Electronic Structure of Ytterbium Bis-indenyl and - American Chemical

Article pubs.acs.org/Organometallics

Electronic Structure of Ytterbium Bis-indenyl and -cyclopentadienyl α-Diimine Complexes: A DFT and MS-CASPT2 Investigation Nuno A. G. Bandeira,† Chantal Daniel,‡ Alexander Trifonov,§ and Maria José Calhorda*,† †

Departamento de Química e Bioquímica, CQB, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal ‡ Laboratoire de Chimie Quantique, Institut de Chimie, UMR 7177−CNRS/UDS, 4 Rue Blaise Pascal, B.P. 1032 F-67070 Cedex, Strasbourg, France § G. A. Razuvaev Institute of Organometallic Chemistry of Russian Academy of Sciences, Tropinina 49, 603950 Nizhny Novgorod, GSP-445, Russia S Supporting Information *

ABSTRACT: The electronic structure of Yb(Cp′)2(N−N) complexes with Cp′ = η5C5R5 (Cp*) or η5-C9H7 (Ind) and N−N = DAB (N,N′-tert-butyl-1,4-diazabutadiene), bpy (2,2′-bipyridine), and pyca ((E)-N-(pyridine-2-ylmethylene)aniline) was investigated by means of DFT and ab initio (CASSCF/CASPT2) calculations. Whereas the agreement between experimental features and theory is fair for the Yb(Ind)2bpy molecule, the description of the electronic ground state of Yb(Ind)2DAB and of the Cp* complexes is more problematic. The relative energies of the closed-shell singlet, lowest open-shell singlet, and triplet were calculated for Yb(Ind)2DAB with various functionals at the DFT level, which overstabilize the closed-shell singlet. All functionals place the open-shell singlet energetically close to the triplet state. The best functionals (B3LYP, M06, TPSSh) estimate the singlet−triplet energy gap in the range 17−28 kJ·mol−1, in disagreement with the experimental data. The electronic structure of the smaller and more symmetric system Yb(η5C5H5)2(N−N) (N−N = DAB, bpy), for which DFT fails at describing the ground state, has been investigated by CASSCF/ CASPT2 calculations. The lowest energy electronic ground state corresponds to a (4f(Yb))2(π*DAB)0-(4f(Yb))0(π*DAB)2 (1A1) state, nearly degenerate to the triplet 4f(Yb)1(π*DAB)1 configuration according to a diradical picture.

1. INTRODUCTION The organometallic chemistry of ytterbium has been very much studied in recent years, and metallocene derivatives contribute significantly to this interest.1 α-Diimines are among the ligands that can stabilize bis(metallocene)Yb derivatives, leading to a variety of complexes displaying unusual properties and reactivity.2 The most stable oxidation states of Yb are YbII and Yb III , leading to a complete 4f 14 shell or a 4f 13 configuration, respectively.3 The combination of redox noninnocent 1,4-diazabutadiene ligands (DAB)4 and ytterbium ion, in one molecule, had a considerable impact on the development of the redox organolanthanide chemistry.2 This idea turned out to be fruitful and revealed new challenging phenomena such as solvent-mediated redox transformations5 and temperatureinduced redox isomerism.6 Moreover, the studies on the reactions of ytterbocenes with diimines recently demonstrated new examples of the effect of steric factors on the outcome of redox reactions. The possibility to govern the metal−ligand electron transfer process by modification of the steric demand of the ligands attached to the ytterbium atom as well as of that of the diimine molecule has proved to be a reality.7 Noticeable electron-accepting properties of diazabutadienes8 normally allow oxidation of ytterbocenes, Cp2Yb(THF)2 (Cp = C5H5, C5Me5, C9H7, CH2-1-C9H6),5,9 to afford the metallocene-type Yb(III) complexes Cp2YbIII(DAB−•), containing the radical anionic diazabutadiene ligand. Magnetic measure© 2012 American Chemical Society

