Open Access Article
Théo P.
Gonçalves‡
,
Indranil
Dutta‡
and
Kuo-Wei
Huang
*
KAUST Catalysis Center and Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia. E-mail: hkw@kaust.edu.sa
First published on 9th February 2021
Unlike the conventional model of transition metal catalysis, ligands in metal–ligand cooperative (or bifunctional) catalysis are involved in the substrate activations. Such processes have offered unique mechanistic understandings and led to new concepts for the catalyst design. In particular, unprecedented activities were discovered when the ligand could undergo dearomatization–rearomatization reactions during the catalytic cycle. Aromatization can provide an extra driving force to thermodynamics; consequently, it brings a new perspective to ligand platform design for catalysis. While numerous applications were demonstrated, the influences of changing ligand aromatic properties were often overlooked. In this article, representative ligand systems will be highlighted and a comparison between the Milstein and the Huang pincer systems will be discussed to provide theoretical and conceptual insights.
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| Fig. 1 Different modes of substrate activations in conventional and metal–ligand cooperative catalysis. | ||
MLC has been identified in several hydrogenative and dehydrogenative processes catalyzed by naturally occurring metalloenzymes (alcohol dehydrogenase, hydrogenase catalase, hydrolase, etc.).3–5 Following the pioneering works by Shvo6–9 and Noyori10–14 in the mid-1980s and 1990s, respectively, this concept has gained increasing attention and has been incorporated into the design of synthetic catalysts. The synergistic interplay between metal and ligand(s) accounts for the improved reactivity and selectivity that would not have been achieved if the metal had acted alone, opening up a new dimension for bond activation and catalysis.15–19
The Noyori-type reactivity has been well studied and developed.15,16 In a typical catalytic cycle (Fig. 2),20 the coordinatively unsaturated active intermediate (NB) is generated via a base mediated conversion of the coordinatively saturated precursor (NA). NB subsequently facilitates the heterolytic cleavage of molecular hydrogen (H2) (or using isopropanol as the H2 source) across the Ru–amide bond to generate an amino Ru–hydride species (NC). The carbonyl substrate then binds to NC in the second coordination sphere and two hydrogens of antagonistic polarities are transferred to the substrate in a concerted manner via an outer-sphere mechanism with the regeneration of the active catalyst (NB). The term, bifunctionality, was coined to underline the roles of the Lewis basic ligand(s) and the Lewis acidic metal center to polarize a neutral H2 molecule,21–24 and analogous MLC reactivities were observed in many recent examples.25
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| Fig. 2 Ketone hydrogenation and interconversion of amido/amine forms in Noyori's catalyst (Ru: ruthenium, Ar = aryl, and R = alkyl). | ||
Unlike the Noyori's model, a non-coordinating atom in the ligand partakes in the Shvo MLC system (Fig. 3). The cyclopentadienone ligand in SA is converted to an aromatic hydroxycyclopentadienyl moiety in SB upon treatment with a H2 donor (e.g. isopropanol) along with the change of the formal oxidation state of Ru from 0 to +2. However, the roles of the ligand aromatic properties did not receive much attention until another groundbreaking discovery was made on MLC involving aromatization–dearomatization processes of PNP and PNN pyridine-based pincer complexes by Milstein and co-workers (Fig. 3).26–29 Finally, inspired by the distinct kinetic and thermodynamic properties in our PN3(P) pincer ligand platform by replacing the CH/CH2 spacers in the Milstein system to N/NH arms (Fig. 3),30–32 the influences of aromatic stabilization energies (ASE) on the thermodynamics of MLC were elucidated.33 In this distinctive subclass, MLC via aromatization–dearomatization, the relation between metal and ligand is even more rigorous. In this article, representative systems where ligands undergo aromatization–dearomatization during MLC will be highlighted. A comprehensive comparison between the Milstein and the Huang pincer systems will be provided. After introducing the known MLC system via aromatization–dearomatization, and a short introduction to the theoretical aspect of the aromaticity, a comprehensive comparison between the Milstein and the Huang pincer systems will be provided. Our aim is to familiarize the readers with the recent conceptual understanding of aromaticity and its contribution to the thermodynamics of the catalytic reactions.
