Relativistic Environmental Effects in 29Si NMR Chemical Shifts of

Article pubs.acs.org/JPCA

Relativistic Environmental Effects in 29Si NMR Chemical Shifts of Halosilanes: Light Nucleus, Heavy Environment Sergey V. Fedorov, Yury Yu. Rusakov, and Leonid B. Krivdin* A.E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia ABSTRACT: Relativistic calculations of 29Si NMR shielding constants (chemical shifts) in the series of halosilanes SiXnH4‑n (X = F, Cl, Br and I) are performed within a full fourcomponent relativistic Dirac’s scheme using relativistic Dyall’s basis sets. Three different theoretical levels are tested in the computation of 29Si 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.

■

INTRODUCTION A vast amount of structural studies of organosilicon compounds by means of 29Si NMR is presented in the literature.1,2 Nowadays, within the progress of theory of magnetic resonance parameters derived from a spin-Hamiltonian as the linear response functions,3−5 the question of the high-accuracy highlevel computation of 29Si NMR magnetic resonance parameters arises. In continuation of our previous results on the computation of 29Si NMR chemical shifts,6−9 and 29Si−1H and 29Si−13C spin−spin coupling constants,10−13 in this paper we investigate the “environmental” relativistic effects of halogens in 29Si NMR shielding constants of halosilanes. The manifestation of indirect (secondary) relativistic effects in shielding constants (chemical shifts) of “light” nuclei induced by “heavy” environment known as the “Heavy Atom on Light Atom” (HALA) effect14,15 is well documented for a number of systems, such as transition-metal complexes,16 organomercury hydrides,17 organomercury compounds and halogen derivatives,18 halogenides of the main IVth group elements,19 and many others. A good number of papers report on the HALA effect in silanes with silicon treated as a “light” nucleus. In the early paper by Jaszuński and Ruud,20 the self-consistent field and multiconfigurational self-consistent field wave functions were applied to calculate shielding constants in the XH4 hydrides, X = C, Si, Ge, Sn, and Pb with the relativistic corrections to the nonrelativistic shielding constants included to the fourth order of the fine structure constant. It was found that even for unsubstituted silane (providing no HALA effect) relativistic corrections are essential to improve the values of 29 Si NMR absolute shielding constants.20 In two consequent publications21,22 dealing with the gas-phase NMR experiment extrapolated to zero density in combination with ab initio calculations of shielding constants to evaluate nuclear magnetic © XXXX American Chemical Society

dipole moments, it was demonstrated that taking into account relativistic corrections noticeably improves the absolute shielding scale for 29Si nucleus. In line with this finding, in our later publication6 based on the two-component relativistic ZORA (Zeroth Order Regular Approximation)23−25 calculations, we estimated a relatively small but far from being neglected primary relativistic effect of about 3% in the total shielding constant of silicon coated in “light” environment. In two recent papers by Aucar and coauthors,19,26 the HALA relativistic effects in halogenides of the main IVth group elements were treated at the uncorrelated RPA (Random Phase Approximation)27−33 level. In the first paper,26 the absolute nuclear magnetic shielding of tetramethylsilane (TMS), used as a reference compound for both experimental measurement of 29Si NMR chemical shifts and for converting calculated shielding constants into NMR chemical shifts scale, was found based on the experimental chemical shifts and accurate nuclear magnetic shielding calculations at the relativistic RPA level. The reported value of σTMS = 421.28 ± 29.33 ppm26 was essentially larger than that determined ealier from spin-rotation constants (368.5 ± 10 ppm).34 In the second paper, Aucar et al.19 employed the linear response elimination of small components (LRESC) formalism35,36 to calculate shielding constants in the series of MH4‑nYn (n = 0−4; M = Si, Ge, Sn, and Y = H, F, Cl, Br, I) and to learn whether including the salient relativistic correction terms is sufficient to quantitatively reproduce the full relativistic value. It was found that shielding constants in MH4−nYn series increases with the number of heavy halogen substituents Received: March 10, 2015 Revised: May 5, 2015

A

DOI: 10.1021/acs.jpca.5b02337 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

determined the choice of the basis sets employed in this study, namely, the relativistic basis sets introduced by Dyall,43−50 who derived his relativistically optimized basis sets from the nonrelativistic ones within the framework of a four-component Dirac−Hartree−Fock formalism using Gaussian nuclear charge distribution model.51,52 For the sake of consistency, the same uncontracted Dyall’s basis sets were used not only in all relativistic calculations, either at the RPA or the DFT level, but also in all nonrelativistic calculations as well. Both relativistic and nonrelativistic calculations of 29Si NMR shielding constants were carried out within a framework of a Gauge Including Atomic Orbitals scheme (GIAO).53−56 At either nonrelativistic or relativistic DFT levels, we employed NMR-oriented and well approved in the calculations of chemical shifts generalized gradient functional of Keal and Tozer with the gradientcorrected exchange and correlation terms (KT3).57 Herewith, we examined four most representative types of relativistic Dyall’s basis sets, namely, valence dyall.vXz, diffuse valence dyall.avXz, core valence dyall.cvXz, and diffuse core valence dyall.acvXz, X = 2, 3, and 4. The uncontracted Dyall’s basis sets were placed on all atoms in the calculation of 29Si NMR isotropic absolute shielding constants of tetrafluorosilane 5 and iodosilane 14 at the four-component relativistic RPA and DFT levels. We chose tetrafluorosilane as a benchmark for this study taking into account two points of its advantages: first, this molecular system is small enough for the calculations of the second-order molecular property with huge quadruple-ζ Dyall’s basis sets, and, second, tetrafluorosilane is a very rigorous test due to its four fluorine atoms providing strong correlation effects. On the other hand, iodosilane is “the most relativistic” computationally achievable molecular system for the four-component relativistic calculations using the quadruple-ζ Dyall’s basis sets. The results are compiled in Table 1 and illustrated in Figures 1 and 2, so that one can see that all four types of Dyall’s basis sets are converged to Complete Basis Set (CBS) limit58−61 at the triple-ζ quality at the four-component relativistic RPA and DFT levels for both “nonrelativistic” tetrafluorosilane and “relativistic” iodosilane. This fact encouraged us to use in all our further calculations of 29Si NMR shielding constants in the whole series of halosilanes 1−17 three types of Dyall’s basis sets of triple-ζ quality. Namely, we used valence dyall.v3z, diffuse valence dyall.av3z, and core valence dyall.cvXz basis sets, in particular, to estimate the effect of diffuse and core functions. The result is that the effect of adding diffuse functions to the valence dyall.vXz basis sets vanishes starting from triple-ζ level while adding core functions does not damp down even at quadruple-ζ level, as can be seen in Figures 1 and 2.

(and, accordingly, with their weights). However, the pattern of σ(M) generally did not not exhibit the normal halogen dependence behavior observed in similar molecular systems containing carbon atoms. Also, they analyzed each relativistic correction evaluated by the LRESC method and split them into core-dependent and ligand-dependent contributions, so that it became possible to analyze electronic mechanisms involved in the different relativistic effects and in the total relativistic values of the main IVth group elements, and silicon in particular. Herewith, we address relativistic effects in 29Si NMR shielding constants (chemical shifts) in the series of 16 halosilanes SiXnH4‑n (X = F, Cl, Br, and I) benchmarked to a halogen-free parent silane, SiH4, within a full four-component relativistic Dirac’s scheme at both RPA and DFT levels taking into account solvent effects, in particular, to estimate the importance of electronic correlation and solvent effects. Also, we analyze the performance of different Dyall’s relativistic basis sets optimized within the framework of the four-component Dirac−Hartree− Fock formalism used in this paper for the relativistic calculations of 29Si NMR chemical shifts.