ments of crystalline samples of complexes (C9H7)2Yb(tBuNCHCHNtBu),5c (C9H6CH2)2Yb(tBuNCHCHNtBu),5c (C9H7)2Yb(iPr2C6H3NCHCHNC6H3iPr2),5b and (C5MeH4)2Yb(iPr2C6H3NCHCHNC6H3iPr2)6 in the temperature range 2−300 K showed that the experimental values of the magnetic moments are considerably lower than expected for molecules containing two noninteracting paramagnetic centers (Table 1). Indeed, for complexes containing noninteracting spins their contribution to the molar magnetic susceptibility is additive. Trivalent ytterbium is paramagnetic with electron configuration 4f13, and the expected magnetic moment of YbIII complexes is 3.8 μB at 5−30 K and 4.5 μB at 90−300 K.10 Yb(III) complexes should have a ground state with one unpaired f electron, with the term symbol of the metal 2 F7/2, and a magnetic moment (μ) of 4.53 μB.1 An YbIII complex additionally containing a radical anion should show a magnetic moment of 4.2 μB in the temperature range 5−30 K and 4.8 μB in the temperature range 90−300 K, provided that the spins of the two unpaired electrons do not interact. In order to rationalize such a decrease of the values of magnetic moments of the above-mentioned complexes, the phenomena of redox tautomerism between diamagnetic (C9H7)2YbII(L0) (1 in Scheme 1) and paramagnetic (C9H7)2YbIII(L−•) (2 in Scheme Received: February 2, 2012 Published: June 19, 2012 4693

dx.doi.org/10.1021/om300081j | Organometallics 2012, 31, 4693−4700

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(pyridine-2-ylmethylene)aniline) (pyca) diimine complex are scarce,19 this system can be considered as intermediate between DAB and bpy in terms of π system and was therefore included. Computational work has been performed in order to understand several aspects of bonding and properties of ytterbium complexes using DFT approaches. Several authors have reproduced the main structural features.20−27 Andersen and co-workers published extensive work on the experimental and computational chemistry of Yb metallocene derivatives, going from a DFT approach to CASSCF in the more recent papers.11,12,16,28−30,17,31 The relevant results will be discussed later. CASSCF and CASPT2 studies were also carried out to study the nature of the metal−metal bond between a lanthanide or actinide metal and a d-transition or main group metal.32 The aim of the present work is to analyze the bonding and magnetic properties of the bis-indenyl ytterbium Yb(C9H7)2 complexes with the DAB, pyca, and bpy ligands (Scheme 2) using DFT calculations. In order to overcome the limitations of the DFT methodology,33 a MS-CASPT234 approach was used to study the smaller cyclopentadienyl analogues, which also have higher symmetry.

Table 1. Magnetic Moments for Yb(Cp*)2 and Yb(Ind)2 Complexes with α-Diimines (DAB and bpy)

a

complex

μeff (2 K, 300 K), μB

ref

(C9H7)2Yb(tBuNCHCHNtBu) (C9H6CH2)2Yb(tBuNCHCHNtBu) (C9H7)2Yb(iPr2C6H3NCHCHNC6H3iPr2) (C5MeH4)2Yb(iPr2C6H3NCHCHNC6H3iPr2) (C5Me5)2Yb(tBuNCHCHNtBu) (C5Me5)2Yb(bpy) (C9H7)2Yb(bpy) (C9H6R)2Yb(bpy), R = SiMe2NtBu

