W. W.
Lukens
*^{a},
M.
Speldrich
*^{b},
P.
Yang
*^{c},
T. J.
Duignan
^{d},
J.
Autschbach
*^{d} and
P.
Kögerler
^{be}
^{a}Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. E-mail: wwlukens@lbl.gov
^{b}Institute of Inorganic Chemistry, RWTH Aachen University, Aachen, Germany. E-mail: manfred.speldrich@ac.rwth-aachen.de
^{c}Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. E-mail: pyang@lanl.gov
^{d}Department of Chemistry, University at Buffalo, State University of New York, Buffalo, NY, USA. E-mail: jochena@buffalo.edu
^{e}Jülich-Aachen Research Alliance (JARA-FIT) and Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich, 52425 Jülich, Germany
First published on 31st May 2016
The electronic structures of 4f^{3}/5f^{3} Cp′′_{3}M and Cp′′_{3}M·alkylisocyanide complexes, where Cp′′ is 1,3-bis-(trimethylsilyl)cyclopentadienyl, are explored with a focus on the splitting of the f-orbitals, which provides information about the strengths of the metal–ligand interactions. While the f-orbital splitting in many lanthanide complexes has been reported in detail, experimental determination of the f-orbital splitting in actinide complexes remains rare in systems other than halide and oxide compounds, since the experimental approach, crystal field analysis, is generally significantly more difficult for actinide complexes than for lanthanide complexes. In this study, a set of analogous neodymium(III) and uranium(III) tris-cyclopentadienyl complexes and their isocyanide adducts was characterized by electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility. The crystal field model was parameterized by combined fitting of EPR and susceptibility data, yielding an accurate description of f-orbital splitting. The isocyanide derivatives were also studied using density functional theory, resulting in f-orbital splitting that is consistent with crystal field fitting, and by multi-reference wavefunction calculations that support the electronic structure analysis derived from the crystal-field calculations. The results highlight that the 5f-orbitals, but not the 4f-orbitals, are significantly involved in bonding to the isocyanide ligands. The main interaction between isocyanide ligand and the metal center is a σ-bond, with additional 5f to π* donation for the uranium complexes. While interaction with the isocyanide π*-orbitals lowers the energies of the 5f_{xz2} and 5f_{yz2}-orbitals, spin–orbit coupling greatly reduces the population of 5f_{xz2} and 5f_{yz2} in the ground state.
Common approaches to studying bonding in actinides and lanthanides are comparing ions with either similar ionic radii, e.g., Ce(III) vs. U(III), or similar electronic structures, e.g., Nd(III) vs. U(III). In the latter case, the main difference is the larger radial extent of the 5f-orbitals relative to the 4f-orbitals. More recently, the relative energies of the ligand and metal orbitals have received increased attention due to their roles in increasing metal-ligand orbital mixing by ‘accidental degeneracy’ (increased mixing due to the similar ligand and metal orbital energies).^{6–8,11} A particularly attractive and well-studied system for the comparison of 4f and 5f bonding are the tris(cyclopentadienyl) complexes, Cp_{3}M, where Cp is cyclopentadienyl or a substituted cyclopentadienyl ligand and M is a lanthanide or actinide element. In addition to the parent Cp_{3}M complexes, the isocyanide adducts provide additional information about the roles of the 4f and 5f-orbitals. Conejo et al. studied isocyanide adducts of Cp_{3}Ce and Cp_{3}U and concluded that Cp_{3}U was a better π-donor towards isocyanide ligands than Cp_{3}Ce.^{12}
The electronic structures of Cp_{3}Nd (4f^{3}) complexes have been extensively studied by Amberger and co-workers using UV-Vis-NearIR spectroscopy in conjunction with crystal field modeling to determine the splitting of the 4f-orbitals due interactions with the ligands.^{13–19} This system is particularly amenable to crystal field analysis since the charge-transfer bands and the 4f–5d transitions are in the UV, which provides a wide window for observing the weak f–f transitions on which the analysis is based. In favorable cases, up to 80 transitions have been assigned, which allows many parameters to be varied during crystal field modeling.^{20} In Cp_{3}Nd, the f_{y(3x2−y2)}-orbital (a′_{2} in D_{3h} symmetry) interacts with one set of the Cp highest occupied molecular-orbitals (HOMOs). The destabilization of this orbital may be seen in the experimentally derived molecular-orbital (MO) diagram, which is determined by performing a crystal field calculation for an f^{1} ion with no spin–orbit coupling using the crystal field parameters determined for the Cp_{3}Nd complex.^{14,16,18,19} The role of this orbital in bonding may also be observed by photoelectron spectroscopy although the effect is more pronounced in the Cp_{3}M^{+} molecular cations.^{21} Amberger's work provides an excellent basis for understanding the electronic structures of neodymium complexes and a starting point for exploring the electronic structures of the uranium complexes.
