Solvent Coordination Effect on Copper-Based Molecular Catalysts for Controlled Radical Polymerization

Abstract

The equilibrium of copper-catalyzed atom transfer radical polymerization was investigated in silico with the aim of finding an explanation for the experimentally observed solvent effect. Various combinations of alkyl halide initiators and copper complexes in acetonitrile (MeCN) and dimethyl sulfoxide (DMSO) were taken into consideration. A continuum model for solvation, which does not account for the explicit interactions between the solvent and metal complex, is not adequate and does not allow the reproduction of the experimental trend. However, when the solvent molecules are included in the coordination sphere of the copper(I,II) species and the continuum description of the medium is still used, a solvent dependence of process thermodynamics emerges, in fair agreement with experimental trends.

1. Introduction

Atom transfer radical polymerization (ATRP) is a controlled radical polymerization technique characterized by a unique mechanism to control the growing chains, allowing for the synthesis of polymers with narrow molecular weight distribution, well-defined composition and controlled architectures [1,2,3].

In Scheme 1, we present the typical mechanism of conventional ATRP. The process is based on a dynamic equilibrium between a dormant species (P_n − X) and a propagating polymer chain (P_n^•) and is catalyzed by a transition metal complex. A large variety of metal complexes with good catalytic properties for ATRP are known. Very often, however, copper complexes with polydentate amine ligands (L) are used [4]. Polymerization is triggered by the reaction of a metal catalyst at a low oxidation state (e.g., [Cu^IL]⁺) with an alkyl halide used as an initiator (RX). This activation step occurs via an inner-sphere electron transfer or atom transfer mechanism [5,6,7], yielding a propagating radical together with the metal complex at a higher oxidation state (e.g., [XCu^IIL]⁺). The radical (P_n^•) is rapidly deactivated back to a dormant state (P_n − X) through the transfer of the halogen atom from the metal catalyst. Usually, the initiator is more active than the dormant species, so all RX molecules are converted to P_n − X at the beginning of the reaction. Chains then grow at the same rate, leading to a polymer with a narrow molecular weight distribution. One of the main characteristics of ATRP is that the equilibrium constant K_ATRP is << 1, hence, the equilibrium is shifted towards the reactants, minimizing the rate of radical termination [8,9].

A drawback of copper-catalyzed traditional ATRP is that it requires starting with a high concentration of O₂-sensitive [Cu^IL]⁺. Besides the necessity of using an appropriate experimental setup such as a Schlenk line to preserve [Cu^IL]⁺ stability, the catalyst must be removed from the polymer at the end of the reaction. Several advanced ATRP techniques have been developed in the last two decades to overcome this problem [10]. They all start with O₂-stable [Cu^IIL]²⁺ or [XCu^IIL]⁺ at a very low concentration, with the (re)generation of the [Cu^IL]⁺ activator complex by using chemical reducing agents (ARGET ATRP) [11,12,13], metallic copper (SARA ATRP) [14,15,16], traditional radical initiators (ICAR ATRP) [17,18] or external stimuli such as photochemistry [19,20,21], electrochemistry [22,23,24,25,26] or sonochemistry [27].

The equilibrium constant, K_ATRP, provides an excellent measurement of the activity of a given catalyst/initiator couple [9]. Several parameters influence the equilibrium constant, such as the nature of the ligand [4,8,9,28,29], the type and structure of the alkyl halide [9] and the reaction conditions (solvent, temperature and pressure) [30,31,32,33,34]. The solvent, in particular, appears to have greater effect on ATRP compared to other radical reactions. Indeed, the solvent affects the redox properties of copper catalysts, their structure in solution and the kinetics of activation reactions, all of which contribute to the dependence of K_ATRP on the reaction medium [32,35].

The thermodynamic and the kinetic aspects of ATRP have been investigated with computational methods during the past years, focusing in particular on the ligand, initiator and transition metal atom [5,36,37,38,39]. Although a lot of effort has been invested in understanding the mechanism of copper-catalyzed ATRP, some important details remain elusive [5]. Among these, the identification of the transition state is still unreached because of the variation in the multiplicity of spin that characterizes the passage from the reagents to the products and vice versa. Moreover, an exhaustive explanation of the solvent effect on K_ATRP is missing, even if deeply investigated experimentally [23,40]. In particular, the role of the solvent on the optimal geometry of both the activator and deactivator complexes, i.e., [Cu^IL]⁺ and [XCu^IIL]⁺, respectively, is not clear. In order to shed some light on some of these open questions, especially the role of polar organic solvents, we present the results of a computational investigation on K_ATRP for some well-known copper complexes that are commonly used as catalysts in ATRP in two selected solvents, namely, acetonitrile (MeCN) and dimethyl sulfoxide (DMSO). These solvents were chosen not only because they are among the most used polar media for ATRP processes but also because experimental data on K_ATRP are available for them, especially in MeCN. Additionally, although both are very polar solvents, a strong difference in K_ATRP has been reported [30]. Therefore, they were picked as the best candidates for a computational study aiming to shed light on the role of the solvent on ATRP activation/deactivation equilibrium.

