Research article Received: 7 June 2014
Revised: 9 July 2014
Accepted: 11 July 2014
Published online in Wiley Online Library: 22 August 2014
(wileyonlinelibrary.com) DOI 10.1002/mrc.4122
Towards the versatile DFT and MP2 computational schemes for 31P NMR chemical shifts taking into account relativistic corrections Sergey V. Fedorov, Yury Yu. Rusakov and Leonid B. Krivdin* The main factors affecting the accuracy and computational cost of the calculation of 31P NMR chemical shifts in the representative series of organophosphorous compounds are examined at the density functional theory (DFT) and second-order Møller–Plesset perturbation theory (MP2) levels. At the DFT level, the best functionals for the calculation of 31P NMR chemical shifts are those of Keal and Tozer, KT2 and KT3. Both at the DFT and MP2 levels, the most reliable basis sets are those of Jensen, pcS-2 or larger, and those of Pople, 6-311G(d,p) or larger. The reliable basis sets of Dunning’s family are those of at least penta-zeta quality that precludes their practical consideration. An encouraging finding is that basically, the locally dense basis set approach resulting in a dramatic decrease in computational cost is justified in the calculation of 31P NMR chemical shifts within the 1–2-ppm error. Relativistic corrections to 31P NMR absolute shielding constants are of major importance reaching about 20–30 ppm (ca 7%) improving (not worsening!) the agreement of calculation with experiment. Further better agreement with the experiment by 1–2 ppm can be obtained by taking into account solvent effects within the integral equation formalism polarizable continuum model solvation scheme. We recommend the GIAO-DFT-KT2/pcS-3//pcS-2 scheme with relativistic corrections and solvent effects taken into account as the most versatile computational scheme for the calculation of 31P NMR chemical shifts characterized by a mean absolute error of ca 9 ppm in the range of 550 ppm. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: 31P NMR; chemical shift; magnetic shielding constant; GIAO-DFT; GIAO-MP2; locally dense basis set; organophosphorous compounds
Introduction Since the first days of the discovery of NMR phenomenon, 31P NMR plays a major role in the structural elucidation of organophosphorous compounds and is widely used in biological studies like those of phospholipid bilayers and biological membranes in native conditions, studies of enzymatic reactions, elucidation of biochemical pathways, and many other biological studies. Basically, 31 P NMR chemical shifts provide a straightforward structural information falling into the range of roughly 250 to +250 ppm relative to the 85% water solution of H3PO4 (used as a common standard), with the 31P NMR signals being usually well resolved in the 31P NMR spectra and resonating at characteristic frequencies. In this context and within the progress of the theory of magnetic resonance parameters derived from a spin Hamiltonian as the linear response functions,[1] the development of high-precision and versatile computational schemes for the 31P NMR chemical shifts is of utmost importance in the structural studies of organophosphorous compounds. In continuation of our previous papers dealing with calculation of 31P NMR chemical shifts,[2] in this paper, we report our most effective computational schemes for the 31P NMR chemical shifts at the density functional theory (DFT) level and within a pure nonempirical MP2 framework.
Results and discussion
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Level of theory, DFT functionals, and basis sets In this paper, we have tested the most common and, alternatively, more specialized NMR-oriented DFT and MP2 methods to calculate the phosphorous absolute shielding constant of phosphine, σ(P), used as a benchmark. At the DFT level, among the functionals tested herewith are the hybrid exchange-correlation functionals B3LYP[4,5] and B3PW91,[4,6] the local spin density approximation functional LSDA (also known as SVWN)[7] in combination with Vosko, Wilk, and Nusair correlation functional,[8] and the generalized gradient approximation (GGA) hybrid Perdew–Burke–Ernzerhof functional (PBE0),[9] and also NMR-oriented exchange-correlation
* Correspondence to: Leonid Krivdin, A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia. E-mail: krivdin_offi[email protected] A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033, Irkutsk, Russia
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Discussed in this paper are the main methodological factors affecting the accuracy and computational cost of different
computational schemes used for the calculation of 31P NMR chemical shifts of diverse organophosphorous compounds – first of all, the level of theory, the quality of the basis sets including the applicability of the locally dense basis sets (LDBSs), the problem of converting calculated absolute shielding constants into a chemical shift scale, relativistic corrections, and solvent effects. All these points are addressed herewith at the DFT and MP2 levels of theory within the framework of a gauge including atomic orbital (GIAO) scheme.[3]
S. V. Fedorov, Y. Y. Rusakov and L. B. Krivdin GGA functionals of Keal and Tozer, KT2[10] and KT3.[11] Six functionals (B3LYP, B3PW91, LDA, PBE0, KT2, and KT3) mentioned previously were tested in combination with three different families of basis sets – those of Pople,[12] from 6-31 + G(d) through aug-6-311++G(3d,2p), those of Dunning,[13] from cc-pVDZ through aug-cc-pV6Z, and those of Jensen,[14] from pcS-1 through aug-pcS-4. The three earlier discussed families of basis sets were tested also at the MP2 level. The most accurate theoretical value of the phosphorous shielding constant σ(P) in phosphine, PH3, to the best of our knowledge, was evaluated in the paper by Jaszuński et al.[15] at the coupled cluster singles and doubles with a noniterative perturbative triples correction level, CCSD(T),[16] with cc-pwCV5Z basis set within the GIAO scheme to give 606.110 ppm, in good agreement with the previous GIAO-CCSD(T)/cc-pCVQZ[17] and GIAO-CCSD(T)/cc-pwCVQZ[18] results (giving accordingly 605.831 and 605.002 ppm) and the “best experimental” value of 599.93 ppm.[19] This nonrelativistic GIAO-CCSD(T)/cc-pwCV5Z
shielding constant was then corrected by evaluating relativistic contribution at the four-component Dirac–Coulomb level to give 624.309 ppm and finally rovibrationally and temperature corrected to give 614.758 ppm.[15] Thus, it follows that relativistic correction to σ(P) contributes a noticeable value of 18.780 ppm increasing shielding of phosphorous nucleus, the zero-point vibrational correction totals 9.227 ppm, while temperature effect is as small as 0.324 ppm.[15] In the present benchmark study of PH3, we took σ(P) = 606.11 ppm as a reference, i.e. the GIAO-CCSD(T)/cc-pwCV5Z value without relativistic, rovibrational, and temperature corrections. In other words, we have tested the performance of the DFT and MP2 methods currently used for the calculation of chemical shifts in larger molecules versus the most accurate CCSD(T) level. Shown in Fig. 1 are the absolute errors (AEs) of σ(P) in phosphine calculated herewith at the DFT level (six functionals and three families of basis sets) versus the CCSD(T) result (606.11 ppm).[15]
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Figure 1. Absolute errors of the phosphorous absolute shielding constant in phosphine calculated at the GIAO-DFT level using different functionals in combination with different basis sets of Pople (top), Dunning (middle), and Jensen (bottom), as compared with the CCSD(T) result.