In addition to the spectroscopically observable f–f transitions, the magnetic properties of Cp_{3}Nd could be used to model the crystal field, which would avoid the difficulty of observing and assigning the f–f transitions. However, magnetic data generally contains less information. The number of independent data in powder magnetic susceptibility measurements may be determined conservatively using van Vleck's theorem (eqn (1)), where the energy of state E_{i} in a magnetic field, H, is E_{i} = E^{(0)}_{i} + HE^{(1)}_{i} + H^{2}E^{(2)}_{i} + higher order terms.^{22,23}
(1) |
To second order, the ground state provides two independent data (E^{(1)}_{0} and E^{(2)}_{0}), and each excited state that is appreciably thermally populated provides three additional independent data (E^{(0)}_{i}, E^{(1)}_{i}, E^{(2)}_{i}). Electron paramagnetic resonance (EPR) spectroscopy can provide additional information. Due to the limited independent data in magnetic measurements, refining all parameters in a crystal field analysis is not possible. However, performing an analysis to determine specific information, such as the splitting of the f-orbitals, may be possible.
The electronic structures of Cp_{3}U (5f^{3}) complexes have not received extensive spectroscopic study.^{24} The 5f–6d transitions are in the visible and tail into the near IR, which makes observing and assigning the weak f–f transitions difficult. Like Cp_{3}Nd, Cp_{3}U has three unpaired f electrons, and magnetic measurements can provide information about its electronic structure. For instance, this approach has been effectively used to determine the oxidation states of uranium in K_{6}Cu_{12}U_{2}S_{15} from its magnetic susceptibility.^{25} While spectroscopic studies of Cp_{3}U electronic structure are few, this system has been studied computationally starting with an MO description of the bonding in the Cp_{3}U^{+} fragment.^{26} Bonding in Cp_{3}U, its Lewis base adducts, and the lanthanide analogs were studied using Xα-SW methodology.^{27–30} More recently, bonding between Cp_{3}U and CO has been studied using DFT,^{31} and covalency in Cp_{3}U and its transuranic analogues has been studied by Kaltsoyannis.^{8} Overall, these studies suggest that the 5f-orbitals do not participate extensively in bonding with two important exceptions. As observed in Cp_{3}Nd, the Cp_{3}U f_{y(3x2−y2)}-orbital interacts with one set of the Cp HOMOs. In addition, the f_{z3}-orbital can interact when an additional ligand is coordinated along the C_{3} axis. Interestingly, the f_{xz2} and f_{yz2}-orbitals, which could form a back-bond with π-acceptor ligands, such as CO, are only weakly stabilized, and work by Maron et al. suggests that backbonding by the 5f-electrons to the ligand π-acceptor-orbitals does not greatly stabilize these complexes.^{31} On the other hand, DFT and multi-reference wavefunction calculations have indicated strong, covalent π-interactions in Cp_{3}U^{IV}–NO involving the 5f π-orbitals and antibonding π*-orbitals of the NO ligand, such that the ground state is non-magnetic.^{32,33}
In this manuscript, we report the syntheses of complexes Cp′′_{3}M and Cp′′_{3}M·L, where Cp′′ is 1,3-bis-(trimethylsilyl)cyclopentadienyl, M = La, Nd, U, and L is tert-butylisocyanide (tBuNC) or cyclohexylisocyanide (CyNC). The complexes (1: Cp′′_{3}Nd; 2: Cp′′_{3}Nd·tBuNC; 3: Cp′′_{3}Nd·CyNC; 4: Cp′′_{3}U; 5: Cp′′_{3}U·tBuNC; 6: Cp′′_{3}U·CyNC; 7: Cp′′_{3}La; 8: Cp′′_{3}La·tBuNC) were characterized using IR spectroscopy (1–8), EPR spectroscopy (1–6), and magnetic susceptibility (1–6). The electronic structures of the complexes were determined from the magnetic data (magnetic susceptibility and EPR spectra) using the full crystal field model implemented in the computational framework CONDON.^{34} The electronic structures of (1–6) were also determined computationally by density functional theory (DFT) and multireference wavefunction calculations. The goals of this study were to determine whether the electronic structures of these compounds may be determined using magnetic data and “free ion” parameters taken from similar compounds. The results of the analysis are compared with previous crystal field analyses of Cp_{3}Nd complexes and with computational models. The roles of the 4f and 5f-orbitals in the parent Cp′′_{3}M complexes and their interactions with the electron-accepting isocyanide ligands are discussed.
