Metal Bonding with 3d and 6d Orbitals: An EPR and ENDOR Spectroscopic Investigation of Ti³⁺–Al and Th³⁺–Al Heterobimetallic Complexes

Abstract

Accessing covalent bonding interactions between actinides and ligating atoms remains a central problem in the field. Our current understanding of actinide bonding is limited because of a paucity of diverse classes of compounds and the lack of established models. We recently synthesized a thorium (Th)–aluminum (Al) heterobimetallic molecule that represents a new class of low-valent Th-containing compounds. To gain further insight into this system and actinide–metal bonding more generally, it is useful to study their underlying electronic structures. Here, we report characterization by electron paramagnetic resonance (EPR) and electron–nuclear double resonance (ENDOR) spectroscopy of two heterobimetallic compounds: (i) a Cp^tt₂ThH₃AlCTMS₃ [TMS = Si(CH₃)₃; Cp^tt = 1,3-di-tert-butylcyclopentadienyl] complex with bridging hydrides and (ii) an actinide-free Cp₂TiH₃AlCTMS₃ (Cp = cyclopentadienyl) analogue. Analyses of the hyperfine interactions between the paramagnetic trivalent metal centers and the surrounding magnetic nuclei, ¹H and ²⁷Al, yield spin distributions over both complexes. These results show that while the bridging hydrides in the two complexes have similar hyperfine couplings (a_iso = −9.7 and −10.7 MHz, respectively), the spin density on the Al ion in the Th³⁺ complex is ∼5-fold larger than that in the titanium(3+) (Ti³⁺) analogue. This suggests a direct orbital overlap between Th and Al, leading to a covalent interaction between Th and Al. Our quantitative investigation by a pulse EPR technique deepens our understanding of actinide bonding to main-group elements.

Short abstract

The electronic structures of Ti³⁺−Al and Th³⁺−Al heterobimetallic complexes are probed by electron−nuclear double resonance spectroscopy, revealing a much larger spin density on the Al center in the latter and the presence of a covalent Th−Al bonding interaction caused by the direct orbital overlap between Th and Al.

Introduction

The chemistry of actinides is not only of fundamental interest but also of practical importance in nuclear fuel processing and recycling,^1,2 as well as in the expansion of their industrial applications.³ Their unique properties arise, in part, because of the large radial extension of 5f and 6d orbitals combined with strong spin–orbital couplings and relativistic effects.⁴ Owing to the complex interplay between these factors and the small number of differing classes of actinide compounds, it is difficult to predict and model their behavior. Central to these problems is understanding the covalency of bonding—the extent of mixing between the ligand and metal orbitals—that is crucial in describing the electronic structures and thus predicting the chemical properties of actinide compounds.^5,6 Covalent interactions are of particular importance for early actinides because they have large atomic radii that allow both 5f and 6d orbitals to participate in bonding. This results in rich redox chemistry that resembles transition metals, although their larger size and more diffuse orbitals give rise to unique bonding patterns.^5,7−9 To what extent these orbitals engage in covalent bonding remains an active field of study with computational and experimental challenges; however, work with uranium (U) compounds has shown the importance of both sets of orbitals.¹⁰⁻¹⁴

A variety of spectroscopic methods have been used to directly probe and quantify the covalency in transition-metal complexes, including photoelectron, Mössbauer, ligand K-edge X-ray absorption, and electron paramagnetic resonance (EPR) spectroscopies.¹⁵⁻¹⁷ They have also recently been applied to the f-block elements, providing insights into the covalency of both lanthanide and actinide compounds.^{10,14,18−21} For systems containing unpaired electrons, EPR spectroscopy is a particularly useful tool to probe the electronic structure of the molecule. For example, when the first thorium(3+) (Th³⁺) compound was synthesized, EPR spectroscopy provided the key evidence that the ground-state configuration is 6d¹ instead of 5f¹.²² Moreover, the chemistry of actinide molecules and materials is oftentimes governed by small differences in the ligand environment and covalent interactions, and it remains a challenge to experimentally probe and quantify these subtle but important differences. Pulse EPR techniques are particularly adept at measuring ligand hyperfine interactions (HFIs), which can be used to map the spin distribution and analyze the bonding properties of the molecule.¹⁷ The application of pulse EPR techniques in actinide chemistry was recently demonstrated by the pioneering work of Formanuik et al., in which hyperfine sublevel correlation (HYSCORE) spectroscopy was employed to investigate the covalency in a (Cp^tt)₃Th (Cp^tt = 1,3-^tBu-C₅H₃) complex and a (Cp^tt)₃U analogue.²³ By measuring the hyperfine couplings from the ¹³C and ¹H nuclei in the aromatic ligands, it was concluded that the spin delocalization onto the Cp^tt ligand in the U complex is at least 3 times larger than that in the Th analogue and is caused by a symmetry-driven orbital overlap between the 5f electrons and ligand orbitals. While this demonstrates the power of this technique in elucidating the electronic structure of actinide complexes, it also leaves open the question as to how to contextualize this understanding in terms of the established models developed for transition-metal complexes.

To directly compare the actinide electronic structure with transition-metal behavior, we recently synthesized a new class of Th³⁺ complexes containing an anionic aluminum hydride (alanate) ligand, together with a titanium(3+) (Ti³⁺) analogue (Scheme 1).^24,25 As mentioned above, Th³⁺ ions generally adopt a 6d¹ ground-state electronic configuration. Compound 2 is therefore a system well-suited to the use of EPR spectroscopy to directly probe the properties of 6d orbitals and to understand their roles in actinide bonding. The aluminum (Al) ion and bridging hydrides in these molecules possess magnetic nuclei (I = ⁵/₂ for ²⁷Al and ¹/₂ for ¹H, respectively) and thereby provide direct probes to quantify covalency. Our previous quantum chemical study implied the presence of a Th–Al bonding interaction.²⁵ This unique metal–metal interaction suggests that the study of Th–Al bimetallic compounds may inform models of actinide–group 13 interactions that are important in the safe handling of nuclear fuels, as well as provide insight into the synthesis and properties of Th–Al alloys.^26,27

Scheme 1. M³⁺–Al Heterobimetallic Complexes Used in This Study.