1.6, 3.4 1.5, 3.0 1.54, 3.40 1.64, 4.06 3.6 (4.1)a 2.4a 0 0

5c 5c 5b 6 12 (5a) 11 5b 13

300 K.

Scheme 1

2. COMPUTATIONAL DETAILS

1) isomers and antiferromagnetic coupling of the two unpaired electrons in (Ind)2YbIII(L−•) (L = diazadiene; 2 in Scheme 1) were invoked. Trifonov et al.7b also studied the magnetic properties of bpy complexes, having found that Yb(Ind)2(bpy) is diamagnetic. However, Yb(η5-Cp*)2(bpy) (Cp* = C5(CH3)5), with the same diimine but a different ring, is already paramagnetic, with a magnetic moment value of 2.4 μB.11 Magnetic moments of these complexes are listed in Table 1. These facts led, as mentioned above, to two hypotheses to account for the magnetic behavior of Yb(η5-Cp*)2(bpy): there is either spin coupling between the Yb(III) and bpy•− fragments or tautomerism14 between the two forms with oxidation states Yb(II) and Yb(III), as 1 and 2 in Scheme 1. This second hypothesis was refuted by further experimental evidence;15 namely, the UV−visible spectrum is invariant with temperature, meaning that somehow there must be a charge transfer between ytterbium and the ligands and intramolecular spin coupling. In order to explain the reduced values of magnetic moment of complex Yb(η5-Cp*)2(κ2-bpy), Andersen and co-workers invoked the ytterbium intermediate valence due to a multiconfigurational electronic state (Kondo effect).16,17 The complexes of the two diimines, DAB and bpy, also differ in their reactivity in several reactions. 5b While Yb(Ind)2(RNCHCHNR) with R = 2,6-iPr2Ph forms easily from the Yb(Ind)2(THF)2 precursor, the analogous reaction of the Yb(η5-C13H9)2(THF)2 (C13H9 = fluorenyl) derivative occurs with C−H bond activation or C−C bond formation.18 In this reaction, besides the different ring, the steric influence of the rings may also play a role. These facts led us to investigate the electronic structure of the three diimine complexes depicted in Scheme 2. Although experimental results on the (E)-N-

DFT calculations33 were performed with the ADF program.35 Gradient-corrected geometry optimizations36 were performed using the local density approximation of the correlation energy (Vosko− Wilk−Nusair)37 and the generalized gradient approximation (Becke38 and Perdew39 exchange and correlation corrections). Relativistic effects were treated with the ZORA Hamiltonian.40 Unrestricted calculations were performed for open-shell species. Geometries were optimized in the closed-shell singlet and triplet states for the three bisindenyl-Yb (no symmetry) and three bis-CpYb (C2v symmetry) complexes. A triple-ζ uncontracted Slater-type basis set with two polarization functions (TZ2P) and a frozen core was used in all the elements except hydrogen, namely, [Pd] for Yb and [He] for C and N. There were convergence difficulties with Yb-DAB and Yb-pyca (Scheme 2), which were overcome by a thermal population smearing with an initial value of 0.01 hartree. The resulting minima were again reoptimized with integer occupations. Single-point calculations of the Yb-DAB complex listed in Table 4 were performed for the closed-shell singlet, open-shell singlet, and

Table 2. Relevant Distances (Å) of the Optimized (BP86) Geometries of Yb-DAB, Yb-pyca, and Yb-bpy

triplet states, using a variety of functionals, and the geometries were optimized with BP86 for each spin state. An all-electron basis set was used in these single-point runs since the frozen core approximation is not rigorously correct for hybrid functionals. Three-dimensional representations of the structures and isosurface plots were obtained with Chemcraft.41 Complete active space perturbation theory second-order (CASPT2) calculations,34 based on multiconfigurational CASSCF42 reference wave functions, were performed with the program43 MOLCAS 7.6. An

Scheme 2

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Yb-bpy complexes were optimized using the BP86 functional (ADF) in both spin multiplicities, singlet and triplet, based on the structures of Yb(Ind) 2 (tert-butyl-DAB) 5c and Yb(Ind)2(bpy),5b shown in Figure 1 and depicting the orientation of the two indenyl ligands. The singlet-state geometry had the lowest energy for the three complexes.

