A Comprehensive Analysis of the Metal–Nitrile Bonding in an Organo-Diiron System

Nitriles (N≡CR) are ubiquitous in coordination chemistry, yet literature studies on metal–nitrile bonding based on a multi-technique approach are rare. We selected an easily-available di-organoiron framework, containing both π-acceptor (CO, aminocarbyne) and donor (Cp = η5−C5H5) ligands, as a suitable system to provide a comprehensive description of the iron–nitrile bond. Thus, the new nitrile (2–12)CF3SO3 and the related imine/amine complexes (8–9)CF3SO3 were synthesized in 58–83% yields from the respective tris-carbonyl precursors (1a–d)CF3SO3, using the TMNO strategy (TMNO = trimethylamine-N-oxide). The products were fully characterized by elemental analysis, IR (solution and solid state) and multinuclear NMR spectroscopy. In addition, the structures of (2)CF3SO3, (3)CF3SO3, (5)CF3SO3 and (11)CF3SO3 were ascertained by single crystal X-ray diffraction. Salient spectroscopic data of the nitrile complexes are coherent with the scale of electron-donor power of the R substituents; otherwise, this scale does not match the degree of Fe → N π-back-donation and the Fe–N bond energies, which were elucidated in (2–7)CF3SO3 by DFT calculations.

In principle, the metal-nitrile bond can be described in terms of four resonance structures (Scheme 1).
Structure A accounts for a purely electrostatic interaction: the metal attracts the nitrile electrons (both σ and π), thus strengthening the triple N≡C bond with a polarization toward the nitrogen (N ← C). Structure B represents the σ metal-nitrile bond, where the polarization is still N ← C (bond strengthening) because of the formal charge on the nitrogen. Structure C shows the back-donation of an electron pair from the metal to one π * orbital of the nitrile. In this case, the polarization is N → C and thus the N≡C bond is weakened. As two empty π * orbitals are available on the nitrile, the metal may back-donate an additional electron pair, leading to the limit structure D, wherein the N → C polarization and the carbon-nitrogen bond weakening reach their extreme. Scheme 1. Resonance structures contributing to a generic metal-nitrile bond.
In most literature cases, end-on nitriles have been regarded as essentially σ-donor ligands, with a possible secondary contribution to the bond with the metal arising from π-back-donation [1,24,25]. Pombeiro placed nitriles and phosphines approximately on the same level of a scale of net π-electron acceptor minus σ-donor character, based on electrochemical studies [26][27][28].
Casarin and co-workers estimated the π-backbonding in [PtCl 2 (NCR) 2 ] adducts as 30-40% of the total Pt-N bonding interaction, and pointed out the negligible effect of the R group; these authors concluded that ῦ N≡C values are not correlated with the strength of the nitrile bond [38]. Back-donation was investigated by DFT also on other metal-nitrile systems [27,[39][40][41].
In this scenario, a comprehensive description of metal-nitrile bonding, embracing crystallographic, spectroscopic and computational methods, is scarcely available. Our long experience with the chemistry of diiron µ-aminocarbyne complexes ( Figure 1, structure IV) [42][43][44] prompted us to exploit such a versatile and easily-accessible molecular framework to elucidate the iron-nitrile bonding picture [4]. With this purpose in mind, the considered system offers some advantageous features: (1) the effectiveness of the nitrile substituent is suggested by previous findings, according to which the N≡CR ligand undergoes addition by anionic nucleophiles [45][46][47], leading to different outcomes depending on R [46][47][48]; (2) the presence of two types of π-acceptor co-ligands, i.e., the carbonyls and one (variable) aminocarbyne, amplifies the possibility of evaluating the electronic influence of R; (3) in principle, the formal +I oxidation state of the iron centres might enable an appreciable iron to nitrile back-donation despite the net cationic charge of the complex.
Trends of experimental data from our multi-technique approach will be examined in detail; we will discuss their correlation with the electronic properties of the nitrile substituents and with the degree of π-back-donation and the Fe-N bond energies, which have been estimated by DFT in the distinct cases.

