Investigation of the Electronic Structures of Organolanthanide

Article pubs.acs.org/JPCA

Investigation of the Electronic Structures of Organolanthanide Sandwich Complex Anions by Photoelectron Spectroscopy: 4f Orbital Contribution in the Metal−Ligand Interaction Natsuki Hosoya,† Keizo Yada,† Tomohide Masuda,† Erika Nakajo,† Satoshi Yabushita,† and Atsushi Nakajima†,‡,* †

Department of Chemistry, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ‡ JST-ERATO, Nakajima Designer Nanocluster Assembly Project, 3-2-1 Sakado, Takatsu-ku, Kawasaki 213-0012, Japan S Supporting Information *

ABSTRACT: The electronic structures of lanthanide (Ln) ions sandwiched between 1,3,5,7-cyclooctatetraene (COT), Ln(COT)2−, have been investigated by anion photoelectron spectroscopy. Complexes of 12 Ln atoms were investigated (excluding promethium (Pm), europium (Eu), and ytterbium (Yb)). The 213 nm photoelectron (PE) spectra of Ln(COT)2− exhibit two peaks assignable to the highest occupied molecular orbital (HOMO; e2u) and the next HOMO (HOMO−1; e2g) approximately at 2.6 and 3.6 eV, respectively, and their energy gap increases as the central metal atom progresses from lanthanum (La) to lutetium (Lu). Since lanthanide contraction shortens the distance between the Ln atom and the COT ligands, the widening energy gap represents the destabilization of the e2u orbital as well as the stabilization of the e2g orbital. Evidence for 4f orbital contribution in the metal−ligand interaction has been revealed by the Ln atom dependence in which the same e2u orbital symmetry enables an interaction between the 4f orbital of Ln atoms and the π orbital of COT.

1. INTRODUCTION Lanthanides (Ln) are a series of 14 elements succeeding lanthanum (La) in the periodic table. The Ln atoms have common electron configurations of a xenon core and some number of occupied 6s, 5d, and 4f orbitals.1,2 With increasing atomic number (AN), the electrons of Ln atoms gradually fill the 4f orbitals. This electron-shell filling is accompanied by a steady decrease in atomic and ionic radius along the Ln series, known as “lanthanide contraction.” Ln elements are generally characterized by the incomplete ability of 4f electrons to shield the outer electrons from increasing nuclear charge. The most stable oxidation state of all Ln elements is in general Ln(III). Therefore, organolanthanides in the trivalent state have been extensively studied in past decades.3 Recently, organolanthanide complexes have attracted significant attention4−9 for their applicability to molecular magnets,10−13 molecular catalysis,14,15 and luminescent devices.16,17 Furthermore, the stability of the half-filled f7 and completely filled f14 electronic configurations renders the +2 oxidation state accessible to europium (Eu) and ytterbium (Yb), respectively, and divalent compounds of these elements have been extensively employed in organic synthesis.18,19 Recently, the 1,3,5,7-cyclooctatetraene (C8H8; COT) dianion and its derivatives have played an important role in organo-f element chemistry.20 In particular, bulky silylsubstituted COT ligands, such as 1,4-bis(trimethylsilyl)© 2014 American Chemical Society

cyclooctatetraenide, have been useful in synthesizing novel sandwich complexes of f-elements, yielding multiple-decker structures.21−25 COT molecules possess nonplanar tub-like structures and are nonaromatic (i.e., they do not satisfy Hückel’s rule).26 However, since COT molecules can be converted to planar molecules by electron attachment27−32 or metal coordination,20−25,33−40 the planar dianion ligands of COT2− permit a new coordination environment that provides a unique ligand field around the spin carrier of Ln ions. Metal− ligand interactions, including 4f orbital splitting in the field of organic molecules, have been revealed in spectroscopic studies of the formation and properties of Ln−COT complexes. Previously, we reported the formation of multiple-decker sandwich Ln−COT complexes of [Lnn(COT)n+1] (Ln = cerium (Ce), neodymium (Nd), Eu, holmium (Ho), and Yb) and their characterization by mass, photoionization, and anion photoelectron (PE) spectroscopy.41−44 The formation mechanism and bonding nature of the organolanthanide complexes were further analyzed by wave function theory and density functional theory (DFT) calculations.45−47 In addition, the magnetic moments of [Lnn(COT)m] (Ln = Eu, terbium (Tb), Ho, thulium (Tm)) were measured by Stern−Gerlach magnetic Received: November 27, 2013 Revised: April 2, 2014 Published: April 18, 2014 3051

