## Main

The discovery and study of organometallic species spurred the development of synthetic methods that have had a transformative impact on society, from the preparation of essential medicines to the production of modern materials1,2. A broad family of essential catalytic reactions, which include Ziegler–Natta polymerization, Mizoroki–Heck cross-coupling and alkyl C–H activation, rely on transition metal–alkyl intermediates3. These complexes are notably unstable, as they are prone to decompose through rapid β-elimination reactions of either a hydride (β-Η) or a heteroatom (β-Χ) to generate an alkene and a M–H or M–X bond, respectively3. Depending on the desired synthetic outcome, these eliminations need to be either prevented or promoted, which makes understanding and predicting this behaviour essential to the design of catalytic reactions, as they lead to chemically distinct products.

β-Η elimination is the main decomposition pathway for transition metal–alkyl complexes, and often hinders their use in cross-coupling reactions (Fig. 1a)1,3,4. It is also an integral part of catalytic cycles for many important reactions, which include the Mizoroki–Heck reaction, which is used in the synthesis of highly complex and clinically important molecules, such as cethromycin (Fig. 1a)5,6,7,8. As such, it was studied extensively, with many metals and organic substrates being examined3,9. β-X elimination is related to β-H and is similarly ubiquitous, but generally less studied and understood. It is also a transition metal–alkyl decomposition pathway, with important implications in polymer chemistry, where it inhibits the co-polymerization of ethylene and vinyl halides or vinyl ethers and their derivatives (Fig. 1b)10,11,12. Many examples of stoichiometric β-X eliminations are reported, and involve metals such as Ni, Pd, Co, Rh and others13,14,15,16,17,18,19. This fundamental step is also exploited in catalysis. Examples include Mizoroki–Heck-type reactions (Fig. 1a) and asymmetric catalysis by Paioti et al., as well as the work of Tran et al., which shows a wide variety of X groups being eliminated in a synthetically relevant context (Fig. 1c)7,20,21,22,23.

As both β-elimination reactions proceed through metal–alkyl complexes, they are often in direct competition, which leads to chemically distinct alkene products; such competitions have thus far been optimized empirically and are comprehensively reviewed by Le Bras and Muzart24. Despite this inherent competition in most systems, the ubiquity of both β-elimination reactions and the potential to control the reactivity to produce chemodivergent outcomes, there is a paucity of systematic studies that examined the factors controlling their competition. Such studies would ideally reveal general mechanistic trends, and offer in-depth understanding and predictive power for reaction design. To the best of our knowledge, only two examples that study such competitions exist, by Zhang et al.25 and Zhu et al.26 (Fig. 1c). These studies are limited to a narrow set of parameters (a few X groups and no added ligands) and offer no general guidelines for reaction control. A thorough investigation of the β-Η/β-Χ competition should provide fundamental understanding and insight into how to control it, and thereby increase chemists’ ability to design chemoselective catalytic reactions. Such findings will have a wide impact, as transition metal–alkyl intermediates are of increasing importance because saturated species are critical in the development of both materials science and medicinal chemistry27,28,29.

We report mechanistic investigations into the β-Χ/β-Η competition in phosphine-ligated palladium–alkyl complexes (Fig. 1d). We were able to understand the origin of the observed selectivity and to derive selection rules to divert the intermediate selectively down either pathway. Such information may aid chemists in manipulating β-eliminations in the design of chemoselective catalytic transformations.

## Results and discussion

### Effect of leaving group

For our investigation, we selected Pd as the metal of interest and monophosphines as the ligands, given that this combination represents one of the most used classes of catalyst in synthetically important reactions, such as the Suzuki–Miyaura, Mizoroki–Heck, Negishi, Tsuji–Trost and Kumada–Corriu reactions30. As transition metal–alkyl complexes are quite unstable, we generated them in situ through the oxidative addition of benzyl bromides, which bear the X group of interest at the homobenzylic position (Fig. 1d).