Synthesis of Diiron µ-Aminocarbyne Complexes with Nitrile-and Other Nitrogen-Ligands
The triflate salt [Fe 2 Cp 2 (CO) 2 (µ-CO){µ-CN(Me)(Cy)}]CF 3 SO 3 ((1a)CF 3 SO 3 ) [43] was selected as a starting material, bearing in mind that two aminocarbyne substituents of considerably different size (i.e., methyl and Cy = cyclohexyl) could supply information about steric factors related to nitrile coordination. More precisely, the aminocarbyne group possesses some iminium character, whereby the rotation around the carbyne-nitrogen bond is inhibited at room temperature; therefore, the replacement of one CO with a nitrile ligand may result in the formation of two isomers with a ratio depending on the relative hindrance of nitrile and Y (Figure 2), vide infra. The novel complexes (2-7)CF 3 SO 3 were prepared from the reactions of (1a)CF 3 SO 3 with the appropriate nitrile reactant, in the presence of a slight excess of Me 3 NO·2H 2 O (Scheme 2). The products were purified by alumina chromatography and finally isolated as air-stable solids in 69-83% yields. By using a similar procedure, the new complexes (8)CF 3 SO 3 and (9)CF 3 SO 3 , containing respectively an imine and an amine as monodentate N-donor ligands, were also synthesized for comparative purposes (58-62% yields, Scheme 2). Moreover, in order to evaluate the possible effect of the aminocarbyne substituents on iron-nitrile bonding, complexes (10-12)CF 3 SO 3 were obtained from the respective tris-carbonyl precursors, (1b-d)CF 3 SO 3 , in 64-77% yields (Scheme 3). Isomerism in asymmetric diiron µ-aminocarbyne complexes (Cp rings in cis or trans position). Y = CH 2 Ph or 2,6-C 6 H 3 Me 2 . X = Ph, alkyl, dithiocarbamate, halide/pseudohalide (neutral complexes); X = nitrile, isocyanide, phosphine, imine, carbene (cationic complexes). When X = nitrile, α and β correspond to E and Z isomers, respectively. Scheme 2. Carbonyl-substitution reactions on a (N-methyl, N-cyclohexyl)aminocarbyne diiron complex (CF 3 SO 3 − salts).

Analysis of IR Spectra
IR spectra were recorded both in dichloromethane solution and in the solid state. They share a common pattern consisting of three main absorptions in the 2300-1500 cm −1 region, ascribable to the terminal and bridging carbonyls and the carbyne-nitrogen bond; isomers (see Section 3) are not distinguishable. Data indicate that the µ-(C-N) bond possesses some double bond character (iminium character), as usually found in related compounds (Scheme 4) [42,51,52]. The nature of the nitrile has negligible influence on the CO, µ-CO and µ-CN stretching vibrations which, for compounds (2-7)CF 3 SO 3 , fall within the narrow intervals 1982-1985, 1818-1821 and 1559-1561 cm −1 , respectively (in CH 2 Cl 2 ). Complexes (8,9)CF 3 SO 3 display significantly lower values for the CO wavenumbers, thus pointing out the stronger electron-donor power of ethylamine and, to a less extent, benzophenone imine with respect to the investigated nitriles. The relatively high electron donation supplied by NH 2 Et also enhances the metal-to-carbyne back-donation (Scheme 4, resonance structures R1 and R2) with consequent weakening of the µ-C-N bond (ῦ = 1532 cm −1 ). The nitrile N≡C stretching gives rise to a weak absorption in the 2230-2280 cm −1 region.

Analysis of NMR Spectra
As expected, the NMR spectra of (2-12)CF 3 SO 3 reveal the existence in solution of E-Z isomers, with reference to the different orientations assumed by the aminocarbyne (iminium) substituents with respect to the terminal CO and L ligands. This kind of isomerism was previously recognized in many other diiron aminocarbyne complexes of general formula [Fe 2 Cp 2 (CO)(X)(µ-CO){µ-CN(Me)(Y)}] 0/+ (X = anionic or neutral ligand = CO; Y = Me), and isomers were generally named α and β ( Figure 2); in most cases, Y and X are bulkier than Me and CO, respectively, therefore the α form is expected to be favoured over the β one for steric reasons [42,45,53,54].