To gain further and more quantitative insights into the bonding properties, especially the M–Al interaction, in these complexes, we now report thorough EPR and electron–nuclear double resonance (ENDOR) spectroscopic characterizations of these two complexes. The HFIs of the bridging hydrides and Al ions are measured for both the Ti³⁺ and Th³⁺ complexes. A detailed analysis and comparison of the electronic structures of 1 and 2 and the covalent bonding of Ti or Th with the Al center are discussed.

Materials and Methods

Sample Preparation

Complexes 1a, 1b, and 2 were synthesized and characterized as in previous studies.^24,25 To make EPR samples, 2 mM toluene solutions of these compounds were transferred into EPR sample tubes in a glovebox with O₂/H₂O < 0.5 ppm. The tubes were flame-sealed and stored in liquid nitrogen prior to use.

EPR Spectroscopy

EPR spectroscopy was performed in the CalEPR center in the Department of Chemistry, University of California at Davis. Continuous-wave (CW) EPR spectra were recorded on a Bruker Biospin EleXsys E500 spectrometer with a superhigh Q resonator (ER4122SHQE) in perpendicular mode. Cryogenic temperature was achieved by using an ESR900 liquid-helium cryostat with a temperature controller (Oxford Instrument ITC503) and a gas flow controller. All CW EPR spectra were recorded under slow-passage, nonsaturating conditions. Spectrometer settings were as follows: conversion time = 40 ms, modulation amplitude = 0.3 mT, modulation frequency = 100 kHz, and parameters in the corresponding figure legends. Pulse Q-band ENDOR experiments were performed on the Bruker Biospin EleXsys 580 spectrometer equipped with a R. A. Isaacson cylindrical TE₀₁₁ resonator.²⁸ The following pulse sequences were employed: free-induction-decay field-swept EPR (π/2–FID), electron spin–echo-detected field-swept EPR (π/2−τ–π–τ–echo), and Davies ENDOR (π–RF−π/2−τ–π–τ–echo). Simulations of CW and pulse EPR spectra were performed in Matlab 2014a with the EasySpin 5.1.10 toolbox.²⁹ Euler angles relate the principal coordination system of A tensors to g tensors and follow the zyz convention.

For nuclei with nuclear spin I = ¹/₂ (¹H in this study), the ENDOR transitions for the m_s = ±¹/₂ electron manifolds are observed, to a first-order approximation, at the frequencies ν_± = |ν_N ± A/2|, where ν_N is the nuclear Larmor frequency and A is the orientation-dependent hyperfine coupling.³⁰ In the weak coupling limit [ν_N > A/2, exemplified by all of the ¹H HFIs presented in this study], the ENDOR peaks are centered at ν_N and separated by A. In the strong coupling limit (ν_N < A/2, as seen, for example, for ²⁷Al in 2 in this study), the ENDOR peaks are centered at A/2 and separated by 2ν_N. For nuclei with I > ¹/₂ (for ²⁷Al, I = ⁵/₂ in this study), the two ENDOR branches are further split by the orientation-dependent nuclear quadrupole interaction (NQI, P), defined as P = [P₁, P₂, P₃] = e²Qq/4I(2I – 1)h × [−1 + η, −1 – η, 2] with the asymmetry parameter η = (P₁ – P₂)/P₃, ranging from 0 to 1, corresponding to an axially symmetric and rhombic electric field gradient at the nucleus, respectively. The frequencies for the m_I ↔ (m_I – 1) ENDOR transition are observed at ν_±,mI = |ν_N ± A/2 ± (3P/2)(2m_I – 1)|, which gives a total of 10 ENDOR peaks for ²⁷Al at each field position. At the edges of the absorption envelope where the EPR spectra are “single-crystal-like”, these peaks are usually well-resolved. At other field positions, however, ENDOR peaks are usually broadened and overlapped, and spectral simulations are necessary to extract the parameters.

The signs of the ¹H hyperfine tensors were determined by variable-mixing-time (VMT) Davies ENDOR experiments.³⁰ In VMT Davies ENDOR, different mixing times after the radio-frequency (RF) pulse are used. With longer mixing time, relaxation of the α-electron-spin manifold (m_s = +¹/₂) decreases the ENDOR signal intensity (relative to the other ENDOR peak) corresponding to this manifold. The larger observed ENDOR frequency (ν₊) corresponds to the α-electron-spin manifold (and, hence, has decreased relative intensity at elongated mixing time) if A < 0 and vice versa.

Computational Details

The EPR parameters for compounds 1a and 2 are calculated in ORCA 4.0.1.³¹ Previously optimized geometries of 1a and 2 were adopted for calculations.^24,25 The electronic structure and spectroscopic parameters were calculated at the DFT level using the unrestricted Kohn–Sham formalism and employing the hybrid meta-generalized-gradient-approximation TPSSh wave functional³² along with the chain-of-sphere (RIJCOSX) approximation.³³ Triple-ζ valence polarization def2-TZVP basis sets and the decontracted auxiliary basis sets def2/J coulomb fitting³⁴ were used. The basis set of EPR-II was used for all H atoms, and the basis set of cc-PCVTZ (triple-ζ with core correlation) was used for Ti and Al atoms. For compound 2, the all-electron scalar relativistic basis set SARC-ZORA-TZVP was used for the Th atom with the SARC/J coulomb-fitting auxiliary basis sets.³⁵⁻³⁸ The zero-order regular approximation (ZORA) was used to account for the scalar relativistic effects. Increased integration grids (Grid4 and GridX4 in ORCA convention) and tight self-consistent-field convergence were used throughout the calculation of all EPR parameters. The conductor-like polarizable continuum model (CPCM) was used to model the dielectric effects from the solvent toluene (ε = 2.38) used for EPR samples. Typical input files including the coordinates are shown in the Supporting Information (SI).

