin coupling constants involving the most popular NMR-active nuclei: 1H, 13C, 15N, and 19F.

New J-oriented tin basis sets, acvXz-J (X = 2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data., (© 2021 John Wiley & Sons, Ltd.)

An accurate quantum chemical (QC) modeling of 77 Se and 125 Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of 77 Se and 125 Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of 77 Se and 125 Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques., (© 2020 John Wiley & Sons, Ltd.)

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 31 P 77 Se and 31 P 125 Te 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 31 P 77 Se and 31 P 125 Te 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 31 P 77 Se and 31 P 125 Te 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 77 Se 31 P and 125 Te 31 P SSCCs, calculated within the four-component DFT formalism for a broad series of tertiary phosphine selenides and tellurides with different substituents at phosphorus., (© 2020 John Wiley & Sons, Ltd.)

A new basis set of triple-ζ quality for carbon, 3z-S, is developed and tested at the DFT, MP2, and CCSD(T) levels, taking into account solvent and vibrational corrections for a number of molecules ranging from the smallest fluoromethane, CH 3 F, to the largest 5,10,15,20-tetraphenylporphyrin, C 44 H 30 N 4 . The proposed highly economical 3z-S basis set has been proven to provide very good accuracy in all examinations, comparable to that of the NMR-oriented Jensen's pcS-2 basis set, which is about 50% larger than 3z-S.

An accurate quantum chemical modeling of 125 Te NMR spectra is of great importance in the NMR structural assignment for real-life tellurium compounds, which represent a growing interest in organic and inorganic chemistry nowadays. This work reports a computationally modest combined approach based on the density functional theory only, which provides an excellent accuracy against the experiment and can be effectively applied for the routine large-scale calculations of tellurium chemical shifts. The role of solvent, vibrational, and relativistic corrections has been thoroughly investigated. Special attention was paid to the effect of taking into account the scalar relativistic effects during the geometry optimizations on the calculated tellurium chemical shifts.

The relativistic HALA effect has been shown to depend on the spatial deformation of the lone electron pairs of a heavy atom, as demonstrated for alkyl and alkene phosphine tellurides. It was found that HALA effect on phosphorous nuclear magnetic resonance shielding constant is strongly dependent on the spatial arrangements of light substituents on phosphorus, resulting in the deformation of the lone electron pairs of tellurium., (© 2019 John Wiley & Sons, Ltd.)

New basis sets, acvXz-J (X = 2, 3, 4), were designed for tellurium and selenium atoms for the calculation of indirect nuclear spin-spin coupling constants involving selenium or tellurium nuclei. Saturation of angular spaces was performed in an even-tempered manner till achieving the convergence of spin-spin coupling constants under consideration. The high-accuracy correlated SOPPA(CCSD) method was employed in this procedure. Saturated basis sets were contracted by approximately 30% using the coefficients obtained from the atomic self-consistent field (SCF) closed-shell calculations of selenium and tellurium anions, Se 2- and Te 2- . Final basis sets of acvXz-J showed sufficiently high accuracy in comparison with previous special basis sets.

Phosphorus-carbon spin-spin coupling constants in a series of salient heterocyclic phosphines were calculated at the SOPPA(MP2) level including evaluation of relativistic and solvent effects. A number of the locally dense basis set schemes were thoroughly investigated in terms of their accuracy versus computational demands. The most effective computational scheme was tested in a benchmark series to provide a very good correlation between 2 J PC calculated at the SOPPA(MP2) level and experiment. A marked dihedral angle dependence of 2 J PC was demonstrated, and this could be used in stereochemical studies of a wide series of organophosphorus compounds based on the phosphorus-carbon coupling constants.

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., (Copyright © 2018 John Wiley & Sons, Ltd.)

A number of computational schemes for the calculation of 15 N and 31 P 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 15 N and 31 P 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 15 N and 31 P NMR chemical shifts at the DFT level in the diverse series of nitrogen- and phosphorus-containing heterocycles. Benchmark calculations of 15 N and 31 P 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.

