Research article Received: 15 May 2014
Revised: 29 June 2014
Accepted: 1 July 2014
Published online in Wiley Online Library: 15 July 2014
(wileyonlinelibrary.com) DOI 10.1002/mrc.4112
Relativistic effects in the one-bond spin–spin coupling constants involving selenium Irina L. Rusakova, Yury Yu. Rusakov and Leonid B. Krivdin* One-bond spin–spin coupling constants involving selenium of seven different types, 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31 P, 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 © 2014 John Wiley & Sons, Ltd. Keywords: 77Se NMR; spin–spin coupling constant; SOPPA(CCSD); relativistic effects; selenides
Introduction
500
Relativistic effects including electron spin–orbit coupling (the interaction of the spin magnetic moment of an electron with the magnetic field induced by its own orbital motion) and scalar effects – Darwin term (relativistic fluctuation of an electron about its mean position) and mass-velocity corrections (relativistic increase in the mass of an electron with its velocity approaching the speed of light) resulting in the ‘relativistic contraction’ of the s-shells and inner p-shells and in the ‘relativistic expansion’ of the d-shells and f-shells – are of major importance in the calculation of the second-order molecular properties for molecular systems involving ‘heavy’ atoms.[1] In line with a general breakthrough in theory and computation of nuclear magnetic resonance parameters,[2] relativistic calculations of spin–spin coupling constants, in particular those at the scalar and spin–orbit zeroth order regular approximation[3] levels have now become popular, see salient review by Autschbach.[4] As an example, the isotropic average and the anisotropies of 77Se-13C and 77 Se-77Se spin–spin coupling tensors in carbon diselenide were derived by Jokisaari and Autschbach[5] from the zeroth order regular approximation and density functional theory (DFT) calculations in comparison with experimental nuclear magnetic resonance data in liquid crystalline solutions. In continuation of our recent relativistic calculations of the one-bond, geminal, and vicinal spin–spin coupling constants silicon–carbon,[6] selenium–carbon[7] and tellurium–hydrogen,[8] which demonstrated a noticeable contribution (up to 30%) of relativistic effects in their total values, in this paper, we report the results on the contribution of relativistic effects to the onebond spin–spin coupling constants involving selenium of seven different types evaluated within the full four-component relativistic Dirac’s method. In other words, we have investigated the ‘relative relativism’ of the one-bond spin–spin coupling constants 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31P, and 77Se.
Magn. Reson. Chem. 2014, 52, 500–510
In a number of papers dealing with relativistic calculations of spin–spin coupling constants involving or across IVa, Va, VIa, and VIIa group elements in simple hydrides, XH4 (X = C, Si, Ge, Sn, Pb),[9] XH3 (X = N, P, As. Sb, Bi),[10] XH2 (X = O, S, Se, Te, Po), 9g–11 and XH (X = F, Cl, Br, I),[12] together with three our papers cited in the previous text,[6–8] it has been demonstrated that relativistic effects could not only substantially contribute but even dominate spin–spin coupling mechanism involving or propagating through ‘heavy’ nuclei. For example, full four-component relativistic random phase approximation (RPA) calculations of 1 J(X,H) in XH4 (X = C, Si, Ge, Sn, Pb) series showed that very small relativistic effects are observed in methane and silane while for germane, stannane, and plumbane, the relativistic coupling is increased by accordingly 12%, 37%, and 156% mainly due to the scalar relativistic contraction of s-shells.[9a] Alternatively, in some other papers, relativistic effects in spin–spin coupling were interpreted mainly in terms of the dominant spin–orbit interaction.[9b,9c] It was thus a challenging task and a prime goal of the present study to evaluate the relative contributions of a total relativistic effect in the values of different one-bond spin–spin coupling constants involving selenium and to estimate the ratio of scalar relativistic contraction and spin–orbit interaction in the total value of relativistic effect in each particular case.