Results

1. Ti³⁺–Al Complexes (1a and 1b)

1.1. EPR Characterization

The X-band (9.4 GHz) liquid-phase CW EPR spectrum of 1a recorded at 200 K in a 2 mM toluene solution is dominated by a complex multiline pattern (Figure 1A), which arises from the hyperfine couplings to aluminum (²⁷Al: 100%, I = ⁵/₂) and the bridging hydrides (¹H, I = ¹/₂). The spectrum also contains two “wings” flanking the central region (zoom-in insets in Figure 1A), which can be attributed to the hyperfine couplings from the two most-common magnetic isotopes of Ti (⁴⁷Ti, 7.44%, I = ⁵/₂; ⁴⁹Ti, 5.41%, I = ⁷/₂). The solution EPR spectrum is well-simulated by using an isotropic g value of g_iso = 1.9984 and four isotropic HFI values of |a_iso| [⁴⁷Ti, ²⁷Al, ¹H, ¹H] = [17.4, 9.4, 9.8, 9.8] MHz.³⁹ These spectral simulation parameters are corroborated by the CW EPR spectrum of compound 1b in which the hydrides in the alanate ligand are replaced by deuterides (²H: I = 1). The central pattern and flanking wings of the solution EPR spectrum of 1b indicate hyperfine couplings from ²⁷Al, ²H, and Ti. Simulation of this spectrum reveals the same isotropic g value of g_iso = 1.9983 and also four isotropic HFI values: |a_iso| [⁴⁷Ti, ²⁷Al, ²H, ²H] = [17.4, 9.0, 1.5, 1.5] MHz. These parameters are essentially identical with those determined in 1a, and especially the a_iso value of ²H matches well with that of ¹H in 1a scaled by the ratio of their nuclear g values (g_n; ²H:¹H = 1:6.51). The solution CW EPR spectra of 1a and 1b represent one of the few examples where the a_iso²⁷Al values are clearly resolved in the CW EPR spectra⁴⁰⁻⁴² and a rare case showing the Ti hyperfine coupling.⁴³

Figure 1.

EPR spectra of 1a and 1b. (A) X-band CW EPR spectra of 1a (top) and 1b (bottom) recorded at 200 K (black traces) and simulations (red traces). The wing regions of the spectra showing Ti HFI are shown in the zoomed-in insets. (B) Pseudomodulated Q-band FID-detected EPR spectra of 1a recorded at 30 K (black trace) and simulation (red trace). The directions of the principal g values are noted in part B. The xyz frame is chosen as g₁ = g_z. Parameters: (A), microwave power = 0.02 mW; modulation amplitude = 0.1 mT; (B) π/2 = 1 μs; modulation amplitude = 0.5 mT.

At cryogenic temperature (30 K), the g anisotropy of 1a and 1b in the solid state is revealed. In the Q-band FID-detected EPR spectra (Figure 1B), both 1a and 1b have a rhombic g tensor = [2.003, 1.992, 1.971], which exactly satisfy the relationship g_iso² = ¹/₃(g₁² + g₂² + g₃²), indicating a conserved electronic structure at lower temperatures. These values are consistent with the 3d¹ configuration of the Ti³⁺ ion with a d_z² ground state because the largest principal g value (g₁) is almost identical with that of the free electron (g_e = 2.0023). The g tensor is also similar to that found in the single-crystal EPR study of the vanadium(IV) metallocenes (Cp₂VCl₂) doped into the corresponding Ti⁴⁺ diamagnetic host.^44,45 On the basis of the single-crystal EPR study of Cp₂VCl₂ and the EPR characterization of another titanium(3+) metallocene, Cp₂TiOAc,⁴⁶ the directions of the principal g values of 1a are assigned as follows: the intermediate g value, g₂ = 1.992, lies in the Ti–H–H plane and bisects the H–Ti–H angle; the largest g value, g₁ = 2.003, lies also in this plane, perpendicular to the plane formed by two Cp centroids and the Ti center (Figure 1B). This assignment is consistent with the molecular orbital (MO) description of 1a from both the well-understood frontier orbitals of bent metallocenes^46,47 and our DFT calculations: the singly occupied molecular orbital (SOMO) of 1a is a nonbonding a₁ orbital dominated by Ti 3d_z², and the g₁ that we assigned is coaxial to the longitudinal lobe of the 3d_z² orbital.²⁵

1.2. ¹H ENDOR

The ¹H HFI observed in the solution CW EPR of 1a was further analyzed by field-dependent Q-band Davies ENDOR spectra collected across the absorption envelope of frozen samples of 1a and 1b in order to extract the hyperfine tensors. The ENDOR features in the outer region of the spectra are present in the spectra of 1a (Figure 2A, black trace), but not 1b (Figure 2A, blue trace), and therefore must be attributed to the bridging hydrides. This is one of a few examples of ¹H HFI analyzed by ENDOR in metal hydrides.⁴⁸⁻⁵³ The terminal hydride, the protons from the Cp rings, and the CTMS₃ moiety contribute to the central regions of the ENDOR spectra.

Figure 2.

¹H Davies ENDOR spectra of 1a and 1b. (A) Q-band field-dependent Davies ENDOR spectra of 1a (black trace) and 1b (blue trace) and simulation for the bridging hydrides (red trace). (B) VMT Davies ENDOR spectra of 1a collected at g = 1.971 using different t_mix values. Spectra are normalized with respect to the low-frequency ENDOR manifold of the bridging hydride. Parameters: temperature = 25 K, inversion pulse = 80 ns, π/2 pulse = 12 ns, τ = 300 ns, RF pulse = 15 μs. Simulation: g = [2.003, 1.992, 1.971]; A¹H = [6.8, −15.2, −20.7] MHz; Euler angles = [63, 3, 0]°.