■

COMPUTATIONAL DETAILS Geometry optimizations of 1−17 and tetramethylsilane (TMS) used as a standard for converting calculated shielding constants into 29Si NMR chemical shift scale were performed at the MP2/6-311G(d,p) level with the GAMESS code.37 Enumeration of the compounds under investigation is given in Scheme 1. Scheme 1. List of Compounds

All nonrelativistic calculations of 29Si NMR isotropic magnetic absolute shielding constants were carried out with DALTON package38 and/or GAUSSIAN 09 program39 while all relativistic calculations were performed within a full fourcomponent relativistic Dirac’s scheme using the DIRAC program code.40 In both nonrelativistic and relativistic calculations of 29Si NMR shielding constants, the same uncontracted relativistic Dyall’s basis sets were used throughout. Calculated 29Si NMR absolute shielding constants were converted to 29Si NMR chemical shifts scale referenced to tetramethylsilane, TMS (δ, ppm), using the equation δ = (σTMS − σ)/(1 × 10−6σTMS), as recommended by IUPAC,41,42 where σ (ppm) and σTMS (ppm) are the 29Si NMR isotropic absolute shielding constants of, accordingly, a compound under consideration and TMS calculated at the same level of theory. In all geometry optimizations and calculations of 29Si NMR chemical shifts, solvent effects were taken into account within a Supermolecule Solvation Scheme, as described in the text. Basis Sets Convergence. In this paper, all relativistic calculations of 29Si NMR shielding constants were performed using a full four-component relativistic Dirac’s scheme which

■

RESULTS AND DISCUSSION Relativistic Effects. In general, relativistic effects in the values of the second-order magnetic properties (NMR shielding constants and spin−spin coupling constants) include 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 massvelocity corrections (relativistic increase in the mass of an electron with its velocity approaching the speed of light), with the latter resulting in the “relativistic contraction” of s- and inner p-shells and in the “relativistic expansion” of d- and f-shells which strongly affects the values of NMR parameters.62−66 B


Article


Table 1. 29Si NMR Absolute Shielding Constant (ppm) of Tetrafluorosilane 5 and Iodosilane 14 Calculated at the FourComponent Relativistic RPA and DFT Levels Using Different Dyall’s Basis Sets tetrafluorosilane

iodosilane

basis set

# AO

GIAO-RPA

GIAO-DFT

# AO

GIAO-RPA

GIAO-DFT

dyall.v2z dyall.v3z dyall.v4z dyall.av2z dyall.av3z dyall.av4z dyall.cv2z dyall.cv3z dyall.cv4z dyall.acv2z dyall.acv3z dyall.acv4z

623 1071 1749 788 1391 2299 661 1266 2286 826 1586 2836

536.7 531.6 529.3 541.6 531.8 529.3 526.4 525.1 525.1 531.6 525.5 525.2

484.9 481.4 480.2 489.7 482.3 480.4 477.3 474.7 475.1 482.0 475.7 475.4

692 1114 1682 800 1341 2094 792 1372 2192 900 1599 2604

507.3 492.4 488.8 507.1 492.6 488.9 489.1 483.3 483.1 489.1 483.6 483.4

489.4 475.1 472.5 491.9 473.0 472.3 471.1 465.0 465.4 473.0 461.1 466.0

Figure 1. 29Si NMR shielding constant convergence to the CBS limit with a zeta quality of the Dyall’s basis sets for tetrafluorosilane 5 within a full four-component relativistic Dirac’s scheme at the RPA and DFT levels. Basis sets tested: valence dyall.vXz, diffuse valence dyall.avXz, core valence dyall.cvXz, and diffuse core valence dyall.acvXz (X = 2, 3, and 4).

Figure 2. 29Si NMR shielding constant convergence to the CBS limit with a zeta quality of the Dyall’s basis sets for iodosilane 14 within a full four-component relativistic Dirac’s scheme at the RPA and DFT levels. Basis sets tested: valence dyall.vXz, diffuse valence dyall.avXz, core valence dyall.cvXz, and diffuse core valence dyall.acvXz (X = 2, 3, and 4).

“Primary” relativistic effects are very well pronounced in NMR shielding constants of “heavy” nuclei starting with fourth period and rapidly increasing with atomic number, but considerable “secondary” relativistic effects are also to be expected in the shielding constants (chemical shifts) of “light” nuclei in “heavy”

chemical environment as well (HALA effect). The latter is the case of the studied series of halosilanes where the thirdperiod silicon is surrounded by the halogen atoms going from the second-period light fluorine to the fifth-period heavy iodine. C


Article


Table 2. 29Si NMR Absolute Shielding Constants and Their Relativistic Contributions Calculated at the Four-Component Relativistic GIAO-DFT-KT3 Level Using Different Dyall’s Basis Sets of Triple-Zeta Quality in the Series of 1−17a dyall.v3z

dyall.av3z

dyall.cv3z

compd

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

482.8 384.7 388.2 440.6 481.4 399.4 360.6 362.5 397.9 436.4 418.7 442.6 514.4 475.1 502.9 614.1 846.5

470.1 371.6 374.2 425.3 465.2 383.9 339.5 328.1 336.0 408.0 362.0 335.8 324.0 421.0 366.0 321.5 293.4

12.7 13.1 14.0 15.3 16.2 15.5 21.1 34.4 61.9 28.4 56.7 106.8 190.4 54.1 136.9 292.6 553.1

2.7 3.5 3.7 3.6 3.5 4.0 6.2 10.5 18.4 7.0 15.7 31.8 58.8 12.9 37.4 91.0 188.5

483.7 385.7 389.3 441.7 482.3 400.2 361.4 363.3 398.6 436.8 419.7 443.5 514.7 473.0 503.6 614.6 844.3

470.5 372.2 374.9 426.0 465.7 384.3 339.9 328.5 336.2 408.5 362.5 336.2 324.2 421.4 366.4 321.7 293.3

13.2 13.5 14.4 15.7 16.6 15.9 21.5 34.7 62.4 28.3 57.2 107.3 190.5 51.6 137.2 292.9 551.0

2.8 3.6 3.8 3.7 3.6 4.1 6.3 10.6 18.6 6.9 15.8 31.9 58.8 12.2 37.4 91.0 187.9

473.1 375.5 380.4 433.8 474.8 391.0 353.6 354.0 392.8 426.4 408.9 433.2 505.2 464.9 493.2 604.2 835.7

460.3 362.4 366.3 418.5 458.6 375.4 332.5 322.4 331.1 397.9 352.5 327.2 316.2 411.3 357.4 314.0 286.9

12.8 13.1 14.1 15.3 16.2 15.6 21.1 31.6 61.7 28.5 56.4 106.0 189.0 53.6 135.8 290.2 548.8

2.8 3.6 3.8 3.7 3.5 4.2 6.4 9.8 18.6 7.2 16.0 32.4 59.8 13.0 38.0 92.4 191.3

All shielding constants and their relativistic contributions are given in ppm. Relativistic contributions, Δσrel, are evaluated as the difference between total DFT-KT3 relativistic value and its nonrelativistic counterpart. a

Table 3. 29Si NMR Absolute Shielding Constants and Their Relativistic Contributions Calculated at the Four-Component Relativistic GIAO-RPA Level Using Different Dyall’s Basis Sets of Triple-Zeta Quality in the Series of 1−17a dyall.v3z

dyall.av3z

dyall.cv3z

compd

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

496.5 425.2 437.5 489.3 531.5 434.0 409.6 409.4 423.4 458.9 444.9 456.4 493.8 492.4 518.6 599.8 748.6

482.7 410.8 422.0 472.8 514.7 417.5 387.5 377.6 375.3 433.7 397.6 371.6 351.0 445.4 403.7 361.8 320.3

13.8 14.4 15.5 16.5 16.8 16.5 22.1 31.8 48.1 25.2 47.3 84.8 142.8 47.0 114.9 238.0 428.3

2.9 3.5 3.7 3.5 3.3 4.0 5.7 8.4 12.8 5.8 11.9 22.8 40.7 10.6 28.5 65.8 133.7

496.8 425.6 437.9 489.8 531.8 434.2 409.9 409.7 424.1 459.1 445.1 456.7 494.2 492.6 518.9 600.2 749.6

