Using J_PP to Identify Ni Bidentate Phosphine Complexes In Situ

Abstract

Identifying intermediates of Ni-containing reactions can be challenging due to the high reactivity of Ni complexes and their sensitivity toward air and moisture. Many Ni bidentate phosphine complexes are diamagnetic and can be analyzed in situ via ³¹P NMR spectroscopy, but the oxidation state of Ni is difficult to determine using ³¹P chemical shift analysis alone. The J-coupling between P atoms, J_PP, has been proposed to correlate with oxidation state, but few investigations have looked at how J_PP is affected by parameters such as length of the linker or identity of the phosphine or other ligands. The present investigation into the J_PP values of Ni bidentate phosphine complexes with two-carbon and three-carbon linkers shows that the J_PP values observed in ³¹P NMR spectra, ∣J_PP∣, are competent indicators of the oxidation state at Ni. For complexes with two-carbon linkers, ∣J_PP∣ > 40 Hz is typical of Ni⁰ while ∣J_PP∣ < 30 Hz is typical of Ni^II; this trend is reversed for complexes with three-carbon linkers. Additionally, the Lewis acidity of the Ni and Lewis basicity of the phosphine ligand affect J_PP predictably. For example, increased P-to-Ni donation arising from more-donating phosphines or more-withdrawing ligands trans to the P atoms causes a more negative J_PP. These results should enable the oxidation state of Ni and properties of ligands in Ni bidentate phosphine complexes to be determined in situ during reactions containing these species.

Graphical Abstract

INTRODUCTION

Nickel complexes bearing bidentate phosphine ligands (Scheme 1a) are ubiquitous in many synthetically relevant transformations.¹ The oxidation state of Ni typically determines the reactions available to the complex, with electron-rich Ni⁰ complexes reacting via addition and insertion, while Ni^II complexes commonly undergo elimination.². Kumada,^3-11 Suzuki,^12-20 Negishi,^21-30 and Stille³¹ couplings and the Buchwald–Hartwig amination^32-41 utilize these reactivity differences to activate C─X bonds (where X = Cl, Br, I) by addition to Ni⁰ and form C─C and C─N bonds by elimination from Ni^II. Given the relevance of Ni complexes to these synthetically important bond-forming reactions, many investigations involving Ni complexes have utilized ligand design to impart control over reactivity. Bidentate phosphine complexes are useful in this regard, because the linker and other groups bound to P atoms are easily varied. Short linkers between the P atoms enforce a cis geometry at the metal center, enabling facile reductive elimination in comparison to complexes with a trans geometry.^2,42 The other groups bound to the P atoms enable control over the coordination environment, imparting stereoselectivity or modified reactivity.¹ Additionally, due to the high abundance of the spin-active ³¹P isotope,⁴³ obtaining spectra via nuclear magnetic resonance (NMR) spectroscopy is easier in comparison to complexes of C-, N-, O-, and S-based ligands.

Scheme 1.

Ni Bidentate Phosphine Complexes and Their J_PP Values

Ni bidentate phosphine complexes can be characterized by NMR spectroscopy because many are diamagnetic,⁴⁴ giving well-resolved spectra that are free of paramagnetic shifts and associated line broadening.⁴⁵ Ciofini and coworkers noted in a recent study, however, that predicting and rationalizing ³¹P chemical shifts of metal complexes is complicated by the contrasting effects of ligand donation and back-bonding.⁴⁶ This challenge in rationalizing ³¹P chemical shifts makes analyzing organometallic reaction mixtures less straightforward in comparison to using ¹H and ¹³C chemical shifts for organic molecules.^47,48 Additionally, this influence of donation and back-bonding prevents identifying the oxidation state of the metal by chemical shift because σ-donation and π-back-bonding in P─M bonds can change dramatically with oxidation state.⁴⁷ The utility of NMR spectroscopy—which otherwise is a convenient means for the in situ analysis of reactions—is therefore limited by its inability to assign the oxidation state. Instead, the oxidation state must be identified via other methods, which often require isolation or purification of the desired complex. This ex situ characterization can be especially challenging for reactive intermediates, which may be short-lived or difficult to isolate. Given the ease of obtaining NMR spectra from reactions of Ni bidentate phosphines, and the ability to easily keep NMR samples moisture- and air-free,^49,50 a protocol for understanding the structure of Ni bidentate phosphine complexes via ³¹P NMR spectroscopy would be useful.