dx.doi.org/10.1021/jp411660e | J. Phys. Chem. A 2014, 118, 3051−3060

The Journal of Physical Chemistry A

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deflection experiments.48−50 Other researchers measured the mass-selected photodissociation spectra of organolanthanide complex ions of samarium (Sm), dysprosium (Dy), and Nd,51 while association and dehydrogenation products were observed when Ln+ reacts with COT.52−54 Complementing experimental studies, Dolg et al. theoretically investigated the Ln(COT) complex (Ln = Nd, Tb, and Yb) and found that trivalent Ln atoms possess a 4f n electron configuration.55−60 Very recently, the electronic states and molecular structures of monoligand M(COT) (M = scandium (Sc), yttrium (Y), lanthanum (La), Ce, praseodymium (Pr), Nd, and gadolinium (Gd)) were elucidated by pulsed-field ionization zero electron kinetic energy spectroscopy and theoretical calculations.61−63 Most researchers agree that the 4f orbitals are localized and play a marginal role in bonding, which is consistent with the common assumption that the Ln 4f orbitals are not usually involved in the chemistry and bonding of the Ln elements. This phenomenon can be explained by the significant contraction of the 4f orbitals relative to the 5d and 6s orbitals. Indeed, theoretical calculations with small core (4f orbitals in the valence) and large core (4f orbitals in the core) effective core potentials (ECPs) predict similar molecular geometries.64−66 However, the electronic complexity of organolanthanide complexes presents considerable challenges to spectroscopy and quantum chemistry because of the unpaired 4f electrons and the competition of possible 4f → 5d and 6s → 5d electron promotions during complex formation. Several studies reported that 4f orbitals may turn out to be involved in the metal−ligand interaction if their energy approaches that of the interacting ligand orbitals.67,68 Furthermore, the molecular architecture of organolanthanide complexes is not easily controlled because, in addition to lanthanide contraction, Ln ions can adopt multiple higher coordination numbers. Therefore, a systematic analysis of their metal-dependent electronic properties is essential for understanding common organolanthanide complexes. The interaction between COT2− and atomic d and f orbitals of heavy metals has been extensively investigated for actinideCOT (actinocene).69,70 Among actinocenes, uranocene, U(COT)2, was first synthesized,33,34 and after the synthetic study, the electronic structures have been studied experimentally and theoretically.69−72 Since 10 π electrons in COT2− have valence electronic configurations of (Lσ(a1g))2(Lπ(e1u))4(Lδ(e2g))4, the symmetrized fragment orbitals of two COT2− interact dominantly with the metal valence d orbitals of dσg, dπg, and dδg, resulting in the orbitals of a1g and a1u from Lσ(a1g), of e1g and e1u from Lπ(e1u), and of e2g and e2u from Lδ(e2g), in order of increasing energy.69,70 For actinocenes, 6d orbitals are involved in the interaction, and the peaks in their UPS spectra were successfully assigned by the interaction scheme.69−72 Interestingly, it has been theoretically pointed out that the e2u orbitals can significantly interact with one of 5f orbitals (5fδ(e2u)).69 For Ln-COT, a similar interaction scheme seems applicable to understand the electronic structures with 5d and 4f, and indeed for Ce(COT)2, the electronic states have been revealed in experiments and calculations.55−60,73 Major difference in the interaction scheme between Ln and actinide systems exists in the degree of involvement of their 4f and 5f orbitals, respectively. Another motivation of this study is, though the above energy order has been explained successfully using the orbital overlap model, as discussed later, this simple model alone cannot explain the Ln dependence observed in the PE spectra.

Here we report a systematic study of the anion PE spectroscopic investigation of 12 species of Ln(COT)2− complexes (excluding promethium (Pm), Eu, and Yb). These Ln(COT)2− sandwich anions possess a highly symmetrical ionic-bonded sandwich structure (D8h). By investigating these species, we aim to elucidate their electronic structures systematically under identical environmental ligand effects. The PE spectrum yielded two peaks corresponding to the highest occupied molecular orbital (HOMO) and the next HOMO (HOMO−1). Note that HOMO−1 is the same with SHOMO, which abbreviates the notation of the second highest occupied molecular orbital. Since both of the e2u and e2g orbitals are doubly degenerate, the names of HOMO and HOMO−1 come from their energy levels. As the central metal atom progresses across the series from La to Lu, the energy gap, primarily representing the interaction of the Ln 5d orbitals with the ligand π orbitals of Lδ, widenes, because of the lanthanide contraction. The Ln atom dependence also reveales the interaction between the 4f orbitals of Ln atoms and the π orbitals of COT.