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Copyright © 2014 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2014, 52, 699–710
Computational schemes for 31P NMR chemical shifts
Magn. Reson. Chem. 2014, 52, 699–710
Figure 2. Absolute errors of the phosphorous absolute shielding constant in phosphine calculated at the GIAO-DFT-KT2 and GIAO-MP2 levels using different basis sets of Pople (top), Dunning (middle), and Jensen (bottom), as compared with the CCSD(T) result.
The basic conclusions that can be reached at based on the data presented in Figs. 1 and 2 are as follows: At the GIAODFT level, the best functionals for the calculation of σ(P) are those of Keal and Tozer KT2 and KT3. Both at the GIAO-DFT and GIAO-MP2 levels, the most reliable basis sets are those of Jensen pcS-2 or larger ones from the same family and Pople’s 6-311G(d,p) or larger ones. The reliable basis sets of Dunning’s family are those of at least penta-zeta quality that precludes their practical consideration. LDBS schemes High-level ab initio and DFT calculations of NMR shielding constants with large basis sets can be successfully performed for small
Copyright © 2014 John Wiley & Sons, Ltd.
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The very first observation arising from these data is that NMRoriented GGA functionals of Keal and Tozer, KT2 and KT3, show essentially better results as compared with the more common functionals PBE0, LDA, B3LYP, and B3PW91. The best results are achieved with the KT2 functional giving an AE of about 5–10 ppm depending on the basis set that totals to less than 1.5% of the value of the absolute shielding constant σ(P). For large basis sets, AE is reduced to about 5 ppm, which is less than 1% of the total value of σ(P). Indeed, this is a very encouraging result. On the contrary, a much worse performance is demonstrated by the hybrid functionals B3LYP and B3PW91 characterized by an AE of about 30–40 ppm (5–7%) with the most popular B3LYP functional being the worst. Especially noteworthy is that the combination of the latter with the highest-quality basis sets of Pople, such as 6-311++G(3d,2p), Dunning (such as cc-pV6Z and aug-cc-pV6Z), and Jensen (pcS-4 and aug-cc-pcS-4) results in the largest values of AEs reaching almost 50 ppm (8%). At the same time, the combinations of B3LYP with small basis sets like 6-31G(d), cc-pVDZ, or pcS-1 give AEs twice and even thrice as small thus markedly demonstrating the effect of a fortuitous cancellation of errors. The rest of the examined functionals (LDA and PBE0) show more modest results with an AE of about 25 ppm (depending on the basis set), which is about 4% of the total value of σ(P). Based on these results, at the DFT level, we will consider the most reliable NMR-oriented GGA functional of Keal and Tozer KT2 for a further evaluation of the accuracy factors. The results of a systematic study of a basis set effect on the accuracy of the phosphorous absolute shielding constant calculation in phosphine at the GIAO-DFT-KT2 and GIAO-MP2 levels are compiled in Fig. 2. Again, the same three families of basis sets were examined – those of Pople, Dunning, and Jensen. It is seen that at the GIAO-DFT-KT2 level, the most reliable results are achieved with the Pople’s family of basis sets beginning from 6-311++G(d,p) to 6-311++G(3d,2p). In this case, the AE is as small as 3–5 ppm. Surprisingly, a small AE of about 1 ppm for the KT2 combinations with small basis sets of Dunning’s and Jensen’s families is apparently because of the fortuitous cancellation of errors at the DFT level. Indeed, for larger basis sets of those families, the AEs are much larger reaching almost 10 ppm. At the GIAO-MP2 level, Pople’s basis sets are also good beginning with 6-311++G(d,p) and going toward larger ones characterized by AEs of about 5–7 ppm. However, they are not as good as that at the GIAO-DFT-KT2 level (AE 3–5 ppm). Dunning’s basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, and Q) work apparently badly at the GIAO-MP2 level showing AEs of about 20–30 ppm. The situation critically improves only for the penta-zeta Dunning’s sets cc-pV5Z and aug-cc-pV5Z giving AEs of 1–2 ppm. However, these basis sets are too large to make sense of any practical consideration of their applicability for the calculation of 31P NMR chemical shifts of the medium-size molecules. On the other hand, all Jensen’s basis sets demonstrate very good performance at the GIAO-MP2 level with the exception of small pcS-1 and aug-pcS-1 basis sets of roughly double-zeta quality. Also, it should be noted that using diffuse functions, either in Dunning’s or in Jensen’s series of basis sets, exercises almost no effect on the accuracy of σ(P) calculations in phosphine at either GIAO-DFT or GIAO-MP2 levels, at the same time, noticeably increasing the computational cost of such calculations.