Six alkyl halides RX (R = methyl-2-propionate (MePr), ethyl α-isobutyrate (EtⁱBu) and allyl (Al); X = Cl, Br) together with three ligands, namely, tris [2-(dimethylamino)ethyl]amine (Me₆TREN), tris(2-pyridylmethyl)amine (TPMA) and N,N,N′,N′′,N′′-pentamethyldiethylenetriamine (PMDETA) were chosen for this study (Chart 1).

The Cu complexes are labeled as [CuⁿLX_z]^n-z, where n indicates the oxidation state of copper(I or II), L denotes one of the three ligands here considered, i.e., Me₆TREN, PMDETA and TPMA, and X is a halide ion, i.e., chloride or bromide. The total charge of the complex (n–z) can be +1 or +2, obtained as the difference between the copper oxidation state and the number of halide ions coordinated to the metal center.

2. Results and Discussion

The overall initial ATRP process described in Scheme 1 and Equation (1), can be partitioned into two fundamental steps: (i) the homolytic RX dissociation (Equation (2)) and (ii) the oxidation of the Cu^I catalyst (Equation (3)), with each step characterized by a defined equilibrium constant (e.g., K_ATRP for Equation (1)) [2]. The thermodynamics associated with Equation (2) have been well described in earlier works [5], revealing a relatively small effect of the solvent. Thus, we first focus on the oxidation of the copper(I) complexes (Equation (3)).

$$\mathrm{RX} + {\left[{\mathrm{Cu}}^{\mathrm{I}}\mathrm{L}\right]}^{+} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\mathrm{L}\mathrm{X}\right]}^{+} + {\mathrm{R}}^{●}$$

(1)

$$\mathrm{RX} \rightleftarrows {\mathrm{X}}^{●} + {\mathrm{R}}^{●}$$

(2)

$${\left[{\mathrm{Cu}}^{\mathrm{I}}\mathrm{L}\right]}^{+} + {\mathrm{X}}^{●} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\mathrm{L}\mathrm{X}\right]}^{+}$$

(3)

2.1. Oxidation of Cu^I Complexes by the X^• Radical

The oxidation of the Cu^I catalyst (Equation (3)) is an important step of the ATRP mechanism [4]. This reaction involves the interaction between the halogen p_z orbital and the HOMO of the Cu^I catalyst, with the formation of a Cu-X bond with almost equivalent metal and ligand contributions (55% and 45% [Cu^I(Me₆TREN)]⁺, 50% and 50% [Cu^I(PMDETA)]⁺, 54% and 46% [Cu^I(TPMA)]⁺) (Table S1). Upon oxidation, significant structural changes occur in the copper complexes, especially in the coordination number (Tables S2–S4). The calculated ΔE_r and ΔG_r values for reaction (3) in the gas phase and implicit solvent (see Materials and Methods section) are reported in

Table 1. ΔE_r and ΔG_r (kcal/mol) of reaction (3) calculated in gas phase and in solution; level of theory: (PCM-)M06/6-311+G(d,p).

Reaction	ΔEr	ΔGr
	Gas phase	Gas phase	In MeCN 1	In DMSO 1
[CuI(Me6TREN)]+ + Cl• → [CuII(Me6TREN)Cl]+	−62.2	−51.8	−59.2	−59.3
[CuI(Me6TREN)]+ + Br• → [CuII(Me6TREN)Br]+	−47.1	−37.2	−43.8	−43.9
[CuI(PMDETA)]+ + Cl• → [CuII(PMDETA)Cl]+	−59.8	−49.6	−58.5	−58.6
[CuI(PMDETA)]+ + Br• → [CuII(PMDETA)Br]+	−44.9	−35.5	−43.3	−43.4
[CuI(TPMA)]+ + Cl• → [CuII(TPMA)Cl]+	−59.1	−48.9	−57.1	−57.1
[CuI(TPMA)]+ + Br• → [CuII(TPMA)Br]+	−44.5	−34.6	−42.0	−42.0

¹ The ΔmRTln(M/0.0409) correction with Δm = −1, already included in the reported results, is: −3.64 kcal/mol for MeCN (19 M) and −3.46 kcal/mol for DMSO (14 M).

.

When Cl^• rather than Br^• is involved, the process is thermodynamically favored, in agreement with the experimental evidence [41,42]. In solution, ΔG_r values become more negative. It is to be noted that there is no appreciable difference between the reaction Gibbs free energy values computed in MeCN and DMSO. In fact, the dielectric constants of these two solvents are very similar.