A magnetically isolated, f^{3} metal ion in a ligand environment with a specific point symmetry is described by the following Hamiltonian in the presence of an external magnetic field:
(2) |
The temperature dependence of thermodynamic parameters (susceptibility, specific heat contributions, etc.) in an applied magnetic field, B, is introduced by Ĥ_{mag} shown in eqn (2).^{34,45,46} The component of the molar magnetization in direction α = x, y, z of the applied field B, M_{m,α}, is determined using Boltzmann statistics (eqn (3)).
(3) |
The molar magnetic susceptibility along α is calculated as χ_{m,α} = μ_{0}M_{m,α}/|B| (μ_{n,α} = μ_{n}⋅B/|B|), which is also accurate at higher magnetic fields where the magnetization is not linear with respect to the field, as we are including not only the multiplet ground state but the entire multiplet energy spectrum. The mean value χ_{m,av} is given by the averaged sum of its principal components, χ_{m,av} = (χ_{xx} + χ_{yy} + χ_{zz})/3 = tr(χ_{m})/3.^{47} Since the trace of a tensor is independent of the choice of the basis, any basis may be selected as long as the three diagonal elements of χ_{m} are calculated in that basis and averaged to obtain χ_{m,av}.
The IR stretching frequencies of isocyanide ligands and carbon monoxide coordinated to Cp_{3}U have been previously investigated, and Cp_{3}U complexes were found to act as effective π-donors towards isocyanide ligands.^{12} The CN stretching frequency of the coordinated isocyanide ligand reflects the relative roles of the metal center as a σ-acceptor and a π-donor. Interaction between unoccupied metal orbitals and the filled isocyanide σ-orbital increases the CN stretching frequency, and π-donation from occupied metal orbitals into the unoccupied π*-orbitals lowers the stretching frequency.^{67} In Cp′′_{3}La·tBuNC (8), the CN stretching frequency increases by ∼30 cm^{−1} relative to the free ligand, suggesting that tBuNC acts only as a σ-donor in this complex as one would expect since the La(III) center has no f-electrons to donate to the isocyanide π*-orbitals. Interestingly, the CN stretching frequency of the Cp′′_{3}Nd adduct is identical to that of Cp′′_{3}La, which strongly suggests that the Nd 4f electrons do not to back-bond to the ligand. Similar behavior has been observed previously in isocyanide adducts of Cp_{3}Ce.^{12} On the other hand, the CN stretching frequency for the Cp′′_{3}U adduct is significantly lower in energy than in either lanthanide complex, which suggests that the 5f electrons, unlike the 4f electrons, can back-bond with the isocyanide π*-orbitals (Table 1).
tBuNC | (C_{5}H_{5})_{3}Nd·tBuNC (2′) | (C_{5}H_{5})_{3}U·tBuNC (5′) | |
---|---|---|---|
M–C (Å) | — | 2.603 | 2.466 |
CN (Å) | 1.170 | 1.165 | 1.175 |
N–C (tBu) (Å) | 1.436 | 1.439 | 1.436 |
Angle (CNC) | 179.8° | 178.7° | 179.4° |
CN stretching freq. calc (cm^{−1}) | 2178 | 2198 | 2114 |
CN stretching freq. expt (2 and 5) (cm^{−1}) | 2146 | 2178 | 2140 |
Ligand binding energy (kcal mol^{−1}) | — | −16.37 | −21.77 |
The bonding interaction of the isocyanide ligand with the trivalent metal center is dominated by the σ-donation to the d_{z2}-orbital, shown in Fig. 1. In 2′, the 4f electrons are almost exclusively localized at the Nd center in singly occupied molecular orbitals (SOMOs) and result in the spin density of 3.0. SOMOs 1–3 are mainly f_{xz2}, f_{z3} and f_{x(x2−3y2)}, respectively, and are nearly degenerate. In 2′, the f-orbital coordinate system is not aligned with the molecular C_{3} axis (f_{z3}, SOMO-2 in Fig. 1, does not lie on the C_{3} axis). With respect to the C_{3} axis, SOMO-2 has π symmetry and corresponds to f_{yz2} due to the change in coordinate system. Interestingly, the ordering of the orbitals is the same as if back-bonding were important; that is, the lowest lying SOMOs are those with the proper symmetry to interact with the tBuNC π*-orbitals. Nevertheless, the SOMOs depicted in Fig. 1 illustrate that the 4f electrons have little or no overlap with the tBuNC ligand and do not back donate to the ligand as reflected by the spin density and the experimental and calculated values of v(CN).