2. EXPERIMENTAL SECTION The experimental setups are detailed elsewhere.41,74,75 Briefly, Ln(COT)2− cluster anions were produced at room temperature by mixing laser-vaporized Ln atoms with vaporized COT molecules. Twelve Ln complexes from La to Lu (excluding Pm, Eu, and Yb) were prepared in this manner. Among the excluded species, Pm is radioactively unstable, and therefore is not available commercially, and Eu and Yb preferentially adopt the +2 over the +3 oxidation state, as previously reported.42−44 To record the PE spectra of the 12 Ln−COT species, cluster anions were coaxially extracted by a pulsed electric field of −3.0 and −1.5 keV in mass analysis and PE spectroscopy measurements, respectively. Once the cluster beam had decelerated, the mass-selected anion clusters were photodetached by a Nd3+: YAG laser pulsed at the third harmonic (355 nm, 3.49 eV), fourth harmonic (266 nm, 4.66 eV), and fifth harmonic (213 nm, 5.82 eV). The PE signal was accumulated from 30,000 to 50,000 shots by a multichannel scaler/averager, achieving an energy resolution of approximately 20 meV full width at half-maximum (fwhm) at 1 eV electron energy. The kinetic energy of the PEs was calibrated with the 1S0 → 2S1/2 and 1S0 → 2D5/2 transitions of gold (Au−).76,77 The range of photodetachment laser power was 1− 5 mJ/cm2 at 213 nm and 10−20 mJ/cm2 at 355 nm. For comparison, the PE spectra of yttrium (Y) COT cluster anions were also measured using a Y rod. 3. COMPUTATIONAL DETAILS Ab initio Hartree−Fock (HF) and DFT calculations have been performed for Ln(COT)2− to optimize the structures with the large core ECPs and (7s6p5d)/[5s4p3d] basis functions of the Stuttgart/Cologne group78 for Ln and 6-31+G(d) for the COT part. Furthermore, to estimate the splitting energies of the X and X′ states of the neutral Ln(COT)2 complexes for Ln = La, Gd, Tb, and Lu, which are described later, spin-unrestricted DFT calculations have been conducted for the high-spin as well as the low-spin states. In these calculations, the 4f valence ECPs and the basis sets by Cundari and Stevens79 for the Ln atoms were used on the optimized structures for each anion complex with the large core ECPs, as described above. The DFT 3052



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calculations employed the B3LYP functional80 in the Gaussian 98 package.81 On the basis of their symmetries, the eight π molecular orbitals (MOs) of the COT ligand are denoted as nondegenerate Lσ, doubly degenerate Lπ, Lδ, and Lϕ, and nondegenerate Lγ. Thus, the valence electronic configurations of COT2− and COT− are Lσ2Lπ4Lδ4 and Lσ2Lπ4Lδ3, respectively. The symmetry of the aromatic ground state COT2− is D8h. For COT−, several isomeric structures (with symmetries of D4h, D2d, D4, etc.) have been reported.82,83 The valence electronic configurations of the ground states of La3+, Gd3+, Tb3+, and Lu3+ are 4f0, 4f7, 4f8, and 4f14, respectively.

4. RESULTS AND DISCUSSION Figure 1 shows the PE spectra of Ln(COT)2− sandwich anions (Ln = La−Lu) measured by 355, 266, and 213 nm detachment lasers. The PE spectra are independent of photon energy, although the energy resolution worsens in the low bindingenergy region with increasing photodetachment energy. Notably, all of the spectral features are attributable to photodetachment from an anion to a corresponding neutral, with negligible photoabsorption into electronically excited anionic states. 4.1. Two Major X and A Peaks. In the 266 and 213 nm spectra, two peaks (denoted X and A in Figure 1) appear consistently around electron binding energies of 2.6 and 3.6 eV. The vertical detachment energies (VDE) are shown in Table 1. The high similarity of the spectral features indicates common ionic bonding between Ln3+ and COT2− in the sandwich anions of Ln(COT)2−. Under D8h symmetry, the X and A peaks in the La(COT)2− spectrum could be assigned to electron detachments from the HOMO; Lδ(e2u) and HOMO−1; Lδ(e2g), respectively, as shown in Figure 2. The calculated respective energies of the detachments (2.36 and 3.55 eV) estimated from the negative of the HF orbital energies are indicated by red (e2u) and blue (e2g) bars in Figure 2a, and the HOMO (e2u) and HOMO−1 (e2g) are characterized as antibonding and bonding orbitals, respectively (Figure 2b). The calculated metal−ligand distance is 2.248 Å, and the La3+ ion is centralized in the La(COT)2− anions (D8h). This assignment should apply to each Ln(COT)2− anion in Figure 1. The ionic bonding configuration in the HOMO and HOMO−1 is common to all Ln(COT)2− anions because the electron number varies only in the 4f orbitals, which are core-like relative to the 5s and 5p orbitals, and thus play no essential role in bonding.64−66 Figure 1 shows that the intensity ratio between peaks X and A depends on the photodetachment energy; the peak A intensity is enhanced relative to the peak X intensity at higher detachment energy. This phenomenon can be explained by a well-known threshold rule for an atomic ion (Wigner’s law).84 In fact, the atomic angular momentum rules can be extended to molecules by group theory when the departing electron experiences a long-range potential because of polarization with the neutral and centrifugal potential. By assigning effective angular momentum to the MO of the photodetached electron, the selection rules developed by Reed et al.85−87 have been successfully applied to molecular systems.85−90 However, in this study of the ionic complexes of COT2−Ln3+COT2−, the intensity ratio between peaks X and A cannot be well reproduced by Wigner’s law (Supporting Information, part S1). This is likely because strong coupling by Coulomb interactions occurs when a departing electron leaves an

