Mireille Aymar

Romain Guérout

Olivier Dulieu
email: olivier.dulieu@u-psud.fr

Structure of the Alkali-metal-atom-Strontium molecular ions: towards photoassociation and formation of cold molecular ions

Keywords: numbers: 31.15.AR, 31.15.Ct, 31.50.Be, 31.50.Df

come

I. INTRODUCTION

As illustrated by two recent review papers [1,2], the success story of researches on ultracold neutral molecules is developing for more than ten years since their first detection in an ultracold cesium gas [3][4][5]. Ultracold molecules indeed offer exciting prospects for fundamental quantum physics and physical chemistry, as well as for interdisciplinary physics and possible applications and for technology. The ultimate control of their external degrees of freedom down to kinetic energies equivalent to temperatures far below 1 mK, and of their internal degrees of freedom at the single (lowest) quantum level [6][7][8][9][10][11][12][13][14], is a crucial path towards the realization of a degenerate quantum gas of ultracold molecules in their absolute ground state. Ensembles of ultracold molecules in well-defined quantum states allow for the observation of cold collisions between atoms and molecules [15][16][17][18]. The control of elementary chemical reactions is now at reach [19][20][21][22][23][24][25], while new light on the quantum behavior of few-body systems is brought through the demonstration of predicted universal laws [26,27].

Many-body physics could be engineered with ultracold polar molecules serving as models for spin lattices with tunable interactions [28], or as quantum bits in the perspective of the long-term achievement of a quantum information device [29,30]. The unprecedented accuracy on transition frequency measurements induced by their ultra-low kinetic energy makes polar molecules suitable for testing fundamental theories, like for instance the variance of the electron-to-proton mass ratio m e /m p [31][32][33] or electron dipole moment (EDM) [17,34].

Besides, molecular ions are well-known for their crucial role in the evolution of many environments like stellar atmospheres or interstellar media [START_REF] Klemperer | Proc. Nat. Acad. Sci[END_REF][START_REF] Herbst | The chemistry of cold interstellar cloud cores[END_REF], and it is highly desirable to create samples of cold molecular ions in order to learn all the details of their quantum dynamics and to control their reactivity [START_REF] Gerlich | The production and study of ultra-cold molecular ions[END_REF][START_REF] Willitsch | [END_REF]. In this matter, electromagnetic traps for ions have long been used [START_REF] Gerlich | The production and study of ultra-cold molecular ions[END_REF]. Novel developments occurred with the demonstration of sympathetic cooling of molecular ions with laser-cooled atomic ions thus forming so-called ion crystals where individual ions are kept at a well-defined positions in space [START_REF] Willitsch | [END_REF]. It is nowadays possible to drive such ions into selected rotational level through additional laserpumping mechanisms [39][40][41]. Just like neutral molecules, cold molecular ions are promising candidates for m e /m p variance [42] or EDM [43,44] measurement.

For such studies, the prerequisite step is obviously the formation of a cold and trapped sample of the desired species of molecular ions which would be sympathetically cooled by laser-cooled and trapped atomic ions. It is now established that excited ions in the trap and surrounding molecular species introduced on purpose easily react together to produce molecular ions, as demonstrated for the first time in Ref. [45] with Mg + and H 2 yielding cold and trapped MgH + ions. With the developing experimental trend of merging traps of lasercooled atoms and ions like Yb-Yb + [46], Rb-Yb + [47,48], Rb-Ba + [49], new opportunities could be investigated to create diatomic molecular ions in situ via e.g. the photoassociationstabilization sequence A + B + + hν → (AB + ) * → AB + + hν ′ , or via magnetoassociation involving Feshbach resonances [50], just like routinely done with cold atoms [2,51,52].

Charge exchange between the neutral and ionic atomic species should also be considered, as explored in the Na-Ca + system [50,53].

The main drawback for accurate theoretical modeling of these formation mechanisms often arises from the poor knowledge of the molecular structure of such mixed species beyond their electronic ground state. As mentioned in our previous work [54] (hereafter referred to as paper I), this is particularly true for the diatomic systems, either neutral or charged, formed from an alkali-metal atom and Strontium. The Strontium ion is indeed an attractive system for trapping and laser-cooling experiments (see for instance Refs. [55,56]). Following paper I, the present work is devoted to the theoretical determination of the electronic structure of (A-87 Sr) + ions (where A= 6 Li, 23 Na, 39 K, 85 Rb, 133 Cs) using the method briefly recalled in Section II. Results for potential energy curves and permanent and transition dipole moments are given in Section III and IV respectively. In Section V we explore the possibility to create cold (A-Sr) + ions via photoassociation followed by spontaneous decay, and the expected reactivity of these ions with surrounding cold neutral atoms. Atomic units for distances (1 a.u.= a0 = 0.052 917 720 859 nm), energies (1 a.u.= 2R ∞ = 219474.63137054 cm -1 ), and dipole moment (1 a.u. =2.541 58 Debye) will be used throughout the paper, except otherwise stated.

II. COMPUTATIONAL APPROACH

The present calculations actually represent an intermediate step of those performed in paper I for neutral A-Sr molecules, which were modeled as effective three-electron systems.

The A-Sr + ion has two valence electrons, and its electronic structure is, at least in terms of values of quantum numbers, similar to the one of alkali dimers. Therefore we describe the A-Sr + ion as an effective two-electron system following the same steps than in paper I and in Ref. [57], which are briefly recalled below.

Each of the closed-shell ionic cores A + and Sr 2+ are represented by an effective core potential (ECP) from Durand and Barthelat [58,59] and Fuentealba et al. [60,61] respectively, completed by the core-polarization potential (CPP) depending on the angular momentum ℓ of the valence electron, along the lines of ref. [62] and revisited by Guérout et al. [63].

The valence electron wave functions are expanded on a Gaussian orbitals centered at each ionic core. The molecular orbitals are determined by restricted Hartree-Fock single electron calculations, including the CPP term yielding the potential curves for the relevant molecular double-charged cations. Then a full configuration interaction (FCI) is performed for each relevant molecular symmetry, providing potential curves, and permanent and transition dipole moments. The calculations are performed through an automatic procedure [57] based on the the CIPSI package (Configuration Interaction by Perturbation of a multiconfiguration wave function Selected Iteratively) [64]. As mentioned in paper I we use for the Sr + ion a large uncontracted basis set {7s6p7d} derived from the {5s5p6d1f } used in Ref. [65], and {8s7p4d}, {7s6p5d}, {7s5p7d}, {7s4p5d}, and {7s4p5d} uncontracted basis sets for Li, Na, K, Rb, and Cs, respectively. All exponents of the Gaussian orbitals, as well as the cut-off radii and the core polarizabilities [66,67] appearing in the CPP term for the alkali species, were already reported in paper I and are not repeated here. The cut-off radii for the Sr 2+ CPP related to the {7s6p7d} basis set are slightly adjusted compared to paper I, i.e. ρ s = 2.13035, ρ s = 2.183, ρ s = 1.70616, in atomic units. The quality of the basis sets is settled through several criteria. First of all, the cut-off radii are adjusted to reproduce the experimental energy of the lowest levels of the alkali atoms and and of the Sr + ion (see Table 3 in paper I). Next, as the lowest dissociation limit of the A-Sr + ions is A + +Sr, the lowest energy level of the -effective two-electron-Sr atom calculated by the FCI above should be well reproduced. As shown in paper I, the present basis set is quite efficient in this respect, as the Sr ground state and 5s5p 3 P , and 5s5p 1 P excited state energies are calculated with a difference of 185 cm -1 , 269 cm -1 , and 434 cm -1 compared to the experimental values, respectively. The corresponding excitation energies of the 5s5p 3 P and 5s5p 1 P levels are obtained with a difference of 87 cm -1 , and 262 cm -1 compared to the experimental values, which represents an accuracy comparable to the one achieved in the recent high-accuracy calculations on Calcium by Bouissou et al. [68].

In addition, the quality of the electronic wave functions of the Sr + ion can be checked against the calculated static dipole polarizability, which has been studied theoretically for several energy levels in various contexts: the broadening of spectral lines due to collisions with hydrogen atoms [69], the long-range interaction between the Sr + ion and various atomic species [70,71], or the search for stable and reproducible atomic frequency standards based on the 5s -4d 5/2 clock transition in 88 Sr + [72][73][74]. All these calculations are based on the summation over oscillator strengths at various levels of approximations, namely including transitions towards the continuum [70,71] or not [69,73,74]. Here we use the finite field method [75] for the contribution of the valence electron, as in Ref. [76] and in our previous work on alkali atoms [77]. More precisely we calculated the energies of the 2ℓ+1 components of an atomic state with angular momentum ℓ in the presence of an electric field varying from 0.002 to 0.004 a.u., and extracted the polarizability from the quadratic dependence of the averaged values against the electric field magnitude. Finally we add the contribution of the Sr 2+ core (5.67 a.u after Ref. [66]), as pointed out in Ref. [78]. Our results are reported in Table I for the 5s, 4d, 6s, 5d, and 5p levels. Our values for the 5s and 4d states agree well with all other values except the oldest one of Ref. [76], and are in reasonable agreement with the most recent ones of Ref. [71] for the excited p and s levels. The underestimation visible in our calculations for the d levels could be due to the absence of f orbitals in our basis sets.

We calculated with the same approach the polarizability of Sr in its ground state (Table I) which agrees with less than a 10% difference with the experimental value of Ref. [79], as well as with the recent theoretical value of Ref. [80]. All other theoretical determinations are larger by 20% or more. A new experimental determination of electric dipole polarizability of strontium then seems desirable to discriminate among all determinations.

III. POTENTIAL CURVE CALCULATIONS

An overview of the results obtained from the procedure above for the potential curves of the A-Sr + ions is provided in Figs. 2 to 6, while the main spectroscopic constants are reported in Tables II to VI. In the tables, we recall for convenience the dissociation energies compared with other calculated values. We added the Sr 2+ polarizability of 5.67 a.u. [66] to the values of Refs. [69,73]. The indexes DF and HF hold for Dirac-Fock and Hartree-Fock level of calculation, respectively. The static dipole polarizability for the Strontium ground state is also displayed, compared to several theoretical values, and an experimental result [79].

of the asymptotic limits as displayed in paper I. Let us note that no other results for these systems have been previously published. The corresponding numerical data are provided as additional material accompanying the paper.

For all ions, the ground state X 1 Σ + of the system correlates at large distances to a ground-state neutral Sr atom and a closed-shell alkali-metal ion. The ordering of the well depths is the same than with neutral A-Sr molecules [54]: the deepest wells are by far the LiSr + and NaSr + ones (11157 cm -1 , and 8330 cm -1 , respectively), while the well depths of KSr + , RbSr + , CsSr + are significantly smaller (Fig. 1). This can be understood as the energy spacing between the two lowest dissociation limits increases with increasing alkalimetal atom mass: the X 1 Σ + state is less and less repelled by the next (2) 1 Σ + state, and the X state behaves more and more like a van der Waals molecule composed of two closedshell systems A + and Sr(5s 2 ). The equilibrium distances are comparable to the typical values of alkali dimers (see for instance Ref. [84] where a sketch of potential curves for all heteronuclear alkali-metal dimers is displayed) as the molecules are formed by two openshell partners. At the second dissociation limit, one valence electron is attached to each atomic partner, giving rise to a singlet and a triplet state at short internuclear distances. Despite this similarity with the lowest electronic states of ground state alkali-metal pairs, the situation is here strikingly different: the lowest triplet state (1) 3 Σ + (also referred to as the a 3 Σ + state) potential curve is strongly attractive while the accompanying singlet state (2) 1 Σ + (also referred to as the A 1 Σ + state) potential curve is mostly repulsive, due to the strong repulsion induced by the X 1 Σ + ground state. The (2) 1 Σ + would actually represent a strong dissociation channel induced by spin-orbit coupling for the (1) 3 Π state if collisions between alkali-metal ions and neutral Strontium were studied. However, as a reciprocal effect of the larger and larger energy spacing between dissociation limits invoked above, the heavier A-Sr + molecule, the deeper long-range potential well in the (2) 1 Σ + potential curve.