482.6 410.9 422.2 473.0 514.8 417.4 387.5 377.8 375.6 433.6 397.6 371.6 350.9 445.3 403.7 361.8 320.3

14.2 14.7 15.8 16.8 17.0 16.8 22.3 31.9 48.6 25.5 47.6 85.1 143.3 47.2 115.2 238.4 429.3

2.9 3.6 3.7 3.6 3.3 4.0 5.8 8.4 12.9 5.9 11.9 22.9 40.8 10.6 28.5 65.9 134.0

487.0 416.7 429.9 482.5 525.1 425.9 402.6 403.3 418.0 449.5 436.0 447.8 485.5 483.3 510.0 591.1 739.6

473.1 402.2 414.3 465.9 508.2 409.3 380.4 371.5 370.0 424.2 388.7 363.3 343.2 436.1 395.3 354.3 313.6

14.0 14.5 15.6 16.6 16.9 16.6 22.1 31.8 48.0 25.3 47.3 84.5 142.3 47.1 114.7 236.8 425.9

2.9 3.6 3.8 3.6 3.3 4.1 5.8 8.6 13.0 6.0 12.2 23.3 41.5 10.8 29.0 66.8 135.8

All shielding constants and their relativistic contributions are given in ppm. Relativistic contributions, Δσrel, are evaluated as the difference between total RPA relativistic value and its nonrelativistic counterpart. a

constants rapidly increase with the total atomic number of the atoms forming the chemical environment of silicon (Figure 3) and with the number of halogens attached to silicon (Figure 4), in line with earlier results by Aucar and co-workers.19,26 The secondary relativistic effect of fluorine is next to negligible. Indeed, even in tetrafluorosilane 5 with four fluorine atoms attached to silicon, relativistic contribution to 29Si NMR absolute shielding constant amounts to only 16−17 ppm (about 4% of the nonrelativistic counterpart) as compared to 13−14 ppm (about 3%) in the fluorine-free silane 1, the latter providing only primary relativistic effect of silicon. Chlorine atoms provide more noticeable secondary relativistic effect amounting to some 50 ppm (about 14%) in tetrachlorosilane 9.

Of special interest in this study was tetraiodosilane 17 as a remarkable computational challenge for the four-component relativistic calculations of the second-order magnetic property in a huge electronic system and, on the other hand, for a molecule with four fifth-period heavy iodines with strong secondary relativistic effects on the shielding constant of the third-period silicon with available experimental benchmark provided. Given in Tables 2−4 are the “environmental” secondary relativistic effects of halogens evaluated as the relativistic contributions to 29Si NMR absolute shielding constants of 1−17 at the relativistic GIAO-DFT-KT3 and GIAO-RPA levels within a full four-component relativistic Dirac’s scheme. As one can see from these data, relativistic effects in 29Si NMR shielding D


Article


Table 4. 29Si NMR Absolute Shielding Constants Calculated at the Nonrelativistic GIAO-MP2 Level and Corresponding Relativistic Contributions Calculated at the Four-Component Relativistic GIAO-RPA Level Using Different Dyall’s Basis Sets of Triple-Zeta Quality in the Series of 1−17a dyall.v3z

dyall.av3z

dyall.cv3z

compd

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

σtotal

σnr

Δσrel

%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

495.6 404.3 377.6 448.3 489.7 419.0 384.2 379.8 394.9 447.3 425.3 433.7 471.8 483.6 501.1 577.2 726.2

481.8 389.9 362.1 431.8 472.9 402.5 362.1 348.0 346.8 422.1 378.0 348.9 329.0 436.6 386.2 339.2 297.9

13.8 14.4 15.5 16.5 16.8 16.5 22.1 31.8 48.1 25.2 47.3 84.8 142.8 47.0 114.9 238.0 428.3

2.9 3.7 4.3 3.8 3.6 4.1 6.1 9.1 13.9 6.0 12.5 24.3 43.4 10.8 29.8 70.2 143.8

496.3 404.6 396.2 462.2 502.9 419.3 384.8 380.8 396.6 447.8 426.0 434.5 473.0 483.9 501.6 577.7 727.3

482.1 389.9 380.4 445.4 485.9 402.5 362.5 348.9 348.0 422.3 378.4 349.4 329.7 436.7 386.4 339.3 298.0

14.2 14.7 15.8 16.8 17.0 16.8 22.3 31.9 48.6 25.5 47.6 85.1 143.3 47.2 115.2 238.4 429.3

2.9 3.8 4.1 3.8 3.5 4.2 6.2 9.1 14.0 6.0 12.6 24.3 43.5 10.8 29.8 70.3 144.1

480.8 388.6 395.4 448.4 489.8 403.8 369.4 365.8 381.2 431.0 408.5 416.6 454.8 466.9 483.0 556.9 703.7

466.8 374.1 379.8 431.8 472.9 387.2 347.3 334.0 333.2 405.7 361.2 332.1 312.5 419.8 368.3 320.1 277.8

14.0 14.5 15.6 16.6 16.9 16.6 22.1 31.8 48.0 25.3 47.3 84.5 142.3 47.1 114.7 236.8 425.9

3.0 3.9 4.1 3.8 3.6 4.3 6.4 9.5 14.4 6.2 13.1 25.4 45.5 11.2 31.1 74.0 153.3

All shielding constants and their relativistic contributions are given in ppm. Relativistic contributions, Δσrel, are evaluated as the difference between total RPA relativistic value and its nonrelativistic counterpart. a

DFT and RPA results, originating in the manifestation of correlation effects taken into account at the DFT level, is too much essential to be neglected, especially when comparing calculations with experiment, as discussed later. A general conclusion following from the present study of relativistic effects in 29Si NMR absolute shielding constants of halosilanes is that they are next to negligible (up to several ppm) in fluorosilanes, noticeably larger (up to several dozens of ppm) in chlorosilanes, much larger (up to 200 ppm) in bromosilanes and remarkably large (several hundreds of ppm) in iodosilanes. Thus, it follows that nonrelativistic calculations of 29Si NMR absolute shielding constants (chemical shifts) are adequate for fluorosilanes, admissible for chlorosilanes, and absolutely inadequate and unacceptable for silanes bearing at least one atom of either bromine or iodine attached to silicon. For the latter, only relativistic level is appropriate, better than that within a full four-component relativistic Dirac’s scheme. Solvent Effects. All calculations dealing with evaluation of relativistic effects in 29Si NMR absolute shielding constants of halosilanes were performed herewith in gas phase. It was also interesting to estimate the importance of solvents effects, especially in view of the further comparison with experiment. Here, we evaluated the solvent effect of chloroform (all experimental data discussed later refer to chloroform) within a Supermolecule Solvation Model (SSM) with one molecule of solvent (chloroform) placed into calculation space in an explicit way and taking into account the bulk effect of the solvent within Polarizable Continuum Model (PCM) using the Integral Equation Formalism (IEF), IEF-PCM.67,68 We used SSM to describe solvent effects in the series of 1−17 because it is well-known that, within the PCM scheme, the solvent effect is simulated as an apparent charge distribution spread on the cavity surface not taking into account the solute−solvent interactions at short distances, so that all solvent effects calculated within the PCM scheme are constrained not to take into account any specific solvation effects. Optimized structures of the solvate supermolecules of halosilanes used in the

Figure 3. Relativistic contribution to 29Si NMR shielding constant in the series of 1−17 as a function of the total atomic number of the environment calculated at the RPA and DFT levels within a full fourcomponent relativistic Dirac’s scheme using dyall.av3z basis set.

