Effect of Noncovalent Interactions on the 31P Chemical Shift Tensor of

Article pubs.acs.org/JPCC

Effect of Noncovalent Interactions on the 31P Chemical Shift Tensor of Phosphine Oxides, Phosphinic, Phosphonic, and Phosphoric Acids, and Their Complexes with Lead(II) Ilya G. Shenderovich* Faculty of Chemistry and Pharmacy, University of Regensburg, Universitaetstrasse 31, 93053 Regensburg, Germany S Supporting Information *

ABSTRACT: The effect of noncovalent interactions such as C−H···O and O−H···O hydrogen bonds and coordination to Pb2+ on the 31P NMR chemical shift tensor in the titled compounds has been studied experimentally and simulated theoretically using the density functional theory gauge-invariant atomic orbital (DFT-GIAO) approach. It has been shown that only in few cases the most suitable measure of these interactions is the isotropic 31P NMR chemical shift. In contrast, the analysis of the anisotropy and the principal components of the 31P NMR chemical shift tensor can be very useful to discriminate between different interactions and to characterize their properties. A great advantage is that these NMR parameters can be correctly simulated at relatively inexpensive levels of theory, namely, B3LYP/cc-pVDZ and B3LYP/6-311G**. Thus, a combination of 31P NMR and time-efficient calculations can be used to study the structural pattern in polycrystalline and noncrystalline materials. An illustrative result is the demonstration of the similarity of the unknown crystal structures of methylphosphonic acid, diphenyl hydrogen phosphate, and lead(II) methylphosphinate to the known crystal structures of tert-butylphosphonic acid, bis(4-chlorophenyl) hydrogen phosphate, and lead(II) vinylphosphonate, respectively. The scope of this approach is wide and covers the study of the local chemical structures in amorphous materials, at surfaces and interfaces.

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INTRODUCTION A detailed understanding of local structural patterns in noncrystalline and polycrystalline solids is often crucial for the elucidation of the mechanical and chemical properties of these materials. One of the most popular methods to solve this problem is to inject into the system of interest spin labels and to use magnetic resonance spectroscopy.1−4 As an alternative, the labeling can be done by selective or nonselective isotope substitution.5,6 Especially attractive is the use of magnetically active nuclei of the original system. Despite clear progress in solid-state NMR of protons,7 its impact is mainly restricted to a rough estimation of hydrogen bond geometry because of a narrow spread of chemical shift values. The effect of noncovalent interactions on the 13C NMR chemical shifts is in general too small for a serious analysis.8,9 In contrast, 31P NMR seems to be a promising tool for monitoring local structural patterns10−12 and complex mixtures.13 31P exhibits a wide range of chemical shifts and is often involved in multiple noncovalent interactions either directly or by means of covalently attached groups. These features can be used to go beyond the conventional schema of structure elucidation and to target the understanding of noncovalent interactions that govern specific biochemical14,15 or heterogeneous processes.16−19 For these purposes one needs to know how NMR parameters are affected by different noncovalent interactions. This can be done by comparing the values of these parameters in an isolated molecule and the molecule incorporated in the model environments. When the NMR © 2013 American Chemical Society

sensor is optimally selected one can discriminate between different interactions in quite complex systems.20−22 The easiest NMR parameter to measure is the isotropic chemical shift that is used to elucidate the chemical structure in the conventional liquid-state NMR. However, the chemical shielding of a nucleus depends on the electron distribution around the nucleus, which is, in general, not isotropic. As a result, the observed value of chemical shift depends on the orientation of a molecule with respect to the external magnetic field. One speaks about the anisotropy of chemical shift and describes this in terms of a tensor. There are three mutually perpendicular orientations of the molecule for which the rotation along the direction of the external magnetic field does not affect the value of chemical shift. The values that correspond to these orientations are called the principal components of the chemical shift tensor (CST). If the electron distribution around the nucleus is affected by a noncovalent interaction, the principal components of the CST change their numerical values and, in some cases, the orientation with respect to the molecular frame. These changes can be observed when the reorientation of the molecule is slow on the NMR time scale of milliseconds. In solution one observes the average value that is the isotropic chemical shift. Thus, the isotropic 31P NMR chemical shift can be useful in the analysis of a certain Received: October 15, 2013 Revised: December 4, 2013 Published: December 4, 2013 26689

dx.doi.org/10.1021/jp4102064 | J. Phys. Chem. C 2013, 117, 26689−26702

The Journal of Physical Chemistry C

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noncovalent interaction only when this interaction results in changes of the principal components of the 31P NMR CST which do not compensate each other. If this is not the case, one can try to characterize the interaction using its effect on the parameters of CST. Although the latter approach can be timeconsuming, it can still be attractive taking into account the high sensitivity of 31P NMR. A systematic experimental search for the most appropriate 31 P NMR sensor of noncovalent interactions in a specific system is not the most effective way to solve the problem. A much more promising strategy is to employ theoretical calculations. Density functional theory (DFT) has proven to provide reliable estimates of the 31P NMR chemical shift.23,24 However, the chemical shift calculations often need to be performed at sufficiently high levels of sophistication.25 The strategic goals of this work were (i) to study the effect of noncovalent interactions on the parameters of the 31P NMR CST of phosphine oxides and phosphinic, phosphonic, and phosphoric acids in the presence of multiple noncovalent interactions and (ii) to describe a calculation strategy and a minimal basis set which could semiquantitatively reproduce the experimental data. This goal was subdivided into three specific objectives, aiming to study the effects of (i) weak hydrogen bonds, (ii) strong hydrogen bonds, and (iii) coordination to a metal cation on the 31P NMR CST in the crystalline state. These objectives have been specifically selected due to the following reasons. Phosphine oxides are good proton acceptors26 and are effectively used as cocrystallization agents.27 Phosphinic, phosphonic, and phosphoric acids are strong proton donors and are promising species for applications that involve proton transfer.17,28 All these species often serve as ligands to metal centers29 and are potentially useful in the removal of metal contaminants from water and wastewaters.19,30,31 Thus, the achievement of our objectives can shed light on the potential of the 31P NMR as a tool to study noncovalent interactions in complex systems at the atomic scale. In Figure 1 are depicted substances that have been used as model systems. One does not expect the presence of strong specific interactions between the molecules of methyl(diphenyl)phosphine oxide (1) and triphenyl-phosphine oxide (2). In contrast, the molecules of diphenylphosphinic acid (3), methylphosphonic acid (4), and diphenyl hydrogen phosphate (5) form in the crystalline state characteristic hydrogen bond networks. Hydrogen bonding can also affect the 31P NMR parameters of triphenylphosphine oxide hemihydrate. Complex coordination networks are present in the crystals of lead(II) methylphosphonate (6) and lead(II) bis(diphenylphosphinate) (7).