Bridging Hydride ¹H HFI

Although there are two bridging hydrides in 1a, their HFI tensors are likely to be similar because of the presence of a pseudo mirror plane. Indeed, the outer region of the ENDOR spectra of 1a can be well-simulated with one ¹H HFI tensor (Figure 2A, red trace) of A¹H = [6.8, −15.2, −20.7] MHz with Euler angles of [63, 3, 0]° relative to the g frame (Table 1). Decomposition of A gives an a_iso of −9.7 MHz that is consistent with the value determined from CW EPR and an anisotropic component of T = [16.5, −5.5, −11.0] MHz. The relative signs of the principal A values are determined by spectral simulation; the absolute sign of A is determined by VMT Davies ENDOR spectra collected at g₃, where A_max is observed (Figure 2B). As the mixing time is increased from 1 to 200 μs, the relative intensity of the ENDOR peak at higher RF decreases (Figure 2B), which is a characteristic of the corresponding nuclear spin-flip transition being between levels within the α-electron-spin manifold, and therefore the sign of A₃ has to be negative. This result is reasonable with a positive T_max (16.5 MHz) for ¹H (g_n > 0) because T is dominated by the through-space electron–nuclear dipolar interaction. According to the g-frame directionality assigned above, the Euler angle used in the optimized simulation indicates that A is rotated primarily within the g₁–g₂ plane (Ti–H–H plane) along the g₃ axis for 63° (α = 63°) but tilted slightly out of the plane (β = 3°). Given the H–Ti–H angle of 72° as observed in the X-ray structure of 1a,²⁵ the resulting orientation of the ¹H A tensor essentially gives an A₁ pointing from the Ti center to one of the bridging H atom (Figure S1), which is consistent with T₁ (16.5 MHz) being the largest principal T value. It also suggests that the two hydrides are locked in a static symmetric MH₂ system at the temperature of the ENDOR experiments (25 K), in contrast to the free rotating H₂ found in a cobalt–H₂ complex.⁵⁴ Our DFT calculation gives A¹H = [12.7, −11.3, −17.2] and [11.9, −12.3, −18.3] MHz (Table S1), which are reasonably consistent with the ENDOR-derived results. These two predicted values are also very similar, supporting the fact that we only observe one set of ¹H values.

Table 1. Summary of the EPR Parameters for 1a and 2.

		1a	2
g values		[2.003, 1.992, 1.971]	[1.967, 1.899, 1.788]
μ-1H	aisoa	–9.7	–10.7
	Aa,b	[6.8, −15.2, −20.7] ± 0.1	[-6.0, −11.1, −15.0] ± 0.1
	[α, β, γ]°b	[63, 3, 0] ± 2	[103, 30, 0] ± 2
27Al	aisoa	9.4	34
	Aa,b	[6.0, 14.6, 7.6] ± 0.1	[23, 46, 33] ± 1
	[α, β, γ]°b	[90, 10, −90] ± 5	[35, 35, −35] ± 5
	e2Qq/ha,b	20.0 ± 1	∼20
	[α, β, γ]°b	[90, 25, −90] ± 5	0
	η	0.34	∼0

^aHFI and NQI parameters are in megahertz.

^bErrors were estimated from spectral simulation.

The negative a_iso, −9.7 MHz, corresponds to a small s-orbital spin density of −6.8 × 10^–3 on each bridging hydride atom (a₀ ¹H = 1420 MHz⁵⁵). The relatively small |a_iso| of this hydride species could be explained by the MOs of bent metallocenes as previously described, which suggested that the hydrides in such Cp₂MH₂ molecules with a d¹ electron configuration lie close to the nodal cone of the singly occupied d_z² orbital, leading to a small Fermi contact.⁴⁷ The negative sign of a_iso also indicates that the spin on the bridging hydride arises mainly from a spin-polarization mechanism, which leads to excess β spin on the hydrides.

The anisotropic component of ¹H HFI arises solely from the through-space electron–nuclear dipolar interactions due to the absence of any local contribution from p-, d-, and f-type orbitals. For a mononuclear Ti³⁺ center with very small g anisotropy, as in the case of 1a, if the distance between Ti³⁺ and the magnetic nuclei is large (r > 2.5 Å), the point-dipole approximation would lead to an axial T = [2T, −T, −T], where T = ρ_Tig_eg_nβ_eβ_n/r³ (ρ_Ti is the spin density on Ti).⁵⁶ This approximation does not hold in the case of 1a because the distances between the bridging hydrides and the Ti³⁺ center are relatively short (averaged r_Ti–H = 1.892 Å). As a result, the experimental T, [16.5, −5.5, −11.0] MHz, is fairly rhombic. This rhombicity in T can be modeled using the empirical approximation previously applied to the 2p_z orbital;⁵⁷ that is, we assume that the spin-density distribution in the Ti 3d_z² orbital can be treated as three discrete spin centers on the z axis (Figure 3): A and C at (0, 0, ±r_A) represent the two longitudinal lobes of 3d_z² with ρ_A = ρ_C = 0.25ρ_Ti, and B at (0, 0, 0) represents the donut shape near the nucleus with ρ_B = 0.5ρ_Ti. Three point-dipole interactions generated from these spin centers, T_A, T_B, and T_C, are summed to give the total T_cal (see the SI):⁵⁸T_cal = ρ_AT_A + ρ_BT_B + ρ_CT_C. If we use ρ_Ti ∼ 0.95 (obtained from the DFT calculation) and by varying r_A, the best match to the experimental T is obtained when r_A = 1.4 Å, which yields T_cal = [16.6, −5.3, −11.3] MHz. In comparison, the r_A value used for the C 2p_z orbital in the previous study was 0.68 Å.⁵⁷ A calculation study on the spin polarizations of different atomic orbitals suggested that the radial distribution of a singly occupied 3d orbital is about twice as large as that of the 2p orbitals,⁵⁹ which provides some basis for the magnitude of this r_A value. To further test if our model is reasonable in other systems with half-filled 3d_z², we applied this method to analyze the ¹H HFI of the bridging hydride in the Ni–C state of the [NiFe] hydrogenase.⁵³ The three-point model agrees well with the experimental results (T_exp = [21.9, −7.3, −14.5] MHz, T_cal = [16.9, −6.0, −10.9] MHz; see the SI for details). In both cases, this empirical treatment rationalizes the origin of the ¹H hyperfine anisotropy for a hydride bound to a (3d_z²)¹ configuration metal center.