In more “heavy” tetrabromosilane 13, relativistic contribution totals to about 200 ppm (more than 40%), while in tetraiodosilane it exceeds 500 ppm (almost 150%)! It is seen in Figure 4 that relativistic contribution rapidly increases with the number of halogens, and noteworthy, this increase is not linear. This tendency is most pronounced in the iodosilanes series: at the GIAO−DFT-KT3/dyall.av3z level, relativistic contribution of the first iodine atom is about 52 ppm, that of the second iodine is 85 ppm, that of the third iodine is 156 ppm, and that of the fourth one amounts to as much as 258 ppm (see Table 2). Also it should be noted that DFT results give larger relativistic effects as compared to the RPA results which is most pronounced in iodosilanes. For example, for the most rigorous tetraiodosilane 17 GIAO-DFT-KT3/dyall.av3z calculations give relativistic contribution of 551 ppm as compared to the GIAO-RPA/dyall.av3z result of 429 ppm. This difference in the E


Article


NMR chemical shifts were measured in chloroform elsewhere, see data for 1,69 2−4, 11−12, 5, 6−7, 9, 14−16,70,71 10,72 13, and 17,73 referenced to TMS used as internal standard. Our four-component calculations at the GIAI-DFT-KT3/dyall.av3z level give the absolute shielding constant for tetramethylsilane σTMS = 381.7 ppm, in very good agreement with that of Jameson’s value (368.5 ± 10 ppm)34 determined from the spin-rotational constants as compared to that of Aucar (421.28 ± 29.33 ppm)26 derived from the four component RPA calculations. Actually, we used three different theoretical levels to compute 29Si NMR chemical shifts of 1−17 in comparison with experiment, namely, four-component relativistic GIAODFT-KT3 (Table 6), four-component relativistic GIAO-RPA (Table 7), and a hybrid scheme of nonrelativistic GIAO-MP2 with taking into account relativistic corrections at the fourcomponent relativistic GIAO-RPA level (Table 8). In each case, we applied three different relativistic Dyall’s basis sets: valence dyall.v3z, diffuse valence dyall.av3z, and core valence dyall.cv3z taking into account solvent effects (chloroform) within supermolecule solvation model at the nonrelativistic GIAO-DFTKT3 level, as described earlier. First of all, it should be emphasized that taking into account relativistic effects dramatically decreases mean average error (MAE) of 29Si NMR chemical shifts calculated at any of all three tested theoretical levels versus experiment, as illustrated in Figure 6. It is seen that MAE decreases from about 75 to about 20−25 ppm for the four-component relativistic GIAO-DFT-KT3 method and to about 10−15 ppm for the four-component relativistic GIAO-RPA method and for a hybrid scheme of nonrelativistic GIAO-MP2 combined with four-component relativistic GIAO-RPA. The importance of relativistic effects is also illustrated in Figure 7 showing the dependence of 29Si NMR chemical shifts of iodosilanes SiInH4−n as a function of the number of iodine atoms attached to silicon. Indeed, nonrelativistic GIAO-MP2 calculations increase δSi from −60 to +80 ppm when going from monoiodosilane to tetraiodosilane, while experimental shifts decrease from −83 to −352 ppm thus giving the difference of 23 ppm for monoiodisilane, 90 ppm for diiodosilane, 220 ppm for triiodosilane, and 432 ppm (!) for the most “relativistic” tetraiodosilane. Taking into account four-component GIAORPA relativistic corrections to nonrelativistic GIAO-MP2 results gives a hybrid nonrelativistic GIAO-MP2 with relativistic GIAORPA curve perfectly corresponding with experiment. It is seen in Figure 8 that relativistic pure nonempirical wave function methods perform much better as compared to relativistic DFT methods with any of three Dyall’s basis sets. Either diffuse or core functions in Dyall’s diffuse valence basis sets show no effect as compared to the valence ones, and taking into account solvent effects (chloroform) also do not affect the accuracy (MAE) of any of the three tested methods. The best result of MAE = 8.5 ppm in the range of 400 ppm is achieved with GIAO-RPA/dyall.cv3z, as illustrated in Figure 9. Thus, for the computation of 29Si NMR chemical shifts in silicon compounds containing heavy elements (of the fourth period and higher), we strongly recommend relativistic methods or a hybrid schemes employing nonrelativistic calculations with taking into account relativistic effects. All relativistic calculations are to be performed with relativistic basis sets like those of Dyall optimized for the full four-component relativistic calculations. It is noteworthy that pure nonempirical wave function methods like RPA at the four-component relativistic level perform much

Figure 4. Relativistic contribution to 29Si NMR shielding constant as a function of the number of halogen atoms attached to silicon in SiXnH4−n (X = F, Cl, Br, I) series calculated at the RPA and DFT levels within a full four-component relativistic Dirac’s scheme using dyall.av3z basis set.

nonrelativistic GIAO-DFT-KT3 calculations of their 29Si NMR absolute shielding constants (Table 5) are shown in Figure 5. It is seen that solvent corrections to 29Si NMR shielding constants of 1−17 are negative (deshielding) being in average of about 3−5 ppm and slightly decreasing in absolute value with the number of halogen atoms attached to silicon. Thus, for monohalosilanes, solvent corrections range from −4 to −11 ppm while for tetrahalosilanes they do not exceed 2 ppm in absolute value. The largest solvent corrections are observed in fluorosilanes reaching −11.4 ppm in monofluorosilane 2. Generally, solvent corrections are essentially smaller as compared to relativistic corrections, especially in bromo- and iodosilanes providing dramatically large relativistic effects. Experimental Benchmark. To compare the results of our calculations with experiment, all calculated absolute shielding constants of halosilanes 1−17 were converted into 29Si NMR chemical shifts δ-scale referenced to tetramethylsilane (TMS) calculated at the same level of theory in each particular case, as described in Computational Details. All experimental 29Si F


Article


Table 5. Solvent Corrections (Chloroform) to 29Si NMR Absolute Shielding Constants (Δσsolv) of 1−17 Calculated within a Supermolecule Solvation Model (SSM) at the Nonrelativistic GIAO-DFT-KT3 Level Using Different Dyall’s Basis Sets of Triple-Zeta Qualitya σ (gas phase), ppm

a

σ (solvent, SSM), ppm

Δσsolv, ppm

compd

dyall.v3z

dyall.av3z

dyall.cv3z

dyall.v3z

dyall.av3z

dyall.cv3z

dyall.v3z

dyall.av3z

dyall.cv3z

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

470.1 371.6 374.2 425.3 465.2 383.9 339.5 328.1 336.0 408.0 362.0 335.8 324.0 421.0 366.0 321.5 293.4

470.5 372.2 374.9 426.0 465.7 384.3 339.9 328.5 336.2 408.5 362.5 336.2 324.2 421.4 366.4 321.7 293.3

460.3 362.4 366.3 418.5 458.6 375.4 332.5 322.4 331.1 397.9 352.5 327.2 316.2 411.3 357.4 314.0 286.9

466.3 360.2 366.3 423.3 467.3 376.7 333.0 324.4 335.6 404.3 357.8 332.7 324.0 415.8 361.7 316.3 291.8

466.6 360.7 366.9 424.0 467.8 377.0 333.5 324.9 336.0 404.6 358.2 333.2 324.2 416.0 362.0 316.6 291.8

456.5 351.4 358.7 416.6 460.7 368.6 326.3 318.8 330.8 394.4 348.5 324.2 316.1 406.3 353.3 309.0 285.4

−3.8 −11.4 −7.9 −2.0 2.1 −7.2 −6.5 −3.7 −0.4 −3.7 −4.2 −3.1 0.0 −5.2 −4.3 −5.2 −1.6

−3.9 −11.5 −8.0 −2.0 2.1 −7.3 −6.4 −3.6 −0.2 −3.9 −4.3 −3.0 0.0 −5.4 −4.4 −5.1 −1.5

−3.8 −11.0 −7.6 −1.9 2.1 −6.8 −6.2 −3.6 −0.3 −3.5 −4.0 −3.0 0.1 −5.0 −4.1 −5.0 −1.5

Solvent corrections to shielding constants (Δσsolv) are determined as the difference of shielding constants calculated in a solvent and in a gas phase.