Based on cross-comparison with the NMR data from a library of compounds, (2-12) + exhibit cis geometry of the Cp rings, and the E (α) isomer (Y and L placed on opposite sides) is prevalent in (2) + and (3) + , and slightly prevalent in (4) + , (5) + , (6) + , (8) + and (9) + . On the other hand, the Z (β) isomer is major in (11) + , and slightly prevalent in (12) + . Looking at the ratios reported in Table 1, it is presumable that additional factors, other than the steric hindrance of Y and X, somehow contribute to the relative amount of E and Z isomers in the solution. The NMR spectra of (10) + consist of four sets of resonances, arising from E-Z isomerism and, in addition, conformational isomerism resulting in two possible frozen orientations for the aryl substituents (Cl and Me) with respect to the Fe-Fe axis [55].
The increase of the 13 C chemical shift affecting the nitrile carbon upon coordination (∆δ, see Table 1) agrees with the tendency of the nitrile to donate charge to the metal (R = 4-C 6 H 4 NO 2 < 4-C 6 H 4 F < Ph < 4-C 6 H 4 NMe 2 < t Bu) and is almost identical for E and Z pairs. Coherently, ∆δ slightly increases upon replacing the cyclohexyl on the aminocarbyne with a more electron-withdrawing group in the acetonitrile adducts (2) + (Y = Cy) and (12) + (Y = 4-C 6 H 4 OMe); charge donation from the NCMe ligand to the iron was enhanced in (12) + compared to (2) + . In this framework, it is not surprising that, for aromatic substituents (complexes 4, 5, 6 and 7), δ(N≡C) correlates quite well with the Hammett parameter σ p .
The influence of the nitrile substituent on the 13 C NMR resonances of the carbonyl ligands is not appreciable within the series of complexes (2-7)CF 3 SO 3 (δ for terminal and bridging CO ligands occur in the ranges 212.3-213.6 ppm and 265.2-266.7 ppm, respectively). Otherwise, the collected 13 C data for the carbyne carbon permit a correlation with the electronic properties of the nitriles. In general, in diiron aminocarbyne complexes, the aminocarbyne centre resonates in the 305-390 ppm interval, and its chemical shift increases on increasing the [FeFe] to carbyne back-donation, which is enhanced by the electron withdrawing power of the N-substituents [56]. Here, this tendency is verifiable in the series of acetonitrile complexes (2Z) + , (11Z) + and (12Z) + [δ = 330.2 (Y = Cy), 333.4 (Y = allyl), 338.1 (Y = 4-C 6 H 4 OMe)]. Accordingly, within (2-7) + , the lowest value of carbyne chemical shift has been detected for (6) + (R = 4-C 6 H 4 NO 2 , δ = 329.0-329.2 ppm), corresponding to the minimum nitrile-to-iron donated charge (see also C TOT in Table 4), thus resulting in less back-donation to the aminocarbyne {CNMe(Cy)}. In summary, the strongly π-acceptor bridging aminocarbyne moiety, rather than the carbonyl ligands, is sensitive to the nitrile substituent R, and the chemical shift of the former is informative about the electronic behaviour of the latter.

X-ray Diffraction Studies
The molecular structures of (2Z)CF 3
In summary, the X-ray structures of homologous diiron aminocarbyne complexes and an overview of relevant literature data suggest that both the nitrile substituent and the coordination environment around the iron centre may influence iron-nitrile bonding. This feature is noticeable by looking at the Fe-N bond distance values, whereas the N≡C distance is almost unvaried in the different cases.