Fig. 1 Bonding analysis of (C_{5}H_{5})_{3}Nd·tBuNC (2′) and (C_{5}H_{5})_{3}U·tBuNC (5′) from DFT calculations. Isosurfaces at ±0.03 atomic units for both 2′ and 5′. |
Unlike the 4f-orbitals, the 5f-orbitals display strong overlap with the ligand π*-orbitals. The lowest lying-orbitals in 5′, SOMO-1 and SOMO-2 are those with π-symmetry with respect to the molecular 3-fold axis (mainly f_{xz2} and f_{yz2}). SOMO-3 is an orbital with ϕ-symmetry, f_{x(x2−3y2)}, which has no overlap with either the Cp or isocyanide ligands. The 5f electrons back-donate to the π*-orbitals of the ligand (Fig. 1), which reduces the spin density at the uranium center to 2.68. As a consequence, the CN bond distance is lengthened, and the CN stretching mode is decreased. The calculated reduction in v(CN) in 5′ is large compared to experiment (64 cm^{−1}versus 6 cm^{−1}), especially in light of the agreement between the calculated and experimental values in 2′. This difference may be attributed to spin–orbit coupling as addressed below.
The impact of the ligand field on electronic structure is significantly larger in the actinides than in the lanthanides because the greater radial extent of the 5f-orbitals allows better metal ligand overlap. The ligand field removes the (2J + 1)-fold degeneracy of the ground state giving rise to 2J + 1 sublevels with m_{J} = −J, −J + 1, … , J. The degeneracies of the resulting m_{J} sublevels are determined by the site symmetry of the metal ion. The energies of the m_{J} sublevels depend on the orientation and strength of the ligand field. The ligand field also allows excited states with J ± 1 to mix into the ground state. The aforementioned mixing of excited states into the “free ion” ground state complicates the mixing and splitting of the 5f-orbitals. The degree of mixing depends on the relative strengths of the single ion effects (H_{ee}, H_{so}, H_{cf}), which can produce complex electronic structures for actinide complexes. In many cases, energies of the lowest sublevels are smaller than kT at room temperature, and the effective magnetic moment, μ_{eff}, is highly temperature dependent. Because the single-ion effects (H_{ee}, H_{so}, H_{cf}) are similarly strong in actinide complexes, using a perturbation approach to model the crystal field is inaccurate. To determine the 5f electronic structure from physical measurements, the full Hamiltonian (eqn (2)) must be diagonalized with respect to all single-ion effects simultaneously.
To assess whether our approach to the magnetic structures of Cp′′_{3}Nd (1), Cp′′_{3}U (4), and their isocyanide adducts is effective, the parameters determined by modeling the magnetic properties are compared with DFT computational results and crystal field parameters previously obtained by fitting the energies of the f–f transitions. The parameters that we are primarily interested in are the crystal field parameters (B^{k}_{q}), which reflect f-orbital splitting and the strength of their bonding interactions with the ligands.
The EPR spectra of the neodymium and uranium complexes are shown in Fig. 2 and their g-values, determined by fitting the spectra, are given in Table 3. The spectra of Cp′′_{3}Nd·L are easily interpreted since the individual g-components are distinct. Both spectra are nearly axial with that of 3 showing slightly more distortion than that of 2. The EPR spectra of all the neodymium complexes are remarkably similar to each other. While the spectrum of 1 appears quite different from those of 2 and 3, the main difference is that the spectrum of 1 is much broader. The other difference is that g_{||} of 1 is at a field greater than 1 T and is not observed. The EPR spectrum of 4 is similar to that of 1, except that it is somewhat broader and g_{⊥} is greater. The spectra of 5 and 6 are somewhat similar to 2 and 3.