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molecules (like that of phosphine), while going on to larger molecular systems results in an unreasonably high computational cost and causes insuperable technical hindrance, at least nowadays. An efficient way to overcome this obstacle originates in the idea of the LDBSs that consists in the employing of a large high-quality basis set on particular atoms of interest and of much smaller basis sets elsewhere in the molecule.[20] The use of different LDBS schemes enables to perform calculations of NMR parameters (chemical shifts and spin–spin coupling constants) with high accuracy at much less computational cost. In this study, the “atom of interest” is, of course, phosphorous for which the 13P NMR chemical shift is to be calculated, while the “rest of molecule” consists of all other atoms in the molecule under consideration. To the best of our knowledge, no such approach has been verified (at least, systematically) for the 31P NMR chemical shifts, and in this paper, we have tested the reliability and the effectiveness of the LDBS computational protocol for the 31P NMR shielding constants in the representative benchmark set of 13 diverse phosphorous-containing compounds – trimethylphosphine, trimethylphosphine oxide, and trimethylphosphine sulfide – and their chlorine analogs – trichlorophosphine, trichlorophosphine oxide, and trichlorophosphine sulfide, sterically strained phosphirane and phosphetane, unsaturated and/or aromatic phosphorouscontaining heterocycles (phosphole, isophosphole, oxazaphosphole, and triazatriphosphinine), as shown in Table 1. In that way, the typical bonding environment of phosphorous in diverse organophosphorous compounds was well reproduced in the title benchmark series to test the reliability of the LDBS protocol in the calculation of 31P NMR chemical shifts. Based on the results presented in Fig. 2, we have tested four LDBS schemes – two at the GIAO-DFT-KT2 level and two within the GIAO-MP2 framework. The more economical LDBS scheme implies Pople’s 6-311++G(3d,2p) on phosphorous and 6-311++G(d,p) for the rest of the molecule, while the more computationally demanding one implies Jensen’s pcS-3 on phosphorous and pcS-2 for the rest of the molecule. The NMR-oriented Jensen’s pcS-2 and pcS-3 basis sets contain tight p-functions that are of prime importance for the reliable evaluation of NMR absolute shielding constants and roughly could be described as being of triple and quadruple-zeta quality, respectively. The results of the subject LDBS calculations of 31P NMR shielding constants versus full basis set (FBS) data in the benchmark series of 13 title compounds are compiled in Table 1 and illustrated in Fig. 3. It should be emphasized that AEs and absolute percentage errors (APEs) given in Table 3 and mean absolute errors (MAEs) and mean absolute percentage errors (MAPEs) shown in Fig. 3 are the errors characterizing different LDBS schemes as compared with the FBS results thus being unrelated to experimental data. The most encouraging result following from these data is that basically, the LDBS approach is justified in the calculation of 31P NMR chemical shifts within the 1–2 ppm MAE (as compared with the FBS data) and is as small as 0.03 ppm (MAPE 0.1%) for the GIAO-DFT-KT2/pcS-3//pcS-2 computational scheme. Relative computational costs of different LDBS and FBS computational schemes are presented in Table 2. We see that depending on the level of theory (DFT or MP2) and molecular
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size (small, medium, and large), relative central processing unit time for different computational scheme changes by several orders of magnitude. Benchmark calculations Presented in Tables 3 and 4 are the results of the benchmark calculations of 31P NMR chemical shifts in a representative series of diverse organophosphorous compounds 1–53 including the most important classes – phosphines, phosphine oxides, phosphine sulfides, phosphorous acids and their derivatives, chlorophosphorous compounds, and phosphorous-containing heterocycles, in comparison with available experimental data for 1,[21] 2–4, and 10;[22] 5 and 7–9,[23] 6;[24] 11;[25] 12;[26] 13 and 16;[27] 14, 52, and 53;[28] 15;[29] 17;[30] 18;[31] 19;[32] 20;[33] 21;[34] 22;[35] 23;[36] 24 and 25;[37] 26 and 27;[38] 28;[39] 29;[40] 30;[41] 31;[42] 32;[43] 33;[44] 34;[45] 35 and 38;[46] 36;[47] 37;[48] 39;[49] 40;[50] 41;[51] 42 and 43;[52] 44;[53] 45;[54] 46;[55] 47;[56] 48;[57] 49;[58] 50;[59] and 51[60] referenced to the 85% water solution of H3PO4. The last three compounds from this series, 51, 52, and 53, presented a challenge task for this study because of their size of up to 35 atoms (including 20 secondperiod elements and a third-period phosphorous atom).
Copyright © 2014 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2014, 52, 699–710
Computational schemes for 31P NMR chemical shifts
Magn. Reson. Chem. 2014, 52, 699–710
Copyright © 2014 John Wiley & Sons, Ltd.