In place of the chemical shift, J-coupling constants have been investigated to understand the structure and properties of bidentate phosphine complexes.⁵¹ J-coupling arises when spin-active nuclei in different electronic environments interact through bonds via magnetic interactions with electrons.⁵² The strength of this interaction is described using a J-coupling constant denoted as ⁿJ_XY, where X and Y are the nuclei that are coupled and n is the number of bonds separating the nuclei. J-coupling constants involving protons, such as J_HH, have been useful for obtaining chemically meaningful information. For example, the sign of J-coupling (positive or negative) identifies whether J_HH arises from two-bond coupling (²J_HH) or three-bond coupling (³J_HH) because the former tends to be negative and the latter is positive.^{53-58 2}J_HH of CH₂ groups can give electronic information about the substituents on the carbon atom, with more σ-withdrawing substituents or π-donating substituents making ²J_HH less negative.⁵⁹ The ³J_HH coupling gives structural information on the dihedral angle between the two H atoms via the Karplus equation, enabling chemists to understand the geometry of pairs of H atoms from the J-coupling alone.⁶⁰ For this reason, analyses based on three-bond J-couplings have proven useful for the structural characterization of small molecules^61,62 as well as polymers,⁶³ peptides,^64,65 and proteins.^66,67

Similar to the case for J_HH, J_PP can convey important electronic and structural information about pairs of P atoms and the metals they are bound to.⁶⁸ For metal complexes with multiple monodentate phosphines, the magnitude of ²J_PP can indicate a cis or trans geometry, with ²J_PP being larger for complexes with trans phosphine ligands.^{51 2}J_PP can also provide electronic information about the P atoms because ²J_PP depends on the electronegativity of the groups bound to P.^48,69 Additionally, complexes with cis-monodentate phosphine ligands tend to have different J_PP values in comparison to complexes with bidentate phosphine ligands. For example, in Mo and W phosphine complexes, J-coupling between P atoms through the metal (the only J_PP coupling pathway for monodentate phosphine complexes) results in a negative ²J_PP while coupling through the metal and the carbon linker (only available in bidentate phosphine complexes) results in a positive J_PP.⁷⁰

For Ni complexes, systematic studies into the structural effects on J_PP are lacking, but many authors have noted that the J_PP of Ni bidentate phosphine complexes correlates with the oxidation state of Ni.^71-79 Desnoyer et al. state that bidentate phosphine Ni^II complexes often have a low J_PP (less than 30 Hz), and Ni⁰ complexes have a higher J_PP (45–80 Hz; Scheme 1b)⁸⁰ and propose that the dependence of J_PP on oxidation state is influenced by the electronegativity of ligands trans to the phosphines (trans ligands). Similar insights have aided in identifying Ni complexes from reaction mixtures,^81-83 but structural parameters that are commonly varied, such as linker length and R groups, have not been explored with respect to their effect on J-coupling. Additionally, most 1-D NMR spectra give only the magnitude of J_PP (denoted herein as ∣J_PP∣);⁸⁹ the sign of J_PP, which can be obtained experimentally by 2-D NMR spectroscopy,⁷⁰ has not yet been explored but may contain useful chemical information. A deeper understanding of J-coupling in Ni bidentate phosphine complexes is needed to fill these knowledge gaps and improve our ability to identify Ni complexes in situ.

Herein a systematic survey of Ni bidentate phosphine complexes with two-carbon linkers (2C) and three-carbon linkers (3C) is used to understand how the J_PP value varies with the chemical structure. Notably, we show that J_PP trends with the oxidation state and linker length, where 2C linker complexes have J_PP distinct from that of 3C linker complexes. Additionally, calculations show the sign of J_PP is related to the chemical structure, with Ni⁰ complexes having a more positive J_PP in comparison to Ni^II complexes and 2C complexes having a more positive J_PP in comparison to 3C complexes (Scheme 1c). Finally, using charge transfer analysis, J_PP is shown to vary with P-to-Ni donation, with more-donating phosphines or more-withdrawing trans ligands causing a more negative J_PP. This study gives a more complete framework for identifying Ni complexes via ³¹P NMR spectra and for interpreting J_PP in Ni bidentate phosphine complexes.

