Evan L Werkema

Richard A Andersen

Ahmed Yahia

Laurent Maron

Odile Eisenstein

Hydrogen for X-group exchange in CH 3 X, X = Cl, Br, I, OMe and NMe 2 by Monomeric [1,2,4-(Me 3 C) 3 C 5 H 2 ] 2 CeH: Experimental and Computational Support for a Carbenoid Mechanism

The reaction between [1,2,4-(Me 3 C) 3 C 5 H 2 ] 2 CeH, referred to as Cp' 2 CeH, and CH 3 X where X is Cl, Br, I, OMe and NMe 2 , are described. The reactions fall into three distinct classes. Class a, where X = Cl, Br and I rapidly form Cp' 2 CeX and CH 4 without formation of identifiable intermediates in the 1 H NMR spectra. Class b, where X = OMe proceeds rapidly to Cp' 2 Ce(η 2 -CH 2 OMe) and H 2 and then to Cp' 2 CeOMe and CH 4 . The methoxymethyl derivative is sufficiently stable to be isolated and characterized and it is rapidly converted to Cp' 2 CeOMe in presence of BPh 3 . Class c, where X = NMe 2 does not result in formation of Cp' 2 CeNMe 2 , but deuterium labeling experiments show that H for D exchange occurs in NMe 3 . Density functional calculations DFT(B3PW91) on the reaction of (C 5 H 5 ) 2 CeH, referred to as Cp 2 CeH, and CH 3 X showthat the barrier for α-CH activation, resulting in formation of Cp 2 Ce(η 2 -CH 2 X), proceeds with a relatively low activation barrier (ΔG ‡ ) but the subsequent ejection of CH 2 and trapping by H 2 has a higher barrier; the height of the second barrier lies in the order F, Cl, Br, I < OMe << NMe 2 , consistent with the experimental studies. The DFT calculations also show that the two-step reaction, which proceeds through a carbenoid intermediate, has a lower barrier than a direct one-step σ bond metathesis mechanism. The reaction of Cp 2 CeCH 2 OMe and BPh 3 is calculated to be a low barrier process and the ylide, CH 2 (+) BPh 3 (-) , is a transition state and not an intermediate.

Introduction

The reaction between CH 3 F and [1,2,4-(Me 3 C) 3 C 5 H 2 ] 2 CeH, referred to as Cp' 2 CeH in this article, to give CH 4 and Cp' 2 CeF has been described recently. 1 The net reaction involves a Ce-H for C-F exchange that is strongly exoergic;ΔG for the model system (C 5 H 5 ) 2 CeH and CH 3 F in gas phase was calculated by DFT methods to be -77 kcal mol -1 . Although the C-F BDE in CH 3 F is 108 kcal mol -1 , 2 the Ce-F bond is considerably stronger, the average Ce-F bond enthalpy of CeF 3 (g) is 153 kcal mol -1 , 3 and the net reaction is exothermic. The mechanism of the exchange reaction does not proceed by aσ-bond metathesis transition state as shown by calculational and experimental studies. The calculated activation energy in the model system for a σ-bond metathesis is 31 kcal mol -1 relative to the reactants, too high for a reactionthat is rapid and irreversible at 20°C. The high energy barrier originates from the methyl group occupying the β-site in the 4c-4e metathesis transition state I, resulting in a five coordinate carbon atom that is high in energy. Calculations showed that an activation energy of only 18 kcal mol -1 was required when an α-CH activation occurs in transition state II. In transition state II, the product, CH 4 , was derived from trapping of the CH 2 fragment by dihydrogen. Thus the lower activation energy pathway suggested by the calculation is a stepwise or indirect process that proceeds by way of carbenoid fragment III.The indirectα-CH activation pathway discovered in the calculational studies was supported by experimental studies, such astrapping the CH 2 fragment with cyclohexene. Accordingly, the carbenoid pathway for the reaction between CH 3 F and Cp' 2 CeH was placed on a firm foundation, but the question of generality was not addressed in the original article.

In this article, the results of the reaction between CH 3 X, X = Cl, Br, I, OMe, NMe 2 and Cp' 2 CeH are described from a calculational and experimental perspective with the general result that the carbenoid pathway is followed for these simple substituted methane derivatives.

Results

General Experimental Studies

The experimental methodology that was used in the earlier article is used in the present one. 1 The time evolution of the reaction between Cp' 2 CeH and the MeX derivatives is followed by 1 H NMR spectroscopy in either C 6 D 6 or C 6 D 12 at 20°C.

Since the reactant and product metallocenes are paramagnetic, the Me 3 C-resonances on the 1,2,4-(Me 3 C) 3 C 5 H 2 rings are a convenient probe to assay the extent, relative rates, and cleanliness of the net reactions; the ring methyne-resonances are often not observed. After the reactions are complete, hydrolysis (H 2 O) and GCMS analysis of the hydrosylate is used to identify the organic products in each experiment. As described in the earlier article, the reactions between the metallacycle, [1,2,4-( Me 3 C) 3 C 5 H 2 ] [(Me 3 C) 2 C 5 H 2 C(CH 3 ) 2 CH 2 ]Ce,1,abbreviated Cp'[(Me 3 C) 2 C 5 H 2 C(CH 3 ) 2 CH 2 )Ce or simply as metallacycle, 1, with the MeX derivatives are followed by 1 H NMR spectroscopy and the identity of the organic products is determined by GCMS after hydrolysis.

In the reactions of 1, dihydrogen is not present and cannot serve as a trap for the methylene fragment and therefore intermediates may be observed in the 1 H NMR spectra. In addition, added trapping reagents that do not react with 1 may be employed. The cerium containing products Cp' 2 CeX are prepared independently, isolated and characterized as outlined in the Experimental Section or in the text.

Reaction of Cp' 2 CeH or metallacycle, 1, with CH 3 X, X = Cl, Br, and I

The reaction between Cp' 2 CeH and CH 3 X, X = Cl, Br, and I, are rapid and clean at 20°C, as only resonances due to Cp' 2 CeX and CH 4 are observed in the 1 H NMR spectrum, eq 1.

Cp' 2 CeH +CH 3 X -> Cp' 2 CeX + CH 4 X = Cl, Br, I

Thus, the net reactions of all of the methylhalides are similar. The reaction between the methylhalides and the metallacycle is slightly more complicated. After approximatively three days, the conversion is complete; since the solubility of Cp' 2 CeCl is low in these solvents, mass balance cannot beobtained by integration of the NMR spectrum. When the reaction is complete, hydrolysis of the mixture and analysis of the hydrolysate by GCMS shows the presence of Cp'H and Cp"H where Cp" represents the isomers of 1,2-(Me 3 C)-4-(Me 2 EtC)C 5 H 3 as observed in the reaction with CH 3 F. 1 Thus the net reaction between the metallacycle, 1, with CH 3 F and CH 3 Cl give similar final products, but intermediate, Q F , is not detected. 1 As in the reaction of CH 3 F, a CH-bond of a Me 3 C group in the Cp'-ring acts as a trap of the CH 2 fragment, eq 2.

Since the final products in the case of CH followed by heating the mixture to 60°C for a day, then cooling to 20°C and examining the 1 H NMR spectrum shows resonances due to Q OMe and metallacycle, 1, in a 11:1 ratio; heating to 60°C for three days does not alter the ratio of Q OMe :1 from 11:1. Thus, Q OMe has an appreciable lifetime in absence of H 2 and should be isolable, see below. In addition, Q OMe and the metallacycle are in equilibrium, eq 4.

The equilibrium, illustrated by eq 4, is substantiated by exposing the The bond distances and angles in the Cp' 2 Ce fragment are similar to those previously reported for this fragment. 4a,5,7 The Ce(η In the reaction illustrated in eq 5, BPh 3 is a better trap for CH 2 than H 2 since the methoxymethyl derivative is formed in presence of H 2 , eq 3. This observation begets the question of which reagent is a better trap for a CH 2 group when the postulated compound Cp' 2 CeCH 2 X, Q X , is neither detected nor isolated, i.e., the reaction shown in eq 1. This is an important question since the only experimental evidence for formation of Cp' 2 CeCH 2 F is derived from experiments in which H 2 is absent, i.e., eq 2. The success of this type of experiment requires that BPh 3 does not react irreversibly with Cp' 2 CeH.

An NMR tube experiment shows that mixing BPh A comparison between the geometrical parameters in Cp' 2 CeH, the adduct with BPh 3 , and BPh 3 , is shown in Table 1. The cyclopentadienyl ring carbon atoms are nearly eclipsed in the starting hydride and the Cp'(centroid)-Ce-Cp'(centroid)

angle is 155°. 5 The refined position of the hydride atom lies off the C 2 -axis of the metallocene. When BPh 3 interacts with the hydride, the Cp'(centroid)-Ce-Cp'(centroid) angle closes to 136°, the cyclopentadienyl-ring carbons on the Cp'rings are now staggered, but the Cp'(centroid)-Ce distances are essentially equal in the two structures. The HBPh

(C 5 H 5 ) 2 V(H)(B(C 6 F 5 ) 3 )
, where the V-H-B angle is 153°. 24 The H-B distance tends to be longer by about 0.2 Å when the HBR 3 group is inner sphere rather than outer sphere since, for example, the H-B distance in

[(C 5 H 5 ) 2 V(CO) 2 ][HB(C 6 F 5 ) 3 ] is 1.14(2)
Å 25 a) For averaged values, the deviation is the average deviation from the mean.

b) The relative orientation of the carbon atoms in the Cp'-rings. are gone. This result is also consistent with the equilibrium reaction shown in the Scheme.

Computational studies

The metallocene used in the experimental studies, Cp' 2 CeH was modeled by (C 5 H 5 ) 2 CeH, symbolized as [Ce]H, as in earlier articles. 1,4a, 5 The results obtained with CH 3 F are incorporated into this article for completeness. The free energy profiles for the reaction of CH 3 X with [Ce]H to form [Ce]X and CH 4 are shown in Figure 5; the activation barrier is defined as the difference in free energy between the reactant and the transition state and symbolized as ΔG ‡ .

The metathesis pathway with a transition state shown as I in the Introduction, has an activation barrier of 31.1 kcal mol -1 for CH 3 F. 1 The calculated activation barriers are 30.4 kcal mol -1 for CH 3 I and 43.5 kcal mol -1 for CH 3 OMe. These two systems are representative of the series of CH 3 X species discussed in this article and the metathesis pathway is unlikely to be followed. The pathway that proceeds via a transition state of type II and on to intermediate III was proposed in the case of CH 3 F and this pathway is explored as an alternative pathway below. The activation energy for the CH activation steps in the five reactions is similar but the activation energy for trapping of CH 2 and formation of Cp 2 CeX is strongly dependent on the identity of X, Figure 5. The reaction begins by coordination of CH 3 X to [Ce]H by a lone pair on X.

Coordination just compensates the loss of translational entropy in the system and the free energy of the adducts is similar to that of the separated reactants; for this reason the adducts are not shown on Figure 5. From the adduct, the hydrogen atom transfers as a proton from the methyl group to the hydride as described for the CH 3 F reaction.

At the transition state, the carbon atom, the hydrogen atom that is leaving the methyl group, and the hydrogen atom attached to Cp 2 Ce are essentially co-linear as shown in The activation barrier (ΔG ‡ ) for the proton transfer reactions is similar for all X: the lowest value of 13.8 kcal mol -1 is obtained for X = OMe, the highest value of 18 kcal mol -1 is obtained for F and values for X = Cl, Br, I and NMe 2 are in between at about 15 kcal mol -1 . The values do not follow the experimental gas phase proton dissociation enthalpies for CH 3 X, since the values as a function of X, in kcal mol -1 are NMe 2 (> 406), OMe (407), Cl (396), Br (393), I (391). 28 Thus, the activation barrier is not just determined by the acidity of the α-CH bond, even though the relative acidity is the primary reason for the higher activation energy when H 2 and CH 4 are compared, and the identity of X plays a role in determining the barrier. 1 The free energy of formation of [Ce](η 2 -CH 2 X) is only mildly influenced by X with the heavier halides and the methoxy group being slightly more stable than the reactant and the fluoride and NMe 2 slightly less; therefore the reactants, [Ce]H and CH 3 X, and [Ce](η 2 -CH 2 X) are essentially isoenergetic.