Complex | g _{1} | g _{2} | g _{3} | g _{||} (expt)^{a} | g _{⊥} (expt)^{a} | g _{||} (calc)^{b} | g _{⊥} (calc)^{b} |
---|---|---|---|---|---|---|---|
a The high field component is assigned to g_{||} with respect to the pseudo-C_{3} axis of the molecule, and the low field g-components are averaged to give g_{⊥} based on the work by Amberger and coworkers. b From the crystal field model derived from CONDON simulations. | |||||||
1 | 2.44 | 2.06 | <0.7 | <0.7 | 2.25 | 0.69 | 2.27 |
2 | 2.25 | 2.08 | 0.87 | 0.87 | 2.17 | 1.02 | 2.17 |
3 | 2.51 | 1.77 | 0.89 | 0.89 | 2.14 | 0.90 | 2.22 |
4 | 3.03 | 2.31 | <0.7 | <0.7 | 2.69 | 0.45 | 2.75 |
5 | 2.42 | 1.75 | <0.7 | <0.7 | 2.09 | 0.81 | 2.12 |
6 | 2.40 | 1.68 | 1.04 | 1.04 | 2.04 | 1.06 | 2.06 |
As noted above, modeling the temperature-dependent magnetic moments of 1–6 requires accounting for all single-ion effects including determining the approximate starting values for the crystal field parameters (B^{k}_{q}), spin–orbit coupling (ζ), and Slater–Condon electron–electron repulsion parameters (F^{n}). For both U and Nd, the values of ζ and F^{n} were taken from those determined for Tp_{3}M, where Tp is hydrotris(1-pyrazolyl)borato, since this is the only system for which parameters are available for both Nd(III) and U(III).^{15} Starting values of B^{k}_{q} were taken from (C_{5}HMe_{4})_{3}Nd and Tp_{3}U for the neodymium and uranium compounds, respectively.^{13,15} To avoid over parameterizing the fit, only B^{k}_{q} are varied while the values of ζ, F^{2}, F^{4}, and F^{6} were fixed. The fixed parameters mainly reflect the overall covalency in the complex and are not expected to vary significantly between Cp′′_{3}M and Cp′′_{3}M·L; moreover, these parameters do not directly affect the splitting of the f-orbitals—as such, fixing ζ, F^{2}, F^{4}, and F^{6} to appropriate values should not significantly impact the crystal field parameters, which are the focus of this study.
To reduce the number of crystal field parameters, the site symmetries of Cp′′_{3}M and Cp′′_{3}M·L are assumed to be D_{3h} and C_{3v}, respectively, which leads to the crystal field Hamiltonians given in eqn (4) and (5).
(4) |
(5) |
Using these crystal field Hamiltonians, the magnetic susceptibility and EPR values of 1–6 were fitted using CONDON to determine the values of the crystal field parameters. The fitting results are shown in Fig. 3, and the modeling parameters are given in Table 4. The values of B^{k}_{q} determined for 1 may be compared with those of other Cp_{3}Nd complexes with bulky Cp ligands. As shown in Table S1,† crystal field parameters are very similar for all complexes, which supports the notion that the B^{k}_{q} determined by modeling the magnetic data are consistent with those determined by fitting the energies of the excited states. The average relative uncertainty in the values of B^{k}_{q} in Table 4 is 10%, which is approximately twice as large as the uncertainty in the values of B^{k}_{q} determined by fitting optical data.^{20} The greater uncertainty is due, in part, to the limitation on the number of variables in the CONDON fit imposed by the independent data available in magnetic data. Nevertheless, the uncertainties in the values of B^{k}_{q} determined by fitting the magnetic data are small relative to the values of B^{k}_{q}.
Cp′′_{3}Nd (1) | Cp′′_{3}Nd·tBuNC (2) | Cp′′_{3}Nd·CyNC (3) | Cp′′_{3}U (4) | Cp′′_{3}U·tBuNC (5) | Cp′′_{3}U·CyNC (6) | |
---|---|---|---|---|---|---|
a Quality of fit: . | ||||||
F ^{2} | [71714] | [71714] | [71714] | [36305] | [36305] | [36305] |
F ^{4} | [52182] | [52182] | [52182] | [26452] | [26452] | [26452] |
F ^{6} | [35286] | [35286] | [35286] | [23130] | [23130] | [23130] |
ζ | [881] | [881] | [881] | [1516] | [1516] | [1516] |
B ^{2}_{0} | −3184 ± 56 | −1395 ± 13 | −2781 ± 13 | −777 ± 189 | −3165 ± 103 | −3660 ± 135 |
B ^{4}_{0} | 1597 ± 25 | 828 ± 91 | 733 ± 186 | 6418 ± 830 | 5890 ± 631 | 2744 ± 336 |
B ^{4}_{3} | — | −156 ± 79 | −557 ± 176 | — | −2410 ± 251 | −1280 ± 276 |
B ^{6}_{0} | 973 ± 27 | 1199 ± 45 | 925 ± 149 | 752 ± 21 | 5700 ± 141 | 4705 ± 318 |
B ^{6}_{3} | — | −475 ± 18 | −672 ± 47 | — | 3650 ± 204 | 3250 ± 142 |
B ^{6}_{6} | −2665 ± 43 | −1697 ± 15 | −1959 ± 89 | −8220 ± 215 | −1160 ± 76 | −2290 ± 127 |
ΔE | 60.2 | 63.0 | 62.1 | 90.0 | 49.0 | 73.0 |
LFOS, ^{4}I | 7161 | 6840 | 6968 | 9400 | 9370 | 9460 |
LFOS, ^{4}I_{9/2} | 1110 | 781 | 780 | 1514 | 1720 | 1570 |
Ground state (m_{J}) | ∓5/2 (67%) | ∓5/2 (68%) | ∓5/2 (64%) | ∓5/2 (53%) | ∓5/2 (45%) | ∓5/2 (61%) |
±7/2 (32%) | ±7/2 (27%) | ±7/2 (25%) | ±7/2 (46%) | ±1/2 (44%) | ±7/2 (10%) | |
±1/2 (4%) | ±1/2 (9%) | ±1/2 (26%) | ||||