Figure 5. Solvate supermolecules of halosilanes 2−17 in polarizable continuum medium (chloroform) optimized at the MP2/6-311G(d,p) level. Interatomic distances are given in Å.

the series of halosilanes SiXnH4−n (X = F, Cl, Br, and I) within a full four-component relativistic Dirac’s scheme using relativistic Dyall’s basis sets optimized within the framework of a fourcomponent Dirac−Hartree−Fock formalism - the most appropriate basis sets for the relativistic calculations at this level of theory. Four most representative types of relativistic Dyall’s basis sets, namely, valence dyall.vXz, diffuse valence dyall.avXz,

better as compared to relativistic DFT methods. In some cases, taking into account solvent effects slightly improves agreement with experiment but this is not a matter of principle.

■

CONCLUDING REMARKS

In the present paper, we have performed the study of relativistic effects in 29Si NMR shielding constants (and chemical shifts) in G


Article


Table 6. 29Si NMR Chemical Shifts of 1−17 Calculated at the Four-Component Relativistic GIAO-DFT-KT3 Level Using Different Dyall’s Basis Sets of Triple-Zeta Qualitya dyall.v3z

dyall.av3z

dyall.cv3z

compd

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

exptb

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

−101.4 −2.8 −5.5 −56.6 −96.5 −15.2 29.3 40.6 32.7 −39.3 6.7 32.9 44.7 −52.3 2.7 47.3 75.4

−0.1 −0.4 −1.4 −2.6 −3.5 −2.9 −8.5 −21.7 −49.3 −15.7 −44.1 −94.2 −177.8 −41.5 −124.3 −280.0 −540.7

3.6 11.2 7.8 1.8 −2.3 7.0 6.3 3.6 0.2 3.5 4.1 2.9 −0.1 5.1 4.1 5.0 1.4

−97.9 8.0 0.9 −57.4 −102.3 −11.1 27.1 22.5 −16.4 −51.5 −33.3 −58.4 −133.2 −88.7 −117.5 −227.7 −463.9

−101.8 −3.4 −6.1 −57.2 −97.0 −15.5 28.9 40.3 32.6 −39.7 6.3 32.6 44.6 −52.6 2.4 47.1 75.5

−0.3 −0.5 −1.5 −2.7 −3.6 −2.9 −8.5 −21.8 −49.4 −15.3 −44.2 −94.4 −177.7 −38.7 −124.3 −280.0 −538.2

3.8 11.3 7.7 1.8 −2.3 7.0 6.3 3.5 0.0 3.6 4.2 2.9 −0.2 5.2 4.2 4.9 1.3

−98.3 7.4 0.1 −58.1 −102.9 −11.4 26.7 22.0 −16.8 −51.4 −33.7 −58.9 −133.3 −86.1 −117.7 −228.0 −461.4

−103.8 −5.8 −9.8 −62.0 −102.1 −18.9 24.1 34.1 25.4 −41.4 4.0 29.4 40.4 −54.8 −0.9 42.5 69.7

−0.1 −0.4 −1.4 −2.6 −3.5 −2.9 −8.4 −18.9 −49.0 −15.8 −43.7 −93.4 −176.4 −40.9 −123.2 −277.5 −536.3

3.6 10.8 7.4 1.7 −2.3 6.6 6.0 3.4 0.2 3.3 3.9 2.8 −0.1 4.9 3.9 4.8 1.4

−100.3 4.6 −3.8 −62.9 −107.9 −15.2 21.7 18.6 −23.4 −53.9 −35.8 −61.2 −136.1 −90.8 −120.2 −230.2 −465.2

−95.6 −17.4 −28.5 −77.8 −117.4 −36.1 −11.3 −9.6 −18.5 −48.5 −30.4 −43.3 −92.7 −83.3 −99.6 −179.8 −351.7

All chemical shifts and their relativistic and solvent corrections are given in ppm. Relativistic corrections, Δσrel, are evaluated as the difference between those of a standard (TMS) and a substance under consideration at the GIAO-DFT-KT3 level, while solvent corrections (chloroform) are determined as the difference between those of a standard (TMS) and a substance under consideration within supermolecule solvation model at the nonrelativistic GIAO-DFT-KT3 level. bTaken from different sources; see text for references. a

Table 7. 29Si NMR Chemical Shifts of 1−17 Calculated at the Four-Component Relativistic GIAO-RPA Level Using Different Dyall’s Basis Sets of Triple-Zeta Qualitya dyall.v3z

dyall.av3z

dyall.cv3z

compd

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

exptb

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

−89.3 −17.4 −28.6 −79.4 −121.4 −24.1 5.9 15.8 18.1 −40.3 −4.2 21.8 42.4 −52.0 −10.4 31.5 73.1

0.0 −0.6 −1.7 −2.7 −3.0 −2.7 −8.2 −17.9 −34.3 −11.4 −33.5 −71.0 −129.1 −33.2 −101.1 −224.2 −414.7

3.6 11.2 7.8 1.8 −2.3 7.0 6.3 3.6 0.2 3.5 4.1 2.9 −0.1 5.1 4.1 5.0 1.4

−85.7 −6.8 −22.5 −80.3 −126.7 −19.8 4.0 1.5 −16.0 −48.2 −33.6 −46.3 −86.8 −80.1 −107.4 −187.7 −340.2

−89.5 −17.8 −29.0 −79.9 −121.7 −24.3 5.6 15.3 17.6 −40.5 −4.4 21.5 42.3 −52.2 −10.6 31.3 72.9

−0.3 −0.8 −1.9 −2.9 −3.1 −2.9 −8.4 −18.0 −34.7 −11.6 −33.7 −71.2 −129.5 −33.4 −101.4 −224.6 −415.5

3.8 11.3 7.7 1.8 −2.3 7.0 6.3 3.5 0.0 3.6 4.2 2.9 −0.2 5.2 4.2 4.9 1.3

−86.0 −7.3 −23.2 −81.0 −127.1 −20.2 3.5 0.8 −17.1 −48.5 −33.9 −46.8 −87.4 −80.4 −107.8 −188.4 −341.3

−91.3 −20.4 −32.6 −84.2 −126.5 −27.5 1.3 10.2 11.8 −42.4 −6.9 18.4 38.5 −54.4 −13.6 27.5 68.1

0.0 −0.6 −1.7 −2.7 −3.0 −2.7 −8.2 −17.8 −34.1 −11.4 −33.4 −70.6 −128.4 −33.2 −100.8 −222.9 −412.2

3.6 10.8 7.4 1.7 −2.3 6.6 6.0 3.4 0.2 3.3 3.9 2.8 −0.1 4.9 3.9 4.8 1.4

−87.7 −10.2 −26.9 −85.2 −131.8 −23.6 −0.9 −4.2 −22.1 −50.5 −36.4 −49.4 −90.0 −82.7 −110.5 −190.6 −342.7

−95.6 −17.4 −28.5 −77.8 −117.4 −36.1 −11.3 −9.6 −18.5 −48.5 −30.4 −43.3 −92.7 −83.3 −99.6 −179.8 −351.7

All chemical shifts and their relativistic and solvent corrections are given in ppm. Relativistic corrections, Δσrel, are evaluated as the difference between those of a standard (TMS) and a substance under consideration at the GIAO-RPA level, while solvent corrections (chloroform) are determined as the difference between those of a standard (TMS) and a substance under consideration within supermolecule solvation model at the nonrelativistic GIAO-DFT-KT3 level. bTaken from different sources; see text for references. a

the valence dyall.vXz basis sets vanishes starting from triple-ζ level while adding core functions does not damp down even at quadruple-ζ level. In line with the earlier results by Aucar and others,19,26 it was found that the most pronounced trend is that relativistic effects in 29Si NMR shielding constants rapidly increase with the total atomic number of the atoms forming the chemical environment of silicon and with the number of halogens attached to silicon and, noteworthy, this increase is not linear. Thus, it was confirmed

core valence dyall.cvXz, and diffuse core valence dyall.acvXz (X = 2, 3, and 4), were examined using most rigorous computationally achievable tests, with “nonrelativistic” tetrafluorosilane providing strong correlation effects and “relativistic” iodosilane providing strong relativistic effects. It was found that, at both four-component uncorrelated RPA and “correlated” DFT levels, all four types of Dyall’s basis sets were converged to complete basis set limit at triple-ζ quality for both compounds. It is also noteworthy that the effect of adding diffuse functions to H