Figure 1. Substances used as model systems in this work. Methyl(diphenyl)phosphine oxide (1), triphenylphosphine oxide (2), diphenylphosphinic acid (3), methylphosphonic acid (4), diphenyl hydrogen phosphate (5), lead(II) methylphosphonate (6), and lead(II) bis(diphenylphosphinate) (7).

NMR Measurements. The solid-state 31P and 207Pb NMR measurements were performed on an Inf inityplus spectrometer system (Agilent) operated at 7 T, equipped with a variabletemperature Chemagnetics-Varian 6 mm pencil CPMAS probe. The {1H}-31P and {1H}-207Pb CPMAS and static spectra were recorded using a cross-polarization contact time of 5 ms, and the typical 90° pulse lengths were about 4.0 μs. The 31P and 207 Pb NMR spectra were indirectly referenced to H3PO4 (85% in H2O) and Pb(NO3)2, respectively. The strong temperature dependence of the chemical shift of Pb(NO3)2 was neglected and put equal to −3495 ppm.33−35 Thus, the reported 207Pb NMR chemical shifts can be affected by a considerable systematic error. However, they are not of interest to this study. The numerical NMR parameters have been extracted from the experimentally obtained spectra using the WSolids136 program package. DFT Calculations. The Gaussian 09.C.01 program package was used.37 The calculations were done with the most popular DFT functional B3LYP. The geometry optimization was done at the standard convergence criteria. 31P NMR parameters were calculated using the gauge-invariant atomic orbital (GIAO) approximation. A number of conventional basis sets were tested. The SDD pseudopotential with the keyword MWB78 was used to treat Pb2+ cations. This approach cannot provide realistic NMR parameters for the 207Pb NMR CST, so the latter is not discussed here.

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EXPERIMENTAL SECTION Materials. All chemicals were purchased from SigmaAldrich and used without additional purification. The polycrystalline monoclinic and orthorhombic modifications of 2 were obtained by evaporation of toluene and hexane/ dichloromethane solutions under vacuum, respectively.32 Polycrystalline triphenylphosphine oxide hemihydrate was obtained by evaporation of an aqueous solution of ethanol under vacuum. Polycrystalline 6 and 7 were prepared by the precipitation method from lead(II) acetate and the corresponding acid in aqueous solutions. The solutions were stirred for 1 h at 365 K in open laboratory flasks. The precipitates were filtrated and dried under vacuum.

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RESULTS AND DISCUSSION 1. Effect of Weak Hydrogen Bonds. Methyl(diphenyl)phosphine Oxide. There is only one polymorph of 1.38 Its structure is reported in the Cambridge Structural Database (CSD) under the Refcode NEXBOI.39 In Figure 2a are depicted the 31P NMR CPMAS and static spectra of 1 and the approximate directions of the principal components of the 31P NMR CST. The numerical values of the 31P NMR CST are 26690



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ray diffraction (XRD) experiment.38 Despite some changes the trend of the discrepancy remains, and the increase of the basis set size increases the discrepancy (Table 1). We are aware that chemical shifts obtained in our calculations must differ from the experimental ones. The former correspond to a certain geometry of the molecule, while the latter are affected by vibrational averaging.41 However, the observed discrepancy should also include the effect of noncovalent interactions with adjacent molecules that have been neglected in the calculations but are present in the solid state. It is a challenge to incorporate noncovalent interactions in the calculation schema. When these interactions are considered in the liquid state one can use molecular clusters which are considered to be appropriate to the circumstances and treat the other interactions as the effect of polar media. In most cases, this schema provides qualitative (but not quantitative) agreement with experiments.42−44 In solid-state computations one can account for noncovalent interactions using the periodical boundary conditions45−47 implemented into the Crystal09 code.48 This approach is time-consuming and cumbersome. In contrast, one can adapt the structure of the appropriate molecular cluster from XRD data. The applicability limits of the cluster approximation for description of noncovalent interactions in crystals are discussed elsewhere.49,50 In Figure 2b is depicted a molecular cluster of four methyldiphenyl oxide molecules adapted from the available XRD structure. Only the 31P NMR chemical shift of the central molecule is considered. The corresponding phosphorus atom is indicated in Figure 2b. The calculation results are reported in Table 1. The discrepancy between the experimental and calculated values of Δσ is less for all used basis sets. Moreover, the experimental value is between the one obtained with the smallest basis set and the values obtained with the larger ones. We attribute this improvement to the fact that in the crystalline state the oxygen atom at the phosphorus atom of 1 is involved in a number of noncovalent interactions with the C−H groups of neighboring molecules. The shortest among them are contacts to the protons of two methyl groups and one phenyl ring. The corresponding O···H distances are 2.36, 2.47, and 2.63 Å.38 The two shortest contacts are shown in Figure 2b. These interactions can be classified as van der Waals or

Figure 2. Static and CPMAS {1H}-31P spectra of 1 and the approximate directions of the principal components of 31P NMR CST (a). The structure of the cluster used in the final calculations of this tensor (b).

collected in Table 1. These values are the reference values for the accuracy of DFT calculations. However, these calculations provide not the chemical shift (δs) but the absolute chemical shielding (σs) that can be converted to δs if the absolute chemical shielding of a reference compound (σref) is known: δs = σref − σs. The absolute chemical shielding of an isolated molecule of H3PO4 can differ strongly from that in aqueous solution.40 For this reason, we will use as a criterion of quality the anisotropy (Δσ) of the 31P NMR chemical shift. This parameter is defined as Δσ = δ11 − (δ22 + δ33), where δii are the principal components of CST. In all cases, when both geometry and the NMR parameters of 1 are calculated, the resulting value of Δσ is larger than the experimental one (Table 1). The calculated values of the absolute chemical shielding are reported in the Supporting Information. In the tables included in the main text these values are converted into chemical shifts using σref, for which the origin is explained below. To estimate the effect of geometry optimization on the calculated NMR parameters we have adapted the geometry of 1 from the X-