RESULTS AND DISCUSSION

Literature Survey of Measured ∣J_PP∣ Values.

To understand the relationship between the complex structure and J_PP, a Reaxys⁸⁴ search was performed to find Ni bidentate phosphine complexes with reported NMR spectra (see the Supporting Information). For the 2C data set, the results were limited to species that also had single-crystal X-ray structures, to verify the oxidation state of Ni. This search yielded a sizable data set of 449 complexes. A similar search for three-carbon-linker complexes yielded a data set of only 67 complexes, the majority of which did not contain a resolvable ∣J_PP∣ due to paramagnetism or symmetry. Therefore, 3C complexes without reported X-ray crystal structures were added to the data set, giving 243 complexes (see the Supporting Information). Afterward, the 2C and 3C data sets were screened to remove species that did not have an observable J_PP, such as fluxional complexes or C₂-symmetric complexes. Complexes of other linkers (e.g., one-carbon, four-carbon, etc.) were not included because few examples were available. The 2C and 3C data sets both had more Ni^II complexes in comparison to Ni⁰ complexes. This difference in representation may be due to survivorship bias, because Ni⁰ complexes have high sensitivity toward air and moisture,^85,86 making isolation or characterization more difficult. Additionally, Ni⁰ π-complexes often form fluxional structures in solution, in equilibrium with other π-complexes, causing peak broadening in NMR spectra and reventing a clear assignment of ∣J_PP∣.^87,88 Therefore, information provided by these data sets is limited to complexes that are stable enough and rigid enough to show ∣J_PP∣ and may not represent all possible ∣J_PP∣ from all possible Ni⁰ and Ni^II bidentate phosphine complexes.

The data sets enabled examining the relationships between oxidation state and J-coupling (Figure 1a). The distributions of ∣J_PP∣ were compared statistically by analyzing the variance in ∣J_PP∣ for each oxidation state/linker length pair. The distribution of ∣J_PP∣ between oxidation states for each linker are significantly different, as indicated by the small p-values for the 2C Ni⁰/Ni^II pair (p < 0.0001) and the 3C Ni⁰/Ni^II pair (p = 0.0034). This statistical difference between oxidation states and the small overlap of the data ranges (Table 1) indicate that it is possible to accurately assign oxidation states via experimentally observed ∣J_PP∣ when the linker length is known. For the 2C data set, the Ni⁰ complexes have a higher ∣J_PP∣ in comparison the Ni^II complexes, matching the relationship proposed by previous authors.^71-80 For the 3C linker data set, however, we observed the opposite relationship, with Ni⁰ complexes giving a lower ∣J_PP∣ in comparison to the Ni^II complexes, albeit with considerable overlap. Information about the ³¹P chemical shift was also obtained from these data sets and analyzed, but we did not observe a relationship with the oxidation state (Figure S8) or J_PP (Figures S9-S11).

Figure 1.

(a) Violin plots showing the distributions of experimentally observed ∣J_PP∣ for different Ni oxidation states (Ni⁰, Ni^II) and phosphine linker lengths (two-carbon, three-carbon). Bold lines represent medians, and fine lines represent the 25th and 75th percentiles. Probability that an observed ∣J_PP∣ represents a Ni⁰ or Ni^II complex for (b) 2C and (c) 3C data sets. The gap at the 60–70 Hz range is due to the lack of 3C complexes with ∣J_PP∣ in that range.

Table 1.

