Metallocenes, namely complexes of metal ions with cyclopentadienide anion (Cp -) are among the most important and widely studied organometallic complexes dating back to the pioneering work of Wilkinson and Fischer. 1 Homoleptic biscyclopentadienide complexes, [MCp2] n+ , can be neutral, such as in ferrocene (M = Fe II ), 2 chromocene (M = Cr II ), 3 or vanadocene (M = V II ), [4][5] but can also be cationic, such as popularized ferrocenium (M = Fe III ) 6 or nickelocenium (M = Ni III ) salts. 7 Even after over 70 years since the discovery of ferrocene, new developments in fundamental metallocene chemistry are possible such as in the synthesis and characterization of a "perferrocenium", that contains Fe IV8 and the very recent report of the first structurally characterized 4d metallocene anion, interestingly with a metallocene countercation: [Co III (C5Me5)2][Rh I (C5Me5)(C5(CF3)5)]. 9 One member of the homoleptic biscyclopentadienide series that has been given relatively short shrift is chromocenium, [Cr III Cp2] + , despite its original synthesis by the metallocene pioneer E. O. Fischer early on (ca. 10 years after ferrocene). 10 The paucity of studies on [CrCp2] + is also notable given the widespread study of Cr III complexes in general 11 and the importance of organochromium species in catalysis, [12][13] in particular the oligomerization and polymerization of ethylene [14][15][16][17] as well as co-polymerization reactions to make polycarbonates. [18][19] As part of our earlier experimental and computational study of [VCp2], [4][5] we realized that isoelectronic [CrCp2] + merited a similar analysis.
Moreover, as discussed below, although a few crystal structures of [CrCp2] + with varying counteranions had been reported, [20][21][22] none had a "classic" weakly coordinating counteranion, of which BAr F (tetrakis[ (3,5trifluoromethyl)phenyl]borate) is a paradigm example. 23 Having a more innocent counter anion is critical, as demonstrated by the structural distortions promoted by the anion in the case of [FeCp2] 2+ . 8 We describe here the synthesis, structural, and spectroscopic characterization of [CrCp2][BAr F ] (1). The spectroscopic techniques used are conventional (X-band) electron paramagnetic resonance (EPR), its high-frequency and -field variant (HFEPR), which has been applied to related complexes, 18,24 and magnetic circular dichroism (MCD), which is a powerful technique for unraveling electronic structure, [25][26][27][28][29][30] but has been relatively less applied to early transition metal ion complexes. Using both classical ligandfield theory (LFT) and modern quantum chemical theory (QCT) ab initio computational methods, we describe the electronic structure of this hitherto somewhat neglected member of the [M(Cp)2] + family and compare it to its neutral isoelectronic congener with V II . We note that a comprehensive computational study on paramagnetic [MCp2] 0 (M = V, S = 3/2; Cr, S = 1; Mn, S = 5/2; Ni, S = 1) complexes was made by Vaara and co-workers, 31 mainly in the context of calculating 1 H NMR spectra, but the spin Hamiltonian parameters (D, E/D, and g values) were calculated for these metallocenes along with a different Cr III complex as they apparently had no relevant information on any [CrCp2] + species.
Synthesis. S1 (Supporting Information). Due to the volatility of neutral [MCp2], it is possible to determine their "true" (i.e. absent any packing effects) structures using gas phase electron diffraction. This method has been applied to many such complexes, the two of which that are relevant here are [VCp2] and [CrCp2]. The former is isoelectronic with 1, but with V II and the latter is the neutral, Cr II (3d 4 , S = 1) parent complex.
Gard et al. determined the gas phase structures of both of these complexes. 33 They favored an eclipsed (D5h symmetry) structure, but could not rule out staggered (D5d). The M-C bond distances are 2.280(5) Å and 2.169(4) Å in [VCp2], and [CrCp2], respectively. The C-C bond distances are essentially the same (1.434(3) Å and 1.431(2) Å, respectively). In the solid state, [VCp2] has been studied in detail by Antipin and Boese. 34 Their best results were obtained at 108 K (CSD code: CPNDYV03) and displayed a staggered conformation of the Cp -ligands and gave a mean V-C distance of 2.269(1) Å and a mean C-C distance of 1.417 Å. In the case of [CrCp2], the sole complete structural report 35,36 was by Flower and Hitchcock who determined the crystal structure at 173 K (CSD: CYCPCR01) and found a Cr-C distance of 2.151(13) Å with a mean C-C distance of 1.401(11) Å. 37 For 1, we find a mean Cr-C distance of 2.196(2) Å. This value is shorter than for the neutral [VCp2] also with its larger V II ion, but still longer than in [CrCp2] wherein the "electron imbalance" 33 (i.e., the deviation from the "ideal" bonding situation as found in [FeCp2], namely (e1,a1) 6 e1 0 ) is smaller (3 for d 3 , (e1,a1) 3 e1 0 and 2 for low-spin d 4 , being (e1,a1) 4 e1 0 ). The average C-C distance is 1.400 Å, the same as in [CrCp2]. Numerous structures have been reported for [CrCp*2] + (Cp* = pentamethylcyclopentadienide anion) species as the cation in charge transfer salts, with a variety of electron acceptors, starting with the pioneering work of Miller and Epstein, 38 followed by others. [39][40][41][42][43][44][45] In these cases, however, not only is Cp* markedly different from Cp as a ligand, 46 there is magnetic interaction between the [CrCp*2] + and the electron acceptor -the raison d'être of such studies, in contrast to our interest in the electronic structure of isolated "plain vanilla" (i.e., C5H5