The activation barriers for insertion of CH 2 into H 2 vary over a large range of values. For the halides, Cl, Br and I, the activation barriers are about 24 kcal mol -1 . A significantly higher activation barrier of 39 kcal mol -1 is calculated for X = OMe and the barrier is even higher, 56 kcal mol -1 , for X = NMe 2 . The formation of [Ce]X and CH 4 is strongly exoergic for all of the X substituents but the nature of X influences the value of ∆G of the reaction which decreases in the order F, Cl, Br, I > OMe >> NMe 2 . Figure 5 shows a clear relationship between the activation energies for insertion of CH 2 into H 2 and the change in free energy of reaction since the highest activation barriers are associated with the lowest thermodynamic driving force. The proton transfer step is a low activation barrier process for all CH 3 X reactants but the insertion of CH 2 into dihydrogen proceeds with a higher barrier and is therefore rate determining.

The carbon atom that is part of the three-membered ring, [Ce](η 2 -CH 2 X), is a carbenoid, 29 since it shows reactions associated with a carbene, for example, insertion into H 2 , as well as that of an alkyl group, for example, as a proton acceptor, see Scheme. However, the identity of X plays an role in the height of the activation barrier since the CH 2 group is a carbenoid and not a free carbene, which inserts into H 2 without an energy barrier. 30 The values of the activation energy become progressively higher as X changes from F to OMe and to NMe 2 . In the latter example, a calculated activation barrier of 56 kcal mol -1 is prohibitively high consistent with the experimental observation that [Ce]NMe 2 does not form from CH 3 NMe 2 , even though the net reaction is exoergic by -33 kcal mol -1 . In the case of [Ce](η 2 -CH 2 OMe) going to [Ce](OMe) and CH 4 , the calculated activation barrier of 39 kcal mol -1 seems too high for an experimental reaction that occurs, albeit slowly at 20°C, but consistent with the experimental fact that Cp' 2 CeCH 2 OMe is an isolable compound. Similarly, an activation barrier of 24 kcal mol -1 when X is F, also seems excessive for a net reaction that is rapid at 20°C. The calculated structures of Ce(η 2 -CH 2 X) when X is a halide are very similar to those for X = F. 1 Descending the halide series results in longer C-Xbondsand an increase in the Ce-C-X angle that varies from 71° for F to 86° for I. For X = OMe, the Ce-C-O angle is close to that for X = F while for X = NMe 2 , the Ce-C-N angle is 76°, midway between that for F (71°) and for X = Cl (80°). An important aspect of the calculated structure, which is not obtained from the crystal structure of Cp' 2 CH 2 OMe, is the position of the two hydrogen atoms on the methylene group, Figure 7.This geometrical parameter is related to the hybridization at the carbon atom and therefore to the carbenoid character in the CH 2 X group. For all X, the two hydrogen atoms are oriented in such a way that the Ce-C axis is essentially in the plane defined by carbon and the two hydrogen atoms. The H-C-H angle is close to 120° for all X. These results show that the hybridization of carbon is sp 2 and that the C-X bond is essentially constructed from a p-orbital on the carbon atom. Similar geometrical features have been found in the calculated structures of LiCH 2 X (X = F, Cl, Br, I, OH, OMe, NH 2 ). 31 Thus changing X does not change the orientation of the CH 2 relative to the Ce-C bond nor the H-C-H angle, but changing X changes the Ce-C-X angle, which is the smallest for F (71°) and largest for I (86°). This difference is a consequence of the increasing C-X bond length down the halide column.

Discussion

The reactions between Cp' 2 CeH and CH 3 X compounds fall into three distinct classes, depending on the identity of X. When X is a halide, F, Cl, Br or I, class a, the net reaction is a simple H for X exchange that proceeds rapidly without any intermediates detected by fragment and capture by H 2 , a higher barrier process whose value is strongly correlated with the identity of X. The latter barriers define the classes a, b or c.

The net reaction of Cp' 2 CeH and CH 3 X, eq 1, is thermodynamically favorable since the experimentally determined or estimated changes in the enthalpy are exothermic for the reaction shown in eq 7. [START_REF] Nolan | The values for X = OMe and NMe 2 are given in this article and the values for X = Cl, Br, and I are determined using BDE values[END_REF] (C 5 Me 5 ) 2 SmH + MeX  (C 5 Me 5 ) 2 SmX + MeH ( 7)

∆H (kcal mol -1 ): X = Cl, -66; Br, -65; I, -64; OMe, -48; NMe 2 , -22.

Although the experimental values are only available for the samarium metallocenes, the trends in ∆H should be similar when the metal is a lanthanide in general, and when the metal is cerium in the present article. As shown in the experimental and calculational results described in this article, even though the net reaction is thermodynamically favorable for all X, the reactions are under kinetic control. The calculated potential energy surfaces for the gas phase reaction between Cp 2 CeH and MeX parallel and therefore illuminate the experimental reactions between Cp' 2 CeH and MeX. The calculated free energy profiles show that the net reaction is exoergic, in agreement with experiments, and that a σ-bond metathesis transition state has a higher activation barrier.

A mechanism that is calculated to proceed by a lower energy pathway for X = a halide, is a two-step process in which the first step is aα-CH activation that forms Q X and H 2 , followed by trapping of CH 2 by H 2 , that proceeds with a higher activation barrier, its height defining the classification as either a, b, or c. Since the rate controlling elementary step is the conversion of Q X into the products, thestructure and bonding in Q X is of paramount importance. Accordingly, the structure is calculated for all of the X's studied and calibrated with the experimentalgeometry observed in Cp' 2 Ce(η 2 -CH 2 OMe). In general Q X , Cp' 2 Ce(η 2 -CH 2 OMe), is a three-membered ring in which the carbon atom is sp 2 -hybridized and therefore the CH 2 fragment is a carbenoid. The bonding between the carbene and M … X, when M is electropositive and X is electronegative, is maximized when the σ-lone pair of the carbene interacts with M and the empty 2p orbital of the carbene interacts with X; this is the basis of Bent's rule. 33 At the transition state, the C-X bond lengthens as the Ce-X bond forms. The orientation of the CH 2 group is such that the carbon p-orbital points toward dihydrogen. The activation barrier for trapping of CH 2 by H 2 parallels the free energy of reaction. When X is a halide, the change in the C-X bond distance going from

[Ce][η 2 -CH 2 X) to the transition state is similar for all halides but larger when X is OMe and NMe 2 . In addition, the H … H distance in the transition state is longer when X is OMe and NMe 2 . Thus, the transition state for trapping of CH 2 by H 2 is higher in energy when X is OMe and NMe 2 , which in turn implies that the CH 2 fragment in

[Ce][η 2 -CH 2 X
) is closer to a free carbene when X is a halide.

Conclusion

At first glance, the reactions illustrated in eq 1 are simple H for X metathesis reactions. The reactions, however, are deceptively simple since the mechanism deduced by DFT calculations and trapping experiments is not a one-step, synchronous σ-bond metathesis, but a two-step process in which a relatively rapidα-CH activation results in formation of H 2 and Cp 2 Ce(η 2 -CH 2 X), in which the CH 2 fragment is a carbenoid. The reactivity patterns are therefore correlated with how closely the carbenoid fragment resembles a free carbene fragment, on one hand, and a methyl group on the other: the closer the resemblance to CH 2 , the lower the barrier. The calculational and experimental studies outlined in this and an earlier article 1 show that the mechanisms of the H for X exchange reaction between Cp' 2 CeH and CH 3 X is a two-steppathway, and this is a general reactivity pattern. The reactants, CH 3 X, studied in these articles have onlyα-CH bonds and therefore the question of selectivity does not arise. It will be of interest to examine CH 3 CH 2 X reactants in which the choice between α-and β-CH activation processes are available; this selectivity issue will be addressed in another article.

Experimental Section

General

All manipulations were performed under an inert atmosphere using standard Schlenk and dry box techniques. All solvents were dried and distilled from sodium or sodium benzophenoneketyl. Anhydrous methylchloride, methylbromide, dimethylether, and trimethylamine were used without further purification.

Methyliodide was obtained commercially and purified by distillation onto activated 4 Å molecular sieves. Triphenylboron was obtained commercially and purified by sublimation under dynamic vacuum. NMR spectra were recorded on Bruker AV-300

or AV-400 spectrometers at 20°C in the solvent specified. J-Young NMR tubes were used for all NMR tube experiments. Electron impact mass spectrometry and elemental analyses were performed by the microanalytical facility at the University of California, Berkeley. The abbreviation Cp' is used for the 1,2,4-tri-tertbutylcyclopentadienyl ligand. Unless otherwise specified, samples for GC-MS were prepared by adding a drop of nitrogen-purged H 2 O, agitating, and allowing the samples to stand closed for 10 min. The samples were then dried over magnesium sulfate, filtered, and diluted ten-fold with pentane. A 1 µL sample was injected into a HP6890 GC system with a J&W DB-XLB universal non-polar column, attached to an HP5973 Mass Selective Detector. For samples hydrolyzed with basic hydrogen peroxide, a 3N aqueous NaOH solution was sparged for 10 minutes with nitrogen, and a drop was added to the sample under nitrogen flush. The sample was closed, agitated, and allowed to stand for 10 minutes, after which time a drop of 30% aqueous H 2 O 2 was added, the sample was closed briefly, agitated, then opened and allowed to stand for five minutes. The organic and aqueous layers were separated, and the aqueous layer was extracted twice with diethylether. The combined organic layers were then analyzed by GC MS as before.

Cp' 2 CeCH 2 OMe: Cp' 2 CeH 5 (0.5g, 0.82 mmol) was dissolved in pentane (10 mL).

The headspace was evacuated and replaced with dimethylether (1 atm). The solution color changed from purple to red as it was stirred over the course of one hour. The volume of the solution was reduced to 5 mL under reduced pressure, and the solution was cooled to -15°C, yielding red crystals. Yield, 0.20 g (0.31 mmol, 37% Cp' 2 CeBr: Cp' 2 CeOTf 5 (0.25g, 0.31 mmol) was dissolved in pentane (10 mL) and Me 3 SiBr (120µL, 0.91 mmol) was added via syringe. The solution was stirred for one day, then taken to dryness under reduced pressure. The yellow solid was dissolved in pentane and filtered. The yellow solution was concentrated until precipitation occurred, warmed to dissolve the precipitate, then cooled to -15°C, yielding a yellow powder. Yield, 0.095 g (0.13 mmol, 42%). MP 266-270°C. MS (M) + m/z (calc, found) 733 (100, 100) 734 (37, 37) 735 (19, 19) 736 (6,5). Anal.

Calcd Cp' 2 CeH was dissolved in cyclohexane-d 12 in an NMR tube. The tube was cooled in a liquid nitrogen isopropanol bath, and the head space was evacuated. In the case of CH 3 Br, 1 atm of the gas was added, while in the case of CH 3 I, an excess of the liquid was added via vacuum transfer followed by N 2 (1 atm). In both cases, upon warming to 19°C, the solution immediately turned yellow and a yellow precipitate formed.

The The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with dimethylether or trimethylamine (1 atm).

In the case of dimethylether, the tube was warmed to 19°C, and the deep purple solution rapidly turned red. After 30 minutes, the only paramagnetic resonances in the Cp' 2 CeH was dissolved in cyclohexane-d 12 , and a slight excess of BPh 3 was added.

The purple solution immediately turned yellow, and the 1 H NMR spectrum contained only resonances due to Cp' 2 CeHBPh 3 . The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with CH 3 F (1 atm).

The sample was warmed to 19°C, and the solution color became slightly more orange.

After 10 minutes, the resonances due to free BPh 3 had grown substantially in the Cp' 2 CeH was dissolved in cyclohexane-d 12 , and a slight excess of BPh 3 was added.

The purple solution immediately turned yellow, and the 1 H NMR spectrum contained only resonances due to Cp' 2 CeHBPh 3 . The tube was cooled in a liquid nitrogen reactants and products. The zero point energy (ZPE) and entropic contribution have been estimated within the harmonic potential approximation. The Gibbs free energy, G, was calculated at T = 298.15K. Using gas phase calculations for evaluating the entropic contribution to reactions in solution is an approximation; in particular, the translational degrees of freedom are exaggerated. [START_REF] Leung | [END_REF] However, the trends are properly calculated especially for a similar set of molecules as is the case here. This is supported by the observation that using E in place of G gives similar profiles and similar ranking as a function of X as shown in the Supporting Information. Thus, the trends in G are reliable even though the absolute values are not. The NBO analysis 42 was carried out replacing Ce by La because of the technical requirement to have an even number of f electrons for the calculations; these values are included in the Supporting Information for the inquisitive reader. Since the solvent used in the experimental studies was a hydrocarbon, such as cyclohexane or benzene, no large solvent effect on the reactants and products is expected. Consequently, no solvation effects were introduced in the computational studies.