Table 1. Experimental 31P NMR CST of 1 and Its DFT-GIAO Estimate in Different Local Environments 31

geometry exp. d 6-31G** d 6-31G** d 6-31G** d 6-31G** d 6-31++G** d 6-31++G** NEXBOIe NEXBOIe NEXBOIe clusterf clusterf clusterf clusterf

P NMR

d

6-311G** d cc-pVDZ d cc-pVTZ d 6-311++G** d 6-311++G** MP2/6-31G* d 6-311G** d cc-pVDZ d cc-pVTZ d 6-311G** d cc-pVDZ d cc-pVTZ d 6-311++G**

Δσa

δisob

δ11c

δ22c

δ33c

200 254 224 244 255 252 234 241 211 239 227 195 210 232

31.4 22g 23h 26i 21g 21h 24i 24g 23h 29i -

116.8 124g 111h 127i 120g 110h 118i 111g 98h 111i -

78.8 89g 84h 88i 83g 72h 89i 89g 79h 87i -

−101.7 −147g −127h −136i −139g −120h −135i −127g −107h −112i -

a The anisotropy of CST, ppm. bThe average value of the principal components, ppm. cThe principal components of CST, ppm. dB3LYP. eThe molecular structure of the molecule of 1 is adapted from XRD.38 fThe molecular structure of a cluster of four molecules of 1 is adapted from XRD.38 g σref = 317 ppm. hσref = 403 ppm. iσref = 335 ppm.

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three neighboring phenyl rings. The shortest O···H distances are 2.51, 2.67, and 2.67 Å.32 The shortest among them is shown in Figure 3b. We consider a cluster adapted from the available XRD structure and depicted in Figure 3b and only the 31P NMR chemical shift of the indicated nucleus. The discrepancy between the experimental and calculated values of Δσ is small for all used basis sets (Table 2). The experimental value is again between the calculated values obtained with the smallest and larger basis sets. The absolute chemical shielding of the reference compound can be estimated for the B3LYP/ccpVDZ, B3LYP/6-311G**, and B3LYP/cc-pVTZ approaches as: 402, 316, and 341 ppm, respectively. In Figure 4a are depicted the 31P NMR CPMAS and static spectra of the orthorhombic modification of 2. The numerical values of the 31P NMR CST are collected in Table 2. Although these values are close to the values obtained for the monoclinic modification, these two polymorphs can easily be distinguished by 31P NMR. For further calculations we have used the XRD structure reported in CSD under the Refcode TPEPH04.39 The anisotropy of the 31P NMR CST calculated for an isolated molecule is again larger than the experimental one in all cases. In contrast, for a cluster of four molecules of 2 adapted from this XRD structure, the discrepancy is reduced dramatically (Table 2). The used cluster is depicted in Figure 4b. The three shortest O···H distances in this polymorph are 2.41, 2.53, and 2.61 Å.32 The two shortest among them are shown in Figure 4b. Similar to the structures considered above, the 31P NMR CST values calculated for this cluster are close to the experimental ones, and the latter are between the calculated values obtained with the smallest and larger basis sets (Table 2). The absolute chemical shielding of the reference compound can be estimated for the B3LYP/cc-pVDZ, B3LYP/6-311G**, and B3LYP/cc-pVTZ approaches as: 404, 318, and 328 ppm, respectively. We have now enough data to estimate the accuracy of our calculations. We conclude that noncovalent C−H···O interactions remarkably affect the 31P NMR CST values, although the former are much weaker as compared to the strength of conventional hydrogen bonds.51 If these interactions are taken into account, the reliable estimation of the 31P NMR CST values can be obtained by B3LYP/cc-pVDZ, B3LYP/6311G**, and B3LYP/cc-pVTZ approaches. The general trend is that the first approach underestimates the anisotropy of the 31 P NMR CST, while the other two overestimate it. These interactions in both polymorphs of 2 are weaker as compared to the interactions in 1. Thus, the inevitable inaccuracy in accounting for these interactions in the calculation schema used in this work should affect the resulting NMR data the least in the case of 2 compared to 1. For this reason one can convert the values of the 31P NMR chemical shieldings obtained with the B3LYP/cc-pVDZ, B3LYP/6-311G**, and B3LYP/ccpVTZ approaches to the chemical shifts using the following averaged values of the absolute chemical shielding of the reference compound: 403, 317, and 335 ppm, respectively. Using these values one can estimate the values of the principal components of the 31P NMR CST with accuracy better than 15 ppm (Tables 1 and 2). Although this accuracy is insufficient to discriminate between different modifications of 2, it is sufficient either to study the effect of noncovalent interactions on the 31P NMR CST parameters or to characterize noncovalent interactions in the condensed phase on the base of the experimental values of these NMR parameters.

hydrogen bond. For the sake of clarity we prefer the latter. It is not surprising that these interactions affect molecular arrangement in crystals,51 but it is remarkable how strong they can affect the chemical shifts of distant nuclei. If needed, the partial effect of each contact can be estimated by a gradual decrease of the size of the cluster. It can be concluded that a reliable theoretical estimation of the anisotropy of the 31P NMR CST of 1 in the crystalline state requires the inclusion of interactions between the oxygen and the closest C−H protons. However, the calculations of the 31P NMR CST can be done using relatively small basis sets, such as B3LYP/cc-pVDZ, B3LYP/6-311G**, and B3LYP/cc-pVTZ. It does not seem that a further increase of the basis set can increase the accuracy. Triphenylphosphine Oxide. A number of different crystal structures of the orthorhombic32,52−54 and monoclinic32,55,56 polymorphs of 2 and of its hemihydrate57,58 are available in the CSD. Thus, 2 fits perfectly to inspect the limits of our model calculations. The easiest to obtain is the monoclinic polymorph. In Figure 3a are depicted the 31P NMR CPMAS and static

Figure 3. Static and CPMAS {1H}-31P spectra of the monoclinic modification of 2 and the approximate directions of the principal components of 31P NMR CST (a). The structure of the cluster used in the final calculations of this tensor (b).

