Gian Pietro Miscione
email: gianpietro.miscione@unibo.it

Maria Angels Carvajal

Andrea Bottoni

Juan J Novoa

Pietro

Maria Angels

Gian Pietro

A Theoretical Investigation on the Oxidation States of Palladium Complexes and their Role in Carbonylation Reaction

Keywords: carbonylation, DFT, palladium, reaction mechanism, catalysis carbonylation, DFT, palladium, reaction mechanism, catalysis

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Introduction

Mixtures of Pd(II) compounds, especially Pd(OAc) 2 and tertiary phosphines are widely used in many catalytic reactions. Well known examples of this usage are Suzuki [1], Heck [2], Tsuji-Trost [3] and cross-coupling [4] reactions. In spite of the synthetic importance of these processes and the large amount of experimental and theoretical work available in literature, several issues still remain unclear. One Experimental and theoretical works either proposing Pd(II) complexes as active catalytic species or supporting the opposite idea (i.e. Pd(0) intermediates as true catalysts) can be found. Even if several experimental evidences support the hypothesis of a Pd(II) catalytic species [5][6][7][8][9][10], it is quite likely that both species can act as a catalyst [5][6][7][8], depending on the reaction conditions and the nature of the pre-catalyst complex. This hypothesis is enforced by the fact that Pd complexes can easily undergo redox transformations in both directions. Another interesting point, which certainly does not contribute to clarify the problem, is that an excess of phosphines enhances the catalytic rate. This promoting effect is assumed to be caused by the stabilization of the catalytic species. Since phosphines can form complexes either with Pd(0) or Pd(II), this evidence adds further uncertainty to the matter. Furthermore, the mechanism of the possible conversion between the two oxidation states is not obvious. Kinetic studies carried out by Amatore [11] and coworkers for Pd(OAc) 2 /PPh 3 mixtures show that the rate-limiting step is an intramolecular process that affords a Pd(0) species, which is unstable in the absence of a ligand excess. This species is characterized by two different 13 P NMR signals and reacts with iodobenzene. These authors have carried out additive oxidation of iodobenzene [12] to Pd(0) complexes together with cyclic voltammetry experiments (that allow to ascertain the amount of Pd(0) species) to establish the oxidation state (i.e. Pd(0)) of the intermediates. When the reaction takes place in an excess of phosphines, it is possible to stabilize the Pd(0) species (that shows only one broad 13 The existence and stability of Pd(0) anionic intermediates, i.e.

Pd 0 (PPh 3 ) n (OAc) -(n = 2,3) has been demonstrated either experimentally [14] or by means of theoretical calculations [15]. The role of water molecules in the reduction process has been investigated by Ozawa and collaborators [16]. They found that water molecules are necessary to produce Pd(0) species in the reaction of Pd(AcO) 2 with three equivalents of BINAP. In addition, labelling experiments using 18 O suggest that the oxygen atom of the phosphine oxide comes from the acetate ligands.

The first purpose of the present paper is to clarify some of the abovementioned aspects. In particular we intend to shed light on the real nature of Pd(0) and Pd(II) complexes which form when Pd(II) compounds bearing oxygenated ligands (such as Pd(OAc) 2 ) and tertiary phosphines are combined, as occurring in many reactions catalyzed by this metal. Furthermore we aim to understand how these complexes form from the starting reagents.

In addition to these aspects, the mechanism of carbonylation reactions of allyl halides catalyzed by Pd(0) complexes is investigated. We have chosen this reaction because of its importance in both academic and industrial environment: carbonyl group certainly represents one of the most versatile functional groups in organic synthesis. Transition metal-based carbonylation chemistry has been central to an extraordinary progress in catalysis during the last half century after the pioneering work by Roelen [17] on ethene hydroformylation catalyzed by cobalt tetracarbonyl hydride HCo(CO) 4 . The well-known Reppe carbonylation, for instance, is the result of an extensive research program in carbonylation chemistry carried out by Reppe and co-workers [18]. However, in all cases, high temperature (in the range 50°-150°), high CO pressure, expensive autoclave equipment and large quantities of dangerous volatile and unstable catalysts such as HCo(CO) 4 and Fe(CO) 5 are required.

The severe conditions needed in Roelen and Reppe carbonylation processes remained approximately the same for more than twenty years. Nevertheless, during the last three decades, the work of many researchers, in particular Wilkinson, Heck

and Tsuji [19], led to the development of new stable and effective catalysts based on rhodium and palladium. As a result, new carbonylation procedures under mild conditions (low temperature and pressure) are now available. To carry out many of these reactions, very small amounts of stable catalyst precursors such as Pd(PH 3 )Cl 2 and RhCl(CO) 4 (PPh 3 ) 2 are necessary [START_REF] Colquhoun | Carbonylation: Direct Synthesis of Carbonyl Compounds[END_REF]. A special case is represented by the carbonylation of allyl halides. For this reaction several papers proposing different transition metal complexes as catalysts, have appeared [START_REF] Beller | [END_REF][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Nickel tetracarbonyl Ni(CO) 4 [22,31,37] was proposed for the first time by Chiusoli [22,31]. However, even if this reaction can be carried out at room temperature and under atmospheric or low CO pressures (2-3 atm.) [33], a large amount of nickel tetra-carbonyl is required.

Since the direct manipulation of Ni(CO) 4 is not easy because of its high toxicity, this species has been extensively replaced by palladium complexes. As a consequence, during the last three decades, several different reaction conditions and techniques have been proposed to improve the palladium-catalyzed carbonylation of allylic systems [38][39][40][41][42][43][44][45][46][47][48][49][50][71][72][73].

Recently we have reported a theoretical investigation of the mechanism of palladium-catalyzed carbonylation of allylic systems to afford β,γ-unsaturated acyl derivatives [51][52][53]. A model-system consisting of the Pd(PH 3 )Cl 2 complex (emulating the real catalyst Pd(PPh 3 ) 2 Cl 2 with the metal in its +2 oxidation state), a CO molecule and allyl choride was used [53]. This study demonstrated the existence of two different reaction pathways leading to the β,γ-unsaturated acyl chloride. In one case (η 2 pathway) the carbonylation proceeds via the formation of α-allyl palladium intermediates. In the other case the process involves a direct attack of the CO molecule onto the metal (σ pathway). Along the η 2 pathway the process is characterized by a rather complex mechanism: the CO unit does not insert directly into a Pd-C bond, but interacts simultaneously with one of the two Cl ligands and the closest carbon atom of the allyl double-bond. This affords a cyclic structure including the acyl chloride group. The highest transition state along this path is 43.9 kcal mol -1 above reactants. A lower transition state (33.4 kcal mol -1 above reactants) characterizes the σ pathway: this reaction channel is definitely favoured with respect to that involving η 2 -complexes.

In the present study we examine in details the reaction mechanism of allyl chloride carbonylation catalyzed by Pd(0) species that form according to the mechanism above reported. This study should outline in details the mechanistic changes with respect to the Pd(II)-based carbonylation of a similar system and permits the understanding of the effect of the oxidation state change [53]. Pd(0) species are considered in many cases to be the active catalytic species [13,[63][64][65][66][67][68][69][70], so a systematic study comparing both oxidation states will be very insightful. It is worth to mention that here a more realistic model-system including triphenylphosphine ligands instead of simple PH 3 units (as done in previous papers) is considered. This should provide much more reliable information on the mechanism of this reaction.

Computational Procedures

All DFT computations have been performed with the Gaussian 03 [START_REF] Gaussian | Gaussian[END_REF] series of programs using the non-local hybrid Becke's three-parameter exchange functional [START_REF] Becke | [END_REF] denoted as B3LYP in the Gaussian formalism and a locally dense basis set (LDBS) approach [56]. According to the LDBS approach, the system has been partitioned into two different regions, which were assigned basis sets of different accuracy. One region contains the atoms which play the most important role in the reaction: the metal, the allyl moiety, the acetate fragments, the CO molecule and the phosphorous atoms. For the atoms belonging to this region we have used the DZVP basis, which is a Local Spin Density (LSD)-optimized basis set of double-zeta quality [57]. For the other region, comprised of all the remaining atoms (the phenyl rings), the 3-21G* basis set [START_REF] Gaussian | Gaussian[END_REF] has been employed. When not otherwise specified, the reported energy values and/or geometrical parameters have been obtained with this basis denoted as DZVP/3-21G*.

To check the reliability of this approach we have carried out additional computations (with full geometry optimization) using the DZVP basis set on all atoms and we have compared the results to those obtained at the DZVP/3-21G* level. In these computations we have considered some of the key critical points located on the PES.

We have found that the more accurate representation provides results (energetics and geometrical parameters) very similar to the DZVP/3-21G* basis. Thus, we can state with confidence that the 3-21G* basis satisfactorily emulates the DZVP representation. These data are reported in details in the Supporting Information material.

We have performed frequency computations to determine the nature of the various critical points. In most cases, the shape of the transition vector provided by the frequency computations clearly indicates which intermediates a given transition state is connected to. However a series of IRC computations has been carried out starting from the most important transition states. The relative graphics and figures are available in the Supporting Information section. Furthermore, to roughly evaluate the solvent effects, single-point calculations have been carried out on the gas-phase optimized structures with the Polarized Continuous Model method (PCM based on the integral equation formalism model) [58] available in Gaussian 03: a dielectric workers (denoted as sdd pseudopotentials in the Gaussian 03 formalism) [59] has been employed for palladium, the TZVP basis set [60] for the allyl moiety, the acetate fragments, the CO molecule and the phosphorous atoms and the DZVP basis set for the phenyl rings. This level of accuracy is denoted in the following as sdd/TZVP/DZVP level. The results of these calculations are discussed in a specific section.

Results and Discussion

3.A. Palladium Oxidation-Reduction in Phosphine-Palladium Complexes: a Mechanistic Hypothesis.