An outer-sphere mechanism was proposed for the transfer hydrogenation of ketones. Extensive mechanistic studies including kinetic isotope effects, deuterium labelling experiments and theoretical calculations, suggested a concerted proton (–OH group at the hydroxycyclopentadienyl ligand) and hydride (Ru–H) transfer from the 18e complex (SB) to the carbonyl group with the concurrent formation of SA (Fig. 4).37,38 This simultaneous proton/hydride transfer step requires only one single coordination site around the metal and hence may proceed without any ring slippage. The outer-sphere route was also supported by the kinetic isotope effects in the alcohol dehydrogenation, where SA served as an active catalyst.39 Overall, the Shvo MLC is realized by the reversible interconversion between the aromatic η5-hydroxycyclopentadienyl ligand and the η4-cyclopentadienone moiety along with the 2e redox activity of the Ru center to facilitate bond activation events.
The Shvo-type MLC reactivities appear to be general. Analogous iron hydride hydroxycyclopentadienyl systems were investigated by Casey and Guan.40 The Knölker complex (2)41 was found to be efficient towards hydrogenation of carbonyl compounds and aldimines, and alcohol oxidation.40,42 Similar to the Shvo catalyst, interconvertible iron species are accounted for by the bifunctional substrate activation. The iron hydride species 2 is active for hydrogenation whereas the resulting coordinatively unsaturated 3 is active for dehydrogenation (oxidation). Extensive kinetic studies, stoichiometric experiments, and computational analysis support a concerted proton/hydride transfer process in an outer-sphere mechanism where hydrogen transfer from 2 is the rate-limiting step (Fig. 5).40,43
Nozaki and co-workers have designed a number of iridium (Ir) and rhodium complexes bearing a hydroxycyclopentadienyl ligand and tested their catalytic activities towards acceptor-less dehydrogenation of C–C single bonds.44 The Ir complex having an OH group in the Cp ring (4) displayed the best activity compared to those of other silyl-protected ones and the rhodium analog (Fig. 6). The design principle was guided by MLC and the –OH group in alkyl hydride complex 7 (18e) was hypothesized to drive the release of dihydrogen via heterolytic bond formation with concurrent generation of unsaturated 16e alkyl complex 8, followed by a successive β-hydride elimination to afford the alkene product. H/D exchange studies and computational analysis suggest that this β-hydride elimination is the rate limiting step. The regenerated complex 5 may then undergo an intramolecular proton transfer to give intermediate 6, which has two open coordination sites suitable for oxidative addition of a C–H bond. Very interestingly, complex 4 is also active for catalyzing the hydrogenolysis of C–O bonds of arenols and aryl methyl ethers (Fig. 7).45 The unique reactivity and selectivity was proposed to proceed via a similar concerted transition state to that of ketone hydrogenation by the Shvo catalyst.
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| Fig. 6 MLC assisted dehydrogenation of C–C single bonds catalyzed by the Ir analog (4) of the Knölker complex. | ||
Pioneering work from Yamaguchi, Fujita, and co-workers also established the decisive role of the –OH group(s) during the dehydrogenative alcohol oxidation catalyzed by an Ir complex tethered to 6,6′-dihydroxy-2,2′-bipyridine.52,53 The pivotal role of ligand assisted alcohol activation involving aromatization–dearomatization was realized. In the proposed mechanism (Fig. 9), H2O is removed from the dicationic precatalyst (13) to generate a coordinatively unsaturated monocationic active catalytic species (14) followed by the alcohol activation to produce an alkoxo Ir intermediate (15). Subsequent elimination reaction results in the formation of the carbonyl product and a hydrido Ir intermediate (16) that releases H2 to complete the catalytic cycle.
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| Fig. 9 Proposed mechanistic pathway for alcohol dehydrogenation using the Cp*Ir complex bearing dihydroxy-2,2′-bipyridine. | ||
Another unique example of MLC was observed in Ru complex 17 possessing a 4,5-diazafluorenide ligand towards heterolytic H2 activation.54 The proton migrates to the 9th position of the central ring of 17 leading to dearomatization, and the hydride goes to the Ru center to generate 18 (Fig. 10). Controlled studies using D2 resulted in D incorporation into the 9th position of the ring and the formation of a Ru–D bond. Interestingly, D incorporation was also observed at the ortho-C–H of the PPh3 ligands, which was attributed to the concomitant reversible cyclometalation. Reaction of partially deuterated 17 with H2 led to protium re-incorporation in the ring, Ru and ortho-C of PPh3, further confirming the reversibility of the process.