Distribution of ∣J_PP∣ Values (in Hz) Reported in the 2C and 3C Data Sets

	2C Ni0	2C NiII	3C Ni0	3C NiII
90th percentile	73.6	47.6	37.1	95.0
75th percentile	66.0	27.1	32.7	83.0
median	57.3	17.7	28.0	44.7
25th percentile	48.0	8.9	12.1	38.9
10th percentile	40.7	4.0	3.7	33.4

On the basis of the data sets, we also determined the probability of an experimentally observed ∣J_PP∣ arising from a Ni⁰ or Ni^II complex of a given linker length. When experimental ∣J_PP∣ < 30 Hz or ∣J_PP∣ > 40 Hz, the oxidation state can be assigned on the basis of J_PP and the number of atoms in the linker. For example, if a Ni bidentate phosphine complex with a two-carbon linker is present in a reaction mixture, and the ³¹p NMR spectrum reveals a set of doublets with ∣J_PP∣ = 57 Hz, there is a high likelihood (89%) that it is a Ni⁰ complex (Figure 1b). If ∣J_PP∣ is instead 23 Hz, then there is a higher likelihood (93%) of it being a Ni^II complex. For 2C complexes with ∣J_PP∣ within the range of 30–40 Hz, there is nearly an equal likelihood of the complex being Ni⁰ (52%) or Ni^II (48%). Similar results are observed for the 3C complexes (Figure 1c), where ∣J_PP∣ in the range of 30–40 Hz has a 60% chance of arising from a Ni^II complex and a 40% chance of arising from a Ni⁰ complex. Therefore, ∣J_PP∣ in the range of 30–40 Hz cannot reliably identify the oxidation state of Ni in a bidentate phosphine complex, while ∣J_PP∣ values outside of this 30–40 Hz range can provide an oxidation state assignment. The reason ∣J_PP∣ increases with increasing oxidation state for 2C complexes and decreases with increasing oxidation state for 3C complexes was not immediately obvious; therefore, quantum chemical calculations were used to elucidate the physical origin.

Signs of J_PP for Ni Bidentate Phosphine Complexes.

J_PP, like all J-couplings, can have a positive or negative sign. A negative J corresponds to a more stable antiparallel nuclear spin alignment, while a positive J corresponds to a more stable parallel nuclear spin alignment.⁸⁹ Although most ³¹P NMR experiments can give the magnitude of J_PP (i.e., ∣J_PP∣), few can give the sign. We sought to understand the signs of the experimentally observed ∣J_PP∣ in our data sets because the sign of J_PP was shown to relate to the structure in other studies of J_PP in metal complexes.⁷⁰ To obtain signs for our data set, quantum chemical simulations were used (see the Supporting Information for computational details). The absolute values of the computed J_PP trend linearly with the experimental values (J_PP^experimental = 0.913∣J_PP^computed∣ + 2.24 Hz; R² = 0.852), indicating that the coupling can be computed with reasonably good accuracy.

Two-bond couplings, such as the J_PP values arising from the through-Ni coupling pathway, are expected to have a negative sign.^47,70,89,90 Simulations show that this is not always true for Ni bidentate phosphine complexes, with many complexes having a positive J_PP (Figure 2). Generally, the 3C complexes have more a negative J_PP in comparison to 2C complexes by ~40 Hz, and Ni^II complexes have a more negative J_PP in comparison to Ni⁰ by ~60 Hz regardless of linker length. The observation that Ni^II complexes have a more negative J_PP in comparison to Ni⁰ regardless of linker length appears to contrast with the relationships observed with ∣J_PP∣, where 2C complexes had the smallest ∣J_PP∣ for Ni^II and 3C complexes had the largest ∣J_PP∣ for Ni^II (Figure 1). These differences between J_PP and ∣J_PP∣ become consistent when it is recognized that a more negative J_PP results in a smaller ∣J_PP∣ when J_PP is positive and a larger ∣J_PP∣ when J_PP is negative. Therefore, ∣J_PP∣ is largest when both the linker length and oxidation state are associated with the same shift in J_PP, such as in 2C Ni⁰ complexes (both shift J_PP more positive) and 3C Ni^II complexes (both shift J_PP more negative), explaining the odd relationship among J_PP, linker, and oxidation state derived from Figure 1. To relate the effects of structure and oxidation state on J_PP, the sign of a measured ∣J_PP∣ therefore needs to be considered (vide infra).

Figure 2.

