Assigning the Cerium Oxidation State for CH2CeF2 and OCeF2 Based

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Assigning the Cerium Oxidation State for CHCeF and OCeF Based on Multi-Reference Wavefunction Analysis 2

Oliver Mooßen, and Michael Dolg J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03770 • Publication Date (Web): 20 May 2016 Downloaded from http://pubs.acs.org on May 23, 2016

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The Journal of Physical Chemistry

Assigning the Cerium Oxidation State for CH2CeF2 and OCeF2 Based on Multi-Reference Wavefunction Analysis Oliver Mooßen∗ and Michael Dolg∗ Theoretical Chemistry, University of Cologne, Greinstr. 4, 50939 Cologne, Germany E-mail: [email protected]; [email protected] Phone: ++49 (0)221 470 6894. Fax: ++49 (0)221 470 6896

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To whom correspondence should be addressed

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Abstract The geometric and electronic structure of the recently experimentally studied molecules ZCeF2 (Z=CH2 , O) was investigated by density functional theory (DFT) and wavefunction-based ab initio methods. Special attention was paid to the Ce-Z metalligand bonding, especially to the nature of the interaction between the Ce 4f and the Z 2p orbitals and the possible multi-configurational character arising from it, as well as to the assignment of an oxidation state of Ce reflecting the electronic structure. Complete active space self-consistent field (CASSCF) calculations were performed, followed by orbital rotations in the active orbital space. The methylene compound CH2 CeF2 has an open-shell singlet ground state, which is characterized by a two-configurational wavefunction in the basis of the strongly mixed natural CASSCF orbitals. The system can also be described in a very compact way by the dominant Ce 4f 1 C 2p1 configuration, if nearly pure Ce 4f and C 2p orbitals are used. In the basis of these localized orbitals the molecule is almost mono-configurational and should be best described as a Ce(III) system. The singlet ground state of the oxygen OCeF2 complex is of closed-shell character, when a mono-configurational wavefunction with very strongly mixed Ce 4f and O 2p CASSCF natural orbitals is used for the description. The transformation to orbitals localized on the cerium and oxygen atoms leads to a multi-configurational wavefunction and reveals characteristics of a mixed valent Ce(IV)/Ce(III) compound. Additionally, the interactions of the localized active orbitals were analyzed by evaluating the expectation values of the charge fluctuation operator and the local spin operator. The Ce 4f and C 2p orbital interaction of the CH2 CeF2 compound is weakly covalent and resembles the interaction of the H 1s orbitals in a stretched hydrogen dimer. In contrast the interaction of the localized active orbitals for OCeF2 shows ionic character. Calculated vibrational Ce-C and Ce-O stretching frequencies at the DFT, CASSCF, secondorder Rayleigh-Schrödinger perturbation theory (RS2C), multi-reference configuration interaction (MRCI) as well as single, doubles and perturbative triples coupled-cluster (CCSD(T)) level are reported and compared to experimental infrared absorption data in Ne and Ar maxtrix.

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Introduction The assignment of oxidation states to atoms in molecules is a fundamental aspect of chemistry 1 and is also the subject of a recent IUPAC rechnical report, where various approaches of determining the oxidation state are discussed. 2 According to Karen et al. "the oxidation state of a bonded atom equals its charge after ionic approximation". Further, "in the ionic approximation the atom that contributes more to the bonding molecular orbital becomes negativ". This prescription works well for systems where a mono-configurational description is sufficient, however, attributing oxidation states to, e.g., transition metal atoms in compounds with strong multi-configurational character is not considered in this report. Due to the presence of several significant configurations in the wavefunction and the resulting partial occupation of orbitals involved in bonding the partitioning of the electrons in systems which are not well described by a single determinant wavefunction becomes less obvious and it is a quite difficult task to assign oxidation states. This is especially true if not just a formal assignment is desired, but one which actually reflects the experimentally observed charge distribution, e.g., relates to the number of electrons in an atomic-like d shell of a transition metal such as iron (Fe3+ 3d5 → Fe(III), Fe2+ 3d6 → Fe(II)). In particular metal-organic cerium complexes often exhibit multi-configurational character and therefore it is a complicated problem to assign the oxidation state of cerium (Ce3+ 4f 1 → Ce(III), Ce4+ 4f 0 → Ce(IV)) in consistency with experimental data, e.g., Ce 4f populations determined from X-ray absorption near-edge structure (XANES) measurements. Popular examples where the oxidation state of cerium was controversely discussed are the sandwich complexes Ce(C8 H8 )2 and Ce(C8 H6 )2 . Several theoretical and experimental results were published supporting either a Ce(III) 3–9 or a Ce(IV) 10–13 oxidation state for cerium in cerocene. A similar controversy exists for the bis(η 8 -pentalene)cerium compound, which was also interpreted as a Ce(III) 14 as well as a Ce(IV) 15,16 compound. It should be noted that in both cases singlet ground states are formed, i.e., whereas for the Ce(IV) case all electrons are paired in an orbital picture, for the Ce(III) case the spin of the single electron in the 3