Table 3. Energy Difference (eV) between the Singlet and Triplet States of the Three Yb-DAB, Yb-pyca, and Yb-bpy Complexes Calculated with the BP86 and OPBE Functionals (relative to the more stable singlet state) complex

BP86

OPBE

Yb-DAB Yb-pyca Yb-bpy

+0.615 +0.580 +0.918

+0.539 +0.549 +0.808

Table 4. Relative Energies (eV) between Different Configurations in Yb-DAB: Singlet, Triplet and Open-Shell Singlet (OSS) functional

Esinglet

Etriplet

EOSS

% HF exchange

B3LYP*56 B3LYP57 BH&H58 RPBE59 OPBE53 OP8660,39 Becke0061 OPBE052 BP8638,39 τ-HCTH-h62 TPSSh63 M0664 M06-L65

0.0 0.0 0.281 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.267 0.176 0.0 0.510 0.607 0.600 0.355 0.162 0.511 0.311 0.288 0.174 0.464

0.324 0.243 0.215 0.511 0.599 0.600 0.372 0.237 0.544 0.373 0.367 0.293 0.554

15.0 20.0 50.0 0.0 0.0 0.0 11.7 25.0 0.0 15.0 10.0 27.0 0.0

Figure 1. Relevant bond lengths (Å) of the crystal structures of YbDAB5c and Yb-bpy5b taken from the literature.

Some results are summarized in Table 2. The Yb−N distances are always longer in the singlet state (diamagnetic YbII) than in the triplet state (paramagnetic YbIII), as discussed later. The experimental distances Yb−N, NC, and C(sp2)− C(sp2) in Yb-DAB (Figure 1) are closer to those of the triplet model, while the same distances in Yb-bpy (Figure 1) are closer to the optimized singlet model (Yb−N and C(sp2)−C(sp2) bonds are further apart). In the case of Yb-pyca no comparison can be made, but, owing to the asymmetry of the ligand (pyca) itself, the two interatomic distances Yb−N and NC will always be different. The electronic structure of the closed-shell singlet models has two interesting features (Figure 2). The HOMO−LUMO

ab initio model potential and basis set published by Seijo and Casarrubios44 for ytterbium were used with 24 electrons in the valence shells and the following primitive functions (14s10p9d8f3g) contracted to [6s5p5d4f1g]. In the remaining elements the atomic natural orbital basis sets of Roos and Widmark45−47 were used with two s and one p function on hydrogen and three s functions, two p, and one d function on carbon and nitrogen. In the CASPT2 perturbational treatment only the chemical valence electrons were correlated in each atom; all specifications used were the program defaults. The C2v point group symmetry was imposed. The Cholesky integral decomposition and density fitting technique48 was used to improve computational speed. Strong damping was applied (SXDAMP = 5 × 10−5) in the active space orbital optimization. A nonstandard IPEA of 0.0 was used in the zeroth-order Hamiltonian. An imaginary level shift49 of 0.2 hartree was used in the perturbational part of the calculation. The 1,3A1, 1,3A2, 1,3B1, and 1,3B2 wave functions were computed at the CASSCF level of theory. When necessary, in case of neardegeneracy of strongly interacting states, state average CASSCF wave functions were computed including the two lowest states. Sixteen electrons were correlated in 13 active orbitals, namely, three orbitals in a1, a2, and b2 symmetries and four orbitals in b1, whereby an attempt was made to correlate the orbitals in each of the chemical fragments [π(Cp), π(κ2-CH3NCHCHNCH3) and the 4f AOs] in a balanced and computationally feasible way. CASSCF calculations including 14 electrons in 8 active orbitals or 24 electrons in 13 active orbitals have been performed in order to obtain a correct “single-determinant” description of each low-lying singlet and triplet state and to validate the 16e13a CASSCF where electronic relaxation is taken into account. The geometries used were those of the triplet state (BP86, see above) since they better reflect the experimental geometries.

