The Reaction Mechanism of the Cu(I) Catalyzed Alkylation of Heterosubstituted Alkynes

Abstract

Alkynes may be regioselectively alkylated to alkenes by organocopper reagents in a reaction known as “carbocupration”, where an alkylCu(I) binds to the alkyne and transfers its organic moiety to one of the alkyne carbon atoms. Alkynes hetero-substituted with third-row elements yield alkenes with a regiochemistry opposite to that obtained when using alkynes hetero-substituted with second-row elements. Early computational investigations of his reaction mechanism have identified the importance of the organocopper counter-cation (Li⁺) to the achievement of good reaction rates, but in the subsequent two decades no further progress has been reported regarding the exploration of the mechanism or the explanation of the experimental regiochemistry. In this work, density-functional theory is used to investigate the mechanism used and to describe a model that correctly explains both the reaction rates at sub-zero temperatures and the regiochemistry profiles obtained with each of the heteroalkynes. The rate-determining step is shown to vary depending on the heterosubstituent, and the alkyl transfer is consistently shown to occur, somewhat counter-intuitively, to the alkyne carbon that is complexed by Cu rather than to the “free” alkyne carbon atom, which instead interacts with the counter-cation that stabilizes the developing electronic charge distribution.

1. Introduction

Organocopper reagents may add to alkynes to produce alkenyl copper products [1,2], and this strategy may be used to generate regio-defined heterosubstituted alkenes from the corresponding heterosubstituted alkynes. The reaction occurs in most cases in a syn-pathway, where both Cu and the organic moiety add to the same side of the alkyne (Figure 1), and is very stereospecific: when oxygen- or nitrogen-substituted alkynes are used the organic portion usually adds to the heteroatom-bearing alkyne carbon atom (leading to the formation of the “branched” or β isomer), whereas in sulfur- or phosphorous-substituted alkynes the organic portion binds to the non-heteroatom-substituted carbon instead, leading to the production of the “linear” or α-isomer [2,3]. The different effects of second-row and third-row heteroatoms on the regioselectivity are usually explained by invoking the possibility of electron back-donation to the alkyne by the lone pairs of oxygen and nitrogen (which render the alkyne β-carbon more nucleophilic), which contrasts with the lack of this effect when sulfur or phosphorous (which simply polarize de σ-bond density away from the alkyne α carbon, rendering it nucleophilic) are present. For the N- and O-substituted alkynes, reversal of the regioselectivity occurs when electron-pair-withdrawing groups are attached to the heteroatom (as in alkynyl amides or alkynyl esters) [1,2]. Reactions with alkoxy-substituted alkynes are usually carried out at very low temperatures (−78 °C to −30 °C) due to the instability of the intermediate alkenyl copper compounds, which are prone to undergo β-elimination of the copper alkoxide at temperatures above −20 °C [1,2], whereas the reaction of aminoalkynes, which only undergo β-elimination above +20 °C, is tolerant of higher temperatures (up to 0 °C). The regiochemistry may be inverted in some O- and N-substituted alkynes by attaching other functional groups to the heteroatom (such as by using internal amides or esters as alkyne substituents) [1,2,3], presumably through a directing effect due to the interaction of the carbonyl (in internal amides or internal esters) with the Cu(I) atom. The regiospecificity of these reactions has made them useful components in complex reaction chains aiming at the facile generation of precisely stereodefined chiral allenes [4] or quaternary carbon compounds [5,6].

Computational studies on these reactions are scarce: a 1992 study using HF/3-21G [7] to explore the addition of CH₃Cu(I) and (CH₃)₂Cu(I)^- to simple heteroatom-substituted acetylenes successfully reproduced the effects of the heteroatoms in the regioselectivity but yielded very high activation energies (around 45 kcal/mol) incompatible with the experimental data. A later effort using higher levels of theory and better descriptions of the metal reactants (Me₂CuLi·LiCl, (Me₂CuLi)₂ or Me₂CuLi instead of MeCu or Me₂Cu^-) yielded a pathway involving the formation of a π-complex between metal and alkyne, electron flow from Cu to alkyne (yielding a formal Cu(III) intermediate), followed by methyl movement to one end of the alkyne bond, facilitated by strong stabilization of the negative charge that accumulates on the other alkyne carbon through interaction with the Li⁺ ion, and which afforded much better activation energies (13.6 to 15.8 kcal/mol) [8]. The influence of acetylene substituents on reaction rates or regioselectivity has not, however, been studied with theoretical methods so far. In this article, DFT methods were used to analyze and describe the reaction mechanism of carbocupration of methoxy-, amine-, methylthio-, and phosphine-substituted alkynes using either Cu(CH₃), Cu(CH₃)₂Li, [Cu(CH₃)₂Mg]⁺, or Cu(CH₃)₂MgBr.