spectra of this modification and the approximate directions of the principal components of the 31P NMR CST. The numerical values of the 31P NMR CST are collected in Table 2. The anisotropy of the 31P NMR CST calculated for an isolated molecule of 2 whose geometry has been optimized at the B3LYP/6-31G** level is larger than the experimental one regardless of the level of calculation. The numerical values of the 31P NMR CST change slightly when one uses the geometry of the molecule adapted from the XRD structure reported in CSD under the Refcode TPEPH06.39 These variations can be tentatively attributed to the different orientation of the phenyl rings and the associated changes in the ring-current effect. However, there is still a remarkable discrepancy between the experimental and calculated values of Δσ. Thus, to reproduce correctly the 31P NMR CST of 2 in the crystalline state, one needs to incorporate into the calculations relevant noncovalent interactions. These are C−H···O contacts to the protons of 26692



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Table 2. Experimental 31P NMR CST of 2 and Its DFT-GIAO Estimate in Different Local Environments geometry a

6-31G** a 6-31G** a 6-31G**

31

P NMR

a

6-311G** a cc-pVDZ a cc-pVTZ

Exp. monoclinic a TPEPHO06b 6-311G** b a TPEPHO06 cc-pVDZ a TPEPHO06b cc-pVTZ a clusterc 6-311G** a clusterc cc-pVDZ a clusterc cc-pVTZ Exp. orthorhombic a TPEPHO04b 6-311G** b a TPEPHO04 cc-pVDZ a TPEPHO04b cc-pVTZ a clusterc 6-311G** a clusterc cc-pVDZ a clusterc cc-pVTZ Exp. hemihydrate a clusterd 6-311G** d a cluster cc-pVDZ a clusterd cc-pVTZ a clustere 6-311G** a clustere cc-pVDZ a clustere cc-pVTZ Protonated cation of 2 a a 6-31G** 6-311G** a a 6-31G** cc-pVDZ a a 6-31G** cc-pVTZ

Δσ

δiso

δ11

δ22

δ33

224 195 220 189.8 222 192 221 211 179 202 194.5 220 189 218 209 180 198 136.5 214 184 207 205 176 204

30f 30g 31h 27.4 24f 23g 23h 28f 28g 21h 28.8 25f 24g 26h 28f 28g 36h 29.6 22f 22g 19h 23f 23g 27h



−119f −100g −116h −99.1 −124f −106g −124h −113f −91g −114h −101.0 −121f −102g −120h −111f −92g −96h −61.4 −121f −101g −119h −114f −95g −109h

58 50 60

84f 78g 78h

124f 115g 116h

82f 74g 79h

46f 45g 38h

a

B3LYP. bThe molecular structure of the molecule of 2 is adapted from XRD.32 cThe molecular structure of a cluster of four molecules of 2 is adapted from XRD.32 dThe molecular structure of a cluster of two molecules of 2 symmetrically bonded to one molecules of water is adapted from XRD,57 and the positions of the mobile protons are optimized at the B3LYP/6-311G** level. eThe molecular structure of a cluster of two molecules of 2 symmetrically bonded to one molecules of water is adapted from XRD,58 and the positions of the mobile protons are optimized at the B3LYP/6311G** level. fσref = 317 ppm. gσref = 403 ppm. hσref = 335 ppm.

Figure 5. Static and CPMAS {1H}-31P spectra of the hemihydrate of 2 (a). The structure of the cluster used in the final calculations of 1P NMR CST (b).

Figure 4. Static and CPMAS {1H}-31P spectra of the orthorhombic modification of 2 (a). The structure of the cluster used in the final calculations of 31P NMR CST (b).

modification of 2. However, the 31P NMR CST of the hemihydrate can be easily obtained as the one of the latter polymorph is known (Table 2). The dramatic decrease of the anisotropy of the former CST is indicative of the presence of strong noncovalent interactions involving the P−O group. CSD

In Figure 5a are depicted the 31P NMR CPMAS and static spectra of the hemihydrate of 2. In the run of NMR experiments this complex converts slowly to the monoclinic 26693



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reports two XRD structures of the hemihydrate of 2 with the Refcodes JEDTOB0157 and JEDTOB02.58 The characteristic structural units in both cases are one molecule of water hydrogen bonded between two molecules of 2. A cluster adapted from the former XRD structure is depicted in Figure 5b. Such hydrogen bonds are not very strong even in the case of stronger bases such as pyridine.40 On the other hand, we are aware that the available estimations based on XRD data systematically reduce the shorter and increase the longer distance of hydrogen bonds.59,60 This inaccuracy will affect the results of the NMR calculations if the structure is directly adapted from XRD data. To obtain the correct positions of mobile protons, we have carried out the partial optimization of hydrogen bonds in the structural units under study at the B3LYP/6-311G** level. The coordinates of all atoms with the only exception of the mobile protons were taken from the XRD and kept unchanged. This calculation schema has been successfully used in the past.51,61 We have not used this schema to correct the C−H···O relevant distances due to the insignificance of the expected effect. The two coupled O−H···O hydrogen bonds in the clusters adapted from the JEDTOB01 and JEDTOB02 structures become unequal after the optimization. We have not attempted to correct these artifacts. The mean geometric parameters of these bonds are: d(O−H) = 0.966 Å, d(H···O) = 1.961 Å, a(OHO) = 167°, and d(O−H) = 0.968 Å, d(H···O) = 1.91 Å, a(OHO) = 165° for JEDTOB01 and JEDTOB02, respectively. The values of the 31P NMR CST calculated for these geometries are collected in Table 2. For both structures the calculated Δσ are larger as compared to the experimental ones. The increase of the level of the partial optimization of the hydrogen bonds in the cluster adapted from the JEDTOB02 structure to the B3LYP/6-311++G** one does not result in any remarkable effect. Although we cannot exclude that the structure of our polycrystalline sample does not correspond to either of the known XRD structures, it is more reasonable to suppose that the observed discrepancy should be attributed to the fact that crystalline water is mobile on the NMR time scale. This mobility should strongly affect the 31P NMR CST but cannot be reproduced in our approach. Can 1 and 2 be recommended as NMR sensors to study the hydrogen bond? This question can be answered by calculating the limiting values of the 31P NMR CST in a fictitious protonated cation of 2. The geometry of this cation was optimized at the B3LYP/6-31G** level (Table 2). The NMR parameters calculated for the isolated molecule and the cation differ dramatically. The expected span of the isotropic 31P NMR chemical shift values is about 50 ppm. Thus, the isotropic chemical shift can be used as an effective measure of the P−O··· H distance if phosphine oxide is interacting with a very strong acid. In other cases, for example water, one should better use the anisotropy of the 31P NMR CST and especially the value of its most shielded component directed along the P−O bond whose span is expected to be about 150 ppm. It is worth mentioning that the changes of this component are responsible for the reduction of Δσ in phosphonium salts.62 Our data also suggest that the other two components of CST can change nonmonotonically with the O···H distance. However, the analysis of this effect is out of the scope of this study. 2. Effect of Strong Hydrogen Bonds. Diphenylphosphinic Acid. There is only one polymorph of 3 that is reported in the CSD under the Refcodes DPPHIN,63 DPPHIN01,64 and DPPHIN02.65 In Figure 6a are depicted the 31P NMR CPMAS

