A DFT Study on FeI/FeII/FeIII Mechanism of the Cross-Coupling between Haloalkane and Aryl Grignard Reagent Catalyzed by Iron-SciOPP Complexes

To explore plausible reaction pathways of the cross-coupling reaction between a haloalkane and an aryl metal reagent catalyzed by an iron–phosphine complex, we examine the reaction of FeBrPh(SciOPP) 1 and bromocycloheptane employing density functional theory (DFT) calculations. Besides the cross-coupling, we also examined the competitive pathways of β-hydrogen elimination to give the corresponding alkene byproduct. The DFT study on the reaction pathways explains the cross-coupling selectivity over the elimination in terms of FeI/FeII/FeIII mechanism which involves the generation of alkyl radical intermediates and their propagation in a chain reaction manner. The present study gives insight into the detailed molecular mechanic of the cross-coupling reaction and revises the FeII/FeII mechanisms previously proposed by us and others.

More specifically, iron catalysts have proven useful for cross-coupling reactions of non-activated haloalkanes, a synthetically valuable yet challenging substrate, which is prone to undergo β-hydrogen elimination in the conventional palladium-catalyzed cross-couplings to form undesired alkene byproducts [20][21][22][23]. Numerous synthetic and mechanistic studies have thus appeared on this class of iron-catalyzed cross-coupling. The use of the controlled-addition technique of Grignard reagent in Kumada-Tamao-Corriu (KTC) coupling or using less reactive boron reagents in Suzuki-Miyaura (SM) coupling have proven, in combination with the use of bulky bisphosphine ligands, to be the successful strategy for the iron-catalyzed haloalkane coupling reactions [24][25][26][27].
Fürstner, [22] Neidig [32,33], and us [19,34]. Our group and the Neidig group have independently crystalized iron-bisphosphine complexes, such as Fe II X2(SciOPP), Fe II XAr(SciOPP), Fe II Ar2(SciOPP), where X=halide and Ar=Ph or Mes [32][33][34]. Furthermore, we identified the presence of Fe II BrMes(SciOPP), Fe II Mes2(SciOPP) in the reaction mixture of the cross-coupling reaction by using solution-phase synchrotron X-ray absorption spectroscopic (XAS) studies [34]. According to this study, we proposed an Fe II /Fe II mechanism based on identification of Fe II Ar2(SciOPP) (Figure 1a, Ar = Mes and X = Br). The Neidig group also identified the presence of iron(II) complexes in the solution phase through intensive mechanistic studies, consisting of Mössbauer and magnetic circular dichroism (MCD) spectroscopy, and synthetic approaches [32,33]. They identified that Fe II XAr(SciOPP) is the active iron species of the cross-coupling reaction suppressing undesired βhydrogen elimination reactions (Figure 1a, Ar = Ph). On the other hand, the Bedford group crystalized iron(I) species, [Fe I Br(dpbz)2] which is formed from iron(II)-precatalyst and they proposed a lowcoordinate iron(I)-phosphine species is involved in the cross-coupling reactions [35]. Identification of such low-coordinate iron(I)-complexes in the reaction mixture was not fully successful, and their involvement in the reaction mechanism remains elusive. The active iron-species that generate alkyl radical intermediates and the iron-species that react with the radical intermediate to effect the carbon-carbon bond formation have also remained unknown. Figure 1. (a) Proposed catalytic cycle for cross-coupling between an alkyl halide and Grignard reagent catalyzed by iron-SciOPP complexes. (b) Proposed catalytic cycle based on a recent study involving iron-BenzP* catalyzed cross-coupling between α-chloroesters and Grignard reagent. (c) The iron-SciOPP-catalyzed cross-coupling reaction chosen for the current density functional theory (DFT) mechanistic study [26,27].
Recently, our group developed enantioselective cross-coupling reactions using chiral bisphosphine ligands and proposed that the radical species may not react with the iron(III)-species which takes part in the generation of the radical (in-cage mechanism) [36,37]. We further performed the detailed DFT analysis of the reaction of α-chloroesters with the Grignard reagent in presence of chiral bisphosphine ligand and found that Fe I /Fe II /Fe III mechanism operates in the reaction ( Figure  1b) [38]. The iron(I) species activates the carbon-halogen bond of halo-ester substrates leading to the generation of α-ester-radical. In the next step, another molecule of Fe II XAr (active species) traps the generated radical (out-of-cage or chain mechanism) and lead to product formation through iron(III) species. Parallelly, the Gutierrez group reported DFT mechanistic study of the same reaction leading    [26,27].
Recently, our group developed enantioselective cross-coupling reactions using chiral bisphosphine ligands and proposed that the radical species may not react with the iron(III)-species which takes part in the generation of the radical (in-cage mechanism) [36,37]. We further performed the detailed DFT analysis of the reaction of α-chloroesters with the Grignard reagent in presence of chiral bisphosphine ligand and found that Fe I /Fe II /Fe III mechanism operates in the reaction (Figure 1b) [38]. The iron(I) species activates the carbon-halogen bond of halo-ester substrates leading to the generation of α-ester-radical. In the next step, another molecule of Fe II XAr (active species) traps the generated radical (out-of-cage or chain mechanism) and lead to product formation through iron(III) species. Parallelly, the Gutierrez group reported DFT mechanistic study of the same reaction leading to the virtually same conclusion [39]. Despite these recent mechanistic insights, the use of electronically and sterically different iron-bisphosphine complexes, different substrates, and reagents in cross-coupling reactions make it difficult to generalize the mechanism understanding.
The iron-SciOPP catalysts have been known as a superior catalyst for the cross-coupling of alkyl halides and Grignard reagent [26]. Due to bulky nature and strong chelation ability of the ligand, it avoids the formation of multinuclear or multiligand iron-phosphine complexes and also suppresses the formation of undesired ate complexes, which presumably responsible for increased reactivity and selectivity by minimizing side reactions. The mechanistic studies by Neidig showed that Fe II BrPh(SciOPP) complex reacts with a haloalkane to give the corresponding cross-coupling product selectively, but the detailed mechanism has remained unclear [33]. In our pursuit to identify the iron species involved in the elementary steps of the iron-catalyzed haloalkane coupling, DFT is used to study the reaction between Fe II BrPh(SciOPP) and bromocycloheptane (Figure 1c), which has been believed as the key for the selective cross-coupling of a haloalkane with an aryl metal reagent in the presence of an iron-bisphosphine catalyst. The plausible reaction pathways, Fe II /Fe II , and Fe I /Fe II /Fe III are examined and compared in this study.