In this paper, we have investigated the cumulative peculiarity of the "heavy atom on light atom" effect on the 13 C NMR chemical shifts, initiated by the adjacent chalcogens. For this purpose, the most accurate hybrid computational scheme for the calculation of chemical shifts of carbon nuclei, directly bonded with several heavy chalcogens, is introduced and attested on the representative series of molecules. The best hybrid scheme combines the nonrelativistic coupled cluster-based approach with the different types of corrections, including vibrational, solvent, and relativistic. The dependences of the total relativistic corrections to carbon shielding constants in 2 series of model compounds, namely, X═ 13 C═Y (X, Y = O, S, Se, Te) and C(XH) m (YH) n (ZH) p (QH) s H 1-m H 1-n H 1-p H 1-s (X, Y, Z, Q = S, Se, Te and m, n, p, s = 0, 1), on the total atomic number of the adjacent chalcogens have been obtained., (Copyright © 2018 John Wiley & Sons, Ltd.)

Long-range β- 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, β- 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., (Copyright © 2017 John Wiley & Sons, Ltd.)

Four-component relativistic calculations of 125 Te NMR chemical shifts were performed in the series of 13 organotellurium compounds, potential precursors of the biologically active species, at the density functional theory level under the nonrelativistic and four-component fully relativistic conditions using locally dense basis set scheme derived from relativistic Dyall's basis sets. The relativistic effects in tellurium chemical shifts were found to be of as much as 20-25% of the total calculated values. The vibrational and solvent corrections to 125 Te NMR chemical shifts are about, accordingly, 6 and 8% of their total values. The PBE0 exchange-correlation functional turned out to give the best agreement of calculated tellurium shifts with their experimental values giving the mean absolute percentage error of 4% in the range of ∼1000 ppm, provided all corrections are taken into account.

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., (Copyright © 2016 John Wiley & Sons, Ltd.)

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., (© 2016 Wiley Periodicals, Inc.)

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., (Copyright © 2015 John Wiley & Sons, Ltd.)

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%)., (© 2015 Wiley Periodicals, Inc.)

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%., (Copyright © 2015 John Wiley & Sons, Ltd.)

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.

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., (Copyright © 2014 John Wiley & Sons, Ltd.)

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., (Copyright © 2014 John Wiley & Sons, Ltd.)

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., (Copyright © 2014 John Wiley & Sons, Ltd.)

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)., (Copyright © 2014 John Wiley & Sons, Ltd.)

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., (Copyright © 2014 John Wiley & Sons, Ltd.)

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., (Copyright © 2013 John Wiley & Sons, Ltd.)

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.

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., (Copyright © 2012 John Wiley & Sons, Ltd.)

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., (Copyright © 2012 John Wiley & Sons, Ltd.)

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., (Copyright © 2012 John Wiley & Sons, Ltd.)

A new polarization propagator approach to indirect nuclear spin-spin coupling constantans is formulated within the framework of the algebraic-diagrammatic construction (ADC) approximation and implemented at the level of the strict second-order approximation scheme, ADC(2). The ADC approach possesses transparent computational procedure operating with Hermitian matrix quantities defined with respect to physical excitations. It is size-consistent and easily extendable to higher orders via the hierarchy of available ADC approximation schemes. The ADC(2) method is tested in the first applications to HF, N(2), CO, H(2)O, HCN, NH(3), CH(4), C(2)H(2), PH(3), SiH(4), CH(3)F, and C(2)H(4). The calculated indirect nuclear spin-spin coupling constants are in good agreement with the experimental data and results of the second-order polarization propagator approximation method. The computational effort of the ADC(2) scheme scales as n(5) with respect to the number of molecular orbitals n, which makes this method promising for applications to larger molecules.

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., (Copyright © 2012 John Wiley & Sons, Ltd.)

Benchmark calculations of geminal and vicinal (29) Si-(1) H spin-spin coupling constants across double bond in three reference alkenylsilanes have been carried out at both DFT and SOPPA levels in comparison with experiment. At the former, four density functionals, B3LYP, B3PW91, PBE0 and KT3, were tested in combination with five representative basis sets. At the latter, three main SOPPA-based methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), were examined in combination with the same series of basis sets. On the whole, the wavefunction methods showed much better results as compared to DFT, with the most efficient combination of SOPPA/cc-pVTZ-su2 characterized by a mean absolute error of only 0.4 Hz calculated for a set of nine coupling constants in three compounds with a sample span of around 40 Hz., (Copyright © 2012 John Wiley & Sons, Ltd.)

Conformational study of five derivatives of 2-(pyrazol-4-yl)-1,3-diselenane together with related 1,2-diselenolane in respect to the stereochemical trends of geminal and vicinal (77)Se-(1)H spin-spin coupling constants has been carried out by means of high-level theoretical calculations in combination with experiment. The marked dihedral angle dependences for both types of couplings accounted for the lone pair effect in the case of geminal coupling constants and the Karplus-type relationship for vicinal couplings have been established, which is of major importance for the stereochemical analysis of saturated selenium containing heterocycles., (Copyright © 2012 John Wiley & Sons, Ltd.)