SQ^{a} | 0.007 | 0.008 | 0.009 | 0.010 | 0.010 | 0.010 |
A more detailed understanding of the bonding in these complexes may be obtained by examining the splitting of the f-orbitals illustrated in Fig. 5. In D_{3h} symmetry, the crystal field only splits the orbitals but does not mix them (Table S2†). In 1, a single orbital, f_{y(3x2−y2)}, interacts significantly with the ligand-orbitals, while the other f-orbitals show little interaction. This result is consistent with previous crystal field studies, which show essentially the same splitting of the 4f-orbitals and a similar ordering (the relative order of the nearly degenerate f_{z3} and (f_{xyz}, f_{z(x2−y2)})-orbitals varies).^{14,16,17} In 4, the splitting of the f-orbitals is approximately twice as large as that in 1, which can be attributed to the greater radial extent of the 5f-orbitals. As in 1, the most strongly destabilized-orbital is f_{y(x2−3y2)}; however, the f_{z3}-orbital is also destabilized. As previously shown, the f_{y(x2−3y2)} is ideally configured to interact with the HOMO of the Cp ligands.^{24,26,28} In addition, none of the 6d-orbitals has the appropriate symmetry, a′_{2}, to interact with this Cp MO. The same is true for the f_{z3}-orbital, which can interact with the Cp HOMO with a′′_{2} symmetry via the two equatorial lobes. The overlap with f_{z3} is not as large as with f_{y(x2−3y2)} since the lobes of the latter point directly at the Cp ligands. That these f-orbitals interact most strongly with the ligands may be viewed as a consequence of the FEUDAL (“f's essentially unaffected, d's accommodate ligands”) principle in which bonding in actinide and lanthanide ions largely involves the d-orbitals.^{72} The f-orbitals only participate substantially in bonding when no d-orbital possesses the appropriate symmetry to interact with the ligand MOs.
Fig. 5 Comparison of the experimentally-based, crystal field MO schemes of Cp′′_{3}Nd (1, left) and Cp′′_{3}U (4, right). MO schemes are plotted with their barycenters at 0 cm^{−1}. |
Fig. 6 Ligand-field splitting and the composition of m_{J} substates (in the absence of an applied magnetic field) of 2 and 3. |
A more detailed picture of the change in electronic structure of the Nd center upon coordination of an isocyanide ligand along the z-axis emerges from the splitting of the f-orbitals (Fig. 7). The identities of the low-lying-orbitals determined by crystal field fitting may be compared with those determined by DFT (Fig. 1) using the coordinate system defined by the molecular C_{3} axis as the z axis. SOMO-1 and SOMO-2 in Fig. 1 correspond to the degenerate f_{xz2} and f_{yz2}-orbitals in Fig. 7 since they have π symmetry with respect to the C_{3} axis. Both the crystal field fit and calculation provide the same ordering of the lowest energy f-orbitals (f_{xz2},f_{yz2}) < f_{x(x2−3y2)} in 2. The ordering in 3 is slightly different; f_{xz2} and f_{yz2} are lowest in energy, but the ordering of the next highest orbital is f_{z3}. Nevertheless, the agreement between the DFT calculation and the experimentally derived MO supports the accuracy of the crystal field model for 2 and 3.
Fig. 7 Experimentally-based, crystal field MO schemes of the Nd complexes 1, 2 and 3. MO schemes are plotted with their barycenters at 0 cm^{−1}. |
The highest and lowest lying orbitals are unchanged upon coordination of the ligand; however, the total splitting of the f-orbitals is decreased as previously observed for (C_{5}H_{5})_{3}Nd isocyanide adducts.^{16} The reduction in f-orbital splitting seems to suggest that coordination of an additional ligand weakens the overall interaction between the f-orbitals and the ligands. However, the splitting of the f-orbitals reflects the anisotropy of their interactions with ligands as well as the strength of those interactions (a spherically symmetric crystal field does not split the orbitals regardless of the strength of the interaction). Coordination of an isocyanide ligand to Cp′′_{3}Nd makes the system less anisotropic. Previous work by Schulz et al. shows that coordination of a second ligand along the z-axis, to form a pseudo-trigonal bipyramidal complex, further decreases the splitting of the f-orbitals.^{19} Both experimentally and computationally, coordination of the isocyanide ligand does not greatly destabilize the f_{z3}-orbital relative to 1 and does not stabilize the (f_{xz2},f_{yz2})-orbitals that could interact with the π*-orbital of the ligand in agreement with the SOMOs illustrated in Fig. 1. In short, coordination of an isocyanide ligand to 1 does little except make the ligand field slightly more isotropic.