-) [CrCp2] + . We note however the complex [CrCp*2][Cp*CrCl3], 47 (CSD: NAQQIF) as a representative example of an "innocent" [CrCp*2] + cation. In this case, the structure is staggered with a Cr-C distance of 2.193(5) Å and a Cr-Cp centroid distance of 1.83 Å. 47 We next turn to the structures reported for [CrCp2] + with other counteranions. In [CrCp2][CpCr(CO)3] (CSD: FUTGIK10), the structure is eclipsed with the Cr-C distance being 2.181(5) Å and an average Cr-Cp(centroid) distance of 1.840(2) Å. 20 We see no clear reason for the eclipsed structure, although there may be weak H-bonding between the [CrCp2] + Cp ring H atoms and the carbonyl O atoms of the anion. In the complex with [Cp2DyI2] -(CSD: VEBYEH), there is an almost fully eclipsed conformation of the Cp -ligands with a Cr-C average distance of 2.197(4) Å and Cr-Cp centroid distance 1.846(2) Å. 22 In this structure there seems to be a weak H-bonding interaction of the [CrCp2] + Cp ring H atoms to an iodide atom of the Dy-containing anion. In the complex with hydroxoborate anion (CSD: LAWROQ), there is a staggered conformation of the Cp -ligands with a Cr-C average distance of 2.205(3) Å and the Cr-Cp centroid distance is 1.8488(14) Å. 21 In our structure, as shown in Figure S1 (Supporting information) there is a weak stacking interaction between a phenyl ring of BAr F anion and a Cp ring of the cation of interest. 48 Thus even with BAr F counteranion it may not be possible to have a truly "naked" [CrCp2] + complex. With this caveat we find that spectroscopic studies of 1 are consistent whether solid state or solution forms are investigated. Conventional EPR spectroscopic studies of 1. The conventional (i.e., X-band) EPR spectrum of [CrCp2][BAr F ] (1) is characteristic of an S = 3/2 species with zero-field splitting (ZFS, given by the axial parameter D and the rhombic parameter E) much larger than the microwave quantum ( << cD) and with axial symmetry (E 0). Such a spectrum is shown in Figure 2 for 1 in toluene/thf (tetrahydrofuran) solution (1:1 v/v). The spectrum can be simulated using an effective spin, S = 1/2, with g' = [3.97, 3.97, 2.00] (i.e., g⊥ = 3.97, g = 2.00) and nearly isotropic linewidths (see Figure S2, Supporting Information). Figure 2 shows a simulation using the real S = 3/2 with parameters determined from HFEPR (see below). In contrast to vanadium ( 51 V, I = 7/2, ~100% abundance), the natural abundance of non-zero nuclear spin chromium is very low (only 53 Cr, I = 3/2, 9.5% abundance). Although satellites due to hyperfine coupling to 53 Cr can sometimes be observed in X-band EPR (e.g. in a formally Cr I organometallic radical 49 and in [Cr I (C6H6)2]I, 50 ) none was observed here for 1, in contrast to the situation with [VCp2] for which 51 V hyperfine coupling was readily observed. [4][5] The X-band EPR spectrum shown here for isolated, analytically pure
1 can be compared to that reported earlier for [CrCp2] + found as an impurity in [CrCp2] diluted into a host lattice of diamagnetic [MgCp2]. 51 This work was part of a monumental study by Ammeter on a wide variety of paramagnetic metallocenes such as [Mn II Cp2], [Fe III Cp2] + , [Co II Cp2], and [Ni III Cp2] + , all of which are Kramers (half-integer spin) systems, as are [VCp2] and [CrCp2] + . Ammeter's attempt to observe X-band EPR of [CrCp2] was apparently unsuccessful (its S = 1 ground state exhibits large ZFS 3 and is thus "EPR-silent" using conventional spectrometers), but an oxidation product was observed, with an unknown counter anion, in the [MgCp2] matrix. Intrinsic g values of g⊥ = 1.977(2) and g = 2.002(2) were reported. 51 The g⊥ value deviates slightly more from ge than seen here, which may be a consequence of interactions with the matrix as opposed to the isolated molecules studied here, with the large and relatively non-interacting BAr F counter anion. We also note the report of X-band EPR spectra from [CrCp*2] + in charge transfer salts with fullerene acceptors, with effective g values of g⊥ = 3.42 -3.97, g = 2.01. 42,52 These [CrCp2] + -fullerene species clearly lack the axial symmetry expected for isolated [CrCp*2] + , but their g values are similar to what is seen for 1 (g⊥ = 3.97, g = 2.00). The upper inset shows an expansion of the g⊥ region and the lower of the g region.