Violin plots showing distributions of computed J_PP values for different Ni oxidation states (Ni⁰, Ni^II) and phosphine linker lengths (two-carbon, three-carbon). Bold lines represent medians, and fine lines represent the 25th and 75th percentiles.

After we identified that J_PP correlates with the ligand structure and oxidation state, an explanation is still needed to answer why J_PP becomes more negative upon oxidation from Ni⁰ to Ni^II or upon increasing the linker length from 2C to 3C. Given the observed dependence of ∣J_PP∣ on linker length and oxidation state, J_PP may be described as

$$J_{\text{PP}}={}^2{J}_{\text{PP}}+{}^{m+1}{J}_{\text{PP}}$$ (1)

where the ²J_PP term arises from through-Ni coupling and the ^m+1J_PP term arises from through-linker coupling (m = number of carbons in the linker). The effect of changes in oxidation state and linker length on the values of through-Ni and through-linker coupling was therefore explored further with this model in mind.

Effect of Ligand Donation on J_PP.

J-coupling links pairs of nuclei through bonding electrons;⁵² thus, it is expected that changes to the electron density in bonds along the coupling pathway can affect J. This dependence is evidenced by the electronic effects observed for many ²J_HH and ²J_CH couplings.^59,91 For Ni bidentate phosphine complexes, the ²J_PP (i.e., through-Ni) coupling term in eq 1 would likely depend on the electron density in the P─Ni bonds. Therefore, charge transfer analysis using absolutely localized molecular orbitals^92-95 was used to understand P─Ni bonds, including the effects of P-donation and back-bonding (see the Supporting Information for computational details).

The charge transfer analysis showed a strong correlation of J_PP with the σ-bonding P-to-Ni charge transfer (CT_P-to-Ni) (Figure 3), whereas the back-bonding Ni to P charge transfer showed a worse correlation with J_PP (Figure S12). The relationship of J_PP with CT_P-to-Ni indicates that J_PP should become more negative with increased charge donated to Ni. Notably, the slopes of the 2C and 3C lines of best fit do not differ significantly (p-value = 0.3066), indicating that CT_P-to-Ni is independent of the linker length. This independence of CT_P-to-Ni from linker length signifies that P-to-Ni charge transfer solely affects the through-Ni ²J_PP term in eq 1. In principle, increased P-to-Ni donation can arise from an increasing Lewis basicity of P, an increasing Lewis acidity of Ni, or an increasing overlap of Ni and P orbitals. The relationship between J_PP and P-to-Ni charge transfer also provides a rationale for why J_PP varies with oxidation state, because Ni^II is generally more Lewis acidic than Ni⁰, inducing more charge donation from P atoms.

Figure 3.

Plot of J_PP versus P-to-Ni charge transfer with regression lines shown in black. 2C line of best fit: J_PP = −1.648 Hz/me⁻ CT_P-to-Ni + 108.6 Hz. 3C line of best fit: J_PP = −1.542 Hz/me⁻ CT_P-to-Ni + 50.22 Hz. Gray areas indicate the 95% confidence interval for lines of best fit. A single outlier, complex 2-2329, is shown as a gray circle and was excluded from the analysis.

While J_PP trends with P-to-Ni charge transfer, the physical origin of this dependence needed further elucidation. According to Ramsey, J-coupling occurs via four different mechanisms.⁵² The Fermi contact mechanism is the dominant J-coupling mechanism for J_PP in other compounds^96,97 and was therefore expected to be dominant for complexes in our data set. Indeed, calculations of the four different Ramsey contributors to J_PP indicated that the Fermi contact contribution dominated the total J_PP (see the Supporting Information). In the Fermi contact mechanism, J-coupling arises via spin-pairing of s electrons with a nucleus due to their nonzero electron density at the nuclei of atoms.^89,52 Given this, and the high 3s character of the lone pairs of trivalent P atoms, it follows that the value of J_PP should be strongly affected by the donation of P lone pairs into Ni.

