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. 2019 Nov 8;4(21):19452–19461. doi: 10.1021/acsomega.9b02905

Reaction Mechanism of Li and Mg Carbenoid Cyclopropanations: Metal-π and σ Interactions

Daniel Villablanca †, Rocio Durán †, Al Mokhtar Lamsabhi ‡,§,*, Barbara Herrera †,*
PMCID: PMC6868892  PMID: 31763569

Abstract

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The mechanism of the reaction of lithium and magnesium carbenoids with ethylene to give cyclopropane has been explained in detail in all the steps at the G4 level of theory. We explored the lithium and magnesium interaction toward πC=C and σC–C bonds in the reactants and the products. We have also investigated the reaction path by means of the force profile formalism in order to highlight the electronic and the structural rearrangements along the potential energy surface of the cyclopropanation. The results indicate that all of the reactions are stepwise, exoenergetic, with low barriers. All our findings were confirmed by dynamic simulations for chlorometal carbenoids. Furthermore, from the intrinsic reaction coordinate procedure, we were able to find out the intermediates that can take place when the reaction is descending from the transition state to the products or reactants. The reaction force analysis at B3LYP/6-311G(d,p) indicates that the energy barriers are mostly due to structural rearrangements which are produced by the approach of the carbenoid to ethylene. Quantum theory of atoms in molecules and electron localization function analyses indicate that products, reactants, and intermediates form complexes stabilized by attractive forces between Li/Mg and single/double bonds.

Introduction

In molecular synthesis, there are many possible pathways that can connect the reactants and products. Hence, the proposed mechanisms usually involve different types of intermediates. Rather often, a wise combination of imagination and experimental pieces of evidence may suggest molecular structures that are rather far from chemical intuition. In chemical textbooks, the possible intermediates in a chemical reaction are classified into four groups: cations, anions, radicals, and carbenes. In particular, carbenes have been proved to be systems with unique reactivities,1−6 although normally under extreme conditions due to their high reactivity. Closely related to carbenes are the so-called carbenoids, a term used for the first time by Closs and Moss in the early sixties7,8 to designate any system having the characteristics of a carbene or able to produce carbenes, in other words, systems that may react as carbenes even though they are not free divalent carbon species.9 Carbenoids have been shown to be particularly useful in cyclopropanation reactions,10−12 in organic synthesis, and as catalysis intermediates.13−17

Recovering the way to gain cyclopropane derivatives may be considered as a springboard to attain many valuable compounds, including natural products and biologically active species.18−21 Understanding their chemistry becomes mandatory before exploring the paths to reach them. In gas phase and precisely by computational methods, the study of reactivity in chemistry has largely showed its validity to understand complex systems.

The main aim of the present paper is to explore the simplest way to reach cyclopropane within reactants as lithium and magnesium carbenoids. Why do we choose these reactants? The main reason for this choice, besides the ones cited above, is to be able to apply the highest level of theory such as the G4 theory and describe adequately the stationary points. The second reason is to try to offer a novel point of view on the interaction of lithium and magnesium with double and single covalent bonds. Hence our survey on cyclopropanation reactions, involving carbenoids with a metalated carbon atom, such as an alkyl lithium or alkyl magnesium R2C(X)M (M = Li, Mg; X = F, Cl, Br), is to get a new picture of the insertion of CH2 to ethylene.

The second goal of our work is to explore the reactivity toward ethene as a simple model for more complex systems.22−25 The reaction mechanism of cyclopropanation reactions involving carbenoid systems vary depending on the carbon bonded to the metal and the metal itself. It can be either a single-step reaction, concerted, or a stepwise mechanism. Actually, cyclopropanation reactions involving iodomethyl zinc iodide carbenoids seems to proceed by a concerted mechanism.13,26 Other studies reported on lithium carbenoids have shown that the concerted pathway was always favored over a stepwise or carbometallation mechanism that exclusively occurs with lithium aggregates.27−29 All these analyses were based on the use of low-level theoretical methods, and no detailed exploration of the reaction mechanism was done. On this sense, our main aim in this study is to use specific mechanism analysis formalisms, such as the reaction force and the reaction electronic flux,30,31 to unambiguously recover the nature of the mechanism involved. This analysis will be combined with other reactivity descriptors to gain further insights on the intrinsic changes that occur when ethene is transformed to cyclopropane by the action of lithium and magnesium carbenoids, including halogen atoms (F, Cl, and Br) as leaving groups.