To complete the whole ATRP process described in Equation (1), one must include in the oxidation process the homolytic dissociation of the carbon–halogen bond in RX (see

Table 2. ΔE_r and ΔG_r (kcal/mol) of reaction (1) calculated in gas phase and in solution; level of theory: (PCM-)M06/6-311+G(d,p).

Reaction	ΔEr	ΔGr
	Gas Phase	Gas Phase	In MeCN	In DMSO
[CuI(Me6TREN)]+ + AlCl $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + Al•	7.3	6.1	1.0	0.9
[CuI(Me6TREN)]+ + AlBr $\rightleftarrows$ [CuII(Me6TREN)Br]+ + Al•	8.2	7.0	2.5	2.4
[CuI(Me6TREN)]+ + EtCliBu $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + EtiBu•	10.7	7.4	1.4	1.3
[CuI(Me6TREN)]+ + EtBriBu $\rightleftarrows$ [CuII(Me6TREN)Br]+ + EtiBu•	11.1	7.5	2.0	2.0
[CuI(Me6TREN)]+ + MeClPr $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + MePr•	12.1	10.3	4.4	4.3
[CuI(Me6TREN)]+ + MeBrPr $\rightleftarrows$ [CuII(Me6TREN)Br]+ + MePr•	13.3	11.4	6.1	6.0
[CuI(PMDETA)]+ + AlCl $\rightleftarrows$ [CuII(PMDETA)Cl]+ + Al•	9.7	8.3	1.8	1.7
[CuI(PMDETA)]+ + AlBr $\rightleftarrows$ [CuII(PMDETA)Br]+ + Al•	10.4	8.7	3.0	2.9
[CuI(PMDETA)]+ + EtCliBu $\rightleftarrows$ [CuII(PMDETA)Cl]+ + EtiBu•	13.2	9.5	2.1	2.0
[CuI(PMDETA)]+ + EtBriBu $\rightleftarrows$ [CuII(PMDETA)Br]+ + EtiBu•	13.3	9.2	2.6	2.5
[CuI(PMDETA)]+ + MeClPr $\rightleftarrows$ [CuII(PMDETA)Cl]+ + MePr•	14.5	12.5	5.2	5.1
[CuI(PMDETA)]+ + MeBrPr $\rightleftarrows$ [CuII(PMDETA)Br]+ + MePr•	15.5	13.0	6.6	6.5
[CuI(TPMA)]+ + AlCl $\rightleftarrows$ [CuII(TPMA)Cl]+ + Al•	10.3	9.0	3.2	3.1
[CuI(TPMA)]+ + AlBr $\rightleftarrows$ [CuII(TPMA)Br]+ + Al•	10.8	9.6	4.4	4.3
[CuI(TPMA)]+ + EtCliBu $\rightleftarrows$ [CuII(TPMA)Cl]+ + EtiBu•	13.8	10.3	3.5	3.4
[CuI(TPMA)]+ + EtBriBu $\rightleftarrows$ [CuII(TPMA)Br]+ + EtiBu•	13.7	10.0	4.0	3.9
[CuI(TPMA)]+ + MeClPr $\rightleftarrows$ [CuII(TPMA)Cl]+ + MePr•	15.1	13.2	6.6	6.5
[CuI(TPMA)]+ + MeBrPr $\rightleftarrows$ [CuII(TPMA)Br]+ + MePr•	15.9	13.9	8.0	7.9

). The reaction occurs through an atom transfer mechanism in which the carbon–halogen bond is homolytically broken while a new halogen–copper bond is formed (Scheme 2). The reaction also involves the oxidation of Cu(I) to Cu(II). As expected, both ΔE_r and ΔG_r of reaction (1), either in the gas phase or in the implicit solvent, have positive values due to the large amount of energy required for the homolytic dissociation of the initiator [9,43]. Still, no significant difference in the energetics is found between the two solvents, indicating that a continuum model for solvation is not adequate to describe the interactions between the solvent and metal complex. Hence, solvent molecules should be included explicitly

Nevertheless, few comments on the trends can be made in comparison with some experimental observations [9]. In terms of reaction Gibbs free energy, the reactivity of the copper(I) complexes having different ligands with the same initiator follows the order Me₆TREN > PMDETA > TPMA, whereas the experimental trend found in MeCN is Me₆TREN > TPMA > PMDETA. When considering the same ligand and the same halogen atom, the activity of the initiator changes in the order Al > EtⁱBu > MePr in the chloride series, and EtⁱBu > Al > MePr in the bromide series. The experimental findings common to RCl and RBr show the following reactivity trend: Al > EtⁱBu > MePr.