To gain information about iron-nitrile bonding, [M1] + was split into two fragments, i.e., [Fe 2 Cp 2 (CO) 2 (CNMe 2 )] + and NCMe. According to energy decomposition analysis (EDA), the dissociation energy BDE is −46.1 kcal/mol, which is the sum of the interaction energy E int (−48.9 kcal/mol) and the deformation energy (+2.8 kcal/mol). E int can be further divided into steric (sum of the Pauli and the electrostatic term, E st , 19.3 kcal/mol), dispersion (E disp , −8.6 kcal/mol) and orbital (E orb , −59.6 kcal/mol) contributions. The latter is composed of four terms (ETS-NOCV analysis), namely ∆ρ k (k = 0-3, Figure 4). ∆ρ 0 is the most relevant one (∆E 0 = −33.2 kcal/mol) and, given the position and the local symmetry of the accumulation/depletion regions (blue/red coloured in Figure 4), it is associated with Fe ← N σ donation, accompanied by N ← C polarization of the N≡C bond (see Scheme 1). Notably, accumulation regions are present also on the other iron atom and on the bridging carbonyl ligand. ∆ρ 1 is still relevant (∆E 1 = −11.1 kcal/mol) and can be associated with a Fe → N π back-donation; in this regard, the polarization of the triple bond is N → C. ∆ρ 2 is slightly weaker than ∆ρ 1 (∆E 2 = −9.6 kcal/mol) and is related to Fe → N π back-donation on a plane perpendicular to that for ∆ρ 1 . The sum of the two back-donation contributions (20.7 kcal/mol) represents 34.7% of the total orbital interaction. Finally, ∆ρ 3 appears to be a simple N ← C polarization of the nitrile, likely due to the electrostatic attraction between the metal and the σ electrons on the ligand. Contributions from k > 3 are negligible, with an associated ∆E k < 0.6 kcal/mol. For a more detailed analysis, the different ∆ρ k functions can be integrated along the Fe-N axis (charge displacement (CD) analysis), affording the CD k functions shown in Figure 5. Each of them quantifies, at each point of the space, the number of electrons involved in the electronic rearrangement due to the Fe-N bond formation. In CD k functions, positive and negative values correspond to a charge flux from right to left and left to right, respectively. Indeed, the integration of ∆ρ 0 leads to CD 0 , which is always positive and describes a displacement of electrons from the ligand to the metallic fragment (σ donation). Between the two fragments (isoboundary), such a displacement is equal to CT 0 = 0.167 e, whereas at the middle of the triple bond it is CT CN,0 = 0.046 e, in accordance with the structures A and B in Scheme 1, and limited to σ electrons. Indeed, there is not one-to-one correspondence between CD k curves and the resonance structures shown in Scheme 1, but each CD k can be seen as a combination of more resonance structures.
The integration of ∆ρ 1 and ∆ρ 2 leads to CD 1 and CD 2 , respectively, which display a more complex shape. At the isoboundary, CT 1 and CT 2 are −0.102 and −0.043 e, thus indicating a remarkable Fe → N back-donation. The total is CT π tot = −0.145 e, which is only slightly smaller than CT 0 (0.167 e). Note that both CD 1 and CD 2 are positive at the nitrile bond, since the N ← C polarization prevails (CT CN,1 = 0.018, CT CN,2 = 0.047 e). Being back-donation and polarization opposite in sign, there is a point where the sum of the two functions is null, generally around the z coordinate of the N atom. Therefore, despite the large back-donation, the N≡C bond is reinforced (∆ῦ > 0), as the polarization of the π electrons due to structures A and B (Scheme 1) is more than that due to back-donation (structures C and D).
Note that, in terms of displaced electrons, the back-donation is almost equivalent to the donation, (CT 1 + CT 2 )/CT 0 = 0.86, whereas in terms of energy the ratio is lower, (∆E 1 + ∆E 2 )/∆E 0 = 0.62. This depends on the fact that the energy contributions are related to the whole molecule, including all the polarization regions that could be indirectly related to the iron-nitrile bond, whereas CD functions are calculated at a specific point of the molecule (in this case at the boundary between the two fragments [Fe 2 Cp 2 (CO) 2 (CNMe 2 )] + and NCMe, see Computational Details).
Finally, ∆ρ 3 can also be integrated, leading to CD 3 . The latter is negligible in the organometallic region, and slightly positive within the N≡C bond. As pointed out before, this is a small, additional polarization of the N≡C bond (0.012 e) upon coordination to the iron. The latter contribution is coherent with structure A in Scheme 1. The total polarization of the triple bond is CT CN = 0.121 e. The sum of all components between the iron and the nitrogen is CT tot = 0.034 e.
The polarization is remarkable even in the region of the methyl group (∆q = 0.036 e, at the carbon, and 0.017 e, at the hydrogen atoms). The electronic polarization of the methyl group is in alignment with the marked acidity manifested by the acetonitrile ligand in diiron aminocarbyne complexes, 21a as well as in other organometallic systems [68,69]. We extended the computational analysis to the terminal {Fe-CO} bond within (M1) + ( Figure S48) and we found that the interaction energy is much stronger for {Fe-CO} than {Fe-NCMe} (E int = −65.7 kcal/mol vs. −45.4 kcal/mol). In addition, for {Fe-CO}, the orbital contribution of back-donation (E 1 + E 2 = −56.1 kcal/mol) is even larger than the orbital contribution of the donation (E 0 = −49.2 kcal/mol), while the contrary occurs for {Fe-NCMe} (E 1 + E 2 = −20.7 kcal/mol, E 0 = −33.2 kcal/mol).