The (1) 3 Σ + is significantly deeper (several thousands of cm -1 ) than the one of alkalimetal dimers (generally having a few hundreds of cm -1 depth, see Ref. [84] again). Indeed, the charge-induced dipole long-range attraction (varying as R -4 , where R is the internuclear distance) between Sr + and the alkali-metal atom is stronger than in the alkali-metal pairs (varying as R -6 ), and dominates the (repulsive) exchange interaction down to short distances. As the static dipole polarizability (determining the strength of the long-range A-Sr + interaction) increases with increasing alkali-metal atom mass, the depth of the (1) 3 Σ + increases, and becomes even larger than the X 1 Σ + well depth for KSr + , RbSr + , CsSr + . Note that this trend is similar to what is also observed for the RbBa + ion [85].

The combination of the excitation energies of Sr + , of Sr, and of the alkali-metal atoms induces the main differences for excited molecular states among the five different A-Sr + species. For instance, the LiSr + molecule is the only one where the dissociation limit with the alkali-metal atom excited in its lowest p level has an energy larger than the one involving Sr(5s5p 1 P ). The Li(2p)+Sr + (5s) dissociation limit actually lies only 178 cm -1 above the Li(2s)+Sr + (4d) one. Similarly, the LiSr + and NaSr + species are the only ones in which the dissociation limit involving the Sr + (4d) level has a binding energy smaller than the one involving Sr(5s5p 1 P ). In this respect, the KSr + , RbSr + , CsSr + exhibit similar patterns in their excited states. Let us note that due to these differences, the lettered labels A, B, C, D, E, a, b, c of the molecular states, which is historically related to their energy ordering, will not always be attached to the same dissociation limits in the A-Sr + series. The consequences of such characteristics for the dynamics of the A-Sr + systems will be further addressed in Section V below. Among all the excited states, there are two cases where the corresponding potential curves exhibit remarkable features. First the (2) 3 Σ + curve is strongly repelled by the attractive (1) 3 Σ + one so that it strongly interact through an avoided crossing with the (3) 3 Σ + curve located in the 9-12 a.u. distance range. For all species but LiSr + , it induces a strong mixing of the 3 P and 3 D states of Strontium, starting from large distances. This will undoubtedly lead to significant predissociation of the (3) 3 Σ + bound levels, without charge exchange. This creates a second long-range well in the (2) 3 Σ + curve, which almost disappears in CsSr + due to the continuous decrease of the ionization potential of the alkali species with increasing mass. In the LiSr + , this would actually represent a channel for charge exchange, as the (3) 3 Σ + is correlated to the Li(2s)+Sr + (4d) limit.

Second, the pair of states (3) 1 Σ + and (4) 1 Σ + show a similar pattern while slightly more complicated. For the KSr + , RbSr + , and CsSr + species, these two states dissociate toward the neighboring A + +Sr( 1 D) and A + +Sr( 1 P ) limits, resulting into an avoided crossing in the 12-15 a.u. distance range, with a second long-range potential well in the (3) 1 Σ + curve. In LiSr + a similar pattern is predicted between these two states, except that their interaction corresponds to an exchange of excitation for the Li atom, due to the different ordering of the excitation energies in the various species. In between, the NaSr + ion should exhibit a curious feature: the interaction between these two states results from the proximity of the Na(3s)+Sr + (4d) and Na + +Sr( 1 D) limits, so that two successive avoided crossings are visible. Our results suggest that these crossings are quite small, so that it could well be that these two states behave independently in a collision process. The (4) 1 Σ + is expected to have a double-well structure as well, which disappears in RbSr + and CsSr + . These features are actually at the limit of the capabilities of our computations and would require a much larger basis set for an appropriate representation.

IV. PERMANENT AND TRANSITION DIPOLE MOMENTS, STATIC DIPOLE

POLARIZABILITIES

Permanent dipole moments (PDM) are relevant to the present study, i.e. if molecular ions in the X 1 Σ + ground state or in the a 3 Σ + metastable state are created in experiment manipulating cold Sr + and alkali-metal atoms: PDMs will determine the ability to perform vibrational or rotational cooling following for instance methods recently demonstrated for MgH + [40] and HD + [39]. The PDM is here calculated in the body-fixed frame with respect to the origin placed at the center-of-mass of the molecule, and is therefore characterized by a linear divergence at large internuclear distances expressing the increasing distance between the negative and positive center-of-charge. Our results are reported in Fig. 7 for these two electronic states and for all A-Sr + species, confirming this pattern. The molecular axis is oriented along the Sr + -A direction, so that the positive sign of the ground state PDM indicates an excess of electron charge on the alkali-metal atom, which is less pronounced as its mass increases. This is compatible with the decrease of the electron affinity of alkalimetal species with their increasing mass. The PDM is almost linear in the region of the minimum of the ground state, so that radiative transitions among vibrational levels levels should be possible. Its magnitude is also significant, so that rotational transitions should be observed. In contrast the sign of the triplet PDM, while mostly positive, cannot be easily interpreted over the whole distance range. Note that its dissociation limit is different from the ground state one, so that its divergence at large distances is different. Its magnitude is almost constant (and even close to zero for CsSr + ), which therefore is probably not a good candidate for cooling of internal degrees of freedom. As a complement to the description of the properties of the A-Sr + molecules, we computed their static dipole polarizabilities (SDP), which will be relevant for instance when considering the long-range interaction with surrounding cold neutral alkali-metal atoms in a merged cold ion/atom trap experiment.

+ (2) 1 Σ + (3) 1 Σ + (2) 1 Π (1) 1 Π (1) 3 Σ + (2) 3 Σ + (1) 3 Π Li(2p)+Sr + (5s) (1) 1 Σ
+ (2) 1 Σ + (3) 1 Σ + (2) 1 Π (1) 1 Π (1) 3 Σ + (2) 3 Σ + (1) 3 Π Na + +Sr( 1 D) Na + +Sr( 3 D) (1) 1 Σ
As pointed out in Ref. [78], the SDP includes a core contribution (5.67 a.u. here, see Table II of paper I) in addition to the valence contribution, the latter being evaluated using the finite field method [75]. Both parallel α (along the internuclear axis), and perpendicular α ⊥ components (see Fig. 8) exhibit an R-variation similar to the one obtained for alkali dimers [77], alkali hydrides [86], for MgH + [87], or for the hydrogen molecule [88]. In all these systems, α has a maximum at a distance larger than the equilibrium distance R e of the system, while α ⊥ always has a smaller magnitude than α , and monotonically increases towards the asymptotic limit. Around the equilibrium distance, α ranges between 200 and 250 a.u., and α ⊥ between 120 and 150 a.u.. As for the well depth the maximum of α increases as the mass of the A-Sr + molecule decreases. At large distances, both components converge (1)

1 Σ + (2) 1 Σ + (3) 1 Σ + (2) 1 Π (1) 1 Π (1) 3 Σ + (2) 3 Σ + (1) 3 Π K + +Sr( 1 D) K + +Sr( 3 D) K + +Sr( 1 P) (2) 3 Π (3) 3 Σ + FIG. 4
. Same as Fig. 3 for KSr + .

toward a unique limit corresponding to the sum of SDP of the Sr ground state and the (small) SDP of the alkali-metal ions. Finally, the electronic transition dipole moments (TDM) are relevant when considering for instance the possibility for radiative charge exchange (RCE) in these systems [50,53], or for photoassociation (PA) and spontaneous emission (SE) (see next section). We have computed all TDMs of all A-Sr + species, whose numerical data are provided through the EPAPS system. In order to illustrate them, we chose the LiSr + and the RbSr + molecules as being representative of the A-Sr + species (see Section III). We represent in Figs. 9 and 10 the TDMs involving X 1 Σ + , (2) 1 Σ + and a 3 Σ + as the lowest states. For the sake of clarity, we will use both numbered (in parenthesis) and lettered (when available, in brackets) notations for the molecular states. Various patterns can be analyzed in these figures.

The most obvious one is when the TDM function connects two molecular states which dissociate towards atomic states connected by a resonant transition, as for the (1) (1)

1 Σ + [X] -
1 Σ + (2) 1 Σ + (3) 1 Σ + (2) 1 Π (1) 1 Π (1) 3 Σ + (2) 3 Σ + ( 1
1 Σ + [X]-(2) 1 Σ + [A], (1) 1 Σ + [X]-(1) 1 Π[B]
, and (1) reflect the different ordering of the asymptotic limits compared to the other species. For both species represented in 9b and 10b, the TDM functions for the (1

1 Σ + [X]- (3
) 3 Σ + [a] -(2) 3 Σ + [c]
( The experiments aiming at merging a cold Sr + trap and a cold alkali-metal atom trap involve molecular states connected to the second dissociation limit, i.e. the (2) 1 Σ + [A] and the (1) 3 Σ + [a] states. Despite the strong variation of the [X] -[A] TDM between 10 and 20a.u., it is most probable that the RCE process during a cold collision between ground state alkali-metal atom A and Sr + will be weak as the TDM rapidly vanishes with R. This is actually the trend already reported in Ref. [53] for Na-Ca + collisions. However, as it is possible to trap clouds of laser-cooled Sr + ions for hours, it may be possible to observe the slow decreasing of Sr + ions, while the A + alkali-metal ions will manifest as dark spots in the ion crystal. The trapped ions are continuously illuminated by the cooling lasers, so that excited alkali-metal atom A * in their lowest p state are present. In this perspective, the Li-Sr + exhibits a peculiar situation: as noticed in Section III the Li(2p)+Sr + (5s) limit lies only 178 cm -1 above the Li(2s)+Sr + (4d) one. The transition between the [D] and [E] II.

[X]-[A] [X]-[C] [X]-[B] [X]-[D] [A]-[C] [A]-[B] [A]-[D] [X]-[E] [A]-[E] [A]-[E]
mechanism is predicted for the formation of metastable (1) 3 Σ + ions in deeply-bound levels via the excitation of the (3) 3 Σ + . PA of Rb and Sr + pairs are expected using a wavelength detuned to the red of the 5s 2 -5s5p 1 P Sr + resonance. An efficient decay is expected to take place from the inner turning point of the (4) 1 Σ + . Another path could be the excitation at the turning point of the (2) 1 Σ + toward the (2) 1 Π, which would be stabilized into the lowest ground state levels. No triplet states will ba accessible in such a scheme. But the spin-orbit coupling have been neglected so far. It is quite large in the Sr + ion (280.34 cm -1 for the 4d level, and 801.46 cm -1 for the 5p level [START_REF] Moore | Atomic energy levels[END_REF]), and comparable in some cases with the one of alkali-metal atoms (0.29, 17.2, 59.7, 237.9, and 551.3 cm -1 , for Li, Na, K, Rb, and Cs, respectively). This will induce additional couplings between molecular states of various symmetries. For instance, the spin-orbit interaction will strongly mix the (2) 1 Π and the (3) 3 Σ + , probably leading to strong predissociation channels with charge exchange into the Once ASr + ions are formed, the important issue of their stability against charge exchange with the surrounding cold alkali-metal atoms is raised, just like in the proposal of Ref. [START_REF] Hudson | [END_REF] looking at possible sympathetic cooling of molecular ions by laser-cooled atoms.

