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

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 Cptt2ThH3AlCTMS3 [TMS = Si(CH3)3; Cptt = 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 ( aiso = -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.

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 (Cptt)3Th (Cptt = 1,3-tBu-C5H3) complex and a (Cptt)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 Cptt 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 ).[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 ms = ±1/2 electron manifolds are observed, to a first-order approximation, at the frequencies ν± = |νN ± A/2|, where νN is the nuclear Larmor frequency and A is the orientation-dependent hyperfine coupling.[30] In the weak coupling limit [νN > A/2, exemplified by all of the 1H HFIs presented in this study], the ENDOR peaks are centered at νN and separated by A. In the strong coupling limit (νN < A/2, as seen, for example, for 27Al in 2 in this study), the ENDOR peaks are centered at A/2 and separated by 2νN. 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 mI ↔ (mI – 1) ENDOR transition are observed at ν±, = |νN ± A/2 ± (3P/2)(2mI – 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 (ms = +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 functional[32] 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 fitting[34] 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

Ti3+–Al Complexes (1a and 1b)

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 A), 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 A), 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 giso = 1.9984 and four isotropic HFI values of |aiso| [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 giso = 1.9983 and also four isotropic HFI values: |aiso| [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 aiso value of 2H matches well with that of 1H in 1a scaled by the ratio of their nuclear g values (gn; 2H:1H = 1:6.51). The solution CW EPR spectra of 1a and 1b represent one of the few examples where the aiso27Al values are clearly resolved in the CW EPR spectra[40−42] 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. 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 B), both 1a and 1b have a rhombic g tensor = [2.003, 1.992, 1.971], which exactly satisfy the relationship giso2 = 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 ground state because the largest principal g value (g1) is almost identical with that of the free electron (ge = 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 B). 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, and the g1 that we assigned is coaxial to the longitudinal lobe of the 3d orbital.[25]

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 A, black trace), but not 1b (Figure A, 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 tmix 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 A, red trace) of A1H = [6.8, −15.2, −20.7] MHz with Euler angles of [63, 3, 0]° relative to the g frame (Table ). Decomposition of A gives an aiso 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 Amax is observed (Figure B). As the mixing time is increased from 1 to 200 μs, the relative intensity of the ENDOR peak at higher RF decreases (Figure B), 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 Tmax (16.5 MHz) for 1H (gn > 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

HFI and NQI parameters are in megahertz.

Errors were estimated from spectral simulation.

The negative aiso, −9.7 MHz, corresponds to a small s-orbital spin density of −6.8 × 10–3 on each bridging hydride atom (a0 1H = 1420 MHz[55]). The relatively small |aiso| 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 orbital, leading to a small Fermi contact.[47] The negative sign of aiso 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 = ρTigegnβeβn/r3 (ρTi 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 rTi–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 orbital;[57] that is, we assume that the spin-density distribution in the Ti 3d orbital can be treated as three discrete spin centers on the z axis (Figure ): A and C at (0, 0, ±rA) represent the two longitudinal lobes of 3d with ρA = ρC = 0.25ρTi, and B at (0, 0, 0) represents the donut shape near the nucleus with ρB = 0.5ρTi. Three point-dipole interactions generated from these spin centers, TA, TB, and TC, are summed to give the total Tcal (see the SI):[58]Tcal = ρATA + ρBTB + ρCTC. If we use ρTi ∼ 0.95 (obtained from the DFT calculation) and by varying rA, the best match to the experimental T is obtained when rA = 1.4 Å, which yields Tcal = [16.6, −5.3, −11.3] MHz. In comparison, the rA value used for the C 2p 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 rA value. To further test if our model is reasonable in other systems with half-filled 3d, 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 (Texp = [21.9, −7.3, −14.5] MHz, Tcal = [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)1 configuration metal center.

Figure 3

Illustration of the three-point-dipole model to describe the spin-density distribution on the Ti 3d orbital in 1a. In this case, rTi–H = 1.89 Å, rA = 1.4 Å, and φ = 54°. The unique axes for the dipolar contribution from each point (A–C) are noted as TA, TB, and TC, 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 2pπ 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 A), 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 aH values of Cp 1H are positive, as observed by VMT Davies ENDOR spectra recorded at different field positions (Figure S3). The positive aH 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 aH values of negative sign. Rather, direct spin delocalization of Ti3+(d) → Cp(e2g), 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.