The Milstein group reported a tetradentate phenanthroline-based bisphosphine ligand and the corresponding Ru complex (19).55 Upon treatment with a base, the resulting dearomatized species 20 could undergo unusual stepwise MLC aromatization/deconjugation processes in the presence of H2 to give complex 22 with trans-dihydride complex 21 as a possible intermediate (Fig. 11). Further reaction of 22 with H2 was not observed. Notably, hydrogenation of the C
C double bond of the ligand backbone is reversible as complex 20 can be formed by heating 22 in an open system. Both 20 and 22 catalyze the dehydrogenative coupling of primary alcohols to esters efficiently, however, they show limited activity in the hydrogenation of esters.
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| Fig. 11 Reversible H2 activation by a Ru phenanthroline–bisphosphine complex (LiHMDS: lithium bis(trimethylsilyl)amide). | ||
C bond, the electron lone pair of the dearomatized pyridine's nitrogen, and two σ electrons of H2. The aromaticity from the involvement of six electrons may stabilize the transition states to form the rearomatized trans-dihydride 25. Hydride transfer from 25 to a carbonyl substrate, such as methyl formate, can then occur to yield intermediate 26, which undergoes proton transfer from the CH2 moiety to the bound methoxymethoxide. The significant discoveries by the Milstein group encourage the development of synthetic applications of a series of pyridine-based transition metal pincer catalysts.25,27,66
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| Fig. 12 Computed plausible mechanism by Wang for the first step of methyl formate hydrogenation catalyzed by Milstein's catalyst 23. | ||
Motivated by Milstein's work and other studies on coordination chemistry,67–69 we were prompted to examine the effects by replacing the CH2 arm(s) with one or two NH groups in the conventional PNN and PNP systems because of the different acidity and bond strengths of the C–H and N–H bonds.31,32,70,71 Remarkably, in our PN3(P) complexes, distinct thermodynamic and kinetic properties were observed compared to those of CH2 analogs.30,72–74 For example, in the hydrogenation reaction, the MLC rearomatization from MA to MB or 23 to 25 is exergonic, but that of HA to HB is endergonic. Furthermore, proton transfer shuttles (e.g. water or alcohol) play a crucial role in mediating the H2 activation and transfer processes in the Huang system. A two-water shuttle is needed to convert HA and H2 to HB, through transition state 27, while the hydrogen transfer steps from HB to carbonyl substrates (transition state 28) only require one-water shuttle (Fig. 13). Indeed, diverse catalytic activities were identified across different transition metal complexes on the Milstein-type 2,6-lutidine-based PNN/PCN and Huang's PN3(P) platforms.70 All these observations suggest that a closer look at the effects of aromaticity to understand energetics between various reaction pathways is necessary.
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| Fig. 13 Computed plausible mechanism of acetaldehyde hydrogenation catalyzed by Huang's catalyst HA. | ||
“aromatic”
smell. Kekulé in 1865 suggested the cyclohexatriene
benzene
structure, which is considered to be the origin
of the structural
basis
of aromaticity.77 One year later, Erlenmeyer noticed that in aromatic structures substitution was more favorable than addition, providing evidence of the connection between aromaticity and reactivity for the first time.78 Remarkably, Hückel theoretically explained unusual aromatic stability by the theory
of
cyclic
(4n
+
2)π
electron
systems,79,80 and finally Pauling associated resonance and valence
bonds
with aromaticity.81 The experimental proof of additional aromatic stability was later provided by Kistiakowski to support Pauling's statement.82 Aromaticity was soon recognized as one of the most fundamental concepts in organic chemistry.83–89 As it is not the intention of this article to provide an in-depth review on aromaticity, interested readers are referred to the relevant literature.
