Irina L. Rusakova

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 Dyalls 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

Algebraic-diagrammatic construction polarization propagator approach to indirect nuclear spin-spin coupling constants

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.

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 = 1H, 13C, 15 N, 19 F, 29Si, 31P, and 77Se, 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

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

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 13C1H 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

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, 1J(125Te,13C), in four representative compounds: Te(CH3)2, Te(CF3)2, Te(CCH)2, and tellurophene. A high‐level computational treatment of 1J(125Te,13C) 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 1J(125Te,13C) reaching as much as almost 50% of the total value of 1J(125Te,13C) 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.

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

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

On the significant relativistic heavy atom effect on 13C NMR chemical shifts of β- and γ-carbons in seleno- and telluroketones

ABSTRACT Unexpectedly large ‘Heavy Atom on Light Atom’ (HALA) effects have been found in 13C NMR (Nuclear Magnetic Resonance) chemical shifts of β- and γ-carbons of seleno- and telluroketones established by means of the high-accuracy calculations of 13C NMR chemical shifts in three representative real-life compounds, 2,2,5,5-tetramethyl-3-cyclopentene-1-selone, selenofenchone and 1,1,3,3-tetramethyl-1,3-dihydro-2H-indene-2-tellurone. The proposed computational scheme consists of the combination of accurately correlated coupled-cluster singles and doubles model approach for the non-relativistic calculations of shielding constants taking into account the solvent, vibrational and relativistic corrections, the latter obtained within the 4-component fully relativistic gauge-including atomic orbitals KT2 approach resulting in a very good agreement of the performed calculations with the experiment. The stereochemical dependence of the ‘long-range’ γ-HALA effect on the dihedral angle has been established in the model seleno- and telluroketones providing the largest shielding effect in the orthogonal orientation of the X=Cα–Cβ–Cγ (X=Se, Te) moiety.

Calculation of 125Te NMR Chemical Shifts at the Full Four-Component Relativistic Level with Taking into Account Solvent and Vibrational Corrections: A Gateway to Better Agreement with Experiment

Four-component relativistic calculations of 125Te 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 Dyalls 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 125Te 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.

Relativistic heavy atom effect on 13C NMR chemical shifts initiated by adjacent multiple chalcogens

In this paper, we have investigated the cumulative peculiarity of the “heavy atom on light atom” effect on the 13C 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═13C═Y (X, Y = O, S, Se, Te) and C(XH)m(YH)n(ZH)p(QH)sH1‐mH1‐nH1‐pH1‐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.