We have investigated the conversion and reduction mechanism of Pd(OAc) 2 to Pd(0) complexes. The model-system consists of one Pd(OAc) 2 molecule (palladium in the +2 oxidation state) and five tri-phenylphosphine (PPh 3 ) molecules which come into play at different stages of the process. All energy values discussed in this section are relative to these non-interacting species, which represent the asymptotic limit (AL).

The consecutive addition of two triphenylphosphine units to the starting Pd(OAc) 2 complex occurs in the first stage of the reaction. Although Pd(OAc) 2 in its crystal structure is actually a trimer, we believe that the monomer is a good model for the calculations, since we can expect that the monomeric complex Pd(OAc) 2 (PPh 3 ) 2 will be formed via an analogous mechanism from the trimer. The corresponding energy profile is shown in Figure 1. A schematic representation of the structure of the various critical points is given in Scheme 1 and selected bond lengths are collected in (Scheme 1 here)

The definitive binding of the second phosphine to palladium is a crucial point of the process. As a matter of fact, the resulting complex Pd(OAc) 2 (PPh 3 ) 2 can exist in two different configurations (cis and trans) and each of them originates a unique reaction pathway (denoted here as cis and trans channel) leading to palladium reduction.

We first discuss the trans-channel. The corresponding energy profile is depicted in Figure 2. The various structures located along the reaction path are donating a certain amount of charge from the ring π system (in particular, two carbon atoms of the benzene ring become rather close to the metal, the corresponding carbonpalladium distances being 2.402 and 2.686 Å). Thus, this transition state describes a situation where ligands and electron density are exchanged between the phosphorus (P1) and the palladium atoms, which are involved in a oxidation and reduction process, respectively. Also, the phosphorus atom (P1) is becoming penta-coordinated, because the low energy d-orbitals make possible the interaction with the oxygen atoms of the migrating acetate. Even though penta-coordinated phosphorus complexes may be quite unusual, they have been characterized experimentally [61]. TS3 is 25.5 kcal mol -1 above the previous intermediate (M5) and 22.7 kcal mol -1 below the AL (in the presence of solvent these values become 33.9 and 7.9 kcal mol -1 , respectively).

TS3 leads to M6, which is 35.8 kcal mol -1 below M0, in which both acetates have completed the migration to phosphorus, even if in one case a weak interaction with palladium is still observed (Pd-O2 = 3.743 Å). The π system of one phenyl ring of the leaving phosphine strongly interacts with the metal. The aromatic ring is simultaneously bonded to P1 and behaves as a metal ligand, allowing a significant charge transfer to the palladium and determining a strong stabilization of the system, as it has been observed in this kind of processes [13].

(Scheme 2 here) (Scheme 3 here)

The redox process is completed with the transition state TS4 (second step) that corresponds to the definitive detachment of the phosphorus atom (bearing five ligands) from palladium. The phosphorous ligands include now the original three phenyl rings (one is still partly bonded to Pd) and the two acetates fragments. The separation of the five-coordinated phosphorous is helped by the approach of a new phosphine ligand to the metal (P3-Pd = 3.544 Å), which has now a unsaturated coordination sphere. The resulting intermediate M7 (41.8 kcal mol -1 below the starting reactants in gas phase and 36.2 kcal mol -1 in solvent) is formed by the Pd(PPh 3 ) 2 and PPh 3 (OAc) 2 complexes. The two acetates that coordinate the palladium in the starting species have been replaced by two phosphines. Thus, the metal has been reduced and the resulting oxidation state is now zero, while the phosphorus oxidation state has increased to five. The diagram of Figure 2 shows that the final species M7 is higher in energy than M4. This is mainly a consequence of the "holes" in the coordination sphere of palladium which can accept two more phosphine ligands, thus restoring the optimum tetra-coordination state.

We must stress an additional aspect concerning the redox process. Since TS4

is almost degenerate to M6, it is more cautious to consider this transition state as a computational shortcoming (which could easily disappear when changing the computational level) and the redox transformation a very asynchronous concerted process occurring in two phases. Furthermore, it is important to note that the redox transformation appears to be the rate-determining step of the whole process. This would be in agreement with the results of experimental kinetic studies [11] for mixtures Pd(OAc) 2 /PPh 3 that show that the rate-limiting step of the reaction is an intra-molecular endothermic process affording a Pd(0) species. On the other hand, it is important to mention that the presence of a third ligand does not imply that the reaction is first order in phosphine, since it remains always at a non bonding distance from the palladium atom, and it is not involved in the bond breaking and forming process (TS3). Indeed, the interaction between the metallic centre and such a PPh 3 is very week and could be suppressed for instance if the solvent was considered explicitly, so the proposed mechanism is still zero order in PPh 3 , as it was determined experimentally.

The binding of two additional phosphines to Pd(PPh 3 ) 2 again involves the preliminary formation of weakly bound intermediates corresponding to shallow minima on the potential surface. One phosphine ligand weakly interacts with Pd(PPh 3 ) 2 and affords M8 without overcoming any activation barrier. M8 is 45.8 kcal mol -1 below the asymptotic limit (35.8 kcal mol -1 at the PCM level). The energy barrier ( E(TS5) -E(M8)) for the definitive phosphine binding leading to M9 is very low, being only 0.23 kcal mol -1 (0.92 kcal mol -1 when solvent effects are included).

M9 is a planar tri-coordinated palladium complex Pd(PPh 3 ) 3 which lies 55.6 kcal mol - 1 below reactants (45.0 kcal mol -1 in the presence of solvent). The addition of a further phosphine follows the same pattern. M10 is the preliminary weakly bound complex, (60.1 kcal mol -1 more stable than reactants; 43.2 kcal mol -1 at the PCM level) and 4. In summary, the role of the additional phosphines is mostly to stabilize the resulting Pd(0) species. This result agrees this the fact that in the absence of one excess of ligand the products decompose rapidly.

(Table 4 here)

As above mentioned, a second reaction path (denoted as cis-channel)

originates from M3. The energy profile is reported in Figure 2 and a schematic representation of the structures located on the initial part of this path is given in Scheme 4. The corresponding geometry parameters are collected in Table 5. A transition state TS7 leads from M3 to a (Pd(OAc) 2 (PPh 3 ) 2 cis complex M12, by overcoming an energy barrier (E(TS7) -E(M3)) of 10.3 kcal mol -1 (7.4 kcal mol -1 in solvent). This barrier is 5.8 kcal mol -1 larger than that associated with transition state TS2 leading to the trans complex and M12 is 7.0 kcal mol -1 higher in energy than the corresponding trans-complex M4. This difference is certainly caused by the steric repulsion between the two adjacent phosphine ligands. The key step for Pd oxidation, i.e. transfer of the two acetate ligands from the metal to the phosphine phosphorous atom, involves the transition state TS8 where the migration of the two acetate to the metal (Pd-O3) = 2.252 Å) and its interaction with the approaching phosphine is much weaker (P3-O2 = 2.941 Å). In summary, the incoming phosphine "captures" the two acetates helping their expulsion from the coordination sphere of the metal that retains the electrons of the Pd-OAc bonds, thus reducing its oxidation state. However, TS8 is characterized by a rather high energy barrier (41.8 kcal mol -1 in gas phase and 52.2 kcal mol -1 in solvent) and lies 20.3 kcal mol -1 (19.7 kcal mol -1 at the PCM level) above the highest transition state located along the trans pathway. Thus, the cis channel cannot effectively compete with the trans one and for this reason we do not discuss further.

(Table 5 here) (Scheme 4 here)

(Figure 3 here)

The phosphorous species that forms after TS4 (PPh 3 (OAc) 2 ) easily converts into the corresponding phosphine oxide, which is detected experimentally at the end of the reaction, by reaction with one water molecule. The intermediates and transition states along this path are represented in Scheme 5, while the energy profile is 3. From now on, we refer to the separated reagents of this process (PPh 3 (OAc) 2 and one water molecule) as M13. The interaction between these two species leads to the barrierless formation of a complex (M14) characterized by a hydrogen bond between H1 and O2 that keeps the two molecules together and lowers the energy of the system by 7.4 kcal mol -1 with respect to the isolated reactants. As expected this energy stabilization is smaller when the solvent effects are introduced in a PCM calculation and becomes 2.9 kcal mol -1 . In the next step (TS9), the water molecule closely approaches the phosphorus atom causing a significant series of chemical transformations, which directly lead to the product. In TS9, the water molecule is strongly interacting with the phosphorus: the O5-P1 distance is 1.918 Å.

Simultaneously, each of the two water hydrogen atoms is hopping to one acetate oxygen, namely the one which is not bonded to the phosphorus atom. This double transfer is not synchronous: H1 is almost equally shared between O2 and O5 (H1-O2 kcal mol -1 below the asymptotic limit (36.2 kcal mol -1 when the solvent is considered), it is reasonable to assume that the system will have energy enough to overcome the barrier easily. In spite of the above-mentioned asynchronicity, an IRC calculation demonstrated that TS9 is directly connected to the final product of this process: M15.

This species corresponds to the phosphine oxide Ph 3 P=O (where the phosphorous has still the formal oxidation state +5) interacting with two acetic acid molecules. The phosphine oxide features a tetrahedral geometry and the two hydrogen bonds which keep this complex close to the acetic acid molecules are almost identical: H1-O5 = 1.728 Å and H2-O5 = 1.735 Å. M15 lies largely below the initial reactants: 47.1 kcal mol -1 (37.8 kcal mol -1 at the PCM level). In conclusion, the formation of the phosphine oxide is strongly exothermic and characterized by an energy barrier quite small: hence the process seems to be rather easy.