Figure 2

 2 Figure 2 shows an ORTEPof Cp' 2 Ce(η 2 -CH 2 OMe); important bond distances

  3 and Cp' 2 CeH in C 6 D 6 results in a rapid color change from purple to yellow and disappearance of the resonances due to Cp' 2 CeH. On a synthetic scale, addition of Cp' 2 CeH and BPh 3 in toluene at room temperature results in the appearance of a yellow solution and yellow crystals form on standing overnight. The crystals are due to formation of a 1:1 adduct, whose crystal structure is shown in the ORTEP in Figure 3. Some bond distances and angles are given in the Figure Caption.

Figure 3 .

 3 Figure 3. ORTEP of [1,2,4-(Me 3 C) 3 C 5 H 2 ] 2 Ce(H)(BPh 3 ), 50% probability ellipsoids

  and 1.06(6) Å in [(C 5 Me 5 ) 2 ZrH][HB(C 6 F 5 ) 3 ]. 26 The B-C distance lengthens by 0.05 Å on complex formation and the C-B-C angles contract from 120° in planar BPh 3 , in which the phenyl groups are orientated as the blades of a propellar, to 111.8 ± 3.2° (ave.) in the complex. However, the C-B-C angles are unequal in the adduct: they range from 107.0(2)° for C(35)-B-C(47) to 114.3(3)° and 114.0(3)° for the other two angles at boron. The geometrical parameters in Cp' 2 Ce(H)(BPh 3 ) are consistent with the view that the Ce-H-BPh 3 interaction is a 3 center-2 electron bond and the obtuseCe-H-B angle implies a closed 3-center interaction in the solid state, i.e., there is electron density shared between the Ce and B atoms.27

Figure 5 .

 5 Figure 5. Free energy profiles, in kcal mol -1 , for the reaction of Cp 2 CeH, [Ce]H, and

FigureFigure 6 .

 6 Figure 6a for X = OMe where the H … H … C angle is 170°. The transfer of the proton

Figure 7 .

 7 Figure 7. Optimized structure of [Ce](η 2 -CH 2 OMe).

Figure 8 .

 8 Figure 8. The free energy profile, in kcal mol -1 , for the reaction of [Ce]H, CH 3 OMe,

  03. Full crystallographic details are included as Supporting Information. Triclinic cell space group P1(bar): a = 10.4888(5) Å, b = 10.9920(5) Å, c = 15.9639(7) Å, α = 99.137(1)°, β = 104.458(1) °, γ = 95.703(1) °, V = 1740.9(1) Å 3 .

Cp' 2

 2 CeI: CeI 3 • 3 THF34 (18.1 g, 25.0 mmol) and Cp' 2 Mg35 (12.0g, 24.0 mmol) were stirred at reflux in a mixture of pyridine (10 mL) and toluene (100 mL) for 24 hours. The orange-brown suspension was taken to dryness under reduced pressure.The solid residue was loaded into an extraction thimble (dried at 120°C for three days) and extracted with pentane (200 mL) in a Soxhlet extractor for three days. After stopped and the flask containing the precipitat was cooled to -15°C, yielding dirty orange powder. The suspension was filtered, and the flask containing the mother liquor was reattached to the extraction apparatus. The extraction was continued until the solution around the extraction thimble was colorless. Recrystallization of the combined orange powder from toluene (100 mL) yielded small, opaque, bright orange crystals. Yield, 10.2 g (14 mmol, 56%). MP 309-311°C. 1 H NMR (C 6 D 6 , 300MHz): δ 3.20 (18H, ν 1/2 = 430 Hz), -8.03 (18H, ν 1/2 = 430 Hz), -15.14 (18H, ν 1/2 = 220 Hz).

  Information. Monoclinic cell space group P2 1 /n: a = 10.6158(5) Å, b = 22.808(1) Å, c = 20.588(1) Å, β = 100.579(1) °, V = 4900.3(4) Å 3 . The crystal used for structural determination was grown in a C 6 D 12 solution in an NMR tube, and the asymmetric unit contained half a molecule of C 6 D 12 . NMR tube reaction of CH 3 Br or CH 3 I and Cp' 2 CeH in cyclohexane-d 12 .

CH 3 I

 3 was added by vacuum transfer. The tube was warmed to 19°C, the headspace was refilled with N 2 (1 atm), and the sample was allowed to stand. After 40 minutes, the solution was red-orange, and only resonances of Q I remained in the spectrum. A less than an equimolar amount of BPh 3 was added, the sample was agitated and allowed to stand. The resonances due to Q I disappeared and those of Cp' 2 CeI appeared over the course of 1 hour. Integration relative to the solvent residual proton peak indicated that the conversion of Q I to Cp' 2 CeI was quantitative. The sample was hydrolyzed with basic hydrogen peroxide, and GC MS analysis showed that the sample contained a fraction with (M) + m/z 108 (C 6 H 5 CH 2 OH) and a smaller fraction with (M) + m/z 122 (C 6 H 5 (CH 2 ) 2 OH) in addition to Cp'H. No fraction corresponding to C 6 H 5 OH was observed. NMR tube reaction of CH 3 F and Cp' 2 CeHBPh 3 in cyclohexane-d 12.

1 H

 1 NMR spectrum, and the only significant paramagnetic resonances were those of Cp' 2 CeF. Integration relative to the solvent residual proton peak indicated that the conversion of Cp' 2 CeH to Cp' 2 CeF was approximately 20%. In a separate experiment, Cp' 2 CeF and an excess of BPh 3 were dissolved in benzene-d 6 in an NMR tube. The 1 H NMR spectrum contained only resonances due to the two individual components with no perturbation to their chemical shifts or line shapes. The orange solution was heated at 60°C. After three days, the 1 H NMR spectrum had not changed. NMR tube reaction of CH 3 Br and Cp' 2 CeHBPh 3 in cyclohexane-d 12.

  The reaction with CH 3 Cl is clean, since the resonances in the 1 H NMR spectrum due to metallacycle, 1, in C 6 D 12 disappear within approximately 15 minutes and a new set of Me 3 C-resonances, referred to as Q Cl ,appear atδ -1.36 andδ-8.54 in ratio of 2:1, in addition to resonances due to Cp' 2 CeCl, and the metallocene. Over time, the resonances due to Q Cl disappear and resonances due to Cp' 2 CeCl increase in intensity.

Reaction of Cp' 2 CeH and metallacycle, 1, with CH 3 OMe.

  CeH or the CH bond of a Me 3 C-group in the Cp'-ring when H 2 is absent. The only difference between the CH 3 F and CH 3 Cl reactions is that Q Cl builds up in the latter reaction and Q F does not.The reaction of CH 3 Br and CH 3 I with the metallacycle, 1, is similar to that of CH 3 Cl, eq 2. In the case of CH 3 Br, the resonances attributed to Q Br appear atδ-1.36 andδ-8.16 in a ratio of 2:1. Exposure of the metallacycle, 1, to CD 3 Br in toluene and examining the organic products, after hydrolysis, by GCMS shows the presence of Cp'H and Cp"H-d 2 . This result shows that Q Br eliminates CD 2 , which is trapped by the Me CeOMe.4 The ratio of Q OMe : Q' OMe : Cp' 2 CeOMe is 40: 50: 1. Heating at 60°C for 27 days increases the quantity of Cp' 2 CeOMe since the ratio is now 3:1:7, eq 3, which only shows the ceriumcontaining compounds that are identified.Cp' 2 CeH + CH 3 OMe -> Q OMe and Q' OMe + H 2 -> Cp' 2 CeOMe + CH 4 (3)The identity of Q OMe is presumably similar to that of Q X , X = Cl, Br, I since the pattern of the chemical shifts of the Me 3 C-resonances is similar. The identity of Q' OMe , remains unknown, though it might be a Me 2 O adduct of either Q OMe and Cp' 2 CeH, since evaporation to dryness and dissolution in C 6 D 6 results in resonances only due to Q OMe and Cp' 2 CeH.

	Mixing Cp' 2 CeH and CH 3 OMe in C 6 D 6 in an NMR tube results in
	disappearance of the resonances due to Cp'

3 F and CH 3 Cl are similar, both reactions presumably follow similar mechanisms, viz, the generation of a carbenoid intermediate, Q X , followed by ejection of CH 2 and trapping by H 2 in the case of Cp' 2 3 C-groups on the Cp'-ring. No deuterium is detected in solvent toluene and therefore the intramolecular trapping of CD 2 is more efficient than is intermolecular trapping by the solvent CH bonds. In the CH 3 I reaction, two resonances in a 2:1 ratio due to Q I atδ-1.3 and δ-7.8 appear within 10 minutes of mixing. After approximately 3 hours resonances due to Cp' 2 CeI form and the ratio of Q I : Cp' 2 CeI is 6:1. After 5 days at 20°C, Q I disappears and only those resonances due toCp' 2 CeI remain. In all three reactions, the resonances attributed to Q X have similar chemical shifts which implies that the Me 3 Cgroups on the Cp'-rings are in a similar geometrical arrangement; a postulated structure is shown in eq 2 for all three intermediates. This deduction is developed in more detail in the next section. 2 CeH within 15 minutes and appearance of two new setsofMe 3 C-resonances atδ-1.11 and δ -10.9 (2:1), Q OMe , and δ-2.38 andδ -4.43 (2:1), Q' OMe . After two days at 20°C an additional set of resonances appears due to Cp' 2 The reaction of CH 3 OMe with metallacycle, 1, is rather more straightforward since mixing the two reactants results in appearance of resonances due to Q OMe within 20 minutes at 20°C. Evaporation of the solution to dryness, dissolution in C 6 D 12

  CD 3-x H x ) 3 groups forming over this period of time. Heating to 60°C for three days results in appearance of resonances due to Me 2 O-d 1 , which appear as a 1:1:1 pattern in the 1 H NMR spectrum atδ H = 3.16 and J HD = 1.2 Hz. The 1 H NMR spectrum also shows resonances due to H for D exchange in the Me 3 C groups on the Cp' rings. After three days at 60°C, the deuterium is preferentially located at the unique Me 3 C group, but heating the mixture at 60°C for 81 days results in a 1 H NMR spectrum in which a single hydrogen atom is statistically distributed into the three Me 3 C groups, see Experimental Section for details. The labeling study shows thatinsertion of the CH bond of CH 3 OMe into the metallacycle Ce-C bond is rapid but elimination of CH 2 DOMe is slow, which rationalizes why Q OMe is an isolable compound. CeCH 2 OCH 3 showing the Me 3 C resonances on the Cp' rings and the OMe resonance.

	The observation that all of the Me 3 C-groups are chemically inequivalent at
	temperatures below about -30°C is rare in Cp' 2 M(X)(Y) metallocene derivatives.
	Generally, the two Cp'-rings are free to oscillate about their pseudo C 5 axes
	generating a molecule with averaged C 2v symmetry and the CMe 3 groups are observed
	in a 1:2 ratio. As the temperature is lowered the time averaged mirror plane and the C 2
	axes are removed and the CMe 3 groups appear in a 1:1:1 ratio. The inequivalence of
	all six Me 3 C-groups was observed in one metallocene, viz., Cp' 2 UN(Me)C(Ph)C(Ph) 6 .
	In Cp' 2 CeCH 2 OMe, the molecule can have averaged C 2v symmetry if the CH 2 OMe is
	monodentate and C s symmetry if bidentate, accounting for the 1:2 and 1:1:1 pattern,
	respectively. The inequivalence of all six CMe 3 groups means that the molecule has
	C 1 symmetry at the temperature below -30°C, ΔG ‡	(Tc= 250K) = 10.6 kcal mol -1 ; the Cp'
	rings cannot be freely rotating, and the η 2 -CH 2 OMe group must be responsible. The
	ORTEP in Figure 2 shows that the Ce(η 2 -CH 2 OMe) fragment is not planar. Perhaps
	the orientation of the methyl group, C(36), is sufficient to prevent the Cp' group from
	oscillating resulting in a molecule with C 1 symmetry at low temperature.

perdeuterometallacycle, 1-d 53 to CH 3 OMe in C 6 D 12 .The 1 H NMR spectrum shows resonances due to the C(CD 3-x H x ) 3 groups and Q OMe after 30 minutes at 20°C. The relative amounts change little over two days. The 2 H NMR spectrum also shows resonances due to the C(On a synthetic scale, addition of an excess of dimethylether to a solution of Cp' 2 CeH in pentane results in a color change from purple to red. Concentrating and cooling the solution gives red crystals of Cp' 2 CeCH 2 OMe in 37% yield. The methoxymethyl derivative turns deep purple on heating in a sealed tube at 135°C and then melts at 210-213°C. No molecular ion is observed in the mass spectrum but the fragment with highest m/e is [M-CH 2 OMe] + ; a similar fragmentation pattern is observed for Cp' 2 CeCH 2 Ph, i.e., [M-CH 2 Ph] + . 5 The 1 H NMR spectrum of Cp' 2 CeCH 2 OMe at 20°C shows the Me 3 C-resonances in a 1:2 ratio, though the resonance of area 2 is broadened, and the OMe resonance is a singlet; the methylene resonance and the ring-methyne resonances are not observed. The variable temperature 1 H NMR spectrum for the Me 3 C-groups is shown as a δvs T -1 plot in Figure 1. The methoxymethyl group resonance is a curve and therefore does not follow Curie law.