Figure 1. Photoelectron spectra of 12 species of organolanthanide sandwich complex anions (Ln(COT)2−; Ln = La−Lu) measured at detachment laser wavelengths 355, 266, and 213 nm: (a) La, (b) Ce, (c) Pr, (d) Nd, (e) Sm, (f) Gd, (g) Tb, (h) Dy, (i) Ho, (j) Er, (k) Tm, and (m) Lu. The X, X′, and A labels identify the electronic states of the corresponding neutrals, while the labels 1 and 2 correspond to excited vibrational states. 3053



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at other wavelengths (Figure 1). This result is expected because, as the photodetachment wavelength increases, the electrons are detached with a lower kinetic energy, and energy resolution is proportional to 1/√ΔE, where ΔE is the PE kinetic energy.91,92 In the PE spectra, electronic transitions between the electronic ground states of the anions and neutrals appear as the “X” peak accompanied by two vibrational excited states of the neutrals (“1” and “2”). The “1” and “2” states are assignable to a transition to an excited state of the corresponding neutral state. The energy separation is approximately 0.19 eV (1530 cm−1). Since an electron is detached from the antibonding molecular orbital of the COT carbon ring, as mentioned above, a plausible transition is an excited state of the vibrational stretching mode of CC (e2g). The reported CC stretching vibrational mode of COT2− in M−COT ranges from 1450 to 1498 cm−1.93−96 The observed vibrational mode is strictly that of the corresponding neutral of Ln3+(COT1.5−)2 or Ln3+(COT2−)(COT−), which accounts for the closely matched vibrational frequency. Similar features are observed in the spectra of Ce(COT)2−, Pr(COT)2−, and Nd(COT)2−, and these species exhibit the same energy gap between peaks X and 1 (0.18−0.20 eV). The PE spectral features of Ln(COT)2− (Ln = Sm, Gd, Tb, Dy, and Ho), however, differ considerably from those of La(COT)2−. These spectra are characterized by a pair of prominent peaks and accompanying smaller peak(s). Notably, toward the heavier side of the Ln series (Ho to Lu), the spectra return to a simple structure. Thus, the spectral features of middle-range Ln elements are more complicated than those of lighter and heavier elements in the series. As mentioned above, the HOMO is characterized by Lδ(e2u) symmetry, and the 4fδ orbital is apparently involved in metal−ligand interactions. According to this result, the spectral features are linked to the number of 4f electrons. To reveal the 4f-electron contribution, the PE spectra of Y(COT)2− clusters were measured. Y atoms preferably exist in the +3 oxidation state, and their ionic radius is similar to that of Ln atoms.97 Figure 3a and 3b show the PE spectra of Y(COT)2− and Tb(COT)2− at 355 nm, respectively. The ionic radii of Y3+ and Tb3+ are approximately equal (0.102 and 0.104 nm, respectively). Figure 3 shows that the PE spectrum of Y(COT)2− differs from that of Tb(COT)2− but is similar to that of La(COT)2−. This result clearly indicates that the pair of prominent peaks in the PE spectrum for Tb(COT)2− can be assigned to two different electronic states (X and X′ in Figures 1 and 3). Since Tb3+ ions possess eight 4f electrons, the spectral pattern changes in middle-range Ln elements can be attributed to the number of 4f electrons. Among the 4fσ, 4fπ, 4fδ, and 4fϕ orbitals, the 4fδ orbital appears important because the HOMO has ligand δ character (Lδ(e2u)), which enables mixing because of the same orbital symmetry, although the genuine exchange interaction is very weak between the Lδ(e2u) and 4fδ orbitals. In the photodetachment from the HOMO in Ln(COT)2−, the ground state anions can result in two spin states of low- and high-spins for the corresponding neutrals because the HOMO for the PE ejection is characterized by ligand MOs, and the spin and orbital (L−S) state of the 4f electron part should be conserved without involving bonding. For example, from the octet state (7/2 spins) of Gd(COT)2− in the ground state, nonet (8/2 spins), and septet (6/2 spins), neutral states are accessible by photodetachment (Supporting Information, Figure S1). In addition to the probing selectivity for the two