HFEPR Spectroscopy of 1. High-frequency and -field EPR (HFEPR) spectroscopy has been successfully applied in studying a variety of 3d ion systems with S > 1/2. [53][54][55] Of relevance here, besides [VCp2], [4][5] are studies on organochromium(III) complexes based on a quinoline-substituted Cp ring coordinated to a CrCl2 moiety, which, as is the case here, exhibit relatively large ZFS (D 3 cm - ). 18,24 As was the case with [VCp2], HFEPR spectra recorded for solid-state 1
were of relatively poor quality in terms of exhibiting features from individual microcrystallites. Fortunately, as was also the case with [VCp2], frozen solution HFEPR spectra of 1 gave good quality spectra with minimal baseline artefacts and decomposition/oxidation byproducts. A representative HFEPR spectrum of 1 in tetrahydrofuran (thf) solution recorded at 20 K and 208.0 GHz is shown in Figure 3. In contrast to neutral [VCp2], toluene was not a viable solvent for the ionic complex 1, but acceptable spectra were also recorded in dichloromethane (dcm)
and an additional spectrum recorded at 20 K and 104 GHz is presented in Figure S3 (Supporting Information). It is clear that the sign of D is positive, namely that the mS = 1/2 doublet is lower in energy, which agrees with the X-band results, and with the finding for [VCp2]. Figure 4 presents a 2D map of turning points in the powder spectra versus multiple microwave frequencies with calculated lines. This type of presentation has been widely used for HFEPR data 53 and shows here the accuracy and precision of the S = 3/2 spin Hamiltonian least-squares fit to the entire data set, namely D = 4.815(5) cm - , E = 0.0003(3) cm - , gx(⊥) = 2.004(2), gz() = 2.012 (7).
Given the experimental precision, a more realistic set of S = 3/2 spin Hamiltonian
The g-values, being essentially the free electron value, are uninformative as to electronic structure; however, the ZFS is informative. Qualitatively, two points can be noted here. First, as was the case for [VCp2], 1 has rigorously axial electronic symmetry as expected from its crystal structure. Second, the positive sign of D is the same as for [VCp2], but is larger in magnitude (by ~70%), which can be the consequence both of greater spin-orbit coupling (SOC) in Cr III versus V II and potentially the stronger bonding interactions for a 3+ versus 2+ ion. Ligand-field theory (LFT) and quantum chemical theory (QCT) calculations will address these points quantitatively below. MCD Spectroscopy. The low-temperature magnetic circular dichroism (MCD) spectrum of a mull sample of 1 shows a rich collection of temperature-dependent C-terms (Figure S4) 56 from 15 000 -28 500 cm -1 (Figure 5, top). 25 At lower-energy, the MCD spectrum contains a progression of at least twelve sharp features, beginning at 15 500 cm -1 and stretching to 19 000 cm -1 (Figure 5, bottom). The higher-energy region of the spectrum (23 000 -29 000 cm -1 ) contains the most intense MCD features, including positive bands at 24 950 and 26 600 cm -1 and a negative feature near 23 500 cm -1 . Some fine structure is observed for the bands at 23 500 and 24 950 cm -1 . The band energies and amplitudes are given in Table S2 (Supporting Information). The positions of these features correspond well to The low-energy MCD feature of 1, which consists of a series of closely-spaced bands (Figure 5, bottom), is attributed to a set of Franck-Condon vibronic progressions. In a vibronic profession, the individual MCD features arise from excitations to different vibrational sublevels of an electronic excited state. Such progressions are often simulated under a harmonic approximation by using the following Poisson distribution:
where → and E→ are respectively the intensity and energy of the first vibronic transition (i.e., the first peak in the progression), S is the Huang-Rhys factor that reflects the width and displacement of the excited-state potential energy surface relative to the ground state, E is the photon energy, E is the vibrational spacing, and fwhm is the full-width at half-maximum of each vibronic band. [27][28][29][30] An analysis of the positions of the band maxima shows an irregular spacing, with the band-to-band separation varying from 240 to 356 cm -1 . This spacing, as well as an unusual intensity distribution, indicate that this progression contains contributions from more than one excited state. In support, attempts to simulate this progression as a standard Poisson distribution describing a single excited state (see equation 1) led to very poor fits. A minimum of three separate excited states, each with its own Franck-Condon vibronic progression, was required to obtain even modest agreement between experiment and theory over a limited energy range (Figure S5, top). In these simulations, common bandwidths (fwhm) were assumed for each excited state, Huang-Rhys factors (S) were varied slightly for each excited state, while the electronic excited-state origins (E0→0) and MCD intensities (0→0) were varied parameters. A very crude fit, however, was also obtained using an EPR simulation program (DDPOWH by J. Telser) that gives a semi-quantitative picture of the vibronic coupling. This "Ansatz" procedure is described in Supporting Information and shown in Figure S6.
A possible origin of this vibronic coupling can be gleaned from vibrational (IR and Raman) studies on [MCp2] complexes by Aleksanyan et al., [58][59] including [VCp2] and [CrCp2]. For these two complexes as solids at 90 K there are low frequency Raman active bands as follows: 58 (E2u in D5d, which is a Cp-M-Cp bend 60 ) at 183 cm - (M = V, weak; not seen for M = Cr), (A1g, which is a Cp-M symmetric stretch [60][61] ) 62 at 258 cm - (M = V, medium), 273 cm - (M = Cr,, strong) and (E1g, which is a ring tilt [60][61] ) at 331 cm - (M = V, medium), 370 cm - (M = Cr, very weak). Equally relevant is an IR active band (A2u, which is a Cp-M asymmetric stretch [60][61] ) at 380 cm - (M = V, strong intensity), 408 cm - (M = Cr, medium). We have no explanation as to why vibronic coupling was not observed previously in vanadocene, 5 and purely vibrational studies on 1 would be complicated by the BAr F counteranion, so we do not know the exact energies of 4 and 11 or other possibly relevant modes such as 16 or 21. Nevertheless, it appears that in [CrCp2] + there is vibronic coupling observed between electronic transition(s) and Cp-M stretches as well as possibly other low energy modes involving the metal ion.