(Table 6 here) (Scheme 5 here)

3.B. Allyl Chloride Carbonylation Catalyzed by Pd(0) Complexes

In this section, we discuss the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes that easily form when Pd(OAc) 2 species are used in the presence of an excess of phosphines. To this purpose we use a model-system consisting of Pd(PPh 3 ) 4 , a CO molecule and the allyl chloride molecule. These three noninteracting chemical species represent now the asymptotic limit (AL).

(Figure 4 here) This pathway (σ-pathway) originates from a direct, weak and initial interaction of the chlorine atom with the metal and leads to the formation of allyl-palladium σ complexes. The corresponding reaction profile is shown in Figure 4 and a schematic representation of the various structures located along it is given in Scheme 6. Selected bond lengths for the critical points are reported in Table 7. of the cumbersome phenyl rings prevents palladium to adopt the more typical planar tetra-coordination. This transition state is 24.9 kcal mol -1 above the asymptotic limit (15.0 kcal mol -1 at the PCM level) and the corresponding barrier (E(TS11) -E(M17) is 33.0 kcal mol -1 (26.8 kcal mol -1 in solvent). It is important to point out that in this step, which is rate-determining for this pathway, the Pd formal oxidation state is changing from 0 to +2.

(Scheme 6 here) (Table 7 here)

The resulting intermediate (M18) is rather stable being 13.2 kcal mol -1 below the asymptotic limit. The palladium has reached a square planar tetra-coordination and is surrounded by one chlorine atom, the ally carbonyl chain and two phosphines.

The third phosphine has been almost definitely expelled (the Pd-P3 bond length is

3.B.2 .The π η 3 -allyl-palladium complexes pathway

As previously shown, after the initial displacement of a phosphine, in Pd(PPh 3 ) 3 , the metal can accept a chloro-allyl group as new ligand. However, this time, the resulting complex, M19 (see Scheme 7), features a π-η 2 metal coordination through the C1-C2 prevent stronger interaction between the ligands and the metal. The incapability of the palladium to adopt the typical and preferred square-planar coordination reflects this quite unstable setting. As a matter of fact, the displacement of one phosphine from M19 can very easily take place through the next transition state, TS13, which is associated to an energy barrier of 0.2 kcal mol -1 only. This leads to a complex, M20, in which the palladium is coordinated by three ligands only and which is 3.3 kcal mol - 1 more stable than the three-phosphine complex M19 (and 4.6 kcal mol -1 above the AL). At the PCM level, this complex is, on the contrary, a little bit more stable than the AL: 1.5 kcal mol -1 . As observed several times in the present study, the loss of a phosphine from crowed tetra-coordinated palladium complexes is easy and may lead to a negative energy variation as consequence of the strengthening of the remaining metal-ligands interactions. In M20, the C1-C2 double bond is a little longer (1.396 Å)

indicating that the allyl-palladium bond has become stronger. Also the two phosphines on the palladium move closer and strengthen their bond with the metal.

Furthermore, a very loose interaction between the palladium and the expulsed phosphine can still be detected (Pd-P3 = 4.877 Å).

(Table 8)

In the next transition state (TS14), the chlorine atom shows once again its great migrating attitude, passing from the allyl group (namely the C3 carbon atom) to the palladium. Also in this case, it is interesting to highlight the long distance between the halogen atom and the metal (Cl-C3 = 3.298 Å): it is evident that these two centres do not need to closely approach each other for their interaction to be effective. The analysis of the eigenvector associated to the negative eigenvalue of the Hessian matrix indicates that also the approaching of C3 to the palladium is actually taking place. and its intrinsic activation energy (E(TS14) -E(M20)) is 17.6 kcal mol -1 (12.5 at the PCM level). The Pd formal oxidation state is passing from 0 to +2. It is important to underline that this critical point, that results to be the highest along the reaction channel that is being discussed, is slightly lower in energy than TS11, the highest transition state located on the σ σ σ σ-pathway described in the previous section: by 2.7 kcal mol -1 (2.8 kcal mol -1 at the PCM level). Another significant result is that an analogous transition state describing the migration of the chlorine atom, in which three (and not two) phosphines are bonded to the palladium (i.e. proceeding directly from M19) lies 5.4 kcal mol -1 above TS14, so that the pathway featuring two phosphines on the metal is favoured. As above-anticipated, the migration of the chlorine onto the palladium has the consequence of yielding a π η 3 type interaction between the allyl fragment and the metal centre (M21) in which all the three carbon atoms are practically at the same distance from the palladium: C1-Pd = 2.247 Å, C2-Pd = 2.251 Å and C3-Pd = 2.268 Å. In this configuration, being still bonded to two phosphines, the palladium electronic shell is saturated (just like it was surrounded by the usual four ligands). For this reason, the chlorine atom remains partially detached from the metal (as noted above, chlorine-palladium interactions can be effectual even at large distances): the Cl-Pd distance is 2.968 Å, about 0.5 Å longer than an ordinary chlorine-palladium bond. Also the slight separation of the third "spectator" phosphine that is now basically not interacting with the metal (Pd-P3 = 5.124 Å) has certainly the same motivation. All these transformations do not lead to any significant energy variation though: M21 has the same energy as M20. The subsequent step (TS15) is, once more, an easy removal of a phosphine that allows to make room around the palladium coordination sphere for the incoming new ligand. Even in this case, the process is favoured by the strengthening of the interaction between the palladium and the groups, which remain bonded to it. As a matter of fact in TS15, while one phosphine moves away (Pd-P2 = 2.905 Å), the allyl moiety and especially the chlorine atom (which stayed farther in M21) approach the metal (Pd-Cl = 2.576 Å). In this case, the energy activation is higher than for TS13: 5.8 kcal mol -1 (7.7 kcal mol -1 at the PCM level) because, in this case, not only the breaking of the palladium-phosphorous is taking place, but also a motion of the chlorine atom, which moves to a trans position with respect to the allyl fragment. Hence in the next complex, M22, the palladium is surrounded by a chlorine atom, the ally fragment (again in a π-η 3 fashion) and a single phosphine. The expulsed phosphine still retains a partial, weak interaction with the metal (P2-Pd = 4.540 Å), while, as anticipated above, the chlorine is now 0.53 Å closer to it with respect to M21 (Pd-Cl = 2.440 Å). Also in this case, the loss of a phosphine causes only a small energy change, M22 being 0.8 kcal mol -1 above M21 and 5.4 kcal mol -1 above the reactants.

(Table 9 here)

The next stage involves the entering of the CO molecule into the palladium coordination sphere (TS16). The approach of the new ligand, which is forming the (Table 10)

(Figure 5 here) (Scheme 7 here)

In the next intermediate, M23, the palladium has reached its typical and stable square planar tetra-coordination, which, until this point was impossible for the presence of two (or more) cumbersome triphenylphosphines in the metal coordination sphere. The other important feature of this structure is the presence, among the metal ligands, of the two groups between which the new C-C will form (i.e. the allyl group and the CO molecule). In particular, the distance between the two carbon atoms, C3 and C4, which will establish the bond, is 2.813 Å. A weak, but not negligible interaction is active between one "spectator" phosphine and the metal (P2-Pd = 3.977 Å). Several attempts of bonding this phosphine to the palladium failed: however, since the steric hindrance is allowing it, a slight interaction is present and surely contributes to stabilize this complex, which is 4.7 kcal mol -1 above the AL. It is interesting to note that, all the intermediates located until now along this pathway lie more or less at the same energy level, regardless of the nature of the metal ligands (allyl, chlorine, phosphine or CO molecule), except for M19 where three cumbersome triphenylphosphines are bonded to the palladium). In M23, the palladium oxidation number is still +2. Before proceeding along this reaction channel, it is necessary to point out that before the CO comes into play, from M21 the system can evolve to M23 in a different way (a schematic representation of the structures of this alternative part of the reaction pathway is given in Scheme 8). The diffuse nature of the π-η 3 bonding in M21 allows an easy conversion to an α-allyl-palladium complex in which the allyl is attached to the metal through a single σ carbon-metal bond (C3-Pd). In this case, this transformation takes place before and not simultaneously with the CO approach, like it happens in TS16. In the transition state TS17 the Pd-C1 bond is clearly elongating

(Pd-C1 = 2.890 Å), C1-C2 is assuming a double bond character (C1-C2 = 1.365 Å)
and the chlorine atom is approaching the palladium (Pd-Cl = 2.616 Å), which is being taken off part of the charge density previously donated from the allyl unit. Since only a rearrangement of the allyl-palladium bonding is taking place, the energy barrier associated to TS17 is quite modest: 3.2 kcal mol -1 . As anticipated, the complex that forms, M24, is characterized by a σ carbon-palladium bond and by a square-planar coordination. However, M24 is less stable than both M21 and M22 (it is located 6.7 kcal mol -1 above the AL). This is a sign of a slight bigger strength of the π-η 3 interaction over a σ-bond and of the weakness of the palladium-triphenylphosphine bond when the system is crowed and electronically saturated. The next transition state TS18 involves the approach of the CO molecule to the palladium and the simultaneous expulsion of one phosphine: this leads the system to the abovedescribed M23 complex. Even in this case the forming Pd-C4 bond is almost formed (Pd-C4 = 2.292 Å) and TS18 is only 0. above at the PCM level), that is the corresponding transition state for the Pd-C4 bond formation from the π-η 3 M22 complex. In TS18 no electronic rearrangement is needed for the allyl-palladium interaction and also a phosphorous-palladium bond is being broken (Pd-P2 = 3.173 Å). TS18 has an activation energy of 7.2 kcal mol -1 (this point is 13.9 kcal mol -1 above the reagents) confirming that the forming of the palladium-CO bond requires a certain amount of energy. An energy analysis of the two alternative paths proceeding from M21 to M23 allows us to conclude that both are possible and competitive; the differences between them are actually slight and rely basically on the timing by which the ligands are added and removed from the palladium before reaching the M23 intermediate (see also Figure 5).

