Sourabh Kumara,
Dillon Button-Jennings
b,
Timothy P. Hanusa
b and
Ashlie Martini
*a
aDepartment of Mechanical Engineering, University of California Merced, Merced, California 95343, USA. E-mail: amartini@ucmerced.edu; sourabhkumar@ucmerced.edu
bDepartment of Chemistry, Vanderbilt University, Nashville, Tennessee 37235, USA. E-mail: dillon.a.button-jennings@vanderbilt.edu; t.hanusa@vanderbilt.edu
First published on 9th April 2025
Solvents have long been integral to the success of synthetic chemistry, influencing reaction rates, mechanisms, and product selectivity. However, mechanochemistry—typically involving the grinding and mixing of solid reagents—offers an alternative environment that is solvent-free or at least greatly minimizes solvent use, and that drives reactions through mechanical force. In a recent study, the reaction between the salt of a bulky allyl anion, K[A′] (A′ = 1,3-(SiMe3)2C3H3), and a nickel halide gave very different outcomes depending on whether the reaction was conducted without solvent using a solid material, with a starting solvated complex, [Ni(py)4Cl2], modified by a small amount of pyridine, or in pyridine solution. Under certain conditions, halide metathesis occurred, forming the allyl complex in near quantitative yield. Under others, a redox reaction dominated, generating allyl radicals that coupled and left {A′}2 (1,3,4,6-tetrakis(trimethylsilyl)hexa-1,5-diene) as the major product. To understand these differing outcomes, the formation mechanisms of
under varying solvent conditions were investigated here using Density Functional Theory (DFT). The effects of the reaction conditions on factors such as Gibbs free energy change, bond energy behavior, and transition states collectively suggest that electrostatic stabilization dominates in the solvent phase. In the case of solvate-assisted conditions, a complete energy profile diagram of the reaction between [Ni(py)4Cl2] and 2K[A′], leading to
and KCl, was calculated, with evidence for one of the intermediates ([A′Ni(py)Cl]) being provided by experiments. Calculations confirm that coordination of pyridine to the nickel, whether from the free liquid or (preferentially) from the pyridine solvate, weakens the Ni–Cl bond so that metathesis can proceed easily. If pyridine is absent (i.e., under solvent-free conditions), the redox route will have a kinetic advantage in the reaction. This study provides molecular-level insights for understanding and optimizing solvent-assisted grinding processes.
A variation on the LAG technique, in which LAG quantities of solvents are initially present as metal solvates or hydrates, rather than the free liquid, has been termed “solvate-assisted grinding” (SAG).10 As a result, LAG and SAG are critical adjuncts to mechanochemical synthesis, offering more efficient and sustainable alternatives for synthesizing compounds ranging from pharmaceuticals11 and organometallic compounds10 to metal–organic frameworks12 and covalent organic frameworks.13
To study the contribution of solvents in chemical reactions, it is common to compare different solvents' effects on the reaction outcomes.14 The solvent choice depends on the reaction's aim, but solvents can be usefully classified based on the magnitude of their dielectric constant (ε).14 The dielectric constant (relative permittivity) of a solvent describes the material's response to an external electric field, and studies have shown that global parameters such as chemical potential and hardness decrease from the gas phase (i.e., solvent-free) to the solvent phase due to the increase in the dielectric constant.15 The effect of changes in the dielectric constant on mechanochemical synthesis can take various forms, but changes in reaction selectivity are possible outcomes.16 For example, combining a solvent's dielectric constant (under LAG conditions) with appropriate counter-ion pairing enhanced the selectivity of a Wittig reaction.17 In another case, the relative polarity (and hence the dielectric constant) of a LAG additive was a key factor in switching the kinetics and chemoselectivity of the reaction between a difluorinated diketone and (PhS)2.18 A detailed understanding of solvent contributions to mechanochemical reactions will involve evaluating dielectric constants' effects, an area that has been poorly explored in organometallic contexts.
Computational tools are well-suited for exploring the reaction consequences of changes in dielectric constants,19 and among these, density functional theory20,21 (DFT) has often been used to explore solution-based methods for synthesizing materials. For example, DFT was used to show that suppression of the collective response of solvent molecules resulted in a decrease in the dielectric permittivity.22 In another investigation, a combination of DFT and molecular dynamics (MD) simulations was employed to demonstrate that the dielectric constant was influenced by varying temperatures and electrolyte compositions.23 A recent computational study highlighted the disparities between reactions performed under dry and LAG conditions.24 In this case, DFT coupled with microkinetic modeling was used to investigate the influence of solvent concentration and the dielectric environment on Diels–Alder reactions and the synthesis of N-sulfonylguanidines.