Article


Table 8. 29Si NMR Chemical Shifts of 1−17 Calculated at the Nonrelativistic GIAO-MP2 Level Taking into Account Relativistic and Solvent Corrections Using Different Dyall’s Basis Sets of Triple-Zeta Qualitya dyall.v3z

dyall.av3z

dyall.cv3z

compd

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

δnr

Δδrel

Δδsolv

δtotal

exptb

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

−104.9 −12.9 14.9 −54.8 −96.0 −25.5 14.9 29.0 30.2 −45.1 −1.0 28.1 48.0 −59.6 −9.2 37.8 79.2

0.0 −0.6 −1.7 −2.7 −3.0 −2.7 −8.2 −17.9 −34.3 −11.4 −33.5 −71.0 −129.1 −33.2 −101.1 −224.2 −414.7

3.6 11.2 7.8 1.8 −2.3 7.0 6.3 3.6 0.2 3.5 4.1 2.9 −0.1 5.1 4.1 5.0 1.4

−101.3 −2.3 21.0 −55.7 −101.3 −21.2 13.0 14.7 −3.9 −53.0 −30.4 −40.0 −81.2 −87.7 −106.2 −181.4 −334.1

−105.1 −12.8 −3.4 −68.4 −108.9 −25.4 14.6 28.2 29.1 −45.3 −1.4 27.6 47.4 −59.7 −9.3 37.8 79.1

−0.3 −0.8 −1.9 −2.9 −3.1 −2.9 −8.4 −18.0 −34.7 −11.6 −33.7 −71.2 −129.5 −33.4 −101.4 −224.6 −415.5

3.8 11.3 7.7 1.8 −2.3 7.0 6.3 3.5 0.0 3.6 4.2 2.9 −0.2 5.2 4.2 4.9 1.3

−101.6 −2.3 2.4 −69.5 −114.3 −21.3 12.5 13.7 −5.6 −53.3 −30.9 −40.7 −82.3 −87.9 −106.5 −181.9 −335.1

−107.6 −14.9 −20.5 −72.6 −113.8 −28.0 11.9 25.3 26.0 −46.5 −2.0 27.1 46.7 −60.6 −9.0 39.1 81.4

0.0 −0.6 −1.7 −2.7 −3.0 −2.7 −8.2 −17.8 −34.1 −11.4 −33.4 −70.6 −128.4 −33.2 −100.8 −222.9 −412.2

3.6 10.8 7.4 1.7 −2.3 6.6 6.0 3.4 0.2 3.3 3.9 2.8 −0.1 4.9 3.9 4.8 1.4

−104.0 −4.7 −14.8 −73.6 −119.1 −24.1 9.7 10.9 −7.9 −54.6 −31.5 −40.7 −81.8 −88.9 −105.9 −179.0 −329.4

−95.6 −17.4 −28.5 −77.8 −117.4 −36.1 −11.3 −9.6 −18.5 −48.5 −30.4 −43.3 −92.7 −83.3 −99.6 −179.8 −351.7

All chemical shifts and their relativistic and solvent corrections are given in ppm. Relativistic corrections, Δσrel, are evaluated as the difference between those of a standard (TMS) and a substance under consideration at the GIAO-RPA level, while solvent corrections (chloroform) are determined as the difference between those of a standard (TMS) and a substance under consideration within supermolecule solvation model at the nonrelativistic GIAO-DFT-KT3 level. bTaken from different sources; see text for references. a

Figure 6. Mean absolute errors of 29Si NMR chemical shifts of 1−17 calculated using the GIAO-DFT-KT3, GIA-RPA, and GIAO-MP2 methods, in gas phase (GP) at the nonrelativistic level (yellow bars), in gas phase taking into account relativistic effects (red bars), and in gas phase taking into account relativistic and solvent effects (green bars) with different Dyall’s basis sets of triple-ζ quality. I


Article


Figure 9. Correlation plot of 29Si NMR chemical shifts o f 1−17 calculated at the four-component relativistic GIAO-RPA/dyall.cv3z level with taking into account solvent effects within the SSM scheme versus experiment (best result).

admissible for chlorosilanes and absolutely inadequate and unacceptable for silanes bearing at least one atom of either bromine or iodine attached to silicon. An interesting finding of the present study is that 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. This difference is too much essential to be neglected, especially when comparing calculations with experiment. Solvent corrections to 29Si NMR shielding constants are negative (deshielding) being in average of about ca. 3−5 ppm and decreasing with the number of halogen atoms attached to silicon. Thus, for monohalosilanes, they range from −4 to −11 ppm, while for tetrahalosilanes they do not exceed 2 ppm in absolute value. The largest solvent corrections are observed in fluorosilanes reaching −11.4 ppm in fluorosilane. Generally, solvent corrections are essentially smaller as compared to relativistic corrections, especially in bromo- and iodosilanes providing dramatically large relativistic effects of several hundreds of ppm. Using experimental 29Si NMR chemical shifts as a rigorous benchmark of the present four-component relativistic calculations, it was found that taking into account relativistic effects dramatically decreases MAE of calculated 29Si NMR chemical shifts versus experiment. In this study, we compared the performance of three different theoretical levels to compute 29Si NMR chemical shifts of the representative series of halosilanes in comparison with experiment, namely, four-component relativistic GIAO-DFT-KT3, four-component relativistic GIAO-RPA, and a hybrid scheme of nonrelativistic GIAOMP2 with taking into account relativistic corrections at the fourcomponent relativistic GIAO-RPA level. In each case, we applied three different relativistic Dyall’s basis sets, valence dyall.v3z, diffuse valence dyall.av3z, and core valence dyall.cv3z, and taking into account solvent effects (chloroform) within the supermolecule solvation model at the nonrelativistic GIAODFT-KT3 level. It was found that MAE decreases from about 75 ppm to about 20−25 ppm for the four-component relativistic GIAO-DFT-KT3 method and to about 10−15 ppm for the

Figure 7. 29Si NMR chemical shifts of iodosilanes SiInH4−n calculated at the nonrelativistic MP2 level (depicted as GIAO-MP2); within a full four-component relativistic Dirac’s scheme at the RPA level (depicted as GIAO-4RPA); and using a hybrid scheme of nonrelativistic MP2 with taking into account relativistic corrections at the four-component relativistic RPA level (depicted as GIAO-MP2+GIAO-4RPA), as compared to experiment.