While the low-energy region of the MCD spectrum of 1 required the inclusion of vibronic effects, the higher-energy region (22 000 -28 500 cm -1 ) could be analyzed in a more conventional fashion, [63][64] with each electronic transition approximated by a broad, Gaussian function (Figure S5, bottom). This analysis revealed the presence of at least five electronic transitions. Two of these bands (bands 2 and 3) appear to form a pseudo-A term, which are two oppositely-signed and energetically adjacent MCD bands that give rise to a derivative-shaped feature. 25 Both components of this pseudo-A term show fine structure, with sharp features observed from 23 557 -25 907 cm -1 . These features are spaced at irregular intervals, ranging from 234 to 355 cm -1 , but the average energy spacing is close to that observed for the Franck-Condon progression at lower energy. Because of this similarity in energy spacing, we attribute the fine structure on bands 2 and 3 to a Franck-Condon vibronic progression. Because the progression is coincident with bands 2 and 3, a detailed simulation was not performed. The remaining three MCD bands (bands 1, 4, and 5) are positively-signed and show no vibronic structure.
Following our analysis of the optical properties of the isoelectronic [VCp2], 5 we expect three spin-allowed ligand-field transitions for [CrCp2] + :foot_0 A2g → 4 E1g(I), 4 A2g → 4 E2g, and 4 A2g → 4 E1g(II), using symmetry labels from the D5d point group. Each excited state arises from a one-electron excitation relative to the 4 A2g (a1g) 1 (e2g) 2 (e1g) 0 configuration, as summarized in Table 1. Because each excited state is orbitally degenerate, under ideal conditions, each should appear as a pseudo-A term in the MCD spectrum of [CrCp2] + . However, overlap of the bands can lead to cancelation of the positive and negative components, complicating spectral interpretation. This appears to be the case for [CrCp2] + , where only one pseudo-A term (bands 2 and 3) is apparent. Given this complication, we developed assignments of the MCD features using electronic structure computations, as described below. Electronic Structure Computations for [CrCp2] + . 65 Ligand-Field Theory (LFT) Calculations Electronic Transitions. The application of LFT to the 3d 3 metallocene complexes
[VCp2] and [CrCp2] + was pioneered by Pavlík and co-workers, 57 They reported a synthetic procedure only for [VCp2] and its spectra in n-pentane and Et2O were presented, but it is unclear from their paper whether they recorded any electronic absorption spectra themselves for the Cr III complexes (the biscarborane complex [Cr(1,7-B9C2H11)2] -and mixed carborane-metallocene complex [CrCp(1,7-B9C2H11)]
were also studied). Nevertheless, they reported bands at 560 nm (17 860 cm - ; = 270 L mol - cm - ), 455 nm (21 980 cm - ; = 210 L mol - cm - ), and 370 nm (27 030 cm - ; = 630 L mol - cm - ). These were assigned to the three transitions given in Table 1: 4 A2g → 4 E1g(I), 4 A2g → 4 E2g, and 4 A2g → 4 E1g(II), respectively. They employed the classical crystal-field parameters of Ballhausen, 66 as also done by Warren, 67 to quantify the bonding. We have reproduced their results, in which the bands are fitted exactly using (in cm - ): Dq = 0 (since this is a purely axial system, with no cubic crystal-field interaction), Ds = -4299.7 (our phase definition is opposite to that used by Pavlík 57 who had Ds = +4299), Dt = 2087, and Racah B = 513 (55% of the free-ion value; 68 Racah C is set large for fitting purposes; use of free-ion C/B = 3.97 69 gives C = 2040). The resulting energy levels are given in Table S3 (Supporting Information). The larger (magnitude) Ds parameter for 1 versus [VCp2] indicates stronger bonding in the 3+ versus 2+ ion complex.
Our optical spectra, however, support a different assignment, namely that the band near 17 000 cm - is likely from a doublet excited state, and the three spinallowed bands (in cm - ) are closely spaced at: 23 500 ( 4 A2g → 4 E1g(I)), 25 000 ( 4 A2g → 4 E2g), and 28 000 ( 4 A2g → 4 E1g(II)). In this case, perhaps because the lines are closely spaced, the fit can go awry (e.g., drive B to a very low value), but with care it is possible to fit the three bands exactly using the following parameters (in cm - ):
Ds = -4216, Dt = 2714, and B = 253 (only 27% of the free-ion value, 68 so that the freeion C/B gives C = 1005). These crystal-field (bonding) parameters are close to those reported earlier. 57 The low B value is peculiar and the correspondingly low value for C gives very low-lying doublet excited states with none near ~17 000 cm - . We therefore included another band for the fitting, namely a doublet at this energy.
The fit was repeated allowing C to vary within a reasonable range. This procedure allowed the nominally spin-forbidden band to be matched exactly. Allowing Ds, Dt, B, and C all to vary within narrow ranges led to deviations between experiment and calculation of < 1 cm - , far better than the experimental precision. The final fit parameters were (in cm
- ): Ds = -4215.77, Dt = 2713.89, B = 252.975, and C = 2626.86 (71% of the free-ion value). It is less common, but not impossible that the Racah B
and C parameters diverge differently from their free-ion values. [70][71] The resulting energy levels are given in Table S4 (Supporting Information). Lastly, we note that even the earlier band assignments 57 give a doublet excited state calculated at ~19 000 cm - (Table S3) roughly in the range proposed by our optical spectroscopy.