Figure 1. δvs. 1/T plot for Cp' 2

Reaction of Cp' 2 CeH and metallacycle, 1, with CH 3 NMe 2 .

	Figure 2. ORTEP of [1,2,4-(Me 3 C) 3 C 5 H 2 ] 2 CeCH 2 OMe, 50% probability ellipsoids. that the oxygen atom in [Me 3 O][AsF 6 ] is decidedly pyramidal since the angles around
	The non-hydrogen atoms are refined anisotropically and the hydrogen atoms (not oxygen sum to 340°. 16
	shown) are included in calculated positions but not refined: Ce-C ave = 2.84 ± 0.05 Å,
	range = 2.778(3) to 2.926(3) Å, Ce-C(ring centroid) = 2.57 Å, Cp'(ring centroid)-Ce-
	Cp'(ring centroid) = 147°, Ce-C(35) = 2.488(4) Å, Ce-O =2.406(2) Å, C(35)-O = Unlike the reactions illustrated in eqs 1 and 3, addition of trimethylamine to a
	1.466(4) Å, C(36)-O = 1.414 (4) Å, Ce-O-C(35) = 75.7(2)°, Ce-C(35)-O = 69.5(2)°, C 6 D 6 solution of Cp' 2 CeH does not perturb the chemical shift of the Me 3 C-resonances
	at 20°C in the 1 H NMR spectrum. However, mixing trimethylamine with C(36)-O-C(35) = 117.2(3)°, C(36)-O-Ce = 160.3(2)°. 2 -CH 2 OMe) fragment is not planar since the metallacycle, 1, in C 6 D 12 results in appearance of a new set of Me 3 C-resonances in
	dihedral angle formed by intersection of the planes defined by CeO(1)C(35) and Two other structural comparisons are particularly revealing relative to the 1:1:1 ratio, though the resonances due to the amine cannot be identified with
	O(1)C(35)C(36) is 164°. The Ce-C(35) distance of 2.488(4) Å is shorter than that electronic structure of the methoxymethylene fragment. In organic molecules confidence and a structure analogous to Q X , X = NMe 2 , seems to be a reasonable
	found in (C 5 Me 5 ) 2 Ce[CH(SiMe 3 ) 2 ], 2.535 Å, 8 and (C 5 Me 5 ) 2 CeCH 2 Ph, 2.596(5)Å. 9 The containing the Me-OC(sp 3 ) fragment, the average C-O distance is 1.416 Å, 12 which is postulate. After one hour, the ratio of the metallacycle, 1, to Q NMe2 is 1:3 and this ratio
	Ce-O distance of 2.406(2) Å is shorter than the Ce-O distance in Cp' 2 CeO 2 S(O)(CF 3 ), identical to the C(36)-O(1) distance in the methoxymethyl derivative; the C(35)-O(1) changes to 1:6 after a day at 20°C. Heating to 60°C from 2 to 15 days then cooling to
	where the four independent Ce-O distances in the two individual molecules in the unit distance of 1.466(4) Å is 0.05 Å longer. Further, the C-O bond in the H 3 C-OR group room temperature establishes the thermodynamic ratio as 1:1.3. Further support for an
	cell average to 2.601±0.008 Å 10 but longer than that in (C 5 Me 5 )CeO[2,6-lengthens by 0.12 Å when it is deprotonated at theα-carbon atom as shown by equilibrium is obtained by heating metallacycle, 1-d 53 , with CH 3 NMe 2 in C 6 D 12 . After
	(Me 3 C) 2 C 6 H 3 )] 2 where the Ce-O distance is 2.253 ± 0.002 Å, 11 or in the cis and trans calculations on the hypothetical gas phase molecule LiCH 2 OH relative to CH 3 OH. 13 one day at 60°C, resonances in the
	enediolate isomers of Cp' 2 CeOCH=CHOCeCp' 2 where the Ce-O distances are 2.171 The lengthening of the C-O bond is interpreted as arising from increased carbene
	± 0.001 Å and 2.118(3) Å, respectively. 4a character in the methylene carbon of the CH 2 OH anion. In another comparison, the
	crystal structure of the methoxymethyl complex, Cp 2 Zr(Cl)(η 2 -CH 2 OMe), shows that
	the CH 2 -O distance of 1.414(6)Å is shorter than that of the CH 3 -O distance of
	1.449(6) Å. 14 The crystal structure of the benzyloxymethyl complex, Cp 2 Zr(Cl)(η 2 -
	CH 2 OCH 2 Ph), shows that the CH 2 -O distance is 1.455(8) Å and close to that of the O-
	C(benzyl) distance which is 1.456(7) Å. 15 These distances are therefore rather
	different from those in Cp' 2 Ce(η 2 -CH 2 OMe), Figure 1. In addition, the oxygen atom
	in Cp 2 Zr(Cl)(η 2 -CH 2 OMe) is out of the plane defined by the ZrC 2 atoms by 0.51 Å,
	resulting in the authors description of the Zr(η 2 -CH 2 OMe) fragment as an
	"intramolecularly stabilized onium ylide". This description is strengthened by noting

1

H NMR spectrum due to metallacycle, 1, increase in intensity at the expense of those in the 2 H NMR spectrum. In addition, a triplet is observed in the 2 H NMR spectrum due to CH 2 DNMe 2 , δ= 2.12, J CD = 2Hz. Heating the sample for 33 days at 60°C results in an increase in the paramagnetic resonances due to the C(CD 3 ) 2 (CD 2 H) group of the Cp'-rings and their corresponding decrease in the 2 H NMR spectrum. The 2 H NMR resonance due to trimethylamine-d x increases in intensity and complexity and the 13 C { 1 H} NMR spectrum contains a resonance as a 1:1:1 pattern at δ= 46.59 and J CD = 20 Hz, in addition to a singlet at δ 46.90 due to CH 2 DNMe 2 and CH 3 NMe 2 , respectively, after 33 days at 60°C. The H for D exchange experiment supports an equilibrium similar to that shown in eq 4, for Q NMe2 . Thus, H

Reactions of Cp'

2 CeCH 2 OMe with BPh 3

  It is clear that H 2 is not able to trap efficiently the CH 2 fragment in Cp' 2 CeCH 2 OMe. Cyclohexene is not able to trap the CH 2 fragment, since norcarane is not formed when the two reagents are mixed, in contrast to the reaction of the metallacycle, 1, with CH 3 F.1 Thus, another trap that is compatible with the metallocene is needed. Although the perfluoro derivative, (C 6 F 5 ) 3 B, is a stronger Lewis acid it is not compatible with Cp' 2 CeH.23 The utility of BPh 3 as a trap for CH 2 in Cp' 2 CeCH 2 OMe is outlined next. to Cp' 2 CeOMe within 10 minutes. Although resonances that may be attributed to an arylboron derivative are apparent in the spectrum, their identification is not clear cut; the 11 B NMR spectrum offers no help since the quantity of (Ph 3-x )B(CH 2Ph) x is small and the paramagnetism of the cerium compound is likely to shift the broadened resonance. However, hydrolysis of the solution with alkaline hydrogen peroxide and examination of the hydrolysate by GCMS conclusively shows that PhCH 2 OH and PhOH, in addition to Cp'H, are formed. Thus BPh 3 is able to abstract the CH 2 group resulting in the net reaction shown in eq 5.Cp' 2 CeCH 2 OMe + BPh 3 -> Cp' 2 CeOMe + Ph 2 BCH 2Ph (5)

1

Triphenylboron, and indeed BX 3 compounds in general, react with diazomethane, CH 2 N 2 , with formation of polymethylene, a reaction described by Meerwein eighty years ago; 17 a review of this reaction is available.

18

The specific reaction between BPh 3 and CH 2 N 2 yields polymeric material and(Ph 3-x )B(CH 2

Ph)

x , since on reaction with hydrogen peroxide, PhOH and PhCH 2 OH are formed.

19

Two related reactions should be mentioned; reaction of Ph 3 PCH 2 and BPh 3 yields a 1:1 adduct that gives (PhCH 2 ) 3 B, Ph 3 BPPh 3 and PPh 3 on heating to 205°C

20

and the nitrogenylide Me 3 NCH 2 •LiBr, and BPh 3 gives PhCH 2 OH and PhOH on alkaline hydrogen peroxide hydrolysis. 21 More recently, the adduct between BPh 3 and Me 2 S(O)(CH 2 ) is isolated and after heating and oxidation, PhCH 2 OH and PhOH are obtained. 22 Thus, BPh 3 appears to be an efficient trap for the CH 2 fragment, presumably by forming a Lewis acid-base adduct that subsequently rearranges to a benzylboron compound. Mixing Cp' 2 CeCH 2 OMe with BPh 3 in an NMR tube in C 6 D 6 at 20°C results in disappearance of the resonances due to the methoxymethyl derivative and appearance of resonances due

  3 group does not lie on the C 2 -axis of the complex, but it is oblique to the Cp' 2 Ce fragment with a Ce-H(80)-B angle of 139(1)°. This orientation forces the BPh 3 group close to the Cp' 2 Ce fragment with a Ce …. B distance of 3.423(3) Å. The Ce-H distance in the complex increases to 2.35 Å from 1.90 Å in the BPh 3 -free complex and the H-B distance is 1.26 Å. The refined H-B distance seems reasonable since an equivalent distance of 1.34 Å is found in

Table 1 .

 1 Comparison of Bond Lengths and Angles in Cp' 2 CeH, Cp' 2 Ce(H)(BPh 3 ) and

	BPh 3 .
		Cp' 2 CeH	Cp' 2 Ce(H)(BPh 3 )	BPh 3	c
	Ce-C(Cp') ave , a Å	2.81 ± 0.02	2.82 ± 0.09
	Ce-C(Cp') range, Å	2.757(7) to	2.713(3) to 2.933(3)
		2.840(6)
	Ce-Cp'(centroid) ave . Å	2.53	2.54

Other reactions of Cp' 2 Ce(η 2 -CH 2 OMe), Q OMe .

  BPh 3 ) with CH 3 F results in formation of Cp' 2 CeF and free BPh 3 . The conversion is only about 20% after 10 minutes and thereforethe rate of reaction decreases in the adduct. In a separate experiment, the resonances due to Cp' 2 CeF are not perturbed in presence of BPh 3 at 20°C. Similarly, addition of CH 3 Br to Cp' 2 (H)(BPh 3 ) in C 6 D 6 results in formation of Cp' Ce(η 2 -CH 2 OMe) to D 2 results in deuterium being detected in two positions; the Me 3 C-groups of the Cp'-ring and the Ce-D sites, i.e., (Cp')(Cp'-d 1 )CeD, as shown by the intensity changes in the In the case of MeBr, resonances due to Q OMe , Cp' 2 CeBr, Cp' 2 CeOMe and Q Br are observed after 1 day at 20°C in a ratio of 8:8:1:2along with Me 2 O. After 4 days, only resonances due to Cp' 2 CeBr and Me 2 O are observed. In a separate experiment, Cp' 2 OMe is not converted to Cp' 2 CeBr by MeBr, which shows that the disappearance of the small amount of Cp' 2 CeOMe is not due to reaction with MeBr. Methylfluoride also reacts with Cp' 2 Ce(η 2 -CH 2 OMe) but the rate is slower that that of MeBr. After 2 days at 20°C, only resonances due to Cp' 2 CeCH 2 OMe and Cp' 2 CeF are observed, but heating for 1 day at 60°C,resonances due to Cp' 2 CeOMe appear. In a separate experiment, Cp 2 'CeOMe and MeF do not react. After 9 days at 60°C, the relative ratio of Cp' 2 CeF and Cp' 2 CeOMe is 1.5:1 and the resonances due to Cp' 2 Ce(η 2 -CH 2 OMe)

	0:0.4:0.09 and after
	11 days at 60°C the ratio is 2.0:0.12:0.025.

c) Zettler, F.; Hausen, H. D.; Hess , H. J.