Figure 6. Static and CPMAS {1H}-31P spectra of 3 and the approximate directions of the principal components of 31P NMR CST in an isolated molecule (a). The structure of the cluster used in the final calculations of this tensor (b).

and static spectra of 3 and the approximate directions of the principal components of the 31P NMR CST in an isolated molecule. The numerical values of the 31P NMR CST are collected in Table 3. The anisotropy of the 31P NMR CST calculated for the isolated molecule of 3 whose geometry has been optimized at the B3LYP/6-31G** level is twice as large as the experimental one. In contrast to 1 and 2 the numerical values of the 31P NMR CST in 3 are very sensitive to the geometry. This becomes obvious from the data obtained for the Table 3. Experimental 31P NMR CST of 3 and Its DFTGIAO Estimate in Different Local Environments geometry

31

P NMR

Exp. a a 6-31G** 6-311G** a a 6-31G** cc-pVDZ a a 6-31G** cc-pVTZ a DPPHIN01b 6-311G** a DPPHIN01b cc-pVDZ a DPPHIN01b cc-pVTZ a Clusterc 6-311G** a Clusterc cc-pVDZ a Clusterc cc-pVTZ a Opt. clusterd 6-311G** a Opt. clusterd cc-pVDZ a Opt. clusterd cc-pVTZ Deprotonated anion of 3 a a 6-31G** 6-311G** a a 6-31G** cc-pVDZ a a 6-31G** cc-pVTZ

Δσ

δiso

δ11

δ22

δ33

132.5 241 210 232 218 195 207 175 154 162 160 140 147

29.0 42e 39f 44g 21e 17f 25g 23e 19f 27g 23e 19f 27g

106.7 160e 140f 157g 128e 110f 128g 116e 97f 114g 114e 95f 113g

39.6 85e 78f 85g 59e 54f 61g 46e 43f 47g 39e 37f 40g

−59.3 −119e −101f −111g −125e −113f −113g −94e −84f −81g −83e −75f −71g

277 248 268

11e 9f 13g

160e 130f 154g

46e 53f 50g

−174e −156f −166g

a

B3LYP. bThe molecular structure of the molecule of 3 is adapted from XRD.64 cThe molecular structure of a cluster of three molecules of 3 is adapted from XRD.64 dThe molecular structure of a cluster of three molecules of 3 is adapted from XRD,64 and the positions of the mobile protons are optimized at the B3LYP/6-311G** level. eσref = 317 ppm. fσref = 403 ppm. gσref = 335 ppm. 26694



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structure adapted from the XRD structure DPPHIN01. We attribute this finding to elongated P−O distances in the latter case. However, the calculated value of Δσ is larger than the experimental one also for this structure. The crystal pattern of 3 is governed by two PO···H−O−P hydrogen bonds. These contacts are depicted in Figure 6b. The corresponding O···O distances vary for different crystal structures: 2.449,64 2.469,63 and 2.47965 Å. The former structure has been used in our calculations because it exhibits the smallest R-factor. In Figure 6b is depicted the structure of a cluster adapted from the available XRD data.64 The positions of all atoms including the mobile protons have been kept unchanged, and only the 31P NMR chemical shift of the indicated nucleus is reported. The discrepancy between the experimental and calculated values of Δσ decreases for all used basis sets but remains remarkably larger than the experimental one (Table 3). Then, the positions of the mobile protons have been optimized at the B3LYP/6-311++G** level keeping the positions of other atoms unchanged. The two O−H···O hydrogen bonds in the original XRD structure are equal, and their geometrical parameters are: d(O−H) = 0.902 Å, d(H···O) = 1.553 Å, a(OHO) = 172°. After the optimization they become slightly different: d(O−H) = 1.026 and 1.028 Å, d(H··· O) = 1.428 and 1.426 Å, a(OHO) = 172° and 175°. As we do not expect that this artifact can remarkably affect the results of calculations, we have not tried to correct it. The correction of the hydrogen bond geometries reduces further the difference between the values of the experimental and calculated Δσ. We attribute the residual difference to the fact that the motion of the mobile protons is totally neglected in our calculations. The arbitrariness in the selection of the reference crystal structure cannot be the main reason for this difference since the elongation of the O···O distances results in a weakening of the corresponding hydrogen bonds that will lead to an increase of the anisotropy of the 31P NMR CST. To inspect whether 3 can be recommended as an NMR sensor to study hydrogen bond interactions, we have calculated the limiting values of the 31P NMR CST in a fictitious deprotonated anion of 3. The geometry of this anion was optimized at the B3LYP/6-31G** level (Table 3). The NMR parameters calculated for the isolated molecule, the molecule forming two hydrogen bonds, and the anion differ dramatically. It is not surprising because the orientations of the principal components of the 31P NMR CST differ in these cases. The general trend is that the isotropic chemical shift is not a good indicator of hydrogen bonding and deprotonation of 3. Both processes are accompanied by a decrease of its value. In contrast, the structure of hydrogen bonds and proton transfer can be monitored by the changes of the 31P NMR CST and its anisotropy. While hydrogen bonding results in a very strong decrease of Δσ, deprotonation causes an increase of it. This feature can be used to study proton exchange or proton transfer, for example, in proton-conducting polymers.17 Methylphosphonic Acid. In Figure 7a are depicted the 31P NMR CPMAS and static spectra of 4 and the approximate directions of the principal components of the 31P NMR CST in an isolated molecule. The numerical values of the 31P NMR CST are collected in Table 4. The anisotropy of the 31P NMR CST calculated for the isolated molecule of 4 whose geometry has been optimized at the B3LYP/6-31G** level is four times larger than the experimental one. The CSD does not report any crystal structure of 4. What is the most reliable way to include into the calculations hydrogen