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Ce 4f shell is compensated by the opposite spin of another unpaired electron in a ligand orbital. 3,4 Since the 4f shell of Ce is quite deep in energy, photoelectron spectra will not yield an indicative low-energy peak resulting from the 4f 1 occupation in such Ce(III) systems. 5 In the above cases it is thus not trivial to distinguish experimentally between Ce(III) and Ce(IV) compounds. In previous studies we investigated the reasons of the different theoretical results for cerocene with regard to the cerium oxidation state 17 and found that the invariance of the complete active space self-consistent field (CASSCF) wavefunction and the corresponding total energy with respect to an unitary transformation in the active orbital space was the cause for these different interpretations. An essentially mono-configurational wavefunction based on strongly mixed orbitals may correspond to a multi-configurational wavefunction when orbitals are used, which are localized on the atoms. Similarly, a multi-configurational wavefunction based on strongly mixed orbitals may actually correspond very well to a singleconfigurational wavefunction built from localized orbitals. In our opinion it is reasonable to generate localized, i.e., atomic-like orbitals to study the charge distribution in molecules by analyzing the weights of the various configurations contributing to the wavefunction. Orbitals localized on atoms/ions closely resemble those which would be used in a purely ionic picture, i.e., they are very useful for the "ionic approximation". We therefore used such orbital rotations to create nearly pure Ce f and ligand π orbitals and analyzed the configuration contributions of the corresponding CASSCF ground state wavefunctions for Ce(C8 H8 )2 17 and Ce(C8 H6 )2 . 18 In this situation dominant leading Ce 4f 1 ringπ 3 and Ce 4f 1 ringπ 1 configurations were obtained for the singlet ground states of the two systems, which is in a good agreement with the experimental XANES data pointing to a Ce 4f 1 occupation in both cases. Therefore, we characterized the two sandwich complexes as Ce(III) compounds. Their electronic structure can be viewed as the one of a molecular analogue of a so-called Ce(III)-based Kondo-system, as proposed originally by Neumann and Fulde for cerocene in 1989: 3 the cerium impurity in a metal corresponds to the cerium central atom in

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the sandwich complex, whereas the role of the conduction band of the solid is played by the π orbitals of the two organic rings. As an open question remained if such bonding situation is present in cerium compounds other than sandwich-type complexes. In recent experimental studies Andrews and coworkers condensed laser-ablated lanthanide metal atoms with CH2 F2 and OF2 in excess neon or argon at temperatures of 4 to 6 K. 19,20 New infrared (IR) absorption bands were observed and assigned to oxidative addition products of the type CH2 LnF2 and OLnF2 . The Ln-C and Ln-O stretching frequencies and the corresponding matrix shifts were used as indicators for the type of bonding present in the Ln-C and Ln-O bonds. The CH2 LnF2 and OLnF2 systems were also investigated by quantum chemical methods, and oxidation states were assigned to the lanthanides. Interestingly the CH2 LnF2 molecules were predicted to be multi-radicals, with a Ln-C σ bond, and a single electron in a C 2p orbital weakly coupled to the Ln 4f n (n=1 (Ce), 2(Pr), ...) shell. In particular a corresponding triplet ground state was found for CH2 CeF2 at the unrestricted DFT/B3LYP as well as at the CASSCF level, whereas a singlet state turned out to be slightly lower after including also dynamic correlation by second-order perturbation theory (CASPT2). In view of the very brief description of the wavefunction-based ab initio calculations given in the work of Andrews and coworkers 19 and the fact, that for the related hypothetical CH2 CeCp2 system we recently found an open-shell singlet ground state, 21 we decided to study the CH2 CeF2 molecule in more detail and to investigate the possible presence of a Kondo-analogue ground state. We also include the OCeF2 system as a reference. Since oxygen is more electronegative than carbon a higher oxidation state at the metal center is favored for OCeF2 . In fact Andrews and coworkers 20 found a high cerium-oxygen stretching frequency and thus assigned OCeF2 as a Ce(IV) system with an essentially ionic bonding between Ce4+ and O2− . The fully occupied 2p orbitals on oxygen hereby donate into the empty 5d and 4f orbitals of cerium, resulting in one polarized σ and two pseudo-π bonds between cerium and oxygen. For the heavier lanthanides either mixed Ln III/IV oxidation states (Pr, Tb) or Ln III oxidation states (all others) were proposed.