[X]-[A] [X]-[C] [X]-[B] [X]-[D] [A]-[C] [A]-[B] [A]-[D] [X]-[E] [A]-[E]
In our case, the ionization potential (IP) of alkali-metal atoms should be larger than the IP of the related neutral molecule. Combining the present results with those of paper I for the ground state of neutral ASr molecules, we estimate their IP by the energy difference between the minimum D e of their ground state potential curves according to: IP(ASr)=IP(A)+D e (ASr)-D e (ASr + ). Using the experimental IP for alkali-metal atoms [START_REF] Moore | Atomic energy levels[END_REF], namely 43487, 41449, 35009, 33691, and 31046 cm -1 for Li, Na, K, Rb, and Cs respectively, we find IP(LiSr)=34848 cm -1 , IP(NaSr)=34716 cm -1 , IP(KSr)=31198 cm -1 ,

State Label

Diss. limit E diss (a.u.) δ(cm -1 )) R e D e ω e

(1) 1 Σ + X Li + +Sr(5s ) and the harmonic constant ω e (in cm -1 ). For convenience, we recall the calculated dissociation energies E diss , and their difference with the experimental ones [54]. The ( * ) sign denotes double-well potentials, for which the barrier height and the energy at the minimum of each well are displayed (in italic) with respect to the dissociation limit, besides their position in R.

State Label

Diss. limit E diss (a.u.) δ(cm -1 )) R e D e ω e

(1) The ω e value is not reported for the (3) 3 Σ + curve, as it is not significant, due to the peculiar shape of the well induced by the interaction with the (2) 3 Σ + state.

FIG. 1 .

 1 FIG.1. Potential energy curves of the X 1 Σ + ground state of A-Sr + ions, all referring to the energy origin fixed at the A+Sr + dissociation.

FIG. 3 .

 3 FIG.3. Potential energy curves of the NaSr + molecule computed in the present work. Line types as in Fig.2. Note that curves of ∆ symmetry are not drawn for clarity sake.

FIG. 5 .( 1 S - 1 P

 511 FIG.5. Same as Fig.2for RbSr + .

) 1 Σ

 1 + [C] vanishes at large distances, with strong variations at short internuclear distances again related to strong configuration interaction. The same analysis holds for transitions involving the [A] state. In particular, the states connected to [A], i.e. [C], [D], and [E] have vanishing TDMs at large distances, as they correspond asymptotically to different charge states of the separated atoms. A similar reasoning can be made for LiSr + , where the results

+FIG. 6 .

 6 FIG.6. Same as Fig.3CsSr + .

FIG. 7 .

 7 FIG. 7. Permanent dipole moments (a.u.) of (a) the X 1 Σ + ground state and (b) the a 3 Σ + metastable state of the A-Sr + molecules computed in the present work. The origin is taken at the center-of-mass of the molecule, considering the 87 Sr, 6 Li, and 85 Rb isotopes. The position of equilibrium distances are shown with vertical dashed lines.

1 ΣFIG. 8 .

 18 FIG. 8. (a) Parallel and (b) perpendicular components of the static dipole polarizability (in a.u., 1 a.u.=0.148 184 709 3 Å3 ) of the X 1 Σ + ground state of the A-Sr + molecules computed in the present work. The position of equilibrium distances are shown with vertical dashed lines.

FIG. 9 .

 9 FIG. 9. Selected transition dipole moments between (a) singlet states, and (b) triplet states, for LiSr + . Molecular states are labeled with letters as in TableII.

FIG. 10 .

 10 FIG. 10. Selected transition dipole moments between (a) singlet states, and (b) triplet states, for RbSr + . Molecular states are labeled with letters as in TableV.

TABLE I .

 I Static dipole polarizability of 5s 4d, 5d and 6p states of Sr + ion (in atomic units)

	State This work [71]	[73]	[74] [70] [69] [76]
	5s	92.7	89.8	84.6	91.3 91.47 93.1 130.5
	4d	53.3	61.77	53.7	62	57
	5p	-49.2	-23.13			-32
	6s	1305	1089
	5d	1294	2099
	6p	-2016	-2056
		This work [79] [81]-DF-HF [82] [83] [76] [80]
	5s 2	200	186±14 228-241 186 225 245.7 197.2

TABLE II .

 II Main spectroscopic constants of the lowest electronic states (with their conventional spectroscopic label) of the LiSr + molecule: the equilibrium distance R e (in atomic units), the well depth D e (in cm-1

				2 1 S) -0.61548	-184	6.37 11126 246
	(2) 1 Σ +	A	Li(2s)+Sr + (5s) -0.60350	0	15.33 277 35.4
	(1) 3 Σ +	a	"	"	"	7.48 4865 163
	(1) 3 Π	b Li + +Sr(5s5p 3 P ) -0.54890	-274	5.90 11087 268
	(2) 3 Σ + ( * ) c	"	"	"	6.90 -5086 190
	2 nd well		"	"	"	12.1 -3205 76
	barrier		"	"	"	9.80 -2652 -
	(1) 1 Π	B	Li(2s)+Sr + (4d) -0.53641	0	7.14 6150 175
	(3) 1 Σ + ( * ) C	"	"	"	7.32 -5479 130
	2 nd well		"	"	"	13.8 -1297 -
	barrier		"	"	"	12.9 -1259
	(3) 3 Σ +		"	"	"	9.54 5722 69
	(2) 3 Π		"	"	"	7.21 6098 58
	(1) 1 ∆		"	"	"	6.92 7851 194
	(1) 3 ∆		"	"	"	6.97 8003 193
	(2) 1 Π	D Li(2p)+Sr + (5s) -0.53559	0	6.64 2460 198
	(4) 1 Σ + ( * ) E	"	"	"	7.87 -1183 260
	2 nd well		"	"	"	12.59 -1255 157
	barrier		"	"	"	9.32 +591 -

TABLE III .

 III Same as TableIIfor NaSr + . For the (3) 1 Σ + state, the barrier actually refers to the position of its pseudocrossing point with the (4) 1 Σ + curve. Due to the peculiar shape of the latter potential curve, two barriers are identified.

	1 Σ +	X	Na + +Sr(5s 2 )	-0.61548	-184 6.92 8330 121
	(2) 1 Σ +	A	Na(3s)+Sr + (5s) -0.594215	0	14.8 319 21
	(1) 3 Σ + (1) 3 Π State Label a b Na + +Sr(5s5p 3 P ) -0.54890 " " Diss. limit E diss (a.u.) δ(cm -1 )) R e " 8.03 4363 83 D e ω e -274 6.58 7491 127 (1) 1 Σ + X Rb + +Sr(5s 2 ) -0.61548 -184 8.49 3638 55 (2) 3 Σ + ( * ) c " " " 7.43 -2765 98 (2) 1 Σ + A Rb(5s)+Sr + (5s) -0.55886 0 14.0 848 21 2 nd well " " " 13.1 -2417 39 (1) 3 Σ + a " " " 9.41 6121 48
	barrier (2) 3 Π (1) 3 Π (2) 3 Σ + ( * ) c b Rb + +Sr(5s5p 3 P ) -0.54890 " " Na + +Sr(5s4d 3 D) -0.52991 " " (1) 3 ∆ " " 2 nd well " " (3) 3 Σ + " " (1) 1 Π B barrier " " Na(3s)+Sr + (4d) -0.52712 (2) 3 Π Rb + +Sr(4s3d 3 D) -0.52991 (3) 1 Σ + ( * ) C " " (1) 3 ∆ " " 2 nd well " " (3) 3 Σ + " "	" -274 7.90 3390 59 9.8 -1017 -343 7.80 5542 85 " 8.83 +1492 46 " 7.45 7091 98 " 18.0 -864 15 " 9.90 4297 148 " 11.2 +2537 -0 7.64 5911 90 343 9.32 2122 42 " 7.95 -5402 86 " 8.90 2632 47 " 13.4 -2536 -" 11.3 1529 -
	barrier (1) 1 Π (1) 1 ∆ (3) 1 Σ + ( * ) C B Rb + +Sr(5s4d 1 D) -0.52073 " " " " " " (3) 3 Π " " 2 nd well " " (4) 3 Σ + " " barrier " " (2) 3 ∆ " " (2) 1 Π (1) 1 ∆ " " D Na + +Sr(5s4d 1 D) -0.52073 (2) 1 Π D Rb + +Sr(5s5p 1 P ) -0.51779 (4) 1 Σ + ( * ) E " " " " 2 nd well (4) 1 Σ + E " "	" 460 " " " " " " " " 460 -442 9.18 1554 33 12.2 -2113 -9.0 3056 43 7.41 7438 98 9.15 -2650 44 17.8 149 131 16.0 -1135 17 19.0 175 91 13.6 -941 -17.9 157 134 8.77 3989 50 7.32 3166 90 " 8.15 -2008 129 " 14.3 -1191 106 " 13.7 925 -
	1 st barrier		"	"	"	9.79 -516 -
	2 nd barrier		"	"	"	13.6 -1158 -

TABLE V .

 V Same as TableIIfor RbSr + . The ω e value is not reported for the (3) 3 Σ + and (4) 1 Σ + curves, as it is not significant, due to their peculiar shape.

	State Label	Diss. limit	E diss (a.u.) δ(cm -1 )) R e	D e ω e
	(1) 1 Σ +	X	Cs + +Sr(5s 2 )	-0.61548	-184 9.05 2714 44
	(2) 1 Σ +	A	Cs(6s)+Sr + (5s) -0.54845	0	13.9 1133 20
	(1) 3 Σ +	a	"	"	"	9.90 7003 41
	(1) 3 Π	b Cs + +Sr(5s5p 3 P ) -0.54890	-274 8.30 2738 49
	(2) 3 Σ + ( * ) c	"	"	"	9.38 +2293 37
	2 nd well		"	"	"	22.5 -62 5
	barrier		"	"	"	12.0 -1133
	(2) 3 Π		Cs + +Sr(4s3d 3 D) -0.52991	343	9.90 1450 33
	(1) 3 ∆		"	"	"	9.46 1779 37
	(3) 3 Σ +		"	"	"	12.4 794 -
	(1) 1 Π	B Cs + +Sr(5s4d 1 D) -0.52073	460	9.41 2358 33
	(3) 1 Σ + ( * ) C	"	"	"	9.67 -1874 35
	2 nd well		"	"	"	17.0 -784 13
	barrier		"	"	"	14.2 -607
	(1) 1 ∆		"	"	"	9.29 2987 41
	(2) 1 Π	D Cs + +Sr(5s5p 1 P ) -0.51779	-442 9.67 1277 30
	(4) 1 Σ +	E	"	"	"	14.6 597 58

TABLE VI .

 VI Same as Table II for CsSr + .

IP(RbSr)=31126 cm -1 , IP(CsSr)=29416 cm -1 . Therefore we predict that the ASr + ions will be all stable against charge exchange with alkali-metal atom A. ACKNOWLEDGMENTS R.G. gratefully acknowledges support from Institut Francilien de Recherches sur les Atomes Froids. This work has been performed in the framework of the network "Quantum Gases of Dipolar Molecules" of the EUROQUAM program of the European Science Foundation (ESF).

State Label

Diss. limit E diss (a.u.) δ(cm -1 )) R e D e ω e

(1) 1 Σ + X K + +Sr(5s The ω e value is not reported for the (3) 3 Σ + curve, as it is not significant due to the peculiar shape of the well induced by the interaction with the (2) 3 Σ + state.