Table 4. Experimental 31P NMR CST of 4 and Its DFTGIAO Estimate in Different Local Environments geometry

31

P NMR

Δσ

Exp. 55.8 a a 6-31G** 6-311G** 206 a a 6-31G** cc-pVDZ 173 a a 6-31G** cc-pVTZ 197 a Opt. clusterb 6-311G** 65 a Opt. clusterb cc-pVDZ 51 a Opt. clusterb cc-pVTZ 59 Singly deprotonated anion of 4 a a 6-31G** 6-311G** 253 a a 6-31G** cc-pVDZ 217 a a 6-31G** cc-pVTZ 247

δiso

δ11

δ22

δ33

38.1 56c 44d 56e 41c 32d 44e

66.0 127c 105d 125e 65c 51d 66e

47.5 121c 99d 118e 60c 46d 62e

1.0 −82c −71d −75e −2c −2d 5e

31c 22d 35e

150c 119d 149e

81c 70d 85e

−138c −122d −130e

a

B3LYP. bThe molecular structure of a cluster of three molecules of 4 is adapted from XRD;66 tert-butyl groups are changed to methyl groups; and the positions of the mobile protons are optimized at the B3LYP/6-311G** level. cσref = 317 ppm. dσref = 403 ppm. eσref = 335 ppm.

bond interactions that should be responsible for the observed anisotropy of the 31P NMR CST in the condensed state? The conventional way is to construct a cluster of two to four molecules and to optimize its structure. Technically it can be done for 4, but this strategy can work only if such dimers, trimers, or tetramers are identifiable structural units of the crystal pattern of 4. In contrast, the crystal structure of tertbutylphosphonic acid reported in the CSD under the Refcode XABCAF66 demonstrates that the molecules are arranged in 2D sheets whose structure cannot be reproduced by the most energetically favorable structures of small clusters. The problem can be solved in another way. (i) The structure of the cluster of three tert-butylphosphonic acid molecules has been adapted from the XRD structure. (ii) The tert-butyl groups have been changed to methyl groups. (iii) The positions of the mobile protons have been optimized at the B3LYP/6-31++G** level. 26695



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Table 5. Experimental 31P NMR CST of 5 and Its DFTGIAO Estimate in Different Local Environments

We are aware that this strategy induces uncontrolled inaccuracy in the calculation of NMR parameters. However, we have every reason to believe that this inaccuracy is not critical. The structure of the cluster is shown in Figure 7b. There are four O−H···O hydrogen bonds with the O···O distances of 2.58, 2.60, 2.62, and 2.65 Å. The two shortest of them are indicated in Figure 7b. In Table 4 are reported the 31P NMR parameters obtained for the indicated nucleus. These values are very close to the experimentally observed ones. One is safe to conclude that the crystal patterns of tert-butylphosphonic acid and of 4 should be very similar. Deprotonation as the limiting case of the interaction of 4 with proton acceptors affects the 31P NMR CST in a similar way to 3. The geometry of a singly deprotonated anion of 4 was optimized at the B3LYP/6-31G** level (Table 4). The obtained data demonstrate that both hydrogen bonding and deprotonation have a similar effect on the isotropic chemical shift. In contrast, the anisotropy of the 31P NMR CST reflects, in a very characteristic way, every change in the positions of the mobile protons. Diphenyl Hydrogen Phosphate. In Figure 8a are depicted the 31P NMR CPMAS and static spectra of 5 and the

geometry Exp. a 6-31G** a 6-31G** a 6-31G** Opt. clusterb Opt. clusterb Opt. clusterb

31

a

P NMR

6-311G** cc-pVDZ a cc-pVTZ a 6-311G** a cc-pVDZ a cc-pVTZ a

Δσ

δiso

δ11

δ22

δ33

152 243 204 232 181 158 174

−10.5 8c 4d 10e −22c −25d −15e

77.0 100c 84d 97e 66c 49d 69e

4.0 79c 59d 77e 10c 7d 16e

−112.0 −154c −132d −145e −143c −131d −131e

a

B3LYP. bThe molecular structure of a cluster of three molecules of 5 is adapted from XRD67 and partially modified, and the positions of the mobile protons are optimized at the B3LYP/6-311G** level. See text for details. cσref = 317 ppm. dσref = 403 ppm. eσref = 335 ppm.

phosphate molecules forming the hydrogen-bonded cluster has been adapted from the XRD structure. (ii) The chlorophenyl groups of the outer molecules have been changed to methyl groups. (iii) The chlorophenyl groups of the central molecule have been changed to phenyl groups. (iv) The positions of the mobile protons have been optimized at the B3LYP/6-31++G** level. The structure of the cluster is shown in Figure 8b. There are two O−H···O hydrogen bonds with the O···O distances of 2.40 Å. These bonds are shown in Figure 8b. The H···O and O−H distances for the central molecule are 1.378 and 1.021 Å, respectively. In Table 5 are reported the 31P NMR parameters calculated for the indicated nucleus. These values are very close to the experimental ones, and the residual difference should be attributed to the inaccuracy of the applied model structure and the ignorance of hydrogen bond dynamics. Thus, even this rough approach provides correctly the most important trends in the effect of noncovalent interaction on the 31 P NMR CST parameters. Besides that we can speculate that that crystal pattern of bis(4-chlorophenyl) hydrogen phosphate and of 5 should be similar. 3. Effect of Coordination to a Metal Cation. Lead(II) Methylphosphonate. In Figure 9 are depicted the 31P NMR CPMAS and static spectra of 6 and the 207Pb NMR CPMAS spectrum of 6. The numerical values of the 31P NMR CST are collected in Table 6. The isotropic value and the anisotropy of the 207Pb NMR CST are about −560 and 2800 ppm, respectively. Both the isotropic value and the anisotropy of the 31P NMR CST of 6 differ strongly from that of 4 and its singly deprotonated anion (Table 4). The CSD does not report any crystal structure of 6. What is known is the structure of lead(II) vinylphosphonate that is listed under the Refcode QANVOS.68 A cluster for our calculations has been constructed in the following way. (i) The geometry of nine vinylphosphonate molecules and four lead atoms forming the cluster has been adapted from the XRD structure. (ii) The vinyl groups have been changed to methyl groups. (iii) The charges of the outer phosphonate molecules of the cluster have been compensated by protons. Thus, the final cluster includes one doubly deprotonated, six singly deprotonated anions, two molecules of 4, and four Pb2+ cations. The structure of the resulting cluster is depicted in Figure 9c. In Table 6 are reported the 31P NMR parameters calculated for the central molecule of this cluster. These values perfectly reproduce the experimental ones. One can be sure that the crystal patterns of lead(II) vinylphosphonate and of 6 are very similar and that the applied calculation approach can be used to study the effect of coordination to a metal cation.