2. Results

2.1. Addition of Tetrahydrofuran-Solvated Cu(CH₃) to Alkynes

Exploration of the reaction mechanism of the addition of tetrahydrofuran-complexed Cu(CH₃) to alkynes shows that the initial formation of the π-complex between catalyst and alkyne is energetically favorable by 3–13 kcal·mol⁻¹ in all cases, in spite of the entropic penalty incurred due to the loss of translational and rotational freedom upon the formation of one complex from two separated molecules. The explicit consideration of metal solvation by one molecule of tetrahydrofuran significantly lowers the computed activation energy (

Table 1. Relative energies (kcal·mol⁻¹) of infinitely-separated reactants, π-complexes, transition states and products of the addition of THF-solvated Cu(CH₃) to alkynes of the form R-C≡C-CH₃. For each alkyne, all energies are shown relative to the energy of its most stable π-complex. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K.

		Branched Pathway				Linear Pathway
R=	CH3	NH2	OCH3	PH2	SCH3	NH2	OCH3	PH2	SCH3
Separated reactants	3.6	13.5	10.2	6.1	8.8	13.5	10.2	6.1	8.8
π-complex	0.0	6.3	0.0	3.2	2.2	0.0	1.9	0.0	0.0
TS	29.5	33.0	24.6	30.7	30.8	31.2	23.4	26.6	24.7
product	−26.8	−25.5	−33.8	−23.6	−28.2	−25.4	−36.3	−27.0	−31.1

) vs. the previously predicted [7,8] activation energies (>45 kcal·mol⁻¹). The barriers obtained in this mechanism are, however, still too high to enable the experimentally measured high rates at sub-zero temperatures, as they entail that temperatures as high as 160 °C (for the slowest-reacting, N-substituted, alkyne) or at least 40 ºC (for the fastest-reacting, O-substituted, alkyne) would be needed to achieve a reaction rate of 1 h⁻¹. This mechanism also predicts, in contrast to the experimental observations for the N- or O-substituted alkynes, that the transition states leading to the linear isomers are always favored over those leading to the branched isomers for all tested hetero-substituted alkynes. The structural properties of the transition states are very similar for all alkynes tested (Figure 2): in both isomers, the Cu⁺ ion binds to the two C atoms in the alkyne bond with bonds of approximately the same length (1.90–1.93 Å vs. 1.96–1.99 Å in the branched isomer; 1.93–1.96 Å vs. 1.90–1.93 Å in the linear isomer), and the transferred methyl group lies 2.07–2.11 Å from the accepting alkyne C atom. As a consequence of the high similarity of the transition states, no correlations exist between their geometrical features and the height of the respective activation barriers. Interestingly, the preference for the pathway leading to the linear isomer in this mechanism increases markedly (from 1.1–1.8 kcal·mol⁻¹ to 4.2–6.1 kcal·mol⁻¹) when the heteroatom changes from a second-period element (N or O) to a third-period element, which may be argued to be consistent with the larger experimental preference for linear regioselectivity in the third-period-substituted alkynes versus the N- and O-substituted alkynes. It is, however, clear from the combined data that this mechanism does not agree either quantitatively or qualitatively with the experimental observations.