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Among numerous attempts to create an absolute 31P shielding scale related to the 85% water solution of H3PO4, the most known are that of Appleman and Dailey[61] based on a measured spin–rotation constant of gaseous PH3 and a measured chemical shift of liquid PH3 at 90 °C referenced to the 85% water solution of H3PO4: that of Jameson et al.[62] derived from the gas-phase 31P NMR studies and molecular beam data for gaseous PH3 and the most recent one that of Jaszuński et al.[15] based on the state-of-the-art coupled cluster singles and doubles with a noniterative perturbative triplet correction CCSD(T) calculations taking into account relativistic correction together with a zero-density limit gas-phase NMR data for PH3. The absolute shielding constant of phosphorous in the 85% water solution of H3PO4 was found accordingly, 356 ppm, as reported by Appleman and Dailey,[61] 328.35 ppm suggested by Jameson et al.[62] and 351.6 ppm reached at by Jaszuński et al.[15] In our calculations of 31P NMR chemical shifts in the series of 1–53, we referenced calculated 13P absolute shielding constants of the molecules under consideration to 351.6 ppm taken as the absolute shielding constant of phosphorous in the 85% water solution of H3PO4 as a standard. The main reason of this choice was that the absolute shielding constant for H3PO4 reported by Jaszuński et al.[15] takes into account relativistic contribution, in line with our consideration of relativistic effects (refer to succeeding texts). Based on the results discussed previously (presented in Tables 1, 2 and in Figs. 1–3), four different LDBS computational schemes were benchmarked in the series of 1–53 – two at the DFT level using the most reliable Keal–Tozer functional KT2 and two at the pure nonempirical MP2 level, both within the GIAO framework. At both levels, the first LDBS scheme employed Pople’s basis sets 6-311++G(3d,2p) on phosphorous and 6-311+ +G(d,p) in the rest of the molecule, while the second LDBS scheme used Jensen’s basis sets pcS-3 (roughly quadruple-zeta quality) on phosphorous and pcS-2 (roughly triple-zeta quality) in the rest of the molecule. Solvent corrections were evaluated within all four LDBS schemes as the difference of 31P NMR chemical shifts calculated using the integral equation formalism polarizable continuum model (IEF-PCM)[63] solvation scheme and those calculated in gas phase (i.e. without taking into account solvent effects). For obvious computational reasons, relativistic corrections were calculated only at the DFT level using the most economical LDBS computational scheme, GIAO-DFT-KT2/6-311++G(d,p)//6-31 + G(d),
S. V. Fedorov, Y. Y. Rusakov and L. B. Krivdin Table 1. Absolute errors (AEs) and absolute percentage errors (APEs) of different locally dense basis set (LDBS) schemes in a sample set of compounds as compared to the full basis set (FBS) results. Compounda
Method
Phosphorous (CH3)3P
(CH3)3P=O
(CH3)3P=S
Cl3P
Cl3P=O
Cl3P=S
31
Basis set
Absolute P NMR shielding constant σ, ppm
Rest of the molecule
LDBS
FBS
AE, ppm
APE, %
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
394.4 390.1 409.5 407.7 314.0 306.4 309.4 305.2 310.9 304.6 306.2 302.4 61.8 59.9 79.4 82.7 317.5 311.9 299.3 297.2 290.6 283.5 256.4 252.5 657.6 654.7 684.3 681.2
396.4 390.2 408.3 404.8 314.7 306.2 310.7 304.9 312.7 304.6 306.4 301.2 67.8 61.3 83.6 83.5 319.2 312.4 301.8 301.3 292.5 284.7 257.0 253.8 659.5 655.5 680.7 678.8
2.0 0.1 1.2 2.9 0.7 0.2 1.3 0.3 1.8 0.0 0.2 1.2 6.0 1.4 4.2 0.8 1.7 0.5 2.5 4.1 1.9 1.2 0.6 1.3 1.9 0.8 3.6 2.4
0.5 0.0 0.3 0.7 0.2 0.1 0.4 0.1 0.6 0.0 0.1 0.4 8.8 2.3 5.0 1.0 0.5 0.2 0.8 1.4 0.7 0.4 0.2 0.5 0.3 0.1 0.5 0.4
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
350.9 346.4 366.7 365.9
352.7 346.7 365.3 363.3
1.8 0.3 1.4 2.6
0.5 0.1 0.4 0.7
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
367.8 362.7 366.2 361.5
368.8 362.5 360.2 357.1
1.0 0.2 6.0 4.4
0.3 0.1 1.6 1.2
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
94.7 87.3 92.9 85.2
93.0 86.5 83.6 81.5
1.7 0.8 9.3 3.7
1.8 0.9 11.0 4.6
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
277.1 271.6 278.7 270.4
275.7 270.3 268.1 265.3
1.4 1.3 10.6 5.1
0.5 0.5 4.0 1.9
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
102.6 90.6 76.3 64.7
96.0 88.4 69.5 66.4
6.6 2.2 6.8 1.7
6.8 2.5 9.8 2.6
704
(Continues)
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Copyright © 2014 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2014, 52, 699–710
Computational schemes for 31P NMR chemical shifts Table 1. (Continued) Compounda
Method
Phosphorous GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
31
Basis set
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
Absolute P NMR shielding constant σ, ppm
Rest of the molecule
LDBS
FBS
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
222.4 215.5 207.8 204.6
222.1 215.4 206.4 b
AE, ppm
APE, %
0.3 0.1 1.4
0.1 0.1 0.7
b
b
a
All geometry optimizations are performed at the MP2/6-311G(d.p) level with solvent effects taken into account within the IEF-PCM scheme. Conformationally labile compounds are adopted in their favorable conformations. b Not affordable for computational reasons.
Presented in Fig. 4 are the MAEs of all four computational schemes related to the experiment in the whole series of 1–53. It is seen that basically, a good agreement with the experiment is achieved when relativistic effects are taken into account with the GIAO-DFT-KT2 schemes performing noticeably better. Relativistic corrections are of major importance in all four computational schemes reaching ca 20–30 ppm (on average, about 7% of the absolute shielding constant). For example, for the most accurate GIAO-DFT-KT2/pcS-3//pcS-2 scheme, taking into account relativistic corrections, decreases MAEs from 26.0 to 9.5 ppm. Further, more moderate decreasing of MAEs by 1–2 ppm can be obtained by taking into account solvent effects. Surprisingly or not surprisingly, the most accurate results were obtained at the DFT (rather than MP2) level with the most reliable GIAO-DFT-KT2/pcS3//pcS-2 computational scheme characterized by an MAE of 9.4 ppm in the range of 31P NMR chemical shifts of about 550 ppm (i.e.