As regards the role of halogen atoms in the initiators, the chloro-derivatives are found to be more active than the corresponding bromo ones (Table 2), while, experimentally, it is observed that bromo-based initiators have higher K_ATRP, i.e., less positive ΔG_r. However, this disagreement is not due to the energy required to accomplish the sole homolytic cleavage reported in Equation (2) (see Table S5), which is in agreement with previously calculated and measured values [38,43]. The nature of the inverted trend resides in the stabilization given by the Cu–X bond formation (see Table 1), which is more favored for X = Cl than Br [41,42].

2.2. Solvent Coordination to Copper Complexes

2.2.1. Analysis of Solvent Coordination to Copper(I/II) Centers

As mentioned in the previous section, it is well known that the catalytic activity in ATRP is influenced by the solvent, likely due to the coordination of solvent molecules to the metal center [32,40,44,45]. Indeed, [Cu^IL]⁺ complexes have vacancies in the coordination sphere of the metal center [8], and, depending on the ligand type, one or more solvent molecules may be able to coordinate the copper atom.

Aiming at understanding how DMSO and MeCN behave in the presence of copper complexes, a model system formed by single Cu^I/II ions and one solvent molecule (S) was initially investigated. In principle, MeCN can coordinate using the lone pair on the N atom (end-on coordination) or the nitrile π system (side-on coordination), although this second type of coordination is less common and affords a weaker coordination mode. DMSO can coordinate with the metal center via S or O donor atoms (Figure 1).

Furthermore, exploring the O-coordination modes of DMSO, two possible conformations can be found: the Cu^IDMSO-κOα, characterized by the methyl substituents pointing away from the metal and the S lone pair oriented toward the coordination sphere of the copper atom; or the Cu^IDMSO-κOβ, with the methyl substituents pointing towards the metal and the S lone pair away from it. The model systems built with Cu^I as well as with Cu^II ions interacting with one molecule of either MeCN or DMSO were fully optimized in the gas phase as well as in the implicit solvent. The Gibbs free energies of the formation of these adducts are reported in

Table 3. ΔG_r (kcal/mol) of [Cu^I/II(S)]^+/2+ formation from Cu^I/II and S (S=MeCN, DMSO) calculated in gas phase and in implicit solvent; level of theory: (PCM-)M06/6-311+G(d,p).

S	CuI		CuII
	Gas Phase	In Solvent 1	Gas Phase	In Solvent 1
MeCN (end-on)	−51.7	−24.8	−161.6	−38.7
DMSO-κOα	−57.5	−23.7	−208.2	−86.0
DMSO-κOβ	−56.0	−24.2	- 2	- 2
DMSO-κS	−35.8	−15.2	−183.6	−71.2

¹ The ΔmRTln(M/0.0409) correction with Δm = −1, already included in the reported results, is: −3.64 kcal/mol for MeCN (19 M) and −3.46 kcal/mol for DMSO (14 M). ² In the gas phase, only α complex was obtained.

.

The π-coordinated acetonitrile adduct (side-on coordination) could not be obtained, either in the gas phase or the condensed phase, not even by constrained optimization.

According to the results reported in Table 3, the Cu^I center has an evident preference for coordination by DMSO-κO than by MeCN in the gas phase, while in a solvent, Cu^I does not discriminate much in the coordination between MeCN and DMSO-κO. The coordination of DMSO via S is disfavored in both models. On the other hand, the coordination of a solvent molecule to the Cu^II center is always in favor of DMSO, especially CuDMSO-κO. This is in agreement with the increased hard character of Cu^II with respect to Cu^I.

In both Cu^I and Cu^II, DMSO-κOα and DMSO-κOβ are only 1.5–0.2 kcal/mol apart, which is of the same order as RT at ambient conditions and close to the computational error. However, analyzing the structures of Cu^I/II complexes having coordinated DMSO, retrieved from the Cambridge Crystallographic Database (ca. 340 entries) [46], CuDMSO-κOα coordination was always displayed (see, for example, [47,48]). Thus, in all the starting geometries employed in the calculations reported from now on, only this type of oxygen coordination, DMSO-κOα, was taken into consideration.

2.2.2. Cu^I/IIL(S)]^+/2+ Complexes

Next, we expanded the simple [Cu^I/II(S)]^+/2+ model by introducing the effect of the ligand to describe the formation of the complexes [Cu^I/IIL(S)]^+/2+. The main difference between the ligands here discussed is that PMDETA acts as a tridentate ligand, while both Me₆TREN and TPMA can occupy four coordination sites around the copper ions. Furthermore, one should keep in mind that the copper(I) complexes are usually 18e⁻, tetracoordinated species with distorted tetrahedral coordination geometry, while the copper(II) ones are often pentacoordinated with trigonal bipyramidal or tetragonal pyramidal arrangements, depending on the ligand set. The structural features of copper(I) and copper(II) complexes with the ligands investigated in this work have been extensively studied using several techniques and also deeply discussed in a review in 2005 [49].