(Scheme 9 here)

The transition state TS19 following M23 (see Scheme 9) is the critical point, which describes the other crucial transformation of the process: the formation of the C3-C4 bond. The two atoms are part of the allyl chain and the CO molecule, which are in cis position around the metal, so that their approach is not difficult (C3-C4 = 2.053 Å). The transition state is characterized by a three-cantered structure: apart from the C3-C4 approach, simultaneously, the C4 bond is moving closer to the palladium (Pd-C4 = 1.903 Å), whereas C3 is moving away from it (2.404 Å) so that only the former will remain bonded to metal. The energy barrier related to this process is 15.8 kcal mol -1 (13.3 kcal mol -1 at the PCM level) and furthermore TS19 lies 1.7 kcal mol -1 (0.6 kcal mol -1 at the PCM level) lower than TS14, the highest point located on this reaction pathway. The structure of TS19 is emblematic of how the metal performs its catalytic, assisting role, by acting as a "dock" to which two groups can attach to, which one more phosphine is on the metal, has been located: this structure is 4.1 kcal mol -1 less stable than TS19. Once again, even if bonded to the metal, an additional phosphine does not afford an energy stabilization. After the discussed C-C bond formation, the system evolves to an intermediate, M25, in which the palladium is bearing three ligands only: one phosphine, one chlorine atom and the allyl carbonyl chain. The CO unit has inserted into the carbon-palladium bond and now the metal is linked to a 4-carbon chain. In spite of the unsaturated metal coordination sphere, this complex is more stable than all the other structures determined so far, because of the formation of a new carbon-carbon bond (M25 lies 0.4 kcal mol -1 below the AL and 5.1 lower than the previous intermediate). At this point, there is space for an easy approach of a triphenylphosphine to the unsaturated palladium (TS20, activation energy= 0.4 kcal mol -1 ) that brings the system to the already discussed M18. The subsequent steps are obviously those already described in the section 3.B.1 and terminates the catalytic cycle. It is worth mentioning that a transition state for an approach of the chloroallyl unit to the palladium in the initial Pd(PPh 3 ) 3 complex that would eventually lead directly to its oxidation has been found. This transition state would lead to M24 (see Scheme 8), after the concerted breaking of the allylic carbonchlorine bond and the formation of the relative carbon-palladium and chlorinepalladium bonds. Additionally, one phosphine leaves the metal. Although this transition state exists, it is located very high in energy compared to any other points discussed so far: 39.6 kcal mol -1 . It is evident that there is a high cost of energy for the system when a single carbon atom is involved in the breaking of a bond and the simultaneous forming of an interaction with the palladium. In all the cases of carbonmetal σ-bond formation described above, the carbon atom was previously involved in a π-interaction (η 2 or η 3 ) with the palladium that makes smooth and quite easy the establishment of the subsequent bond.

(Table 11) and the Pd-C2 forming is almost complete. A cyclic structure can be recognized involving the following five atoms: C2, Pd, P1, C4 and C1 that forms completely in the following intermediate M26. However TS21 is 45.1 kcal mol -1 above the starting reagents and 22.9 kcal mol -1 higher than TS14 (these values become 12.3 and 30.4 kcal mol -1 when solvent effects are taken into account). M26 is also very high in energy being 35.1 kcal mol -1 less stable than the reagents. Thus, the η 2 pathway cannot compete with the π-η 3 (and not even with the σ pathway) and will not be discussed further.

3.B.

3.C. Extended Basis Set (sdd/TZVP/DZVP) Results

In this section, we discuss the results obtained at the extended sdd/TZVP/DZVP level for the following critical points: (a) M3, TS2, M4, M5, TS3, M12 and TS8 for the conversion and reduction mechanism of Pd(OAc) 2 to Pd(0) complexes (Figure 1 and The most important aspects evidenced by these computations (compared to the DZVP/3-21G* energetics) can be summarized as follows:

(i) The Pd(II) Pd (0) reduction remains an easy process and the general pattern of the energy profile does not change appreciably. The trans pathway is still favored over the cis one being TS8 15.9 kcal mol -1 higher in energy than TS3. Also the corresponding intrinsic energy barrier is higher for the cis pathway Furthermore the π-η 3 pathway is more favored with respect to the σ-pathway: the highest transition state found along the former pathway (TS14) lies now 10 kcal mol -1 lower than the highest transition state on the latter (TS11).

(iii) The transition state TS21 for the rate-determining step of the third possible carbonylation pathway (η 2 -pathway), lies 45.2 kcal mol -1 above the AL and 37.2 kcal mol -1 higher than TS14. Thus, even according to the extended basis set computations, this channel to carbonylation cannot compete with the two above discussed π-η 3 and σ reaction pathways.

Conclusions

Our results can be summarized as follows:

1) The reduction process of Pd(II) to Pd(0) requires an excess of phosphines that react easily (low barriers and high exothermicity) with the starting reagent Pd(OAc) 2 .

2) The consecutive interaction of two phosphines with Pd(OAc) 2 leads to the tetra-coordinated trans-Pd(OAc) 2 (PPh 3 ) 2 species (M4) where the metal is still in the +2 oxidation state. The actual reduction goes first through an intra-molecular rearrangement where the two acetate fragments move toward the phosphorus atom of one phosphine ligand bound to the metal. Then, an additional phosphine enters the system leading to the formation of Pd(PPh 3 ) 2 and PPh 3 (OAc) 2 . In the final stage, the involvement of two more phosphines affords the final product Pd(PPh 3 ) 4 where the oxidation state of the metal is zero. We would like to point out that our computations, because of the approximations that feature our model-system, do not completely rule out the conclusions reached by Amatore and Jutland [11] who suggest the involvement of ionic species.

[74]

3) An alternative path leading to reduction involves the tetra-coordinated cis-Pd(OAc) 2 (PPh 3 ) 2 complex exists, but it is highly disfavoured since it requires the overcoming of larger energy barriers.

4) The existence of three pathways leading to the carbonylation of allyl chloride catalyzed by Pd(0) species such as Pd(PPh 3 ) 4 has been demonstrated. In the σ-pathway, the first significant coordination to the palladium complex is that of CO.

Then, the allyl is involved in the formation of a cyclic transition structure, where the CO molecule interacts at the same time with the allyl chain and the metal.

Simultaneously the chlorine atom migrates to the palladium. This transition state (TS11, 24.9 kcal mol -1 above the reactants) corresponds to the rate-determining step of the process. The catalytic cycle terminates after a second migration of the chlorine atom and a final addition of a phosphine to the palladium complex. This regenerates the initial catalyst Pd(PPh 3 ) 4 . This mechanism is very similar to that determined in a previous work for the same reaction catalyzed by Pd(II) species (PdCl 2 (PR 3 ) 2 ) [53].

The second pathway (π-η 3 -pathway) features the formation of η 3 complexes that follows the initial coordination of the allyl substrate in a π η 3 fashion. This step, which corresponds to the rate determining step of the process (TS14, 22.2 kcal mol -1 above the reactants), is associated with the chlorine migration to the metal that oxidizes to Pd(II). In a subsequent step the CO molecule also binds to palladium before insertion into the palladium-allyl bond. A second migration of the chlorine atom terminates the catalytic cycle and determines the release of the product. A final addition of a phosphine to the palladium complex leads to the regenerated catalyst Pd(PPh 3 ) 4 . Since the transition states for the rate-determining steps of these two Finally, a third pathway (η 2 -pathway) involves the CO attack on a π η 2 allylpalladium complexes, which anticipates the chlorine migration. However, in this case, the transition state of the rate-determining step (TS21) is much higher in energy than the above-mentioned transition states, so that this reaction path cannot compete with the two above described.

5) Our computations clearly indicate that, when using catalysts such as Pd(OAc) 2 with an excess of phosphines, the real catalyst is a Pd(0) species.

6) During the carbonylation the Pd formal oxidation state changes from 0 to +2 and then to 0 again.

7)

The inclusion of solvent effects, computed with the PCM approach, does not significantly affect the mechanistic scenario obtained from gas-phase computations 8) The chlorine atom plays a determinant role in this kind of processes, thanks to its significant migrating attitude and capacity of interacting with the metal even at long distances.

9) The cumbersome phosphines influence the course of the reaction and the stability of the various complexes: in several cases, the metal prefers to expel a phosphine in order to reduce the steric hindrance in the coordination sphere and hence allowing stronger bonds with the remaining ligands.

10) The computations at the extended sdd/TZVP/DZVP level do not significantly affect the mechanistic picture provided by the DZVP/3-21G* basis set.

The intrinsic energy barriers computed for the key steps of the various reaction paths 5. Selected bond lengths (Å) for the critical points TS7, M12 and TS8. Table 6. Selected bond lengths (Å) for the critical points M13, M14, TS9 and M15. Table 7. Selected bond lengths (Å) for the critical points M16, TS10, M17, TS11, M18 and TS12. Table 8. Selected bond lengths (Å) for the critical points M19, TS13, M20. Table 9. Selected bond lengths (Å) for the critical points TS14, M21, TS15 and M22. Table 10. Selected bond lengths (Å) for the critical points TS16, M23, TS17, M24 and TS18 Table 11. Selected bond lengths (Å) for the critical points TS19, M25 and TS20 [11], we have carried out PCM calculations on the two following systems: a) PPh 3 (OAc) 2 + Pd(PPh 3 ) 2 (M7) and the alternative charged system b) PPh 3 (OAc) (+) + Pd(PPh 3 ) 2 (OAc) (-) which would form in the case of a ionic pathway. The solvent emulated by the PCM calculations was nitromethane (ε = 38.2). The computational results show that system a) is 29.6 kcal mole -1 more stable than system b). Also, we have compared, in the same medium, the relative stability of PPh 3 (OAc) 2 and PPh 3 (OAc) + + (OAc) -. Even in this case the neutral system turns out to be more stable (by 6.4 kcal mol -1 ) than the charged one. The above described computational findings suggest that, at least for the present model, the mechanism proposed in our study seems to be favoured with respect to a reaction pathway involving ionic species. However, it is possible, even if unlikely if we consider the significant energy difference between system a) and system b), that the approximations of an implicit solvent model (such as PCM) affect this conclusion and that the employment of a larger model system (possibly with explicit solvent description) may lead to different results.

