Experimental and DFT study of 2-ferrocenylpropan-2-ol cyclodimerization products

1,1′-(1-Ferrocenyl-1,3,3-trimethylpropane-1,3-diyl)ferrocene and 1,2-(1-ferrocenyl-1,3,3-trimethylpropane-1,3-diyl)ferrocene are formed as cyclodimeric products during the synthesis of  -ferrocenyl carbinols, in relative ratios which depend on the reaction conditions. Their ratios and stabilities are examined, and calculated at the BP86 level of theory and several different isomers of the homoannular product were examined by DFT calculations.


Introduction
Ferrocenyl alcohols are very useful synthetic intermediates in the synthesis of many biologically active compounds, industrially important compounds, as ligands in homogenous catalysis, in material science (e.g. in nonlinear optics) and in bio-organometallic chemistry as redox-active probes or candidates for drugs. 1,2In a previous paper 3 we studied the nucleophilic substitution of diethyl malonate with ω-ferrocenylalkanols, derived carbinyl acetates, bromides and quaternary salts to -ferrocenylalkylmalonates.These substrates can easily be reduced into the prochiral 2-(ω-ferrocenylalkyl)propane-1,3-diols.Furthermore, we examined the enzymatic esterification of these prochiral diols in order to determine a degree of desymmetrization depending on the length of the side chain, i.e., the distance between the ferrocene moiety and stereogenic center. 4The compound 4, 1,2-(1-ferrocenyl-1,3,3-trimethylpropane-1,3-diyl)ferrocene, was prepared as a part of our research on bio-catalyzed acylations of secondary -ferrocenylalkanols.
It was shown earlier that secondary ferrocenyl carbinols can be dehydrated to give the corresponding vinyl-ferrocenes which under mild conditions undergo dimerization resulting in linear olefinic products.For example, treatment of 1-ferrocenylethanol with acid-washed alumina in refluxing benzene produces 1,3-diferrocenyl-1-butene. 5 If the analogous dehydration of secondary ferrocenyl carbinol is performed in more acidic medium (i.e.40% H2SO4 or 90% HCOOH) no linear dimeric product is obtained; only cyclodimers are formed resulting from homoannular or heteroannular cyclodimerization. 6In this work we show that in the case of tertiary ferrocenyl carbinols the only products of acid catalyzed dehydration are cyclodimers.No linear dimeric product has been observed, in either weak or strong acid medium, and the only operative mechanisms are homo-and heteroannular cyclodimerization.

X-Ray crystal structure analysis
In order to confirm the rearrangement we proposed, and to determine the exact structure of the dimeric products 3 and 4 we tried to obtain single crystals for X-ray crystal structure analysis.Unfortunately, we succeeded in obtaining only a single crystal of compound 4 7 (Figure 1).Neither crystallographic nor spectroscopic data ( 13 C-NMR; see below) are known for 3.
The five-membered ring (C-1/C-2/C-21/C-22/C-23) of 4 is fused to the ferrocene cyclopentadienyl (Cp) ring via common carbon atoms C-1 and C-2.Also, a monosubstituted ferrocenyl moiety, which is oriented in an exo-position with respect to the 1,2-disubstituted Cp ring, is linked to the five-membered ring.The five-membered ring adopts an envelope conformation, with the C-22 atom displaced above the mean plane of the other ring atoms by 0.352(4) Å.

Computational results
At the BP86/AE1 level of theory only one isomer of 3 can be located as stable minima for the product of heteroannular cyclodimerization (Figure 3).The two cyclopentadienyl rings in both ferrocenyl moieties of 3 are eclipsed with respect to each other.We have performed optimization with the starting geometry in which relative conformations of corresponding Cp rings are staggered.However, during geometry optimization, using either BP86 or B3LYP method, staggered conformations converged back to eclipsed ones (Cp ring rotation occurs during optimization procedure).In the case of the homoannular cyclodimerization product 4 three different rotational isomers, with respect to the rotation about the C-11-C-21 bond (atom numbering defined in Figure 1), can be located as stable minima, namely, 4a, 4b, and 4c (Scheme 2).In 4a, which is similar to the structure that have been characterized by X-ray crystallography, both the disubstituted ferrocenyl moiety and C-21-methyl group are oriented in an endo-position, i.e., the position below the cyclopentadienyl ring of the mono-substituted ferrocene, whereas structures 4b and 4c are characterized by exo-position of the disubstituted ferrocenyl moiety and exoposition of the C-21-methyl group, respectively.