Analogously to what we have reported in the previous section, we calculated ΔG_r for the coordination of MeCN and DMSO to complexes [Cu^I/IIL]^+/2+ both in the gas phase and in the continuum solvent (see

Table 4. ΔE_r and ΔG_r (kcal/mol) of reaction (1) calculated in gas phase and in solution; level of theory: (PCM-)M06/6-311+G(d,p).

Reaction	ΔEr Gas Phase			ΔGr Gas Phase			ΔGr In Solution 1
	MeCN	DMSO-κO2	DMSO-κS	MeCN	DMSO-κO2	DMSO-κS	MeCN	DMSO-κO2	DMSO-κS
[CuI(Me6TREN)]+ + S $\rightleftarrows$ [CuI(Me6TREN)(S)]+	−17.9	−20.8	−15.2	−7.5	−9.4	−2.6	−4.4	−2.2	0.4
[CuI(PMDETA]+ + S $\rightleftarrows$ [CuI(PMDETA)(S)]+	−23.0	−24.2	−19.6	−12.6	−11.6	−5.5	−6.3	−3.3	−2.6
[CuI(PMDETA)(S)]+ + S $\rightleftarrows$ [CuI(PMDETA)(S)2]+	−11.4	−18.2	-	−1.8	−6.4	-	1.7	0.2	-
[CuI(TPMA)]+ + S $\rightleftarrows$ [CuI(TPMA)(S)]+	−16.8	−18.9	−13.6	−6.7	−7.5	−1.8	−4.0	−2.7	−0.4
[CuII(Me6TREN)]2+ + S $\rightleftarrows$ [CuII(Me6TREN)(S)]2+	−44.7	−55.6	−30.5	−33.9	−41.8	−16.1	−10.1	−32.2	−11.7
[CuII(PMDETA)]2+ + S $\rightleftarrows$ [CuII(PMDETA)(S)]2+	−48.7	−60.3	-	−36.6	−46.1	-	−18.7	−31.0	-
[CuII(PMDETA)(S)]2+ + S $\rightleftarrows$ [CuII(PMDETA)(S)2]2+	−29.1	−38.5	-	−18.5	−24.2	-	−6.3	−17.0	-
[CuII(TPMA)]2+ + S $\rightleftarrows$ [CuII(TPMA)(S)]2+	−43.7	−52.7	−32.0	−31.8	−39.5	−18.3	−19.1	−29.6	−15.7

¹ The ΔmRTln(M/0.0409) correction with Δm = −1, already included in the reported results, is: −3.64 kcal/mol for MeCN (19 M) and −3.46 kcal/mol for DMSO (14 M). ² DMSO-κOα.

). In the case L = PMDETA, the coordination of a second molecule of solvent has also been explored, although, according to the literature, it has never been observed when crystals of PMDETA copper(I) complexes were isolated [49,50].

Having both the effect of ligands and explicit solvent molecules, we observe that it is possible to discriminate between the thermodynamic effects of the two solvents. Both in the gas phase and in the continuum solvent, MeCN appears as the stronger coordinative solvent in the case of Cu^I. On the other hand, the harder character of Cu^II privileges, once again, oxygen coordination instead of nitrogen, despite both solvents producing very stable complexes.

The nature of the ligand plays an important role in the stabilization effect of the solvent for both Cu^I and Cu^II complexes, which is always greater in the latter case.

[Cu^I(PMDETA)]⁺ gives the most stable complex with a single molecule of acetonitrile. The coordination of a second molecule of MeCN, however, is disfavored in the continuum solvent but favored in the gas phase. The very same effect is observed in the case of DMSO. Similarly to what was observed for [Cu^I/II(S)]^+/2+ (Table 3), coordination via DMSO-κS is disfavored when compared to DMSO-κO.

A survey of the data reported in Table 4 highlights the importance of considering both the implicit and explicit solvent effects for the correct description of the thermodynamics of this class of copper complexes. This aspect is evident in the coordination of the second molecule of solvent in [Cu^I(PMDETA)]⁺. Indeed, although this coordination appears as stabilizing in the gas phase, it turns out to be unstable when also the implicit polar medium is accounted for, in agreement with the crystallographic observations [50].

2.2.3. Analysis of the Isomers [Cu^II(PMDETA)X(S)]⁺

The Cu^I/II complexes with PMDETA deserve further discussion. The metal center in [Cu^IPMDETA(S)]⁺ has a structure close to a distorted tetrahedron, where three positions are occupied by PMDETA and the fourth is saturated by one solvent molecule (see Chart 1). From the calculations presented in Table 4 and the crystallographic information [50], we have excluded the possibility of the formation of a pentacoordinated complex through coordination with a second solvent molecule. This aspect makes [Cu^IPMDETA(S)]⁺ a special case because the reaction with an initiator can produce four different isomers (Figure 2), depending on the direction of halogenation. Despite that few crystallographic data are available for the structure of [Cu^II(PMDETA)X(S)]⁺ complexes [51], we decided to further investigate this aspect.