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The related OCeCp2 system was assigned a mixed valent Ce III/IV oxidation state in our previous work. 21 In the following we will thus analyze the multi-reference (MR) character of the ground states of CH2 CeF2 and OCeF2 , mainly by applying unitary transformations to the smallest number of CASSCF active orbitals still allowing a correct description of their electronic structure.

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Computational Details The two cerium complexes are investigated at various levels of theory in this work. All wavefunction-based ab initio calculations were performed with the program package MOLPRO 2012.1. 22 In the majority of these calculations the scalar-relativistic small-core ECP28MWB pseudopotential 23 was applied for Ce with a corresponding generalized contracted ANO basis set using s, p, d, f and g functions. 24 For the other atoms contracted correlation-consistent polarized triple-zeta basis sets (cc-pVTZ) consisting of s, p and d functions for H and s, p, d and f functions for C, N, O and F were adopted. 25 In order to investigate the convergence with respect to the basis set size also sets of double-zeta (cc-pVDZ; H: sp; C, O: spd) and quadruple-zeta (cc-pVQZ; H: spdf ; C, O: spdf g) quality were applied. In the latter case a single h function was added to the Ce basis set. In the following these basis sets are referred to as VXZ (X = D, T, Q). The corresponding augmented basis sets for H, C and O are abbreviated as aVXZ (X = D, T, Q). The presented density functional theory (DFT) calculations were performed with TURBOMOLE version 6.6. 26 In these calculations also the ECP28MWB pseudopotential 23 with segmented contracted def-SV(P) and def2-TZVP basis sets for Ce was used. 27 For all other atoms H, C and O the corresponding def-SV(P) and def2-TZVP basis sets were selected. 28 In the following these basis sets are abbreviated as SVP and TZVP. For the DFT calculations different functionals (BP86, 29,30 B3LYP 31,32 and M06 33 ) were used and both the standard Kohn-Sham (KS) approach for closed-shell systems as well as the unrestricted Kohn-Sham (UKS) approach for open-shell singlet and triplet cases were applied. Corresponding Hartree-Fock calculations (HF, UHF) were performed for reference. Geometry optimizations were performed and vibrational frequencies were calculated at the DFT, HF, complete active space self-consistent field (CASSCF) 34,35 , coupled cluster with singles, doubles and perturbative triple excitations (CCSD(T)), 36,37 Rayleigh-Schrödinger second-order perturbation theory (RS2C) 38 and multi-reference configuration interaction (MRCI) 39,40 level. No excitations were allowed from the Ce 4s, 4p, 4d, C 1s, and O 1s 7



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shells at the CCSD(T), RSC2 and MRCI level. The main focus of this work lies on the MR character of the molecules, i.e., the major static electron correlation effects, as well as on the relevance of the Ce 4f orbitals for their electronic structure. Therefore CASSCF 34,35 calculations with various active orbital spaces were performed. The character of the active orbitals in the sense of contributions of the atomic orbitals were calculated by Mulliken population analysis. 41 The corresponding CI coefficients were evaluated using the multireference configuration interaction (MRCI) 39,40 code of MOLPRO. In these calculations only excitations within the CASSCF active orbital space were allowed. Note that the CASSCF space was always chosen to capture the dominant part of the wavefunction and that the presumably small changes in the charge distribution by dynamical electron correlation effects cannot be described intuitively in simple orbital-based pictures of chemical bonding anyhow. For the localized orbitals the occupation number fluctuations and the local spin 42,43 were determined to analyze the nature of the interaction of the active orbitals for both complexes.