Experimental work can complement computational efforts to analyze solvent effects in mechanochemistry. A recent experimental study systematically compared solvent effects on the synthesis of organometallic complexes under various milling conditions.10 The synthesis of sterically bulky bis(allyl) complexes from the binary metal chlorides, MCl2 (M = Cr, Fe, Co, Ni) and solvated metal chloride complexes, MLnCl2 (L = tetrahydrofuran (THF), pyridine) in various conditions, including solvent-free, LAG, SAG (using a pyridine-solvated complex), and pure solution (THF and pyridine) was examined.10 Two distinct pathways were identified during the reactions, each accompanied by characteristic products. One involved halide metathesis, leading to the formation of
complexes; the other involved a redox process, generating neutral radicals from the starting allyl anions that then coupled to form 1,3,4,6-tetrakis(trimethylsilyl)hexa-1,5-diene
.
The presence of solvent was found to influence the reaction outcome significantly. It should be noted that in the case of nickel, [Ni(py)4Cl2] was the metal solvate used; it provided an amount of pyridine equivalent to η = 0.55, which is both well within the standard LAG region and is not greatly different from the amount used with separately added liquid pyridine (η = 0.70). Hence, the LAG/SAG reactions differed primarily in whether the pyridine was initially present as a free liquid or was metal-bound, not in its amount relative to nickel. The results of this study10 are summarized in Fig. 1, which shows that the NiCl2 reaction with two equivalents of K[A′] led to different proportions of the bis(allyl)metal complex . The underlying reasons for the solvent effect on the reaction outcome remained uncertain, and further investigation is required to explore the mechanisms responsible for this phenomenon. It was unclear, for example, why a pyridine-coordinated nickel complex provided the
complex with a much greater yield than the equivalent amount of NiCl2 + free pyridine.
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Fig. 1 Reaction schemes for ![]() ![]() ![]() |
In the family of transition metal allyl complexes, those containing nickel were among the first to be synthesized,25 and nickel derivatives continue to be important in developing high-performance catalysts for olefin polymerization.26–29 Thus, of the possible systems to study, we focused on the molecular-level reaction mechanism of formation under different conditions (solvent-free, in solvents, and using a solvated starting material) using DFT calculations complemented with experimental evidence. This molecular-level approach is a critical first step in understanding larger-scale LAG and SAG processes.
The level of steric congestion in [Ni(py)4Cl2] can be visualized in the encapsulation of the metal coordination sphere. As estimated with the program Solid-G,41 and in particular by the value of Gcomplex (the net percentage of the coordination sphere covered by the ligands), the value for [Ni(py)4Cl2] is high (92.8%) (Fig. 2(A and B)). The observed bond lengthening and inferred steric crowding suggest that the complex may be primed for ligand dissociation. Moreover, the ELF and electron densities at the BCP were studied for NiCl2 and [Ni(py)4Cl2] molecules. As shown in Fig. 2(C), in NiCl2, the ELF plots reveal significant overlap of the outer electron clouds between Ni and Cl atoms, indicating a strong interaction in Ni–Cl bonds. This overlap is absent in [Ni(py)4Cl2], where pyridine ligands around Ni reduce electron cloud overlap with Cl (Fig. 2(D)). Additionally, the electron density at the Ni–Cl bond critical point (shown by white points between Ni and Cl atoms) is higher in NiCl2 (0.1243 a.u.) than in [Ni(py)4Cl2] (0.0493 a.u.), confirming a stronger Ni–Cl interaction in NiCl2 due to the absence of competing pyridine ligands.
The stoichiometric addition of pyridine into a hexanes solution of [{A′Ni(μ-Cl)}2] produces [A′Ni(py)Cl]. Attempts to coordinate additional pyridine molecules by using excess pyridine were not successful. Orange crystals of [A′Ni(py)Cl] were obtained from the slow evaporation of a hexanes solution, and a single crystal X-ray study established its monomeric nature (Fig. 3). The complex displays an η3-bonded allyl ligand and terminal chloride and pyridine ligands, arranged so that the Cl, N, and C1/C3 carbons of the allyl ligand form a roughly square planar arrangement around the nickel (sum-of-squares error for the least-squares plane through the four atoms = 0.051 Å2). The TMS groups on the A′ ligand are in a syn, anti-relationship. As is typical for transition metal-bound A′ ligands,42 the silicon atom of the syn substituent (Si2) is deflected somewhat from the C3 allyl plane toward the nickel atom (0.36 Å). Conversely, the silicon atom of the anti-substituent (Si1) is strongly displaced from the C3 plane (0.83 Å), away from the metal center.