A Theoretical Investigation on the Oxidation States of Palladium Complexes and their Role in Carbonylation Reaction

Andrea Bottoni (a) , Maria Angels Carvajal (b) ,* Gian Pietro Miscione (a) ,* Juan J. Novoa (c) Email: gianpietro.miscione@unibo.it

A. Full geometry optimizations with the DZVP basis set on all atoms

To check the reliability of the approach using the DZVP basis set on all atoms except the phenyl rings (on which the 3-21G* basis set has been employed), we have carried

  palladium oxidation state of the active catalytic complexes.

  P NMR signal). The authors propose the formation of anionic Pd(0) catalytic active species [Pd(PPh 3 ) n (OAc) 2 ] 2-(n = 2, 3) and also suggest the following reaction mechanism for the reduction of Pd(OAc) 2 by PPh 3 : Pd(OAc) 2 + 2PPh 3 → Pd(OAc) 2 (PPh 3 ) 2 fast Pd(OAc) 2 (PPh 3 ) 2 → Pd 0 (PPh 3 )(OAc) -+ AcO-PPh 3 + slow Pd 0 (PPh 3 )(OAc) -+ PPh 3 → Pd 0 (PPh 3 ) 2 (OAc) -fast Pd 0 (PPh 3 ) 2 (OAc) -+ PPh 3 → Pd 0 (PPh 3 ) 3 (OAc) -fast OAc-PPh 3 + + H 2 O → AcOH + O=PPh 3 + H + fast

constant of 7 .

 7 58 emulating the tetrahydrofuran (THF) solvent has been used. An additional set of single-point computations with a more accurate basis set has been carried out on the most important critical points. The system has been again divided into different regions which were assigned basis sets of different accuracy. In particular the energy-adjusted pseudo-potential basis set proposed by Preuss and co-

Page 13 of 69 URLTS6

 69 is the transition state leading to the formation of the final tetra-coordinated complex M11, which adopts a tetrahedral structure, typical of d 10 metals like Pd(0) that also minimizes the repulsion between the cumbersome PPh 3 ligands. This steric hindrance is responsible for the small stabilization associated with the entering of the forth phosphine in the metal coordination sphere: M11 lies 62.4 kcal mol -1 below the reactants, and only 2.3 lower than M10 (these values become 44.4 and 1.2 kcal mol -1 , respectively, in the presence of solvent). Selected bond lengths for the intermediate complexes (M8, M9, M10 and M11) and the corresponding transition structures (TS5 and TS6) are collected in Table

= 1 . 8 Page

 18 172 Å and H1-O5 = 1.244 Å), while H2 is only weakly interacting with O4 (H2-O4 = 1.968Å). The behaviour of the two acetates on the phosphorus is analogous: the P1-O1 bond has evidently elongated (P1-O1 = 2.131 Å) so that an acetic acid molecule is almost formed and being expelled from the phosphorus coordination shell. On the contrary, the corresponding P1-O3 bond, because of the weakening of the trans effect associated to Pd-O1, is shorter than in M14 (1.750 Å): the acetate is still bonded to the phosphorus, which is octahedrally coordinated. The TS9 transition state lies 9.3 kcal mol -1 above the isolated reactants (PPh 3 (OAc) 2 + H 2 O) and the relative activation energy with respect to the previous intermediate (M14) is 16.7 kcal mol -1 . The energy barrier rises to 21.5 kcal mol -1 at the PCM level, because the stabilizing hydrogen bond network loses strength and importance when the solvent effects are considered. On the other hand, since the precursor M7 lies already 41.

  Palladium complexes such as Pd(PPh 3 ) 4 are characterized by a high steric hindrance, which makes difficult the entering of an additional group in the metal coordination sphere. To avoid the formation of penta-coordinated transient species (bipyramidal configuration) with strong steric repulsions, the replacement of one ligand by a new group must occur in two steps. Thus, in the present case, the expulsion of one phosphine from Pd(PPh 3 ) 4 anticipates the binding of a chloroallyl molecule, as a new ligand. This stage (expulsion of PPh 3 ) is the same as the reverse of the final step (M9 M11) of the process described in the previous section and will not be discussed again. In the resulting trigonal complex Pd(PPh 3 ) 3 there is now enough room to allow the allyl unit to approach the metal. This affords a preliminary intermediate, M16, where a very weak interaction involving the chlorine atom (Cl-Pd distance = 4.697 Å) binds the allyl molecule to the metal. In M16, which is 3.0 kcal mol -1 above the AL (1.6 kcal mol -1 below when solvent effects are included), the metal retains its planar trigonal configuration. When a CO molecule approaches the complex, a more stable complex (M17 8.1 kcal mol -1 below the AL) forms, through a shallow transition state TS10: the new bond (Pd-C4 = 2.015 Å) is quite strong despite the crowded coordination sphere. Actually the important step of the reaction is the next one when the CO molecule establishes a simultaneous interaction with the palladium and the allyl group (transition state TS11). In TS11 the carbon atom C4 of the CO unit forms two new bonds: one with palladium and one with the C1 allyl carbon. The formation of the C1-1.912 Å) causes important structural changes in the allyl moiety: while the C2-C3 bond increases its double bond character (C2-C3 = 1.399 Å), C1-C2 is turning into a single bond (C1-C2 = 1.419 Å). As a consequence the chlorine atom migrates from C3 (allyl system) to palladium: the C3-Cl and Pd-Cl bond lengths are 2.392 and 4.654 Å, respectively. This structural rearrangement also leads to a significant weakening of the Pd-P3 bond (2.626 Å): for electronic and, above all, steric reasons, the palladium cannot bear so many ligands. The remarkable migrating and bridging attitude of chlorine and halogens in general has already been observed in several systems of this kind and it has been demonstrated to represent a crucial step in the carbonylation reaction [62,52,53]. An approximate tetrahedral structure of palladium characterizes TS11. Once again, the presence of five groups and the steric hindrance

4 .(

 4 291 Å) and the Pd oxidation state is now unquestionably +2. In the subsequent step transition state TS12), we observe a back migration of the chlorine atom from the palladium to the carbonyl atom C4; the Pd-carbon bond breaks (Pd-C4 = 2.384 Å) and a phosphine enters again the palladium coordination sphere (Pd-P3 bond length = 2.698 Å). Hence, the palladium oxidation state changes again: from +2 to 0. It is interesting to highlight the role of the chlorine atom which "assists" the carbonylation process. Its double migration forward and backward the metal allows to complete the carbonyl insertion and to undergo the internal rearrangement of the allyl moiety necessary to afford the final product i.e. the acylchloride and the Pd(Ph 3 ) 3 complex (6.4 kcal mol -1 below reactants). An additional phosphine ligand can approach the metal, give back the regenerated catalyst Pd(PPh 3 ) 4 (lying 13.4 kcal mol -1 below the AL), thus closing the catalytic cycle.

  double bond that gives rise to an actual binding between Cl-CH 2 -CH=CH 2 and the palladium. M19 is a tetrahedral intermediate where the typical donation/back donation pattern can be observed: electron density is donated from the C1=C2 π bonding orbital to the empty metal d-orbitals and back-donated from the filled d-orbitals to the C1=C2 π * anti-bonding orbital. The slight elongation of the C=C bond (C1-C2 = 1.373 Å) is a clear indication of this situation. M19 is rather unstable and lies 7.9 kcal mol -1 above reactants: (Pd(PPh 3 ) 4 + chloro-allyl + CO). It is also higher in energy than Pd(PPh 3 ) 3 + chloroallyl + CO + PPh 3 : therefore, the binding of the allyl fragment to Pd(PPh 3 ) 3 destabilizes the system, probably for steric reasons that

  new C4-Pd bond (2.244 Å), causes a change of the way through which the allyl unit interacts with the metal: one carbon atom moves away from the palladium (Pd-C1 = 2.253 Å), while another metal-carbon bond (Pd-C3 = 2.247 Å) is becoming a single σ-bond. In other words the allyl chain remains connected to the palladium through C3 only. Also the chlorine atom and the phosphine are slightly moving far from the metal, as consequence of the incoming of the CO molecule. Although the addition of is not sterically hindered, the activation energy associated to the process is neither negligible nor very high: 9.1 kcal mol -1 : especially the formation of the new C4-Pd bond requires a certain degree of electronic re-organization on the metal.

3 .

 3 Formation of π η 2 -allyl-palladium complexes: an alternative way to carbonylation? The investigation of the potential surface has shown the existence of a third carbonylation pathway involving the formation of π η 2 complexes between the allyl moiety and the metal (η 2 pathway). From the above-discussed M19 tetrahedral intermediate, the CO molecule can enter the metal coordination sphere (transition state TS21, see Scheme 10) and simultaneously interacts with the allyl chain (C1-C4 = 1.766 Å) and one of the three phosphine units (C4-P1 = 2.434 Å). As a consequence of these interactions the C1C2 double bond becomes much longer (C1-C2 = 1.425 Å)

(Scheme 10 )

 10

Figure 2 )

 2 Figure 2); (b) M17 and TS11 for the carbonylation along the σ-pathway (Figure 4);

(55. 2 kcal mol - 1 )

 21 than for the trans pathway (43.3 kcal mol-1 ). The energy difference between TS3 and TS8 and the starting reagents becomes larger at the sdd/TZVP/DZVP level: thus both critical points are now (more realistically) above the AL (ii) The mechanistic pattern describing the possible reaction channels for the carbonylation of allyl chloride catalyzed by Pd(PPh 3 ) 4 does not change significantly.The values of the intrinsic energy barriers for the most important transition states of the π-η 3 pathway (TS14, TS16, TS18 and TS19) are very similar to those obtained with the DZVP/3-21G* basis set. The most significant difference has been found for the M22 → TS16 energy barrier, which is now 3.7 kcal mol -1 lower. Therefore. the to evolve from M21 to M23 along the TS16 channel instead of the TS18 channel (these points were almost degenerate at the DZVP/3-21G* level).