Theoretical Framework

The theoretical descriptors are used for the analysis of the reaction mechanisms; energetic and electronic properties of carbenoid cyclopropanation reaction are defined in the following paragraphs:

Reaction Force

To characterize reaction mechanisms, the evaluation of energy is the most important task that gives information about the reaction energy (ΔE°) and the height of the reaction barrier (ΔE⧧).

The reaction force is the first derivative of the reaction energy over the reaction coordinate and is defined as30−35

graphic file with name ao9b02905_m001.jpg 1

In a single step potential, this function presents two critical points, a minimum ξ1 and a maximum ξ2. These points delimit three zones: the reactant zone (from ξR to ξ1) where the structural rearrangements occur, the transition-state zone (from ξ1 to ξ2) where all of the electronic rearrangements take place and the product zone defined from ξ2 to ξP where structural relaxation of the system occurs to lead to products. From these partitions, it is possible to get the works associated with structural and electronic phenomena.36

Electronic Chemical Potential

From conceptual density functional theory, various response functions or local and global reactivity descriptors can be defined.37,38 One of the most important properties is the electronic chemical potential or the escaping tendency of electrons from an equilibrium state. It has been associated with the negative of electronegativity defined by Mulliken. For an N electron system, chemical potential is defined as37,38

graphic file with name ao9b02905_m002.jpg 2

Owing to the discontinuity of the energy along the number of particles, the finite difference approximation can be used to get an analytic expression of μ in terms of the ionization energy I and the electron affinity A. Also within Koopman’s theorem, this index can be expressed in term of the frontier orbital of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), εHOMO and εLUMO.38

graphic file with name ao9b02905_m003.jpg 3

Reaction Electronic Flux

The relation between electron flux and the gradient of the chemical potential is used to define the reaction electronic flux.32,35,39,40 This index measures the electronic reorganization in a chemical reaction and is defined as

graphic file with name ao9b02905_m004.jpg 4

In analogy with thermodynamics, this property can be associated with the spontaneity of the electronic processes. When J(ξ) is positive, it may point out to a spontaneous reorganization of the electron cloud, indicating bond forming or strengthening, and when it is negative, the electronic changes are then nonspontaneous meaning bond breaking or weakening.31,41

Results and Discussion

Lithium and magnesium are known by their ability to donate their valence electrons when interacting with new species. Its electronic charge in a molecule where they are inserted usually approaches unity for lithium and two for magnesium. This makes the adjacent atoms chemically more reactive. The lithium carbenoid inserts easily CH2 into a double bond in ethene or ethylene, leading a rupture of π bond substituted by two new σ bonds.

In order to analyze in detail the mechanism of the cyclopropane formation, that is, the energetic, structural, and electronic profiles of this transformation, a series of G4 calculations of the reactants, products, and transition states connecting them have been carried out. The calculations have been achieved considering different halogen atoms as substituents in order to counteract the electropositive effect of the alkaline metal and consequently explore their effect on electronic distribution in this reaction. Our research was additionally extended to consider the magnesium-containing carbenoids in order to explore the differences that could exist between alkaline and alkaline-earth metals.

The first step to have a complete picture of the reaction mechanism is to explore the nature and strength of the interactions between the reactants. The optimized structures show that the most stable configuration corresponds to the metal interacting with the double bond of ethylene with interatomic distances between the metal and the double bond of about 2.3 and 2.5 Å for lithium and magnesium, respectively (see Figure S1). As far as the nature of the interaction is concerned, the electron localization function (ELF) shows the existence of a trisynaptic basin (M, C, C) (M = Li, Mg) associated with the polarization of the C=C double bond toward the metal center (see Figure 1). This is consistent with the presence of a bond critical point(BCP) between the metal and the π cloud of the C=C bond, with an electronic density about 0.016 a.u.