Scheme 2
These three BP86-optimized conformers span a range of ca. 3 kcal/mol.The most stable isomer in the gas phase was found to be 4a which correspond to the crystal structure (optimized at the BP86/AE1 level).It is calculated to be 1.8 and 2.9 kcal/mol more stable than rotamers 4b and 4c, respectively.If the model solvent (chloroform,  = 4.7) is implicitly included by using PCM-BP86 calculations, the isomer 4a becomes even more stable than 4b or 4c (Table 1).Both results from the gas phase and from solvent model calculations are consistent with experimental data, i.e. the most stable structure is 4a which corresponds to geometry obtained from X-ray analysis.
Transition state structures TS4a4b, TS4a4c, and TS4b4c connecting these three minima have been located and each has been characterized by one imaginary frequency which corresponds to the rotation around C11-C-21 bond (see Supplementary Material).All calculated energy barriers separating these three different rotamers are below 4 kcal/mol (Table 1) suggesting fast interconversions between rotamers in equilibrium.However, on the basis of the relative energy differences between the conformers 4a, 4b and 4c, one can estimate that relative populations of 4b and 4c in the equilibrium mixture are relatively small.All three isomers of homoannular cyclodimerization product 4 are more stable than the main heteroannular cyclodimerization product 3.As expected, the energy barrier for rearrangement of carbocation intermediates, which are involved in formation of 3, is lower than the corresponding barrier for carbocation rearrangements leading to 4 6 .
The similar calculated geometries of 3, 4a, 4b, and 4c, and the same relative energies were calculated at the B3LYP/AE1 level of theory.These results are in agreement with earlier findings that the efficiency of the BP86 method and comparable DFT levels have proven quite successful for transition-metal compounds and are well suited for the description of structures, energies, vibrational frequencies, and other properties 8 .Table 2. 13 C-and 57 Fe-NMR chemical shifts (in ppm) for 3 and rotamers 4a, 4b, and 4c calculated at the GIAO-B3LYP level (using BP86 geometries) C-NMR and 57 Fe-chemical shifts for 3 and three conformers 4a, 4b, and 4c (Table 2) have been calculated at the B3LYP level (using BP86 optimized geometries).Only the calculated 13 C-NMR chemical shift values of ferrocenyl moieties were considered for comparison with experimental results.Comparison between experimental and calculated data allow correct assignment for ipso-carbons (C-2, C-6, and C-11 in 3; C-1, C-2, and C-11 in 4), but also for C-3, C-4 and C-5 atoms in 4. Due to relatively small difference of 13 C-NMR chemical shifts calculated for different structures, it is difficult to predict which rotamer of 4 is the most abundant in the equilibrium.As the time scale of the NMR spectroscopy is not sufficiently fast for detection of individual constituents of an equilibrium mixture, the rotamers 4a, 4b and 4c cannot be resolved neither by experimental NMR method (only averaged 13 C-signal can be obtained) unless separated by large barriers (see above).However, relatively large range of 57 Fe NMR chemical shifts (from 96.2 to 424.0 ppm) is calculated for different rotamers 4a, 4b and 4c, suggesting that 57 Fe-NMR could be a sensitive tool to probe the preferred structure in the equilibrium.
Thus, a new isomer 4e having both ferrocenyl moieties with eclipsed conformation is located.At the BP86 level it is calculated only 0.1 kcal/mol less stable than 4a in the gas phase, but in the model solvent it is for 2.0 kcal/mol less stable (Table 1).We have calculated the transition state structure 4ts for the rotation of the Cp ring in the mono-substituted ferrocenyl moiety.It is characterized by one imaginary frequency of 45i cm -1 (28i cm -1 at B3LYP/AE1 level) which corresponds to the Cp ring rotation.These results are in accord with the low barrier for rotation (ca. 1 kcal/mol at the BP86 level) calculated for ferrocene itself. 9Finally, we have tried several starting geometries with different cyclopentyl moiety conformation, but all these starting structures converged back to cyclopentyl ring conformation as characterized by X-ray crystallography.

Scheme 3
In conclusion, it is shown that at least three different geometries are to be considered in order to fully describe structural properties of the product 4.Both B3LYP and BP86 density functional models are capable to reproduce experimental results.The crystal structure obtained by X-ray is supported by quantum-chemical methods which calculated the corresponding rotamer 4a as the most stable conformer, possibly in solution as well.The experimental 13 C-NMR chemical shifts for 3 and 4 (equilibrium mixture of 4a, 4b, and 4c) obtained in CDCl3 are reproduced by GIAO-B3LYP approach. 57Fe NMR experimental data are needed in order to distinguish three different rotamers of 4.