Figure 1 .

 1 Figure 1. Energy profile of the addition of two tri-phenylphosphine units to the starting Pd(OAc) 2 complex. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 2. Energy profile of the trans-and cis-channel (dashed line) for the palladium reduction process. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 3. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets.Figure 4. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 5. Energy profile of the π η 3 -pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. In dashed line (and italic for lettering), the second possible pathway connecting M21 to M23. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The

Figure 2 .

 2 Figure 1. Energy profile of the addition of two tri-phenylphosphine units to the starting Pd(OAc) 2 complex. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 2. Energy profile of the trans-and cis-channel (dashed line) for the palladium reduction process. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 3. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets.Figure 4. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 5. Energy profile of the π η 3 -pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. In dashed line (and italic for lettering), the second possible pathway connecting M21 to M23. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The

Figure 3 .

 3 Figure 1. Energy profile of the addition of two tri-phenylphosphine units to the starting Pd(OAc) 2 complex. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 2. Energy profile of the trans-and cis-channel (dashed line) for the palladium reduction process. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 3. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets.Figure 4. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 5. Energy profile of the π η 3 -pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. In dashed line (and italic for lettering), the second possible pathway connecting M21 to M23. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The

Figure 4 .Figure 5 .Scheme 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 .

 4512345678910 Figure 1. Energy profile of the addition of two tri-phenylphosphine units to the starting Pd(OAc) 2 complex. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 2. Energy profile of the trans-and cis-channel (dashed line) for the palladium reduction process. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 3. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets.Figure 4. Energy profile of the σ-pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The position of the x axis (energy of asymptotic limit) has been set according to the DZVP/3-21G* values.Figure 5. Energy profile of the π η 3 -pathway for the carbonylation reaction of allyl chloride catalyzed by Pd(0) complexes. In dashed line (and italic for lettering), the second possible pathway connecting M21 to M23. Energy values are in kcal mol -1 . PCM values in round brackets and sdd/TZVP/DZVP values in square brackets. The

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 69

  out additional computations (with full geometry optimization) using the DZVP basis set on all atoms and we have compared the results to those obtained at the DZVP/3-21G* level. The full geometry optimizations have been performed on the following critical points: M5, TS3, M6, TS4, M11, TS11, M20, TS14, corresponding to four key steps. We have found that the more accurate representation provides results (energetics and geometrical parameters) very similar to the DZVP/3-21G* basis.We report here the schematic representation of the eight structures with the values of the most important geometry parameters obtained at the DZVP/3-21G* level and with the full DZVP basis set (values in italic and in brackets). The four activation energy barriers are also displayed: values obtained with the DZVP basis set are in italic and in brackets. calculations A series of IRC computations has been carried out starting from the most important transition state structures in order to confirm the topology connections. The transition states for which the IRC calculations have been performed are the following: TS3 (toward reagents and products), TS4 (toward reagents), TS11 (toward reagents), TS19 (toward reagents and products). In several cases, as the transition state involves the displacement of a phosphine group from the metal, the IRC calculations cannot clearly indicate a complete separation of the two groups. As a matter of fact, once the Pd-P bond has slightly elongated in the first steps of the IRC calculation, the phosphine group tends to maintain a slight interaction with the metal and not to totally separate. However, even in these cases, the vibrational analysis undoubtedly shows that the normal mode with imaginary frequency involves the breaking of the Pd-P bond.We report here the results of the IRC calculations as (i) schematic representation of the structure of the initial transition state, the last point of the IRC and the following intermediate on the PES; (ii) graphics in which the y axis represents the energy of the various IRC points (in kcal mol -1 , the energy of the transition state is the reference) and the x axis the net reaction coordinate.TS3 toward M5 (reagents)

Table

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	Molecular Physics Molecular Physics
	formation of phosphorous-metal bonds. These interactions (mainly H-bonds between bond. In particular, the replacement of one oxygen with a phosphorous atom allows a
	the palladium ligands and the incoming phenyl rings) significantly weaken in a more regular and stable square planar coordination of the metal.
	solvent phase because of electrostatic effects (the PCM values are reported in round
	parenthesis). For completeness, all these points will be discussed. Another important (Table 1 here)
	structural feature of the species that form upon addition of PPh 3 molecules, is the (Figure 1 here)
	well-known palladium propensity to reach a tetra-planar coordination. When the four
	F o r ligands are not remarkably cumbersome and this configuration becomes possible, a strong energy gain is observed. F The energy profile for the addition of a second phosphine ligand is almost o r identical to that previously discussed. A slight stabilization accompanies the
	P e In the starting Pd(OAc) 2 complex (M0) the two acetate fragments chelate the metal and saturate the four coordination sites of palladium, thus leading to an formation of a new preliminary complex M3 (4.3 kcal mol -1 lower than M2 and 33.8 P e kcal mol -1 lower than M0). The weak interactions that stabilize this intermediate
	e r approximately square planar structure. The preliminary complex M1 forms without overcoming any energy barrier upon addition of one phosphine ligand with a (again weak H-bonds) are totally lost in condensed phase, where M3 is 26.7 kcal mol -e r 1 below M0 and hence 1.6 kcal mol -1 higher than M2. Even if this marked
	R stabilization ∆E of 4.7 kcal mol -1 . Weak interactions involving one aromatic ring, the R destabilization of M3 is partly due to the frozen geometry (only PCM single point
	e v i e w metal and one acetate ligand can be detected in M1. As mentioned above, this stabilization is significantly reduced when solvent effects are considered (∆E = -0.6 energy barrier of 0.9 kcal mol -1 ), which remains lower than M0. Thus, the binding of w kcal mol -1 ). A further approach of PPh 3 to the metal involves a transition state (TS1, e calculations have been carried out), these results suggest that the intermediate M3 v e i does not probably exist in condensed phase or that it is in equilibrium with M2.
	O n l y PPh 3 to palladium is a rather easy process that causes the almost complete breaking of one Pd-O bond, as observed in the resulting intermediate M2. The new Pd-P1 bond O n l (2.304 Å) is determined by the interaction between the phosphorus lone pair and the y
	empty metal d orbitals. It replaces the weaker Pd-O1 bond (Pd-O1 = 3.008 Å) and
	results in a significant stabilization of the new complex M2, which is 29.5 kcal mol -1
	lower than M0 (28.3 kcal mol -1 in the presence of solvent effects). A further
	contribution to the overall stabilization is probably due to a strain decrease of the
	palladium-acetate oxygen structure and the corresponding strengthening of the Pd-O2

. It is interesting to outline that, each time a new phosphine ligand is added to the system, shallow minima characterized by weak interactions precede the actual Page 7 of 69 URL: http://mc.manuscriptcentral.com/tandf/tmph

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		Molecular Physics
	schematically represented in Scheme 2 and 3, and the most important geometrical
	parameters are reported in Table 2 and 3. From M3, the transition state TS2 leads to
	the formation of the trans complex M4. In TS2 the length of the new forming
	phosphorus-palladium bond (P2-Pd) is 3.040 Å (i.e. almost identical to the value
	found in TS1) whereas the breaking oxygen-palladium bond Pd-O3 is still rather
	short: 2.377 Å. The corresponding activation barrier (E(TS2) -E(M3)) is 4.5 kcal
	F mol -1 and does not change significantly in the presence of solvent effects (4.1 kcal o r mol -1 ). It is reasonable to believe that a steric hindrance around palladium makes this
	barrier higher than that associated to TS1. The trans complex M4 (Pd(OAc) 2 (PPh 3 ) 2 ) P e exists in a typical planar tetra-coordinated configuration and is characterized by a
	strong energy stabilization: 17.3 kcal mol -1 with respect to M3 and 51.1 kcal mol -1 e r below the AL (this value becomes 45.2 kcal mol -1 in the presence of solvent). In M4,
	R the oxidation state of palladium is still unchanged i.e. +2.
		e
	(Table 2 here) (Table 3 here) (Figure 2 here)	v i e w
	O A barrierless rotation around Pd-O2 connects M4 to the intermediate M5 n l y where the oxygen atom O1 is now facing the phosphorus atom P1 (O1-P1 = 2.884 Å).
	In spite of the new O1-P1 interaction, this structure is slightly higher in energy than
	M4 (2.5 and 3.4 kcal mol -1 in gas-phase and solvent, respectively). This is probably
	due to the unfavourable steric interactions among the phosphine phenyl rings, which
	must stay closer to accommodate the acetate fragment after rotation. The structural
	arrangement of M5 anticipates the next crucial step i.e. the palladium reduction that

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	Molecular Physics
	requires the transfer of the two acetate fragments to the phosphorus atom P1 (that
	becomes oxidized). This process occurs in two steps and involves a third phosphine,
	which enters the palladium coordination sphere. In the first step (transition state TS3)
	one oxygen atom of each acetate forms two almost complete bonds with the
	phosphorus atom P1 (P1-O1 = 1.861 Å and P1-O3 = 1.904 Å). Simultaneously the
	bond between the palladium and the second oxygen atom of each acetate significantly
	F elongates. The lengths of these two palladium-oxygen bonds underline the o r asynchronous character of the acetate migration, Pd-O4 (2.438 Å) being shorter than
	Pd-O2 (2.539 Å). A simultaneous removal of the phosphorus from the palladium is P e observed (P1-Pd = 2.478 Å). To balance the consequent loss of electron density on
	r e the metal orbitals, one of the phenyl group moves closer to the palladium, thus
	R
	e
	v i e
	w
	O n l
	y

  TS14 is located 22.2 kcal mol -1 above the reactants (Pd(PPh 3 ) 4 + chloroallyl + CO)

	Page 21 of 69	Molecular Physics
	F o r
	P
	e
	e r
		R
		e
		v i e
		w
		O n l
		y

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  before connecting to each other. Even in this case, an equivalent transition state, in

	Molecular Physics	Page 26 of 69
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

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	Molecular Physics
	reaction channels are very close in energy, both reaction paths are likely and can
	compete.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

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  and the relative stability of the most important transition states change only slightly, thus confirming the conclusions reached at the less accurate level.