2.2. Addition of [Cu(CH₃)₂]^-to Alkynes

The addition of [Cu(CH₃)₂]^- to the heteroalkynes is, like the addition of THF-coordinated Cu(CH₃), exergonic. Examination of the evolution of charge distribution and bond orders (Figure 3 and Supporting Information) confirms earlier computational suggestions [8] that the reaction proceeds through initial charge transfer from Cu⁺ to the alkyne and formal oxidation of Cu⁺ to Cu³⁺, yielding an intermediate with two Cu-C bonds with almost unified bond order, and a reduction in the bond order of the alkyne to that of an alkene. As the reaction proceeds to completion, CM5 and total bond order return to their initial values, so that Cu returns to the +1 oxidation state. The geometry of the transition states is more variable (Figure 4) than in the previous mechanism, especially in what concerns the position of the catalytic Cu⁺ relative to the added alkyne bond: in several cases, the metal now surprisingly lies closer to the methyl-accepting alkyne carbon than to the remaining alkyne carbon atom, leading to an unintuitive “strained” conformation, which nonetheless does not entail an increase in activation energy. Indeed, this mechanism consistently affords lower activation barriers (20.3–24.0 kcal·mol⁻¹, for the hetero-substituted alkynes, 28.9 kcal·mol⁻¹ for 2-butyne) than the previous mechanism, and again predicts that the linear isomer should be favored in all cases (

Table 2. Relative free energies (kcal·mol⁻¹) of infinitely-separated reactants, π-complexes, transition states and products of the addition of [Cu(CH3)2]^- to alkynes of the form R-C≡C-CH₃. For each alkyne, all energies are shown relative to the energy of its most stable π-complex. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K.

		Branched Pathway				Linear Pathway
R=	CH3	NH2	OCH3	PH2	SCH3	NH2	OCH3	PH2	SCH3
Separated reactants	0.0	1.9	8.1	2.4	6.0	1.9	8.1	2.4	6.0
π-complex	2.3	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
TS	28.9	24.7	25.0	26.8	31.8	24.0	23.5	22.5	20.3
Product	−27.4	−32.2	−25.7	−28.1	−22.0	−34.8	−37.4	−32.2	−34.0

). This preference is highest for the SCH₃-substituted alkyne (11.6 kcal·mol⁻¹) and lowest for the second-row heteroalkynes (0.7–1.5 kcal·mol⁻¹). With the sole exception of the synthesis of the branched isomer of the SCH₃-substituted alkyne, the reaction with the non-heterosubstituted alkyne (2-butyne) is predicted to be slower than almost all others, partly because in this case the initial formation of the π-complex is endergonic, rather than exergonic. The barriers obtained from this mechanism, while higher than those predicted in earlier work [8] using B3LYP/6-31G(d) (without solvent effects) are an improvement relative to the preceding mechanism. Its poor performance in the prediction of the reaction regiochemistry, however, shows that the catalytic mechanism is not solely dependent on the Cu⁺ coordination but that other factors (such as the interaction of the counter-cation with the alkyne or the dimethylcopper species) must be explicitly accounted for.

2.3. Addition of Cu(CH₃)₂·Li to Alkynes

Although the formation π-complexes between Cu(CH₃)₂ Cu(CH₃)₂·Li and acetylene, propyne, or 2-butyne is always spontaneous, its exergonicity depends on the degree of substitution of the alkyne. Each replacement of a terminal alkyne hydrogen by a methyl group decreases the exergonicity by 2.1–2.4 kcal·mol⁻¹ (

Table 3. Relative Gibbs free energies (kcal·mol−1) of π-complexes, transition states, and products of the addition of Cu(CH3)2·Li to small non-functionalized alkynes. For each alkyne, all energies are shown relative to the energy of infinitely separated reactants. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K.

	2-Butyne	Propyne (Linear Pathway)	Propyne (Branched Pathway)	Acetylene
π-complex	−3.3	−5.4	−5.4	−7.7
TS	25.4	20.6	24.1	16.5
product	−27.9	−33.6	−33.6	−39.3
Activation ΔG	28.7	26.0	29.6	24.2

) and increases activation energy by 1–2 kcal·mol⁻¹ (in agreement with the sluggish reaction rates of dialkylsubstituted alkynes vs. those of terminal alkynes [3]), which can be explained by the inductive effect of each methyl group, which increases electron density on the alkyne bond carbons and decreases their ability to accept electrons from Cu⁺ as it undergoes oxidative addition to the alkyne. For the asymmetric alkyne tested (propyne), this mechanistic model predicts the linear pathway to be favored relative to the branched pathway, in contrast to the experimental observations [1].

