JPP, 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. Although most 31P NMR experiments can give the magnitude of JPP (i.e., ∣JPP∣), few can give the sign. We sought to understand the signs of the experimentally observed ∣JPP∣ in our data sets because the sign of JPP was shown to relate to the structure in other studies of JPP in metal complexes. 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 JPP trend linearly with the experimental values (JPPexperimental = 0.913∣JPPcomputed∣ + 2.24 Hz; R2 = 0.852), indicating that the coupling can be computed with reasonably good accuracy.
Two-bond couplings, such as the JPP values arising from the through-Ni coupling pathway, are expected to have a negative sign. Simulations show that this is not always true for Ni bidentate phosphine complexes, with many complexes having a positive JPP (Figure 2). Generally, the 3C complexes have more a negative JPP in comparison to 2C complexes by ~40 Hz, and NiII complexes have a more negative JPP in comparison to Ni0 by ~60 Hz regardless of linker length. The observation that NiII complexes have a more negative JPP in comparison to Ni0 regardless of linker length appears to contrast with the relationships observed with ∣JPP∣, where 2C complexes had the smallest ∣JPP∣ for NiII and 3C complexes had the largest ∣JPP∣ for NiII (Figure 1). These differences between JPP and ∣JPP∣ become consistent when it is recognized that a more negative JPP results in a smaller ∣JPP∣ when JPP is positive and a larger ∣JPP∣ when JPP is negative. Therefore, ∣JPP∣ is largest when both the linker length and oxidation state are associated with the same shift in JPP, such as in 2C Ni0 complexes (both shift JPP more positive) and 3C NiII complexes (both shift JPP more negative), explaining the odd relationship among JPP, linker, and oxidation state derived from Figure 1. To relate the effects of structure and oxidation state on JPP, the sign of a measured ∣JPP∣ therefore needs to be considered (vide infra).
After we identified that JPP correlates with the ligand structure and oxidation state, an explanation is still needed to answer why JPP becomes more negative upon oxidation from Ni0 to NiII or upon increasing the linker length from 2C to 3C. Given the observed dependence of ∣JPP∣ on linker length and oxidation state, JPP may be described as equation where the 2JPP term arises from through-Ni coupling and the m+1JPP 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 JPP.
J-coupling links pairs of nuclei through bonding electrons; 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 2JHH and 2JCH couplings. For Ni bidentate phosphine complexes, the 2JPP (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 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 JPP with the σ-bonding P-to-Ni charge transfer (CTP-to-Ni) (Figure 3), whereas the back-bonding Ni to P charge transfer showed a worse correlation with JPP (Figure S12). The relationship of JPP with CTP-to-Ni indicates that JPP 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 CTP-to-Ni is independent of the linker length. This independence of CTP-to-Ni from linker length signifies that P-to-Ni charge transfer solely affects the through-Ni 2JPP 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 JPP and P-to-Ni charge transfer also provides a rationale for why JPP varies with oxidation state, because NiII is generally more Lewis acidic than Ni0, inducing more charge donation from P atoms.
While JPP 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. The Fermi contact mechanism is the dominant J-coupling mechanism for JPP in other compounds and was therefore expected to be dominant for complexes in our data set. Indeed, calculations of the four different Ramsey contributors to JPP indicated that the Fermi contact contribution dominated the total JPP (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. Given this, and the high 3s character of the lone pairs of trivalent P atoms, it follows that the value of JPP should be strongly affected by the donation of P lone pairs into Ni.
This relationship between JPP and CTP-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 NiII complexes that differ in the number (e.g., 2-2025, 2-2057, 2-2087) or strength (e.g., 2-2046e, 2-2056, 2-2035) of withdrawing groups on the trans ligands demonstrate this relationship between CTP-to-Ni and JPP (Chart 1), with complexes containing more-withdrawing groups having a more negative JPP and a larger ∣JPP∣. Complexes of Ni0 (e.g., 2-2046d, 2-2046f, 2-2291) also exhibit the trend of a more negative JPP with an increased number withdrawing groups on the trans ligand, but because Ni0 complexes generally have a positive JPP, this is manifested as a less positive JPP and smaller ∣JPP∣.
The relationship between JPP and CTP-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 phosphines causing a more negative JPP. However, for complexes with large phosphines, JPP values were less negative and CTP-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 CTP-to-Ni and a less negative JPP than expected on the basis of the Lewis structure.
While the effect of P-to-Ni charge transfer on JPP 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 JPP for 2C in comparison to 3C complexes. This limitation is evidenced by the ranges of CTP-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 JPP of 3C complexes in comparison to 2C complexes may arise from differences in the through-linker m+1JPP coupling due to the difference in linker identity. Alternatively, the negative shift of JPP of 3C complexes may be due to the through-Ni 2JPP term, most likely due to differences in P─Ni─P bite angle caused by the linker.
Effect of Linker Length on JPP.
Many 2J-coupling constants are dependent on the bond angle at the central atom; therefore, the relationship of JPP with P─Ni─P bite angle was evaluated. If the linker affects JPP via the through-Ni (2JPP) coupling term in eq 1, there would be a clear dependence of JPP on bite angle. However, a low correlation was observed between JPP and bite angle for the combined data sets (Figure S16). The poor correlations of JPP with bite angle indicate that the linker does not affect the through-Ni 2JPP coupling term. This finding suggests that differences in JPP between 2C and 3C complexes instead arise from differences in the through-linker m+1JPP coupling terms in eq 1.
The through-linker m+1JPP coupling describes 3JPP and 4JPP for the 2C and 3C complexes, respectively, which should obey Karplus-type relationships that depend on the linker geometry. The range of 3JPP 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. Similarly, the range of 4JPP values is expected to be small, and therefore the average values of m+1JPP are sufficient for eq 1 to be useful.
With these considerations in mind, a three-parameter model was found to be sufficient to describe JPP 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 equation where CTP-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+1JPP. 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 JPP and CTP-to-Ni values could be calculated (Figure 4).
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 JPP is not directly available through measurements. For example, in the case where quantum chemical simulations are available, a computed value of CTP-to-Ni can be used with eq 2 to find JPP, for a comparison to ∣JPP∣ observed in spectra. Except for ∣JPP∣ ≲ 10 Hz, where the sign would be ambiguous, the sign will be apparent if the absolute value of the computed JPP for the simulated Ni complex is near the experimentally observed ∣JPP∣.
The further utility of eq 2 comes from its description of the behavior of JPP. The negative dependence of JPP on P-to-Ni charge transfer enables one to deduce the sign of JPP 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 JPP values. If ∣JPP∣ increases as the phosphine ligands become more donating, the observed JPP values are likely negative. If ∣JPP∣ decreases with more-donating phosphines, the JPP 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 JPP 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 JPP can be used to make an oxidation state assignment. Given the complexities involved in determining the sign of JPP 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 BINAP and SPIRAP, provided a value of L can be determined for the linker.
CONCLUSION
JPP is a convenient NMR parameter for elucidating the structure of Ni bidentate phosphine complexes. For 2C complexes, ∣JPP∣ < 30 Hz and ∣JPP∣ > 40 Hz are indicative of NiII and Ni0, respectively, while the reverse is true for 3C complexes. This seemingly odd relationship among ∣JPP∣, oxidation state, and linker length becomes more easily understood after examining the sign of JPP, where a more negative JPP is observed with a higher oxidation state for both linker lengths.