approximate directions of the principal components of the 31P NMR CST in an isolated molecule. The numerical values of the 31 P NMR CST are collected in Table 5. The anisotropy of the 31 P NMR CST calculated for the isolated molecule of 5 whose geometry has been optimized at the B3LYP/6-31G** level is again larger than the experimental one. It is clear that this discrepancy reflects the presence of a hydrogen bond network in the crystalline state, and we are challenged to explore this network. The CSD does not report any crystal structure of 5. However, the structure of bis(4-chlorophenyl) hydrogen phosphate is listed under the Refcode CLPHOS.67 A cluster for our calculations has been constructed in the following way. (i) The geometry of three bis(4-chlorophenyl) hydrogen 26696



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Table 6. Experimental 31P NMR CST of 6 and 7 and DFTGIAO Estimate in Different Local Environments geometry

31

Exp. 6 Cluster Cluster Cluster Cluster Cluster Cluster Exp. 7

6b 6b 6b 6c 6c 6c

a

Cluster Cluster Cluster Cluster Cluster

7d 7d 7e 7e 7e

a

P NMR

6-311G** cc-pVDZ a cc-pVTZ a 6-311G** a cc-pVDZ a cc-pVTZ a

6-311G** cc-pVDZ a 6-311G** a cc-pVDZ a cc-pVTZ a

Δσ

δiso

δ11

δ22

δ33

74 80 63 80 110 93 107 134 134 156 135 144 123 137

22.2 28f 20g 33h 22f 14g 27h 22.65 23.55 25f 23g 25f 22g 25h

71 90f 67g 95h 93f 70g 95h 112 110 123f 102g 118f 98g 115h

15 19f 15g 24h 25f 21g 31h 21 27 32f 33g 28f 27g 27h

−19 −25f −23g −21h −51f −48g −45h −65 −66 −79f −67g −71f −60g −66h

a

B3LYP. bThe molecular structure of a cluster of one doubly deprotonated, six singly deprotonated anions, and two molecules of 4 and four Pb2+ cations is adapted from XRD.68 cThe molecular structure of a cluster of one doubly deprotonated anion of 4 and four Pb2+ cations is adapted from XRD.68 dThe molecular structure of a cluster of four deprotonated anions and two molecules of 3 and two Pb2+ cations is adapted from XRD.69 eThe molecular structure of a cluster of two deprotonated anions of 3 and two Pb2+ cations is adapted from XRD.69 See text for details. fσref = 317 ppm. gσref = 403 ppm. hσref = 335 ppm.

−487 and 2700 ppm, respectively. While the isotropic value of the 31P NMR CST of 7 differs from that of 3, the anisotropies of the tensors are very similar. In contrast, there is a strong deviation of these parameters in 7 and the depotonated anion of 3. The crystal structure of 7 is reported in the CSD under the Refcodes DPPOPB10.69 There are two crystallographically distinct diphenylphosphinate molecules per unit cell that explain the presence of two signals of equal intensity in the 31 P NMR spectra. A cluster for our calculations has been constructed from four deprotonated anions and two molecules of 3 and two Pb2+ cations. The positions of the atoms have been adapted from the XRD structure. The structure of the resulting cluster is depicted in Figure 10c. The two central diphenylphosphinate molecules in this cluster are crystallographically equal. Thus, our calculation can provide the only set of the 31P NMR parameters. Of course, one can construct a similar cluster centered on the other set of diphenylphosphinate molecules and repeat the calculations of the 31P NMR parameters. However, the experimental data show that the expected difference will be smaller than the margin of errors of the calculations that is about 10 ppm. In Table 6 are reported the calculated 31P NMR parameters. The main trend of the effect of coordination to the metal cation is correctly reproduced, but the deviation between the calculated and experimental values is larger as compared to 6. Can this be a result of the inadequate size of the cluster? We cannot easily increase the number of the molecules in the cluster since even for the discussed cluster we did not succeed to calculate the NMR parameters at the B3LYP/cc-pVTZ level. Instead, one can decrease the size of the cluster to estimate how strongly the NMR parameters can be affected. The simplest possible cluster contains two diphenylphosphinate molecules and two Pb2+ cations. The residual charge of the latter is compensated by hydroxyl anions. The structure of the resulting cluster is

Figure 9. Static and CPMAS {1H}-31P spectra (a) and the CPMAS {1H}-207Pb spectrum (b) of 6. The structure of the cluster used in the final calculations of this tensor (c). The structure of the cluster used in the simplified calculations of this tensor (d).