Figure 3.

Illustration of the three-point-dipole model to describe the spin-density distribution on the Ti 3d_z² orbital in 1a. In this case, r_Ti–H = 1.89 Å, r_A = 1.4 Å, and φ = 54°. The unique axes for the dipolar contribution from each point (A–C) are noted as T_A, T_B, and T_C, respectively.

Cp Ring ¹H HFI

The major features in the ¹H ENDOR spectra of 1b arise from the ¹H on the Cp rings, which are closer to Ti (2.94 Å on average) than the protons in the CTMS₃ moiety (∼5–8 Å). Because of the number of different ¹H on the Cp rings, we analyze the HFI of these ¹H by combining the ENDOR experiments with the DFT calculations. The DFT-calculated spin densities of Cp C atoms and HFI of Cp ¹H are summarized in Table S1 and Figure S2.

A previous study suggested that Cp ¹H HFI may stem from both the through-space dipolar interactions with the spin center and the spin polarization of the C–H bonding electrons by the C 2p_π spin density.²³ The former gives T ∼ 2.8 MHz with a point-dipole approximation or ∼2.2–3.0 MHz using the three-point-dipole model (vide supra). The DFT-calculated Cp ¹H HFIs are all predicted to have anisotropy consistent with our three-point-dipole model, especially for ¹H on C1 and C3 of the Cp ligand (see the SI) where C spin densities are close to zero (Table S1 and Figure S2). ENDOR spectra of 1b collected in resonance with g₂ exhibit ¹H A values as large as ∼9 MHz (Figure 2A), indicating that other hyperfine mechanisms, in addition to the dipolar interactions, contribute. DFT predictions of the HFI for protons bound to C2 and C5 reproduce these A values. The DFT results also predict that these A values and a_H values of Cp ¹H are positive, as observed by VMT Davies ENDOR spectra recorded at different field positions (Figure S3). The positive a_H values cannot be traced to a spin-polarization process of the McConnell type alone because the DFT-predicted spin densities of ∼0.02 on C2/C5 (Figure S2) would only give rise to much smaller a_H values of negative sign. Rather, direct spin delocalization of Ti³⁺(d_z²) → Cp(e_2g), i.e., the Cp character in the 1a₁ MO, could mainly be responsible for the positive hyperfine values on Cp protons. This spin-delocalization mechanism may be analogous to the hyperconjugation mechanism that accounts for the positive ¹H HFI of the β-protons in organic radicals.⁶⁰

According to these analyses and the results from calculations, we roughly simulate the ENDOR spectra of 1b with three sets of HFI tensors corresponding to ¹H on C1, C2/C5, and C3/C4 (Figure S4), which reproduces most features in the ENDOR spectra.

1.3. ²⁷Al ENDOR

The field-dependent Davies ENDOR spectra of 1a in the low-frequency region (2–30 MHz) exhibit wide features that are attributed to the HFI and NQI of ²⁷Al (I = ⁵/₂; Figure 4). Notably, at the “single-crystal-like” g₁ edge, the ENDOR peaks are uniformly spaced by the orientation-dependent NQI splitting, 3P₁ = 3 MHz, representing a rare example of a well-resolved ²⁷Al ENDOR spectrum with a well-resolved NQI pattern.⁶¹⁻⁶³ The large NQI splitting cause an overlap between the two ENDOR branches. Similar patterns are seen at the g₃ edge with 3P₃ ∼ 2 MHz. With these parameters that can be read off from the ENDOR spectra and the ²⁷Al a_iso from CW EPR, the ENDOR spectra are well-simulated using A²⁷Al = [6.0, 14.6, 7.6] MHz with Euler angles of [90, 10, −90]°, and P²⁷Al = [1.00, −0.33, −0.67] MHz with Euler angles of [90, 25, −90]°. The orientation of A is consistent with that of A₂ along the Ti–Al vector, whereas the unique axis of P is close to that of the Al-CTMS₃ vector. The ENDOR spectrum of 1b is essentially the same as that of 1a, except that in 1b extra ENDOR signals arising from the bridging ²H are overlaid with the ²⁷Al signals and are consistent with the bridging ¹H HFI in 1a scaled by the ratio of their nuclear g_n values (Figure S5).

Figure 4.

Q-band ²⁷Al Davies ENDOR of 1a (black traces) and simulations (red traces). A₁/P₁ and A₃/P₃, which can be approximately read off from the spectra, are marked at g₁ and g₃, respectively. Al ENDOR features marked by asterisks arise from NMR flip–spin transitions induced by the third harmonic of normal RF excitation frequencies. Parameters: inversion pulse = 80 ns, π/2 pulse = 12 ns, τ = 300 ns, and RF pulse = 30 μs. Simulation: g = [2.003, 1.992, 1.971], A²⁷Al = [6.0, 14.6, 7.6] MHz, Euler angle = [90, 10, −90]°, P = [1.00, −0.33, −0.67] MHz, and Euler angle = [90, 25, −90]°.