A final application of classical LFT is to calculate the S = 3/2 spin Hamiltonian parameters for [CrCp2] + . To do so, we include spinorbit coupling (SOC) parameterized by the single-electron SOC constant, = 274 cm - for free-ion Cr 3+ ( = 169 cm - , for free-ion V 2+ ). 68 ) Reducing from the freeion value to 210 cm - (77% of the free-ion value, similar to the reduction for C),
gives a zero-field splitting between the mS = 1/2 ground state spin doublet and the mS = 3/2 (i.e., D > 0) of 9.467 cm - ; since the system is axial, D = 9.467/2 = +4.734 cm - . This D value is from only SOC (DSOC); spin-spin coupling (SSC) 72 is not included. As described below in the QCT section the SSC contribution (DSSC) could be as great as one third of the total ZFS. In this case, e.g., = 180 cm -1 (66% of the free ion value) gives DSOC = +3.38 cm -1 , which might be sufficient when combined with DSSC. In any case, the agreement is quite good given the simple model used.
Addition of an external magnetic field (B0 = 350 mT, typical for X-band EPR) for either value gives g⊥ = 3.94, g = 2.00, which agrees remarkably well with the Xband data: g⊥ = 3.97, g = 2.00.
An alternate LFT method is to use the angular overlap model (AOM), [73][74][75] which we have used for "traditional" complexes with coordination numbers of three, 76 four, 77 five, 78 and six, 79 but did not do so in our study on [VCp2]. 5 We have now applied the AOM to were held identical and both types of -bonding (-s(y) and -c(x)) [73][74] were included, but it was found that only -s was needed for successful fitting. As shown in Table S5, in the MCp2 geometry this type of -bonding particularly affects the energy of the S6 and were very close to those obtained from the crystal-field model (see above) although the slightly larger B value is more reassuring, now being 30% of the free-ion value; the C value, determined from fitting, is 70% of its free-ion value. 68 Addition of SOC ( = 180 cm -1 ) and an external magnetic field gave spin Hamiltonian parameters essentially identical to those obtained from the crystal-field model and thus in good agreement with experiment. For comparison with QCT calculations (see below) the calculated electronic transitions including SOC are given in Table 2 and match the observed bands reasonably well. The AOM parameters give single electron d orbital relative energies of 22 , xy xy dd -(e2g) at 0, 2 z d (a1g) at 2687 cm - (0.333 eV), and , xz yz dd(e1g) at 27 785 cm - (3.197 eV). These values should not be taken too literally, but suggest that in [CrCp2] + the 2 z d orbital is relatively low lying in energy (i.e., close to the 22 , xy xy dd -orbitals), which is in agreement with the quantum chemical theory described in the following section.
For completeness, we also applied the same AOM fitting procedure to [VCp2]
using the absorption bands we reported earlier. 5 In this case the relevant angle is 32.08(2) o using the structure obtained at 108 K. 34 The resulting fit parameters (all in cm - ) were: (C) = 3877.5, -s(C) = 4795.5, -c(C) = 0; B = 454.22, C = 1882.26.
These Racah parameters are respectively ~60% and ~65% of the free-ion values for V 2+ , 69 which is quite reasonable. Qualitatively, it can be seen that the bonding parameters, both and , are smaller for vanadocene, particularly the -bonding which is much stronger for [CrCp2] + . The calculated energy levels are given in Table S7. These AOM parameters give 2 z d at 4953 cm - (0.614 eV) and , crystallography, but in excellent agreement with corresponding values from gasphase electron diffraction studies. 5 Thus, the differences in metric parameters between the DFT-and crystallographic [CrCp2] + structures can be attributed, to some extent, to crystal packing effects. These effects are likely more significant in the ionic [CrCp2] + chromocenium complex as opposed to neutral
[VCp2]vanadocene. As will be seen below, the structural differences between these models have only a minor influence on calculated spectroscopic properties.
DFT Bonding Description and Spectroscopic Properties. DFT computations for both structures of [CrCp2] + yield a (a1g) 1 (e2g) 2 (eg) 0 configuration, with a Cr 3+ d-orbital splitting pattern in qualitative agreement with that anticipated on the basis of traditional MO arguments (Figure 6 and Tables S8 and S9). In the spin unrestricted formalism, the spin-up () a1g and e2g orbitals are singly-occupied, with the higherenergy, spin-up e1g orbitals being unoccupied. All spin-down () Cr 3d-based MOs are unoccupied. For metallocenes, it is difficult to predict whether the a1g or e2g
MOs are at lowest energy. The DFT computations for [CrCp2] + predict a very small splitting for these MOs (Figure 6 and Tables S8 and S9), which agrees qualitatively with the LFT AOM analysis given above. In the -spin manifold, the a1g MO is at lowest energy, but is only ~0.1 eV (800 cm - or 2.3 kcal/mol) lower than the e2g set.
The a1g and e2g ordering is inverted for the -spin MOs, with the e2g set lying ~0.45
eV (3 630 cm - or 10.4 kcal/mol) below the a1g MO. For the isoelectronic [VCp2] complex, we demonstrated that the magnitude of the a1g-e2g splitting was sensitive to the choice of density functional, with a larger splitting associated with greater Hartree-Fock character in the functional. 5 For d 3 systems such as [VCp2] and
[CrCp2] + the ordering of these MOs is inconsequential in the sense that both lead to a 4 A2g ground state. Qualitatively, that the a1g and e2g MOs are close in energy means that Hund's rule is obeyed and there is no viable spin doublet ground state (or low-lying excited state). In [CrCp2], however, and later higher d-electron count
[MCp2] 0,+ species, population of the e1g set is unfavorable and the ground state for
[CrCp2] is a spin triplet. S8 and S9.