Organomet. Chem. 1974, 72, 157.

In C 6 D 6 solution the interaction persists, since at 20°C, the resonances due to Cp' 2 Ce(H)(BPh 3 ) and those due to added BPh 3 are observed as separate resonances. The variable temperature 1 H NMR spectra of Cp' 2 Ce(H)(BPh 3 ) are shown as aδvs 1/T plot in Figure 4. At temperatures below 332K (1/T ≅ 0.003) separate resonances are observed for free and coordinated BPh 3 , the para-H resonances are easily distinguished in the adduct and free BPh 3 . Below that temperature the Me 3 C-groups on the Cp'-rings appear in a 1:1:1 ratio consistent with a complex with C s symmetry. At higher temperatures, two of the Me 3 C-resonances coalesce, due to the equilibrium illustrated by eq 6, that averages the BPh 3 environments. Thus, at temperatures above T = 330K, some BPh 3 is present in solution and may function as a trapping reagent.

Figure 4.δvs. 1/T plot for Cp' 2 Ce(H)(BPh 3 ). Accordingly, mixing Cp' 2 Ce(H)(2 CeBr. Hydrolysis of the solution with alkaline hydrogen peroxide and examination by GCMS shows that only phenol is formed. Hence, at the concentrations used, BPh 3 does not compete with dihydrogen for the CH 2 -fragment. As shown in an earlier article, 5 metallacycle, 1-d 53 , is readily prepared by exposing 1-d 0 to C 6 D 6 solvent. The reverse reaction, viz., metallacycle, 1-d 53 in presence of C 6 H 6 gives 1-d 0 and C 6 H 6-x D x implies that aryl CH-bonds in BPh 3 will undergo exchange of H for D with 1-d 53 . This expectation is fulfilled, since mixing 1d 53 with BPh 3 in an NMR tube in C 6 D 12 at 20°C results in a decrease in intensity of the resonances due to the (CD 3 ) 3 C-groups in the 2 H NMR spectrum and an increase in intensity of the resonances of the para-H and meta-H sites; those on the ortho-H sites are not affected. After 2 days at 60°C, the ratio o-H:m-H:p-H is 2.

Several additional reactions of the methoxymethyl derivative are summarized in the Scheme and outlined in this section. Exposure of Cp' 2 1 H and 2 D NMR spectra. In addition, some deuterium accumulates in Me 2 O. These results are consistent with the equilibrium illustrated in eq 4 and in the Scheme.

Scheme

The methoxymethyl derivative reacts with MeX, X = F or Br, as shown in the Scheme.

Table 2 .

 2 The distortion of [Ce](η 2 -CH 2 X) on going to the transition state as H 2 traps the CH 2 fragment is influenced by X as shown in Table2. The distortions are very similar All bond distances are in Å. The first row of each cell gives the distances in Ce-X) where a positive number is an elongation of the bond from the reactant to the transition state. b) The C … H distance given is the shorter of the two C … H distances at the transition state. c) The

	distance is 0.80 Å for all of the halides but it increases from 0.83 to 0.88 Å when X is
	OMe or NMe 2 , respectively.

in the case of Cl, Br, and I; the Ce-C distance increases by around 0.1 Å, the C-X distance increases by about 0.5 Å, while the Ce-X distance decreases by around 0.1 Å. Different and larger distortions are found for X = F, OMe and NMe 2 . In the case of F, the Ce-C distance increases by almost 0.4 Å, four times that found for the heavier halide, while the increase in the C-F distance of 0.47 Å is marginally smaller than that for the otherhalides.The Ce-F bond does not shorten much on going from [Ce](η 2 -CH 2 F) to the transition state. In the case of OMe and NMe 2 , the Ce-C distance increases as found for the heavy halides, but the C-X bond increases more (0.66 Å and 0.8 Å for OMe and NMe 2 respectively). Another difference between the halides and the OMe or NMe 2 cases is the H … H distance at the transition state; the H … H the ground state (gs) of the three-membered ring and the second row gives the distances in the transition states (ts) for insertion of CH 2 into H 2 . a) The changes in the bond lengths are given as Δ(Ce-C), Δ(C-X) and Δ(

Ce](η 2 -CH 2 OMe) with BPh 3

  at the carbenoid carbon. However, this complex has a free energy of 15.7 kcal mol -1 higher than the separated species [Ce](η 2 -CH 2 OMe) and BPh 3 and the difference is mostly due to loss in translational entropy since the energy, E, of the adduct between [Ce](η 2 -CH 2 OMe) and BPh 3 is equal to that of the separatedspecies.From this adduct, [Ce]OMe and Ph 2 BCH 2 Ph are formed in a concerted step with an activation barrier of 29 kcal mol -1 relative to separated reactants [Ce]H, CH 3 OMe and BPh 3 . This activation barrier is lower than that of 39 kcal mol -1 for the insertion of the methylene group into H 2 showing that BPh 3 is a more efficient trap of the methylene group than is H 2 , a result that is supported by experiment. At the transition state, the C-O bond length of 2.07 Å shows that the bond is essentially cleaved. The ylide Ph

	The free energy profile for the reaction of [Ce](η 2 -CH 2 OMe) with BPh 3 is
	shown in Figure 8; the structure of the intermediate and the transition state are shown
	in the Supporting Information. The reaction begins by coordination of BPh 3 to the

methylene group of [Ce](η 2 -CH 2 OMe) yielding a complex where the methylene group is bonded to boron not cerium. Thus, BPh 3 successfully competes with [Ce] for the density 3 B (+) CH 2 (-) is not an intermediate; the geometry of the transition state shows that one phenyl group is bending over the B-CH 2 bond with a C-B-C(phenyl) angle of 79° for one of the phenyl group and 115° for the two other angles. Insertion of the CH 2 group into the B-C bond is therefore concerted with the C-O bond cleavage. The net reaction for [Ce](η 2 -CH 2 OMe) and BPh 3 forming [Ce]OMe and Ph 2 BCH 2 Ph is exoergic by 41 kcal mol -1 .

  CeH gives the H for CH 2 OMe exchange product, Cp' 2 Ce(η 2 -CH 2 OMe), as an isolable compound and H 2 . The 1 H NMR chemical shifts of the Me 3 C-groups at 20°C have similar values as those observed in the reaction between the metallacycle, 1, with CH 3 X, X = Cl, Br, and I, consistent with the postulate that all of these reactions proceed through a common intermediate Q X , eq 2 and 3. Since the reaction with metallacycle, 1, does not generate H 2 , the intermediates Q X are detected, which implies that the barrier for conversion of Q X to Cp' 2 CeX and CH 4 in presence of H 2 , is lower when X is Cl, Br, I than when X is OMe. Class c is the reaction with CH 3 NMe 2 . No net reaction is observed but deuterium labeling experiments show that H for D exchange occurs in trimethylamine, implying that intermediate Q NMe2 forms and that Cp' 2 CeH and Q NMe2 are in equilibrium. This implies that the H for D exchange proceeds with a low barrier but that the conversion of Q NMe2 to Cp' 2 CeNMe 2 has an impossibly high barrier. The reactions between Cp' 2 CeH and CH 3 X proceed by a low barrier intermolecularα-CH activation followed by ejection of the CH 2

1

H NMR spectroscopy. Class b is when X is OMe, as the reaction with Cp' 2

  . for C 34 H 58CeI: C, 55.65; H, 7.96. Found C, 55.76; H, 8.17.

	Cp' 2 CeHBPh 3 : Cp' 2 CeH 5 (0.5 g, 0.72 mmol) and BPh 3 (0.2 g, 0.82 mmol) were
	dissolved in toluene (10 mL). The clear yellow solution was allowed to stand at 19°C
	overnight, resulting in yellow crystals. The 1 H NMR spectrum of the crystals in C 6 D 6
	indicated the presence of toluene of crystallization. Yield, 0.50 g (0.53 mmol, 74%).
	MP 202-205°C. 1 H NMR (C 7 D 8 , 300MHz): δ 5.35 (18H, ν 1/2 = 100 Hz), 4.99 (3H, ν 1/2
	= 25 Hz), 4.08 (6H, ν 1/2 = 30 Hz), -2.42 (6H, ν 1/2 = 100 Hz), -6.68 (18H, ν 1/2 = 70 Hz),
	-14.514 (18H, ν 1/2 = 200 Hz). Anal. Calcd. for C 59 H 82 BCe: C, 75.21; H, 8.77. Found
	C, 74.88; H, 8.67. Full crystallographic details are included as Supporting

NMR tube reaction of dimethylether and Cp' 2 CeH in cyclohexane-d 12 .

  1 H NMR spectra contained only resonances due to CH 4 and either Cp' 2 CeBr or Cp' 2 CeI. Cp' 2 CeH was dissolved in cyclohexane-d 12 in an NMR tube. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated and replaced with dimethylether (1 atm). The tube was warmed to 19°C, and the purple solution rapidly turned red. After 15 minutes, resonances due to Cp' 2 CeH had disappeared from the 1 H NMR spectrum. Resonances due to Cp' 2 CeCH 2 OMe and a new pair of paramagnetic

	resonances [ 1 H NMR (C 6 D 12 )δ -2.38 (36H, ν1/2= 15 Hz), -4.43 (18H,ν1/2= 15 Hz)]
	had appeared. The ratio of Cp' 2 CeCH 2 OMe and the unknown species, Q' OMe , was
	approximately 1.3:1. After two days, resonances due to Cp' 2 CeOMe had appeared in
	the spectrum; the ratio of Cp' 2 CeOMe, Cp' 2 CeCH 2 OMe, and Q' OMe was approximately
	1:40:48. The sample was heated at 60°C. After one day, the ratioof the three species
	was 1:6:5, after 12 days 2.5:2:1, and after 27 days 7:3:1.

NMR tube reaction of trimethylamine and Cp' 2 CeH in cyclohexane-d 12 .

  CeH. The sample was heated at 60°C for 19 days, after which time the 1 H NMR spectrum was unchanged.In the case of CH 3 I, after 15 min, the purple solution had turned redder, and two new paramagnetic resonances in a 2:1 ratio, Q I , had appeared in the 1 H NMR spectrum. After 40 minutes, the solution was red-orange, and only the new resonances remained in the spectrum.1 H NMR (C 6 D 12 )δ -1.29 (ν 1/2 = 260 Hz), -7.82 (ν 1/2 = 10 Hz). After 3 hours, resonances due to Cp' 2 CeI had appeared; the ratioof the Q I to Cp' 2 CeI was 6:1, after five days, only resonances due to Cp' 2 CeI remained.In all cases, GCMS analysis of the hydrolyzate showed one principle component in addition to Cp'H, with (M) + m/z 248 (Cp"H). Resonances due to Cp"Cp'CeCl, Cp"Cp'CeBr, and Cp"Cp'CeI could not be unequivocally assigned; presumably the line widths are broad and the chemical shift differences relative to the resonances of Cp' 2 CeCl, Cp' 2 CeBr, and Cp' 2 CeI are small, unlike in the case of Cp"Cp'CeF where the line widths are narrow.4a The hydrolysis experiments provided unequivocal evidence for the presence of Cp"H.

	Cp' 2 CeH was dissolved in cyclohexane-d 12 , the sample was cooled in a liquid
	nitrogen isopropanol bath, the head space was evacuated, and replaced with
	anhydrous trimethylamine (1 atm). The tube was warmed to 19°C and allowedto
	stand. After 2 days, the 1 H NMR spectrum contained only paramagnetic resonances
	due to Cp' 2

NMR tube reaction of dimethylether and Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce in cyclohexane-d 12 .

  Cp' 2 Ce(CH 2 C 6 H 5 ) was dissolved in cyclohexane-d 12 and heated at 60°C for 12 hours, yielding a solution of Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with dimethylether (1 atm). The tube was warmed to 19°C, and the deep purple solution rapidly turned red. After 20 minutes, the only paramagnetic resonances in the 1 H NMR spectrum were those of Cp' 2 CeCH 2 OMe. The sample was taken to dryness, and the red solid was dissolved in cyclohexane-d 12 . No new paramagnetic resonances appeared in the 1 H NMR spectrum. The sample was heated at 60°C, and after one day, resonances due to Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce had appeared in the 1 H NMR spectrum; the ratio of Cp' 2 CeCH 2 OMe to Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce was approximately 11:1. After three days, the ratio was unchanged. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and the sample was warmed to 19°C. This freeze-pump-thaw procedure was performed two more times, and the headspace was refilled with N 2 (1 atm). The sample was heated for three days at 60°C. The ratio of Cp' 2 CeCH 2 OMe to Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce in the 1 H NMR spectrum remained approximately 11:1.