Cycloheptyl Radical Generation via C-Br Activation by Iron(II)-Species
The reaction mechanism from Fe II BrPh(SciOPP) is studied as it is predicted to be the starting species in cross-coupling reactions. The TSs with lowest energy spin states as found in our previous study were only considered, due to large system size [38]. The first step is the C-Br activation of bromocycloheptane by quintet Fe II BrPh(SciOPP) ( 5 2 PhBr ), through an atom transfer mechanism ( Figure 2). To a tetrahedral geometry of Fe II BrPh(SciOPP), 5 2 PhBr , bromine-atom of substrate (S) approaches in the plane the same as P-Fe-P to form pre-reaction complex 5 2 PhBr-RBr , which is 6.7 kcal/mol higher in energy than the separated molecules. The 5 TS1 has a distorted square-pyramidal geometry, with the incoming bromine-atom positions in the square plane and the other bromine in the pyramidal position. The activation barrier of this process is 24.1 kcal/mol. The Mulliken spin densities on the iron center of the catalyst, and C 1 and bromine of substrate are (Fe) = 3.316, (Br) = −0.055, and (C 1 ) = 0.672, respectively ( Figure S1), indicating that during this step, quintet iron(II) is converted to quartet-iron(III) species with the generation of doublet cycloheptyl radical, 2 R·. The formed 5 3 PhBrBr R and 4 3 PhBrBr species are respectively 21.7 and 14.9 kcal/mol higher in energy than 5 2 PhBr , suggesting the reversible nature of the C-Br activation and will lead to a low concentration of radical 2 R·.
position. The activation barrier of this process is 24.1 kcal/mol. The Mulliken spin densities on the iron center of the catalyst, and C1 and bromine of substrate are ρ(Fe) = 3.316, ρ (Br) = −0.055, and ρ(C1) = 0.672, respectively ( Figure S1), indicating that during this step, quintet iron(II) is converted to quartet-iron(III) species with the generation of doublet cycloheptyl radical, 2 R·. The formed 5 3PhBrBrR and 4 3PhBrBr species are respectively 21.7 and 14.9 kcal/mol higher in energy than 5 2PhBr, suggesting the reversible nature of the C-Br activation and will lead to a low concentration of radical 2 R·.