The same framework as that described for the model adduct (M1) + retains its validity in the nitrile complexes (2-7) + , with numerical differences depending on the nitrile (R) and aminocarbyne (Y), substituents which are detailed in Table 4. A view of the DFT-optimized structures of (2-7) + is provided as Supplementary Materials (Figure S49). Table 4. Calculated infrared wavenumber shift (∆ῦ, in cm −1 ) upon coordination of nitriles to diiron complexes, bond dissociation energy (BDE, in kcal/mol), orbital contributions (∆E k , in kcal/mol) and charge transfer (CT k ) values (in electrons). k = 0 is related to σ donation, k = 1 and 2 are related to π back-donation. CT tot is the net charge transfer; CT π tot = CT 1 + CT 2 . As the crystal structure of [2Z]CF 3 SO 3 is available (Figure 3), we applied the NOCV-CD analysis to both the experimental geometry without further optimization ((2Z exp ) + ) and the optimized geometry ((2Z) + ), to evaluate the influence of crystal lattice on the Fe-N bond (Table 4). Indeed, there is a difference in the experimental and computed bond lengths, as the Fe-N and N-C distances measure 1.924(5) and 1.126(7) Å in the crystal structure and 1.865 and 1.163 Å in the optimized geometry, respectively. Such a difference is reflected on the bonds in (2Z exp ) + and (2Z) + : in the former, both σ and π contributions are smaller than in the latter, in absolute value, in terms of energy and electrons. This is likely due to the longer Fe-N distance in (2Z exp ) + , as all the bonding contributions decrease as distance increases.
In the presence of significantly π-acidic substituents on the nitrile, the polarization may be inverted (N → C), leading to negative ∆ῦ values. Therefore, it has to be remarked that a positive value of ∆ῦ is not an index of absence of back-donation, in analogy to what previously demonstrated for carbonyl complexes, 41 and advising caution in the interpretation of the metal-nitrile bonding based on infrared data only [1,10,12,70,71].
The computed ∆ῦ values in Table 4 correlate well with the relevant bond contributions, the correlation factors varying from 0.89 (with CT π tot and CT CN,tot ) to 0.97 (with CT tot , see Figure 6). It can be concluded that the Fe → N≡CR back-donation is important and tunable, and appreciably influences the IR vibration of the N≡C bond. Similarly, it was proposed for carbonyl complexes that the experimental infrared stretching wavenumber is proportional to the degree of metal to CO π-back-donation and, more precisely, to the polarization of the π electrons on the carbon-oxygen bond [72][73][74].  Table 4). Correlation factors are r 2 = 0.89 for CT π tot , 0.90 for CT π CN , 0.89 for CT CN,tot and 0.97 for CT tot .

Conclusions
Nitriles (N≡CR) have been largely employed in coordination chemistry and, despite being regarded in several cases as relatively weak ligands, the occurrence of metal to nitrile π-back-donation has been proposed. To support this view, experimental and theoretical proofs have been supplied with reference to diverse metal systems, but a comprehensive crystallographic, spectroscopic and computational approach is rare in the literature. Here, we have exploited an easily accessible di-organoiron scaffold to explore the bonding between one iron centre and a range of nitriles, using X-ray, IR, NMR and DFT methods.
Computational results outlined that the relative contribution of Fe → N π-backdonation is normally strong but only marginally dependent on the nature of the nitrile. A comparative view of X-ray structures, extended to additional literature iron compounds, highlighted that different nitrile substituents (R) may affect the Fe-N bond distance but not the N≡C one. More finely, the shifts of infrared stretching vibration (∆ῦ) and 13 C NMR resonance (∆δ) related to the nitrile function upon coordination to the metal rigorously correlate with the electronic properties of R. Besides, DFT studies clarify that a positive value of ∆ῦ is not evidence for a lack of back-donation, as sometimes misconceived in the literature; a parallelism emerges between metal-nitrile and metal-carbonyl bonds, in terms of the relationship between IR stretching vibration and ligand polarization, with the necessary distinctions in terms of donation/back-donation ratio. Note that IR and NMR data clearly demonstrate an interplay between the nitrile ligand and the strongly π-acceptor bridging aminocarbyne ligand. Overall, the established scales of ∆ῦ, ∆δ and 13 C NMR carbyne resonance values are indicators of the electronic behaviour of R holding a predictive potential in such regard. Nevertheless, the degree of back-donation is not strictly correlated with the electron withdrawing power of R; furthermore, increasing the backdonation does not seem a guarantee of strengthening the iron-nitrile bond. DFT outcomes, partially supported here by experimental X-ray analysis, indicate N≡C(4-C 6 H 4 NMe 2 ) as a convenient choice for a nitrile ligand pointing to a relatively stable metal coordination.