NMR tube reaction of trimethylamine and Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce in cyclohexane-d 12 .

  Cp' 2 Ce(CH 2 C 6 H 5 ) was dissolved in cyclohexane-d 12 and heated at 60°C for 12 hours, yielding a solution of Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with

	anhydrous trimethylamine (1 atm). The tube was warmed to 19°C and allowed to
	stand. After 1 hour, the 1 H NMR spectrum contained three newMe 3 C-resonances in
	a 1:1:1 ratio, 1 H NMR (C 6 D 12 ) 6.43 (18H,ν 1/2 = 90 Hz), -2.47 (18H,ν 1/2 = 40Hz), -
	13.60 (18H,ν 1/2 = 40 Hz), Q NMe2 ; resonances due to the CH 2 NMe 2 ligand were not
	observed. The ratio of the new species to Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce was 1:1.3.
	After 3.5 hours, the ratio was 3:1, and after one day, it was 6:1. The sample was
	heated at 60°C for 2 days, and the ratio was 1.3:1; the ratios did not change upon
	heating the sample for an additional 15 days.

NMR tube reaction of dimethylether or trimethylamine and (Cp'- d 27 ){[C(CD 3 ) 3 ] 2 C 5 H 2 [C(CD 3 ) 2 CD 2 ]}Ce in cyclohexane-d 12 .

  Cp' 2 Ce(CH 2 Ph) was dissolved in C 6 D 6 and heated at 60°C for 4 days to perdeuterate the ring t-butyl groups. The sample was taken to dryness and the solid residue was redissolved in fresh C 6 D 6 . The sample was heated for an additional 7 days, then taken to dryness and the solid residue was redissolved in C 6 D 12 . The sample was heated at 60°C for 1 day, yielding a solution of (Cp'-d 27 ){[C(CD 3 ) 3 ] 2 C 5 H 2 [C(CD 3 ) 2 CD 2 ]}Ce.

NMR tube reaction of CH 3 Br and Cp' 2 CeCH 2 OMe in benzene-d 6 .

  H NMR spectrum were those of the Cp'-ring C-H and the OMe group of (Cp'd 27 ) 2 CeCH 2 OMe. The 2 H NMR spectrum contained resonances due to the Cp'-ring tbutyl groups of (Cp'-d 27 ) 2 CeCH 2 OMe. The 13 C NMR spectrum contained a single The ratio of Cp' 2 CeOMe, Cp' 2 CeCH 2 OMe, and Cp' 2 CeD in the 1 H NMR spectrum was approximately 1:7:8. After two days, the ratio was approximately 1:1:7. After 9 days, resonances due to Cp' 2 CeCH 2 OMe had disappeared from the spectrum, and the ratio of Cp' 2 CeOMe and Cp' 2 CeD was approximately 1:5. No resonances for methane were observed. The 2 H NMR spectrum contained resonances due to CH 2 DOCH 3 and deuterium incorporation into the Cp'-ring t-butyl groups of Cp' 2 CeD. Cp' 2 CeCH 2 OMe was dissolved in benzene-d 6 in an NMR tube. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with CH 3 Br (1 atm). The red solution was warmed to 19°C and allowed to stand. After one day, resonances due to dimethylether, Cp' 2 CeBr, Cp' 2 CeOMe, and Q Br , had appeared in the 1 H NMR spectrum; the ratio of Cp' 2 CeCH 2 OMe, Cp' 2 CeBr, Cp' 2 CeOMe, and Q Br was 8:8:1:2. After 4 days, the solution had turned yellow, and only resonances due to Cp' 2 CeBr and dimethylether remained in the spectrum.

	d 27-x ) 2 CeCH 2 OMe had also appeared in the 1 H NMR spectrum; the ratio of the
	integrated intensities of the t-butyl resonances at -1.11 and -10.90 ppm was 1:7. The
	ratio of the corresponding peaks in the 2 H NMR spectrum was 3:1, and a broadened
	triplet (3.20 ppm, J HD = 1.5 Hz) corresponding to partially deuterated dimethylether
	had also appeared. The ratio of the resonance at -10.90 ppm to the dimethylether
	resonance was 1:1. In the 13 C NMR spectrum, a 1:1:1 pattern (59.95 ppm, J CD = 21
	Hz) had appeared just upfield of the signal for dimethylether (60.25 ppm). After
	seven days, the ratio of the integrated intensities of the resonances at -1.11 and -10.90
	ppm in the 1 H NMR and 2 H NMR spectra were virtually unchanged, but the ratio of

1

resonance corresponding to dimethylether. After two days, the spectra were unchanged. The sample was heated at 60°C.After three days, a 1:1:1 pattern (3.16 ppm, J HD = 1.2 Hz) had appeared in the 1 H NMR spectrum just upfield of the signal for dimethylether

(3.18 ppm)

. Resonances due to the Cp'-ring t-butyl groups of (Cp'the resonance at -10.90 ppm to the dimethylether resonance in the 2 H NMR spectrum was 1:4. After 18 days, the ratio of the resonances at -1.11 and -10.90 ppm was 1:2.5

NMR tube reaction of CH 3 F and Cp' 2 CeCH 2 OMe in benzene-d 6 .

  Cp' 2 CeCH 2 OMe was dissolved in benzene-d 6 in an NMR tube. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with CH 3 F (1 atm). The red solution was warmed to 19°C and allowed to stand. After one day, resonances due to dimethylether and Cp' 2 CeF had appeared in the 1 H NMR spectrum; the ratio of Cp' 2 CeCH 2 OMe to Cp' 2 CeF was approximately 30:1. After 2 days, the ratio was 18:1. The sample was warmed to 60°C, and after one day, the red solution had become more orange, and resonances due to Cp' 2 CeOMe had appeared; the ratio of Cp' 2 CeCH 2 OMe, Cp' 2 CeF, and Cp' 2 CeOMe was approximately 6.5:2.5:1.After five days, the ratio was 1:4:2, after nine days, only resonances due to Cp' 2 CeF, and Cp' 2 CeOMe remained in a 1.5:1 ratio.

NMR tube reaction of BPh 3 and Cp' 2 CeCH 2 OMe in benzene-d 6 .

  Cp' 2 CeCH 2 OMe was dissolved in C 6 D 6 in an NMR tube and less than an equimolar amount of BPh 3 was added. After 10 minutes, the only paramagnetic resonances in the 1 H NMR spectrum were those due to Cp' 2 CeOMe. Integration relative to the solvent residual proton peak indicated that the conversion of Cp' 2 CeCH 2 OMe to Cp' 2 CeOMe was quantitative. The sample was hydrolyzed with basic hydrogen peroxide, and GC MS analysis of the combined organic layers showed that the sample contained a fraction with (M) + m/z 108 (C 6 H 5 CH 2 OH) and a smaller fraction with (M) + m/z 122 (C 6 H 5 (CH 2 ) 2 OH) in addition to Cp'H. No fraction corresponding to C 6 H 5 OH was observed.

NMR tube reaction of BPh 3 and Q I in benzene-d 6 .

  Cp' 2 Ce(CH 2 C 6 H 5 ) was dissolved in cyclohexane-d 12 and heated at 60°C for 12 hours, yielding a solution of Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and an excess of

Acknowledgment

This work was supported by the Director, Office of Science, Office of Basic Energy Sciences (OBES), of the U.S. Department of Energy (DOE) under Contract No. DE-AC02-05CH11231. We thank F. J. Hollander at CHEXRAY, the U.C. Berkeley X-ray diffraction facility, for help with the crystallography. L.M thanks the CINES and CALMIP for a generous grant of computing time. L.M. is also member of the Institut Universitaire de France, L.M. and O.E thank the CNRS and Ministère de l'Enseignement Supérieur et de la Recherche for funding, and A.Y. thanks the CEA for PhD fellowship.

Cp' 2 Ce(CH 2 C 6 H 5 ) was dissolved in cyclohexane-d 12 and heated at 60°C for 12 hours, yielding a solution of Cp'[(Me 3 C) 2 C 5 H 2 C(Me 2 )CH 2 ]Ce. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with CH 3 Cl (1 atm), CH 3 Br (1 atm), or an excess of CH 3 I via vacuum transfer followed by N 2 (1 atm). The tube was warmed to 19°C and allowed to stand.

In the case of CH 3 Cl, after 10 min, the purple solution had turned red. Resonances due to the starting material had disappeared from the 1 H NMR spectrum, and a pair of resonances due to Cp' 2 CeCl 4a and two new paramagnetic resonances in a 2:1 ratio, Q Cl , had appeared, 1 H NMR (C 6 D 12 ) -1.36(ν1/2= 25 Hz), -8.54 (ν 1/2 = 10Hz). The ratio of Q Cl to Cp' 2 CeCl was 4:1. After 1 hour, the ratiowas 1:2, and after 2 hours, the solution was orange and the ratio was 1:5. After 3 days, the solution had turned yellow, yellow crystals had formed, and only resonances due to Cp' 2 CeCl remained in the spectrum.

In the case of CH 3 Br, after 10 min, the purple solution had turned deep orangebrown, and two new paramagnetic resonances in a 2:1 ratio, Q Br , had appeared in the in the 1 H NMR spectrum and 12:1 in the 2 H NMR spectrum, and the ratio of the resonance at -10.90 ppm to the dimethylether resonance in the 2 H NMR spectrum was 1:13. After 81 days, the ratio of the resonances at -1.11 and -10.90 ppm was 1:1 in the 1 H NMR spectrum and 2:1 in the 2 H NMR spectrum, and the ratio of the resonance at -10.90 ppm to the dimethylether resonance in the 2 H NMR spectrum was 1:14.

In the case of trimethylamine, the sample was heated at 60°C. After Cp' 2 CeCH 2 OMe was dissolved in cyclohexane-d 12 in an NMR tube. The tube was cooled in a liquid nitrogen isopropanol bath, the head space was evacuated, and replaced with D 2 (1 atm). The tube was warmed to 19°C and allowed to stand. After isopropanol bath, the head space was evacuated, andreplaced with CH 3 Br (1 atm).

The sample was warmed to 19°C, and the solution color became more orange. After 10 minutes, the resonances due to free BPh 3 had grown substantially in the 1

Computational details

The Stuttgart-Dresden-Bonn Relativistic large Effective Core Potential (RECP) 36a was used to represent the inner shells of Ce. The associated basis set 36a augmented by an f polarization function (α = 1.000) was used to represent the valence orbitals. 36b F was also represented by an RECP 37a with the associated basis set of the type (4s5p/2s3p) 37a augmented by two contracted d polarisation gaussian functions (α 1 = 3.3505(0.357851), α 2 = 0.9924(0.795561)). 37b The atoms Cl, Br, and I were represented by an RECP 37c with the associated basis set of the type (4s5p/2s3p) 37c augmented by a single d polarization gaussian function with exponent of 0.643, 0.550 and 0.730 respectively. 37b The atoms C, O, and H were represented by an all-electron 6-31G(d, p) basis set. 38 Calculations were carried out at the DFT(B3PW91) level 39 with Gaussian 03. 40 The nature of the extrema (minimum or transition state) was established with analytical frequencies calculations and the intrinsic reaction coordinate (IRC) was followed to confirm that the transition states connect to

Supporting information

Additional experimental details, X-ray crystallographic data (CIF), CCD numbers, Coordinates and potential energies, E, and Gibbs free energies, G, values in a.u. for all calculated structures. Energy profiles for the reactions shown in Figure 5 using energies E.