While a precise definition has not yet been materialized, experimental scientists and theoreticians continue to develop and explore various tools in an effort to characterize and quantify aromaticity. Although numerous descriptors have been suggested,85 unfortunately, there is no perfect option that can be used as the general quantitative measure.90,91 As aromaticity is connected to induced ring currents, magnetic properties are important for its evaluation and detection.85 The Harmonic Oscillator Model of Aromaticity (HOMA) is a simple and successful tool for aromaticity measuring only based on the geometry,92 but Nucleus Independent Chemical Shifts (NICS) is one of the most widely used for investigating aromaticity based on the magnetic criteria.85,93,94 The negative NICS value of a ring designates the presence of the induced diatropic ring current, which is linked with aromaticity. The positive value indicates the paratropic ring current which is comprehended as antiaromaticity.95 While it is well known that sometimes NICS suffers from inferior results, it is normally accepted despite doubtful views.88 Compared with other indices of aromaticity probes localized in the geometrical center of the ring, (NICS(0)iso) may misalign the results.95 Placing the NICS probe 1 Å above/below the ring, designated as NICS(1)iso, was found to be a better indicator of the ring current.96,97 Further improvement was observed when out-of-plane zz components of the NICS tensor was employed, designated as NICS(1)zz, showing excellent correlation with the other aromaticity indices.94,97 It is also convenient to describe aromaticity with the Aromatic Stabilization Energy (ASE)98 that can be calculated as a difference of the strength of (hyper)conjugation between the cyclic molecule and the acyclic reference compound via an energy decomposition analysis (EDA) approach.99,100 Additionally, the Valence Bond Self-Consistent Field (VBSCF) method can also be useful in such calculations.101
The aromaticity study by the Wu group demonstrated the influences of the hydrogen bonds on the enhancement and reduction of the aromaticity in pyridine based rings.107–109 Those hydrogen-bonded systems are important in biologically relevant processes and aromaticity was found to be one of the driving forces for the selectivity in base-pairing interactions.110 The aromaticity on small dimers with hydrogen bonding interactions increases the cyclic 4n + 2 π-electron delocalization (Fig. 15A) for (pseudo)dearomatized rings. However, hydrogen bonding interactions reduce aromaticity for aromatic sextets.
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| Fig. 15 Aromaticity change in quinoidal/pyridine moiety influenced by hydrogen bonding (A), metal complexation (B) and CH/NH arms pyridine (C). | ||
As we just showed, the pyridine base ligands provide access to many catalytic hydrogenation reactions, and the aromatization/dearomatization catalyst design concepts can be readily practiced on this platform. As discovered by Milstein in 2005,26 a plausible mechanism states that the catalyst becomes aromatic as a result of accepting H2 from desaturation of the substrate (Fig. 16). In the next step, the release of H2 regenerates the initial dearomatized form of the catalyst, therefore closing the cycle. The cycle can follow opposite directions if the right conditions are used.112 Thus, the overall reaction can be seen as the composition of the events related to the bond breaking/forming, aromatization, and hydrogen evolution steps. In the key step of the catalytic cycle, the activation of the substrate (C–H and X–H) is dictated by the energetic balance of bonds being formed/broken (M–H and Z–H) and the gain of the aromaticity. Here, it is worth mentioning that in many dearomatized pyridine structures an aromatic resonance form is present.113,114 Thus the (pseudo)dearomatized concept applies for those molecules with weak aromatic stabilization energy. For historic reasons, herein, we chose the symbol of the sun (sunflower)85 to represent aromatic rings and the moon as the counterpart to illustrate (pseudo)dearomatized (nonaromatic) rings. Prior to our work, there were limited known applications utilizing and discussing aromaticity descriptors in the field of catalysis. The dearomatization–rearomatization process is a key factor to understand the MLC reactivities (Fig. 17). Even though many factors influence the reactivity of the Shvo, Milstein, and Huang systems, the ring nature is the key to understand the thermodynamics differences. Using H2 activation as a model reaction, the Shvo and PNx(P) platforms become aromatized while accepting H2. Simultaneously, the double bond migrates forming an aromatic ring and the interaction between the metal and ligand becomes weaker. Although reactive sides are not part of the pyridine or cyclopentadienyl moiety, aromatization of them contributes to the reaction energy, providing an additional driving force to either promote or inhibit the reactivity. Consequently, the extra electronic stabilization energy arising from the ASE of the ligand has potential in modifying or tuning the reaction energetics.