Figure 1.

Figure 1

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AIM and ELF population analysis on the reactants highlighting the most important points. The electronic density in the BCP is in a.u. while the electronic charge in the mentioned basin is in e. (Li: purple, Mg: yellow, Cl: green, C: gray, Br: red, F: light green, H: white).

The dissociation energy, De, of an AB system is defined as the difference between the energy global system, AB, and the sum of the energies of the two fragments, A and B, when all of them are in their equilibrium conformation. However, additional information on the nature and strength of the interaction can be achieved by evaluating the interaction energy (Eint), defined as the difference between the energy of the global system AB and the sum of the energies of the two fragments, A and B, when they retain the structure they had in the global system. It is obvious, as illustrated in Scheme 1, that De can be decomposed in two terms: the interaction energy, Eint, and the deformation energy (Edef), defined as the energy necessary to distort the structure of the subunits A and B from their equilibrium geometry to their forms in the complex. The results for both sets of compounds are reported in Table 1.

Scheme 1. Thermodynamic Cycle for the Formation of the Reactants for MgCH2X2 and LiCH2X (Li: Purple, Mg: Yellow, X: Green, C: Gray, H: White).

Scheme 1

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Table 1. Energies, in Terms of Enthalpy at 298 K, Calculated at G4 Level of Theory for the Complexation of Halogen-Methyl Lithium and Magnesium with Ethylenea.

  Edef (carbenoid) Edef (ethene) Eint De
LiFCH2 0.0 –0.1 –7.7 –7.8, −8.35b
LiClCH2 –0.1 –0.1 –8.5 –8.7
LiBrCH2 –0.1 –0.1 –8.9 –9.1
MgF2CH2 2.1 –0.1 –11.9 –9.7, −12.57c
MgCl2CH2 2.9 –0.1 –13.6 –10.8
MgBr2CH2 3.0 –0.1 –14.1 –11.2
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a

(Values are in kcal/mol).

b

Value taken form ref (42) for C2H2–LiF interaction obtained at the MP4/6-311++G(d,p)//MP2/6-311++G(d,p) level including BSSE correction.

c

Value taken form ref (43) C2H2–MgF2 interaction obtained at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level including BSSE correction.

The dissociation energies indicate a typical lithium and magnesium bonds toward a π-system which was already highlighted by Ammal et al. for C2H4–LiX (X = H, F)42 complexes and by Li et al. for C2H4–MgX2 (X = H, F) ones.43 The dissociation energies found for the halocarbon are found to be slightly smaller to the ones reported previously by Ammal et al.42 and Li et al.,43 respectively. In the case of Mg, the difference is larger, being the G4 estimates systematically smaller.

We have found that for these systems the deformation energy is negligibly small for Li-containing carbenoids, independent of the nature of the leaving group (F, Cl, Br). Conversely, the same deformation energies are not negligible for the Mg-containing analogues, being up to 21% of the total interaction energy.

The second-order natural bond orbital (NBO) perturbation analysis shows that the interaction between the carbenoid and ethylene involves the bonding πC–C orbital of the former and the σC–M* (M = Li, Mg) antibonding orbital of the carbenoid, with a perturbation energy being of the order of 8.0 kcal/mol (see Figure 2). The partial population of this antibonding orbital predicted by the NBO method is consistent with the lengthening observed for the C–M (M = Li, Mg) bonds on going from the isolated carbenoid to the complex between the carbenoid and ethylene (Figure S1). It should be mentioned that although this effect is weaker for Li- than for Mg-containing systems, it raises the question of why the deformation energy is negligibly small for Li systems, whereas for Mg ones it is not.

Figure 2.

Figure 2

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Electronic donation deduced from the NBO molecular orbital interactions between πC=C of ethylene and the anti-bonding σ* of magnesium chloromethane Mg–C bond.