Reaction of Cycloheptyl Radical with Iron(II)-Species: C-C Bond Formation and Generation of Iron(I) Species
The generated radical intermediate R· can react with either 4 3 PhBrBr (iron(III)-species, in-cage mechanism) or 5 2 PhBr (iron(II)-species, out-of-cage mechanism) present in the reaction mixture [36,38]. For the reaction of cycloheptyl radical (R·) with iron(II) species, the first step involves the out-of-cage movement of 2 R· from the intermediate 4 3 PhBrBr R. Then the 2 R· coordinates to the iron center through 4 TS2 with a lower barrier than 5 TS1 (20.7 kcal/mol from starting 5 2 PhBr and 5.8 kcal/mol from the second 5 2 PhBr , Figure 3). It leads to the formation of lower energy iron(III) species 4 3 PhBrR , which is 11.7 kcal/mol lower in energy. The consequent reductive elimination forms C-C coupling product P1, which proceeds with the activation barrier of 13.1 kcal/mol ( 4 TS3). The reductive elimination process is highly exergonic and the corresponding iron(I)-product complex ( 4 1 Br-PhR ) is 16.6 kcal/mol lower in energy than 4 3 PhBrR . Afterwards, the product will decoordinate from 4 1 Br-PhR leading to the formation of 5.7 kcal/mol higher energy species 4 1 Br , probably through a barrierless process. The transient species 4 1 Br readily reacts with a THF molecule (solvent) leading to the formation of lower energy species 4 1 Br-THF (0.9 kcal/mol lower energy than 4 1 Br-PhR ). The whole process for the reaction of Fe II BrPh(SciOPP) with bromocycloheptane leading to the formation of product and 4 1 Br-THF is exergonic by 13.3 kcal/mol.

Reaction of Cycloheptyl Radical with Fe III Br 2 Ph(SciOPP) (In-Cage Mechanism)
The reaction of cycloheptyl radical with 4 3 PhBrBr leading to a cross-coupling product turns out to have a higher free energy barrier of 26.9 kcal/mol ( Figure S2). This process occurs through an outer-sphere fashion ( 5 TS4), where R· attacks directly the ipso-carbon of the phenyl group and does not coordinate with the iron center. The reaction leading to byproduct alkene formation occurs by the simultaneous transfer of bromine and hydrogen from bromocycloheptane to iron and the ipso-carbon of the phenyl group of 5 2 PhBr , respectively, via 5 TS5 with a 25.2 kcal/mol energy barrier. Both processes for the formation of the cross-coupling and the alkene products are highly exothermic (ca. 35-45 kcal/mol). The formation of alkene is favorable kinetically over the cross-coupling. However, it does not agree with experimental observation.
is highly exergonic and the corresponding iron(I)-product complex ( 1Br-PhR) is 16.6 kcal/mol lower in energy than 4 3PhBrR. Afterwards, the product will decoordinate from 4 1Br-PhR leading to the formation of 5.7 kcal/mol higher energy species 4 1Br, probably through a barrierless process. The transient species 4 1Br readily reacts with a THF molecule (solvent) leading to the formation of lower energy species 4 1Br-THF (0.9 kcal/mol lower energy than 4 1Br-PhR). The whole process for the reaction of Fe II BrPh(SciOPP) with bromocycloheptane leading to the formation of product and 4 1Br-THF is exergonic by 13.3 kcal/mol. The reaction of cycloheptyl radical with 4 3PhBrBr leading to a cross-coupling product turns out to have a higher free energy barrier of 26.9 kcal/mol ( Figure S2). This process occurs through an outersphere fashion ( 5 TS4), where R· attacks directly the ipso-carbon of the phenyl group and does not Although the reaction of cycloheptyl radical with Fe III Br 2 Ph(SciOPP), 4 3 PhBrBr leading to cross-coupling product and alkene formation is highly exothermic, it is unlikely as 5 TS4 and 5 TS5 are 6.2 and 4.5 kcal/mol higher in energy than 4 TS2. Hence, the cross-coupling reaction proceeds by the reaction of alkyl radical with iron(II)-species. Similar to our previous study, iron-SciOPP complexes also do not favor Fe II /Fe III mechanism.