Florence De La Barrière
email: florence.delabarriere@onera.fr

Guillaume Druart

Nicolas Guérineau

Yann Ferrec

Jean Taboury

Jérôme Primot

Random phase mask in a filamentation regime: application to the localization of point sources

We present a new optical system with an extended point spread function (PSF) for the localization of point sources in the visible and infrared spectral ranges with a subpixel precision. This compact system involves a random phase mask (RPM) as its unique component. It exhibits original properties, since this RPM is used in a particular regime, called "filamentation regime", before the speckle region. The localization is performed by calculating the phase correlation between the PSF and the image obtained under off-axis illumination. Numerical simulations are presented to assess the basic optical properties of this RPM in the filamentation regime.

The localization of point sources is an important issue, which has been widely addressed in literature. It has been shown that an extended optical point spread function (PSF) is of particular interest for the localization of point sources which are separated by a subpixel distance with a great precision [1]. Optical systems with an extended PSF have already been described. Some are based on coded apertures, which were originally used for imagery in the fields of X-rays and gamma rays [2], such as random arrays of pinholes [3]. Due to the issues which arise when it comes to adapting coded apertures to the visible and infrared spectral ranges [4], alternatives have been proposed: in [1], a pseudorandom phase mask is associated with a lens, resulting in an extended PSF of the overall system. This principle is emphasized in [5], which describes a multichannel system based on the TOMBO principle [6], where the PSF of each channel is extended thanks to an array of Zernike phase masks. In this Letter, we propose removing the lens in the system described in [1]. Then the random phase mask (RPM) is used as the unique component. This approach follows a general trend which consists in designing optical systems with a minimal number of elements (an aperture stop, an optical component and a detector) [7]. Moreover, we propose making use of the RPM in an original regime, called "filamentation regime", before the speckle region. Based on simulations, this Letter aims at showing that the RPM used in the filamentation regime has an extended PSF which enables the localization of point sources with a subpixel precision.

The RPM which is considered in this study is a thin plate with an index of refraction n. One face of the plate is flat, and the other face has a stationary Gaussian random surface roughness. The height difference between the mean flat surface and the random surface at point r of the surface is denoted h(r) (cf. Fig. 1(a)). The probability density function of the roughness of the surface h(r) is Gaussian, and expressed in the following way:

P h (h) = 1 √ 2Πσ h 2 exp ( - h 2 2σ h 2 ) , (1)
where σ h stands for the standard deviation of the random variable h. The covariance of h is radial, and is given by:

Cov hh (r) = σ 2 h exp ( - r 2 2R 2 c ) . ( 2
)
The RPM is thus described by three parameters: its index of refraction n, the standard deviation σ h of the roughness h, and the size of the spatial pattern of the phase mask R c . We assume that the phase introduced by the mask has smooth spatial variations, which means that R c >> σ h >> λ, where λ is the wavelength. If we consider that the mask is thin, the transmittance t(r) at point r of the component is given by :

t(r) = exp ( j 2Π λ (n -1)h(r) ) disc ( r a ) , ( 3
)
where a is the radius of the pupil, and disc is the function defined as: disc(r) = 1 if ∥ r ∥≤ 1, and disc(r) = 0 otherwise.

To calculate the PSF of the RPM, the component is illuminated by a monochromatic plane wave parallel to its optical axis (λ = 500nm). Using the formalism of Fresnel wave propagation in free space, the intensity distribution is calculated in transversal planes beyond the RPM along the z-axis. We note d the distance between the exit plane of the RPM and the observation plane (cf. Fig. 1(a)). While d increases, we first observe the formation of filaments in the image, followed by the speckle regime. The distance for which the filaments are the thinnest is considered to be the optimal working distance d opt of the RPM, because the energy is concentrated in specific zones of the image. This corresponds to an original regime which we call "filamentation regime". Since our goal is to obtain a very textured image, we define a signal-to-noise ratio by the following equation:

SN R = √ V ar(I) E[I] , ( 4
)
where The optimal working distance d opt can be interpreted in terms of conventional optical components. Indeed, as the shape of the mask is smooth with respect to the wavelength, the RPM can be seen as a collection of small toroïdal lenses, whose focal lengths are given by the local curvatures of the surface. Besides, from several simulations of the RPM (carried out by varying its definition parameters n, R c and σ h ), we have inferred an empirical formula for the optimal working distance of the RPM:

I
d opt = 1 2(n -1) R 2 c σ h (5)
We can notice that d opt is the focal length of a planoconvex lens of diameter 2R c and of on-axis thickness σ h , when R c >> σ h . If we do not take into account the variation of n with λ, we can see that d opt does not depend on the wavelength and thus assume that the filamentation regime is achromatic. The intensity distributions in transversal planes for two values of d are shown in Figs. 1(c) (in the filamentation regime) and 1(d) (in the fully developed speckle regime). These illustrations are obtained with a RPM defined by the following parameters: R c = 80µm, σ h = 3µm and n = 1.45. Figs. 1(c) and 1(d) result of the superposition of monochromatic images obtained for three values of wavelengths: λ blue = 400nm (blue channel), λ green = 500nm (green channel) and λ red = 600nm (red channel). According to the theory related to speckle phenomena, the fully developed speckle regime is chromatic (because the size of the speckle pattern depends on λ). However, as expected, the filaments are white in the filamentation regime, which means that their position in the image plane is achromatic (except a few irisations which we can see in Fig. 1(c)).

An optimal configuration for the localization of point sources is obtained when the size of the RPM is greater than the size of the detector [3]. The on-axis overall PSF of the RPM is illustrated in Fig. 2(a). Fig. 2(b) shows the portion of the on-axis PSF which is imaged on the detector. We now focus on the off-axis behaviour of the RPM: the component is illuminated by a monochromatic plane wave which is tilted with an angle equal to 10 • with respect to the optical axis; the intensity pattern is shown in Fig. 2(c). Fig. 2(d) illustrates the portion of this off-axis pattern imaged on the detector. The phase correlation [9] of the images illustrated in Figs. 2(d) and 2(a) exhibits a two-dimensional very thin spot. The profile of this thin spot along one axis is shown in Fig. 3. Then, the barycentre of this thin spot gives the position of the point source.

The correlation peak can be used to define the angular resolution IF OV of the system: IF OV = F W HM/d opt , where F W HM is the full width at half maximum of the phase correlation peak (cf. Fig. 3). For this simulation, we find a F W HM equal to 8.8µm for d opt = 2.4mm, which leads to IF OV = 0.2 • . It is worth mentioning that in this Letter, the definition parameters of the RPM have not been optimized to decrease IF OV : IF OV can then be chosen for a given application by properly adjusting the RPM parameters.

To conclude, we have shown that a RPM used as the unique component in the filamentation regime generates an extended PSF, which enables to perform the localization of point sources with a subpixel precision. It exhibits several advantages. One of these is that it can be very compact, provided a suitable choice of its parameters n, R c and σ h . Moreover, we can notice that the on-and off-axis images (Figs. 2(a) and 2(c)) are very similar, except from the global translation of the intensity distribution in the observation transverse plane. Therefore, the RPM suffers from a low amount of off-axis aberrations; then, we could expect that this component will have a great field of view. Within future work, we are

  is the intensity in the observation plane, V ar(I) and E[I] are respectively the variance and the mean value of I over the geometric projection of the pupil on the image plane. Thin filaments lead to high SN R. Fig. 1(b) shows the calculated SN R under monochromatic illumination (λ = 500nm) as a function of the distance d. The optimal working distance d opt of the RPM corresponds to the value of d for which the SN R is maximum. When d is greater than Πa 2 /λ (in the Fraunhofer diffraction regime), the curve tends towards 1, which is the value of the SN R of a fully developed speckle [8].

Fig. 1 .

 1 Fig. 1. (Color online) (a) Illumination of the RPM by a plane wave, (b) Calculated SN R under monochromatic illumination as a function of d, (c) Polychromatic intensity distribution at the optimal working distance, (d) Polychromatic intensity distribution in speckle regime.

Fig. 2 .

 2 Fig. 2. (Color online) (a) On-axis monochromatic PSF of the RPM, the red square stands for the position and the size of the detector, (b) Portion of the on-axis PSF imaged on the detector, (c) Off-axis monochromatic illumination of the RPM (angle of incidence of the plane wave: 10 • ), (d) Portion of (c) imaged on the detector.

Informational Fourth Page

In this section, full versions of citations to assist reviewers and editors (OL publishes a short form of citations) are provided.


Michael R Kunze

Rudolf Taube
email: cur.taube@web.de

Prof. Dr Rudolf Taube Fuchsienweg

-Dimethylpentadienyl-Komplexe des Neodyms, Lanthans und Yttriums als Präkatalysatoren für die stereoselektive Butadienpolymerisation 2,4-Dimethylpentadienyl Complexes of Neodymium, Lanthanum and Yttrium as Precatalysts for the Stereoselective Polymerization of Butadiene

Keywords: Butadiene polymerization, Catalysis, Neodymium, Lanthanum, Yttrium Butadiene polymerization, Catalysis, η 5 -2, 4-Dimethylpentadienyl complexes, Lanthanum, Neodymium, Yttrium

To extend the investigation of the applicability of 2,4-dimethylpentadienyl rare earth metal complexes as pre-catalysts for stereoselective butadiene polymerization, a selection of new neodymium, lanthanum and yttrium complexes were previously supplied with detailed structural characterization. We report herein our observations on the catalytically nature of 2,4-dimethylpentadienyl rare earth metal complexes. Under standard conditions the complexes are catalytically inactive. In order to successfully activate the coordinatively saturated complexes aluminium trialkyls AlMe 3 , AlEt 3 , and Al(i-Bu) 3 , aluminoxanes methylaluminoxane (MAO), hexaisobuthylaluminoxane (HiBAO) and modified methylaluminoxane with an Al(i-Bu) 3 additive (MMAO) and diethylaluminium bromide were employed as cocatalysts. The actual catalyst is believed to be a soluble mono(2,4-dimethylpentadienyl)neodymium(III) dianion complex, through which an insertion of 1,3-butadiene in the pentadienylneodymium(III) bond causes the catalysis of the chain growth to be initiated. From these investigations a substantial further insight into the chemistry of (2,4-dimethylpentadienyl)lanthanide(III) complexes was gained and the special applicability of the neodymium complexes for the preparation of highly active catalyst for the 1,4-cis-polymerization of 1,3-butadienes was demonstrated.

Einleitung

Die Katalysatorentwicklung zur stereoselektiven Butadienpolymerisation ist ein wissenschaftlich nach wie vor hochaktuelles Gebiet und auch industriell von besonderem Interesse [START_REF] Porri | Conjugated Diene Polymerization[END_REF][2][START_REF] -H. Thiele | [END_REF][4][5]. Zur Erzeugung des industriell vor allem für die Reifenproduktion in größerem Maßstab produzierten naturkautschukähnlichen 1,4-cis-Polybutadiens werden bereits seit Anfang der 80er Jahre verstärkt auch neodymhaltige ZIEGLER-NATTA-Katalysatoren eingesetzt [6]. Das hat weitere Untersuchungen zur lanthanoidkomplexkatalysierten Butadienpolymerisation außerordentlich stimuliert [7].