Four [Cu^II(PMDETA)Br(S)]⁺ isomers (denoted as In with n = 1, 2, 3, 4) were studied to this end (see Figure 2,

Table 5. ΔG_r (kcal/mol) of the coordination reaction of [Cu^II(PMDETA)Br]⁺ with a solvent molecule calculated in gas phase and in implicit solvent; level of theory: (PCM-)M06/6-311+G(d,p).

Isomer	${\left[{\mathrm{Cu}}^{\mathrm{II}}\right(\mathrm{PMDETA}\left)\mathrm{Br}\right]}^{+} + \mathrm{MeCN} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\right(\mathrm{PMDETA}\left)\mathrm{Br}\right(\mathrm{MeCN}\left)\right]}^{+}$			${\left[{\mathrm{Cu}}^{\mathrm{II}}\right(\mathrm{PMDETA}\left)\mathrm{Br}\right]}^{+} + \mathrm{DMSO} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\right(\mathrm{PMDETA}\left)\mathrm{Br}\right(\mathrm{DMSO}\left)\right]}^{+}$
	ΔEr Gas Phase	ΔGr Gas Phase	ΔGr In MeCN 1	ΔEr Gas Phase	ΔGr Gas Phase	ΔGr In DMSO 1
I1	−15.9	−2.3	4.4	−25.6	−11.0	−0.5
I2	−19.4	−8.1	−1.1	−29.7	−15.1	−4.7
I3	−11.2	0.5	4.6	−25.7	−11.7	−3.9
I4	−6.1	5.5	10.6	−17.8	−3.3	4.5

¹ The ΔmRTln(M/0.0409) correction with Δm = −1 is: −3.64 kcal/mol for MeCN (19 M) and −3.46 kcal/mol for DMSO (14 M).

, Tables S6 and S7 for geometry parameters). The complexes differ in the positions of the halide ion and solvent molecule coordinated by the metal center and the methyl group attached to the central nitrogen atom.

In good accordance with the crystallographic data, I2 was calculated as the most stable isomer in both MeCN and DMSO (see Table 5) [52]. In DMSO (implicit solvation), I2 is clearly the most stable isomer, even if the existence of other isomers should not be excluded. On the other hand, in MeCN (implicit solvation), I2 appears as the only thermodynamically stable isomer.

2.3. Reactions including the Explicit Solvent Coordination

With the results reported in Table 4 and Table 5, we have shown that the coordination of one molecule of solvent is an important aspect to consider for the stability of Cu^I and Cu^II complexes. Moreover, we have also proven the importance of considering both implicit and explicit solvent descriptions in computational models.

Based on these considerations, we have recalculated ΔG_r for the ATRP process, described by Equations (4) and (5), including the effect of the explicit coordination of the solvent. The free energies of the reaction are reported in

Table 6. ΔE_r and ΔG_r (kcal/mol) of reaction (1) calculated in gas phase and in solution; level of theory: (PCM-)M06/6-311+G(d,p).