In contrast to the observations on the non-functionalized alkynes, the π-complexes leading to the branched or linear isomers of heterosubstituted alkynes are not always identical due to the possibility of interactions between the Li⁺ counter-cation and the lone pairs present in the second-row heteroatoms. Determination of the mechanism of formation of each π-complex therefore becomes necessary, and adds increased complexity to the analysis, as described below and in

Table 4. Relative Gibbs free energies (kcal·mol⁻¹) of π-complexes, transition states, and products of the addition of Cu(CH₃)₂·Li to alkynes of the form R-C≡C-CH₃. For each alkyne, all energies are shown relative to the energy of the infinitely separated reactants. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K.

	Branched Pathway				Linear Pathway
R=	NH2	OCH3	PH2	SCH3	NH2	OCH3	PH2	SCH3
TS1	7.7	13.3	14.3	13.4	9.5	11.0	14.3	13.4
π-complex	−5.1	−8.7	−5.2	−5.4	−5.1	−10.9	−5.2	−6.5
TS2	18.7	13.7	21.0	20.9	16.3	11.9	13.1	12.8
product	−36.9	−35.4	−27.9	−30.5	−37.2	−48.7	−31.9	−40.5
Activation ΔG	23.8	22.4	26.2	26.4	21.3	22.9	18.3	19.3

.

For the nitrogen-substituted alkyne, both π-complexes are equally stable. Although the π-complex leading to the branched isomer is kinetically favored (Table 4), equilibrium is expected to be reached very fast, given the moderate activation energies of the reverse reactions (12.8 kcal·mol⁻¹ for the branched π-complex, 14.6 kcal·mol⁻¹ for the linear one). The regiochemistry will therefore be ruled by the rate of the conversion of each π-complex into the corresponding product, which entails a preference for the linear pathway due to its TS₂ lying 2.4 kcal·mol⁻¹ below the TS₂ for the branched mechanism.

For the oxygen-substituted alkyne the energy of the transition state leading to the π-complex (TS₁) is virtually identical to that of the transition state leading away from each π-complex to the corresponding product (TS₂). There is therefore no facile interconversion between the π-complexes leading to each isomer before they react further, and the activation energy for each pathway becomes the difference in energy between its TS₂ and the corresponding π-complex (rather than the most stable π-complex). For this O-substituted alkyne, prediction of regiochemistry is complicated by two factors which oppose each other: on the one hand, branched product formation is marginally more favored in spite of the corresponding TS₂ lying above the TS₂ of the linear pathway because the corresponding π-complex lies above the linear π-complex and is therefore closer to the transition state energy, but on the other hand the initial formation of the linear π-complex is predicted to be faster than that of the branched π-complex. Integration of the rate equations showed that the effect of the faster formation of the linear π-complex completely overwhelms the marginal advantage of the branched pathway in the second step, leading to almost exclusive production of the linear isomer. In contrast to this complex behavior, TS₁ for the third-row substituted alkynes is identical for both isomers, since in these cases Li⁺ interacts more strongly with the alkyne bond than with the heteroatom lone-pairs, and the regiochemistry is straightforwardly governed by the transition states leading away from the π-complexes.

The transition states leading from the π-complexes of heterosubstituted alkynes to the corresponding products feature, like those of the non-functionalized alkynes, significant stabilizing interactions between Li⁺ and the alkyne (Figure 5). As a consequence, Cu no longer coordinates both alkyne carbon atoms, but only the one that will receive the transferred methyl group. As in the previous mechanisms, the formation of the linear products is predicted to be strongly favored for phosphorous- and sulfur- substituted alkynes, in agreement with experimental observations. The predicted activation energies for these conversions are lower than the previous mechanisms and enable good reaction rates at temperatures as low as 250 K (for PH₂-C≡C-CH₃) or 260 K (for CH₃-S-C≡C-CH₃). For the N- and O-substituted alkynes, however, both the linear and branched mechanisms still predict activation energies incompatible with good reaction rates at sub-zero temperatures.