In unter breiter Variation des Lanthanoid(III)-Ions beschrieben worden. Offen bleiben bei diesen und anderen Kombinationen die Bildung und Struktur des eigentlichen Katalysatorkomplexes und damit auch die ursächliche, d. h. mechanistische Begründung der gefundenen katalytischen Eigenschaften hinsichtlich Aktivität und Selektivität. Wie wir gezeigt haben [12,13], bilden Allyllanthanoid(III)-Komplexe die eigentlichen Katalysatoren, die ohne weitere Zusätze das Kettenwachstum durch Butadienkoordination nach dem Allyleinschubmechanismus katalysieren und die von uns unter Klärung des katalytischen Reaktionsablaufs und der Struktur-Wirkungsbeziehungen umfassend untersucht wurden [START_REF] Taube | Catalytic Reaction Mechanisms and Structure-Reactivity Relationships in the Stereospecific Butadiene Polymerization[END_REF][START_REF] Maiwald | [END_REF][16].

Kürzlich sind Struktur und katalytische Eigenschaften der von uns erstmalig beschriebenen kationischen Bis(allyl)lanthanoid-Komplexe [Ln(η 3 -C 3 H 5 ) 2 L 4 ]B(C 6 F 5 ) 4 [START_REF] Taube | Catalytic Reaction Mechanisms and Structure-Reactivity Relationships in the Stereospecific Butadiene Polymerization[END_REF] auch von anderer Seite bestätigt worden [17,18]. Erstmalig haben wir auch die Eignung der 2,4-Dimethylpentadienylkomplexe Nd(η 5 -Me 2 C 5 H 5 ) 3 [19] und Nd 6 (η 5 -Me 2 C 5 H 5 ) 6 Cl 12 (thf) 2 [20] als wirksame Präkatalysatoren für die 1,4-cis-Polymerisation des Butadiens nachgewiesen [21]. Um zu prüfen, ob (

[BD] 0 [mol/l] 1, 25 1,25 1,25 2,00
[BD] 0 /[Nd] 50000 50000 25000 4000

t R [min], (PBD (%))

2 , 4 -

 24 Dimethylpentadienyl)-Komplexe als vinylhomologe Allyl-Verbindungen möglicherweise einen günstigeren direkten Zugang zum katalytisch aktiven Komplex eröffnen könnten, haben wir Tris-Bis-und Mono(2,4-Dimethylpentadienyl)-Komplexe des Neodyms, Lanthans und Yttriums dargestellt, strukturell umfassend charakterisiert [22] und auf ihre Eignung als Präkatalysatoren für die stereoselektive Butadienpolymerisation eingehend untersucht [23]. Über die Ergebnisse der Katalyseversuche und die daraus ableitbaren Schlussfolgerungen zur katalytischen Struktur-Wirkungsbeziehung und zum mechanistischen Reaktionsablauf der Katalyse wird im Folgenden berichtet.

2 . 5 Abb. 1 :Abb. 2 : 4 - oder BH 4 -

 251244 Abb. 1: Möglicher Reaktionsablauf für die Bildung eines Mono(2,4-Dimethylpentadienyl)neodym(III)-Komplexes als eigentlicher Polymerisationskatalysator, ausgehend von den verschiedenen Neodym(III)-Komplexen als Präkatalysatoren und den eingesetzten Lewis-aciden Aluminiumorganylen als Cokatalysatoren.

  jüngster Zeit sind verschiedene neue Katalysatorkombinationen hoher Aktivität und Selektivität, wie -C 5 Me 4 SiMe 3 ){(µ-Me) 2 AlMe 2 } 2 ] / Al i Bu 3 / [Ph 3 C][B(C 6 F 5 ) 4 ] [10] und [2,6-(2,6-R 2 C 6 H 3 N=CH) 2 C 6 H 3 ]LnCl 2 (thf) 2 / AlR 3 / [Ph 3 C][B(C 6 F 5 ) 4 ] [11]

	z. B.
	(Cp * ) 2 Ln[(µ-Me)AlMe 2 (µ-Me)] 2 Ln(Cp * ) 2 / AlR 3 / [Ph 3 C][B(C 6 F 5 ) 4 ] [8],
	[{2-(Ph 2 P)C 6 H 4 } 2 N]Ln(CH 2 SiMe 3 ) 2 (thf) x / [Ph 3 C][B(C 6 F 5 ) 4 ] [9],
	[Ln(η 5

Cokat Cokat/Nd PBD (%) TOF a) cis/trans/1,2 (%) AlEt 2 Cl 2

  Damit konnten unter Standardbedingungen bei 25°C in vier Stunden mit einer Selektivität von 97-98% 1,4-cis-Polybutadien in einer Ausbeute von bis zu 90% gewonnen werden. Wie wir fanden ist eine Aktivierung der Tris-Komplexe [Ln(η 5 -Me 2 C 5 H 5 ) 3 ] (Ln = La, Nd) auch mit den Alumoxanen HiBAO und MAO möglich, vgl. die Ergebnisse in Tabelle 2. Polymerisationsergebnisse mit den Tris-Komplexen [Ln(η 5 -Me 2 C 5 H 5 ) 3 ] (Ln = Nd, La) in Kombination mit MAO bzw. HiBAO (Al/Nd = 30) in Toluol unter Standardbedingungen bei 50°C ohne Katalysatorvorformierung. Polymerisationsergebnisse mit dem Bis-Komplex [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ] in Kombination mit Aluminiumalkylen in Toluol unter Standardbedingungen bei 50°C nach 24 Stunden Katalysatorbildung bei Raumtemperatur. Me 2 C 5 H 5 ) 4 Br 2 ]/AlMe 3 führt zu einer etwas niedrigeren Aktivität bei praktisch unveränderter cis-Vergleich der Polymerisationsergebnisse in Toluol und Cyclohexan unter Standardbedingungen mit der Katalysatorkombination [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/AlMe 3 bei 50°C.

	Page 7 of 20				ZAAC
	2 2.1 wurden außer Aluminiumorganylen AlR 3 (R = Me, Et, i-Bu), verschiedene halogenidhaltige Lewis-Ergebnisse und Diskussion Struktur und Reaktivität der Tris-Bis-und Mono(2,4-Dimethylpentadienyl)-Komplexe Durch Röntgenkristallstrukturanalyse und NMR-spektroskopisch ist für alle Komplextypen eine Säuren und die Alumoxane Hexaisobutylalumoxan (HiBAO) und Methylalumoxan (MAO) eingesetzt. 2.2 Aktivierung der Tris-Komplexe[Ln(η 5 -Me 2 C 5 H 5 ) 3 ] Tabelle 4: LM Al/Nd t KV a) [h] t R [min] PBD [g] (%) TOF cis/trans/1,2(%)
	5 praktisch planare η 5 -Koordination der 2,4-Dimethylpentadienylanionen nachgewiesen. Daraus ergibt 24 50 1,1 (42) 2500 81/18/1 Toluol 5 48 60 1,0 (50) 2500 88/11/1
	sich für die Ln 3+ -Ionen in den Tris-Komplexen [Ln(η 5 -Me 2 C 5 H 5 ) 3 ] (Ln = Nd, La, Y) die Koordinationszahl neun. Die Bis-Komplexe liegen als Halogenide [Ln 2 (η 5 -Me 2 C 5 H 5 ) 4 X 2 ] (Ln, X: Nd, Cl, Br, I; La, Br, I; Y, Br) dimer mit der Koordinationszahl acht vor. Durch Donorliganden L, wie Wie bereits in unseren Untersuchungen mit M. Geitner [21, 24] festgestellt worden war, kann das erstmalig 1982 von ERNST beschriebene [Nd(η 5 -Me 2 C 5 H 5 ) 3 ] [19] unter Standardbedingungen durch Aluminiumorganyle wie AlEt 3 , Al(i-Bu) 3 oder auch Al(i-Bu) 2 H für eine Reaktion mit Butadien nicht aktiviert werden. In Toluol war bei einem Molverhältnis Al/Nd = 0,5-50 und in einem Temperaturbereich von 20-70°C über eine Reaktionszeit von bis zu 15 Stunden keine Polymerisation nachweisbar. 10 168 40 1,5 (43) 3200 81/18/1 5 30 90 1,2 (46) 1500 84/15/1 Cyclohexan 5 36 60 0,9 (36) 1800 83/16/1 10 36 45 0,7 (30) 2000 84/15/1 Tabelle 2: HiBAO 95 0,8 (8) 160 80/11/9 Cokat Al/Nd 5 50 1,1 (42) 2500 81/18/1 t AlMe 3 a) t KV = Katalysatorvorbereitungszeit.
	Dagegen wurden mit den stärker Lewis-aciden halogenidhaltigen Lewis-Säuren AlEt 2 Cl, AlEtCl 2 , [La(η 5 -Me 2 C 5 H 5 ) 3 ] MAO 70 6,9 (56) 2000 77/18/5 AlMe 3 10 40 1,4 (47) 3500 79/20/1
	AlEt 3 AlBr 3 , SnPh 2 Cl 2 und SnCl 4 bei einem optimalen Verhältnis 2 Halogenid/Neodym hochaktive 5 90 1,2 (56) 1900 76/23/1 HiBAO 11 0,2 (7) 1700 80/13/7 AlEt 3 10 170 0,6 (39) 770 78/21/1
	Katalysatorsysteme für die 1,4-cis-Polymerisation des Butadiens erhalten, vgl. die Ergebnisse in Tabelle MAO 8 7,0 (41) 11300 69/28/3 Al(i-Bu) 3 5 95 0,6 (34) 1100 84/15/1
	1.	Al(i-Bu) 3		10	110		0,9 (31)	850	77/20/3
	Tabelle 1: Polymerisationsergebnisse der Kombination [Nd(η 5 -Me 2 C 5 H 5 ) 3 ]/Lewis-Säure in Toluol mit
	8-10 g Butadien unter Standardbedingungen bei 25°C in vier Stunden.
		Ln	Al/Ln	t KV [h]	t R [h]	PBD (%)		TOF	cis/trans/1,2(%)
		Nd	5	48	1		50		2500	88/11/1
			10	168	0,66	83	43	620	3200	98/1,5/0,5 81/18/1
		AlEtCl 2 La	5	1 24	4	90	34	680	400	97/1,5/1,5 77/22/1
	AlBr 3 durch die Wechselwirkung mit den Lewis-aciden Cokatalysatoren homogene Reaktionslösungen 2/3 49 380 10 168 72 30 21 52/46/2 97/2/1 erhalten werden. Für die Katalyseversuche unter Standardbedingungen, bei einer Reaktionstemperatur SnPh 2 Cl 2 1 71 680 98/1/1 SnCl 4 1/2 90 690 Y 5 48 72 6 4 63/32/5 Selektivität. 98/1/1 10 168 72 4 3 72/23/5
	von 50°C, betrug die Lanthanoidkonzentration 5-10 • 10 -4 mol/l, die Butadienkonzentration 2 mol/l, a) Turn over frequency (Umsatzfrequenz) = TOF = mol Butadien/(mol Ln • h); PBD = Ausbeute Polybutadien
	entsprechend einem Verhältnis von [BD]/[Nd] = 2000-4000 und die eingesetzte Butadienmenge 5-10 g. Unter diesen Reaktionsbedingungen erwiesen sich alle 2,4-Dimethylpentadienyllanthanoid(III)-Wie bei den Tris-Komplexen in Kombination mit MAO (Al/Nd = 30), vgl. Tabelle 2, zeigt auch in der Nach geeigneter Katalysatorvorbereitung unter Butadienzusatz resultierte ein brauner Niederschlag in Bis-Komplex-Kombination [Ln 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/AlMe 3 bei Al/Ln = 5 der La-Komplex gegenüber einer gelben Lösung. Vermutlich wird das relativ schwerlösliche Mono(2,4-dimethylpenta-Komplexe, offensichtlich infolge hinreichend stabiler koordinativer Absättigung gegen die für die den Nd-Komplex eine etwa um den Faktor fünf geringere Aktivität. Für den Y-Komplex ergibt sich
	Allyleinschubreaktion erforderliche Butadienkoordination, als katalytisch inaktiv. Zur Aktivierung
					Wiley-VCH