Table 1. Vertical Detachment Energy (VDE) of X, X′, and A Peaks in Ln(COT)2− Spectra (Ln = La−Lu, Excluding Pm, Eu, and Yb) and VDE of Subpeaks 1,2 (eV), Including Those of the Y(COT)2− Spectrum X

a

X′ a

Ln

expt

calcd

La Ce Pr Nd Sm Gd Tb Dy Ho Er Tm Lu Y

2.61 2.60 2.60 2.59 2.32 2.33 2.31 2.31 2.31 2.29 2.28 2.28 2.40

2.619

2.486 2.502

2.444

expt

2.52 2.49 2.49 2.46 2.39

calcda

2.612 2.657

1,2 expt 2.80, 2.80, 2.78, 2.79, 2.69 2.69 2.68 2.67 2.61 2.49 2.47, 2.48, 2.62,

2.98 2.98 2.97 2.98

2.63 2.67 2.79

A expt 3.64 3.67 3.67 3.66 3.64 3.66 3.67 3.69 3.73 3.74 3.75 3.76 3.73

DFT/B3LYP ECP = SBK (ref 79) for Ln and 6-31+G(d) for COT.

Figure 2. Assignment of the X and A peaks in the photoelectron (PE) spectrum of Ln(COT)2−. (a) PE spectrum of La(COT)2− at 213 nm. The values calculated with the Hartree−Fock method (2.36 and 3.55 eV) are indicated by the red (HOMO; e2u) and blue (HOMO−1; e2g) bars. (b) Antibonding HOMO (e2u) and bonding HOMO−1 (e2g) orbitals. (c) Schematic of the electronic configuration of two COT2− ligands interacting with a Ln atom. Orbital interaction preferentially stabilizes the HOMO−1 orbital because of the overlap between the Ln atomic orbital 5dδg (e2g) and the COT π orbital Lδ (e2g).

ionically bonded species behind. In addition to quantitative modeling for the photodetachment of ionic complex anions, it is essential to probe the intensity ratio more quantitatively with a tunable detachment laser together with the efforts to suppress stray electrons, an effect currently being investigated by our group. 4.2. Fine Structure in the First Band. Peak X in the PE spectra of Ln(COT)2− is more highly resolved at 355 nm than 3054



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Figure 4. Schematic for the configuration interaction between (4f)n(Lδ(e2u))3 and (4f)n−1(Lδ(e2u))4: (a) middle-range and (b) endrange Ln elements.

The importance of the configuration interaction in Ce(COT)2 was first pointed out by Dolg et al.;55,56 the oneelectron excited state with an Ln4+ electronic configuration can contribute to the neutral ground state by configuration interaction between (4f)n(Lδ(e2u))3 and (4f)n−1(Lδ(e2u))4. However, the peak pair caused by the configuration interaction for Ln(COT)2 is observed only for middle-range Ln (Figure 1). This is because no 4f electrons occupy the 4fδ(e2u) orbitals in Ln(COT)2− anions of lighter Ln. Notably, this stabilization mechanism is effective only between the two e2u pairs of orbitals, and the exchange interactions between the Lδ(e2u) and the other 4felse orbitals are much weaker. Therefore, other lowspin states not stabilized by the above mechanism can also be involved in the X′ peaks with levels almost degenerate with the high-spin states. The same is true in the single X peak for early Ln complexes. If the above mechanism for the energy gap between the X and X′ states is correct, their energy gap must be calculated consistently with the spin-unrestricted DFT treatment using different orbitals for different spins. For Gd(COT)2−, the VDEs for septet (6/2 spins) and nonet (8/2 spins) states are calculated to be 2.486 and 2.612 eV, while the experimental VDEs are 2.33 and 2.49 eV, respectively. Furthermore, for Tb(COT)2−, the VDEs for sextet (5/2 spins) and octet (7/2 spins) states are calculated to be 2.502 and 2.657 eV, while the experimental VDEs are 2.31 and 2.49 eV, respectively. Owing to the configuration interaction of the same orbital symmetry type, a low-spin state is more stable than a high-spin state in both Gd(COT)2 and Tb(COT)2 neutrals, and their energy difference is well reproduced by spin-unrestricted DFT calculations. Heavier Ln ions possess completely filled 4fδ(e2u) orbitals, and both the low- and high-spin states can be active toward the allowed electron spin configuration interaction (Supporting Information, Figure S1d), resulting in parallel energy shifts. However, the configuration interaction contribution turns out to be less prominent with increasing AN because the increment of fourth ionization energy into Ln4+ weakens the configuration