2.4. Addition of [Cu(CH₃)₂·Mg]⁺to Alkynes

Since the reaction has also been experimentally carried out using magnesium carbocuprates, the reaction mechanisms towards the neutral Cu(CH₃)₂·MgBr and the cationic [Cu(CH₃)₂·Mg]⁺ were also studied.

These computations show that the addition of [Cu(CH₃)₂·Mg]⁺ to the alkynes proceeds, in most cases, through the initial formation of a pre-reactional complex entailing alkyne complexation by Mg²⁺, which then rearranges to an intermediate featuring a bidentate coordination of the alkyne through both Cu(I) and Mg^2+, and where one of the methyl groups bound to Cu also interacts strongly with Mg²⁺. Conversion to this intermediate is quite straightforward, since the corresponding transition states (TS₁ in

Table 5. Relative Gibbs free energies (kcal·mol⁻¹) of the intermediates in the addition of [Cu(CH₃)₂·Mg]⁺ to alkynes of the form R-C≡C-CH₃. For each alkyne, all energies are shown relative to the energy of its most stable pre-reactional complex. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K. N/D: not computed. N/A: formation of bidentate complexes occurred without the intervention of intermediate stages.

		Branched Pathway				Linear Pathway
R=	CH3	NH2	OCH3	PH2	SCH3	NH2	OCH3	PH2	SCH3
Pre-reactional complex	N/D	0.0	1.6	0.0	1.0	N/A	0.0	N/A	0.0
TS1	N/D	16.7	14.5	15.2	11.4	N/A	16.6	N/A	11.4
Bidentate complex	0.0	2.6	0.7	−6.6	−4.0	7.4	12.7	−4.6	−1.8
TS2	8.8	11.8	3.2	3.4	4.8	23.8	11.2	6.6	−3.4
Product	−35.8	−45.1	−47.7	−43.0	−44.3	−30.2	−47.2	−47.2	−45.8

) lie at most 17 kcal·mol⁻¹ above them, and therefore afford acceptable reaction rates at temperatures as low as 230 K.

As in the previous mechanisms, an analysis of the atomic charges and bond orders (Supporting Information) shows that Cu⁺ donates an electron pair to establish a bond with the alkyne and has formally been oxidized to Cu⁺³. In all cases, the bidentate intermediate leading to the branched product is thermodynamically favored over the one leading to the linear product in all cases, but (except for the O-substituted alkyne) the kinetics favor the formation of the complex leading to the linear product instead. The transition states for the conversion of the bidentate complexes into the corresponding products (Figure 6) show similar characteristics, regardless of the heteroalkyne: in all cases, the non-transferred methyl group in the magnesium organocuprate simultaneously coordinates both Mg²⁺ and Cu, the bidentate coordination of the alkyne is maintained, and a methyl group is transferred from Cu to the same alkyne carbon atom to which Cu is attached.

Regiochemical control is achieved through a complex set of factors, entailing both the thermodynamics and the kineticsof both reaction steps. For methylthioalkyne, both linear and branched intermediate complexes form at the same rate, but the subsequent conversion of the intermediate into product occurs without a barrier for the linear pathway, and with a small barrier (of 8.8 kcal·mol⁻¹) for the branched pathway. Integration of the corresponding rate equations predicts that the initial rate of formation of the linear isomer should be larger than that of the branched isomer, but equal amounts of both isomers would eventually be formed. For phosphinealkyne, the branched intermediate is formed many orders of magnitude more slowly than the linear intermediate, and therefore the overwhelming product will be the linear isomer, in spite of the conversion of the linear intermediate into the linear alkyne occurring with a marginally larger barrier than the conversion of the branched intermediate. By contrast, the reaction of the aminoalkyne only yields the branched product because the second transition state for the linear pathway is prohibitively expensive. The most complex behavior is observed for methoxyalkyne: as in the methylthioalkyne, conversion of the linear bidentate intermediate into product occurs without a barrier, but in contrast to methylthioalkyne the reaction rates for the formation of the bidentate complexes are not the same in both pathways. As a consequence of the lower barrier for the formation of the branched intermediate, the product profile overwhelmingly favors the branched isomer. It is interesting to note that in almost all cases the rate-limiting step is shown by these computations to be the initial formation of the bidentate complex, rather than the methyl transfer to the alkyne.