Figure 2. Energy of the frontier orbitals (BP86) of the three closedshell structures with the corresponding LUMOs.

gap is very small and decreases in the order Yb-bpy (0.1 eV) >Yb-DAB (0.06 eV) >Yb-pyca (0.02 eV). This property should be associated with their respective magnetic properties (recall that Yb-bpy is diamagnetic and that Yb-DAB has μ = 3.4 μB). Yb-pyca should have a magnetic moment (∼4.5 μB). The LUMO of all three complexes has a dominant contribution of the π* orbital of the diimine ligand, with a small percentage of a 4f orbital. These LUMOs will be occupied if there is a charge transfer from the metal center to the ligand,

3. RESULTS AND DISCUSSION Electronic Structure of the Bis(indenyl) Complexes: Yb-DAB, Yb-pyca, and Yb-bpy. The geometries of the YbDAB (DAB, Scheme 2, modeled by Me2-DAB), Yb-pyca, and 4695


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spin energetics of the singlet, triplet and open shell singlet states. The latter can be estimated with the broken spin technique.54 In a weak bonding regime, each of the half filled orbitals is localized and their overlap integral is close to zero Sab∼ 0 (here the SOMOs are localized in ytterbium and in the nitrogen base as seen in Figure 3), so the energy of the open-shell singlet is expressed by EOSS = 2EBS − E3ψ (EBS and E3ψ are the broken symmetry and the triplet state energies, respectively) and the broken symmetry wave function is defined as SOMO(Yb)↑ SOMO(π-DAB)↓. The results listed in Table 4 show the difference between functionals with and without exact exchange. All listed functionals, except Becke half and half (BH&H), which is the only outlier, place the singlet state as the lowest energy one. The spin flipping energy is directly proportional to the amount of Hartree−Fock exchange in line with current work on this subject.55 Reiher and Salomon56 showed that the best description of the spin state behavior in iron complexes is obtained using B3LYP functionals with a 15% HF exchange (B3LYP*). Electronic Structure of the Bis(cyclopentadienyl)complexes: Yb-DAB* and Yb-bpy*. In the previous section, it was shown that DFT could describe the properties of the diamagnetic Yb-bpy complex, but there were problems when dealing with the paramagnetic Yb-DAB. On the other hand, the analogous pentamethylcyclopentadienyl complexes Yb(η5Cp*)2(bpy), referred as Yb-bpy*, and Yb(η5-Cp*)(DAB), referred as Yb-DAB*,17,5a are both paramagnetic (Table 1). Thus, these two complexes (Cp will be used instead of Cp*) were also examined with DFT. The structure of the two models Yb-DAB* and Yb-bpy* (Figure 4, showing the higher symmetry of these complexes compared with their indenyl congeners) was optimized at the DFT level, under C2v symmetry, in both the closed shell singlet and the triplet state. The singlet state geometry has a lower energy for both Yb-DAB* (0.737 eV) and Yb-bpy* (1.008 eV), but the structure obtained for the triplet state shows a much better agreement with the experimental ones, as can be seen in Figure 4 for the DAB complexes. The C2−C2′ bond of the diimine is much longer in the singlet state structure. A thorough discussion on the structures of Cp*Yb derivatives of bpy and its substituted forms has been reported.17,31 The HOMO−LUMO gap (closed-shell calculation) of 0.375 eV for Yb-bpy* is higher than the one for Yb-DAB* (0.368 eV), following the same trend already observed for the indenyl derivatives (figure 5). The first virtual orbital of Yb-DAB*

resulting in a possible triplet configuration, as can be seen from the spin densities drawn in Figure 3.

Figure 3. Spin densities (ρα−ρβ) gathered from the triplet state (S = 1) for Yb-DAB, Yb-pyca, and Yb-bpy.