Ground-state zero-field splitting parameters for both models of [CrCp2] + were calculated at the coupled-perturbed (CP) DFT level of theory. Computations for the staggered (C2h) and X-ray structure models of [CrCp2] + yielded D = +3.34 cm - , in reasonable agreement with the experimental value obtained from HFEPR measurements (D = +4.82(1) cm - ). The CP-DFT computations predict the complex to be completely axial (E = 0), also in agreement with experiment. Overall, given the well-documented challenges of DFT methods at treating the zero-field splitting phenomenon, [79][80][81][82][83][84] the level of agreement here is as good as can be anticipated.
Given the reasonable agreement between the CP-DFT D value and its experimental counterpart, we also investigated the contributions to the calculated D value. The dominant contribution comes from spin-orbit coupling (DSOC; see Table S10), as is common, 85 but not universal, 5 for transition-metal systems. In this case, the spin-spin coupling contribution (DSSC) is certainly non-negligible, contributing 35% to the magnitude of D.
We used time-dependent (TD) DFT computations to predict energies for the quartet excited states of [CrCp2] + . These calculations predict the 4 A2g → 4 E1g (I) and 4 A2g → 4 E2g transitions to be very close in energy, both near 25 000 cm - (Table S10).
The 4 A2g → 4 E1g (II) transition is predicted near 28 000 cm - . These predictions are consistent with the prominent and complicated MCD band structure from ~23 000 to 29 000 cm - .
Multireference SORCI and CASSF/NEVPT2 Calculations. To complement our understanding of the bonding and electronic structure of [CrCp2] + derived from DFT computations, we also performed SORCI (Spectroscopy Oriented Configuration Interaction) 86 computations on the computations on the XRDderived model of [CrCp2] + and CASSCF/NEVPT2 computations on both the C2h and XRD-derived models of [CrCp2] + . The theory underlying these approaches, along with their strengths and limitations have been described in detail in several publications. 71,87 In short, both SORCI and CASSF/NEVPT2 methods are more successful, and substantially more reliable, than DFT approaches in calculating ground-state zero-field splitting parameters and electronic transition energies. The SORCI method, which is the more computationally demanding approach, often requires the use of truncated systems. However, the small size of [CrCp2] + makes this system well-suited for the SORCI method. We will first discuss the results of the SORCI computations and then describe the results of the CASSCF/NEVPT2 computations by comparison.
The SORCI computations for [CrCp2] + used as an active space three electrons in five Cr 3d orbitals and coordinates from the X-ray structure of [CrCp2] + .
Although this active space is minimal, our SORCI calculations previously reported for [VCp2] showed very good agreement between experiment (D = +2.836(2) cm -1 )
and theory (D = +2.86 cm -1 ) using the same active space of three electrons in five 3d orbitals. [4][5] As described below, we observe little difference in CASSCF calculations using the X-ray structure of [CrCp2] + or the DFT structure; therefore, we used the X-ray structure for the SORCI calculations. These calculations give D = +5.21 cm -1 , which is less than 10% higher than the experimental value, and E/D = 0. The DSOC contribution is largest (4.40 cm -1 ), with DSSC contributing only 20% of the total value (0.81 cm -1 ). The SORCI calculations provide individual contributions to the spin-orbit coupling terms (DSOC and ESOC) from each excited state (Table S11). These data reveal that the largest contribution to DSOC comes from a 2 A1g excited state (+3.93 cm -1 ). The 4 E1g(1) state also contributes to DSOC (+1.10 cm - ). Each component of this state contributions to ESOC, but these contributions are of the same magnitude but opposite sign, leading to no net contributions.
The SORCI calculations predict many doublet states from ~13 500 -17 600 cm -
(Table 2). The energies for one set of 2 E1g states coincide remarkably well with the observed MCD features at 15 800 and 15 900 cm -1 , lending credence to the assignment of this feature as an excitation to a doublet state rather than the 4 E1g(I) state. In addition, the SORCI calculations predict the pair of 2 A states at 15 411 cm -
( 2 A1g) and 17 654 cm - ( 2 A1g). Overall, the high density of doublet excited states predicted by the SORCI calculations is consistent with the complexity of the MCD spectrum from ~15 000 -19 000 cm -1 (Figure 5, bottom) and is also consistent with the LFT analysis (Tables S3 and S4). The SORCI calculations predict the components of the 4 E1g(I) state at 23 090 and 23 116 cm - . These energies closely match the components of the MCD pseudo-A term (23 500 and 23 710 cm - ), which were determined through a Gaussian deconvolution (Table 2 and Figure S5). The deconvolution of our MCD data also revealed higher energy bands at 24 955, 26 530, and 27 460 cm - , assignments for which were uncertain. The SORCI results now allow us to assign the two lower-energy bands to the 4 E2g state, which is predicted at 24 966 cm - . The higher-energy MCD band corresponds well with the SORCI 4 E1g(II) state that is predicted to give components at 28 388 and 28 399 cm - (Table 2).