Reaction	S = MeCN			S = DMSO
	ΔE Gas Phase	ΔGr Gas Phase	ΔGr 1 In Solution	ΔE Gas Phase	ΔGr Gas Phase	ΔGr 1 In Solution
[CuI(Me6TREN)(S)]+ + AlCl $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + Al• + S	25.2	13.6	4.7	28.1	15.4	3.8
[CuI(Me6TREN)(S)]+ + AlBr $\rightleftarrows$ [CuII(Me6TREN)Br]+ + Al• + S	26.1	14.5	6.2	29.0	16.4	5.4
[CuI(Me6TREN)(S)]+ + EtCliBu $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + EtiBu• + S	28.6	14.9	5.1	31.5	16.7	4.2
[CuI(Me6TREN)(S)]+ + EtBriBu $\rightleftarrows$ [CuII(Me6TREN)Br]+ + EtiBu• + S	29.0	15.0	5.8	31.9	16.9	4.9
[CuI(Me6TREN)(S)]+ + MeClPr $\rightleftarrows$ [CuII(Me6TREN)Cl]+ + MePr• + S	30.0	17.8	8.1	32.9	19.6	7.3
[CuI(Me6TREN)(S)]+ + MeBrPr $\rightleftarrows$ [CuII(Me6TREN)Br]+ + MePr• + S	31.2	18.8	9.8	34.1	20.7	9.0
[CuI(PMDETA)(S)]+ + AlCl $\rightleftarrows$ [CuII(PMDETA)Cl]+ + Al• + S	32.7	20.9	9.4	33.9	19.9	5.8
[CuI(PMDETA)(S)]+ + AlBr $\rightleftarrows$ [CuII(PMDETA)Br]+ + Al• + S	33.4	21.4	10.5	34.6	20.3	7.0
[CuI(PMDETA)(S)]+ + EtCliBu $\rightleftarrows$ [CuII(PMDETA)Cl]+ + EtiBu• + S	36.1	22.2	9.7	37.3	21.2	6.2
[CuI(PMDETA)(S)]+ + EtBriBu $\rightleftarrows$ [CuII(PMDETA)Br]+ + EtiBu• + S	36.3	21.8	10.1	37.5	20.8	6.6
[CuI(PMDETA)(S)]+ + MeClPr $\rightleftarrows$ [CuII(PMDETA)Cl]+ + MePr• + S	37.5	25.1	12.8	38.7	24.1	9.2
[CuI(PMDETA)(S)]+ + MeBrPr $\rightleftarrows$ [CuII(PMDETA)Br]+ + MePr• + S	38.5	25.7	14.1	39.7	24.7	10.6
[CuI(TPMA)(S)]+ + AlCl $\rightleftarrows$ [CuII(TPMA)Cl]+ + Al• + S	27.1	15.7	7.3	29.2	16.4	5.9
[CuI(TPMA)(S)]+ + AlBr $\rightleftarrows$ [CuII(TPMA)Br]+ + Al• + S	27.6	16.3	8.5	29.7	17.0	7.1
[CuI(TPMA)(S)]+ + EtCliBu $\rightleftarrows$ [CuII(TPMA)Cl]+ + EtiBu• + S	30.6	17.0	7.6	32.6	17.7	6.2
[CuI(TPMA)(S)]+ + EtBriBu $\rightleftarrows$ [CuII(TPMA)Br]+ + EtiBu• + S	30.5	16.8	8.1	32.6	17.5	6.7
[CuI(TPMA)(S)]+ + MeClPr $\rightleftarrows$ [CuII(TPMA)Cl]+ + MePr• + S	31.9	19.9	10.7	34.0	20.6	9.3
[CuI(TPMA)(S)]+ + MeBrPr $\rightleftarrows$ [CuII(TPMA)Cl]+ + MePr• + S	32.7	20.6	12.1	34.8	21.3	10.7
[CuI(PMDETA)(S)]+ + AlCl $\rightleftarrows$ [CuII(PMDETA)Cl(S)]+ + Al•	15.0	12.4	5.8	2.7	4.6	−1.0
[CuI(PMDETA)(S)]+ + AlBr $\rightleftarrows$ [CuII(PMDETA)Br(S)]+ + Al•	14.0	14.3	9.4	4.9	5.2	2.4
[CuI(PMDETA)(S)]+ + EtCliBu $\rightleftarrows$ [CuII(PMDETA)Cl(S)]+ + EtiBu•	18.5	13.6	6.1	6.1	5.9	−0.7
[CuI(PMDETA)(S)]+ + EtBriBu $\rightleftarrows$ [CuII(PMDETA)Br(S)]+ + EtiBu•	16.9	13.8	9.0	7.8	5.7	2.0
[CuI(PMDETA)(S)]+ + MeClPr $\rightleftarrows$ [CuII(PMDETA)Cl(S)]+ + MePr•	19.8	16.6	9.2	7.5	8.8	2.4
[CuI(PMDETA)(S)]+ + MeBrPr $\rightleftarrows$ [CuII(PMDETA)Br(S)]+ + MePr•	19.1	17.6	13.0	10.0	9.6	6.0

¹ The ΔmRTln(M/0.0409) correction with Δm = 1, already included in the reported results, is: 3.64 kcal/mol for MeCN (19 M) and 3.46 kcal/mol for DMSO (14 M).

. Concerning Equation (5), the sole [Cu^I(PMDETA)(DMSO-κOα)]⁺ was considered in the reactants in DMSO, whereas only [Cu^II(PMDETA)X(S)]⁺ (I2) was considered as a product in both solvents (see Table 4 and Table 5).

$$\mathrm{RX} + {\left[{\mathrm{Cu}}^{\mathrm{I}}\mathrm{L}\right(\mathrm{S}\left)\right]}^{+} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\mathrm{L}\mathrm{X}\right]}^{+} + \mathrm{S} + {\mathrm{R}}^{●}$$

(4)

$$\mathrm{RX} + {\left[{\mathrm{Cu}}^{\mathrm{I}}\right(\mathrm{PMDETA}\left)\right(\mathrm{S}\left)\right]}^{+} \rightleftarrows {\left[{\mathrm{Cu}}^{\mathrm{II}}\right(\mathrm{PMDETA}\left)\mathrm{X}\right(\mathrm{S}\left)\right]}^{+} + {\mathrm{R}}^{●}$$