Revised: 9 July 2014
Accepted: 11 July 2014
Published online in Wiley Online Library: 22 August 2014
(wileyonlinelibrary.com) DOI 10.1002/mrc.4122
Towards the versatile DFT and MP2 computational schemes for 31P NMR chemical shifts taking into account relativistic corrections Sergey V. Fedorov, Yury Yu. Rusakov and Leonid B. Krivdin* The main factors affecting the accuracy and computational cost of the calculation of 31P NMR chemical shifts in the representative series of organophosphorous compounds are examined at the density functional theory (DFT) and second-order Møller–Plesset perturbation theory (MP2) levels. At the DFT level, the best functionals for the calculation of 31P NMR chemical shifts are those of Keal and Tozer, KT2 and KT3. Both at the DFT and MP2 levels, the most reliable basis sets are those of Jensen, pcS-2 or larger, and those of Pople, 6-311G(d,p) or larger. The reliable basis sets of Dunning’s family are those of at least penta-zeta quality that precludes their practical consideration. An encouraging finding is that basically, the locally dense basis set approach resulting in a dramatic decrease in computational cost is justified in the calculation of 31P NMR chemical shifts within the 1–2-ppm error. Relativistic corrections to 31P NMR absolute shielding constants are of major importance reaching about 20–30 ppm (ca 7%) improving (not worsening!) the agreement of calculation with experiment. Further better agreement with the experiment by 1–2 ppm can be obtained by taking into account solvent effects within the integral equation formalism polarizable continuum model solvation scheme. We recommend the GIAO-DFT-KT2/pcS-3//pcS-2 scheme with relativistic corrections and solvent effects taken into account as the most versatile computational scheme for the calculation of 31P NMR chemical shifts characterized by a mean absolute error of ca 9 ppm in the range of 550 ppm. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: 31P NMR; chemical shift; magnetic shielding constant; GIAO-DFT; GIAO-MP2; locally dense basis set; organophosphorous compounds
Introduction Since the first days of the discovery of NMR phenomenon, 31P NMR plays a major role in the structural elucidation of organophosphorous compounds and is widely used in biological studies like those of phospholipid bilayers and biological membranes in native conditions, studies of enzymatic reactions, elucidation of biochemical pathways, and many other biological studies. Basically, 31 P NMR chemical shifts provide a straightforward structural information falling into the range of roughly 250 to +250 ppm relative to the 85% water solution of H3PO4 (used as a common standard), with the 31P NMR signals being usually well resolved in the 31P NMR spectra and resonating at characteristic frequencies. In this context and within the progress of the theory of magnetic resonance parameters derived from a spin Hamiltonian as the linear response functions,[1] the development of high-precision and versatile computational schemes for the 31P NMR chemical shifts is of utmost importance in the structural studies of organophosphorous compounds. In continuation of our previous papers dealing with calculation of 31P NMR chemical shifts,[2] in this paper, we report our most effective computational schemes for the 31P NMR chemical shifts at the density functional theory (DFT) level and within a pure nonempirical MP2 framework.
Results and discussion
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Level of theory, DFT functionals, and basis sets In this paper, we have tested the most common and, alternatively, more specialized NMR-oriented DFT and MP2 methods to calculate the phosphorous absolute shielding constant of phosphine, σ(P), used as a benchmark. At the DFT level, among the functionals tested herewith are the hybrid exchange-correlation functionals B3LYP[4,5] and B3PW91,[4,6] the local spin density approximation functional LSDA (also known as SVWN)[7] in combination with Vosko, Wilk, and Nusair correlation functional,[8] and the generalized gradient approximation (GGA) hybrid Perdew–Burke–Ernzerhof functional (PBE0),[9] and also NMR-oriented exchange-correlation
* Correspondence to: Leonid Krivdin, A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia. E-mail: krivdin_offi[email protected] A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033, Irkutsk, Russia
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Discussed in this paper are the main methodological factors affecting the accuracy and computational cost of different
computational schemes used for the calculation of 31P NMR chemical shifts of diverse organophosphorous compounds – first of all, the level of theory, the quality of the basis sets including the applicability of the locally dense basis sets (LDBSs), the problem of converting calculated absolute shielding constants into a chemical shift scale, relativistic corrections, and solvent effects. All these points are addressed herewith at the DFT and MP2 levels of theory within the framework of a gauge including atomic orbital (GIAO) scheme.[3]
S. V. Fedorov, Y. Y. Rusakov and L. B. Krivdin GGA functionals of Keal and Tozer, KT2[10] and KT3.[11] Six functionals (B3LYP, B3PW91, LDA, PBE0, KT2, and KT3) mentioned previously were tested in combination with three different families of basis sets – those of Pople,[12] from 6-31 + G(d) through aug-6-311++G(3d,2p), those of Dunning,[13] from cc-pVDZ through aug-cc-pV6Z, and those of Jensen,[14] from pcS-1 through aug-pcS-4. The three earlier discussed families of basis sets were tested also at the MP2 level. The most accurate theoretical value of the phosphorous shielding constant σ(P) in phosphine, PH3, to the best of our knowledge, was evaluated in the paper by Jaszuński et al.[15] at the coupled cluster singles and doubles with a noniterative perturbative triples correction level, CCSD(T),[16] with cc-pwCV5Z basis set within the GIAO scheme to give 606.110 ppm, in good agreement with the previous GIAO-CCSD(T)/cc-pCVQZ[17] and GIAO-CCSD(T)/cc-pwCVQZ[18] results (giving accordingly 605.831 and 605.002 ppm) and the “best experimental” value of 599.93 ppm.[19] This nonrelativistic GIAO-CCSD(T)/cc-pwCV5Z
shielding constant was then corrected by evaluating relativistic contribution at the four-component Dirac–Coulomb level to give 624.309 ppm and finally rovibrationally and temperature corrected to give 614.758 ppm.[15] Thus, it follows that relativistic correction to σ(P) contributes a noticeable value of 18.780 ppm increasing shielding of phosphorous nucleus, the zero-point vibrational correction totals 9.227 ppm, while temperature effect is as small as 0.324 ppm.[15] In the present benchmark study of PH3, we took σ(P) = 606.11 ppm as a reference, i.e. the GIAO-CCSD(T)/cc-pwCV5Z value without relativistic, rovibrational, and temperature corrections. In other words, we have tested the performance of the DFT and MP2 methods currently used for the calculation of chemical shifts in larger molecules versus the most accurate CCSD(T) level. Shown in Fig. 1 are the absolute errors (AEs) of σ(P) in phosphine calculated herewith at the DFT level (six functionals and three families of basis sets) versus the CCSD(T) result (606.11 ppm).[15]
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Figure 1. Absolute errors of the phosphorous absolute shielding constant in phosphine calculated at the GIAO-DFT level using different functionals in combination with different basis sets of Pople (top), Dunning (middle), and Jensen (bottom), as compared with the CCSD(T) result.