Figure 8. Mean absolute errors of 29Si NMR chemical shifts of 1−17 calculated at the four-component relativistic GIAO-DFT-KT3 and GIA-RPA levels, and using a hybrid computational scheme of a combined nonrelativistic GIAO-MP2 and relativistic four-component GIAO-RPA with taking into account solvent effects within the SSM scheme employing different Dyall’s basis sets of triple-ζ quality.

at both four-component RPA and DFT levels that relativistic effects in 29Si NMR shielding constants of halosilanes are next to negligible (up to several ppm) in fluorosilanes, noticeably larger (up to several dozens of ppm) in chlorosilanes, much larger (up to 200 ppm) in bromosilanes and exessively large (several hundreds of ppm) in iodosilanes. Thus, it follows that nonrelativistic calculations of 29Si NMR absolute shielding constants (chemical shifts) are adequate for fluorosilanes, J


Article


density functional theory (DFT) calculations on some iodo compounds. Chem.Eur. J. 1998, 4, 118−126. (16) Kaupp, M.; Malkin, V. G.; Malkina, O. L.; Salahub, D. R. Calculation of ligand NMR chemical shifts in transition-metal complexes using ab initio effective-core potentials and density functional theory. Chem. Phys. Lett. 1995, 235, 382−388. (17) Kaupp, M.; Malkina, O. L. Density functional analysis of 13C and 1 H chemical shifts and bonding in mercurimethanes and organomercury hydrides: The role of scalar relativistic, spin-orbit, and substituent effects. J. Chem. Phys. 1998, 108, 3648−3659. (18) Wodyński, A.; Gryff-Keller, A.; Pecul, M. The influence of a presence of a heavy atom on 13c shielding constants in organomercury compounds and halogen derivatives. J. Chem. Theory Comput. 2013, 9, 1909−1917. (19) Maldonado, A. F.; Aucar, G. A.; Melo, J. I. Core-dependent and ligand-dependent relativistic corrections to the nuclear magnetic shieldings in MH4‑nYn (n = 0−4; M = Si, Ge, Sn, and Y = H, F, Cl, Br, I) model compounds. J. Mol. Model. 2014, 20, 2417. (20) Jaszuński, M.; Ruud, K. Nuclear magnetic resonance shielding constants in XH4 group XIV hydrides. Mol. Phys. 2006, 104, 2139− 2148. (21) Makulski, W.; Jackowski, K.; Antušek, A.; Jaszuński, M. Gasphase NMR measurements, absolute shielding scales, and magnetic dipole moments of 29Si and 73Ge Nuclei. J. Phys. Chem. A 2006, 110, 11462−11466. (22) Jaszuński, M.; Jackowski, K. Nuclear magnetic dipole moments from NMR spectra - quantum chemistry and experiment. Lect. Notes Phys. 2008, 745, 233−260. (23) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic regular two-component Hamiltonians. J. Chem. Phys. 1993, 99, 4597−4611. (24) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic total energy using regular approximations. J. Chem. Phys. 1994, 101, 9783− 9793. (25) van Lenthe, E.; Ehlers, A. E.; Baerends, E. J. Geometry optimizations in the zero order regular approximation for relativistic effects. J. Chem. Phys. 1999, 110, 8943−8954. (26) Maldonado, A. F.; Gimenez, C. A.; Aucar, G. A. NMR espectroscopic parameters of HX and Si (Sn)X4 (X = H, F, Cl, Br and I) and SnBr4−nIn model compounds. Chem. Phys. 2012, 395, 75−81. (27) Bohm, D.; Pines, D. A collective description of electron interactions. I. Magnetic interactions. Phys. Rev. 1951, 82, 625−635. (28) Pines, D.; Bohm, D. A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions. Phys. Rev. 1952, 85, 338−354. (29) Bohm, D.; Pines, D. A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas. Phys. Rev. 1953, 92, 609−626. (30) Aucar, G. A.; Oddershede, J. Relativistic theory for indirect nuclear spin−spin couplings within the polarization propagator approach. Int. J. Quantum Chem. 1993, 47, 425−435. (31) Visscher, L.; Enevoldsen, T.; Saue, T.; Jensen, H. J. Aa.; Oddershede, J. Full four-component relativistic calculations of NMR shielding and indirect spin−spin coupling tensors in hydrogen halides. J. Comput. Chem. 1999, 20, 1262−1273. (32) Gomez, S. S.; Romero, R. H.; Aucar, G. A. Fully relativistic calculation of nuclear magnetic shieldings and indirect nuclear spinspin couplings in group-15 and -16 hydrides. J. Chem. Phys. 2002, 117, 7942−7947. (33) Antušek, A.; Pecul, M.; Sadlej, J. Relativistic calculation of NMR properties of XeF2, XeF4 and XeF6. Chem. Phys. Lett. 2006, 427, 281− 288. (34) Jameson, C. J.; Jameson, A. K. Absolute shielding scale for 29Si. Chem. Phys. Lett. 1988, 149, 300−305. (35) Melo, J.I.; Ruiz deAzúa, M. C.; Giribet, C. G.; Aucar, G. A.; Romero, R. H. Relativistic effects on the nuclear magnetic shielding tensor. J. Chem. Phys. 2003, 118, 471−487. (36) Melo, J. I.; Ruiz deAzúa, M. C.; Giribet, C. G.; Aucar, G. A.; Provasi, P. F. Relativistic effects on nuclear magnetic shielding constants in HX and CH3X (X = Br,I) based on the linear response

four-component relativistic GIAO-RPA method and a combined scheme of nonrelativistic GIAO-MP2 with four-component relativistic GIAO-RPA. Either diffuse or core functions in Dyall’s diffuse valence basis sets showed no effect as compared to the valence ones, and taking into account solvent effects (chloroform) do not affect noticeably the accuracy of any of the tested methods either.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +7(3952)511426. E-mail: krivdin_offi[email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the Russian Scientific Fund (Grant No. 14-13-00215) is greatly acknowledged.

■

REFERENCES

(1) Marsman, H. In NMR Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer-Verlag: Berlin, 1981; pp 65−235. (2) Kennedy, J. D.; McFarlane, W. In Multinuclear NMR; Mason, J., Ed.; Plenum Press: New York, 1987; pp 305−333. (3) Sauer, S. P. A. Molecular Electromagnetism. A Computational Chemistry Approach; University Press: Oxford, 2012. (4) Helgaker, T.; Jaszuński, M.; Ruud, K. Ab initio methods for the calculation of NMR shielding and indirect spin−spin coupling constants. Chem. Rev. 1999, 99, 293−352. (5) Helgaker, T.; Coriani, S.; Jørgensen, P.; Kristensen, K.; Olsen, J.; Ruud, K. Recent advances in wave function-based methods of molecular-property calculations. Chem. Rev. 2012, 112, 543−631. (6) Chernyshev, K. A.; Krivdin, L. B. Quantum-chemical calculations of NMR chemical shifts of organic molecules: VI. Accuracy of DFT calculations of 29Si chemical shifts of four-coordinate silicon compounds. Russ. J. Org. Chem. 2012, 48, 1518−25. (7) Chernyshev, K. A.; Gostevskii, B. A.; Albanov, A. I.; Krivdin, L. B. Quantum-chemical calculations of NMR chemical shifts of organic molecules: VII. Intramolecular coordination effect in the29Si NMR spectra of siletanes. Russ. J. Org. Chem. 2013, 49, 34−41. (8) Chernyshev, K. A.; Gostevskii, B. A.; Krivdin, L. B. Quantumchemical calculations of NMR chemical shifts of organic molecules: X. Dynamic equilibrium effects in the 29 Si NMR spectra of silacycloalkanes. Russ. J. Org. Chem. 2013, 49, 832−837. (9) Fedorov, S. V.; Rusakov, Yu. Yu.; Krivdin, L. B. Relativistic environmental effects in 29Si NMR chemical shifts of halosilanes: light nucleus, heavy environment. Russ. Chem. Bull. 2015, 64, 551−592. (10) Rusakov, Yu. Yu.; Krivdin, L. B. One-bond 29Si-1H spin-spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations, relativistic effects, and vibrational corrections. Magn. Reson. Chem. 2013, 51, 557−561. (11) Rusakov, Yu. Yu.; Krivdin, L. B.; Nosova, V. M.; Kisin, A. V. Benchmark calculations of 29Si−1H spin−spin coupling constants across double bond. Magn. Reson. Chem. 2012, 50, 278−283. (12) Rusakov, Yu. Yu.; Krivdin, L. B.; Nosova, V. M.; Kisin, A. V.; Lakhtin, V. G. Structural trends of 29Si−1H spin−spin coupling constants across double bond. Magn. Reson. Chem. 2012, 50, 665−671. (13) Rusakova, I. L.; Rusakov, Yu. Yu.; Krivdin, L. B. Nonempirical calculations of the one-bond 29Si−13C spin−spin coupling constants taking into account relativistic and solvent corrections. Magn. Reson. Chem. 2014, 52, 413−421. (14) Pyykkö, P.; Görling, A.; Rösch, N. A transparent interpretation of the relativistic contribution to the N.M.R. “heavy atom chemical shift”. Mol. Phys. 1987, 61, 195−205. (15) Kaupp, M.; Malkina, O. L.; Malkin, V. G.; Pyykkö, P. How do spin-orbit-induced heavy-atom effects on NMR chemical shifts function? Validation of a simple analogy to spin-spin coupling by K