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Results and Discussion Geometries The ground state geometries for the two cerium compounds were investigated using the DFT method with several functionals (BP86, B3LYP, M06) and basis sets (SVP, TZVP), as well as various wavefunction-based ab initio methods (cf. below). Geometry optimizations with and without imposing symmetry constraints were performed. The minima were verified by analysing the eigenvalues of the Hessian matrix. All cartesian coordinates and evaluated vibrational frequencies are summarized in the supplementary material. For the methylene compound CH2 CeF2 a (planar) C2v symmetric triplet ground state equilibrium structure was previously reported, 19 whereas for the oxygen complex OCeF2 a (pyramidal) singlet ground state equilibrium structure with Cs symmetry was found. 20 However, in none of our calculations we were able to obtain the C2v symmetry for the CH2 CeF2 ground state equilibrium structure, even when starting from the published geometries for the singlet and triplet states. One or two imaginary values resulted in all frequency calculations based on C2v structures, also when improving the chosen grid and tightening the convergence criteria. We agree with Wang et al. 19 that CH2 CeF2 has a biradical electronic structure which needs to be described at the UKS level, but we rather found a distorted, i.e., unsymmetric (C1 ) global minimum structure, with the singlet state being slightly lower than the triplet state (in eV: UHF 0.018, BP86 0.056, B3LYP 0.011, M06 0.015). The Ce atoms lies approximately in the CH2 plane, whereas the fluorine atoms of the CeF2 unit are bent out of this plane. Depending on the approach the CeF2 unit is also more (e.g. BP86) or less (e.g. B3LYP) twisted around the C-Ce axis with respect to the CH2 unit (cf. additional figures in the supplementary material). Whereas the less twisted structures have nearly a Cs symmetry, the more twisted ones clearly fall into C1 . Although the energy lowering of about 1 kcal/mol (0.04 eV) with respect to the planar ground state equilibrium structure proposed by Wang et al. 19 is small, the geometrical distortion of the molecules is clearly visible. 9



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In order to further confirm our DFT results for the CH2 CeF2 ground state equilibrium structure, we performed HF, UHF, MCSCF, CASSCF(2,2) and CASSCF(2,8) as well as subsequent RS2C and MRCI geometry optimizations with MOLPRO using both C2v and C1 symmetry as well as the VTZ basis sets. The reason for the CASSCF optimizations and the particular chosen active spaces (active electrons, active orbitals) will be explained later. The C2v symmetry calculations did not converge to minimum structures, i.e., even with high energy convergence criteria (10−14 Hartree) (at least) one imaginary frequency was obtained. The corresponding calculations in C1 symmetry yielded global minima for the singlet ground state, which at the highest level, i.e., MRCI, exhibit approximately Cs symmetry. For the oxygen complex OCeF2 the symmetry of the ground state equilibrium structure is clearly Cs . This result was obtained for every method, no matter if symmetry constraints were imposed during the geometry optimization or not. The optimized geometries at the HF/RS2C level are shown in Fig.1 for both systems. Since the geometry optimizations for CH2 CeF2 revealed a distorted minimum structure, all further calculations were performed without using symmetry constraints for both complexes even if the oxygen compound has Cs symmetry. The intention is that one can compare better the results of both complexes using the same conditions.

Electronic ground states As a first step the ground-state spin-multiplicity of both cerium compounds was investigated. Therefore CASSCF(2,8) and RS2C(2,8) calculations were performed including the out-of-plane C/O 2p orbital of the complexes and the seven Ce 4f orbitals. In case of a closed-shell singlet ground state the out-of-plane C/O 2p orbital is doubly occupied and corresponds to the highest occupied molecular orbital (HOMO), whereas the notion out-ofplane refers to an idealized planar geometry of the two complexes. For these calculations the HF/RS2C optimized geometry was used and the lowest singlet and triplet states were optimized separately. The results are presented in Table 1. The OCeF2 molecule clearly fa10


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Table 1: CASSCF/RS2C lowest singlet and triplet state energies using the VTZ basis sets for CH2 CeF2 and OCeF2 . Optimized HF/RS2C structures were used. RS2C(2,8) CH2 CeF2 A state [a.u.] -712.636296 3 A state [a.u.] -712.614732 ∆ET −S [eV] 0.59 1