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Copyright © 2014 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2014, 52, 699–710
Computational schemes for 31P NMR chemical shifts
Magn. Reson. Chem. 2014, 52, 699–710
Figure 2. Absolute errors of the phosphorous absolute shielding constant in phosphine calculated at the GIAO-DFT-KT2 and GIAO-MP2 levels using different basis sets of Pople (top), Dunning (middle), and Jensen (bottom), as compared with the CCSD(T) result.
The basic conclusions that can be reached at based on the data presented in Figs. 1 and 2 are as follows: At the GIAODFT level, the best functionals for the calculation of σ(P) are those of Keal and Tozer KT2 and KT3. Both at the GIAO-DFT and GIAO-MP2 levels, the most reliable basis sets are those of Jensen pcS-2 or larger ones from the same family and Pople’s 6-311G(d,p) or larger ones. The reliable basis sets of Dunning’s family are those of at least penta-zeta quality that precludes their practical consideration. LDBS schemes High-level ab initio and DFT calculations of NMR shielding constants with large basis sets can be successfully performed for small
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The very first observation arising from these data is that NMRoriented GGA functionals of Keal and Tozer, KT2 and KT3, show essentially better results as compared with the more common functionals PBE0, LDA, B3LYP, and B3PW91. The best results are achieved with the KT2 functional giving an AE of about 5–10 ppm depending on the basis set that totals to less than 1.5% of the value of the absolute shielding constant σ(P). For large basis sets, AE is reduced to about 5 ppm, which is less than 1% of the total value of σ(P). Indeed, this is a very encouraging result. On the contrary, a much worse performance is demonstrated by the hybrid functionals B3LYP and B3PW91 characterized by an AE of about 30–40 ppm (5–7%) with the most popular B3LYP functional being the worst. Especially noteworthy is that the combination of the latter with the highest-quality basis sets of Pople, such as 6-311++G(3d,2p), Dunning (such as cc-pV6Z and aug-cc-pV6Z), and Jensen (pcS-4 and aug-cc-pcS-4) results in the largest values of AEs reaching almost 50 ppm (8%). At the same time, the combinations of B3LYP with small basis sets like 6-31G(d), cc-pVDZ, or pcS-1 give AEs twice and even thrice as small thus markedly demonstrating the effect of a fortuitous cancellation of errors. The rest of the examined functionals (LDA and PBE0) show more modest results with an AE of about 25 ppm (depending on the basis set), which is about 4% of the total value of σ(P). Based on these results, at the DFT level, we will consider the most reliable NMR-oriented GGA functional of Keal and Tozer KT2 for a further evaluation of the accuracy factors. The results of a systematic study of a basis set effect on the accuracy of the phosphorous absolute shielding constant calculation in phosphine at the GIAO-DFT-KT2 and GIAO-MP2 levels are compiled in Fig. 2. Again, the same three families of basis sets were examined – those of Pople, Dunning, and Jensen. It is seen that at the GIAO-DFT-KT2 level, the most reliable results are achieved with the Pople’s family of basis sets beginning from 6-311++G(d,p) to 6-311++G(3d,2p). In this case, the AE is as small as 3–5 ppm. Surprisingly, a small AE of about 1 ppm for the KT2 combinations with small basis sets of Dunning’s and Jensen’s families is apparently because of the fortuitous cancellation of errors at the DFT level. Indeed, for larger basis sets of those families, the AEs are much larger reaching almost 10 ppm. At the GIAO-MP2 level, Pople’s basis sets are also good beginning with 6-311++G(d,p) and going toward larger ones characterized by AEs of about 5–7 ppm. However, they are not as good as that at the GIAO-DFT-KT2 level (AE 3–5 ppm). Dunning’s basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, and Q) work apparently badly at the GIAO-MP2 level showing AEs of about 20–30 ppm. The situation critically improves only for the penta-zeta Dunning’s sets cc-pV5Z and aug-cc-pV5Z giving AEs of 1–2 ppm. However, these basis sets are too large to make sense of any practical consideration of their applicability for the calculation of 31P NMR chemical shifts of the medium-size molecules. On the other hand, all Jensen’s basis sets demonstrate very good performance at the GIAO-MP2 level with the exception of small pcS-1 and aug-pcS-1 basis sets of roughly double-zeta quality. Also, it should be noted that using diffuse functions, either in Dunning’s or in Jensen’s series of basis sets, exercises almost no effect on the accuracy of σ(P) calculations in phosphine at either GIAO-DFT or GIAO-MP2 levels, at the same time, noticeably increasing the computational cost of such calculations.