Figure 3. Photoelectron spectra of (a) Y(COT)2− and (b) Tb(COT)2− at 355 nm. (c) Schematic of the electronic configurations in middle-range Ln elements, in which the 4fδ orbital of the Ln3+ ion interacts with the e2u orbital of the (COT)2 ligands.

spin states in the photodetachment, the electron occupation in the 4f orbitals of 4fσ, 4fπ, 4fδ, and 4fϕ can explain the origin of the pair of prominent peaks X and X′. Since lighter Ln ions possess vacant 4fδ(e2u) orbitals, the PE spectra starting from Ln(COT)2− cannot provide information on electronic states involving interaction between 4f δ(e2u) and Lδ(e2u). Figure 3c is a schematic of the electronic interactions in middle-range Ln complexes. Once the 4fδ(e2u) orbital is partially occupied by electron filling to the 4f orbital, such as [(4felse)n−1(4fδ(e2u))1](Lδ(e2u))3, where 4fδ(e2u) consists of doubly degenerate 4fz(xx−yy) and 4fxyz, and 4felse denotes the other 4f components of 4fσ, 4fπ, and 4fϕ, the state can interact with the configuration of [(4felse)n−1(4fδ(e2u))0](Lδ(e2u))4 (characterized as Ln4+(COT2−)2) through configuration interaction allowed by the same spin multiplicity and orbital symmetry (Figure 4); i.e., only when the resultant electron spins in Lδ(e2u) and 4fδ(e2u) orbitals are antiparallel, the lowspin state is stabilized through configuration interaction, forming the stabilized ground state X (Figure 4a). Conversely, when the resultant electron spins in Lδ(e2u) and 4fδ(e2u) orbitals are parallel, the high-spin state is not stabilized, thereby forming the neutral excited X′ state. 3055



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VDE of the X state for middle-range Ln (Ln = Sm, Gd, Tb, Dy, and Ho) includes the additional stabilization of the corresponding neutral because of configuration interaction. These data for the X state were excluded in the fitting procedures, i.e., the VDE values of the X′ state were used for these species. The destabilization rate of e2u is 0.33 eV, which is larger than the e2g stabilization rate of 0.12 eV from La to Lu. These characteristics of the VDE values were calculated consistently with the theoretical HF-SCF and DFT methods. Figure 6 shows Ln atom dependence of orbital energies for the

interaction. Parts a and b of Figure 4 illustrate these situations schematically. When Ln is surveyed from La to Lu, middlerange Ln elements having 4fδ electrons exhibit stabilization of low-spin states via configuration interaction (Figure 4a). For heavier Ln elements, the fourth ionization energy becomes higher compared to lighter and middle-range Ln elements in the series, and the configuration interaction becomes smaller. In fact, the fourth ionization energy for heavier Ln is 1.5−4.0 eV higher than that of middle-range Ln. Moreover, the energy gap between X and X′ is only 0.08 eV for Ho(COT)2 neutral, although Ho(COT)2 possesses an active half-filled 4fδ orbital in our preliminary calculation. Therefore, it seems necessary to satisfy the following two conditions for the configuration interaction to be observed: (1) occupation of the 4fδ(e2u) shell by one or two electron(s), and (2) smaller fourth ionization energy of the Ln atom. Considering these conditions, the PE spectra of Pm(COT)2− should show the peak splitting for the lightest Ln complexes. However, this cannot be measured because of radioactive instability. 4.3. Lanthanide Atom Dependence. Figure 5 shows the VDEs of the Ln(COT)2− clusters (Ln = La−Lu, excluding Pm,

Figure 6. Ln atom dependence of orbital energies for the e2u and e2g states with the Hartree−Fock methods, where the experimental VDEs correspond to the calculated energies with opposite sign based on Koopmans’ theorem.

e2u and e2g states with the HF methods, where the negative of the orbital energies approximate the experimental VDEs based on Koopmans’ theorem. Similarly, the dependence was calculated with the DFT method, and both calculations are in agreement with the experimental results (calculated values in Table 2). In addition, in the calculations, the destabilization rate of e2u is larger than the stabilization rate of e2g; the former is

Figure 5. Vertical detachment energies of the peaks of Ln(COT)2− complexes (Ln = La−Lu, excluding Pm, Eu, and Yb): solid and open circles denote X and X′ states, respectively. Solid squares denote the A state. The relationship between VDEs and atomic number is determined by linear least-squares fitting.