	Molecular Physics
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Table 1 .

 1 Selected bond lengths (Å) for the critical points M0, M1, TS1, M2 and M3.

Table 2 .

 2 Selected bond lengths (Å) for the critical points TS2, M4 and M5

Table 3 .

 3 Selected bond lengths (Å) for the critical points TS3, M6, TS4 and M7

Table 4 .

 4 Selected bond lengths (Å) for the critical points M8,

TS5, M9, M10, TS6 and M11. Table

Table 1 .

 1 Selected bond lengths (Å) for the critical points M0, M1, TS1, M2 and M3.

	Page 53 of 69				Molecular Physics
		Pd-O1	Pd-O2	Pd-O3	Pd-O4	Pd-P1	O1-H1	Pd-P2	O1-H2
	M0	2.094	2.097	2.104	2.101	/	/	/	/
	M1	2.106	2.095	2.100	2.109	3.747	2.439	/	/
	TS1	2.251	2.053	2.163	2.081	3.072	2.440	/	/
	M2	3.088	2.042	2.239	2.119	2.304	/	/	/
	M3	2.991	2.056	2.199	2.132	2.309	/	4.110	2.292

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Table 2 .

 2 Selected bond lengths (Å) for the critical points TS2, M4 and M5

					Molecular Physics			Page 54 of 69
		Pd-O1	Pd-O2	Pd-O3	Pd-O4	Pd-P1	Pd-P2	O1-P1	O3-P1
	TS2	3.048	2.109	2.377	2.125	2.296	3.040	4.087	3.927
	M4	3.005	2.073	3.181	2.082	2.396	2.412	3.427	4.376
	M5	3.137	2.084	3.047	2.064	2.410	2.410	2.884	3.862

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Table 3 .

 3 Selected bond lengths (Å) for the critical points TS3, M6, TS4 and M7

	Page 55 of 69				Molecular Physics
		Pd-O2	Pd-O4 O1-P1 O3-P1 Pd-P1 Pd-P2 P1-C1 Pd-C1 Pd-C2 Pd-P3
	TS3 2.539	2.438	1.861	1.904	2.478	2.504	1.914	2.402	2.686	/
	M6	3.743	5.134	1.857	1.863	5.134	2.355	1.820	2.310	2.397	4.743
	TS4 3.520	4.529	1.861	1.863	4.530	2.361	1.824	3.226	2.446	3.544
	M7	/	/	1.846	1.846	/	2.365	/	/	/	2.365

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Table 4 .

 4 Selected bond lengths (Å) for the critical points M8, TS5, M9, M10, TS6 and M11.

				Molecular Physics		Page 56 of 69
		Pd-P2	Pd-P3	Pd-P4	C3-H3	Pd-P5	C4-H4
	M8	2.365	2.370	4.856	2.800	/
	TS5	2.368	2.371	3.970	3.180	/
	M9	2.431	2.424	2.416	/	/
	M10	2.421	2.413	2.431	/	5.161	2.811
	TS6	2.462	2.465	2.459	/	3.447	/
	M11	2.550	2.543	2.550	/	2.535

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Table 5 .

 5 Selected bond lengths (Å) for the critical points TS7, M12 and TS8.

	Page 57 of 69				Molecular Physics
		Pd-O1	Pd-O2	Pd-O3	Pd-O4	Pd-P1	Pd-P2	O2-P3	O1-P3	O4-P3
	TS7	3.120	2.166	2.117	2.420	2.300	2.787	/	/	/
	M12	2.949	2.118	2.119	2.967	2.327	2.330	/	/	/
	TS8	/	2.649	2.252	3.573	2.513	2.366	2.130	2.572	2.941

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Table 6 .

 6 Selected bond lengths (Å) for the critical points M13, M14, TS9 and M15.

				Molecular Physics			Page 58 of 69
		P1-O1	P1-O3	P1-O5	H1-O2	H1-O5	H2-O4	H2-O5
	M13	1.846	1.846	/	/	0.969	/	0.969
	M14	1.876	1.827	/	1.900	0.980	/	0.968
	TS9	2,131	1.750	1.918	1.172	1.244	1.968	0.980
	M15	4.156	4.032	1.529	0.998	1.735	0.999	1.728

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Table 7 .

 7 Selected bond lengths (Å) for the critical points M16, TS10, M17, TS11, M18 and TS12.

	Page 59 of 69				Molecular Physics
		Pd-P1	Pd-P2	Pd-P3	Pd-Cl	C3-Cl	C4-Cl	Pd-C4	C1-C4
	M16	2.422	2.433	2.424	4.697	1.848	/	/	/
	TS10	2.430	2.453	2.438	8.422	1.842	/	3.244	/
	M17	2.533	2.515	2.518	7.482	1.844	/	2.015	/
	TS11	2.535	2.508	2.626	4.654	2.392	/	2.087	1.912
	M18	2.618	2.408	4.291	2.485	/	2.860	2.048	1.541
	TS12	2.684	2.437	2.698	2.928	/	1.998	2.384	1.530

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Table 8 .

 8 Selected bond lengths (Å) for the critical points M19, TS13, M20.

				Molecular Physics			Page 60 of 69
		Pd-C1	Pd-C2	Pd-P1	Pd-P2	Pd-P3	C3-Cl	C1-C2
	M19	2.386	2.443	2.492	2.506	2.622	1.880	1.373
	TS13	2.321	2.368	2.473	2.481	2.856	1.881	1.381
	M20	2.227	2.263	2.427	2.438	4.877	1.885	1.396

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Table 9 .

 9 Selected bond lengths (Å) for the critical points TS14, M21, TS15 and M22.

	Page 61 of 69				Molecular Physics
		Pd-C1	Pd-C2	Pd-C3	Pd-P1	Pd-P2	Pd-Cl	C3-Cl	C1-C2	C2-C3
	TS14	2.147	2.337	3.040	2.366	2.529	3.298	2.637	1.429	1.392
	M21	2.247	2.251	2,268	2.428	2.442	2.968	/	1.411	1.406
	TS15	2.222	2.240	2.266	2.395	2.905	2.576	/	1.412	1.405
	M22	2.242	2.225	2.201	2.404	4.540	2.440	/	1.402	1.417

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Table 10 .

 10 Selected bond lengths (Å) for the critical points TS16, M23, TS17, M24 and TS18.

					Molecular Physics				Page 62 of 69
		Pd-C1	Pd-C3	Pd-C4	Pd-P1	Pd-P2	Pd-Cl	C4-C1	C1-C2	C2-C3
	TS16	2.247	2.253	2.244	2.389	5.167	2.588	3.445	1.411	1.410
	M23	/	2.164	1.958	2.504	3.977	2416	2.813	1.349	1.471
	TS17	2.890	2.137	/	2.395	2.467	2.616	/	1.365	1.450
	M24	/	2.133	/	2.375	2.568	2.472	/	1.351	1.471
	TS18	/	2.132	2.292	2.396	3.173	2.460	3.924	1.351	1.465

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Table 11 .

 11 Selected bond lengths (Å) for the critical points TS19, M25 and TS20 Supporting information file for the paper:

	Page 63 of 69				Molecular Physics
		C4-O	Pd-C3	Pd-C4	Pd-P1	Pd-P2	Pd-Cl	C4-C1	C1-C2	C2-C3
	TS19	1.164	2.404	1.903	2.387	5.763	2.432	2.053	1.345	1.478
	M25	1.196	/	2.004	2.375	6.238	2.393	1.536	1.338	1.509
	TS20	1.196	/	1.994	2.389	3.367	2.402	1.527	1.337	1.507

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Acknowledgments

Acknowledgment to HPC-Europa program: this work was carried out under the HPC-EUROPA project (RII3-CT-2003-506079), with the support of the European Community -Research Infrastructure Action under the FP6 "Structuring the European Research Area" Programme. Financial support has also been provided by the Spanish Government (Project CQTC-2008-06644-C03-01) and the Generalitat de Catalunya (SGR-2009-462).


S Croce

M Guèye

A C E Korganow

E Chatelus

S M K Guèye

P Diemunsch

C Mathelin
email: carole.mathelin@chru-strasbourg.fr

Pr C Mathelin

Paraneoplastic polymyositis associated with breast cancer: a therapeutic emergency

Keywords: breast cancer, paraneoplastic syndrome, polymyositis

The association of polymyositis and cancer was first described in 1916, the most frequent cancers being mammary and gynecological for women, bronchopulmonary for men and digestive for both. This article reports a severe paraneoplastic polymyositis associated with breast cancer. We discuss its clinical, pathological and therapeutic particularities.