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| Fig. 17 Reactivity of the Shvo, Milstein, and Huang catalyst systems via the aromatization/dearomatization process. | ||
Hence, tuning bond energies and aromatization may influence the chemical output. The aromaticity criteria, as described in the previous paragraph, are still based on the qualitative interpretation. For the study on the ligand aromaticity with small structural changes, the NICS(1)zz descriptor was found to be appropriate for such estimation. Similarly, the bond dissociation energies can be estimated or calculated with reasonable precision with experiments or computational calculations. For example the H2N–H bond is stronger than H3C–H115 by 3.3/1.8 kcal mol−1 (experiments/calculated) and the ArNH–H bond is stronger than ArCH2–H by 2.3/1.6 kcal mol−1 (experiments/calculated).115,116 As strictly different kinetic and thermodynamic properties were observed on the PN3(P) pincer complexes compared to those of their CH2 PNN/PNP counterparts by Milstein, based on our previous studies on aromaticity,117–120 we were prompted to evaluate the potential roles of aromaticity in the MLC processes. Since the N–H bond is stronger than C–H, one might envision hydrogenation should be more thermodynamically favored for the C-arm rather than the N-arm (Fig. 17, Z = C or N). Surprisingly, the trend for the pincer platform is opposite and the “rearomatization” process for the Huang system is endergonic whereas that for the Milstein system is exergonic with around 10 kcal of the spacer effect (Fig. 18A).
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| Fig. 18 Effects of the arms on the (A) thermodynamics of the reaction and (B) NICS(1)zz values and estimated aromatic stabilization energies ΔEaroma for the hydrogenation reaction. | ||
In an effort to elucidate the origin of the distinct thermodynamic trends of the hydrogenation for the Milstein and the Huang systems, the difference in ASE (ΔEAroma) was estimated by the correlation with ΔNICS(1)zz results.33 Although the formation of new Ru–H and C/N–H bonds thermodynamically favors the H2 activation, the energy from aromatization of the central pyridine ring changes the outcome. While the formation of the stronger N–H bond delivers a larger reaction driving force than that of the C–H moiety, the reaction thermodynamics follows an opposite trend than expected and cannot be fully comprehended by only considering those chemical bonds. The main reason lies behind the aromatization of the central pyridine ring (Fig. 18B). The NICS(1)zz values of 0.6 for the Milstein and −7.6 for the Huang complexes, respectively, strongly suggest that the Huang platform has a much higher aromatic character than that of Milstein in the “dearomatized” form. Consequently, the ASE gained from the hydrogenation is larger in the Milstein system than that in the Huang platform. In the PNX(P) model, the hydrogenation thermodynamics follows the formation of a more aromatic ring rather than the generation of stronger chemical bonds.
In comparison to the Shvo system, the PNX(P) pincer platforms have greater room for modifications (Fig. 17 and 19) as they enable diversified designs for various donor atoms (Y and Y′), spacers (Z), other spectator ligands (L), etc. to fine-tune the steric and electronic properties of the resulting complexes. More importantly, the Huang system shows a considerable degree of aromaticity, in a “(pseudo)dearomatized” form. In such a flexible (pseudo)dearomatized frame, the metal center can act as a Lewis acid side and the unsaturated arm as a basic side. Thus as a result of resonance, the system expresses a highly intriguing ligand centered reactivity (Fig. 19, LCR), and can be triggered by the non-innocent character of the ligand and/or enabled by the zwitterionic resonance characters.121,122
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| Fig. 19 Two activation modes in catalysts influenced by the aromatization. Catalytic reduction of CO2 to methanol and methylamines via Ligand Centred Reactivity (LCR). | ||
For instance, the presented LCR leads to activation of Si–H and catalytic reduction of CO2 to methanol122 and methylamines,123 rather than insertion to the Ni–H bond observed in other pincer platforms (Fig. 19B).123
The N spacer of Huang's PN3P ligand platform possesses unique σ electron-donating properties and such ligand-specific reactivity is triggered by the aromaticity and metal ability to stabilize the positive charge. As we already discussed before, the aromatic zwitterionic structure plays a role in the (pseudo)dearomatized ring, and the σ electron-donating properties can be understood by mesomeric effects. Both zwitterionic aromatic forms and electron-donating abilities were investigated by Natural Bond Order analysis and Tolman electronic effects (Fig. 20A).124 The σ-donation of the nitrogen arm in the Ni–H complex was calculated to be stronger than those of nitrogen bases, such as DBU (1,8-diazabicyclo[5.4.0]undec-7-ene), DHIP (2,3-dihydroimidazo[1,2-a]pyridine), and TBD (1,5,7-triazabicyclo[4.4.0]dec-5-ene). The presence of the (pseudo)dearomatized ring increases the zwitterionic contribution from 8.2% → 21.5% in DBU to DHIP and 15.7% → 39.9% in TBD to PN3P*Ni–H which reflects charge distribution within the molecules. A similar trend is observed when the Tolman electronic effect is taken into account. In this approach, the A1 C–O vibrational mode from the ligand–Ni(CO)3 complex is employed as a relative measure of the electron donating or withdrawing ability of a ligand.124 Considering such vibration as the σ electron-donating quality, DHIP is a better electron donor than pyridine, DABCO and PN3P*Ni–H is the strongest, having the lowest frequency of 2060.8 cm−1 (Fig. 20B), clearly indicative of the strong donation ability of the iminic nitrogen. That theoretical findings explain the formation of the molecular structures with distinguishing nitrogen metal interaction (Fig. 20C)121,125 and formation of which can be rationalized by the charge distribution due to the mesomeric form ((pseudo)dearomatized).