Results and Discussion To evaluate the contribution of relativistic effects in the values of 1 J(Se,X), we first performed the nonrelativistic calculation of these * Correspondence to: Leonid Krivdin, Siberian Branch of the Russian Academy of Sciences, A. E. Favorsky Irkutsk Institute of Chemistry, Favorsky St. 1, 664033 Irkutsk, Russia. E-mail: krivdin_offi[email protected] Siberian Branch of the Russian Academy of Sciences, A. E. Favorsky Irkutsk Institute of Chemistry, Favorsky St. 1, 664033, Irkutsk, Russia
Copyright © 2014 John Wiley & Sons, Ltd.
Relativistic effects in the one-bond spin–spin coupling constants involving selenium coupling constants in the model series 1–14 within the secondorder polarization propagator approximation (SOPPA)[13] in combination with coupled cluster single and double (CCSD) excitation model,[14] known as SOPPA(CCSD),[15] one of the most reliable ab initio methods for the second-order molecular properties.[16] On the other hand, relativistic corrections to these basic ‘nonrelativistic’ SOPPA(CCSD) coupling constants were calculated within the fourcomponent relativistic Dirac–Coulomb method at the DFT-PBE0 level, that is, within the DFT framework using the hybrid functional of Perdew, Burke, and Ernzerhof with a predetermined amount of exact exchange (PBE0).[17,18] Relative contributions of total relativistic effects together with those separated into scalar and spin–orbit terms evaluated at both DFT-PBE0 and RPA[19] levels are discussed herewith with respect to the total ‘relativistically corrected’ SOPPA (CCSD) values of 1 J(Se,X). Nonrelativistic results All nonrelativistic calculations of 1 J(Se,X) in the series of 1–14 were performed at the SOPPA(CCSD) level, which nowadays is one of the most accurate pure ab initio methods of the linear response function family for the calculation of spin–spin coupling constants in the medium-sized organic and elementoorganic molecules, especially when it is used with Sauer’s basis sets aug-cc-pVTZJ[20] of triple zeta quality containing tight s-functions optimized for the calculation of the Fermi contact (FC) contribution. Traditionally, in line with the locally dense basis set scheme,[21] we used Sauer’s basis set for the coupled nuclei leaving the rest of molecule being specified with much more economical Dunning’s basis set of double zeta quality, cc-pVDZ.[22] Compiled in Tables 1 and 2 are the results of the present calculations of seven different types of regular and reduced spin–spin coupling constants involving selenium, 1 J(Se,X) and 1 K(Se,X), in 14 compounds performed at the SOPPA(CCSD) level. Four basic Ramsey’s coupling contributions, namely, FC, spin-dipolar (SD), diamagnetic spin–orbital (DSO), and paramagnetic spin–orbital
(PSO) terms were taken into account to contribute to the total values of 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31P, and 77Se. Calculated coupling constants 1 J(Se,X) were compared with available experimental data taken from different sources for compounds 1,[23] 2,[24] 3,[25] 4,[26] 5,[27] 6 and 7,[28] 8,[29] 9,[30] 10,[31] 11, 12 and 13,[32] and 14.[33] Relative contributions of the individual coupling terms to the total calculated values of 1 J(Se,X) and 1 K(Se,X) for the most representative compounds of this series (1–4, 8, 9, and 11) covering different types of spin–spin coupling constants involving selenium are presented on the diagrams in Figs 1 and 2. Not shown on the diagrams are the results for 1 J(Se,Se) and 1 K(Se,Se) concurrently involving two ‘relativistic’ selenium nuclei, which are discussed separately (see in the succeeding text). First of all, it should be noted that FC terms (blue bars on the diagrams in Figs 1 and 2) by far dominate over the overall noncontact contributions and are of the same sign as the total values of the coupling constants (red bars on the diagram) for all considered types of spin–spin coupling constants. For 1 J(Se,C), 1 J(Se,N), and 1 J(Se,P), the FC terms are even larger than the total values of J (the same for reduced couplings K). For example, the relative FC contribution to 1 J(Se,C) totals to as much as about 170%, so that the excessive 70% are compensated by the contribution of the overall noncontact terms of opposite sign. The only exception is 1 J(Se,F) with the FC contribution of only 25% and the overall contribution of PSO + DSO + SD = 75%. Basically, the individual contributions of PSO, DSO, and SD terms are small (