Introduction

Inflammatory polymyositis are a heterogeneous group of disorders affecting skeletal muscle via an inflammatory reaction. Paraneoplastic polymyositis (PP) may precede or occur simultaneously with the discovery of a tumor, and even persist after the treatment of the primary tumor. Moreover significant excesses of cancer are observed after polymyositis treatment and the excess cancer incidence declines steadily with increasing years since initial diagnosis of polymyositis [START_REF] Chow | Cancer risk following polymyositis and dermatomyositis: a nationwide cohort study in Denmark[END_REF][START_REF] Chen | Cancer risks of dermatomyositis and polymyositis: a nationwide cohort study in Taiwan[END_REF]. The central or peripheral nervous system can be affected, as well as the neuromuscular junction and the muscle itself. It was hypothesized that PP could result from an autoimmune attack of normal neuronal or muscular tissue, spurred by similar antigens expressed by tumor cells [START_REF] Toothaker | Paraneoplastic neurological syndromes: a review[END_REF]. This article describes a case of severe PP associated with breast cancer which constituted a therapeutic emergency.

Case report

Mrs V.M., age 55, consulted in October 2009 for a gradual decrease in muscle strength predominating at the proximal segments of the limbs and accompanied by myalgia.

Laboratory tests found rhabdomyolysis associated with an inflammatory syndrome.

C Reactive Protein (CRP) was 90 mg/l (Normal less than 5), Creatine Phospho Kinase (CPK) was 8000 IU/l (Normal between 10 and 200), and Troponin Ic (cTnI) was 1.67 µg/l (Normal less than 0.04), indicating cardiac trouble. All laboratory results were compatible with a connective type of polymyositis or a scleroderma. The patient was admitted in the Department of Immunology for the diagnosis and appropriate management of her collagen disease. Her past medical history included pneumonia in 1999 and 2007 and an active smoking habitus (15 pack-years). She had felt a nodule in the upper-outer quadrant of her right breast, evolving for more than five years but was not motivated for consultation. The autoimmune results showed positive antinuclear antibodies (ANAs) at 1/128, strongly positive anti-Jo1 antibodies, and negative antineutrophil cytoplasmic antibodies (ANCAs). A steroid-based bolus of methylprednisolone was instituted at a dose of 500 mg/day. During her hospital stay, a deterioration of her respiratory status required her transfer to the intensive care Unit.

Hemodynamic stability was obtained on oxygen, furosemide, and catecholamines infusion.

High-dose corticosteroids combined with rituximab were administered. The outcome was favorable and the patient was transferred to the continuing care service. The cardiologist's opinion concluded that progressive cardiac damage was linked to polymyositis as evidenced by elevated troponin levels. After improvement of vital parameters, the patient was admitted to the Senology Unit to treat her right breast mass. Physical examination confirmed her nodule in the upper-outer quadrant of the right breast, 5 cm long axis, indurated, and mobile with skin retraction opposite. The lymph nodes were cancer-free at physical exam. The mammography could not be performed because of unbearable standing position, whereas breast ultrasound showed a heterogeneous mass with irregular outline of 44 mm. The microbiopsy revealed infiltrating ductal carcinoma. The staging in search of distant metastases, including bone scan, brain and thoraco-abdomino-pelvic scan showed no secondary localization. The antigen CA 15.3 was at the upper limit of normal values at 34.4 IU/ml (Normal<30). A right mastectomy followed by axillary lymph nodes dissection (Berg levels I and II) was performed in November 2009. The resected mass was classified as an invasive ductal carcinoma (size 40 mm) grade II, according to the histopathological Elston and Ellis grading system [START_REF] Elston | Pathological prognostic factors in breast cancer. I. The value of histological grade in breast cancer: experience from a large study with long-term follow-up[END_REF], nuclear grade SBRM 4/5 with peritumoral vascular invasions.

The tumor was composed by two different cell populations (Fig 1 ): on one hand, glandular cells well differentiated with mild atypia and rare mitosis; on the other hand, cells organized in solid nests, with neuroendocrine-like features, mild atypia and frequent mitosis (10,9/ mm 2 ). The tumor highly expressed both estrogen (ER) and progesterone receptors (PR) (3+ and 2+ in 100% of the cells, respectively) whereas HER-2 protein was not overexpressed. The proliferative index evaluated with Ki-67 antibody was estimated at 60%. Subsequent immunohistochemical investigations with antibodies against TTF1, Chromogranin A, Synaptophysin and CD56 ruled out the possibility of a metastatic event or a neuroendocrine primary lesion. The tumor was surrounded by an inflammatory lymphocytic wall polymorphous, B and T but CD20, CD3, CD4, CD8 were equally expressed. Three of the sixteen axillary lymph nodes appeared to be metastasized.

The additional treatment consisted of adjuvant chemotherapy (6 cycles of docetaxel and cyclophosphamide), followed, on the right side, by radiotherapy of the wall, the internal mammary chain and the supraclavicular area, and by hormone therapy with aromatase inhibitors. The outcome was uneventful from the surgical point of view and dramatically favorable on the muscular side with disappearance of the biological rhabdomyolysis one month after surgery, normalization of cardiovascular checkup and 5/5 restoration of muscle strength with effective resumption of walk and a score at 1 according to the « performance status of the World Health Organization ».

Discussion

Paraneoplastic syndromes are a group of symptoms that are not due to a direct effect of a tumor, infection, metabolic disorders, vascular diseases and coagulopathies, or to the secondary toxicity of a given treatment [START_REF] Dalmau | Paraneoplastic neurologic syndromes: pathogenesis and physiopathology[END_REF]. PP represent a rare complication of breast cancer which causes inflammation of muscles while dermatomyositis also implies skin lesions with the presence of a rash. Clinically, PP cause progressive muscle weakness predominating at the proximal part of the limbs. Respiratory distress related to respiratory muscles weakness associated with interstitial pneumonia, is a leading cause of death. Cardiac involvement leads to conduction disorders.

The association of polymyositis with cancer was first described in 1916 by Sterz [START_REF] Sterz | Polymyositis[END_REF]. PP occur in adults, mainly between the ages of 40 and 60. They precede the clinical manifestation of the tumor in 60% of cases [START_REF] Minisini | Paraneoplastic neurological syndromes and breast cancer. Regression of paraneoplastic neurological sensorimotor neuropathy in a patient with metastatic breast cancer treated with capecitabine: a case study and mini-review of the literature[END_REF]. The most frequently encountered tumors are lung and prostate cancers, gastrointestinal tumors in men and gynecological tumors in women [START_REF] Minisini | Paraneoplastic neurological syndromes and breast cancer. Regression of paraneoplastic neurological sensorimotor neuropathy in a patient with metastatic breast cancer treated with capecitabine: a case study and mini-review of the literature[END_REF][START_REF] Anderson | Autoimmune pathogenesis of paraneoplastic neurological syndromes[END_REF]. The clinical expression of PP does not differ from that of polymyositis without cancer. The diagnosis of polymyositis rests on the elevated sedimentation rate and muscle enzymes with a myogenic aspect of the electromyographic tracing (too rich for effort, interferential, small polyphasic potentials, and shredded, normal nerve conduction velocity). Immunology is characterized by the presence of specific autoantibodies dominated by certain aminoacyl-tRNA synthetases (anti-synthetases), anti-Jo1 being the main one [START_REF] Anderson | Autoimmune pathogenesis of paraneoplastic neurological syndromes[END_REF]. The presence of onconeural antibodies is not always found. In 2003, Roja-Marcos et al. [START_REF] Rojas-Marcos | Spectrum of paraneoplastic neurologic disorders in women with breast and gynecologic cancer[END_REF] conducted a review of paraneoplastic neurological syndromes associated with breast and gynecological cancers in order to describe their clinical and immunologic characteristics and their relative frequency.

In only half of the patients with breast cancer (25 of 92 patients in total) onconeural antibodies were present.

PP are therapeutic emergencies. Indeed, the functional prognosis depends on early treatment.

However, the tumor is not always found at the time of diagnosis of PP, even after a thorough evaluation [START_REF] Chow | Cancer risk following polymyositis and dermatomyositis: a nationwide cohort study in Denmark[END_REF][START_REF] Chen | Cancer risks of dermatomyositis and polymyositis: a nationwide cohort study in Taiwan[END_REF]. The different immunological treatments are corticosteroids, intravenous immunoglobulin, cyclophosphamide, tacrolimus and rituximab [START_REF] Keime-Guibert | Treatment of paraneoplastic neurological syndromes with antineuronal antibodies (Anti-Hu, anti-Yo) with a combination of immunoglobulins, cyclophosphamide, and methylprednisolone[END_REF]. In 2007, Minisini [START_REF] Minisini | Paraneoplastic neurological syndromes and breast cancer. Regression of paraneoplastic neurological sensorimotor neuropathy in a patient with metastatic breast cancer treated with capecitabine: a case study and mini-review of the literature[END_REF] reported a case of PP associated with a metastatic breast cancer improved after treatment with capecitabine.

Cancer treatment is frequently followed by an improvement of PP symptoms. The manifestations of polymyositis evolve synchronously with the tumor response to treatment [START_REF] Verducci | Gynecologic carcinoma associated with dermatomyositis-polymyositis[END_REF]. The prognosis is usually unfavorable since the diagnosis is most often established at an advanced stage of the cancer. If no improvement of symptoms after the treatment of tumor is observed, causality is difficult to establish especially in case of negative onconeural antibodies. In these cases, a coincidence between the tumor and the neurological disorder cannot be excluded. Other possible paraneoplastic syndromes presentations include atypical paraneoplastic syndromes, absence of onconeural antibodies, and lack of improvement after removal of the tumor [START_REF] Rojas-Marcos | Spectrum of paraneoplastic neurologic disorders in women with breast and gynecologic cancer[END_REF]. The outcome of the PP was favorable in our patient upon treatment with steroids, immunotherapy and surgery. A driving force at 5/5 and a normalization of muscle enzymes were obtained.

Conclusion

Polymyositis in a woman always requires the search for cancer, especially breast cancer.

Early symptomatic treatment of polymyositis associated with curative treatment of the tumor may improve dramatically the outcome of both the cancer and the paraneoplastic syndrome.

Figure legend A

 legend Figure legend