Pyridin oder Tetrahydrofuran, erfolgt eine Spaltung der Halogenidbrücken und Bildung der monomeren Bis-Komplexe [Ln(η 5 -Me 2 C 5 H 5 ) 2 X(L)] unter Erhalt der Koordinationszahl acht. Die Mono-Komplexe, die als Dihalogenide dargestellt wurden, besitzen eine hexamere Struktur [Ln 6 (η 5 -Me 2 C 5 H 5 ) 6 X 12 (thf) m ] (Ln, X: Nd, Cl, Br, m = 2; La, Br, m = 4), in der die Ln(III)-Ionen durch Halogenidbrückenbildung ebenfalls, die offenbar bevorzugte Koordinationszahl acht erreichen. In Einklang mit dem stark elektropositiven Charakter der Lanthanoide, folgt aus den ermittelten Strukturdaten ein weitgehend ionogener Aufbau der 2,4-Dimethylpentadienylkomplexe [22]. Die damit gegebene hohe Carbanionenaktivität bedingt die extreme Luft-und Feuchtigkeitsempfindlichkeit der Komplexe, so dass alle katalytischen Untersuchungen unter sorgfältigem Ausschluss von Luftsauerstoff und Feuchtigkeit durchgeführt wurden. Als Lösungsmittel dienten Toluol und das koordinativ praktisch inerte Cyclohexan. Die Tris-und Bis-Komplexe sind in beiden Lösungsmitteln ausreichend gut löslich, bei den hexamer aufgebauten Mono(2,4-Dimethylpentadienyl)-Komplexen konnten infolge deren Schwerlöslichkeit erst dienyl)neodym(III)-dichlorid gebildet, vgl. Abschnitt 2.4. Komplex Cokat t R [min] a) PBD [g] (%) TOF cis/trans/1,2 (%) [La(η 5 -Me 2 C 5 H 5 ) 3 ] [Nd(η 5 -Me 2 C 5 H 5 ) 3 ] [Nd(η 5 -Me 2 C 5 H 5 ) 3 ] a) t R Reaktionszeit in Minuten. Methylalumoxan zeigt die deutlich stärkere aktivierende Wirkung. Die damit bei den Tris(2,4-Dimethylpentadienyl)-Komplexen erhaltenen Ergebnisse sind sowohl in der erreichten Aktivität als auch in deren Abstufung vom Nd zum La direkt mit den für die entsprechenden Tris(allyl)-Komplexe vorliegenden Ergebnisse [12] vergleichbar. Als Aktivierungsmechanismus kommt eine Pentadienylanion-Abspaltung durch den Lewis-aciden, carbanionaffinen Cokatalysator in Betracht. Dadurch wird die Butadienkoordination am Ln(III)-Zentrum möglich und durch Einschubreaktion mit einem verbleibenden Pentadienylanion kann die Katalyse des Kettenwachstums gestartet werden. Für die Initiatorfunktion des Pentadienylanions spricht die mit den organylgruppenfreien bzw. nicht organylierend wirkenden Cokatalysatoren (AlBr 3 , SnCl 4 , Ph 2 SnCl 2 ) erzielte gleichwertige Aktivierung, da in diesen Fällen eine Initiatorbildung durch eine Reorganylierung des Lanthanoid(III)-Ions ausgeschlossen ist. Tabelle 3: R [min] PBD [g] (%) TOF cis/trans/1,2 (%) Über die Halogenidanionen ist eine stärkere Wechselwirkung mit den Aluminiumalkylen möglich, so dass gleichgewichtsmäßig eine Aufspaltung des dimeren Bis-Komplexes erreicht wird. Damit kann die für die Polymerisationskatalyse erforderliche Butadienkoordination eintreten. Von den eingesetzten Aluminiumalkylen hat sich das AlMe 3 als wirksamster Aktivator erwiesen. Die Verwendung von Cyclohexan als Lösungsmittel, vgl. die Ergebnisse in Tabelle 4, mit der Kombination [Nd 2 (η 5 -Für die Kombination [Ln 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/AlMe 3 wurde der Einfluss der Variation des Ln(III)-Ions (Ln = Nd, La, Y) auf die katalytische Wirkung untersucht. Die unter Standardbedingungen in Toluol bei 50°C erhaltenen Ergebnisse sind in Tabelle 5 gegenübergestellt. Tabelle 5: Polymerisationsergebnisse mit den Katalysatorkombinationen [Ln 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/AlMe 3 (Ln = Nd, La, Y) unter Standardbedingungen in Toluol bei 50°C.

unter diesen Reaktionsbedingungen nur eine außerordentlich geringe, gegenüber dem Nd-Komplex etwa

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  den Faktor 500 niedrigere, Aktivität. Die weiteren Untersuchungen konzentrieren sich deshalb auf das Studium der neodymhaltigen Katalysatorsysteme. So lässt sich der Bis-Komplex [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 X 2 ] wesentlich stärker durch HiBAO aktivieren, wobei wir den Einfluss des Halogenidions X = Cl, Br, I untersucht haben. Polymerisationsergebnisse mit den Katalysatorkombinationen [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 X 2 ] (X = Cl, Br, I)/HiBAO (Al/Nd = 30) unter Standardbedingungen in Toluol bei 50°C. Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/HiBAO (Al/Nd = 30) in zwei Versuchsreihen A und B die Neodym-bzw. die Butadienkonzentration variiert. Die Polymerisationsergebnisse der in Toluol bei 41,5°C als Doppelversuche durchgeführten beiden Reihen zeigt Tabelle 7. Ergebnisse der Butadienpolymerisation, in Doppelversuchen, mit der Katalysatorkombination [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/HiBAO (Al/Nd = 30) in Toluol bei 41,5°C unter Variation der Polymerisationsergebnisse mit dem Mono-Komplex [Nd 6 (η 5 -Me 2 C 5 H 5 ) 6 Br 12 (thf) 2 ] in Kombination mit Aluminiumalkylen unter Standardbedingungen in Toluol bei 50°C. Völlig analog liefert der Chlorid-Komplex [Nd 6 (η 5 -Me 2 C 5 H 5 ) 6 Cl 12 (thf) 2 ] [20, 24] in Kombination mit den halogenidhaltigen Lewis-Säuren AlEtCl 2 und SnPh 2 Cl 2 im Molverhältnis 0,5/Nd unter den in Abspaltung durch die Lewis-aciden Cokatalysatoren haben wir für das Katalysatorsystem [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/Al 2 (i-Bu) 4 Br 2 /10 AlMe 3 direkt nachgewiesen. Versetzt man den Bis-Komplex in Toluol mit einer Lösung von Al 2 (i-Bu) 4 Br 2 in Toluol im Verhältnis Al/Nd = 1, so scheidet sich aus der roten Reaktionslösung ein braunorange gefärbter Niederschlag ab, für den nach Abfiltrieren, Waschen und Trocknen durch Elementaranalyse ein Verhältnis Br/Nd = 1,96 gefunden wurde. Das spricht für eine 2,4-Me 2 C 5 H 5 -Abspaltung und Bildung des Mono-Komplexes gemäß Reaktionsgleichung (1): Me 2 C 5 H 5 ) 6 Br 12 (thf) 2 ] und [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ] als Präkatalysatoren für die selektive 1,4-cis-Polymerisation unter praxisrelevanten Bedingungen untersucht. Die erhaltenen Ergebnisse zeigt Tabelle 9. Ergebnisse der Polymerisationsversuche mit den Komplexen [Nd 6 (Me 2 C 5 H 5 ) 6 Br 12 (thf) 2 ] (M) und [Nd 2 (Me 2 C 5 H 5 ) 4 Br 2 ] (D) in Kombination mit MMAO (Al/Nd = 500) und zum Vergleich von [Nd 2 (Me 2 C 5 H 5 ) 4 Br 2 ]/HiBAO (Al/Nd = 30).