The question now arises as to how far one can reduce the size of the cluster without losing the validity of the calculations. To inspect this problem the structure of the cluster has been drastically simplified. The two outer molecules of 4 have been removed, while hydroxyl anions have been substituted for the six singly deprotonated anions of 4. The structure of this simplified cluster is depicted in Figure 9d. In Table 6 are reported the 31 P NMR parameters calculated for the methylphosphonate molecule of this cluster. The deviation of the calculated values from the experimental ones is obvious. However, the former can be still used to analyze the effect qualitatively. Lead(II) Bis(diphenylphosphinate). In Figure 10 are depicted the 31P NMR CPMAS and static spectra of 7 and the 207Pb NMR CPMAS spectrum of 7. The numerical values of the 31P NMR CST are collected in Table 6. The isotropic value and the anisotropy of the 207Pb NMR CST are about 26697



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dramatic change of one of the principal components of the 15N chemical shift tensor.79 The changes of the other two components practically compensate each other. As a result the isotropic 15N chemical shift depends monotonically on the N···H distance,80 and the spread of its values is about 125 ppm.81 This feature makes pyridines one of the most useful NMR sensors in hydrogen bond studies. 31P NMR may have even a higher potential for the analysis of noncovalent interactions due to the higher natural abundance and gyromagnetic ratio. The NMR parameters that may be used for this analysis are the isotropic 31P NMR chemical shift and the 31P NMR CST. Of course, the former parameter is much more suitable since the peak intensity of the isotropic signal is, as a rule, 2 to 3 orders of magnitude larger than of the anisotropic one. However, the spread of the isotropic chemical shift values is not always sufficient to characterize the effect of the interaction under study in detail. In Figure 11 are visualized the effects of noncovalent interactions on the 31P NMR isotropic chemical shift of 1−5.

Figure 11. Effect of noncovalent interactions on the isotropic 31P NMR chemical shift of substances 1−5. The δiso(31P) values measured experimentally in the polycrystalline phase (●), hemihydrate (◊), and metal complex (*) and calculated at the B3LYP/cc-pVTZ level for the isolated (■), singly deprotonated (▽), and singly protonated (△) molecules.

This picture demonstrates that the δiso(31P) of phosphine oxides (1 and 2) can be a measure of the proton-accepting properties of these species because protonation, as the limiting case of such interactions, causes a 50 ppm increase of the δiso(31P). However, the effect of hydrogen bonding to water in the hemihydrate of 2 is comparable to the effect of the PO··· H−C interactions in the crystal of 2. Thus, this approach can be productive only for the analysis of interactions with strong proton donors. For the studied acids, 3−5, all tested interactions, namely, hydrogen bonding, deprotonation, and coordination to Pb2+, result in a decrease of the δiso(31P) values. Thus, if several interactions are present and compete in the system under study, it might be possible to discriminate between them but not to identify them based on δiso(31P). The effect of the same interactions on the parameters of the 31 P NMR CST is visualized in Figure 12 on the example of substances 3 and 4. First of all, it is clear that deprotonation from one side and hydrogen bonding and coordination to metal from another side have an opposite effect on most of these parameters as compared to the values in isolated molecules. However, since both the formation of coupled hydrogen bonds in the crystalline states of 3 and 4 and the coordination of

Figure 10. Static and CPMAS {1H}-31P spectra (a) and the CPMAS {1H}-207Pb spectrum (b) of 7. The structure of the cluster used in the final calculations of this tensor (c). The structure of the cluster used in the simplified calculations of this tensor (d).

depicted in Figure 10d. The 31P NMR CST calculated for the simplified cluster is accidentally the closest to the experimental one. These changes indicate that the calculated NMR parameters depend on the number of molecules in the cluster. Thus, 7 demonstrates the limiting accuracy with which the effect of coordination to a metal cation can be estimated in the applied approach.

4.

31

P NMR AS A TOOL TO STUDY NONCOVALENT INTERACTIONS The motivation of this study arises from the success achieved in the past in the application of 15N NMR of pyridines for the study of hydrogen bonding and proton transfer in liquids,70−74 crystals,75 and at the surfaces.76−78 The formation of a hydrogen bond between an acid and pyridine gives rise to a 26698



■

Article

ASSOCIATED CONTENT

S Supporting Information *

DFT-GIAO estimates of the 31P NMR absolute chemical shielding tensor of 1-7 in different local environments. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has benefitted from discussions with Dr. Michael Bodensteiner and Dr. Gábor Balázs and the help of Mr. Fritz Kastner, University of Regensburg, and was supported by the Russian Foundation of Basic Research (Projects 11-03-00346).

Figure 12. Effect of noncovalent interactions on the anisotropy (Δσ) and principal components (δii, i = 1, 2, 3) of the 31P NMR chemical shift tensor of substances 3 and 4. The 31P NMR chemical shift tensor parameters measured experimentally in the polycrystalline phase (●) and metal complex (*) and calculated at the B3LYP/cc-pVTZ level for the isolated (■) and singly deprotonated (▽) molecules.

■

REFERENCES

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oxygen atoms to Pb2+ cations in 7 and 6 reduce the difference between the charge densities located at different oxygen atoms of the same molecule, these interactions exhibit similar effects on the 31P NMR chemical shift tensor. It is worth mentioning that noncovalent interactions can affect both the order and the orientation of the principal components of CST with respect to the molecular frame.82 DFT can reproduce these changes quite accurately.83 Although such analysis was outside the scope of our study, it can provide useful information about the local structure in solids.84

■

CONCLUSION In this work we have studied the effect of noncovalent interactions on the parameters of the 31P NMR chemical shift tensor of phosphine oxides, phosphinic, phosphonic, and phosphoric acids in the presence of multiple noncovalent interactions such as hydrogen bonding and coordination to a metal center. Furthermore, we have aimed to describe a calculation strategy and a minimal basis set which could semiquantitatively reproduce the experimental data. It is possible to reach the following conclusions from this study. (i) The parameters of the 31P NMR chemical shift tensor are often very sensitive to noncovalent interactions. However, the effects of different competing interactions can be similar. In such cases neither the isotropic 31P NMR chemical shift nor the 31 P NMR chemical shift tensor provide sufficient information to identify and characterize these interactions and to describe the local structure in detail. It could be recommended to preface experiments with model calculations. (ii) The effect of the local structure on the parameters of the 31 P NMR chemical shift tensor can be estimated semiqualitatively using the DFT-GIAO approach at the B3LYP/6311G** and B3LYP/cc-pVDZ levels. The best result can be achieved by taking the mean of the values calculated at these two levels that reproduces most of the experimental parameters within the margin of error of 10 ppm. An increase of the basis set does not seem to bring any benefits. (iii) The absolute 31P chemical shieldings for the B3LYP/ccpVDZ and B3LYP/6-311G** basis sets are 403 and 317 ppm, respectively. 26699



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