In spite of correctly predicting the reaction regiochemistry and affording activation barriers consistent with experiment, this mechanism has an important drawback: the solution energies of the pre-reactional complexes lie in several cases above those of the infinitely separated reactants, which entails that the real activation energies should be offset by the difference in energies between them. This surprising observation is entirely due to the consideration of solvation effects: indeed, all pre-reactional complexes lie significantly below the energy of the infinitely separate reactants in the gas phase, and almost all of the energy difference is due to considerably higher electrostatic stabilization of the isolated cationic organocuprate, compared to the electrostatic stabilization computed in the complexes and intermediates. Since this result might be an artifact of the use of implicit solvent models (which may give rise to non-cancelling errors when comparing a reactant with a strongly concentrated charge, such as the Mg²⁺ species used, with an intermediate with diffuse charge), I performed additional computations comparing the ease of separating an explicit THF molecule from [Cu(CH₃)₂·Mg·THF]⁺ with the cost of separating an alkyne from the [Cu(CH₃)₂·Mg·alkyne]⁺ complexes. The corresponding results confirmed that the affinity of the cationic organocuprate to the alkynes was indeed inferior to its affinity towards THF: it costs 4.9 kcal·mol⁻¹ to separate the cationic organocuprate from THF, whereas removing the alkynes from the pre-reactional complexes either costs a lower amount (1.2 kcal·mol⁻¹, for aminoalkyne) or is actually exergonic (by 5 kcal·mol⁻¹, for methoxyalkyne to 16.4 kcal·mol⁻¹, for phosphinealkyne).

2.5. Addition of Cu(CH₃)₂·MgBr to Heteroalkynes

To circumvent the unfavorable electrostatic stabilization of the reactants in the previous model, the reaction mechanism using the neutral Cu(CH₃)₂·MgBr was also studied. Several important differences between this model and the previous cationic [Cu(CH₃)₂·Mg]⁺ model arose when comparing the formed intermediates and corresponding transition states: in most instances, the intermediate complexes are no longer properly described as “bidentate” but rather resemble the π-complexes observed in the earlier mechanisms. The transition states, in turn (Figure 7), feature longer C-Mg distances (both relative to the alkyne and to the non-transferred methyl in the organocuprate) due to the enhanced electron density now present on Mg due to its interaction with the Br^- electron cloud. The distances between the transferred methyl and the alkyne are usually decreased, in comparison to those seen in the cationic model.

Except for the linear pathway of methoxyalkyne carbocupration, all of the π-complexes are readily accessible when using Cu(CH₃)₂·MgBr as carbocuprating agent (

Table 6. Relative Gibbs free energies (kcal·mol−1) of the intermediates in the addition of Cu(CH₃)₂·MgBr to alkynes of the form R-C≡C-CH3. For each alkyne, all energies are shown relative to the energy of infinitely separated reactants. Single-point energies were computed at the PBEPW91/6-311G(2d,p)//6-31G(d), including solvation effects in THF and zero-point and vibrational effects at 223 K.

	Branched Pathway				Linear Pathway
R=	NH2	OCH3	PH2	SCH3	NH2	OCH3	PH2	SCH3
Pre-reactional complex	9.1	12.4	18.0	16.9	13.0	13.5	13.8	15.1
π-complex	−2.4	−3.5	2.8	0.7	5.1	19.2	−1.1	2.9
TS	11.9	8.3	19.1	16.9	10.1	20.3	13.2	10.3
product	−41.5	−39.4	−24.9	−28.7	−32.1	−42.5	−26.3	−37.2

). With P- and S-substituted heteroalkynes, conversion of these π-complexes into linear products is favored due to the corresponding transition state being lower in energy by 3–5 kcal·mol⁻¹. With O-substituted alkynes, only the π-complex leading to branched product is thermodynamically accessible at the experimental temperatures, and for aminoalkyne the landscape is more complex because in both alternatives there is one step with a barrier around 10 kcal·mol⁻¹ and another with a barrier around 13 kcal·mol⁻¹. Numerical integration of the reaction rate equations shows that in this case the branched product is predicted to be favored 10-fold over the linear product, in agreement with experimental observations.