Under all conditions examined, the formation of products has negative ΔG° values, indicating the spontaneity of the halide metathesis reaction in the forward direction. Conversely, the positive ΔG° values associated with the
products formed via a redox process imply a non-spontaneous reaction in the forward direction. The solvents' polar nature and their ability to coordinate with metal ions stabilize transition states involved in both reaction types, and the ΔG° values are more positive under solvent-free conditions (by 10% and 26% for the halide metathesis and redox routes, respectively), although the changes are much larger in absolute terms for the halide metathesis path (roughly 42 and 6 kJ mol−1, respectively).
The dielectric constant under solvent-free conditions and with solvents can affect the Ni–Cl and K–C bond energies and the product formation. We thus examined the bond energies in the different environments. As shown in Fig. 4(A), as the Ni–Cl bond length increases, the energy under solvent-free conditions rises rapidly, reaching a constant value at approximately 400 kJ mol−1. In contrast, the energy increases only up to ∼240 kJ mol−1 in either solvent. Similarly, in the case of the K–C bond, in Fig. 4(B), the energy remains low in the solvents when compared to the solvent-free phase. This energy disparity indicates that electrostatic stabilization dominates the solvent phase and causes ionic forms to be much more stable in high dielectric constant environments than in the solvent-free phase. This result implies that electrostatic stabilization in the solvent phase could improve milling efficiency compared to solvent-free conditions.
The rupture of the Ni–Cl and K–C bonds will result in the formation of Ni2+, Cl−, K+, and [A′]– species, and depending on the experimental milling conditions, reduction of Ni2+ to elemental nickel (Ni0) may also happen. If the latter is the case, concomitant oxidation of the [A′]– anion to the neutral [A′]˙ radical will occur, and subsequently, two of the {A′}˙ neutral radicals can combine and form the (hexadiene) molecule. Based on transition state search calculations for forming the
molecule, we explored the reaction's energy profile, which proceeds through a diradical transition state pathway. In our calculations, the dimer
molecule is assigned a singlet spin state, while A* (radical species) was treated as a doublet. During the transition state, the diradical species (A*–A*) was modeled as a triplet. Fig. 5(A) and (B) show the energy profile diagram of
formation by the reaction between identical radical molecules for rac and meso forms. The resulting transition states in the solvent-free phase for the rac and meso forms of
are found at the 153.3 and 172.6 kJ mol−1 energy barriers, respectively. However, these energy barriers do not change appreciably when solvent is present (ca. 2–3% decrease). Hence, there is no significant solvent assistance required for the neutral radicals to combine.
In the previous experimental work, SAG conditions were created by employing the insoluble pyridine solvate complex ([Ni(py)4Cl2]) during grinding.10 Computationally, we used the same solvated complex in the triplet (T1) spin state at the molecular level to study this effect (cf. Fig. S6†). The coordinated pyridine moieties donate electron density to the nickel center, weakening the Ni–Cl interaction and adding steric pressure to boost chloride loss. In describing the behavior of the Ni–Cl bond energy for the solvated complex, as shown in Fig. 4(A), it should be remembered that the bonds were already elongated to 2.443 Å compared to the distance in the NiCl2 molecule (2.023 Å).44 As the bond length increases, the energy rises but remains below that of the NiCl2 molecule in the solvents until ca. 4.2 Å. Some caution should be advised in interpreting this finding, given the difference in how the pyridine is modeled with the solvate (explicit pyridine molecules) and the solution (implicit pyridine via the dialectic content). Nevertheless, it is clear that the coordination of pyridines in [Ni(py)4Cl2] leads to substantial Ni–Cl bond weakening, considerably greater than that in the solvent-free environment.
Fig. 6 shows the computed schematic energy profile diagram illustrating the synthesis of from the reaction of the pyridine-solvated complex [Ni(py)4Cl2] with 2K[A′]. To facilitate understanding of the reaction mechanism, the process was divided into two steps, introducing a single K[A′] species at each step.
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Fig. 6 Schematic representation of the synthesis of the allyl complex ![]() |
Initially, the reaction begins by forming an intermediate (IM 1), accompanied by a modest energy increase (∼22 kJ mol−1), attributable to interactions between both molecules (i.e., K[A′] and [Ni(py)4Cl2]). Subsequently, the formation of an Ni–C bond, and rupture of Ni–Cl and Ni–N bonds causes a substantial energy rise, bringing the system to the first transition state (TS 1). The release of the first pyridine ligand and KCl from TS 1 likely leads to the formation of intermediate IM 2. Loss of another pyridine ligand, likely aided by the steric bulk of the η1–[A′] ligand, leads to the second transition state (TS 2). Electron redistribution resulting in the conversion of the initially η1-bound [A′] ligand to the delocalized η3-bound conformation culminates in the formation of the intermediate IM 3. Further relaxation and pyridine loss occur through transition state TS 3 followed by intermediate IM 4 ([A′Ni(py)Cl]).