A more detailed exploration of the ethylene-M-carbenoid adducts (M = Li, Mg) clearly shows that as mentioned above, the M–CH2 and the M–X (X = F, Cl, Br) of the carbenoid become longer with respect to the separated systems, whereas the X–CH2 distance becomes shorter for the Li-containing systems; this effect is almost inexistent for Mg-containing ones (see Figure S1). This means that for Li the formation of the complex with ethylene implies X–CH2 bond shortening that counterbalance the effect of the Li–CH2 and the Li–X bond lengthening, whereas this effect is practically inexistent for Mg. By contrast, in the later the perturbation induced by the interaction is translated into a deformation of the carbenoid structure. The angle XMgCH2 is reduced from 169° in the isolated reactant to 136° in the chlorine complex. Therefore, the complexation affects the bonds of lithium complexes while in the magnesium systems changes the angle between atoms.

To get in the mechanism of the formation of cyclopropane it is reliable to present the reactants as the interaction between the metal and the double bond of ethylene as reported above. However, from this interaction a first accommodation of the fragments where methylene group needs to get closer to π bond is mandatory. This raises a fundamental question: how do the isolate reactants (Li/Mg halo-carbenoids and ethylene) evolve to products? To answer this question the first step is to find out the transition states that connect reactants and products followed by a detailed description of the different stationary points of potential energy surface of the reaction. Our calculation at the G4 level of theory suggests a transition-state structure where methylene is nearby the π bond of ethene. Its activation energy is about 8.0 and 5.8 kcal/mol above the entrance channel if we take, as example, chlorine derivative in lithium and magnesium reactions, respectively.

To get a detailed picture of the process, an intrinsic reaction coordinate (IRC) calculation was carried out in order to find out the minima in both directions following the reaction coordinate. The results are reported in Figure 3. The most important finding was that in the reaction pathways an intermediate [I(Li)/I1(Mg)] takes place in the reverse direction. This means that the interaction between reactants can go through the minimum previously proposed in the literature42,43 [R(Li)/R(Mg)] then, by a structural reorganization attains the intermediate I(Li)/I1(Mg) to reach the transition state. In the forward direction, the lithium mechanism progresses directly to product while the magnesium reaction goes through an intermediate, namely, [I2(Mg)], before reaching the product (see Figure 3b). It is worth noting that all our tries to find transition states between the intermediates and the reactants or products were unsuccessful. It is quite intuitive because the subtle structural differences between these species suggest the rearrangement between them to be barrierless.

Figure 3.

Figure 3

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Energy profiles of the formation of cyclopropane from the action of metal halocarbenoid on ethylene. (a) Li-halocarbenoid. (b) Mg-halocarbenoid relative energies obtained at the G4 level of theory are in kcal/mol. Color codes are as follows: blue: fluorine, red: chlorine, and green: bromine. Relative energies obtained at the G4 level of theory are in kcal/mol (Li: purple, Mg: yellow, Cl: green, C: gray, H: white).

At this stage, based on the IRC calculation we can conclude that the mechanism of the cyclopropane formation is not concerted, but it is a two-step process. The formation of the two new C–C bonds initially corresponds to the formation of an intermediate I(Li)/I1(Mg), where the first C–C bond begins its assembly to reach the TS(Li)/TS(Mg), which in turn is followed by a formation of second C–C bond leading to the final product P(Li). In the case of magnesium, the second step goes through an intermediary I2(Mg), which collapses directly to the product by a simple accommodation of MgX2 on the cyclopropane ring (see Figure 3).

This description is totally coherent with the results of the noncovalent interaction (NCI) plots and the quantum theory of atoms in molecules (QTAIM) analysis. If we focus on the lithium mechanism (see Figure 4), the NCI analysis of the intermediate shows an attractive region (Figure 4a) between the carbon of the LiClCH2 system and one of the carbon atoms of the ethylene molecule. Consistently, the QTAIM presents a BCP between both carbon atoms (Figure 4b), whereas the energy density in the region (Figure 4c) also indicates a bonding interaction.

Figure 4.