The Yb−N bond lengths are shorter in the triplet state. Taking the Yb-DAB model, for example, the ytterbium formal oxidation state increases when moving to the triplet state. The Hirshfeld50 charges, valued at +0.57 for ytterbium and −0.11 for both nitrogen atoms in the singlet state, shift to +0.64 for Yb and −0.17 for N in the triplet state. The Yb−N Nalewajski51 bond order also increases from 0.8 to 1.0 when changing to the triplet state, while the overlap population between Yb and N increases from 0.09 to 0.12. The N−CH and CH−CH bond lengths change according to the bonding or antibonding character of the π orbital of DAB contributing to the LUMO; namely, the N−C bond will become longer and the CH−CH bond shorter. The BP86 GGA functional has been considered among the worst in a single-determinant ΔSCF assessment of the energetics of different spin multiplicities. Therefore, the geometries of the three Yb-DAB, Yb-pyca, and Yb-bpy complexes were reoptimized with the OPBE52 functional with the intent of testing the theory of competing tautomers. The use of OPTX exchange is known53 to give more accurate results in spin-state energetics. The energies for the closed-shell singlet → triplet transition are listed in Table 3. The results are consistent with the diamagnetism observed for the Yb-bpy complex, but, even assuming a considerable margin of error in the computation, the differences between both multiplicities are still too large, the singlet state being overstabilized. The difficulties in obtaining a self-consistent field in the DFT calculations and the very close proximity in energy of both the HOMO and LUMO in the singlet states all point to a multireference problem for the paramagnetic complexes. The Yb-DAB complex was examined with a little more detail within the DFT methodology. The stationary points for each multiplicity calculated with the BP86 functional were used in single point runs with several other functionals to obtain the

Figure 4. Relevant bond lengths (Å) of the crystal structure of Yb(η5-Cp*)(DAB) (left)5a and the optimized structure (BP86) of the simplified models Yb-DAB* and Yb-bpy* (triplet state). 4696


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have been performed for two complexes representative of the compounds investigated experimentally, namely, Yb-DAB* and Yb-bpy*. For this purpose, various CASSCF active spaces have been built increasing the number of active electrons with a constraint on the virtual space and then increasing the virtual space in order to allow electronic relaxation for a realistic description of the 1,3A1, 1,3A2, 1,3B1, and 1,3B2 spectroscopic states. This complete analysis has been performed for the methyl-substituted DAB complex only. The geometrical structures were kept fixed to the DFT-optimized geometries depicted in Figure 4 (triplet state). The MS-CASPT2 results are reported in Table 5. Table 5. MS-CASPT2 Relative Energies (eV) of the LowLying 1,3A1, 1,3A2, 1,3B1, and 1,3B2 Electronic States of YbDAB* and Yb-bpy*a

Figure 5. Energy of the frontier orbitals (BP86) of the closed shell structures of Yb-bpy* (left) and Yb-DAB* (right) with the corresponding LUMOs.

(14b1) has predominant π character from the nitrogen base and an occupation number of 0.17 electron. The seven highest occupied molecular orbitals shown in Figure 6 are all 4f orbitals from ytterbium with occupation numbers of 1.9. Five of them, namely 14b2, 19a1, 8a2, 13b2, and 13b1, are nearly degenerate 4f orbitals (within 0.1 eV), while the energy of the remaining 18a1 and 12b1 orbitals is lower by about 0.25 eV. According to the results reported in Table 4 and the above DFT analysis of different complexes, it seems that a singledeterminant approach is not adequate for describing the complexity of the electronic structure problem in this class of molecules. Indeed, for all paramagnetic species, the closed-shell singlet was the most stable state, but the experimental geometry was best described by the triplet-state geometry. A more detailed analysis of the role of functionals for Yb-DAB confirmed the overstabilization of the singlet state. Only for the diamagnetic complex Yb-bpy was the lowest energy state correctly identified. A detailed MS-CASPT2 analysis of the lowlying excited states in Cp2Yb(DAB) and Cp2Yb(bpy) is therefore presented in the next section. MS-CASPT2 Analysis of the Low-Lying Electronic States of Yb-DAB* and Yb-bpy* Complexes. In order to decipher the results obtained by means of the DFT approach, MS-CASPT2 calculations based on CASSCF wave functions

state Yb-DAB* a1A1 a3A1 b1A1/b3A1 a1A2/a3A2 b1A2/b3A2 a1B1/a3B1 b1B1/b3B1 a1B2/a3B2 Yb-bpy* a3A1 b1A1/b3A1 a1A2/a3A2 b1A2/b3A2 a1B1/a3B1 b1B1/b3B1 a1B2/a3B2 a