	Die unter Standardbedingungen mit dem optimierten Verhältnis Al/Nd = 30 in Toluol bei 50°C erhaltenen Polymerisationsergebnisse zeigt Tabelle 6. Tabelle 6: X t R [min] PBD [g] (%) TOF cis/trans/1,2 (%) Cl 4,0 3,2 (61) 17200 95/4/1 5,0 4,1 (56) 12500 94/5/1 Br 3,5 3,5 (59) 20100 88/11/1 3,0 2,6 (55) 18200 92/7/1 I 70,0 2,4 (48) 1000 79/18/3 70,0 2,7 (41) 900 82/17/1 ZAAC Tabelle 7: Neodymkonzentration (A) und der Butadienkonzentration (B). [BD] 0 [mol/l] [Nd] [mol/l] [ ] [ ] 0 BD Nd t R [min] PBD [g] (%) TOF cis/trans/1,2 (%) A 1,9 1,9 • 10 -4 10000 10,0 4,1 (57) 34200 96/3/1 2,0 1,9 • 10 -4 10500 10,0 3,2 (53) 33400 96/3/1 2,1 4,1 • 10 -4 5100 6,00 7,1 (60) 30600 93/6/1 2,1 4,3 • 10 -4 4900 6,00 4,4 (63) 30900 89/10/1 2,0 5,8 • 10 -4 3400 4,50 4,2 (51) 23100 90/9/1 2,1 6,1 • 10 -4 3400 4,50 5,0 (47) 21300 94/5/1 2,0 7,4 • 10 -4 2700 3,75 3,6 (49) 21200 88/11/1 2,1 7,8 • 10 -4 2700 3,75 3,3 (57) 24600 88/11/1 2,1 1,0 • 10 -3 2100 3,50 3,5 (59) 21200 88/11/1 2,0 1,0 • 10 -3 2000 3,00 2,6 (55) 22000 92/7/1 B 0,6 8,4 • 10 -4 710 30,0 1,2 (50) 710 82/17/1 0,5 8,0 • 10 -4 625 35,0 0,9 (40) 430 82/17/1 1,1 7,9 • 10 -4 1400 20,0 4,4 (77) 3200 88/11/1 0,9 7,6 • 10 -4 1200 20,0 3,9 (89) 3200 85/14/1 2,1 7,8 • 10 -4 2700 3,75 3,3 (57) 24600 88/11/1 2,0 7,4 • 10 -4 2700 3,75 3,7 (49) 21200 88/11/1 3,6 7,9 • 10 -4 4600 3,00 15,5 (67) 61600 85/13/2 3,8 7,9 • 10 -4 4800 3,00 10,3 (69) 66200 85/13/2 Die Reproduzierbarkeit in den TOF-Werten schwankte bis zu ± 10 %. Diese Schwankungsbreite ist vermutlich auf Feuchtigkeitsspuren zurückzuführen, die mit der angewendeten Schlenk-Technik nicht zu vermeiden waren. Im Variationsbereich der Neodymkonzentration von 5,8 • 10 -4 bis 1,0 • 10 -3 mol/l bleibt die Aktivität mit TOF ≈ 22000 h -1 praktisch konstant. Das spricht für eine Abhängigkeit der Reaktionsgeschwindigkeit von der Neodymkonzentration nach einem Zeitgesetz 1. Ordnung. Page 10 of 20 ZAAC Der TOF-Anstieg bis auf 34000 h -1 und die Zunahme der cis-Selektivität von ca. 90 % auf ca. 96 % bei Erniedrigung der Neodymkonzentration bis auf 1,9 • 10 -4 mol/l zeigt eine Konzentrationsabhängigkeit der Katalysatorbildungsreaktion an. Dies folgt vermutlich aus einer, mit steigender Verdünnung eintretenden, Gleichgewichtsverschiebung der Assoziation des durch Wechselwirkung mit dem HiBAO gebildeten Anions im Katalysatorkomplex. Die Erhöhung der Butadienkonzentration von 0,5 bis auf 3,8 mol/l bei konstanter Neodymkonzentration bewirkt einen überproportionalen Aktivitätsanstieg von TOF = 500 bis auf 65000 h -1 um über zwei Größenordnungen. Das deutet auf eine Abhängigkeit der Reaktionsgeschwindigkeit von der Butadienkonzentration annähernd nach einem Zeitgesetz 2. Ordnung. Möglicherweise wird, wie bei dem direkt vergleichbaren Allyl-Komplex-System [Nd(C 3 H 5 ) 2.4 Aktivierung der Mono-Komplexe[Nd 6 (η 5 -Me 2 C 5 H 5 ) 6 X 12 (thf) 2 ] ( X = Cl, Br) Ebenso wie der Bis-Komplex [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ] kann auch der Mono-Komplex [Nd 6 (η 5 -Me 2 C 5 H 5 ) 6 Br 12 (thf) 2 ] durch Aluminiumalkyle aktiviert werden. Dabei wird unter gleichen Reaktionsbedingungen jedoch eine bedeutend höhere Aktivität erreicht, vgl. die Polymerisationsergebnisse in Tabelle 8 und Tabelle 3. Tabelle 8: Cokat Al/Nd t KV [h] t R [min] PBD [g] (%) TOF cis/trans/1,2 (%) AlMe 3 5 24 7 0,8 (35) 15100 85/13/2 AlEt 3 5 240 14 1,5 (46) 9900 82/17/1 Al(i-Bu) 3 5 24 85 2,9 (38) 1300 84/12/4 Page 11 of 20 Page 9 of 20 ZAAC Tabelle 1 genannten Reaktionsbedingungen bei 25°C mit TOF = 600-700 h -1 und einem 1,4-cis-Gehalt von 97-98% die gleiche Aktivität und Selektivität wie der Tris-Komplex [Nd(η 5 -Me 2 C 5 H 5 ) 3 ] in Kombination mit diesen Lewis-Säuren im Verhältnis 2 Cl/Nd. Alle Befunde sprechen für die Bildung und Funktion eines Mono(2,4-Dimethylpentadienyl)-Komplexes als Initiator der Polymerisationskatalyse. Die dafür aus dem Tris-und Bis-Komplex anzunehmende 2,4-Me 2 C 5 H 5 ->>>einfügen Reaktionsgleichung 1<<< Im gelben Filtrat konnte entsprechend als weiteres Reaktionsprodukt die 2,4-Dimethylpenta-1,3-dienylaluminium-diorganyl Verbindung 1 H-NMR-spektroskopisch nachgewiesen werden [23]. Fügt man als dritte Komponente noch AlMe 3 im Molverhältnis Al/Nd = 5 zum Reaktionsgemisch zu, so unterbleibt die Niederschlagsbildung vermutlich infolge Komplexbildung mit dem AlMe 3 über die Bromidionen. Es entsteht dann gleichgewichtsmäßig nach Reaktionsgleichung (2) der monomere 2,4-Dimethylpentadienyl-Komplex als Initiator der Polymerisationskatalyse. >>>einfügen Reaktionsgleichung 2<<< Damit übereinstimmend zeigt die Kombination [Nd 2 (η 5 -Me 2 C 5 H 5 ) 4 Br 2 ]/Al 2 (i-Bu) 4 Br 2 /10 AlMe 3 unter Standardbedingungen in Toluol bei 50°C mit TOF = 20000 h -1 und der cis-Selektivität von 83% praktisch die gleiche Aktivität und Selektivität wie die Kombination [Nd 6 (η 5 -ZAAC [Nd 6 (η 5 -Tabelle 9: Komplex (M) (D) (D) (D) Cokat 500 MMAO 500 MMAO 500 MMAO 30 HiBAO LM Cyclohexan Cyclohexan Toluol Toluol T [°C] 65 65 65 42 Me 2 C 5 H 5 ) Page 12 of 20 [Nd] [mol/l] 2,5•10 -5 2,5•10 -5 5,0•10 -5 4-6•10 -4
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Bei einer Katalysatorkonzentration [Nd] = 10 -3 mol/l erreicht der Bromid-Komplex mit einer Umsatzfrequenz von 20000 mol BD/(mol Nd • h) die höchste Aktivität und der Chlorid-Komplex bei nur etwas geringerer Aktivität mit 95% die höchste cis-Selektivität. Als deutlich weniger aktiv und auch weniger cis-selektiv erweist sich unter den gegebenen Reaktionsbedingungen der Iodid-Komplex. Um den Konzentrationseinfluss auf die katalytische Wirkung zu klären, wurde mit der Katalysatorkombination [2 Cl(thf) 1,5 ]/HiBAO [15], ein Mono(butenyl)-bis(butadien)neodym(III)-dianion-Komplex als eigentlicher Katalysatorkomplex gebildet. Dafür sprechen auch die Polymerisationsergebnisse, die mit den Mono(2,4-Dimethylpentadienyl)-Komplexen gefunden wurden. 6 Br 12 (thf) 2 ]/AlMe 3 (vgl. Tab. 8). Abschließend wurde noch die Eignung der Nd-Komplexe

  M w = Massemittel, M n = Zahlenmittel der Molmasse, PD = Polydispersität Unter den gewählten Bedingungen zeigen beide Komplexe [Nd 6 (Me 2 C 5 H 5 ) 6 Br 12 (thf) 2 ] und [Nd 2 (Me 2 C 5 H 5 ) 4 Br 2 ] in Cyclohexan praktisch identische katalytische Eigenschaften. In Cyclohexan wird mit einem Zusatz von 500 Äquivalenten MMAO bei 65°C nach über 80%igem Umsatz jeweils eine Aktivität von TOF = 40000 h -1 erreicht. Die cis-Selektivität beträgt dabei 98 bzw. 96%. In Toluol wird unter den gleichen Reaktionsbedingungen bei Einsatz von [Nd 2 (Me 2 C 5 H 5 ) 4 Br 2 ] eine um den Faktor vier

	-6 (60) 24000 (6 min) --------94/5/1 ) sowie eine etwas geringere cis-Selektivität von 91% erhalten. Im 60 (> 78) 60 (> 82) 60 (> 42) 134000 150000 24000 39000 41000 10500 1040000 905000 280000 460000 392000 117000 2,3 2,3 2,4 4,6 5,5 4,8 -107,7 -107,8 -107,9 -7,4 -9,0 -17,1 16 17 3 97,6/1,9/0,5 95,7/3,7/0,6 91,1/8,2/0,7 -1 Vergleich zu der selbst untersuchten Kombination [Nd 2 (Me 2 C 5 H 5 ) 4 Br 2 ]/HiBAO ergibt sich bei t R [min], (PBD (%)) TOF [h -1 ], (nach 15 min) TOF [h -1 ], (nach 60 min) M w [g/mol] M n [g/mol] PD M n ber. / M n exp. Glastemp. [°C] Schmelztemp. [°C] Gelgehalt (%) cis/trans/1,2 (%) Berücksichtigung der um den Faktor 10 höheren Katalysatorkonzentration eine gute Übereinstimmung in den Aktivitätswerten. Die vergleichbare Ausbeute von 60 % wird dementsprechend in einer um den Faktor zehn niedrigeren Reaktionszeit von sechs Minuten erreicht. Vergleicht man die experimentell bestimmten mittleren Molmassen M n mit dem aus dem 1,3-Butadienumsatz pro Neodym berechneten Molmasse, so folgt aus dem jeweils gefundenen Verhältnis M n ber. /M n exp. ≈ 5, dass offensichtlich infolge einer Übertragungsreaktion mit dem MMAO ca. fünf Polymerketten pro Neodym gebildet werden. Der LM = Lösungsmittel, niedrigere Aktivität (TOF = 10500 h Wert der Polydispersität liegt entsprechend bei PD ≈ 2,3.

Wiley-VCH ZAAC

Wiley-VCH ZAAC


Christoph Janiak
email: janiak@uni-freiburg.de

Dr Herbert Schumann

)lanthanides

Keywords: der Universit t, Inst stannocene , tris(cyclopentadienyl)lanthanide, ligand transfer, samarium, ytterbium stannocene, tris(cyclopentadienyl)lanthanide, ligand transfer, samarium, ytterbium

Stannocene as cyclopentadienyl transfer agent in transmetallation reactions with lanthanide metals for the synthesis of tris(cyclopentadienyl)lanthanides

Introduction

The bent sandwich compound bis(cyclopentadienyl)tin(II) [stannocene, (η 5 -C 5 H 5 ) 2 Sn] [1] and the tris(cyclopentadienyl)lanthanides, (η 5 -C 5 H 5 ) 3 Ln [ 2 , 3 ] (also with one or two donor [solvent] molecules) [ 4 , 5 , 6 ] were among the prototypical early cyclopentadienyl-metal compounds synthesized by Fischer and Wilkinson in the 1950s following the discovery of ferrocene. [7] Complexes (η 5 -C 5 H 5 ) 3 Ln are sublimable compounds with interest in their electronic structure, [ 8 ] optical properties, [9] uses as synthetic starting materials [ 10] and dopants [11] for semiconductive thin films, [12] organic UV photocathodes, [ 13 ] or mesoporous activated carbon. [ 14 ] Compounds (η 5 -C 5 H 5 ) 3 Ln are typically synthesized from the metathesis of anhydrous lanthanide trichlorides with a large excess of sodium cyclopentadienide in tetrahydrofuran (THF) (eq. 1). [2,3,4,5,15] LnCl 3 + 3 C 5 H 5 Na (C 5 H 5 ) 3 Ln + 3 NaCl THF (1) Also, molten (C 5 H 5 ) 2 Be or (C 5 H 5 ) 2 Mg were used as cyclopentadienyl transfer reagents with LnX 3 , [ 16 ] and C 5 H 5 Tl [17] or (C 5 H 5 ) 2 Hg [18] in transmetallation reactions with rare earth metal powders (eq. 2) to yield (η 5 -C 5 H 5 ) 3 Ln. [4] Ln 0 + 3 C

Unlike for cyclopentadienylthallium, [ 19 ] we are not aware of any use of stannocene as a cyclopentadienyl transfer agent. There is one report on the reaction of the stannocene derivative (η 5 -C 5 Me 5 ) 2 Sn with YbI 2 to give [(η 5 -C 5 Me 5 ) 2 YbI(THF) 2 ]. [20] Here we report the use of stannocene as a cyclopentadienyl transfer agent in transmetallation reactions with lanthanide metals for the synthesis of tris(cyclopentadienyl)lanthanides.

Results and Discussion

Stannocene, (η 5 -C 5 H 5 ) 2 Sn can be easily prepared in large quantities and good yield from cyclopentadienyl sodium and tin(II) dichloride. It can be very well purified by sublimation, is moderately air-sensitive and storable for prolonged times under inert gas at room temperature.