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 ). 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 aiso 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 gn 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, aiso = 9.4 MHz, and the dipolar part, Tdip = [−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 rTi–Al = 2.78 Å, Tnl; (2) the local contribution from the 3p orbital spin density on Al, Tloc. These two components are not necessarily coaxial with one another. The nonlocal component (here Tnl = [−T, 2T, −T] because A2 is pointing along the Ti–Al vector) can be estimated using the relationship T = ρTigegnβeβn/r3 = 0.9 MHz. Subtracting Tnl from Tdip yields Tloc = [−2.5, 3.4, −0.9] MHz, which gives a total spin density in the three Al 3p orbitals of ∼0.03, following previous procedures[64] 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.

Th–Al Heterometallic Complex (Compound 2)

The EPR analysis of 1a framed our thinking for the more complicated Th system. The EPR spectra of 2 were reported previously[25] and are reproduced here in Figure S6. The 200 K solution spectrum gives a broad peak with giso = 1.886, and the 50 K frozen solution spectrum reveals the rhombic g = [1.967, 1.899, 1.788], which also satisfies giso2 = 1/3(g12 + g22 + g32). These values are consistent with a 6d 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 ge 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 (Cptt)3Th complex reported previously,[23] the directions for the g frame could be assigned as indicated in Figure S6; that is, g1 (g) is perpendicular to the plane constituted by Th and the two centroids of the Cptt 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 (Cptt)3Th complex (1100 μs at 11 K).[23]

The 1H region of the ENDOR spectra of 2 contains two major sets of signals that are just separated, as shown in Figure A. 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 (Cptt)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 tmix. 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 ): one lies on the plane constituted by the Th atom and two Cptt 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 A). Decomposition of this A tensor gives aiso = −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 B).

The negative aiso, −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 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 ρTh ∼ 0.8 from DFT calculations, this T tensor can be reproduced with an empirical rA of ∼3 Å and a resulting Tcal = [4.8, −0.5, −4.3] MHz. This empirical rA 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 Cptt ligands and tBu groups. The averaged HFI values of ∼4 MHz are essentially consistent with the reported 1H HYSCORE for (Cptt)3Th.[23] In this case, however, the VMT Davies ENDOR spectra shown in Figure S7 indicate that the aH values of the Cptt protons are negative, indicating a hyperfine mechanism dominated by spin polarization of the C–H bonding electrons by the Cptt C 2pπ spin density, as pointed out by the previous study on the (Cptt)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.

The field-dependent Q-band 27Al Davies ENDOR spectra of 2 are shown in Figure . Here, the much larger 27Al HFI quantifies the system as being in the strong coupling case, A > 2νAl, 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 ). 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 (ADFT27Al = [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 aiso27Al = 34 MHz and the dipolar part of T = [−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 Tloc = [−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 Tdip 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 ). The MOs for bent metallocenes have been well-described by Lauher and Hoffmann[47] and are shown in Figure 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 mixed with some d), which is essentially nonbonding and interacts only weakly with the ligands. The LUMO, b2, has mainly d 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 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 ge 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]where λ is the atomic spin–orbital coupling constant, ΔE, ΔE, and ΔE are the energies (relative to the ground state) of the excited states of d, d, and d character (that is, the b2, 2a1, and b1 orbitals, respectively), a and b are the coefficients of d and d in the ground state, and k are the orbital reduction factors accounting for the d character (covalency) in each MO.

For the Ti complex, because g (g1 = 2.003) is quite close to ge, we assume b ∼ 0; that being said, the 1a1 ground state is almost pure 3d. The small g shifts of g and g 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) orbital and alanate t2 orbital, which destabilizes the former, leading to a larger ΔE.[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 ge 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 (Cptt)3Th has an axial g = [1.974, 1.880, 1.880].[23] The axiality of this g tensor is caused by the pseudo-C3 ligand field that splits the d orbitals into the ground state A′ (d), the doubly generate E″ (d and d), and the doubly degenerate E′ (d and d), leading to equal ΔE and ΔE. In this scenario, the direction of g 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 and d, and, with that, the axiality of the g tensor. Interestingly, the value of g1 is almost unaffected, suggesting that the direction of g may be unaltered. The presence of the alanate ligand causes a large shift of g3 from 1.880 to 1.788 (ge – g = 0.12–0.21), indicating a significantly decreased ΔE, as indicated from eq . 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 aiso values; both are negative and relatively small, caused by the small overlap between the nonbonding d orbital and the hydride’s 1s orbital. The much larger rhombicity of 1H HFI in 2 reflects the diffuse nature of 6d compared to 3d, 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 aiso 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 aiso 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. 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.