MS-CASPT2 14e/ 8a

MS-CASPT2 24e/ 13a

MS-CASPT2 16e/ 13a

0 0.04 (310) 0.133/0.138 0.164/0.166 0.115/0.117 0.144/0.144 0.176/0.167 0.195/0.191

0 0.001 (260) 0.141/0.140 0.082/0.082 0.033/0.033 0.09/0.08 0.121/0.113 0.162/0.152

0 0.04 (310) 0.451/0.455 0.140/0.146 0.433/0.431 0.219/0.226 0.384/0.379

0.030 (240) 0.145/0.148 0.154/0.155 0.090/0.090 0.114/0.104 0.166/0.161 0.218/0.214

The values in cm−1 are reported in parentheses for the a3A1 state.

The first chosen CASSCF active space includes only the 14 4f electrons localized mainly on the Yb and the lowest π*DAB orbital, leading to a 14e8a CASSCF. In agreement with the

Figure 6. Frontier orbitals of Yb-DAB* in C2v symmetry. The occupied molecular orbitals are 4f Yb, while the LUMO (with a small occupation) is more localized in the DAB ligand. 4697


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Figure 7. MS-CASPT2 (14e/8a) natural orbitals involved in the two lowest 1A1 and 3A1 states for Yb-DAB* (top) and for Yb-bpy* (bottom).

results obtained by Eisenstein et al17,31 for Yb-bpy complexes, the electronic ground state of Yb-DAB corresponds to the a1A1 electronic configuration, which is found to be nearly degenerate with the lowest a3A1 (∼310 cm−1). When increasing the CASSCF active space to 24 electrons correlated in 13 orbitals by adding three filled orbitals in each symmetry (πDAB and πCp), the a1A1−a3A1 energy gap amounts to ∼260 cm−1. Increasing the virtual space by taking 8 occupied orbitals, 2 in each symmetry, and 5 virtual orbitals, we obtain a 16e13a CASSCF and a a1A1−a3A1 energy gap of ∼310 cm−1. The a1A1−a3A1 energy gap is consistent with the observed magnetic properties of this class of molecules with a coupling constant J on the order of a few hundreds of cm−1.17 The study of Yb-bpy* has been limited to the restricted 14e8a CASSCF since the results are very similar to the one obtained for the DAB-substituted complex, in agreement with the experimental findings and with the theoretical results by Eisenstein et al.17 Whatever the CASSCF active space, the electronic structure of the ground state appears to be a diradical with delocalized eigenfunctions over the 4f (Yb) and π*DAB orbitals, namely, a singlet (4f(Yb))2(π*DAB)0−(4f(Yb))0−(π*DAB)2 configuration, based on localized 4f(Yb) and π*DAB orbitals equivalent to the open-shell singlet 4f(Yb))1(π*DAB)1 configuration based on delocalized 4f(Yb)/π*DAB orbitals. According to the “diradical” picture, the singlet state is quasi-degenerate with the triplet electronic 4f (Yb)1(π*DAB)1 configuration. Formally, this scheme depicted in Figure 7 for the A1 states, and that holds for Yb-bpy* as well, should be the same in each of the symmetries. Indeed, this is illustrated by the results reported in Table 5 for the different sets of 1,3A2, 1,3B1, and 1,3B2. This qualitative picture, which cannot be described correctly by DFT methods, is complicated by the mixed composition of the 4f (Yb) orbitals in A1, B2, and B1 symmetries. This electronic distribution (e.g., 14e/8a CAS) generates two lowlying 1,3A1 states corresponding to 4f (Yb, b1) → π*DAB(b1) excitations, two 1,3A2 states corresponding to 4f (Yb, b2) → π*DAB(b1) excitation, two 1,3B1 states corresponding to 4f(Yb, a1) → π*DAB(b1) excitation, and one 1,3B2 state corresponding to 4f (Yb, a2) → π*DAB(b1). A quasi-degeneracy of the low-lying singlet and triplet states for all symmetries is retrieved within 50 cm−1 whatever the CASSCF active space, constrained to one virtual orbital (π* localized on the accepting ligand) or extended to a larger virtual