Reaction of Cycloheptyl Radical with Iron(II)-Species: Alkene Byproduct Formation
From complex 4 3 PhBrR the possibility of formation of alkene is also considered (Figure 4). It involves the transfer of β-hydrogen from a coordinated cycloheptyl group to phenyl ligand ( 4 TS6). The activation barrier for this process is apparently high and 4 TS6 is 14.1 kcal/mol higher in energy than 4 TS3 and the formation of alkene is unlikely from 4 3 PhBrR . The TSs for coupling and alkene formation by the outer-sphere reaction of radical with phenyl of iron(II) species, 5 2 PhBr could not be located.
Further, we checked the possibility of alkene formation by H-atom transfer ( 4 TS7) from cycloheptyl radical to iron-atom of the iron(II) complex, 5 2 PhBr . The activation barrier for this process is 12.9 kcal/mol. It leads to the formation of the iron(III)-hydride complex, 4 3 PhBrH . The following reductive elimination between the hydride and phenyl groups through 4 TS8 lead to the formation of benzene. This pathway is unfavorable as 4 TS7 is 7.7 kcal/mol higher in energy than 4 TS2. Hence, the reaction of the alkyl radical with Fe II BrPh(SciOPP) does not give the alkene byproduct, which is in concert with the experimental observations. Further, we checked the possibility of alkene formation by H-atom transfer ( TS7) from cycloheptyl radical to iron-atom of the iron(II) complex, 5 2PhBr. The activation barrier for this process is 12.9 kcal/mol. It leads to the formation of the iron(III)-hydride complex, 4 3PhBrH. The following reductive elimination between the hydride and phenyl groups through 4 TS8 lead to the formation of benzene. This pathway is unfavorable as 4 TS7 is 7.7 kcal/mol higher in energy than 4 TS2. Hence, the reaction of the alkyl radical with Fe II BrPh(SciOPP) does not give the alkene byproduct, which is in concert with the experimental observations.  The iron(I) species formed during the reaction can react either with another iron(III) species to undergo a comproportionation to generate two iron(II) species, or with haloalkane substrate (of which concentration is larger than iron(III) species) to generate one iron(II) species and an alkyl radical intermediate. For the reaction to proceed the first step is the removal of THF from 4 1 Br-THF to form 4 1 Br and this process is endergonic by 6.6 kcal/mol ( Figure 5). This step is required for both comproportionation and reaction with the haloalkane substrate. The coordination of the substrate through bromide to 4 1 Br , leading to the formation of 4 1 Br-BrR is exergonic by 2.3 kcal/mol. The activation barrier for the Br-atom transfer ( 4 TS9) from 4 1 Br-BrR species is 6.8 kcal/mol (barrier from 4 1 Br-THF ). The process is highly exergonic and leads to formation of cycloheptyl radical and iron(II) species 5 2 BrBr . The generated 5 2 BrBr species will undergo transmetalation and the radical species will react with the available 5 2 PhBr in the reaction mixture, propagating the radical chain reaction [40]. Hence, the reaction will proceed through the out-of-cage mechanism, and similar to our previous study, the current reaction also follows the Fe I /Fe II /Fe III pathway [38].
The comproportionation between 4 1 Br and 4 3 PhBrBr (generated by substrate reaction with iron(II) species 5 2 PhBr ) may be a barrierless process and is a highly exergonic process (37.2 kcal/mol). Since the concentration of the haloalkane substrate is high enough under the catalytic coupling condition, the reaction between the iron(I) species and haloalkane is more likely. Hence, iron(I) species is the active species after its generation during the reaction, which reduces the activation barrier for C-Cl activation from 24.1 to 6.8 kcal/mol. barrier for the Br-atom transfer ( 4 TS9) from 4 1Br-BrR species is 6.8 kcal/mol (barrier from 4 1Br-THF). The process is highly exergonic and leads to formation of cycloheptyl radical and iron(II) species 5 2BrBr. The generated 5 2BrBr species will undergo transmetalation and the radical species will react with the available 5 2PhBr in the reaction mixture, propagating the radical chain reaction [40]. Hence, the reaction will proceed through the out-of-cage mechanism, and similar to our previous study, the current reaction also follows the Fe I /Fe II /Fe III pathway [38]. The comproportionation between 4 1Br and 4 3PhBrBr (generated by substrate reaction with iron(II) species 5 2PhBr) may be a barrierless process and is a highly exergonic process (37.2 kcal/mol). Since the concentration of the haloalkane substrate is high enough under the catalytic coupling condition, the reaction between the iron(I) species and haloalkane is more likely. Hence, iron(I) species is the active species after its generation during the reaction, which reduces the activation barrier for C-Cl activation from 24.1 to 6.8 kcal/mol.