Table 2. Calculated Orbital Energies of HOMO (e2u) and HOMO−1 (e2g) Using HF and DFT Methods and the Difference of Vertical Detachment Energy (ΔVDE) in eV

Eu, and Yb). As the AN increases, the e2u antibonding orbital destabilizes, while the e2g bonding orbital stabilizes. The former and latter phenomena may arise partly from repulsive and attractive interactions between two COT2− ligands, respectively. The attractive interaction occurs because symmetry permits a strong interaction between the Ln 5dδg (e2g) orbital and the COT π Lδ (e2g) orbital (Figure 2c).69−72 Consequently, with increasing AN, the energy gap (ΔVDE) between e2u and e2g would increase as the central Ln atom progresses from La to Lu. However, these simple arguments based on the covalenttype orbital overlap model cannot explain the difference in the larger destabilization rate of e2u and the smaller stabilization rate of e2g (Figure 5). For a more quantitative discussion, the relationship between vertical detachment energies and AN is determined by linear least-squares fitting. As discussed in the previous section, the

HF

3056

DFT

Ln

−εe2u

−εe2g

ΔVDE

ΔDFT(e2u)

ΔDFT(e2g)

ΔVDE

La Ce Pr Nd Sm Gd Tb Dy Ho Er Tm Lu

2.36 2.34 2.32 2.31 2.27 2.25 2.23 2.22 2.21 2.19 2.18 2.15

3.55 3.56 3.58 3.59 3.60 3.62 3.62 3.62 3.63 3.63 3.63 3.64

1.19 1.23 1.26 1.28 1.33 1.37 1.39 1.40 1.42 1.44 1.45 1.49

2.35 2.34 2.32 2.31 2.28 2.26 2.24 2.23 2.22 2.21 2.20 2.17

3.32 3.33 3.34 3.35 3.36 3.38 3.38 3.38 3.38 3.39 3.39 3.39

0.97 1.00 1.02 1.04 1.08 1.12 1.13 1.15 1.16 1.18 1.19 1.22



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Table 3. Experimentally Estimated Metal−Ligand Distances (d) in Ln(COT)2− Anionsa ΔVDE/eVb d/Å

La

Ce

Pr

Nd

Sm

Gd

Tb

Dy

Ho

Er

Tm

Lu

1.03 2.06

1.07 2.04c

1.07 2.04

1.07 2.04

1.12 2.02

1.17 2.00

1.18 1.99

1.23 1.97

1.34 1.93

1.45 1.88

1.47 1.87

1.48 1.87

a Experimentally determined metal−ligand distance of 2.04 Å. The Ce(COT)2− anion is used as a calibration datum. bFor lighter and heavier Ln (La, Ce, Pr, Nd, Er, Tm, and Lu), ΔVDE is given by X and A states, while for middle-range Ln (Sm, Gd, Tb, Dy, and Ho), ΔVDE is given by X′ and A states in Table 1. cReference 98.

metal−ligand distances in Ln(COT)2− anions are shown in Table 3. Although the molecular architecture of these complexes is difficult to control even in the common trivalent state, this systematic analysis of Ln(COT)2− anions and their PE spectra has yielded reasonable metal-dependent estimates of metal−ligand distances.