Experimental Section
General.2-Ferrocenylpropan-2-ol 1 was obtained according to the literature procedure. 5,6roducts were purified by preparative thin layer chromatography on silica gel (Merck, Kieselgel 60 HF254) using the mixture CH2Cl2/EtOAc.Melting point was determined with a Buechi apparatus.An IR spectrum was recorded as CH2Cl2 solution with a Bomem MB 100 mid FT-IR spectrophotometer. 1 H-and 13 C-{ 1 H}-NMR spectra was recorded on a Varian Gemini 300 spectrometer in CDCl3 solution with Me4Si as internal standard.

X-Ray determination of 4
Single crystal of 4 suitable for X-ray single crystal analysis was obtained at room temperature by partial evaporation from a mixture of dichloromethane, methanol and n-hexane (1:1:1).The orange prismatic crystal with dimensions 0.326 x 0.428 x 0.534 mm 3 was selected for X-ray structure analysis.The intensities were collected at 295 K on a Oxford Diffraction Xcalibur2 diffractometer using graphite-monochromated MoK radiation ( = 0.71073 Å) and -scan mode.The data collection and reduction were carried out with the CrysAlis 10 programs.The intensities were corrected for Lorentz and polarization effects and for absorption using the multiscan absorption correction method (CrysAlis RED 10 ).The crystal structure was solved by direct methods.All non-hydrogen atoms were refined anisotropically by full-matrix least-squares calculations based on F 2 .All hydrogen atoms were treated using appropriate riding models.For structure solution, refinement and analysis were used the following programs: SHELXS97, 11 SHELXL97 12 and PLATON. 13The molecular structure drawing was prepared by the PLATON 13 program.CCDC 764215 contains the supplementary crystallographic data for this Paper.These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. Crystal data: C26H28Fe2, M r = 452.

Computational details
Geometries were fully optimized at the RI-BP86 level as implemented in the G03 program 14 , employing the exchange and correlation functions of Becke 15 and Perdew16, respectively, together with a fine integration grid (75 radial shells with 302 angular points per shell), the augmented Wachters' basis 17 on Fe (8s7p4d) and 6-31G* basis on all other elements (denoted AE1 in previous work), and suitable auxiliary basis sets for the fitting of the Coulomb potential.
For comparison, the B3LYP functional was used, which combines Becke's three-parameter exchange functional with the correlation functional of Lee, Yang, and Parr 18 .Harmonic frequencies were computed from analytical second derivatives.Relative energy differences are calculated with ZPE correction included.IRC calculations (intrinsic reaction coordinate as implemented in Gaussian 03) were performed at the corresponding level of theory to identify the minima connected through transition state.Test calculations for selected substrates at the RI-BP86 and at the BP86 level (i.e.without density fitting) confirmed that geometrical parameters and harmonic vibrations were essentially identical with both approaches.This and similar DFT levels have proven to be reliable for calculating structures, molecular energetics and dynamics of organometallics in general, and metallocene compounds in particular. 19agnetic shieldings (σ) were computed at the B3LYP level for the RI-BP86 equilibrium geometries, employing GIAOs (gauge including atomic orbitals) 20 and basis II′, i.e., the augmented Wachters basis 21 which is essentially of polarized triple- quality, on C-and O-, and IGLO-DZ basis on hydrogen.Chemical shifts were calculated relative to ferrocene ( 57 Fe, 13 C, and 1 H-magnetic shieldings -4372.8,106.2, and 28.1 ppm at the same level), and the 13 C-, 1 H-, and 57 Fe-chemical shifts were converted to the usual standards, TMS and Fe(CO)5, using the experimental δ ( 13 C), δ ( 1 H), and δ ( 57 Fe) values of ferrocene, 67.8, 4.2, and 1532 ppm, respectively 22 .This level has been shown to perform very well for transition-metal chemical shifts, including 57 Fe, where further enlargement of the basis set in the NMR part has afforded only minor changes in the computed values.Solvent model calculations were performed at the BP86/AE1 level employing the polarizable continuum model (PCM) of Tomasi and co-workers 24 (using parameters of chloroform, i.e., solvent relative permittivity  = 4.7).

Figure 2 .
Figure 2. A crystal packing diagram of 4, viewed along the c axis, showing the C-H interaction which links the molecules into infinite chains.The C-H interaction is indicated by dotted lines.

Table 1 .
Relative energies (in kcal/mol) calculated for structures involved in this study a BP86/AE1 level:  =4.7