Proposed Catalytic Cycle Based on Fe I /Fe II /Fe III Mechanism
Based on the above theoretical studies, we propose the reaction mechanism depicted in Figure  6. The Fe II XAr(SciOPP) ( 5 2PhBr) is first converted to Fe I XTHF(SciOPP) ( 4 1Br-THF) with the formation of the cross-coupling product. Afterwards, iron(I) species ( 4 1Br-THF) mainly activate the alky halide. Transmetalation of 4 1Br-THF is less likely due to the low concentration of Grignard reagent, which excludes the possibility of involvement of Fe I ArTHF(SciOPP) species. Hence, the catalytic cycle starts with the halogen atom abstraction from the alkyl halide (Alkyl-X) by iron(I) species ( 4 1Br) affording a dihaloiron species Fe II X2(SciOPP) ( 5 2BrBr) along with an alkyl radical intermediate ( 2 R·) ( Figure 6 and Figure S3). The resultant alkyl radical 2 R· escapes from the solvent cage and is further trapped by iron(II) species, Fe II XAr(SciOPP) ( 5 2PhBr) (which have a higher concentration) via the out-of-cage pathway. It led to the formation of iron(III) species Fe III XArR(SciOPP) ( 4 3PhBrR). The reductive

Proposed Catalytic Cycle Based on Fe I /Fe II /Fe III Mechanism
Based on the above theoretical studies, we propose the reaction mechanism depicted in Figure 6. The Fe II XAr(SciOPP) ( 5 2 PhBr ) is first converted to Fe I XTHF(SciOPP) ( 4 1 Br-THF ) with the formation of the cross-coupling product. Afterwards, iron(I) species ( 4 1 Br-THF ) mainly activate the alky halide. Transmetalation of 4 1 Br-THF is less likely due to the low concentration of Grignard reagent, which excludes the possibility of involvement of Fe I ArTHF(SciOPP) species. Hence, the catalytic cycle starts with the halogen atom abstraction from the alkyl halide (Alkyl-X) by iron(I) species ( 4 1 Br ) affording a dihaloiron species Fe II X 2 (SciOPP) ( 5 2 BrBr ) along with an alkyl radical intermediate ( 2 R·) ( Figure 6 and Figure S3). The resultant alkyl radical 2 R· escapes from the solvent cage and is further trapped by iron(II) species, Fe II XAr(SciOPP) ( 5 2 PhBr ) (which have a higher concentration) via the out-of-cage pathway. It led to the formation of iron(III) species Fe III XArR(SciOPP) ( 4 3 PhBrR ). The reductive elimination from 4 3 PhBrR led to the formation of a cross-coupling product and regenerating iron(I) species ( 4 1 Br-THF ).
Based on this mechanism, the detection of both iron(II) and iron(I) species, and their roles in the cross-coupling reaction can be reasonably explained.
Molecules 2019, 24, x FOR PEER REVIEW 7 of 11 elimination from 4 3PhBrR led to the formation of a cross-coupling product and regenerating iron(I) species ( 4 1Br-THF). Based on this mechanism, the detection of both iron(II) and iron(I) species, and their roles in the cross-coupling reaction can be reasonably explained.