We prepared several substrates that bore various synthetically relevant X groups; these included halides, phosphate, sulfonate and carboxylate esters (Fig. 2a). To gain insight on the kinetics of the competition, we monitored the reaction progress over time using 1H NMR spectroscopy. The organic products of the reactions serve as convenient reporters for the reaction selectivity. We initiated our studies using Pd(PtBu3)2 as the model Pd source, as it is a well-defined, highly reactive and commercially available complex, and used as a catalyst in numerous transformations31. On reaction with our substrates it gave rise to a fast oxidative addition, followed by β-H and/or β-Χ elimination, all at room temperature.

The experimentally obtained selectivity was plotted against the aqueous pKa of the conjugate acid (pKaH) of the X group being examined, in analogy to classical physical organic chemistry analyses (Fig. 2b)32. The y axis is a scale that represents the selectivity of the reaction; 1 represents a complete β-Χ selectivity, −1 a complete β-Η selectivity and 0 a 1:1 mixture of the two products (Supplementary Section 3.1). The obtained graph shows a sigmoidal relationship between the two variables, with the function crossing the x axis at a pKaH of approximately −2 (Fig. 2b). The data were fit with a logistic regression function and the confidence intervals for both the fit (dark grey) and the prediction (light grey) are shown (Supplementary Section 3.3). Based on the observed relationship between pKaH and selectivity, we conclude that Pd-assisted β-Χ eliminations are promoted by better leaving groups (Supplementary Sections 3.2 and 4.3). Next, we examined the case of fluoride (pKaH ≈ 3) elimination, as it is a synthetically important example33,34,35 because β-F elimination is common in methods that involve β-X21,23,36,37 and is difficult to circumvent38. Our model predicts that a ratio of 45:1 favours β-Η; indeed, an experimental ratio of >50:1 in favour of β-Η was obtained, which illustrates the predictive capability of the selectivity–pKaH relationship (Fig. 2c). This represents a rare example of β-H being preferred over β-F and is in line with early computational studies, which suggested this could be the case38,39,40.

Having validated our approach and observed a clear trend for a commonly used phosphine–Pd system, we next sought to probe whether the nature of the ligand could influence the overall selectivity of the process, as is the case for many other reactions that involve Pd (refs 41,42). Next, we focused on the most common combination of Pd and phosphine in the literature, namely Pd/PPh3 (searching SciFinder for the formation of a biaryl from an aryl bromide returns 3.1 million results, 1.2 million of which employ tetrakis(triphenylphosphine) palladium (0) as the catalyst). As with Pd(PtBu3)2, the relationship between selectivity and the pKaH of X displayed a sigmoidal relationship, with the same equation describing the function of best fit (Fig. 2d), which further validates our previous findings. The data show that the choice of phosphine strongly affects the preference of Pd-assisted β-Χ eliminations, with a difference of nearly 7 units in the pKaH of X, which results in a 1:1 competition. Interestingly, despite the preference of PPh3 to favour β-Χ, the overall trend remains similar and a clear correlation with the pKaH of the leaving X group is still observed.

### Influence of ligand

To understand the origin of the strong ligand effect, we decided to systematically probe the role of the phosphine ligand on the reaction. As PPh3 and PtBu3 differ in both steric and electronic properties, we decided to first interrogate the effect of varying the electronic properties, as this is easily achieved without affecting the steric parameters by using various para-substituted triarylphosphines. We selected the substrate with X = OAc as the model substrate for these studies, as it displayed a competition near to 1:1 in our studies with PPh3.

We reacted the chosen substrate with isolated homoleptic Pd(0) complexes ligated with para-substituted triarylphosphines that bore electron-withdrawing (Cl) and electron-donating (OMe and NMe2) groups (Fig. 3a). By plotting the obtained selectivity against the Tolman electronic parameter (TEP) for each ligand43,44, we observe that β-Χ was promoted by the more electron-rich ligands.