space taking into account electronic relaxation (CAS 16e18a). This important result is in favor of a diradical picture for the two investigated compounds. The electronic configuration (4f(Yb))2(π*DAB)0 + (4f(Yb))0−(π*DAB)2, corresponding to an ionic state, has a considerably high energy and was not picked up in the third root of A1 symmetry. Indeed a simple CAS-CI analysis of the energy spectrum reveals this configuration to be the eleventh root in the 14e8a active space with a distinctly higher energy than the ground state. The valence tautomerism hypothesis can therefore be discarded. As the electronic problem is very receptive to the methodology, single- or multiconfiguration methods, choice of the basis sets, and level of electronic correlation, it is also extremely sensitive to the acceptor ligand, as illustrated both experimentally and theoretically.17,31 At one extreme, the combination of indenyl with bpy (Yb-bpy above) gives rise to a well-characterized diamagnetic species, which can be studied with a DFT approach.5a,13 Replacing either indenyl by a cyclopentadienyl or bpy by DAB requires multiconfiguration methods. Indeed, depending on the ligands, we travel from a pure ideal diradical solution to a more ionic picture.

4. CONCLUSIONS The ytterbium complexes investigated in the present study illustrate the complexity of the electronic problem involving 4f orbitals in this class of molecules. The presence of nearly degenerate low-lying electronic states makes the use of any DFT method not straightforward. Indeed, the multireference character of the wave function may be responsible for the failure of the DFT approach at determining the correct electronic ground state of the system and consequently its magnetic properties. The influence of the acceptor ligand is dramatic, leading to various situations, from well-characterized diamagnetic species easily described by standard singleconfiguration DFT calculations, such as Yb(Ind)2(bpy), to more complex situations (Yb(Ind)2(DAB)) for which multiconfigurational methods are mandatory. Whereas DFT calculations can be applied on the real molecules investigated experimentally with the drawbacks described above, the ab initio calculations have to be performed on reduced model systems realistic enough for reproducing the electronic 4698


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complexity and specificities of the experimental systems. The lowest (1A1) energy state of Yb(η5-C5H5)2(DAB) corresponds to a 4f (Yb, b1) → π*DAB(b1) excitation, with the valence orbitals localized mainly on the 4fπ(Yb) and π*DAB.

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ASSOCIATED CONTENT

S Supporting Information *

Atomic coordinates for all DFT-optimized species. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.J.C. thanks Fundaçaõ para a Ciência e Tecnologia, Portugal, for financial support (Project PEst-OE/QUI/UI0612/2011) and N.A.G.B. for the Ph.D. grant SFRH/BD/17095/2004. M.J.C. and N.A.G.B. also thank Cooperaçaõ Luso-Francesa− Programa Pessoa 2006/2007 and 2011/2012. The Laboratoire de Chimie Quantique (LCQS) thanks the PHC PESSOA program (Project No. 24854XJ) and GENCI (Paris) for a grant of computer time at the national centers IDRIS and CINES. This work was partially supported by the Program of the Presidium of the Russian Academy of Science (RAS) and RAS Chemistry and Material Science Division.

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Electronic Structure of Ytterbium Bis-indenyl and - American Chemical

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