Materials and Methods
Reactants and solvents were obtained from Alfa Aesar, Merck, Strem and TCI Chemicals and were of the highest purity available. Complexes (1a,c,d)CF 3 SO 3 [43] and (1b)CF 3 SO 3 [27] were prepared according to the literature. Once isolated, all the products were stored under N 2 , or under air, for limited periods of time (<3 days). Synthetic procedures were conducted under N 2 atmosphere using standard Schlenk techniques. CH 2 Cl 2 and THF were dried with the solvent purification system mBraun MB SPS5, while MeCN was distilled from CaH 2 . Chromatography separations were carried out on columns of deactivated alumina (Merck, 4% w/w water). IR spectra of solutions were recorded using a CaF 2 liquid transmission cell (2300-1500 cm −1 ) on a Perkin Elmer Spectrum 100 FT-IR spectrometer. IR spectra of solid samples (650-4000 cm −1 ) and liquid nitriles (acetonitrile and trimethylacetonitrile [49]) were recorded on a Perkin Elmer Spectrum One FT-IR spectrometer, equipped with a UATR sampling accessory. IR spectra were processed with Spectragryph software [75]. NMR spectra were recorded at 298 K on a Bruker Avance II DRX400 instrument equipped with a BBFO broadband probe. Chemical shifts (expressed in parts per million) are referenced to the residual solvent peaks [76] or to external standard ( 19 F, CFCl 3 ). NMR spectra were assigned with the assistance of 1 H-13 C (gs-HSQC and gs-HMBC) correlation experiments [77]. NMR signals due to secondary isomeric forms (where it has been possible to detect them) are italicized. Figures 7-17 show the prevalent isomer detected by NMR for each case. Elemental analyses were performed on a Vario MICRO cube instrument (Elementar). In a 25 mL Schleck tube, a mixture of (1a)CF 3 SO 3 (233 mg, 0.389 mmol), Me 3 NO·2H 2 O (48 mg, 0.43 mmol) and MeCN (5 mL) was stirred for 2 h at room temperature. Afterwards, volatiles were evaporated under vacuum; the solid residue was dissolved in CH 2 Cl 2 and the solution charged on an alumina column. Elution with THF allowed to separate impurities, then the fraction corresponding to the title compound was eluted using neat MeCN. Solvent was removed under reduced pressure and the residue was suspended in Et 2 O (50 mL) for 2 h. The brown powder was recovered by filtration and dried under vacuum. The yield was 180 mg (76%); soluble in MeCN, CH 2 Cl 2 , acetone; insoluble in Et 2 O; X-ray quality crystals of (2)CF 3

General Procedure for the Synthesis of (3-10)CF 3 SO 3
In a Schlenk tube, the starting complex ((1a)CF 3 SO 3 or (1b)CF 3 SO 3 ) and Me 3 NO·2H 2 O (1.1 eq.) were dissolved in THF (7 mL); then, the appropriate organic reactant (ca. 3.5 eq.) was added. The mixture was stirred for 2 h at room temperature, and then charged on an alumina column. Elution with CH 2 Cl 2 and with CH 2 Cl 2 /THF mixture (2:1 v/v) allowed the separation of impurities, then the fraction corresponding to the product was collected using THF/MeOH mixture (10:1 v/v). Volatiles were evaporated under reduced pressure, and the residue was suspended in Et 2 O (15 mL) for 2 h. The obtained powder was recovered by filtration and dried under vacuum.