Stereochemical study of five sterically crowded phenylselanylalkenes obtained via the hydroselenation of either terminal or internal alkynes with benzeneselenol catalyzed by the nanosized Ni complexes has been carried out based on the experimental HMBC measurements and theoretical second order palarization propagator approach (SOPPA) calculations of their (77)Se-(1)H spin-spin coupling constants across double bond in combination with the energy-based theoretical conformational analysis performed at the MP2/6-311G** level. It has been found that studied phenylselanylalkenes adopt mainly skewed s-cis conformation with the noticeable out-of-plane deviations of the phenylselanyl and phenyl groups., (Copyright © 2011 John Wiley & Sons, Ltd.)

A combined theoretical and experimental study on the stereochemical behavior of (77)Se-(1)H spin-spin coupling constants has been performed at the second-order polarization propagator approach level together with heteronuclear multiple-bond correlation technique in the series of selenium-containing four-, five- and six-membered heterocycles including the derivatives of thiaselenetane, selenasilole, thiaselenole, thiaselenolane and dihydrothiaselenine. Geminal and vicinal (77)Se-(1)H spin-spin couplings were shown to have the pronounced stereochemical dependences in respect with the topology of the coupling pathway, internal rotation of the side-chain substituents and ring inversion providing a straightforward tool for the conformational analysis and diastereotopic assignments in the chiral organoselenium compounds., (Copyright © 2011 John Wiley & Sons, Ltd.)

Selenoglycosides are important starting materials in synthetic carbohydrate chemistry and play a role in biological interactions as well. Both aspects are influenced by the conformation around the glycosidic bond. Here, we present a combined experimental and computational approach to measure and evaluate (n)J((77)Se, (1)H) coupling constants for their use in conformational analysis. The measurements were carried out using a modified CPMG-HSQMBC pulse scheme which yields pure absorption antiphase multiplets to allow accurate determination of the (n)J(XH) values regardless of the size of the proton-proton couplings. Theoretical calculations were performed at the Second-Order Polarization Propagator Approach (SOPPA) level. Population-averaged values calculated for geminal and vicinal couplings are in a good agreement with experiment indicating an adequate theoretical level of the calculations. Experimental observations and computations alike have indicated that two-bond (77)Se-(1)H couplings, (2)J((77)Se, (1)H), in a H1-C1-Se-X moiety are very sensitive to the torsion angle around the C1-Se-bond and will, therefore, be useful for conformational studies., (Copyright © 2011 John Wiley & Sons, Ltd.)

A combined theoretical and experimental study of the stereochemical behavior of (31)P-(1)H spin-spin coupling constants has been performed in the series of trivinylphosphine and related trivinylphosphine oxide, sulfide and selenide. Theoretical energy-based conformational analysis of the title compounds performed at the MP2/6-311G** level reveals that each of the four compounds of this series exists in the equilibrium mixture of five true-minimum conformers, namely s-cis-s-cis-s-cis, s-cis-s-cis-gauche, syn-s-cis-gauche-gauche, anti-s-cis-gauche-gauche and gauche-gauche-gauche, which were taken into account in the conformational averaging of (31)P-(1)H spin-spin couplings calculated at the second-order polarization propagator approach/aug-cc-pVTZ-J level of theory. All (31)P-(1)H spin-spin coupling constants involving phosphorus and either of the vinyl protons are found to demonstrate a marked stereochemical dependences with respect to the geometry of the coupling pathway and internal rotation of the vinyl group around the P-C bond which is of major importance in the stereochemical studies of the unsaturated phosphines and phosphine chalcogenides., (Copyright © 2010 John Wiley & Sons, Ltd.)

Experimental measurements and second-order polarization propagator approach (SOPPA) calculations of (77)Se-(1)H spin-spin coupling constants together with theoretical energy-based conformational analysis in the series of 2-substituted selenophenes have been carried out. A new basis set optimized for the calculation of (77)Se-(1)H spin-spin coupling constants has been introduced by extending the aug-cc-pVTZ-J basis for selenium. Most of the spin-spin coupling constants under study, especially vicinal (77)Se-(1)H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2-position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds., (Copyright 2009 John Wiley & Sons, Ltd.)