This relationship between J_PP and CT_P-to-Ni tracks with the presence of electron-withdrawing groups on ligands trans to P atoms, likely by affecting the Lewis acidity of Ni. Structurally related Ni^II complexes that differ in the number (e.g., 2-2025, 2-2057, 2-2087) or strength (e.g., 2-2046e, 2-2056, 2-2035)⁹⁸ of withdrawing groups on the trans ligands demonstrate this relationship between CT_P-to-Ni and J_PP (Chart 1), with complexes containing more-withdrawing groups having a more negative J_PP and a larger ∣J_PP∣. Complexes of Ni⁰ (e.g., 2-2046d, 2-2046f, 2-2291) also exhibit the trend of a more negative J_PP with an increased number withdrawing groups on the trans ligand, but because Ni⁰ complexes generally have a positive J_PP, this is manifested as a less positive J_PP and smaller ∣J_PP∣.

Chart 1.

Three Series of Complexes That Differ in the Identity of trans Ligands

The relationship between J_PP and CT_P-to-Ni also tracks with the donating ability of the phosphine ligand (e.g., 2-2110 and 2-2296 of Chart 2), with more-donating phosphines⁹⁹ causing a more negative J_PP. However, for complexes with large phosphines, J_PP values were less negative and CT_P-to-Ni values were smaller than those of similar complexes with smaller phosphines. This trend is opposite of what is expected, given that large alkyl substituents (such as tert-butyl) are more electron rich than smaller alkyl substituents and should therefore impart greater P-to-Ni charge transfer. This deviation might arise from the increased steric bulk of large ligands, causing P─Ni bonds to elongate, as observed on comparing complexes 2-2020 and 2-2143c (Chart 2). The increased P─Ni bond length in complexes containing sterically bulky ligands may cause a decrease in the effective overlap of P and Ni orbitals, causing a lower CT_P-to-Ni and a less negative J_PP than expected on the basis of the Lewis structure.

Chart 2.

Series of Structurally Similar Complexes with Varied Phosphine and trans Ligands

While the effect of P-to-Ni charge transfer on J_PP is useful for understanding the NMR spectra of Ni bidentate phosphine complexes, the trends observed with P-to-Ni charge transfer do not explain the differences in J_PP for 2C in comparison to 3C complexes. This limitation is evidenced by the ranges of CT_P-to-Ni, which span similar values for 2C complexes (28.2–133.0 me⁻) and 3C complexes (28.4–112.8 me⁻) but have trend lines with significantly different y intercepts (p-value <0.0001). On the basis of eq 1, the negative shift of J_PP of 3C complexes in comparison to 2C complexes may arise from differences in the through-linker ^m+1J_PP coupling due to the difference in linker identity. Alternatively, the negative shift of J_PP of 3C complexes may be due to the through-Ni ²J_PP term, most likely due to differences in P─Ni─P bite angle caused by the linker.

Effect of Linker Length on J_PP.

Many ²J-coupling constants are dependent on the bond angle at the central atom;^100,101 therefore, the relationship of J_PP with P─Ni─P bite angle was evaluated. If the linker affects J_PP via the through-Ni (²J_PP) coupling term in eq 1, there would be a clear dependence of J_PP on bite angle. However, a low correlation was observed between J_PP and bite angle for the combined data sets (Figure S16). The poor correlations of J_PP with bite angle indicate that the linker does not affect the through-Ni ²J_PP coupling term. This finding suggests that differences in J_PP between 2C and 3C complexes instead arise from differences in the through-linker ^m+1J_PP coupling terms in eq 1.

The through-linker ^m+1J_PP coupling describes ³J_PP and ⁴J_PP for the 2C and 3C complexes, respectively, which should obey Karplus-type relationships that depend on the linker geometry.^100,102 The range of ³J_PP values for complexes in the 2C data set is expected to be small because there is little conformational flexibility available to bidentate ligands with such short linkers when they are bound to metals.¹⁰³ Similarly, the range of ⁴J_PP values is expected to be small, and therefore the average values of ^m+1J_PP are sufficient for eq 1 to be useful.