OCeF2 -748.677834 -748.560183 3.20

Electronic structure and active orbital rotations In order to obtain a compact wavefunction, which can still handle the influence of the Ce 4f orbitals correctly, we investigated the behavior of the HF, CASSCF(2,8) and CASSCF(2,2) wavefunctions. In the CASSCF(2,8) calculation all seven Ce 4f orbitals and the out-ofplane C/O 2p orbital were included in the active orbital space, while for the CASSCF(2,2) calculation the active space was reduced to one Ce 4f orbital and the out-of-plane C/O 2p orbital. The reduction is motivated by the fact that the CASSCF(2,8) wavefunctions are dominated by only two configurations with the two electrons distibuted in two orbitals, which indicates that the smaller CASSCF(2,2) provides a sufficiently accurate description for the cerium compounds. This reduction of the active space is also motivated by the natural orbital occupation numbers of MRCI calculations correlating 32 electrons (corresponding to all H, C, O and Ce valence electrons plus those in the Ce 5s and 5p semi-core shells), which are either larger than 1.97 or smaller than 0.02, except for the two active orbitals in CH2 CeF2 , which exhibit occupations of 1.18 and 0.81 (cf. supplementary material). In Table 2 the CASSCF results are presented. First it can be seen that including seven virtual orbitals with high Ce 4f character decreases the ground state energy significantly (≈0.8 eV) for both complexes. According to the variation principle we can conclude that these wavefunctions yield a much better description than HF for the two systems. Further it is shown that the complexes can be described correctly by a CASSCF(2,2) wavefunction. The CASSCF(2,2) ground state energy for the methylene compound differs only by 0.044 eV from the CASSCF(2,8) result, which indicates that these two wavefunctions have an almost equal accuracy. For the OCeF2 compound the situation is slightly different, but still similar to the methylene complex. The 12


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CASSCF(2,2) calculation lowers the ground state energy by ≈0.6 eV compared to the HF calculation. The difference between the CASSCF(2,8) and the CASSCF(2,2) energies is only 0.2 eV, which indicates that the CASSCF(2,2) wavefunction still is a sufficiently accurate and compact description for the oxygen compound. Table 2: HF, CASSCF(2,8) and CASSCF(2,2) 1 A ground state energies using the VTZ basis sets for CH2 CeF2 and OCeF2 . Optimized HF/RS2C structures were used. energy HF CAS(2,8) CAS(2,2) ∆EHF-CAS(2,8) ∆EHF-CAS(2,2)

CH2 CeF2 OCeF2 [a.u.] -711.629470 -747.599643 [a.u.] -711.660414 -747.629032 [a.u.] -711.658813 -747.621434 [eV] 0.84 0.80 [eV] 0.80 0.59

Mulliken population analysis can give a first insight into the occupation of the Ce 4f orbitals and an appropriate description of the electronic structure of the molecules. The results of the different calculations are listed in Table 3. All DFT calculations reveal a high Ce f occupation close to one (≈ 0.9 – 1.3) for both complexes. In case of CH2 CeF2 the analysis of the difference of the density matrices for α and β spin yields a f population, which is almost integral and equal to one for B3LYP (0.99) and M06 (0.98). The corresponding p population on C is also close to one for B3LYP (0.92) and M06 (0.92), supporting the conclusion of Wang et al. 19 that the system has biradical character. BP86 shows somewhat larger deviations from this picture, whereas the UHF approach with almost integral Ce f (0.99) and C p (1.00) populations corresponds best to the proposal of Wang et al.. The UHF results for CH2 CeF2 agree fairly well with the DFT/UKS data, however the HF value for OCeF2 is quite different from the DFT/KS results. The influence of the Ce 4f orbitals in OCeF2 is significant, but their population at the HF level is clearly lower than one (≈ 0.6). We note that the DFT/KS and HF approaches are based on a single determinant and that a f population can only arise when the Ce 4f orbital partially accomodates an electron pair. Since the Ce 4f shell is already quite compact, the interelectronic repulsion 13