We performed CASSCF/NEVPT2 calculations using three active spaces: CAS(3,5), CAS (3,10), and CAS (7,7). Zero-field splitting values that we discuss always include the NEVPT2 corrections. The CAS(3,5) calculations include the Cr 3d manifold (three electrons and five orbitals) in the active space. The CAS (3,10) calculations expands on this initial active space to include five Cr 4d orbitals with no additional electrons. The expansion of the metal d-shell in this manner provides added flexibility to the NEVPT2 treatment. The CAS (7,7) active space expands the initial CAS (3,5) to include the bonding counterparts to the covalent Cr-based eg1
MOs (Figure 2), which adds four electrons and two orbitals. As summarized in Table S10, all calculations predict D values from ~5 to 6 cm -1 and E/D = 0, in excellent agreement with experiment. As differences in calculated values between the X-ray and C2h model are negligible (Table S10), we will focus on the results for the X-ray model. The calculated D values decrease in magnitude from CAS (3,5) to CAS (3,10) to CAS(7,7) (6.04 to 4.64 cm - ). The D value calculated for the CAS (3,5) calculations shows the poorest agreement with experiment (D = 6.04 cm - ), but even this value is only ~1.2 cm - larger than the experimental value. Thus, even with this minimally reasonable active space, the calculations perform quite well.
The CAS (7,7) calculations give D = +4.74 cm - (Tables 2 and S10), essentially ideal agreement with the experimental value, D = +4.82(1) cm - . Given the excellent agreement for this latter method (within 2%), we focus on the CAS (7,7) calculations when discussing the excited state energies and contributions to D and E. b Because we do not observe pseudo-A term for these states, the assignment of the components of these excited states are unclear. Nonetheless, the cluster of MCD features from 25 000 to 30 000 cm - is attributed to these excited states.
c AOM parameters given in Table S6 with the addition of SOC using = 180 cm - .
Metallocenes of general formula [MCp2] 0,+ are among the most iconic of organometallic species. Although chromocenium, [CrCp2] + , was first reported many years ago by E. O. Fischer in the "golden age of discovery" in metallocene chemistry, 10 relatively little attention has been paid to this Cr III species over the years. It is somewhat surprising that such an iconic Cr III complex should be underexplored, given the widespread use and investigation of organochromium(III) complexes in catalysis. [12][13][14][15][16][17][18][19] Work on our own V II and V III complexes, [89][90] led us to revisit [VCp2] [4][5] and thence to prepare [CrCp2] + using a "modern" counter anion, BAr F , 23 to afford [CrCp2][BAr F ], 1, and apply powerful spectroscopic techniques, HFEPR and MCD, to unravel the electronic structure of this S = 3/2 d 3 complex. The MCD spectra for this system are unexpectedly rich, displaying a remarkable set of vibronic progressions extending over 4 000 cm - .
We find that 1 is similar to [VCp2] -both are rigorously axial systems, but 1 is distinctly different from its neutral isoelectronic congener in terms of its larger ZFS -the D value of 1 is ~70% larger than that for [VCp2]. Computational studies using both classical LFT and state of the art QCT show the basis for this difference in terms of the stronger bonding, especially -bonding, in the Cr III cationic complex versus the neutral V II . LFT used crystal-field parameters as pioneered earlier, 57 but also the AOM, which is typically applied to "classical" coordination complexes with more localized bonds. Overall, it appears that the AOM is reasonably successful with respect to describing the electronic structure of both Cr III and V II metallocenes. The results of AOM calculations agree quite well with the CASSCF/NEVPT2 and SORCI calculations both in terms of the ZFS parameters and excited state energies (Table 2). The advantage of AOM is that the parameters are readily linked to metal-ligand bonding. In contrast, the CASSCF and SORCI results are in terms of multi-electron states, the analysis of which can be challenging to relate to discrete elements of bonding. Thus, our approach highlights the complementarity of combining cutting-edge electronic structure methods with traditional approaches. We are therefore inspired and hope others will be as well to apply this methodology to other such paramagnetic metallocene complexes.
The QCT studies show a more quantitative picture of the electronic structure the relative ordering of these orbitals does not change the situation, each MO having an unpaired electron giving the ground state of 4 A2g (in D5d). Information on their relative energies, however, is helpful in understanding [CrCp2] for which its S = 1 ground state could be either 3 A2g or 3 E2g, with the latter proposed many years ago. 3 The recent theoretical study on metallocenes did not explicitly address this question although they were able to calculate 1 H and 13 C NMR chemical shifts for [CrCp2] in good agreement with experiment. 31 The present CASSCF and SORCI calculations not only provide unambiguous support for the 4 A2g ground state of [CrCp2] + , they also aid in assigning its MCD spectra, which are complicated due to vibronic effects and the presence of many closely-spaced electronic excited states. Specifically, the coupled analysis of the MCD data with the SORCI and CASSCF calculations allowed us to partly reassign the spectral features of this complex from the original proposal. 57 Specifically, the excited states near 16 000 cm - , which correspond to sharp, weak MCD features, are now attributed to 2 E1g and 2 A1g states. Both the SORCI and CASSCF calculations predict these states near 16 000 cm - . The cluster of more intense MCD features at higher energies are attributed to spin-allowed electronic transitions to the quartet excited states. These excited states show a uniform shift to higher energy compared to those of [VCp2], which could be due to the increased covalency in
Also of interest is the ZFS in 1 which involves potentially many electronic excited states -quartet and doublet. QCT shows that only one of each is relevant.