Computational Methods
The Gaussian09 program was used for quantum mechanical calculations reported in the study [41]. The DFT method B3LYP [42,43] was used for geometry optimization and energy calculations with the inclusion of solvent effects by the PCM method [44]. Grimme's D3 dispersion correction

Computational Methods
The Gaussian09 program was used for quantum mechanical calculations reported in the study [41]. The DFT method B3LYP [42,43] was used for geometry optimization and energy calculations with the inclusion of solvent effects by the PCM method [44]. Grimme's D3 dispersion correction method was used to include dispersion correction [45]. For geometry optimization, the 6-31G* basis set [46] was used for all atoms as it gave good agreement with the crystal structure of Fe II BrPh(SciOPP) and Fe II Br 2 (SciOPP) ( Figure S4). The geometry optimization with SDD [47] basis set for Fe, Br and 6-31G* for other atoms lead to relatively longer metal ligand distances. Hence, the 6-31G* basis set was used. The hessian calculation was performed to confirm minima (no imaginary frequency) and TS (one imaginary frequency). All TS were confirmed by visual inspection of imaginary frequency. The connectivity between TSs and minima were confirmed by IRC [48] calculations for 20 steps and subsequent optimization of the geometry at PCM/B3LYP/6-31G* level of theory.
The spin-state energies of iron complexes computed by a DFT method depend on the choice of the exchange-correlation functional [50,51]. Various functionals were recommended in the literature, while no consensus has been made for the optimal choice of the DFT method. Hence, care should be taken in choosing functional, especially for iron complexes with the small spin-state energy gaps. The DFT method (B3LYP-D3 Functional) used in this work predicted quintet as the ground state for iron(II) complexes, Fe II BrPh(SciOPP) and Fe II Br 2 (SciOPP), which is in agreement with the experimentally known spin state [33,34]. Additionally, the spin state for related iron(I) complex (Fe(η 2 -[TIPS-CC-H])Br(SciOPP)) was also predicted correctly [52]. Further, the OBPE-D3 functional (which is known to provide reliable spin state gap) [53] gave consistent results with B3LYP-D3 for the ground spin state (quartet) of iron(I) and iron(III) complexes (Table S1). The OPBE-D3 functional failed to give reliable results for the spin state of the Fe II BrPh(SciOPP) complex. Hence, the B3LYP-method reliably predicts the spin state of the current system and is used in this study. Further, we have also checked the effect of long-range-corrected (LC) exchange functional on barrier height [54] using CAM-B3LYP-D3 functional. The CAM-B3LYP-D3 functional led to a similar conclusion as of B3LYP-D3, and some TSs showed a higher energy barrier (details are given in Table S2).

Conclusions
We have studied the mechanism of the reaction between Fe II BrPh(SciOPP) and bromocycloheptane by using DFT methods and identified iron species of different oxidation states involved in a catalytic cycle of the iron-bisphosphine-catalyzed haloalkane couplings. The reaction mechanism follows the Fe I /Fe II /Fe III pathway, where iron(I) activates the C-Br bond of the haloalkane substrate, another molecule of Fe II BrPh(SciOPP) traps the generated alkyl radical species to form iron(III) species leading to the formation of the cross-coupling product and iron(I) species. The iron(I) species then again react with haloalkane generating alkyl radical and the reaction propagates through a radical chain mechanism. The current mechanism mirrors our previous mechanistic study on a chiral bisphosphine-catalyzed enantioselective cross-coupling despite the change of bisphosphine ligand from BenzP* to SciOPP.
The reaction of haloalkane with iron(II) species and the reaction of the alkyl radical with iron(III) species have a higher energy barrier than those of Iron(I) species and iron(II) species, respectively. The obtained energetics exclude the possibility of Fe II /Fe II and Fe II /Fe III pathways proposed previously. Furthermore, we have found that an alkyl radical prefers to coordinate to the Fe II BrPh(SciOPP) species, instead of the β-hydrogen-atom abstraction ending with the alkene byproduct. The generated Fe III BrPh(alkyl)(SciOPP) species favors reductive elimination to give the corresponding coupling product over the alkene byproduct. These results deepen our understanding of the iron-SciOPP catalysis and provide insights into the probable root for the side product formations. Further understanding of the mechanism of alkene formation with Fe II Ph 2 (SciOPP) catalyst will help design better catalysts and synthetic methodology. The theoretical and experimental research in this line is now actively pursued in our laboratory and will be reported in due course.