Stannocene reacts with samarium and ytterbium metal powder in toluene or tetrahydrofuran under formation of tris(cyclopentadienyl)samarium and -ytterbium in high yield. In toluene the base-free form (η 5 -C 5 H 5 ) 3 Ln is isolated directly (eq. 3). In THF the adducts (η 5 -C 5 H 5 ) 3 Ln•THF are obtained in crystalline form (eq. 4), from which THF-free compounds would be available after vacuum sublimation above 200 °C. [2,3] Ln 0 + 3/2 (C 5 H 5 ) 2 Sn (C 5 H 5 ) 3 Ln + Sn 0 toluene Ln = Sm (yield 68 %), Yb (crystals, 77 %)

In THF and a 1:1 molar ratio of Yb:Sn the (excess) ytterbium metal reduces the initially formed (η C 5 H 5 ) 3 Yb•THF (verified by its green color) to bis(cyclopentadienyl)ytterbium•which is isolated as the yellow-orange mono-tetrahydrofuran complex, (η 5 -C 5 H 5 ) 2 Yb•THF complex (eq. 5). (drying) (5) In toluene such a reduction with excess Yb metal is not observed. An excess of samarium metal does not exhibit such a reduction either, in line with the transmetallation with C 5 H 5 Tl which also gave solely (η 5 -C 5 H 5 ) 3 Sm. [ 21 ] Thus, even at a 1:1 molar ratio of Sm and (η 5 -C 5 H 5 ) 2 Sn tris(cyclopentadienyl)samarium is obtained in high yield.

In analogy to the transmetallation reactions of lanthanide metals with C 5 H 5 Tl a tiny amount of mercury was added to the reactions of samarium and ytterbium metal with stannocene. [21] The role of mercury is to facilitate the start of the reaction by cleaning the lanthanide metal surface through amalgamation. A summary of the transmetallation reactions of samarium and ytterbium with stannocene, (η 5 -C 5 H 5 ) 2 Sn is provided in Table 1.

Table 1. Transmetallation reactions of lanthanide metals with stannocene. [a] [a] RT = room temperature. [b] Yield based on the minor stannocene component.

The color, melting points, IR-, Raman-and 1 H-NMR spectra of the (η 5 -C 5 H 5 ) 3 Ln, (η 5 -C 5 H 5 ) 3 Ln•THF (Ln = Sm, Yb) and (η 5 -C 5 H 5 ) 2 Yb•THF products obtained here through transmetallation agree with the literature values of the compounds. [4]

Conclusions

The transmetallation of the lanthanide metals samarium and ytterbium is a facile, high-yield and halide-free route to the tris(cyclopentadienyl)lanthanides (η 5 -C 5 H 5 ) 3 Ln, (η 5 -C 5 H 5 ) 3 Ln•THF (Ln = Sm, Yb) and to bis(cyclopentadienyl)ytterbium, (η 5 -C 5 H 5 ) 2 Yb•THF. The synthetic route should be extendable to (η 5 -C 5 H 5-n R n ) 3 Ln compounds with ring-substituted cyclopentadienyl ligands [4,22 ] for which a wide range of stannocene derivatives is also available. [23]

Experimental Section

Syntheses were routinely carried out under an inert gas atmosphere of dried nitrogen or argon with Schlenk and vacuum techniques. The glass ware was flame dried prior to its usage. Solvent were dried over and distilled from (blue) sodium/benzophenone (ketyl) or liquid Na/K alloy (25 wt.-% Na/75 wt.-% K) and stored under inert gas. Samarium and ytterbium powders were obtained from Auer-Remy/Hamburg. NMR spectra were obtained with samples in sealed NMR tubes on a Bruker WP 80 SI and are referenced against TMS. The line width for the paramagnetic Sm and Yb probes is given as the frequency width at half-hight maximum (FWHM). IR spectra were measured on a Perkin-Elmer 580B infrared spectrometer in CsI (2-3 mg sample/300 mg CsI) with a CsI reference, Raman spectra on a Jobin-Yvon spectrometer (Kr Laser, room temperature, 100-2000 cm -1 ). For both the IR and Raman spectra only peaks classified from weak (w), medium (m) to strong (s) and shoulders (sh) but no very weak peaks are listed. C,H analyses were done on a Perkin-Elmer 240C CHN elemental analyzer. Melting points were measured capillaries which were sealed under vacuum. Cyclopentadienyl sodium was prepared from freshly cracked cyclopentadiene, C 5 H 6 (42.0 ml, 0.51 mol, density ~0.8 g/ml) which was slowly added dropwise to a suspension of finely cut sodium metal (14.0 g, 0.61 mol, excess) in 250 ml of tetrahydrofuran. After stirring for 18 h the slightly pink THF solution was decanted from unreacted excess sodium and the solvent removed under vacuum to yield C 5 H 5 Na as a white powder (43.0 g, 96%).

Bis(cyclopentadienyl)tin(II), stannocene, (C 5 H 5 ) 2 Sn. Solid C 5 H 5 Na (43.0 g, 0.49 mol) and tin(II) dichloride (46.4 g, 0.245 mol) are weighed into a 250 ml Schlenk flask. THF (150 ml) is added under ice cooling to start an immediate exothermic reaction. Stirring is continued for 1.5 h, then the solvent is removed under vacuum with gentle warming. The product is sublimed from the residue at 80 °C/10 -1 Torr and obtained as white to slightly yellow crystals (yield 33.4 g, 55%).

Tris(cyclopentadienyl)samarium, (C 5 H 5 ) 3 Sm. To a mixture of stannocene (2.26 g, 9.08 mmol) and samarium metal powder (1.37 g, 9.08 mmol) is added a very small drop of mercury and toluene (20 ml). The suspension is stirred at 60 °C for 4 d. Additional 50 ml of toluene are added to the off-white to yellow suspension and the product is separated from the metal residue through a glass frit equipped with a bypass to enable a continuous hot extraction. The toluene solution is decanted from the precipitated product in the filtrate and discarded. The orange-yellow product powder is dried under vacuum (yield 1.42 g, 68%, based on stannocene). M.p. 346-348 °C (lit. 365 °C, [3] ca. 330 °C). [24] IR (CsI, cm -1 ): 3100 (m), 3085 (m), 3070 (m), 1607 (m), 1442 (m), 1438 (m), 1363 (w), 1263 (w), 1238 (w), 1072 (w), 1008 (s), 914 (sh), 890 (m), 840 (m), 792 (sh), 770 (vs, br), 664 (m), 621 (w), 550 (w, br) (lit. [24]). Raman (cm -1 ): 1126.

Tris(cyclopentadienyl)samarium

tetrahydrofuran, (C 5 H 5 ) 3 Sm•THF. To a mixture of stannocene (1.49 g, 5.99 mmol) and samarium metal powder (0.60 g, 3.99 mmol) is added a very small drop of mercury and THF (20 ml). After 12 h a yellow, finely crystalline product residue can already be observed. The suspension is stirred at room temperature for 7 d. Then additional 30 ml of THF are added and the clear yellow 68) [b] Sm 2:3 THF RT; 7 (C5H5)3Sm•THF (74) Sm 1:1 THF RT; 7 (C5H5)3Sm•THF (87) [b] Yb 1:1 toluene 50; 7 (C5H5)3Yb (77) [b] Yb 2:3 THF RT; 2 (C5H5)3Yb Finally the volume of the mother liquor was decreased in vacuum to further enhance the yield (1.24 g, 74%). M.p. 348-350 °C with irreversible darkening from 200 °C and softening at 335 °C. A 1:1 molar ratio of stannocene (1.85 g, 7.43 mmol) and samarium metal powder (1.12 g, 7.43 mmol) yields the same product (yield 1.81 g, 87%, based on stannocene). IR (CsI, cm -1 ): 3090 (w), 3075 (sh), 2980 (w), 2890 (w), 2875 (sh), 1660 (w), 1441 (w), 1341 (m), 1244 (w), 1235 (sh), 1060 (sh), 1035 (sh), 1016 (s), 889 (sh), 861 (m), 839 (m), 795 (sh), 786 (vs), 775 (sh), 760 (sh), 755 (vs), 667 (w), 240 (sh), 211 (m) (lit. [21]). Raman (cm -1 ): 1356 (w), 1226 (s), 774 (w), 752 (w), 230 (s), 210 (m), 132 (m to s).

Hz). [25] C 15 H 15 Yb (368.32): calcd. C 48.91, H 4.10; found C 49.87, H 4.13%.

Tris(cyclopentadienyl)ytterbium tetrahydrofuran, (C 5 H 5 ) 3 Yb•THF. To a mixture of stannocene (2.94 g, 11.81 mmol) and ytterbium metal powder (1.36 g, 7.88 mmol) is added a very small drop of mercury and THF (30 ml). After about 5 min the solution starts to turn green and warms up slightly. The suspension is stirred at room temperature for 2 d. Then additional 30 ml of THF are added and the clear green solution is decanted from the metal residue and product precipitate. Cooling (-20 °C) of the THF solution yields darkgreen crystals whose yield is increased through repeated residue extraction and cooling of the bridge-connected residue and product flask. Finally the volume of the mother liquor was decreased in vacuum to further enhance the yield (2.65 g, 76%). M.p. 220-222 °C (lit. 223-226 °C). [15b] . IR (CsI, cm -1 ): 3555 (m), 3095 (w), 3070 (sh), 2980 (w), 2890 (w), 1440 (w), 1331 (w), 1245 (w), 1059 (w), 1040 (sh), 1012 (s), 890 (w), 862 (w), 838 (w), 795 (vs), 770 (s), 735 (sh), 666 (w), 440 (m), 420 (sh), 390 (w), 250 (m) (lit. [15b]). 1 H-NMR (C 6 D 6 , ppm): -48.5 (s, C 5 H 5 , FWHM 345 Hz), 38.7 (s, THF-CH 2 , FWHM 73 Hz), 80.3 (s, THF-CH 2 , FWHM 327 Hz) (lit. in THF-d 8 , -54 ppm, FWHM 280 Hz). [25] C 19 H 23 YbO (440.43): calcd. C 51.82, H 5.26; found C 51.45, H. 5.18%.

Bis(cyclopentadienyl)ytterbium

tetrahydrofuran, (C 5 H 5 ) 2 Yb•THF. To a mixture of stannocene (1.83 g, 7.35 mmol) and ytterbium metal powder (1.27 g, 7.36 mmol) is added a very small drop of mercury and THF (20 ml). The solution immediately turns green, warms up slightly and is soon dark-green. The suspension is stirred at room temperature for 3 d when apparently all Yb metal powder has been consumed. The now violet solution is decanted from the grey tin metal residue. Reduction of the THF volume in vacuum and overlayering with hexane yields yellow-orange crystals of the mono-THF complex and violet, feather-like crystals of the bis-THF complex. The latter turn to a yellow powder upon drying in vacuum by giving off one solvent molecule (yield 2.00 g, 73%). M.p. dec. at about 170 °C (no melting up to 350 °C).

  5 H 5 Tl (C 5 H 5 ) 3 Ln + Tl 0 Ln 0 + 3/2 (C 5 H 5 ) 2 Hg (C 5 H 5 ) 3 Ln + Hg 0 THF

( 3 )

 3 Ln 0 + 3/2 (C 5 H 5 ) 2 Sn (C 5 H 5 ) 3 Ln•THF + Sn 0 Ln = Sm (yield 87%), Yb (76 %) THF crystalline form

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  is decanted from the metal and product precipitate. Cooling (-20 °C) of the THF solution yields yellow crystals whose yield is increased through repeated residue extraction and cooling of the bridge-connected residue and product flask.

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	36 37 38	Yb	1:1	THF	RT; 3	•THF (76) (C5H5)2Yb•THF (73)
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solution

  1 H-NMR (THF-d 8 , ppm): 5.67 (s, C 5 H 5 no line broadening) (lit. in THF-d 8 5.64 ppm). [15b] C 14 H 18 YbO (375.34): calcd. C 44.80, H 4.83; found 44.96, H 5.03%.

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