Figure 4

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(a) NCI analysis of the intermediary I(Li) of the chlorine derivative. (b,c) QTAIM analysis of the electronic density and the energy density respectively of the same compound. (Li: pink, C: light blue, H: white).

To validate our assumption, a molecular dynamics propagation of the nuclei from the transition state was done by means of the atom-centered density matrix propagation (ADMP).44−46 The main objective is to localize the points that the interaction of halocarbenoid with ethene overpasses in its travel from the reactants to products.

Over the 20 explored trajectories in each case we selected the ones which can describe roughly the mechanism in both reactions. In Figure 5 represents the evolution in both directions [reverse (a) and forward (b)] of the chlorocarbenoid Mg mechanism from the transition state to reactants and products, respectively. The chloro-lithium mechanism is reported in the Supporting Information (Figure S2). The first conspicuous result from dynamics is the existence of the intermediate I1(Mg)/I(Li) as one of minima of the mechanism pathway. It appears in the range between 50 and 100 fs with a HOMO orbital involving the lone pair of carbon and the π orbital of the ethene double bond (see Figure 5a). The mechanism elapses then through this, confirming the IRC calculations. In the forward direction, we can deduce that the cyclopropane begins its formation at approximately 50 fs. The intermediate I2(Mg) appears at about 100 fs to get transformed to P(Mg) at about 150 fs. The energy of the mechanism expressed by the dynamics potential energy follows the same trends as in the static calculation. Both potential energy surfaces (Figures 3 and 5), indicate that although the carbenoid reactions follow a stepwise energy, they are extremely favorable, thus with an endoenergetic reaction and low barriers leading to products. These results confirm that the reactions need a small activation, and might be the reason why carbenoid reactions are performed at low temperatures.27

Figure 5.

Figure 5

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Relative potential energy (in kcal/mol) of the Mg-halocarbenoid mechanism to reactants (a) and to product (b) during ADMP simulation of 400 fs. The structure of some selected points is reported by their HOMO and LUMO orbitals.

To understand the structural and electronic contributions to the reaction energy profile, we have determined the reaction force and their associated works that are shown in Table 2 and Figure 6. Because the progress of the reaction profile could not overpass the intermediates in both reactions (Li and Mg), the following analysis will be exclusively focused on the region achieved by the IRC calculation. Therefore, the relative energies and barriers are calculated from now on at this level of theory, taking as reference the intermediates I(Li)/I(Mg). It is to note that the trends with the calculation at the G4-level of theory reported in Figure 3 are conserved.

Table 2. Relative Energies, Barriers, and the Works Associated to the Reaction Zones Defined by the Reaction Force Obtained by IRC Calculations (*) at B3LYP/6-311G(d,p).

  ΔE° (kcal/mol) ΔE⧧* (kcal/mol) W1 (kcal/mol) W2 (kcal/mol) W3 (kcal/mol) W4 (kcal/mol)
Li–F –64.96 6.18 4.23 (68.45%) 1.95 (31.55%) –33.74 –37.40
Li–Cl –66.11 4.70 3.25 (69.15%) 1.45 (30.85%) –33.41 –37.40
Li–Br –63.20 4.97 3.47 (69.82%) 1.50 (30.18%) –33.78 –34.39
Mg–F –58.80 4.21 3.01 (71.49%) 1.20 (28.51%) –31.22 –31.73
Mg–Cl –50.19 8.75 7.26 (82.97%) 1.48 (17.03%) –28.11 –30.73
Mg–Br –46.12 9.30 8.02 (86.23%) 1.31 (13.77%) –28.53 –28.66
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Figure 6.

Figure 6

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Reaction energies and force along the IRC in kcal/mol for Li (a) and Mg (b) carbenoids, black: F, blue: Cl and red: Br.