Article

The Journal of Physical Chemistry A within the elimination of small component approach. J. Chem. Phys. 2004, 121, 6798−6809. (37) GAMESS (US), Release R.1 (2013). Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363. (38) DALTON, a Molecular Electronic Structure Program, Release Dalton2015 (2015). Aidas, K.; Angeli, C.; Bak, K. L.; Bakken, V.; Bast, R.; Boman, L.; Christiansen, O.; Cimiraglia, R.; Coriani, S.; Dahle, P. The Dalton quantum chemistry program system. WIREs Comput. Mol. Sci. 2014, 4, 269−284 See http://daltonprogram.org.. (39) GAUSSIAN 09, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian, Inc., Wallingford CT, USA,(2009). See http:// http://www. gaussian.com. (40) Saue, T.; Visscher, L.; Jensen, H. J. Aa.; Bast, R.; Bakken, V.; Dyall, K. G.; Dubillard, S.; Ekström, U.; Eliav, E.; Enevoldsen, T.; et al. DIRAC, a relativistic ab initio electronic structure program, Release DIRAC14, 2014; see http://www.diracprogram.org. (41) Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Goodfellow, R.; Granger, P. NMR nomenclature. Nuclear spin properties and conventions for chemical shifts. Pure Appl. Chem. 2001, 73, 1795−1818. (42) Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Granger, P.; Hoffman, R. E.; Zilm, K. W. Further conventions for NMR shielding and chemical shifts. Pure Appl. Chem. 2008, 80, 59−84. (43) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the 4s, 5s, 6s, and 7s elements. J. Phys. Chem. A 2009, 113, 12638−12644. (44) Dyall, K. G. Relativistic quadruple-zeta and revised triple-zeta and double-zeta basis sets for the 4p, 5p, and 6p elements. Theor. Chem. Acc. 2006, 115, 441−447. (45) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the 4d elements Y−Cd. Theor. Chem. Acc. 2007, 117, 483−489. (46) Dyall, K. G.; Gomes, A. S. P. Revised relativistic basis sets for the 5delements Hf−Hg. Theor. Chem. Acc. 2010, 125, 97−100. (47) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the 5delements. Hf−Hg. Theor. Chem. Acc. 2004, 112, 403−409. (48) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the actinides Ac−Lr. Theor. Chem. Acc. 2007, 117, 491−500. (49) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the 6d elements Rf−Cn. Theor. Chem. Acc. 2011, 129, 603−613. (50) Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruplezeta basis sets for the 7p elements, with atomic and molecular applications. Theor. Chem. Acc. 2012, 131, 1172. (51) Visser, O.; Aerts, P. J. C.; Hegarty, D.; Nieuwpoort, W. C. The use of gaussian nuclear charge distributions for the calculation of relativistic electronic wavefunctions using basis set expansions. Chem. Phys. Lett. 1987, 134, 34−38. (52) Visscher, L.; Dyall, K. G. Dirac−Fock atomic electronic structure calculations using different nuclear charge distributions. At. Data Nucl. Data Tables 1997, 67, 207−224. (53) Ditchfield, R. Molecular orbital theory of magnetic shielding and magnetic susceptibility. J. Chem. Phys. 1972, 56, 5688−5692. (54) Ditchfield, R. Self-consistent perturbation theory of diamagnetism I. A gauge-invariant LCAO method for N.M.R. chemical shifts. Mol. Phys. 1974, 27, 789−807. (55) Dodds, J. L.; McWeeny, R.; Sadlej, A. J. Self-consistent perturbation theory. Open-shell states in perturbation-dependent nonorthogonal basis sets. Mol. Phys. 1980, 41, 1419−1430. (56) Wolinski, K.; Hinton, J. F.; Pulay, P. Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations. J. Am. Chem. Soc. 1990, 112, 8251−8260.

(57) Keal, T. W.; Tozer, D. J. A semiempirical generalized gradient approximation exchange-correlation functional. J. Chem. Phys. 2004, 121, 5654−5661. (58) Feller, D. Application of systematic sequences of wave functions to the water dimer. J. Chem. Phys. 1992, 96, 6104−6115. (59) Kupka, T.; Lim, C. J. Polarization-consistent versus correlationconsistent basis sets in predicting molecular and spectroscopic properties. Phys. Chem. A 2007, 111, 1927−1932. (60) Kupka, T. Complete basis set B3LYP NMR calculations of CDCl3 solvent’s water fine spectral details. Magn. Reson. Chem. 2008, 46, 851−858. (61) Kupka, T. Prediction of water’s isotropic nuclear shieldings and indirect nuclear spin−spin coupling constants (SSCCs) using correlation-consistent and polarization-consistent basis sets in the Kohn−Sham basis set limit. Magn. Reson. Chem. 2009, 47, 210−221. (62) Autschbach, J. Relativistic Effects on NMR Parameters. In High resolution NMR spectroscopy - Understanding molecules and their electronic structures; Contreras, R. H., Ed.; Elsevier B.V.: The Netherlands, 2013; pp 69−117. (63) Autschbach, J.; Zheng, S. Relativistic computations of NMR parameters from first principles: theory and applications. Annu. Rep. NMR Spectrosc. 2009, 67, 1−95. (64) Autschbach, J. Relativistic calculations of magnetic resonance parameters: Background and some recent developments. Philos. Trans. R. Soc. A 2014, 372, 20120489. (65) Pyykkö, P. Relativistic effects in structural chemistry. Chem. Rev. 1988, 88, 563−594. (66) Pyykkö, P. Relativistic quantum chemistry. Adv. Quantum Chem. 1978, 11, 353−409. (67) Tomasi, J.; Mennucci, B.; Cancès, E. The IEF version of the PCM solvation method: an overview of a new method addressed to study molecular solutes at the QM ab initio level. J. Mol. Struct.: THEOCHEM 1999, 464, 211−226. (68) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum mechanical continuum solvation models. Chem. Rev. 2005, 105, 2999−3094. (69) Fluck, E.; Burger, H.; Goetze, U. 31P- und 1H-Kernresonanzuntersuchungen an Trimethylsilylphosphinen. Isotopeneffekt in der 31 P-Kernresonanzspektroskopie. Z. Naturforsch. 1967, 22B, 912−916. (70) Vongehr, M.; Marsmann, H. C. Die Anwendung von Parametern der gegenseitigen Wechselwirkung in der 29Si-Resonanz. Z. Naturforsch. 1976, 31B, 1423−1424. (71) Marsmann, H. C.; Meyer, E.; Vongehr, M.; Weber, E. F. 29Si NMR-untersuchungen an polykieselsäureestern. Makromol. Chem. 1983, 184, 1817−1822. (72) Ebsworth, E. A. V.; Edward, J. M.; Rankin, D. W. H. Silyl and germyl complexes of platinum and palladium. Part 3. Reactions between silyl and germyl derivatives of Group 6 and four-co-ordinate halogenohydridobis(triethylphosphine)platinum(II)complexes. J. Chem. Soc., Dalton Trans. 1976, 17, 1667−1673. (73) Niemann, U.; Marsmann, H. C. 29Si-Kernresonanzmessungen an Siliciumhalogeniden. 29Si NMR Studies on Silicon Halogenides. Z. Naturforsch. 1975, 30B, 202−206.

L


Relativistic Environmental Effects in 29Si NMR Chemical Shifts of

Recommend Documents