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molecules (like that of phosphine), while going on to larger molecular systems results in an unreasonably high computational cost and causes insuperable technical hindrance, at least nowadays. An efficient way to overcome this obstacle originates in the idea of the LDBSs that consists in the employing of a large high-quality basis set on particular atoms of interest and of much smaller basis sets elsewhere in the molecule.[20] The use of different LDBS schemes enables to perform calculations of NMR parameters (chemical shifts and spin–spin coupling constants) with high accuracy at much less computational cost. In this study, the “atom of interest” is, of course, phosphorous for which the 13P NMR chemical shift is to be calculated, while the “rest of molecule” consists of all other atoms in the molecule under consideration. To the best of our knowledge, no such approach has been verified (at least, systematically) for the 31P NMR chemical shifts, and in this paper, we have tested the reliability and the effectiveness of the LDBS computational protocol for the 31P NMR shielding constants in the representative benchmark set of 13 diverse phosphorous-containing compounds – trimethylphosphine, trimethylphosphine oxide, and trimethylphosphine sulfide – and their chlorine analogs – trichlorophosphine, trichlorophosphine oxide, and trichlorophosphine sulfide, sterically strained phosphirane and phosphetane, unsaturated and/or aromatic phosphorouscontaining heterocycles (phosphole, isophosphole, oxazaphosphole, and triazatriphosphinine), as shown in Table 1. In that way, the typical bonding environment of phosphorous in diverse organophosphorous compounds was well reproduced in the title benchmark series to test the reliability of the LDBS protocol in the calculation of 31P NMR chemical shifts. Based on the results presented in Fig. 2, we have tested four LDBS schemes – two at the GIAO-DFT-KT2 level and two within the GIAO-MP2 framework. The more economical LDBS scheme implies Pople’s 6-311++G(3d,2p) on phosphorous and 6-311++G(d,p) for the rest of the molecule, while the more computationally demanding one implies Jensen’s pcS-3 on phosphorous and pcS-2 for the rest of the molecule. The NMR-oriented Jensen’s pcS-2 and pcS-3 basis sets contain tight p-functions that are of prime importance for the reliable evaluation of NMR absolute shielding constants and roughly could be described as being of triple and quadruple-zeta quality, respectively. The results of the subject LDBS calculations of 31P NMR shielding constants versus full basis set (FBS) data in the benchmark series of 13 title compounds are compiled in Table 1 and illustrated in Fig. 3. It should be emphasized that AEs and absolute percentage errors (APEs) given in Table 3 and mean absolute errors (MAEs) and mean absolute percentage errors (MAPEs) shown in Fig. 3 are the errors characterizing different LDBS schemes as compared with the FBS results thus being unrelated to experimental data. The most encouraging result following from these data is that basically, the LDBS approach is justified in the calculation of 31P NMR chemical shifts within the 1–2 ppm MAE (as compared with the FBS data) and is as small as 0.03 ppm (MAPE 0.1%) for the GIAO-DFT-KT2/pcS-3//pcS-2 computational scheme. Relative computational costs of different LDBS and FBS computational schemes are presented in Table 2. We see that depending on the level of theory (DFT or MP2) and molecular
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size (small, medium, and large), relative central processing unit time for different computational scheme changes by several orders of magnitude. Benchmark calculations Presented in Tables 3 and 4 are the results of the benchmark calculations of 31P NMR chemical shifts in a representative series of diverse organophosphorous compounds 1–53 including the most important classes – phosphines, phosphine oxides, phosphine sulfides, phosphorous acids and their derivatives, chlorophosphorous compounds, and phosphorous-containing heterocycles, in comparison with available experimental data for 1,[21] 2–4, and 10;[22] 5 and 7–9,[23] 6;[24] 11;[25] 12;[26] 13 and 16;[27] 14, 52, and 53;[28] 15;[29] 17;[30] 18;[31] 19;[32] 20;[33] 21;[34] 22;[35] 23;[36] 24 and 25;[37] 26 and 27;[38] 28;[39] 29;[40] 30;[41] 31;[42] 32;[43] 33;[44] 34;[45] 35 and 38;[46] 36;[47] 37;[48] 39;[49] 40;[50] 41;[51] 42 and 43;[52] 44;[53] 45;[54] 46;[55] 47;[56] 48;[57] 49;[58] 50;[59] and 51[60] referenced to the 85% water solution of H3PO4. The last three compounds from this series, 51, 52, and 53, presented a challenge task for this study because of their size of up to 35 atoms (including 20 secondperiod elements and a third-period phosphorous atom).
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Computational schemes for 31P NMR chemical shifts
Magn. Reson. Chem. 2014, 52, 699–710
Copyright © 2014 John Wiley & Sons, Ltd.