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| Fig. 20 Nitrogen σ donation ability via resonances forms. (A) Aromatic zwitterionic resonance form contribution in nitrogen bases. (B) Tolman electronic parameter. (C) Pincer characterized by X-ray. | ||
The experimental126 and computational127 studies on triazine-based PN3PMn complexes also demonstrated the influence of the aromaticity on the thermodynamics (Fig. 21A). Along with deprotonation of the arm which impacts aromaticity of the central ring (NICS(1)zz values 0.17 → −8.53 and 1.08 → −4.43), the reaction energy for the dehydrogenation became less exergonic (−10.8 → −4.8 kcal mol−1). Similar to the PNxP system in Fig. 18, the reaction energies correlate with NICS(1)zz values, although the changes are not as significant (ΔNICS(1)zz values −8.70 and −5.51). Thus, the deprotonation of the arm leads to lower value aromatization (ΔNICS(1)zz) and increases the reaction energy. The experimental measured bond dissociation energy (BDE) of the Mn–H is stronger (60.9 ± 1.2 kcal mol−1) than Ru–H (53.3 ± 3.5 kcal mol−1).128 Hence, in contrast to the Milstein and Huang platforms, the hydrogenation in triazine-based PN3P-pincer complexes gains more energy from bond formation and less from the aromatization. If iridium metal is used instead, the hydrogenation become endergonic (Fig. 20B).74
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| Fig. 21 Trends in aromaticity and thermodynamics for the triazine-based PN3P-pincer catalysts. (A) Mn triazine-based PN3P-pincer complexes and (B) Ir triazine-based PN3P-pincer complexes. | ||
Similar trends are observed for the side reaction in catalytic processes. For example, addition of alcohol and formation of alkoxo complexes have remarkably different outcomes for Ru and Ir (Fig. 22).74 The Ru–O bond is stronger (126 ± 10 kcal mol−1) than Ir–O (99 ± 10 kcal mol−1), and the difference is larger than C–H/N–H bond energy, taking lead in the energy bond balance.128 Although these two platforms are different, on the basis of our previous discussion, one can conclude that Milstein system gains more energy from aromatization and more energy from bond formation (dominated by Ir/Ru–O) than those of trazine-based systems.
It is also expected that the arm with the N–H spacer will interact more strongly with solvents than a less polar C–H spacer. Nevertheless, there is only −0.77 kcal mol−1 energy difference between interaction of ammonia with benzene (H2N–H–π = −2.22 kcal mol−1), and methane and benzene (H3C–H/π = −1.45 kcal mol−1).129 Thus, in toluene, a difference in solvation of the NH and CH2 arm is expected to be less than 1 kcal mol−1. The H2N–H–THF interaction energy is much higher, 3.3 kcal mol−1, as expected from more polar solvents and hydrogen bonding interaction by Sahu et al.130 The solvent–solute interaction will also influence the aromaticity of the ring. The HOMA index of the aniline decreases slightly from 0.966 to 0.959 if water solvent as discovered by Zborowski et al.131 As a result, solvation effects will favor hydrogenation of the PN3P platform but at the same time decrease aromaticity of the ring will disfavor the reaction. Thus, balance between both these should be carefully addressed to make a fair comparison.
Footnotes |
| † This work is dedicated to Professor Tien-Yau Luh on the occasion of his 75th birthday. |
| ‡ These two authors contributed equally to this work. |
| This journal is © The Royal Society of Chemistry 2021 |