²⁷Al HFI

A²⁷Al of [6.0, 14.6, 7.6] MHz can be decomposed into the isotropic part, a_iso = 9.4 MHz, and the dipolar part, T_dip = [−3.4, 5.2, −1.8] MHz. The isotropic hyperfine coupling corresponds to a small Al 3s orbital spin density of 2.4 × 10^–3 using a₀ = 3911 MHz for one unpaired electron on the Al 3s orbital. The dipolar part has two major contributions: (1) the nonlocal through-space electron–nuclear dipolar interaction between the Ti³⁺ center and Al, which are separated by r_Ti–Al = 2.78 Å, T_nl; (2) the local contribution from the 3p orbital spin density on Al, T_loc. These two components are not necessarily coaxial with one another. The nonlocal component (here T_nl = [−T, 2T, −T] because A₂ is pointing along the Ti–Al vector) can be estimated using the relationship T = ρ_Tig_eg_nβ_eβ_n/r³ = 0.9 MHz. Subtracting T_nl from T_dip yields T_loc = [−2.5, 3.4, −0.9] MHz, which gives a total spin density in the three Al 3p orbitals of ∼0.03, following previous procedures⁶⁴ as detailed in the SI. Because the 3p spin density is much larger than the 3s contribution, the total spin density on Al is also ∼0.03.

²⁷Al NQI

The ²⁷Al ENDOR spectra reveal an ²⁷Al NQI tensor of P = [1.00, −0.33, −0.67] MHz, which can be written in another form as P = (e²Qq/h)/[4I(2I – 1)][2, −1 + η, −1 – η], corresponding to e²Qq/h = 20.0 MHz and η = 0.34. These NQI parameters match well with the DFT calculations (Table S1) and are analyzed in the SI.

2. Th–Al Heterometallic Complex (Compound 2)

2.1. EPR Characterization

The EPR analysis of 1a framed our thinking for the more complicated Th system. The EPR spectra of 2 were reported previously²⁵ and are reproduced here in Figure S6. The 200 K solution spectrum gives a broad peak with g_iso = 1.886, and the 50 K frozen solution spectrum reveals the rhombic g = [1.967, 1.899, 1.788], which also satisfies g_iso² = ¹/₃(g₁² + g₂² + g₃²). These values are consistent with a 6d_z² ground state, as found in other Th³⁺ complexes,²² and agree reasonably with the DFT-calculated g values ([1.985, 1.900, 1.823]; Table S2). The deviation of g₁ from g_e is not unprecedented in Th³⁺ complexes (Table S3) and may be caused by high-order spin–orbital coupling or mixing of other d orbitals into the SOMO. In line with the Ti complex and the (Cp^tt)₃Th complex reported previously,²³ the directions for the g frame could be assigned as indicated in Figure S6; that is, g₁ (g_z) is perpendicular to the plane constituted by Th and the two centroids of the Cp^tt ring, and g₂ is approximately pointing along the Th–Al vector. For comparison, the spin–lattice relaxation time constant (T₁) of 2 was determined to be 972 μs at 10 K and 194 μs at 15 K, similar to the values reported for the (Cp^tt)₃Th complex (1100 μs at 11 K).²³

2.2. ¹H ENDOR

The ¹H region of the ENDOR spectra of 2 contains two major sets of signals that are just separated, as shown in Figure 5A. In light of the ENDOR spectra of 1a, the ENDOR signals with larger HFI, ∼10–15 MHz, mostly likely arise from bridging hydrides. This assignment is also supported by comparing the ENDOR spectra of 2 to the reported HYSCORE spectra of (Cp^tt)₃Th showing ¹H HFI from the same ligands, with ¹H HFI < 5 MHz.²³

Figure 5.

¹H Davies ENDOR spectra of 2. (A) Q-band field-dependent Davies ENDOR spectra of 2 (black trace) and simulation for the bridging hydrides (red trace). (B) VMT Davies ENDOR spectra of 2 collected at g = 1.967 using different t_mix. Spectra are normalized with respect to the low-frequency ENDOR manifold of the bridging hydrides. Parameters: temperature = 15 K, inversion pulse = 80 ns, π/2 pulse = 12 ns, τ = 300 ns, and RF pulse = 15 μs. Simulation: g = [1.967, 1.899, 1.788], A¹H = [−6.0, −11.1, −15.0] MHz, and Euler angle = [103, 30, 0]°.

Bridging ¹H HFI

The three hydrides in 2 adopt two different conformations (Scheme 1): one lies on the plane constituted by the Th atom and two Cp^tt centroids, while the other two are located at each side of this plane. Despite such asymmetry, the sharp peaks on the ENDOR spectra collected at both the g₁ and g₃ edges indicate that the ENDOR signals can be attributed to a single set of ¹H HFIs, simulated to be A¹H = [−6.0, −11.1, −15.0] MHz with Euler angles of [103, 30, 0]° (Figure 5A). Decomposition of this A tensor gives a_iso = −10.7 MHz and T = [4.7, −0.4, −4.3] MHz. Similar to the Ti complex, the signs of A are determined by VMT Davies ENDOR spectroscopy collected at g₁ (Figure 5B).

The negative a_iso, −10.7 MHz, corresponds to an s orbital spin density of −7.5 × 10^–3 on each bridging hydride. This gives a total spin density of merely −2.3 × 10^–2 on the three hydrides. The dipolar part of the hyperfine tensor is close to a fully rhombic [T, 0, −T] form, despite an averaged Th–H distance of 2.45 Å, which is usually long enough for point-dipole approximation. This rhombicity is probably caused by the highly diffuse nature of the spin-carrying Th 6d_z² orbital, undercutting the accuracy of the point-dipole approximation. The ∼0.15 spin density on the Al (vide infra) may also have a small contribution to the rhombicity if being considered as a secondary spin center.⁴⁸ If we just consider the spin density on Th, using the three-point-dipole model mentioned above and ρ_Th ∼ 0.8 from DFT calculations, this T tensor can be reproduced with an empirical r_A of ∼3 Å and a resulting T_cal = [4.8, −0.5, −4.3] MHz. This empirical r_A value implies that the radial distribution of the Th 6d orbital could be more than twice that of the Ti 3d orbital.