Revised: 29 June 2014
Accepted: 1 July 2014
Published online in Wiley Online Library: 15 July 2014
(wileyonlinelibrary.com) DOI 10.1002/mrc.4112
Relativistic effects in the one-bond spin–spin coupling constants involving selenium Irina L. Rusakova, Yury Yu. Rusakov and Leonid B. Krivdin* One-bond spin–spin coupling constants involving selenium of seven different types, 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31 P, 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 © 2014 John Wiley & Sons, Ltd. Keywords: 77Se NMR; spin–spin coupling constant; SOPPA(CCSD); relativistic effects; selenides
Introduction
500
Relativistic effects including electron spin–orbit coupling (the interaction of the spin magnetic moment of an electron with the magnetic field induced by its own orbital motion) and scalar effects – Darwin term (relativistic fluctuation of an electron about its mean position) and mass-velocity corrections (relativistic increase in the mass of an electron with its velocity approaching the speed of light) resulting in the ‘relativistic contraction’ of the s-shells and inner p-shells and in the ‘relativistic expansion’ of the d-shells and f-shells – are of major importance in the calculation of the second-order molecular properties for molecular systems involving ‘heavy’ atoms.[1] In line with a general breakthrough in theory and computation of nuclear magnetic resonance parameters,[2] relativistic calculations of spin–spin coupling constants, in particular those at the scalar and spin–orbit zeroth order regular approximation[3] levels have now become popular, see salient review by Autschbach.[4] As an example, the isotropic average and the anisotropies of 77Se-13C and 77 Se-77Se spin–spin coupling tensors in carbon diselenide were derived by Jokisaari and Autschbach[5] from the zeroth order regular approximation and density functional theory (DFT) calculations in comparison with experimental nuclear magnetic resonance data in liquid crystalline solutions. In continuation of our recent relativistic calculations of the one-bond, geminal, and vicinal spin–spin coupling constants silicon–carbon,[6] selenium–carbon[7] and tellurium–hydrogen,[8] which demonstrated a noticeable contribution (up to 30%) of relativistic effects in their total values, in this paper, we report the results on the contribution of relativistic effects to the onebond spin–spin coupling constants involving selenium of seven different types evaluated within the full four-component relativistic Dirac’s method. In other words, we have investigated the ‘relative relativism’ of the one-bond spin–spin coupling constants 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31P, and 77Se.
Magn. Reson. Chem. 2014, 52, 500–510
In a number of papers dealing with relativistic calculations of spin–spin coupling constants involving or across IVa, Va, VIa, and VIIa group elements in simple hydrides, XH4 (X = C, Si, Ge, Sn, Pb),[9] XH3 (X = N, P, As. Sb, Bi),[10] XH2 (X = O, S, Se, Te, Po), 9g–11 and XH (X = F, Cl, Br, I),[12] together with three our papers cited in the previous text,[6–8] it has been demonstrated that relativistic effects could not only substantially contribute but even dominate spin–spin coupling mechanism involving or propagating through ‘heavy’ nuclei. For example, full four-component relativistic random phase approximation (RPA) calculations of 1 J(X,H) in XH4 (X = C, Si, Ge, Sn, Pb) series showed that very small relativistic effects are observed in methane and silane while for germane, stannane, and plumbane, the relativistic coupling is increased by accordingly 12%, 37%, and 156% mainly due to the scalar relativistic contraction of s-shells.[9a] Alternatively, in some other papers, relativistic effects in spin–spin coupling were interpreted mainly in terms of the dominant spin–orbit interaction.[9b,9c] It was thus a challenging task and a prime goal of the present study to evaluate the relative contributions of a total relativistic effect in the values of different one-bond spin–spin coupling constants involving selenium and to estimate the ratio of scalar relativistic contraction and spin–orbit interaction in the total value of relativistic effect in each particular case.