The first conspicuous conclusion from the energy profile is that the primary structural reorganization at the transition state oscillates in the range 4.3–8.0 kcal/mol. In fact, focusing on this step and going deeper on the force profile analysis, we can shed some light on more aspects. Hence, by evaluating the energy and the force profile, the structural reorganization with respect to the electronic reorganization presents about 70% of the activation energy in lithium carbenoids at the determinant step of the reaction. This analysis is reinforced when the works corresponding to each zone of the reaction profile are evaluated. As it can be appreciated in the Table 2 which can be confirmed by the values reported in Figure 3, the reaction is highly exothermic. The halogen electronegativity affects slightly the global activation barriers if the reactant [R(Li)] is taken as reference see Figure 3. However, if we analyze the profile from I(Li) to the products, we can notice that fluorine derivative is the less reactive species in the lithium carbenoid reaction, whereas in the Mg counterparts it appears the most reactive. In the former the energy barrier accounts for the highest activation energy in the lithium set (about 6.2 kcal/mol) while in the latter it accounts for the smallest barrier in the Mg set (about 4.2 kcal/mol). Chlorine and bromine derivatives in the lithium reaction present similar reactivity whereas in the Mg homologues chlorine is slightly more reactive than the bromine derivative. The electronic rearrangement in global trending is similar in all of the reactions considered. The work W2 which reflects these changes oscillates around 2 kcal/mol. However, if we compare its participation in the activation energy, we found that the electronic rearrangement is about 30% in all of the cases with exception of Mg–Cl and Mg–Br that present values of 17 and 13%. This result can be understood by the electronegative capability of the atoms under scrutiny.

With respect to the third and fourth step of the mechanism, W3 and W4 indicate that the electronic rearrangement is slightly higher than the structural relaxation in the formation of the product. These last works might be associated with the bond breaking and the formation of the cyclopropane, and the following formation of the complex between the halide salt and the cyclopropane.

We have so far obtained the energies and the contributions to the main step of the cyclopropanation reactions. However, it is necessary to understand the electronic rearrangements during both reactions and the nature of the reactive intermediaries.

For the electronic analysis, we have used the REF formalism over the IRCs calculations from I(Li) to P(Li) on lithium and from I1(Mg) to I2(Mg) on magnesium carbenoids. The plots of the reaction electronic flux are shown in Figure 6, using the geometries given by the IRC calculations. For all of the systems, this index starts at the reactant zone, indicating that the electronic phenomena are coupled to the structural rearrangements. Most of the changes are concentrated at the transition state. For both Li–X and Mg–X profiles, some electronic activity at the product zone was observed which might be associated with the rotation of the cyclopropane to attain the product. The sign of the flux in this region indicates a spontaneous reaction step, which might be representing bond strengthening/formation. In other words, it could denote the interactions that appears between the metal (Li, Mg) and cyclopropane at the product or intermediary I2(Mg) in the case of magnesium.

With alkyl magnesium carbenoids, all of the systems present changes condensed at the same points of the IRC, indicating a spontaneous rearrangement, followed by a nonspontaneous change that might be associated with the detachment of the CH2 group in order to form the cyclopropane. With lithium, we found mild changes that follow the same trend; this might be attributed to the electronic nature of the alkyl lithium carbenoid, and analyzing the charges of the systems, the CH2 radical has less electronic charge (∼0.8|e|) in contrast to their magnesium counterparts (∼1.0|e|).

Having explored all of the stationary structures of the potential energy surface of the lithium and magnesium carbenoids, it appears necessary to close our study by a discussion of the complexation in products. In other words, lithium and magnesium bonds with cyclopropane are of a great relevance to be analyzed. In fact, in the cyclopropane the interaction is provided by σC–C to the metal which is underlined by a great electronic donation from the σC–C orbital to the empty antibonding orbital σM–X* (see Figure 7). The second-order perturbation analysis in the NBO population quantifies this donation by approximately 2.3 kcal/mol for lithium, whereas for magnesium it is about 1.6 kcal/mol for each Mg–X bond in the case of chlorine derivatives.

Figure 7.

Figure 7

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Reaction electronic flux in lithium and magnesium carbenoids X = F (black), Cl (blue), Br (red).