X-ray Crystallography
Crystal data and collection details for (2)CF 3 SO 3 , (3)CF 3 SO 3 , (5)CF 3 SO 3 and (11)CF 3 SO 3 are reported in Table 5. Data were recorded on a Bruker APEX II diffractometer equipped with a PHOTON2 detector using Mo-Kα radiation. The structures were solved by direct methods and refined by full-matrix least-squares based on all data using F 2 [78]. Hydrogen atoms were fixed at calculated positions and refined using a riding model. All non-hydrogen atoms were refined with anisotropic displacement parameters. The crystals of (2)CF 3 SO 3 appeared to be non-merohedrally twinned. The TwinRotMat routine of PLA-TON [79] was used to determine the twinning matrix and to write the reflection data file (.hkl) containing the twin components. Refinement was performed using the instruction HKLF 5 in SHELXL and one BASF parameter, which refined as 0.262(3).

DFT Calculations
All geometries were optimized with ORCA 4.0.1.2 [80], using the BP86 functional in conjunction with a triple-ζ quality basis set (def2-TZVP). The dispersion corrections were introduced using the Grimme D3-parametrized correction and the Becke Johnson damping to the DFT energy [81]. Relativistic effects were treated with the scalar zeroth-order regular approximation (ZORA) [82,83], in conjunction with SARC/J auxiliary basis sets. Most of the structures were confirmed to be local energy minima (no imaginary frequencies), but in some cases a small, unavoidable negative frequency relative to the Cp rotation around the M-Cp axis was observed.
Energy Decomposition Analysis [84]. The EDA has been performed using ORCA 4.1.0. The EDA allows the decomposition of the bond energy into physically meaningful contributions. The interaction energy (E int ) is the difference of the energy between the adduct and the unrelaxed fragments. It can be divided into contributions associated with the orbital, steric, and dispersion interactions, as shown in Equation (1).
E st is usually called the steric interaction energy and it is the sum of E elst , the classical electrostatic interaction between the unperturbed charge distributions of the fragments (ρ A and ρ B ) at their final positions in the adduct, and the Pauli repulsion (E Pauli ), that is the energy change associated with going from ρ A + ρ B to the antisymmetrized and renormalized wave function. The decomposition of E st is not possible with ORCA 4.1.0, and it comprises the destabilizing interactions between the occupied orbitals; and, it is responsible for any steric repulsion. E orb is the contribution arising from allowing the wave function to relax to the fully converged one, accounting for electron pair bonding, charge transfer and polarization, while E disp is the contribution of the dispersion forces. [85,86]. In the NOCV approach, the electron density rearrangement that takes place upon formation of AB from fragments A and B is defined with respect to a reference system made up of the occupied ψ i A and ψ i B orbitals of A and B orthonormalized with respect to each other (ψ i 0 ). In other words, rather than two separate A and B determinants, their antisymmetrized product is taken as the fragment−fragment noninteracting reference (the so-called "promolecule"). The resulting electron density rearrangement in Equation (2),

Extended Transition State-Natural Orbital for Chemical Valence theory (ETS--NOCV) and Charge Displacement Function Analysis
where ψ i AB is the set of occupied orbitals of the adduct, can be brought into a diagonal form in terms of NOCVs.
These are defined as the eigenfunctions, φ ±k , of the so-called "valence operator" Equation (3) [87][88][89] The NOCVs can be grouped in pairs of complementary orbitals (φ k , φ −k ) corresponding to eigenvalues with the same absolute value but the opposite sign (Equation (4)).
Hence, on formation of AB from the promolecule, a fraction ν k of electrons is transferred from the φ −k to the φ k orbital. Only some NOCV pairs have ν k significantly different from zero, and this subgroup is generally enough to describe the A· · · B interaction. For each value of k, an energy contribution associated with the k-th NOCV pair is given (E k ).
The charge displacement function analysis [90,91] is based on Equation (6) on the relevant ∆ρ' k functions. The function ∆q(z') defines, at each point along a chosen axis, the amount of electron charge that, upon formation of the bond between the fragments, moves across a plane perpendicular to the axis through the point z'. A positive (negative) value corresponds to electrons flowing in the direction of decreasing (increasing) z. Charge accumulates where the slope of ∆q is positive and decreases where it is negative.
To extract a CT value from the ∆q curve, it is useful to fix a plausible boundary separating the fragments in the adducts (isoboundary). Unless otherwise specified, we chose the point on the z axis at which equal-valued isodensity surfaces of the isolated fragments are tangent. At this point, the value of ∆q k is represented by CT k .