Results and Discussion To evaluate the contribution of relativistic effects in the values of 1 J(Se,X), we first performed the nonrelativistic calculation of these * Correspondence to: Leonid Krivdin, Siberian Branch of the Russian Academy of Sciences, A. E. Favorsky Irkutsk Institute of Chemistry, Favorsky St. 1, 664033 Irkutsk, Russia. E-mail: krivdin_offi[email protected] Siberian Branch of the Russian Academy of Sciences, A. E. Favorsky Irkutsk Institute of Chemistry, Favorsky St. 1, 664033, Irkutsk, Russia
Copyright © 2014 John Wiley & Sons, Ltd.
Relativistic effects in the one-bond spin–spin coupling constants involving selenium coupling constants in the model series 1–14 within the secondorder polarization propagator approximation (SOPPA)[13] in combination with coupled cluster single and double (CCSD) excitation model,[14] known as SOPPA(CCSD),[15] one of the most reliable ab initio methods for the second-order molecular properties.[16] On the other hand, relativistic corrections to these basic ‘nonrelativistic’ SOPPA(CCSD) coupling constants were calculated within the fourcomponent relativistic Dirac–Coulomb method at the DFT-PBE0 level, that is, within the DFT framework using the hybrid functional of Perdew, Burke, and Ernzerhof with a predetermined amount of exact exchange (PBE0).[17,18] Relative contributions of total relativistic effects together with those separated into scalar and spin–orbit terms evaluated at both DFT-PBE0 and RPA[19] levels are discussed herewith with respect to the total ‘relativistically corrected’ SOPPA (CCSD) values of 1 J(Se,X). Nonrelativistic results All nonrelativistic calculations of 1 J(Se,X) in the series of 1–14 were performed at the SOPPA(CCSD) level, which nowadays is one of the most accurate pure ab initio methods of the linear response function family for the calculation of spin–spin coupling constants in the medium-sized organic and elementoorganic molecules, especially when it is used with Sauer’s basis sets aug-cc-pVTZJ[20] of triple zeta quality containing tight s-functions optimized for the calculation of the Fermi contact (FC) contribution. Traditionally, in line with the locally dense basis set scheme,[21] we used Sauer’s basis set for the coupled nuclei leaving the rest of molecule being specified with much more economical Dunning’s basis set of double zeta quality, cc-pVDZ.[22] Compiled in Tables 1 and 2 are the results of the present calculations of seven different types of regular and reduced spin–spin coupling constants involving selenium, 1 J(Se,X) and 1 K(Se,X), in 14 compounds performed at the SOPPA(CCSD) level. Four basic Ramsey’s coupling contributions, namely, FC, spin-dipolar (SD), diamagnetic spin–orbital (DSO), and paramagnetic spin–orbital
(PSO) terms were taken into account to contribute to the total values of 1 J(Se,X), X = 1H, 13C, 15 N, 19 F, 29Si, 31P, and 77Se. Calculated coupling constants 1 J(Se,X) were compared with available experimental data taken from different sources for compounds 1,[23] 2,[24] 3,[25] 4,[26] 5,[27] 6 and 7,[28] 8,[29] 9,[30] 10,[31] 11, 12 and 13,[32] and 14.[33] Relative contributions of the individual coupling terms to the total calculated values of 1 J(Se,X) and 1 K(Se,X) for the most representative compounds of this series (1–4, 8, 9, and 11) covering different types of spin–spin coupling constants involving selenium are presented on the diagrams in Figs 1 and 2. Not shown on the diagrams are the results for 1 J(Se,Se) and 1 K(Se,Se) concurrently involving two ‘relativistic’ selenium nuclei, which are discussed separately (see in the succeeding text). First of all, it should be noted that FC terms (blue bars on the diagrams in Figs 1 and 2) by far dominate over the overall noncontact contributions and are of the same sign as the total values of the coupling constants (red bars on the diagram) for all considered types of spin–spin coupling constants. For 1 J(Se,C), 1 J(Se,N), and 1 J(Se,P), the FC terms are even larger than the total values of J (the same for reduced couplings K). For example, the relative FC contribution to 1 J(Se,C) totals to as much as about 170%, so that the excessive 70% are compensated by the contribution of the overall noncontact terms of opposite sign. The only exception is 1 J(Se,F) with the FC contribution of only 25% and the overall contribution of PSO + DSO + SD = 75%. Basically, the individual contributions of PSO, DSO, and SD terms are small (