(5)

As reported in Table 6, accounting for the coordination of the solvent drastically affects the thermodynamic analysis for ATRP reactions performed in different media. The predicted activities are, in most of the cases, in good agreement with the experimental measurements/extrapolations [9]. The most striking result is that the computed value of K_ATRP in DMSO is 1–2 orders of magnitude higher than in MeCN, a prediction matching the experimental observations [9,32,40]. Moreover, the trend of K_ATRP with respect to the ligands is the same as observed experimentally, which means that the activity follows the order PMDETA < TPMA < Me₆TREN in acetonitrile and PMDETA ≈ TPMA < Me₆TREN in DMSO, if we consider reaction (4). In the case of PMDETA, we have also calculated the energetics for reaction (5), considering that a solvent molecule can remain coordinated to the copper center after its oxidation to Cu^II. In this last case, the reactivity trend does not match the experimental one, especially for the DMSO data, since PMDETA appears to outperform the other catalytic systems. This is probably not so surprising considering that with PMDETA several equilibria involving both halide and solvent coordination/dissociation might be present in copper(II) species [44,49].

The calculated activity of the initiator follows the order MeXP < EtXⁱBu ≈ AlX for any given ligand, which fairly matches the experimental trend. The only discrepancy between the predicted and experimental data regards the effect of the halide substituent in the initiator: the reactions involving chloro-derivatives appear to be the most active (smaller ΔG_r), but this is not the trend observed experimentally. However, we must remember that in calculations performed with solvents treated as continuum dielectric constants, the mean unsigned error on solvation-free energy can be of the order of 1 kcal/mol for neutral systems, while for ionic species, the error can increase to the order of a few kcal/mol [53,54]. The systematic inverted trend between bromine and chlorine may be an indication that other solvent interactions could affect the activity of the initiators and, particularly, the stability of the transition state.

3. Materials and Methods

All the calculations were performed using Gaussian 09, Revision B.01 [55]. After testing several functionals for the ligands Me₆TREN, PMDETA and TPMA and the [Cu^I(Me₆TREN)]⁺ and [Cu^I(TPMA)]⁺ complexes, the level of theory M06/6-311+G(d,p) was selected as most suitable for the present study [56]. The structural benchmarking was based on the comparison of selected interatomic distances and angles to those measured in analogous compounds taken from the Cambridge Structural Database. Relevant structural parameters are included in the Supporting Information. All geometry optimizations were carried out without any constraints, and frequency calculations, performed at the same level of theory, were conducted to assess the nature of the stationary points (all positive frequencies). Thermodynamic data (ΔG_r) at 298.15 K and 1 atm were calculated from electronic energies and frequency computations using standard statistical mechanics relationships for an ideal gas. Solvent effects were accounted for using the polarizable continuum model (PCM). A standard cavity was used, and the values of the dielectric constants used for acetonitrile (MeCN) and dimethyl sulfoxide (DMSO) were 37.5 and 46.7, respectively. To account for the correct thermodynamic effect given by the solvent, energies relative to the passage from 1 mol/L in the gas phase to 1 mol/L in solution, given by the term ΔmRTln(M/0.0409), were added as a correction to all free energies calculated in PCM. Δm is the change in number of moles of solvated species in the reaction, and R and T are the universal gas constant [L·bar/K·mol] and the temperature [K], respectively. M is the molarity of the solvent in the liquid phase, which is 19 M for MeCN and 14 M for DMSO. The value 0.0409 stands for the quotient P/RT, where P is the pressure at 1 atm. For Δm = 1, the corrective terms are 3.64 kcal/mol for MeCN (19 M) and 3.46 kcal/mol for DMSO (14 M) [53,54,57]. Orbital analysis was carried out using the GaussSum software package [58].

4. Conclusions

The effects of solvent coordination on the ATRP equilibrium constants were investigated through computational methods. Both acetonitrile (MeCN) and dimethyl sulfoxide (DMSO) were found to be coordinating solvents, but with very different strengths. The greater affinity of Cu(I) to nitrogen atoms and the larger size of DMSO are decisive factors. The different coordinative attitudes of the two solvents towards [Cu^I(L)]⁺ complexes affect the final ATRP ΔG_r, modifying the equilibrium constant K_ATRP.

Only when both the implicit (PCM) and explicit (solvent molecule(s)) effects of the solvent were considered, was it possible to establish a more reliable solvation effect on the thermodynamics of the ATRP reaction performed in different media. In particular, it enabled us to explain why K_ATRP is 1–2 orders of magnitude greater in DMSO than in MeCN.