Fig. 8 Ligand-field splitting and the composition of m_{J} substates (in the absence of an applied magnetic field) of Cp′′_{3}U·tBuNC (5, left) and Cp′′_{3}U·CyNC (6, right). |
The effect of the addition of an isocyanide ligand upon the 5f-orbitals is illustrated in Fig. 9. As in the Nd system, DFT and experiment provide the same lowest lying orbitals, f_{xz2} and f_{yz2}. The next lowest lying orbital is different in 5 and 6, where 6 displays the same ordering as the DFT calculation. The agreement between theory and experiment suggests that determining the crystal field parameters using magnetic data provides an accurate description of the 5f-orbital splitting. As in the Nd system, addition of a ligand decreases the total splitting of the f-orbitals. Unlike the Nd system, coordination of an isocyanide ligand changes the ordering of the U 5f-orbitals. In both 5 and 6, f_{z3} is strongly destabilized, which is consistent with a significant interaction with the ligand σ-donor orbital; however, the main interaction is between 6d_{z2} and the ligand σ-orbital as shown in Fig. 1. In addition, both experiment and calculation show that f_{xz2} and f_{yz2} are stabilized in 5 and 6 relative to 4 due to interaction with the isocyanide π*-orbitals. These results are consistent with significant participation of the 5f-orbitals in bonding with the isocyanide ligand, which was not the case in the Nd system.
Fig. 9 Comparison of the experimentally-based, crystal field MO schemes (splitting of the f-orbitals) of 4, 5 and 6. MO schemes are plotted with their barycenters at 0 cm^{−1}. |
The contribution of the f-orbitals to bonding between the metal and Cp′′ ligands may be evaluated using the MO scheme in Fig. 5 assuming that the lowest energy-orbitals are essentially non-bonding. From the destabilization of the f_{y(3x2−y2)}-orbital, 2860 cm^{−1} and 5824 cm^{−1} in 1 and 4, respectively, the stabilization of the a′_{2} Cp-orbitals are estimated to be 2520 cm^{−1} and 4070 cm^{−1}, respectively. In 1 and 4, stabilization of the doubly occupied a′_{2} Cp-orbitals by interaction with f-orbitals contributes 14 kcal mol^{−1} and 23 kcal mol^{−1}, respectively, to the bond between the metal and three Cp′′ ligands.
The bonding between the metal center and the isocyanide ligands may be similarly examined using the energy of f_{y(3x2−y2)} as a reference. The energy of this orbital should be largely unaffected by coordination of the isocyanide ligand because it has no overlap with the incoming ligand, and because the steric bulk of the Cp′′ ligands prevents them from adopting a different coordination geometry when the isocyanide ligand coordinates to the metal center as illustrated by the structures of Cp′′_{3}Ce and Cp′′_{3}Ce·tBuNC.^{80} The main f-orbital interaction with the isocyanide ligand is stabilization of the isocyanide σ-orbital by f_{z3}. Using f_{y(3x2−y2)} as a reference, the change in the energy of the f_{z3}-orbital can be used to estimate how effectively the f-orbitals stabilize the bond between Cp′′_{3}M and L. In 2 and 3, f_{z3} is destabilized by 1360 cm^{−1} and 340 cm^{−1}, relative to 1, and in 5 and 6, f_{z3} is destabilized by 3480 cm^{−1} and 3850 cm^{−1}, relative to 4. Interaction with the f_{z3}-orbital contributes 4 kcal mol^{−1} and 1 kcal mol^{−1} to the stability of 2 and 3, respectively, and 7 kcal mol^{−1} and 8 kcal mol^{−1} in 5 and 6, respectively. In other words, the increased overlap in Cp′′_{3}U strengthens the σ-bond with the isocyanide ligand by 5 kcal mol^{−1} relative to Cp′′_{3}Nd, which is in agreement with the 5.4 kcal mol^{−1} difference in bond strength determined by DFT (Table 2). The contribution of π-back bonding to the stability of the complexes cannot be readily estimated because the populations of the f-orbitals are more difficult to quantify than that of the ligand orbitals.