Despite having a very similar electronic character (TEP 2,054 and 2,056 cm−1, respectively), P(p-NMe2–C6H4)3 and PtBu3 lead to opposite outcomes, which suggests an overriding influence of steric effects (Fig. 3b). It is known that Pd(PtBu3)2 forms monophosphine T-shaped Pd–aryl complexes after oxidative addition as a result of the large steric demand of the PtBu3 ligand45,46,47,48. In contrast, the less sterically demanding aryl phosphine Pd(0) complexes are known to generally form diphosphine square planar Pd(II) complexes after the oxidative addition of aryl or benzyl electrophiles49. We hypothesized that this sterically controlled change in ligation state of the reactive intermediate could be the reason for the observed discrepancy. To experimentally confirm that the speciation change also occurs with benzyl electrophiles, we reacted Pd(PtBu3)2 with excess BnBr and characterized the product of the reaction by 31P{1H} NMR spectroscopy and single-crystal X-ray diffraction (XRD), which confirmed the presence of only one phosphine (Fig. 3b and Supplementary Sections 3.2 and 6). We also performed in situ variable-temperature NMR spectroscopy experiments, which showed the continued presence of PtBu3 during the course of the reaction, providing additional evidence to support the monophosphine intermediate hypothesis (Supplementary Section 5.6).

To further examine our hypothesis about the effect of the intermediate’s ligation state on β-Χ/β-Η selectivity, we selected another trialkyl phosphine with a similar TEP to that of PtBu3 to evaluate its reactivity. In contrast to PtBu3, PCy3 has been shown to form diphosphine ligated complexes and has the appropriate electronic profile (TEP = 2,056 cm−1, Fig. 3b)50,51,52. If the hypothesis holds, reaction of a substrate that displays a β-Χ/β-Η competition with PtBu3 should give β-Χ exclusively with PCy3. We reacted the appropriate substrate (X = OMs) with both Pd(PtBu3)2 and Pd(PCy3)2 and obtained β-Χ/β-Η competition and exclusive β-Χ products, respectively, in line with the ligation-state hypothesis (Fig. 3c). This was further corroborated by reaction with the substrate with X = OCOAr (Ar = p-NO2–C6H4), in which Pd(PtBu3)2 gave rise to β-Η exclusively and Pd(PCy3)2 to β-Χ exclusively. Note that the ligation state of transition metal–phosphine species was recently shown by Newman-Stonebraker et al. to have a strong influence on reactivity, which further supports our hypothesis53.

To rationalize the striking difference in elimination preference, we undertook experiments using stereochemical probes to investigate the stereochemical requirements of β-X (Supplementary Section 5.5). By using the two diastereomers of 1,2-dibromopropylbenzene, we were able to deduce that both syn- and anti-eliminations are permissible pathways for β-Χ, the latter being preferred; these findings agree with the results reported by others20,54.

Based on the above evidence, we propose that sterically demanding ligands promote the formation of three-coordinate T-shaped intermediates, which accelerate the stereospecific syn-β-Η elimination by virtue of their vacant coordination site. This acceleration of the β-Η elimination has been suggested before as a reason for the inherent challenge of using large ligands (which promote reductive elimination) in alkyl–alkyl cross-couplings55. This is further supported by the fact that multidentate ligands are often employed to suppress β-Η elimination, and that tetracoordinate complexes are found to require the dissociation of one ligand prior to β-Η (refs 56,57). The relative preference for β-Χ is not altered by the vacant coordination site as both syn- and anti-eliminations are accessible. This leads to a relative increase in β-H, which allows selective β-Η in the presence of Χ groups that are eliminated in reactions in which diphosphine intermediates are at play (for example, X = F).

Overall, these investigations led us to derive some selection rules for β-Χ/β-Η competition (Fig. 3d). Electron-rich ligands promote β-Χ, possibly due to an increased electron density, which can be donated into the C–X σ* orbital. Ligands that are small enough to permit the formation of diphosphine–Pd(II) intermediates also promote β-Χ relative to β-Η. Conversely, electron-poor ligands promote β-Η relative to β-Χ, as do large ligands, which promote the formation of monophosphine–Pd(II) intermediates.