Subsequently, introducing the second K[A′] species prompts the formation of a fifth intermediate (IM 5), accompanied by an energy decrease of approximately 44 kJ mol−1 due to interactions between both molecules. Unlike the previous decreasing energy trend, the system shows an increase in the energy and progresses through the formation of the fourth transition state (TS 4), attributed to the Ni–C bond formation and Ni–Cl bond rupture. The release of the KCl from TS 4, associated with the decrease in energy, leads to the generation of the sixth intermediate (IM 6). The transition from IM 6 to the fifth transition state (TS 5) involves an energy rise, associated with converting the second [A′] ligand, originally η1-bound, to the more sterically demanding η3-bound conformation. Ultimately, the system again releases energy, losing the last pyridine, and yields , exhibiting an overall energy release consistent with the exothermic nature of the reaction mechanism. There is no
species in this reaction profile diagram, in agreement with the lack of
in the SAG experimental results.
Given these results, it might initially appear inconsistent that under solvent-free conditions, the formation of is calculated to be spontaneous (ΔG° = −370 kJ mol−1), and the generation of
is non-spontaneous (ΔG° = +31 kJ mol−1), even though the experimental production of
is almost quantitative and the formation of
is only a trace (Fig. 1). Several factors must be considered to put these results into context. One is that the energy involved in K–C bond cleavage, which makes the allyl anion free for subsequent reaction, is considerably less than that for Ni–Cl scission (Fig. 4). Even in the unsolvated case, the energy of disrupting the K–C interaction is roughly half that of Ni–Cl cleavage, and the difference is greater in the presence of solvents (e.g., in pyridine, the K–C/Ni–Cl energy ratio is roughly one-fourth). This is partially a result of separating the anions from either mono-positive (K+) or dipositive (Ni2+) centers, so simple charge considerations (Z+Z–/r) would suggest that the former requires less energy. Hence, the availability of the [A′]– anion is not a critical issue in the reaction scheme, and the differences in reaction outcome must lie in the ease of Ni–Cl bond separation.
A second critical point is that although the coordination of pyridine to NiCl2 weakens the Ni–Cl bond, the coordination process is not immediate under mechanochemical conditions. It has been found that a 10 min grind of NiCl2 with 5 equiv. of pyridine generates a mixture of compounds, primarily [Ni(py)4Cl2] and [Ni(py)2Cl2], the latter being a polymeric sub-solvate of NiCl2.10 Depending on the reagents available, that length of time is sufficient to produce the hexadiene in 98% yield or the
complex in 95% yield (Fig. 1). In solvent-free conditions, and without Ni–Cl bond weakening, the facile separation of the allyl anion from K+ allows the redox process to start immediately, converting the allyl ligand to its radical form and making it unavailable for reaction with a Ni2+ center.
Conversely, when that pyridine is pre-coordinated in the [Ni(py)4Cl2] solvate, Ni–Cl bond cleavage and subsequent metathesis can begin without delay, taking advantage of the generally more favorable free energy condition associated with the metathesis compared to the redox process (Table 1). If pyridine is added as a LAG solvent, however, it takes time for it to coordinate and weaken the Ni–Cl bonds so that metathesis can begin, during which time the redox process can proceed. The result is that provided in Fig. 1B, i.e., both form in comparable amounts.
While our study provides valuable insights, certain aspects warrant further consideration to fully capture the complexities of mechanochemical reactions. First, in this study, a continuum solvent model was employed to estimate the influence of solvent on the mechanochemical reaction. This model assumes a homogeneous and infinite solvent environment, which differs from the highly localized and dynamic solvent distributions in ball milling reactions. In ball milling, the solvent often exists as a thin layer on particle surfaces or confined in small cavities, and its distribution is disrupted by mechanical forces. Although the continuum approximation cannot capture these localized effects, it serves as a useful first approximation for evaluating solvent polarity and dielectric effects on reaction energetics.24 Second, the gas-phase calculations do not fully account for solid-state effects such as lattice stabilization and extended intermolecular interactions. This is a limitation because there are elements of kinetic influence in these reactions that are not fully described with thermodynamic values. Regardless, the calculations reported here offer valuable insights into the intrinsic thermodynamics of the mechanochemical reactions. These calculations also lay the groundwork for future studies. Such studies may incorporate periodic DFT calculations45,46 or hybrid quantum-mechanical/molecular-mechanical (QM/MM) approaches that more accurately capture the structural and energetic influences of the solid environment. They may also employ MD simulations with explicit solvent models or coarse-grained approaches that could better capture the localized nature of solvent in ball milling, including its role under LAG conditions and its impact on reaction pathways. Such refinements will bridge computational predictions with experimental outcomes, yielding a comprehensive picture of mechanochemical reactivity.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 2392374 ([{A′NiCl}2]) and 2392373 ([A′Ni(py)Cl]). For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4mr00136b |
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