To confirm that the implicit-model solvent energies of the pre-reactional complexes were indeed a proper estimate of their ease of formation, they were compared, as in the previous section, with the energy needed to separate an explicit tetrahydrofuran molecule from Cu(CH₃)₂·MgBr·THF. The interaction between the solvent and the organocuprate is, in this neutral model, significantly weaker than in the preceding cationic model: removing THF is now exergonic by 4.3 kcal·mol⁻¹, which entails that the pre-reactional complexes formed when the alkynes replace tetrahydrofuran in the organocuprate solvation shell are actually 4.3 kcal·mol⁻¹ lower in energy than estimated by the THF-free computations depicted in Table 6.

3. Discussion

All mechanisms agree that, contrary to the intuitive view, the transition states for methyl transfer from Cu(I) to alkyne all feature copper coordination to the same alkyne carbon that will receive the transferred methyl group. The activation energies for this step increase as acetylene becomes substituted by one or two methyl groups, and decrease with the introduction of substituents with unshared electron pairs, especially if third-row elements (P or S) are used. Although the explicit introduction of solvent molecules strongly decreases the previously determined [7,8] difference in activation energies between models using CuCH₃ and Cu(CH₃)₂^-, neither of these models can reproduce either the low activation energies observed experimentally or the observed regiochemistry for the heteroalkynes bearing second-row elements. Indeed, the linear isomer is consistently favored, regardless of the identity of the heteroatom bound to the alkyne.

Some improvement in activation energies (especially for S- or P-bearing alkynes) can be achieved by neutralizing the system with Li⁺, which also changes the structure of the key intermediate, since the interaction of Li⁺ with the alkyne prevents Cu from simultaneously binding to both alkyne carbon atoms. With this model the reaction now affords the correct regiochemistry for the O-substituted alkyne, and only the N-substituted alkyne affords the wrong isomer. Activation energies for the O- and N-bearing heteroalkynes were still predicted to be incompatible with the low temperatures used experimentally.

Success was obtained using models bearing Mg²⁺ as counter-cation, especially when the ligand was modeled in its neutral form. In contrast to the simplest models, and as in the reaction with Cu(CH₃)₂Li, formation of the coordinated intermediates was preceded by the formation of stable pre-reactional complexes. With some heteroalkynes, formation of the pre-reactional complex and its conversion to the bidentate complex is rate-determining, whereas in others the slowest step is the methyl transfer from Cu to alkyne carbon atom after the bidentate complex has been produced. The discovery of this complex reactional landscape may be expected to have important consequences for the future rational modification of this interesting reaction to achieve altered regiochemistry profiles.

4. Materials and Methods

All quantum chemistry computations were performed with the Firefly [9] quantum chemistry package, which is partially based on the GAMESS (US) [10] source code. The geometries of putative intermediates and transition states in the reaction mechanism were optimized using autogenerated delocalized coordinates [11], using the PBEPW91 [12,13] functional and the 6-31G(d) basis set for all elements except for Cu, which used the SBKJ VDZ basis set in combination with the SBKJ pseudo-potential [14]. This level of theory has been shown to afford good geometric and/or energetic agreement with high-level CCSD(T) or MP2 benchmarking computations in related Cu⁺-containing model reactions systems [15,16]. Zero-point and thermal effects on the free energies at temperatures between 223 K and 303 K were computed at the optimized geometries. Initial guesses for the transition state geometries were obtained through one- or two-dimensional scans of the respective Cu-C and/or C-C reaction coordinates. After a subsequent optimization to a saddle point, vibrational analysis proved that the optimized transition states did contain a single imaginary frequency, and IRC computations were used to confirm the identity of the respective reactant and product states. Single-point energies of the DFT-optimized geometries were computed using the same functional with the 6-311G(2d,p) for all elements except Cu, which used the s6-31G* basis set developed by Swart et al. [17]. Solvation effects in tetrahydrofuran (including dispersion and repulsion effects [18]) were computed using the polarizable continuum model [19,20,21] implemented in Firefly. Fuzzy bond orders [22] and CM5 charges [23] were computed from the single-point electron densities using Multiwfn [24]. Integration of reaction rate equations was performed using COPASI [25].