Cp ¹H HFI

The central region of the ENDOR spectra of 2 represents HFI from ¹H on the Cp^tt ligands and ^tBu groups. The averaged HFI values of ∼4 MHz are essentially consistent with the reported ¹H HYSCORE for (Cp^tt)₃Th.²³ In this case, however, the VMT Davies ENDOR spectra shown in Figure S7 indicate that the a_H values of the Cp^tt protons are negative, indicating a hyperfine mechanism dominated by spin polarization of the C–H bonding electrons by the Cp^tt C 2p_π spin density, as pointed out by the previous study on the (Cp^tt)₃Th complex.²³ The differences between 1a and 2 thus reflect a larger spin density on the aromatic C atoms in the Th complex (see the SI for DFT results), caused again by the more diffuse 6d orbitals, leading to more Cp character in the SOMO.

2.3. ²⁷Al ENDOR

The field-dependent Q-band ²⁷Al Davies ENDOR spectra of 2 are shown in Figure 6. Here, the much larger ²⁷Al HFI quantifies the system as being in the strong coupling case, A > 2ν_Al, and only the higher-frequency ENDOR transitions at ∼25–40 MHz are recorded. The low-frequency ENDOR transitions, simulated to be centered at ∼4–5 MHz, have weak signal intensity and are complicated by higher-order RF harmonic signals (Figure S8) and, therefore, are not used for data interpretation.

Figure 6.

Q-band ²⁷Al Davies ENDOR spectra of 2 (black trace) and simulation of the ²⁷Al HFI (red trace). Features at 15–22 MHz are the contributions from the third harmonic of the ¹H ENDOR signals (cf. Figure 5). Parameters: inversion pulse = 80 ns, π/2 pulse = 12 ns, τ = 300 ns, and RF length = 30 μs. Simulation: g = [1.967, 1.899, 1.788], A²⁷Al = [22, 45, 35] MHz, Euler angle = [35, 35, −35]°, and P = [−0.5, 1.0, −0.5] MHz, where P is coaxial with A.

The field-dependent ENDOR spectra are simulated using A²⁷Al = [22, 45, 35] MHz. The magnitude of this HFI is reasonably similar to that from DFT calculation (A_DFT²⁷Al = [29.0, 29.9, 37.5] MHz; Table S2) although the dipolar part seems to be underestimated. While no quadrupole features are resolved in the ENDOR spectra, the maximum breadth of the ²⁷Al features (obtained at fields near g₂) allows estimation of the NQI tensor as ∼[−0.5, 1.0, −0.5] MHz, in a magnitude similar to that of the Ti complex; the asymmetry parameter is not estimated. Decomposition of A gives a_iso²⁷Al = 34 MHz and the dipolar part of T_dip = [−12, 11, 1] MHz. The isotropic hyperfine coupling corresponds to an Al 3s spin density of 0.9%. The dipolar part can be analyzed similar to the case of 1a (vide supra; see the SI), yielding a T_loc = [−11.4, 9.8, 1.6] MHz and a 3p spin density of 14%. As one can tell, in the case of 2, the major contribution to T_dip is the local component, caused by a much larger spin density on the Al 3p orbitals. The total spin density on the Al is therefore estimated to be ∼15% with the 3s contribution included. This substantial spin delocalization is consistent with the calculation results that give a Mayer bond order of 0.7 between Th and Al (see the SI).

Discussion

Electronic Structural Origins of g Values

In order to understand the electronic structures of these two complexes and how they are affected by the Alanate ligand, we started to build a qualitative MO diagram for the two complexes (Figure 7). The MOs for bent metallocenes have been well-described by Lauher and Hoffmann⁴⁷ and are shown in Figure 7 using the coordination system in our study. The MOs of complexes 1a/1b and 2 are adapted from those of Cp₂Nb(BH₄), which has a double-bridged structure, and Cp₂Sc(BH₄) with a triple-bridged structure, respectively.⁶⁵ In both cases, the alanate ligand donates a total of four electrons to the Cp₂M⁺ moiety, resulting in a 17e^– system. The unpaired electron occupies the low-lying metal-based 1a₁ orbital (d_z² mixed with some d_x²–y²), which is essentially nonbonding and interacts only weakly with the ligands. The LUMO, b₂, has mainly d_yz character and forms a π-type bond with one of the alanate orbitals derived from the t₂ orbital quantized along the M–Al axis. The 2a₁ orbital, with d_x²–y² character, forms a σ bond with another t₂ orbital, leaving the third t₂ orbital nonbonding.

Figure 7.

Qualitative MO diagrams for double- and triple-bridged Cp₂M⁺ complexes with d¹ configuration. SOMO electrons are shown in blue. Metal f orbitals are not included.

Deviation of the g values from g_e in transition-metal complexes is due to spin–orbit couplings that mix the excited states into the ground states. For bent metallocenes, Peterson and Dahl have shown that the g values can be formulated as follows:^44,66,67

1

where λ is the atomic spin–orbital coupling constant, ΔE_yz, ΔE_xz, and ΔE_xy are the energies (relative to the ground state) of the excited states of d_yz, d_xz, and d_xy character (that is, the b₂, 2a₁, and b₁ orbitals, respectively), a and b are the coefficients of d_z² and d_x²–y² in the ground state, and k_x,y,z are the orbital reduction factors accounting for the d character (covalency) in each MO.