0.21 (0.18) eV, while the latter is 0.09 (0.07) eV from La to Lu with the HF and DFT methods, where the latter values are given in parentheses. Our theoretical analysis shows the AN dependence of the HOMO and HOMO−1 energetics can only be explained by combining several factors. The most important factor is lanthanide contraction, in which the ionic radius decreases with increasing AN, thereby shortening the intermolecular distance RLnCOT between the Ln atom and the COT molecule.1,2 The second factor is the very strong electrostatic interaction created by the formal charges of Ln3+ and COT2−. The importance of such intramolecular electrostatic interactions was emphasized in our previous work for related Ln− COT sandwich clusters.42−44,46,47 As RLnCOT decreases because of the lanthanide contraction, an electron in the HOMO localized in Lδ (e2u) (Figure 2c) is not only destabilized by the antibonding character but is also weakly stabilized by the approach of the positively charged Ln3+. This weak stabilization is also applicable to the HOMO−1 energy. As for the AN dependence of HOMO−1, the stabilization may be explained intuitively based on the covalent-type orbital overlap model between the 5dδg(e2g) and ligand Lδ(e2g) orbitals. However, this is not the right reason because the magnitude of the overlap, and thus their resonance interaction, was calculated to be almost constant across the Ln series. The crucial point overlooked in the simple explanation is the fact that the size of the 5d orbital on the central Ln atom is reduced at the same rate as the shortening of RLnCOT caused by lanthanide contraction. In fact, as the AN increases, their covalent-type interaction alone destabilizes the HOMO−1 energy because the interacting 5d orbital is destabilized by the approach of the negatively charged COT2− (Figure 2c). Therefore, the weak stabilization of the HOMO−1 is caused by the approach of the positively charged Ln3+ rather than by the increase of the orbital overlap; the former is the same electrostatic mechanism explained for the HOMO. Thus, the larger destabilization rate of e2u and the smaller stabilization rate of e2g noticed in Figure 5 can be explained by the differences in RLnCOT and 5d orbital sizes of Ln, and the very strong ionic character of the complexes. Here, the estimation of the metal−ligand distances using the changes in orbital energy is discussed in brief. Although the radii appear to decrease more rapidly at the start of the series, they decrease approximately linearly with increasing AN. From this trend, and the linear relationship between energy gap and AN, we can estimate the metal−ligand distances of Ln(COT)2− anions (Ln = La−Lu) experimentally. Since the difference in the ionic radii of the lightest and heaviest lanthanide elements (La3+ and Lu3+, respectively) is 0.19 Å, the ΔVDE difference of 0.45 eV between La(COT)2 and Lu(COT)2 provides a ratio of 0.42 Å/eV. The metal−ligand distance of the Ce(COT)2− anion is determined experimentally as 2.04 Å,98 providing a reliable calibration index for the other Ln atom−ligand distances in sandwich complexes. The experimentally estimated

5. CONCLUSIONS For Ln(COT)2− sandwich anions produced by laser vaporization, the electronic structures of organolanthanide complexes of 12 Ln atoms were investigated (the excluded species were Pm, Eu, and Yb). Anion PE spectroscopy and theoretical calculations revealed that Ln atoms, except for Eu and Yb, prefer the trivalent state in Ln(COT)2− sandwich anions, resulting in highly ionic species. In the PE spectra of the complexes of middle-range Ln elements, a pair of prominent peaks appears exclusively, revealing that the HOMO characterized by Lδ(e2u) symmetry interacts with the 4fδ orbital selectively in metal−ligand interactions. When the resultant electron spins in the Lδ(e2u) and 4fδ(e2u) orbitals are antiparallel, the low-spin state is stabilized through configuration interaction with the Ln4+ configuration, forming a stabilized ground state X. Furthermore, in the same molecular architecture, the ionic radius decreases with increasing AN because of lanthanide contraction, and shortening the intermolecular distance between the Ln atom and the COT molecule destabilizes the e2u orbital and stabilizes the e2g orbital. In addition to theoretical calculations, this systematic study of Ln atom dependence has quantified the following: (1) configuration interaction involving the ligand Lδ(e2u) and Ln atom 4fδ(e2u) orbitals only occurs for middle-range Ln and (2) the effects of lanthanide contraction on electronic structures causing destabilization of e 2u antibonding orbital and stabilization of the e2g bonding orbital. Essentially, the metaldependent electronic properties can provide fundamental understanding of organolanthanide complexes relative to their applicability in future organolanthanide devices.

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ASSOCIATED CONTENT

S Supporting Information *

Part S1, photodetachment energy dependence of the intensity ratio between peaks X and A in Figure 1, and part S2, electronic configurations of Ln(COT)2− anions and neutrals for Ln = (a) La, (b) Gd, (c) Tb, and (d) Lu, used to support the experimental and theoretical results and discussion. 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]. Telephone: +81-45-5661712; Fax: +81-45-566-1697. Notes

The authors declare no competing financial interest. 3057



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ACKNOWLEDGMENTS This work is partly supported by MEXT-Supported Program for the Strategic Research Foundation at Private Universities, 2009−2013. The computations were partly carried out using the computer facilities at the Research Center for Computational Science, Okazaki National Institutes.

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NOTE ADDED IN PROOF After the manuscript had been submitted for publication, we learned that a recent paper by Dolg et al.99 appeared discussing configuration interaction between the Ce(III) and Ce(IV) states of cerocene and their interpretations based on the wave functions.

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Investigation of the Electronic Structures of Organolanthanide

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