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in it is quite high and the HF approach tends to avoid a partial 4f occupation by electron pairs. The electron interaction in f shells however is not well described by standard DFT and often a tendency to overfill the Ce 4f shell results. The CASSCF calculations can handle the Ce 4f occupation of these complexes more accurately, since also occupancy with unpaired electrons is allowed. The results reveal that the CH2 CeF2 complex has a high (≈ 1.2) f occupation, whereas the oxygen species still shows a f occupation (≈ 0.7) which is similar to the one found by the HF calculation. This leads to the conclusion that the methylene compound has substantial multi-configurational character and might be close to a Ce(III) system, whereas the oxygen compound might resemble a mixed Ce(IV)/Ce(III) system. It has to be noted that the CASSCF numbers listed in Table 3 do not distinguish between contributions from an unpaired electron located in the Ce 4f shell and those from partial donation of electron density by electron pairs of the ligands to the Ce 4f shell. In order to clarify the electronic structure in more detail we investigated this question further by using orbital rotations of the active orbitals at the CASSCF(2,2) level for both complexes. Table 3: Comparison of the Mulliken f populations at the HF, UHF, CASSCF and DFT level. In case of CH2 CeF2 the results obtained from the difference of the UKS/UHF α and β spin density matrices is given in parentheses. method BP86 B3LYP M06 HF UHF

f populations basis CH2 CeF2 OCeF2 TZVP 1.29 (0.87) 1.18 TZVP 1.27 (0.99) 1.03 TZVP 1.29 (0.98) 0.93 TZVP 0.63 TZVP 1.20 (0.99)

HF UHF CAS(2,8) CAS(2,2)

VTZ VTZ VTZ VTZ

0.64 1.19 1.18 1.20

0.66 0.66

In the following an active orbitals rotation angle of 0◦ corresponds to the CASSCF natural orbitals provided by the MOLPRO code. 22 For "normal" closed-shell systems these usually 14


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lead to the most compact wavefunction in terms of the number of significantly contributing determinants in the CI expansion, e.g., a wavefunction with a clearly dominating HF closedshell determinant. In "unusual" situations, e.g., the stretching of a covalent bond, this might not be the case and other than the CASSCF natural orbitals possibly lead to a more compact wavefunction. Similarly, when seeking a reasonable assignment of the electron distribution to individual atoms or fragments, localized orbitals might be more convenient than the usually quite delocalized CASSCF natural orbitals. In the remainder we focus on two cases of active orbitals: the set which leads to the most compact wavefunction and the one which is most localized on Ce respectively C/O. The rotation angle of the active orbitals was varied between 0◦ and 90◦ in steps of 1◦ for both complexes. In each step the character of the orbitals was monitored using Mulliken population analysis and the corresponding CI coefficents were evaluated. After this procedure the orbital rotation was refined in steps of 0.1◦ to obtain the rotation angle with maximized Ce 4f character. These results are shown in Figures 2 and 3 for the two cerium compounds. As it can be seen from Figure 2 and Table 4, nearly pure Ce 4f and C 2p orbitals could be created by applying unitary orbital rotation (42.6◦ ) in the active space for the methylene complex. At this point the configuration contributions to the wavefunction are 92.7%f 1 p1 +5.7f 0 p2 +1.6%f 2 p0 , which means that the CASSCF(2,2) wavefunction is dominated by the Ce 4f 1 C 2p1 configuration. Close to this rotation angle are two choices (37.0◦ , 53.0◦ ) for which the contribution of one of the two closed-shell configurations vanishes, i.e., the wavefunction becomes most compact, despite that is is set up for approximately pure Ce 4f and C 2p orbitals. The CASSCF natural orbitals (0◦ ) also lead to a compact wavefunction with only two contributing closed-shell configurations, however the orbitals are almost 1:1 mixtures of Ce 4f and C 2p. According to these results we conclude that the CH2 CeF2 is best described as a Ce(III) compound and is therefore another example for a molecular analogue of a Ce(III)-based Kondo-system. It is obvious from Figure 3 and Table 4 that the electronic structure of the oxygen compound