For the Ti complex, because g_z (g₁ = 2.003) is quite close to g_e, we assume b ∼ 0; that being said, the 1a₁ ground state is almost pure 3d_z². The small g shifts of g_x and g_y are consistent with the small λ (Ti³⁺) of 155 cm^–1. The g shifts of 1a are even smaller than all other Cp₂TiX (X = F, Cl, Br, OR, NHR, ...) compounds due to the stronger π-type bonding between the metal b₂ (d_yz) orbital and alanate t₂ orbital, which destabilizes the former, leading to a larger ΔE_yz.⁶⁷

For the Th complex, the g values and line shape of the EPR spectrum indicate that the contribution of the f orbital to the ground state is negligible. The much larger separation of principal g values and deviations from g_e compared to that of the Ti complex indicate the much larger spin–orbit coupling of Th³⁺. However, simply extrapolating these MO descriptions established for the 3d elements is less quantitatively informative, and employing this first-order perturbation theory approach for the quantitative analysis of g values may not apply to complexes of much heavier ions.⁶⁸ Furthermore, the ligand-field splittings are unknown because the electronic spectrum of 2 is dominated by the electric-dipole-allowed 6d → 5f transitions, obscuring the Laporte-forbidden d → d transitions.²⁵ Instead, we compare the g values of 2 to those of other Th³⁺ systems (Table S3). The more symmetric molecule (Cp^tt)₃Th has an axial g = [1.974, 1.880, 1.880].²³ The axiality of this g tensor is caused by the pseudo-C_3h ligand field that splits the d orbitals into the ground state A′ (d_z²), the doubly generate E″ (d_xz and d_yz), and the doubly degenerate E′ (d_x²–y² and d_xy), leading to equal ΔE_yz and ΔE_xz. In this scenario, the direction of g_z can be naturally assigned as the C₃ axis of the molecule. In complex 2, one of the Cp ligands is replaced by the alanate moiety, which removes the C₃ axis, the degeneracy of d_xz and d_yz, and, with that, the axiality of the g tensor. Interestingly, the value of g₁ is almost unaffected, suggesting that the direction of g_z may be unaltered. The presence of the alanate ligand causes a large shift of g₃ from 1.880 to 1.788 (g_e – g_y = 0.12–0.21), indicating a significantly decreased ΔE_yz, as indicated from eq 1. Similar g shifts have been observed in another bimetallic Th³⁺ complex, Cp₂ThH₃ThHCp₂, with g = [1.98, 1.94, 1.76], in which three hydrides bridge the Th³⁺ center to a Th⁴⁺ center; however, unlike our Al³⁺ system, DFT calculations suggested that no spin density is delocalized in this Th⁴⁺ center.⁶⁹

M–Al Bonding in 1a and 2

The differences in the ¹H and ²⁷Al ENDOR results of 1a and 2 allow us to compare the bonding pictures between them. The bridging hydrides in 1a and 2 have similar a_iso values; both are negative and relatively small, caused by the small overlap between the nonbonding d_z² orbital and the hydride’s 1s orbital. The much larger rhombicity of ¹H HFI in 2 reflects the diffuse nature of 6d_z² compared to 3d_z², as expected. In contrast, the spin density on Al in 2 is ∼5-fold larger than that in 1a, suggesting a significant overlap between the Th³⁺ SOMO and the Al 3p orbitals. Our previous DFT calculation suggested that the spin density is transferred from the Th 6d-based orbital to an antibonding Al-CTMS₃ orbital with significant Al 3p character, and no such interaction is present in the Ti³⁺ complex. The presence of this interaction suggests that Al acts as an electron acceptor to partially stabilize the highly reducing Th³⁺. The polarity of this interaction is supported by a recently reported electronegativity scale that includes the values for Th and Al.⁷⁰ More importantly, the large a_iso values and spin density on Al in 2 further suggest a significant covalency between Th and Al that is missing in the case of 1a. There are only a handful of ²⁷Al HFIs reported in molecular systems, and ²⁷Al a_iso values with magnitudes of 20–30 MHz are only found when Al is directly bound to C radical centers.^41,42,71

While it is challenging to contextualize this type of metal–metal interaction and examples from transition-metal complexes could differ significantly from those from actinide complexes, a few covalent metal–metal bonds have been suggested in such bridging complexes that may help to understand the Th–Al interaction. The reaction between Cp*(PMe₃)Ir(H₂) and Ph₃Al leads to an bridging hydride adduct, Cp*(PMe₃)IrH₂AlPh₃ (Cp* = η⁵-pentamethylcyclopentadienyl), which is believed to contain a Ir–Al bond bridged by the hydrides.⁷² In the light-induced Ni–L state of the [NiFe] hydrogenase, the presence of a metal–metal bond between a Ni center and a low-spin Fe²⁺ center has been proposed in a quantum-chemical study,⁷³ which suggested a Ni–Fe Mayer bond order of ∼0.4 and a spin density on the Fe²⁺ center of ∼−0.07. In this regard, the Th–Al Mayer bond order of 0.7 and the Al spin density of 0.15 in 2 are indeed indications of significant Th–Al metal–metal bonding character. In comparison, the Ti–Al Mayer bond index in 1a is computed to be merely 0.13, which, together with our ENDOR results, exemplifies the differences of 3d and 6d orbitals in forming such unconventional bonding interactions.

Conclusion

In conclusion, we have characterized by advanced EPR techniques a Th³⁺ complex and a Ti³⁺ analogue, both containing M–H–Al bridges, in order to extract the ¹H and ²⁷Al hyperfine parameters. We further used these parameters to calculate the spin-density distributions in these complexes and to analyze the differences between the M–H and M–Al bonding interactions. Our results indicate that the ¹H HFIs of the bridging hydrides are similar in both complexes and can be explained by using a model of spin polarization by the half-occupied d_z². In contrast, we observed a more dramatic difference in the ²⁷Al HFI between these two complexes, calculated to originate from ∼5 times more spin density on Al in the Th complex. The hyperfine parameters of H and Al in these two complexes indicate direct orbital overlap between Th and Al in the Th complex, leading to significant covalent bonding between them. Our study provides a model for actinide bonding that is a useful reference for studying similar compounds that could have unusual properties and applications.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00720.

• Summary of the calculation results, additional EPR and ENDOR spectra, notes for the three-point-dipole model, and analyses of the ²⁷Al HFI and NQI parameters (PDF)

Author Present Address

^§ T.A.S.: Department of Chemistry, Wake Forest University, Winston-Salem, NC 27101.

The authors declare no competing financial interest.