## Conclusions

In summary, by studying the stoichiometric reactivity of Pd complexes that bear monodentate phosphine ligands, we uncovered the factors that govern the competition between β-Χ and β-Η. The first observation we made was that the ability to perform β-Χ is contingent on the leaving-group ability of the X group; a lower pKaH of X enables β-Χ. More electron-rich ligands promote β-Χ, whereas β-Η is promoted by more electron-poor ligands, although the influence of electronic effects is much smaller than that of steric effects. The size of the ligand influences the reaction by controlling the ligation state of the intermediate. A monophosphine and a diphosphine pathway operate; the former is promoted by large ligands and strongly favours β-Η due to the presence of a free coordination site on Pd. This allows selective β-Η elimination in the presence of X groups with a pKaH > 0 at room temperature. The diphosphine pathway is favoured by smaller ligands and appears to preferentially eliminate X groups with an approximate pKaH < 6 at room temperature.

We believe that this work will serve as a roadmap for further study of this competition and to guide catalyst selection for the development of new methods that incorporate β-Χ and β-Η elementary steps. Further investigations into the role of Lewis acids, salt additives, bases, the choice of metal, the denticity and class of ligand and other factors are still necessary to fully appreciate the opportunities available for control over the selectivity.

## Methods

### Intramolecular competition reactions

The appropriate Pd(0) complex (1.0 equiv.) and hexamethyldisiloxane (internal standard, varying amount) was dissolved in THF-d8 (0.4 ml) on a Schlenk line using an NMR tube adapter. The appropriate benzyl bromide (1.0 equiv.), which was previously dried on the Schlenk-line using vacuum/N2 cycles, was then also dissolved in THF-d8 (0.3 ml) and transferred to the NMR tube using a syringe and metal needle. For reactions that used Pd(PtBu3)2, an 1H NMR spectrum of the sample was then measured within 10 min (time elapsed from the addition of the electrophile solution to the end of the acquisition of the spectrum) from the start of the reaction. The reaction was then periodically monitored by 1H NMR spectroscopy over time to collect kinetic information about the reaction.

### Selectivity expression and regression function

For our analyses, we decided to employ the following function to express the obtained ratios of the β-H and β-X products as a single value:

$$\begin{array}{l}f\left( {\frac{{\left[ {\upbeta-{\mathrm{H}}} \right]}}{{\left[ {\upbeta -{\mathrm{X}}} \right]}}} \right) = 1 - \frac{{\left[ {\upbeta -{\mathrm{H}}} \right]}}{{\left[ {\upbeta -{\mathrm{X}}} \right]}}\,{\mathrm{for}}\,\frac{{\left[ {\upbeta -{\mathrm{X}}} \right]}}{{\left[ {\upbeta -{\mathrm{H}}} \right]}} \ge 1\,{{{\mathrm{or}}}}\,f\left( {\frac{{\left[ {\upbeta -{\mathrm{H}}} \right]}}{{\left[ {\upbeta -{\mathrm{X}}} \right]}}} \right)\\ = \frac{{\left[ {\upbeta -{\mathrm{X}}} \right]}}{{\left[ {\upbeta -{\mathrm{H}}} \right]}} - 1\,{\mathrm{for}}\,\frac{{\left[ {\upbeta -{\mathrm{X}}} \right]}}{{\left[ {\upbeta -{\mathrm{H}}} \right]}} < 1\end{array}$$

This expression ensures a continuous function without asymptotes (for example, expressing the selectivity as a ratio leads to infinity when one of the two products is not detected), which also provides intuitive bounds. A value of 1 represents complete β-X selectivity, −1 represents complete β-H selectivity and 0 represents a 1:1 mixture of the β-H and β-X products.

For building a model that allows for the prediction of new values, we employed a Gompertz equation of the form:

$$f({\rm{p}}K_{{\rm{aH}}}) = A\,{\rm{e}}^{( - e^{(B - C{\rm{p}}K_{{\rm{aH}}})})} + D$$

where A, B, C and D are parameters whose values are determined by nonlinear regression and e is Euler’s number. References 58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86 are relevant to the methods employed in this article and have been discussed in the Supplementary Information.