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differs significantly from the one of the methylene complex. The most compact wavefunction with one strongly dominating closed-shell configuration is obtained for the CASSCF natural orbitals (0◦ ). According to the prescription for determining the oxidation state by Karen et al., 2 given also in the introduction, one has to assign the two active electrons to oxygen and therefore ends up with Ce4+ , i.e., a Ce(IV) compound as assigned by Mikulas et al. 20 This assignment is the better founded the less the bonding orbital is mixed. Here significant Ce 4f and 5d contributions are present besides the dominant O 2p character. No nearly pure Ce 4f orbital could be obtained by active orbital rotation, however the active orbitals could be separated into one orbital with nearly pure O 2p character and one orbital with a mixed but also nearly pure Ce 5d/4f character, for which the f contribution was maximized (32.0◦ ). In this situation it is still possible to clearly assign one orbital to cerium and one orbital to oxygen, which gives us the option to investigate the oxidation state of cerium by analyzing the CI coefficients of the CASSCF(2,2) wavefunction. The configuration contributions of the wavefunction are 50.4%(d/f )1 p1 +46.0%(d/f )0 p2 +3.6%(d/f )2 p0 , which is approximately 50% Ce(III) and 50% Ce(IV), but with a slightly dominating Ce(III) character. According to these values the OCeF2 complex can be classified as a mixed valent Ce(III)/Ce(IV) compound. Table 4: Configuration contributions [%] to the 1 A1 CASSCF(2,2) ground state wavefunction of the CH2 CeF2 and the OCeF2 complexes at their HF/RS2C optimized geometries using an orbital a with dominant p character of carbon (or oxygen) and an orbital b with maximized f character (upper line). The corresponding results for the most compact description with only two configurations are also listed (second line). The Ce f and C (or O) p populations of the active orbitals were obtained from a Mulliken analysis. Z CH2 O

rotation Z p pop. angle of orbital a ◦ 42.6 0.883 53.0◦ 0.870 32.0◦ 0.0◦

0.951 0.614

Ce f pop. Ce d pop. contributions 1 1 of orbital b of orbital b a b a2 b0 a0 b2 0.981 0.020 92.7 5.7 1.6 0.950 0.035 86.3 0.0 13.7 0.417 0.301

16

0.496 0.259


50.4 46.0 0.0 98.4

3.6 1.6

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Ce 4f character of MO a and b

1.0

orbital a orbital b 42.6°

0.8 0.6 0.4 0.2 0.0 0

10

20

30 40 50 60 rotation angle [°]

1.0 configuration contribution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


70

80

90

2 0

a b a0b2 1 1 a b 42.6°

0.8 0.6 0.4 0.2 0.0 0

10

20

30

40

50

60

70

80

90

rotation angle [°] Figure 2: Orbital characters (top) and configuration contributions (bottom) in CH2 CeF2 at the CASSCF(2,2) level using the VTZ basis sets. The vertical line indicates the rotation angle with maximum f -character of orbital b.

17


Page 18 of 31

orbital a orbital b 32.0°

0.4

0.3

0.2

0.1

0.0 0

10

20


70

80

90

1.0 configuration contribution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ce 4f character of MO a and b


0.8

2 0

a b 0 2 a b 1 1 a b 32.0°

0.6 0.4 0.2 0.0 0

10

20


70

80

90

Figure 3: Orbital characters (top) and configuration contributions (bottom) in OCeCH2 at the CASSCF(2,2) level using the VTZ basis sets. The vertical line indicates the rotation angle with maximum f -character of orbital b.

18


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In order to classify the interaction of the active orbitals, occupation number fluctuation and local spin were calculated for the localized orbitals. 42,43 As it can be seen in Figure 4 the interaction Ce4f -C2p of the methylene compound is covalent. The values arising from the Ce4f -C2p interaction in the CASSCF(2,2) space are similar to those found for a stretched hydrogen dimer at a bond distance of about 2 Å. The point for the oxygen complex is located to the left of the curve for a dissociating single bond. The lower value for the local spin is in line with the assigned mixed valency as well as a higher ionic character.

0.8 0.7

H2 R=Re LiF

0.6

^

Au2

CeCp2NH

OCeF2

2

^

2

charge fluctuation: sqrt()

ideal covalent bond dissociated covalent bond

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5

Be2

0.4 -

Cp2CeCH 4f-p CH2CeF Ce(C H )24f-p 4f-π 8 6 2

0.3 0.2

Hg2 o

0.1

He2 0.0 0.0

0.1

Cp2CeCH2(CASSCF) 4f-p 0.2

0.3

0.4

0.5

0.6

0.7

0.8

^ 2> local spin:

Assigning the Cerium Oxidation State for CH2CeF2 and OCeF2 Based

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