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Among numerous attempts to create an absolute 31P shielding scale related to the 85% water solution of H3PO4, the most known are that of Appleman and Dailey[61] based on a measured spin–rotation constant of gaseous PH3 and a measured chemical shift of liquid PH3 at 90 °C referenced to the 85% water solution of H3PO4: that of Jameson et al.[62] derived from the gas-phase 31P NMR studies and molecular beam data for gaseous PH3 and the most recent one that of Jaszuński et al.[15] based on the state-of-the-art coupled cluster singles and doubles with a noniterative perturbative triplet correction CCSD(T) calculations taking into account relativistic correction together with a zero-density limit gas-phase NMR data for PH3. The absolute shielding constant of phosphorous in the 85% water solution of H3PO4 was found accordingly, 356 ppm, as reported by Appleman and Dailey,[61] 328.35 ppm suggested by Jameson et al.[62] and 351.6 ppm reached at by Jaszuński et al.[15] In our calculations of 31P NMR chemical shifts in the series of 1–53, we referenced calculated 13P absolute shielding constants of the molecules under consideration to 351.6 ppm taken as the absolute shielding constant of phosphorous in the 85% water solution of H3PO4 as a standard. The main reason of this choice was that the absolute shielding constant for H3PO4 reported by Jaszuński et al.[15] takes into account relativistic contribution, in line with our consideration of relativistic effects (refer to succeeding texts). Based on the results discussed previously (presented in Tables 1, 2 and in Figs. 1–3), four different LDBS computational schemes were benchmarked in the series of 1–53 – two at the DFT level using the most reliable Keal–Tozer functional KT2 and two at the pure nonempirical MP2 level, both within the GIAO framework. At both levels, the first LDBS scheme employed Pople’s basis sets 6-311++G(3d,2p) on phosphorous and 6-311+ +G(d,p) in the rest of the molecule, while the second LDBS scheme used Jensen’s basis sets pcS-3 (roughly quadruple-zeta quality) on phosphorous and pcS-2 (roughly triple-zeta quality) in the rest of the molecule. Solvent corrections were evaluated within all four LDBS schemes as the difference of 31P NMR chemical shifts calculated using the integral equation formalism polarizable continuum model (IEF-PCM)[63] solvation scheme and those calculated in gas phase (i.e. without taking into account solvent effects). For obvious computational reasons, relativistic corrections were calculated only at the DFT level using the most economical LDBS computational scheme, GIAO-DFT-KT2/6-311++G(d,p)//6-31 + G(d),
S. V. Fedorov, Y. Y. Rusakov and L. B. Krivdin Table 1. Absolute errors (AEs) and absolute percentage errors (APEs) of different locally dense basis set (LDBS) schemes in a sample set of compounds as compared to the full basis set (FBS) results. Compounda
Method
Phosphorous (CH3)3P
(CH3)3P=O
(CH3)3P=S
Cl3P
Cl3P=O
Cl3P=S
31
Basis set
Absolute P NMR shielding constant σ, ppm
Rest of the molecule
LDBS
FBS
AE, ppm
APE, %
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2 GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
394.4 390.1 409.5 407.7 314.0 306.4 309.4 305.2 310.9 304.6 306.2 302.4 61.8 59.9 79.4 82.7 317.5 311.9 299.3 297.2 290.6 283.5 256.4 252.5 657.6 654.7 684.3 681.2
396.4 390.2 408.3 404.8 314.7 306.2 310.7 304.9 312.7 304.6 306.4 301.2 67.8 61.3 83.6 83.5 319.2 312.4 301.8 301.3 292.5 284.7 257.0 253.8 659.5 655.5 680.7 678.8
2.0 0.1 1.2 2.9 0.7 0.2 1.3 0.3 1.8 0.0 0.2 1.2 6.0 1.4 4.2 0.8 1.7 0.5 2.5 4.1 1.9 1.2 0.6 1.3 1.9 0.8 3.6 2.4
0.5 0.0 0.3 0.7 0.2 0.1 0.4 0.1 0.6 0.0 0.1 0.4 8.8 2.3 5.0 1.0 0.5 0.2 0.8 1.4 0.7 0.4 0.2 0.5 0.3 0.1 0.5 0.4
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
350.9 346.4 366.7 365.9
352.7 346.7 365.3 363.3
1.8 0.3 1.4 2.6
0.5 0.1 0.4 0.7
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
367.8 362.7 366.2 361.5
368.8 362.5 360.2 357.1
1.0 0.2 6.0 4.4
0.3 0.1 1.6 1.2
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
94.7 87.3 92.9 85.2
93.0 86.5 83.6 81.5
1.7 0.8 9.3 3.7
1.8 0.9 11.0 4.6
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
277.1 271.6 278.7 270.4
275.7 270.3 268.1 265.3
1.4 1.3 10.6 5.1
0.5 0.5 4.0 1.9
GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
102.6 90.6 76.3 64.7
96.0 88.4 69.5 66.4
6.6 2.2 6.8 1.7
6.8 2.5 9.8 2.6
704
(Continues)
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Copyright © 2014 John Wiley & Sons, Ltd.
Magn. Reson. Chem. 2014, 52, 699–710
Computational schemes for 31P NMR chemical shifts Table 1. (Continued) Compounda
Method
Phosphorous GIAO-DFT-KT2 GIAO-DFT-KT2 GIAO-MP2 GIAO-MP2
31
Basis set
6-311G++(3d,2p) pcS-3 6-311G++(3d,2p) pcS-3
Absolute P NMR shielding constant σ, ppm
Rest of the molecule
LDBS
FBS
6-311++G(d,p) pcS-2 6-311++G(d,p) pcS-2
222.4 215.5 207.8 204.6
222.1 215.4 206.4 b
AE, ppm
APE, %
0.3 0.1 1.4
0.1 0.1 0.7
b
b
a
All geometry optimizations are performed at the MP2/6-311G(d.p) level with solvent effects taken into account within the IEF-PCM scheme. Conformationally labile compounds are adopted in their favorable conformations. b Not affordable for computational reasons.
Presented in Fig. 4 are the MAEs of all four computational schemes related to the experiment in the whole series of 1–53. It is seen that basically, a good agreement with the experiment is achieved when relativistic effects are taken into account with the GIAO-DFT-KT2 schemes performing noticeably better. Relativistic corrections are of major importance in all four computational schemes reaching ca 20–30 ppm (on average, about 7% of the absolute shielding constant). For example, for the most accurate GIAO-DFT-KT2/pcS-3//pcS-2 scheme, taking into account relativistic corrections, decreases MAEs from 26.0 to 9.5 ppm. Further, more moderate decreasing of MAEs by 1–2 ppm can be obtained by taking into account solvent effects. Surprisingly or not surprisingly, the most accurate results were obtained at the DFT (rather than MP2) level with the most reliable GIAO-DFT-KT2/pcS3//pcS-2 computational scheme characterized by an MAE of 9.4 ppm in the range of 31P NMR chemical shifts of about 550 ppm (i.e.