Mt/an entre 2001 et 2003 ; [START_REF] Sabatier | Sediment budget of the Rhône delta shoreface since the middle of the 19th century[END_REF][START_REF] Ollivier | Interface continent-océan: géochimie du Rhône (flux et bilans d'érosion) et transferts d'eaux souterraines en Camargue (apports des isotopes du strontium[END_REF] et une accélération récente de la montée du niveau marin (2mm/an depuis 1 siècle), provoquent un recul du trait de côte pouvant aller jusqu'à 5 à 10 m/an par endroits [START_REF] Sabatier | Sediment budget of the Rhône delta shoreface since the middle of the 19th century[END_REF]. Les différentes masses d'eau douce ou salée, présentes en arrière du trait de côte sont susceptibles de répondre à ces changements. Dans ce contexte d'équilibre instable, le fonctionnement des nappes d'eau souterraine de Camargue a fait l'objet d'une attention particulière et un suivi à long terme a été initié en 2003 dans le cadre de l'Observatoire de Recherche en Environnement RESYST et de la Zone Atelier ORME. Cet article présente les résultats des premières campagnes de mesures géochimiques réalisées sur les eaux souterraines dans le but de comprendre le fonctionnement des nappes, d'identifier les paramètres pertinents à mesurer et de rechercher les différents forçages de leur évolution, et notamment de l'intrusion saline.

Les aquifères de Camargue avaient déjà fait l'objet d'investigations et de mesures, entreprises dans les années 1970 par la Compagnie Nationale d'Aménagement de la Région du Bas-Rhône et du Languedoc à la demande de la Direction Départementale de l'Agriculture des Bouches du Rhône. Après cinq ans de suivi, elles ont été reprises par la DIREN de 1976 à 1978 et en 1982 puis s'étaient arrêtées depuis 1994. Plus récemment, plusieurs études hydrologiques ont été menées en Camargue afin de quantifier le bilan hydrique, de simuler l'évolution des niveaux d'eau et de la salinité des étangs ou d'analyser l'impact de la riziculture et la réponse des milieux à la gestion hydraulique [START_REF] Chauvelon | Hydrologie quantitative d'une zone humide méditerranéenne aménagée : le bassin de fumemorte en grande camargue, delta du Rhône[END_REF][START_REF] Heurteaux | Essai de quantification des termes du bilan hydrique des étangs du système Vaccarès (Camargue, France)[END_REF][START_REF] Chauvelon | Modélisation du fonctionnement hydrologique d'un hydrosystème côtier méditerranéen fortement anthropisé : l'Ile de Camargue[END_REF][START_REF] Franchesquin | Modélisation et simulation multi-agents d'écosystèmes anthropisés : une application à la gestion hydraulique en Grande Camargue[END_REF]. Ces travaux se sont concentrés sur les eaux de surface, mais les processus impliquant les eaux souterraines n'ont pas été abordés. La raison majeure de cette absence n'est pas le manque d'intérêt pour ces nappes, mais plutôt les difficultés que présente leur étude. En effet, les échantillons et les mesures sont difficiles à obtenir, et de plus, la diversité du substrat géologique, la complexité des apports d'eau en surface (irrigation, étangs, mer, anciens chenaux du fleuve) et leurs effets très locaux créent de grandes diversité spatiales.

2-LES AMENAGEMENTS HYDRAULIQUES EN CAMARGUE

De grands travaux d'endiguement terminés aux alentours de 1870 ont coupé la plaine d'une partie de son alimentation naturelle en eau, par le Rhône lors des inondations ou par la mer lors des tempêtes. La partie centrale et triangulaire de cette plaine enserrée entre les deux bras du Rhône en aval d'Arles (750 km2), est d'ailleurs appelée l'Ile de Camargue, ce qui traduit son isolement (Figure 1). Actuellement, la gestion hydraulique est très complexe car elle doit répondre à plusieurs impératifs parfois antagonistes. Dans la partie au nord du Vaccarès dite « Camargue fluvio-lacustre » (car constituée des sédiments du fleuve), l'eau du Rhône est apportée par un système complexe de canaux (presque 1000 km de linéaire de canaux de toutes tailles, [START_REF] Dervieux | La gestion de l'eau en Camargue : une manière moderne de domestiquer la nature ?. Dans : Évaluation des risques environnementaux pour une gestion durable des espaces[END_REF]) et de stations de pompage. Elle sert à l'alimentation des marais de chasse ou roselières et surtout à l'irrigation des cultures dans la partie nord et sud-est (principalement riziculture sur plus de 10000 ha). Une grande partie de l'eau d'irrigation repart au Rhône par des canaux de drainage, le reste se déverse dans l'étang central du Vaccarès (par exemple l'eau du bassin de Fumemorte à l'est). Le Vaccarès et les étangs inférieurs qui lui sont reliés reçoivent donc des eaux d'irrigation, plus les précipitations et les apports d'eau de mer régulés par des pertuis au Grau de la Fourcade, près des Saintes-Maries-de-la-Mer. La salinité moyenne du Vaccarès est actuellement régulée aux alentours de 14 g/l, mais elle a varié très fortement au cours des dernières décennies (entre 20 et 5 g/l). La salinité des étangs inférieurs de plus petits volumes est beaucoup plus variable au cours de l'année : entre 20 et plus de 50 g/l (www.réserve-camargue.org). La sansouïre, paysage végétal où la salicorne domine, occupe une place à part dans ces zones. Elle correspond à des terres basses limoneuses, dans et autour des étangs centraux, soumises ponctuellement à des apports d'eaux lors des pluies ou des montées de niveau des étangs. L'évaporation potentielle (≈1300 mm/an) étant très supérieure aux précipitations moyennes (≈600 mm/an ; [START_REF] Chauvelon | Hydrologie quantitative d'une zone humide méditerranéenne aménagée : le bassin de fumemorte en grande camargue, delta du Rhône[END_REF], ces eaux s'évaporent, entraînant la formation de croûte de sel en surface du sol. Enfin, au sud-est de ces étangs, 11000 ha sont utilisés pour les marais salants et noyés toute l'année sous des eaux saumâtres. La zone des étangs naturels, des sansouïres, des marais saumâtres et salants et du littoral constitue la « Camargue laguno-marine », où l'influence du sel domine.

-CONTEXTE GEOLOGIQUE DU DELTA DE CAMARGUE

La basse vallée du Rhône suit un sillon dont le soubassement est constitué par des formations d'âge Jurassique et Crétacé découpées à l'Oligocène (34 à 28 Millions d'années) lors d'une grande phase de distension tectonique (ayant entraîné notamment la création de la faille de Nîmes). Durant le Miocène (28 à 5,3 M d'a.), un événement majeur est la crise de salinité Messinienne (7,2 à 5,3 M. d'a.) caractérisée par un abaissement de plus de 1000 mètres du niveau marin en Méditerranée ayant entraîné le creusement d'un canyon profond dans la vallée du Rhône. La remontée de la mer au Pliocène (5,3 à 1,8 M. d'a.) a permis le comblement de ce canyon et le dépôt de formations fines (marnes). Par la suite, de nouvelles baisses du niveau marin ont permis à des rivières à forte énergie, notamment la Durance, de transporter des alluvions grossières issues de l'érosion intense des Alpes nouvellement formées. Ces dépôts alluviaux se développent depuis la bordure est (cailloutis de Crau) et forment une couche d'épaisseur très variable (10 à 70 m, [START_REF] Boyer | High resolution stratigraphy and evolution of the Rhône delta plain during Postglacial time, from subsurface drilling data bank[END_REF] qui repose sur une couche de marnes imperméables. La couche de cailloutis affleure dans la Plaine de la Crau, puis son toit s'enfonce progressivement vers le sud-ouest jusqu'à environ 50 m de profondeur au niveau du littoral. En mer cette formation s'étend vers le sud, recouverte par des sédiments plus récents, mais elle pourrait être en contact direct avec le fond marin vers la rupture du plateau continental [START_REF] Boyer | High resolution stratigraphy and evolution of the Rhône delta plain during Postglacial time, from subsurface drilling data bank[END_REF].

-L'EAU SOUTERRAINE

L'eau est omniprésente dans ce mille-feuilles sédimentaire constitué de couches plus ou moins fines et perméables. Deux types de nappes peuvent être différenciés. A faible profondeur, on trouve des eaux de salinités très variables : douce, saumâtre, salée et même sursalée jusqu'à 110 g/l (contre 38 g/l pour l'eau de la Méditerranée). Au dessous, la couche des cailloutis abrite également une nappe de salinité variable, saumâtre au nord (≅2g/l) à salée au sud (≅38g/l). Les différents facteurs qui peuvent contribuer à la salinité de ces eaux souterraines sont la dissolution de sels présents dans les roches encaissantes, le mélange avec l'eau de mer actuelle, ou encore une concentration progressive des sels par l'évaporation très intense dans cette région. Comprendre le fonctionnement de ces systèmes hydrauliques complexes implique de comprendre les rôles respectifs de ces différents facteurs et l'influence des apports par la pluie et par le Rhône. Les outils géochimiques sont dans ce contexte très précieux. La composition isotopique de l'eau (cf encart 1) permet de tracer l'origine des masses d'eau et d'identifier les effets de l'évaporation. Associée à la composition chimique de l'eau, elle apporte des informations sur les interactions entre l'eau et la roche encaissante, les mélanges éventuels avec l'eau de mer et/ou les effets de concentration par évaporation. La relation linéaire qui apparaît entre la concentration en chlore et le niveau piézométrique, et qui passe par une concentration équivalente à celle de l'eau de mer à l'altitude zéro (figure 6) montre la continuité hydraulique qui existe entre les différents points de mesure et la mer. Le mélange de l'eau de cette nappe avec l'eau de mer correspond donc bien au schéma classique du biseau salé décrit par la loi de Ghyben-Herzberg (Encart 3, Figure 2). L'intrusion d'eau salée dans la nappe profonde des cailloutis répond donc à un équilibre hydrostatique, luimême régit à la fois par le niveau marin et par l'hydrodynamique de la nappe. Il est donc nécessaire de bien comprendre les facteurs qui régissent l'hydrodynamique de cette nappe afin de comprendre et peut-être de prévenir la progression de cette intrusion saline dans le futur.

-LA NAPPE PROFONDE DES CAILLOUTIS

Tous les éléments chimiques ne se comportent pas de manière aussi conservative que le chlore et beaucoup montrent des variations dans l'espace qui peuvent être associées à des processus biologiques (via les microorganismes), des phénomènes d'interaction avec la roche (dissolution ou échange d'éléments) ou de précipitations de minéraux. Le calcium est un exemple classique des interactions eau-roche. Sur un diagramme représentant les teneurs en calcium en fonction des teneurs en chlore (Figure 7), les points situés au-dessus de la droite de mélange théorique traduisent un apport important de calcium très probablement lié au lessivage de la matrice des cailloutis. Ce processus n'est toutefois pas le seul en jeu puisque les valeurs en dessous de la droite pour l'eau du piézomètre S5 traduisent une précipitation chimique qui enlève le calcium (sous forme de Calcite CaCO 3 par exemple). Les études sont encore en cours sur d'autres éléments comme le strontium, dont le comportement chimique est similaire à celui du calcium. Cet élément possède en effet des isotopes stables dont la mesure permettra de mieux caractériser les sources d'alimentation de l'eau de la nappe.

Les sulfates sont quant à eux un bon témoin des processus biologiques qui interviennent dans la minéralisation de l'eau de la nappe. En effet, on a pu constater en plusieurs points de la nappe l'absence d'oxygène dans l'eau : le milieu est donc réducteur. Dans ce contexte, certaines bactéries peuvent se développer en utilisant l'oxygène des sulfates (SO 4 2-) comme source d'énergie pour dégrader la matière organique (entraînant la réduction des sulfates). La « sulfato-réduction » produit des sulfures reconnaissables par leur odeur caractéristique d'oeuf pourri. La relation entre les teneurs en sulfates et en chlore (Figure 8) montre que certains points ont une teneur en sulfate beaucoup plus faible que ce que pourrait laisser prévoir un simple mélange entre les deux pôles : cet élément a été « consommé » par des bactéries. L'importance de la sulfato-réduction dans la nappe dépend de la disponibilité de la matière organique mais également de la présence de sulfates, élément généralement en faible proportion dans les eaux douces. Ici, la source de sulfate provient de l'intrusion d'eau de mer dans la nappe. Ainsi la sulfato-réduction rend également compte de l'avancée du biseau salé dans la nappe des cailloutis.

-LES NAPPES DE SURFACE

La lithologie des formations sédimentaires en surface est très variée, allant de matériaux sableux grossiers perméables à des formations plus fines, limoneuses à argileuses, presque totalement imperméables. Cette forte hétérogénéité permet la mise en place de nombreuses petites nappes d'eaux souterraines mal connectées entre elles car la faiblesse de la pente topographique, impliquant de faibles gradients hydrauliques, permet peu de circulations latérales. Une trentaine de piézomètres implantés à des profondeurs de 4 à 6 mètres environ ont été utilisés pour mesurer les eaux des nappes superficielles. Les eaux sont caractérisées par une grande gamme de variation de la salinité, sans que l'on puisse identifier de gradient nord-sud dans leur distribution géographique (Figure 9). Sur la base de la concentration en chlore deux groupes de piézomètres ont été identifiés: les « eaux douces » et les « eaux salées ».