With these considerations in mind, a three-parameter model was found to be sufficient to describe J_PP for 2C and 3C complexes. The best fit for the three parameters (one slope, one intercept, and one correction for 3C linkers) together enables eq 1 to become

$$\begin{gathered} J_{\text{PP}}=-1.594\text{Hz}∕{\text{me}}^{-}(C{T}_{\text{P-to-Ni}})+105.2\text{Hz}+L \\ L=\left\{\begin{array}{c}\hfill 0\text{Hz}\text{for 2C complexes}\hfill \\ \hfill -48.47\text{Hz}\text{for 3C complexes}\hfill \end{array}\right\} \end{gathered}$$ (2)

where CT_P-to-Ni is the numerical value of charge transfer from P-to-Ni from a charge transfer analysis and L is a parameter that describes the difference in average through-linker ^m+1J_PP. Equation 2 shows a good R² = 0.9267 and RMS error of 11.8 Hz for the combined data set of 203 complexes for which J_PP and CT_P-to-Ni values could be calculated (Figure 4).

Figure 4.

Parity plot comparing J_PP values computed from DFT calculations to the J_PP values predicted by eq 2: slope, 1.00; y intercept, 0.00 Hz.

Implications for the Analysis of ³¹P NMR Spectra.

Equation 2 can be used to interpret ³¹P NMR spectra of Ni bidentate phosphine complexes, even when the sign of J_PP is not directly available through measurements. For example, in the case where quantum chemical simulations are available, a computed value of CT_P-to-Ni can be used with eq 2 to find J_PP, for a comparison to ∣J_PP∣ observed in spectra. Except for ∣J_PP∣ ≲ 10 Hz, where the sign would be ambiguous, the sign will be apparent if the absolute value of the computed J_PP for the simulated Ni complex is near the experimentally observed ∣J_PP∣.

The further utility of eq 2 comes from its description of the behavior of J_PP. The negative dependence of J_PP on P-to-Ni charge transfer enables one to deduce the sign of J_PP in a series of Ni bidentate phosphine complexes with varying ligand electronics. For example, for a sequence of Ni bidentate phosphine complexes with varying P-donating abilities, 1-D ³¹P NMR spectroscopy will give a series of J_PP values. If ∣J_PP∣ increases as the phosphine ligands become more donating, the observed J_PP values are likely negative. If ∣J_PP∣ decreases with more-donating phosphines, the J_PP values are likely positive. A similar screening can be performed by keeping the phosphine ligand the same and incorporating withdrawing groups on the trans ligands, because a more negative J_PP is expected for an increased withdrawing ability of trans ligands. Once the sign is deduced, the trends in Figure 2 suggest that the sign of J_PP can be used to make an oxidation state assignment. Given the complexities involved in determining the sign of J_PP via NMR spectroscopy, this approach—while indirect—may prove to be the simplest option in many cases. Additionally, the incorporation of a term (i.e., L) accounting for differences in through-linker coupling may enable a description of other complexes with varied linker lengths or linker identities, such as BINAP¹⁰⁴ and SPIRAP,¹⁰⁵ provided a value of L can be determined for the linker.

CONCLUSION

J_PP is a convenient NMR parameter for elucidating the structure of Ni bidentate phosphine complexes. For 2C complexes, ∣J_PP∣ < 30 Hz and ∣J_PP∣ > 40 Hz are indicative of Ni^II and Ni⁰, respectively, while the reverse is true for 3C complexes. This seemingly odd relationship among ∣J_PP∣, oxidation state, and linker length becomes more easily understood after examining the sign of J_PP, where a more negative J_PP is observed with a higher oxidation state for both linker lengths. The relationships between CT_P-to-Ni and J_PP will enable assignment of the sign of J_PP by examining how ∣J_PP∣ changes with structures that induce P-to-Ni donation. Alternatively, at least for complexes that are structurally similar to any of the 232 complexes of the present data set, the sign may be elucidated by comparison to the J_PP values given in Tables S4 and S5 of the Supporting Information.

Given the ease of obtaining ³¹P NMR spectra of reaction mixtures, the correlations between J_PP and ligand electronics are expected to be useful for identifying reaction intermediates in situ. Similar relationships of J_PP with charge transfer are likely present in other phosphine complexes, but more analysis will be needed to understand the effects of metal identity or metal geometry. Put together, these insights should enable a deeper understanding of the structure and properties of key intermediates in reactions of Ni bidentate phosphine complexes.