It is worth to mention that the interaction between the metal and cyclopropane has been also explored by QTAIM and ELF techniques. The presence of a BCP and trisynaptic basin in the interaction region is a great proof of that (see Figure 8). The effect of halogen substitution is noticeable in the lithium bonding because the electronic density in the BCP between the metal and cyclopropane increases when moving from the most electronegative halogen (F) to the least electronegative one (Br). It is clear that the nature of halogen plays an important role in the interaction. In fact, the high electronegativity of the halogen apparently disfavors the complexation of lithium to the cyclopropane. These results can be ratified if the binding energies involved are analyzed in each case. In fact, the binding energies of LiX and cyclopropane are about 8.8, 10.9, and 11.6 kcal/mol for F, Cl, and Br, respectively. In the case of magnesium complexation even with two halogen atoms attached to the metal, the perturbation to get a complex appears minimal. The electronic densities of the bond critical points and the binding energies of each association can demonstrate it (Figure 9).

Figure 8.

Figure 8

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Electronic donation deduced from second-order NBO perturbation analysis in the orbital interactions between cyclopropane and LiCl and MgCl2.

Figure 9.

Figure 9

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AIM and ELF population analysis on the products highlighting the most important points. The electronic density in the BCP are in a.u. while the electronic charge in the mentioned basin are in e. (Li: purple, Mg: yellow, X: green, C: gray, H: white).

Conclusions

In this study, we have presented the cyclopropanation reactions on magnesium and lithium carbenoids substituted with halogens (F, Cl, Br) with ethylene at the G4 theory level. We found that all of the Li and Mg reactions are stepwise with intermediaries that are basically in between the transition states and do not differ in more than 4 kcal/mol from the reactants and products. Our findings suggest a new mechanism of the cyclopropanations by Li and Mg carbenoid.

The Li and Mg reactants are formed by an electrostatic interaction of the π bond with the electron-deficient metal coming from the carbenoid. These results were confirmed by QTAIM, ELF, and NBO analysis.

The inspection of the works given by the reaction force at the determinant step indicated that the structural work defines the barrier height, being the highest at Mg carbenoids and associated with the transposition of the methyl group and rearrangement of the carbenoid in order to get the transition state.

The REF analysis pointed out that the electronic rearrangements occur mostly at the TS zone where all of the bond forming and breaking take place and are characterized by a spontaneous flux at the beginning of the TS zone and a nonspontaneous by the end of the same zone. At the products zone, there is some electronic activity related to the rearrangement of the cyclopropane in order to give a complex with the halide salt I(Li) and I2(Mg). The QTAIM, ELF, and NBO analysis indicated that an electrostatic interaction between the cyclopropane and the halide lithium and halide magnesium salt is formed.

Computational Details

The optimization of the stationary points of the complexes under study was achieved at the G4-theory level, using a composite technique based on B3LYP-optimized geometries that provides final total energies at an effective CCSD(T,full)/G3LargeXP + HF limit level.47 The connection between reactants and products was established by applying the IRC procedure at the B3LYP/6-311G(d,p)48,49 level of theory, taking into account more than 180 points far from the transition state in each direction. In order to test our assumptions, dynamic simulation was done for some selected systems. ADMP molecular dynamics44−46 was chosen with simulation time of 400 femtosecond and an initial kinetic energy about 6.3 kcal/mol. The selection of the velocities and momentums along the transition-state coordinate is done randomly.

All of the calculations have been carried out by means of Gaussian 09 series of programs.50 The electronic population analysis was done by the QTAIM,51,52 by using the AIMall program,53 NBO,54−56 and the ELF57−59 using TopMOD suite of programs.60 To highlight the weak interaction, we used the NCI method proposed by Contreras-García et al.61

Acknowledgments

This work has been partially supported by the FONDECYT REGULAR 1170837 (BH) DGI projects no. CTQ2015-63997-C2, A generous allocation of computing time at the Centro de Computación Científica of the UAM is also acknowledged (A.M.L.).

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b02905.

  • Geometries; lithium carbenoid dynamics; QTAIM calculations for lithium; and Cartesian coordinates of R, TS, and P of lithium and magnesium carbenoids (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao9b02905_si_001.pdf (563.6KB, pdf)

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