Fig. 11 Contour line plots of the two π-bonding NOs of 5′ of Fig. 10 in perpendicular cut planes. Contour lines from ±0.01 to ±1 atomic units with logarithmic spacing. |
In a scalar relativistic (SR) calculation, i.e. without SO coupling, the ground states are spin quartets related to the ^{4}I_{9/2} ion level. These mix with of other J = 9/2 levels due to SO coupling, and with levels having different values of J due to the low symmetry of the ligand field—as already mentioned. The characterization of the calculated electronic ground states in terms of their metal ion level parentages in Table 5 shows that spin-quartet states derived from the ^{4}I_{9/2} ion levels dominate the two-fold degenerate ground states of the two complexes, with SO coupling causing less than 10% mixing of higher energy spin-doublets into the ground state. It is important to note that the NOs in Fig. 10 were calculated for the ground states including SO effects. When SO coupling is taken into consideration, π and ϕ symmetry f-orbitals couple with those of σ and δ symmetry, and occupation may shift accordingly among these orbitals. Nevertheless, f-orbitals with π and ϕ symmetry relative to the axial ligand, which have occupations of 1 in the SR DFT calculations, also have the largest occupations in the SO wavefunction calculations, as shown in Fig. 10. However, due to SO coupling as well as multi-configurational character of the SCF-SR states, for 5′, the formal U–ligand bond order is less than in the DFT calculation because the combined occupation of the 5f π-bonding-orbitals is only about 1.2 electrons. This difference is presumably the main cause of the deviation between the calculated reduction in ν(CN) upon coordination to Cp′′_{3}U (64 cm^{−1}) compared with the experimental value (6 cm^{−1}). Spin–orbit coupling diminishes the f-electron contribution to back bonding in agreement with the earlier studies by Maron et al. and Gendron et al.^{31,32}
g _{||} | g _{⊥} | g _{||} | g _{⊥} | ||
---|---|---|---|---|---|
Complex | Weight ^{2S+1}L_{J} | (exp) | (calc) | ||
2′ | 97.9 ^{4}I_{9/2}, 2.0 ^{2}H_{9/2} | 0.87 | 2.25 | 1.12 | 2.22 |
5′ CNC linear | 91.6 ^{4}I_{9/2}, 6.6 ^{2}H_{9/2} | <0.7 | 2.09 | 0.61 | 1.97 |
5′ CNC bent | 91.7 ^{4}I_{9/2}, 6.2 ^{2}H_{9/2} | 1.45 | 1.31 |
For both 2′ and 5′, there is reasonably good agreement between the experimental and crystal-field derived EPR g-factors (Table 3) and those from the ab initio calculations (Table 5). In order to match the experimental g-factors more closely, the calculations would likely need to employ a model for the environment of the complex in the solid including crystal packing effects on its structure.^{59} Because of the π interactions with the axial ligand, the g-factors are highly sensitive to structural distortions. When the t-butyl group is bent somewhat out of its axial position, the ground state composition does not change dramatically in terms of the contributions from the ^{4}I_{9/2} and ^{2}H_{9/2} states. However, the U–tBuNC π bonding character increases significantly (Fig. S2†), and the parallel g-factor increases strongly, while the average of the perpendicular components decreases somewhat. Deviations between the calculation and experiment can also be attributed to the missing treatment of the dynamic electron correlation and the size of the active space.
This comparative study showcases the strengths and limitations of simple scalar relativistic (SR) orbital, single-reference descriptions (i.e. single electron MO diagrams) to characterize the bonding in f-metal complexes. For instance, while such a model may reveal the role of the f-orbitals in bonding, it does not take into account the strong mixing of the occupied f-orbitals by spin–orbit coupling, or deviations from formal occupations due to a multi-reference nature of the electronic state, which may be important for a full description of the bonding or magnetic behavior. Such information can be obtained without semi-empirical parameters from natural-orbitals generated from multi-reference wavefunctions including SO effects, or similar types of analysis tools for complex wavefunctions. For instance, CAS calculations confirm the presence of π bonding between the uranium center and the isocyanide ligands, but with less than the formal U–L bond order because the ground state electron density of the open 5f shell has contributions – to varying degrees – from all seven 5f-orbitals.
Motivated by these findings, future implementations of CONDON will include the conversion of the micro state, |m_{J}〉 basis into the real-orbitals (e.g. f_{xz2}) of the ground state, assigning a ligand field splitting to the real-orbitals and identifying the orbitals based on the occupied micro states.
Footnote |
† Electronic supplementary information (ESI) available: Synthesis details, comparison of crystal field parameters, occupation of micro states. See DOI: 10.1039/c6dt00634e |
This journal is © The Royal Society of Chemistry 2016 |