L'intrusion d'un biseau salé, identifiée clairement pour la nappe des cailloutis, pourrait également être invoquée pour expliquer la salinité des nappes de surface. Cependant, la distribution géographique des valeurs de salinité n'indique pas de relation avec la proximité de la mer (Figure 9). De plus, la relation entre la concentration en chlore et en oxygène-18 des eaux montre que la plupart des concentrations des piézomètres « salés » sont largement supérieures à celles que laisserait prévoir un simple mélange avec la mer (en pointillé sur la Figure 10). Par conséquent, si l'influence marine ne peut être formellement exclue, elle n'est pas suffisante pour expliquer les fortes salinités observées. Pour ces eaux, l'influence de l'évaporation se matérialise dans la relation entre δ 18 O et δ 2 H (Figure 11) par une position des points sous la droite météorique mondiale, avec une tendance à s'aligner le long d'une droite d'évaporation dont l'eau de départ aurait une composition proche de celle des précipitations locales. Certains points font exception : il s'agit de points présentant des compositions isotopiques nettement plus appauvries car les sites sont influencés par des eaux provenant de canaux proches apportant de l'eau du Rhône, et d'un point situé sur la droite météorique mondiale car le piézomètre est situé dans une zone temporairement inondée par les eaux de pluie.

Pour les piézomètres « eaux douces », les teneurs en oxygène-18 (δ 18 O= -9.2‰ à -6.4‰) varient entre celles de l'eau du Rhône ou de la Durance et celle des précipitations locales (Figure 10). Cependant, en représentant ces valeurs en fonction des teneurs en deutérium (Figure 11), on constate une dispersion importante, avec dans de nombreux cas une signature témoignant de phénomènes d'évaporation : les points sont nettement sous la droite météorique mondiale. Contrairement au groupe de points représentant l'eau des piézomètres « salés », leur composition isotopique appauvrie montre qu'ils sont sous l'influence de l'eau du Rhône, apportée soit par les canaux servant à l'irrigation, soit par des circulations préférentielles dans les paléochenaux naturels du Rhône.

De manière générale, les eaux douces sont rencontrées dans des zones influencées par l'irrigation ou par des circulations préférentielles dans des anciens chenaux du Rhône. Les eaux salées par contre sont rencontrées dans des zones où les eaux circulent peu.

L'évaporation intense est donc le principal facteur de salinisation, les sels étant apportés petit à petit par la pluie depuis des années et concentrés dans les sols sans pouvoir être évacués par lessivage. Cette situation résulte de l'aménagement hydraulique du cours du Rhône : avant la construction de digues, le fonctionnement naturel du delta entraînait des inondations régulières qui permettaient de lessiver les sels accumulés. Contrairement à la nappe profonde, on ne peut pas parler d'une seule nappe de surface qui sature les sédiments reposant sur la couche des cailloutis, mais plutôt d'un patchwork de petites nappes dont les caractéristiques sont déterminées en grande partie par la gestion hydraulique du delta du Rhône.

7-CONCLUSION

Les résultats présentés ici apportent une première idée sur le fonctionnement des eaux souterraines dans la plaine de Camargue. La situation en subsurface est très complexe en partie à cause des dépôts sédimentaires variés qui constituent les sols, mais aussi en relation avec les aménagements hydrauliques. Réparties dans de petits aquifères mal connectés entre eux, les eaux souterraines proviennent des pluies, des apports par les canaux d'irrigation ou des paléochenaux du Rhône. Leur chimie évolue en fonction de ces apports mais surtout en fonction de l'évaporation qui entraîne des salinisations importantes. Plus en profondeur, l'eau de la nappe des cailloutis témoigne de l'intrusion du biseau salé sur plusieurs kilomètres vers l'intérieur des terres, à cause du faible gradient hydraulique. La chimie n'est plus contrôlée par l'évaporation, mais par l'intrusion de l'eau de mer, à laquelle se rajoute les interactions avec la roche encaissante et des processus biologiques. Les données obtenues depuis 1970 semblent indiquer une augmentation importante de la salinité dans la partie sud, dont la cause doit être encore étudiée. Cette salinisation traduit une avancée du biseau salé vers l'intérieur des terres, un phénomène qui s'est produit de par le monde dans nombre d'aquifères côtiers où les pompages massifs d'eau ont aggravé l'intrusion d'eau de mer dans l'aquifère. En Camargue, la nappe n'a jamais été exploitée intensivement, mais les travaux futurs devront mettre en évidence les rôles respectifs de la diminution des apports d'eau douce (Rhône ou nappe de la Crau) et de la montée du niveau marin (2 mm/an) sur cette salinisation.

  C., Radakovitch O., De Montety V., Hermitte D., Sonzogni C., Ollivier P., Paul M. CEREGE, UMR 6635, CNRS -Université Paul Cézanne Aix-Marseille, BP 80, 13545 Aix-en Provence cedex 4, France 1 -INTRODUCTION Les zones deltaïques résultent d'un équilibre fragile et fluctuant entre les apports sédimentaires continentaux et l'érosion marine. Dans le cas du delta du Rhône, une diminution importante des apports sédimentaires depuis l'amont (27 Mt/an en 1850 contre 7

  Des dépôts fluviatiles ou marins se mettent en place par dessus ces cailloutis. Au nord du Vaccarès, ces dépôts sont uniquement fluviatiles (sables fins et limons du Rhône) et donnent une morphologie de plaine alluviale : dépôts argileux d'inondation, anciennes berges et chenaux colmatés. Au sud, la stratigraphie est plus complexe. La remontée rapide du niveau marin après 18000 ans BP (Before Present) produit une succession de dépôt d'argiles et de limons de plaine côtière entrecoupés de niveaux sableux, l'ensemble avançant progressivement vers l'intérieur des terres. Vers 6000 ans BP, la ligne de rivage est à sa limite maximale dans les terres, au nord du Vaccarès (Vella, 2004). La montée du niveau marin continue mais à une vitesse beaucoup plus faible et l'influence du fleuve reprend le dessus: le delta progresse vers le sud grâce aux apports sédimentaires qui se déposent à l'embouchure (formation de lobes deltaïques). Les changements successifs de lit du fleuve suite à des inondations sont encore visibles. Chronologiquement, on distingue le Rhône de Saint-Férréol, le Rhône d'Ulmet et de Peccais (à l'est du Vaccarès), le Rhône du Bras de Fer et enfin le Rhône actuel de Roustan. (Vella, 2004 ; Figure 1). Les dépôts sédimentaires dans cette partie sud de la Camargue traduisent cette double influence fluviale et marine: paléo-berges et paléo-chenaux du fleuve, anciens cordons littoraux sableux ou dépôt d'argiles de lagunes avec passées tourbeuses. Les relations latérales et verticales entre ces différentes unités sont très difficiles à matérialiser car elles peuvent varier à l'échelle de la dizaine de mètres, comme dans le cas d'un ancien bras colmaté du Rhône.

  Dix piézomètres (forages donnant accès à la nappe) ont été installés en 1969 en haute et moyenne Camargue pour mesurer le niveau et la chimie de cette nappe profonde des cailloutis. Dans le cadre de l'Observatoire de Recherche en Environnement RESYST et d'une thèse en cours au laboratoire d'hydrogéologie d'Avignon (de Montety), des mesures et prélèvements sont réalisés sur cinq d'entre eux, encore opérationnels, et sur quelques forages réalisés par des particuliers. Les eaux prélevées présentent des compositions isotopiques et des concentrations en chlore qui témoignent d'un mélange entre une eau douce de composition isotopique très appauvrie et l'eau de mer (Figures 4 et 5). En effet, l'alignement des compositions isotopiques est caractéristique d'une droite de mélange (voir encart 2) et non d'une droite d'évaporation (voir encart 1 et Figure 3) dont la pente serait plus faible. Ceci est confirmé par l'ordre de grandeur et la linéarité des variations de teneurs en chlore en fonction de la composition isotopique, caractéristique également d'une droite de mélange, et permet d'exclure le rôle de l'évaporation dans la salinisation des eaux de la nappe des cailloutis. L'identification des pôles de mélange et la détermination de leur composition isotopique seraient nécessaires pour pouvoir calculer les proportions de chacun et mieux contraindre ces processus. Un des pôles est représenté par l'eau de mer, l'autre correspond à l'eau douce qui alimente la nappe des cailloutis. Deux sources d'alimentation différentes peuvent être invoquées pour cette nappe: (1) l'eau du Rhône, qui peut être en contact avec la formation des cailloutis (ex : au Seuil de Terrin ou elle est observée au fond du lit du fleuve) et (2) l'eau de la nappe de la Crau, alimentée dans la plaine de Crau à l'est du Grand Rhône où les cailloutis affleurent. Principalement libre et superficielle, la nappe de la Crau a un sens d'écoulement général du nord-est vers le sud-ouest et devient captive sous les sédiments deltaïques de l'Ile de Camargue. En devenant captive, elle perd une grande partie de son débit dans des résurgences naturelles qui forment une série de marais et de zones humides alignés à l'est du Grand Rhône (Figure 1), mais une proportion inconnue continue à s'écouler dans la nappe captive, en Camargue. L'alimentation de la nappe de la Crau est très fortement influencée par l'occupation du sol, car elle reçoit en grande partie les excédents d'irrigation gravitaire issus des nombreux canaux provenant de la Durance. Pour la nappe des cailloutis en Camargue, la composition isotopique du pôle « eau douce », très appauvrie, peut correspondre soit à celle du Rhône, soit à celle de la Durance (prélevée ici dans le canal de Centre Crau). En effet, celles-ci ont des compositions isotopiques très proches car alimentées par l'eau de pluie des Alpes. Sur la base des compositions isotopiques, on ne peut donc pas distinguer les deux sources d'alimentation possibles.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :

 1234 Figure 1 : Carte de localisation de l'Ile de Camargue. Le tracé des paléochenaux (StF : saint Férréol ; U : Ulmet ; BF : Bras de Fer) est adapté de Vella et al (2004).

Figure 5 :Figure 6 :Figure 7 :Figure 8 :

 5678 Figure 5 : relation entre les teneurs deuterium et en oxygène-18 dans l'eau de la nappe des cailloutis : les points s'alignent le long d'une droite de mélange entre un pôle « eau de mer » et une pôle eau douce qui peut être soit de l'eau du Rhône, soit de l'eau de la Durance, prélevée dans le Canal de Centre Crau.

Figure 9 :Figure 10 :

 910 Figure 9 : localisation des piézomètres implantés dans les nappes de surface. La taille des cercles est proportionnelle à la salinité de l'eau.

Figure 11 :

 11 Figure 11 : relation entre les teneurs en deutérium et en oxygène-18 dans l'eau des nappes superficielles

Encart 3 : Les nappes souterraines littorales

Dans les zones côtières, il y a un contact direct entre l'eau douce souterraine et la mer. L'eau salée plus dense que l'eau douce a tendance à « se glisser » sous celle-çi formant ainsi un « biseau salé ». En raison du contraste de densité, le niveau de l'eau douce (niveau piézométrique) doit être supérieur au niveau de la mer pour maintenir l'eau salée en profondeur et l'empêcher de remonter. Pour un aquifère sableux homogène, la loi de Ghyben-Herzberg prévoit que la profondeur du biseau salé (par rapport au niveau de la mer) est égale à 40 fois l'altitude du niveau piézométrique (par rapport au niveau de la mer) (z/h≅40, voir figure 2). Dans des environnements de très faible altitude comme la Camargue, le biseau salé peut donc s'étendre très loin dans les terres. Dans ce type de milieu où les vitesses de circulation sont faibles, on ne distingue pas de contact franc entre les deux masses d'eau, mais une salinité diminuant progressivement vers l'intérieur des terres. On doit s'attendre à trouver l'eau douce pure lorsque la profondeur théorique du biseau salé devient supérieure à la profondeur de la couche imperméable qui sert de « plancher » à la nappe. Cet équilibre hydrostatique peut être modifié dans le temps. Une baisse de niveau piézométrique entraîne en effet une intrusion d'eau de mer dans l'aquifère, et une salinisation difficilement réversible, même dans le cas ou le niveau piézométrique reprend sa position initiale. Une remontée progressive du niveau marin a le même effet.