Among the quartet excited states, only 4 E1g(I) matters, which essentially involves an electron promotion from the half-filled e2g
2 2 2 , xy xy dd - into the empty e1g orbitals. Among the many doublet excited states only a low lying 2 A1g( 2 G, 2 D) matters, which involves a spin-flip within the a1g 1 e2g 2 22 2 1 2 ,, xy z x y d d d - orbital occupancy and indeed has the greatest contribution to ZFS. The first process can be controlled in principle by changing the strength of -donation by the Cp R ligands (i.e., by electron donating or withdrawing Cp substituents) to increase or decrease the relative energy of the e1g orbitals. But we suspect that control of the second process, a spin flip, is difficult to achieve by ligand design, e.g., a stronger field metallocene such as Cp* as opposed to Cp. Larger SOC (i.e., as in the shift from V to Cr) might facilitate this process. We conclude that even these long known and seemingly simple [MCp2] 0,+ systems can still hold interest in questions of electronic structure and potentially in molecular magnetism applications. Experimental Details General procedures: Unless otherwise stated, all operations were performed in a M. Braun Lab Master double-dry box under an atmosphere of purified nitrogen or using high vacuum standard Schlenk techniques under a nitrogen atmosphere. Pentane, toluene, diethylether (Et2O), and dichloromethane were purchased from Fisher Scientific. Solvents were sparged with nitrogen for 20 minutes and dried using a two-column solvent purification system where columns designated for toluene and pentane, were packed with Q5 and alumina respectively. Columns designated for dichloromethane were packed with alumina and columns designated for benzene were packed with Q5. After drying solvents were stored over 4 Å molecular sieves. Deuterated benzene was purchased from Cambridge Isotope Laboratory (CIL). Deuterated benzene was degassed by freeze-pumpthaw cycles and stored over 4 Å molecular sieves. Celite and 4 Å molecular sieves were activated under vacuum overnight at 200 ºC. Compounds [FeCp2][BAr F ]
(BAr F = tetrakis[(3,5-trifluoromethyl)phenyl]borate) was prepared following a literature procedure, 32 but with use of Na[BAr F ] prepared by a more recent method. 23 Chromocene was purchased from Strem Chemicals and recrystallized from toluene prior to use. All other reagents were purchased from either Sigma-Aldrich and Strem Chemicals and used as received. 19 F NMR spectra were recorded on a Bruker 300 MHz NMR spectrometer. 19 F NMR spectra recorded in C6D6 are reported with respect to external CF3CO2H (-78.5 ppm). Elemental analysis was performed at Robertson Microlit Laboratories, Ledgewood, NJ. Crystallographic Details. A suitable crystal for analysis of 1 was mounted on the end of a Cryoloop coated in NVH oil and data collection was performed using a
Bruker APEXII CCD area detector employing Mo Kα radiation (graphite monochromator) at a temperature of 100 K. Rotation frames were integrated using SAINT, 91 producing a listing of unaveraged F 2 and σ(F 2 ) values which were then passed to the SHELXTL 92 program package for further processing and structure solution. The intensity data were corrected for Lorentz and polarization effects and for absorption using SADABS. 93 The structure was solved by direct methods using SHELXS-97. [94][95] Refinement was by full-matrix least-squares based on F 2 using SHELXL-97. [94][95] All reflections were used during refinements. Non-hydrogen atoms were refined anisotropically and hydrogen atoms were refined using a riding model.
EPR Spectroscopy. X-band EPR spectra of 1 were recorded on a modified Varian E-109 spectrometer at 77 K. EPR simulations for S = 1/2 used the program QPOW by Belford 96 (modified by J. Telser) and for S = 3/2 used the program SPIN by A.
Ozarowski, with a standard spin Hamiltonian for S = 3/2. 97 HFEPR Spectroscopy. HFEPR data were acquired at the EMR Facility of the NHMFL using a spectrometer previously described, 98 but modified by the use of low-frequency sources followed by a chain of amplifiers and frequency multipliers (VDI Inc., Charlottesville, VA), which operate in the frequency range of 50 -420 GHz.
MCD Spectroscopy. Magnetic circular dichroism (MCD) spectra were collected using a spectropolarimeter (Jasco J-815) interfaced with a magneto-optical cryostat (Oxford Instruments SM 4000-8). Data were collected for solid samples of [CrCp2][BAr F ] prepared as a mull in Fluorolube ® .
Computational Methods. Ligand Field Theory (LFT) calculations employed the locally written (J. Telser) 99 programs DDN and DDNFIT and the program Ligfield by J. Bendix. 100 All Quantum Chemical Theory (QCT) calculations were performed using ORCA 5.04. [101][102][103] Calculations were performed using the X-ray structure coordinates, with the positions of the hydrogen atoms optimized using density functional theory (DFT) methods. These calculations employed the BP functional [104][105] and def2-TZVP (Cr, C, and H) basis sets. [106][107] The resolution of the identity (RI) approximation was used to speed the calculations. 108 Orbitals were visualized using ChemCraft. 109 Electronic transition energies were calculated by the time-dependent (TD) DFT method [110][111] , the SORCI method, [86][87]112 and the CASSCF/NEVPT2 method. [113][114][115][116] The SORCI and CASSCF methods was also used to calculate ground-state spin Hamiltonian parameters. The CASSCF calculations used several active spaces, as described in the text. These calculations included 10 quartet roots and 40 doublet roots and def2-TZVP basis sets for all atoms, with the def2-TZVP/C and def2/J auxiliary basis sets used with the RIJCOSX approximation. The SORCI calculations used parameters previously described for [VCp2]. 4
A2g(e2g) 2 (a1g) 1 (e1g) 0 NA a 4 E1g (I) b (e2g) 2 (a1g) 0 (e1g) 1 a1g → e1g c