Structure of Diferrocenyl Thioketone: From Molecule to Crystal

Ferrocenyl-functionalized thioketones have recently been recognized as useful building blocks for sulfur-containing compounds with potential applications in materials chemistry. This work is devoted to a single representative of such thioketones, namely diferrocenyl thioketone (Fc2CS), whose structure has been determined here for the first time. Both X-ray crystallography and a wide variety of quantum-chemical methods were used to explore the structure of Fc2CS. In addition to the X-ray structure determination, intermolecular interactions occurring in the crystal structure of Fc2CS were examined in detail by quantum-chemical methods. These methods were also an invaluable tool in studying the molecular structure of Fc2CS, from the gas phase to solutions and to its crystal. Intramolecular interactions governing the conformational behavior of an isolated Fc2CS molecule were deduced from quantum-chemical analyses carried out in orbital space and real space. Our experimental and theoretical results indicate that the main structural features of an isolated Fc2CS molecule in its lowest-energy geometry are retained both upon solvation and in the crystal. The tilt of ferrocenyl groups is only slightly affected by crystal packing forces that are dominated by dispersion. Nonetheless, a network of intermolecular interactions, such as H···H, C···H and S···H, was detected in the Fc2CS crystal but each of them is fairly weak.

Solvation effects on the Fc2CS rotamers were approximated by the COSMO model of solvation. The COSMO model replaces the dielectric medium with a conducting medium. Interlocking spheres are used to generate the cavity. COSMO is a continuum model that is roughly similar to the popular polarizable continuum model (PCM) [S9]. The former uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. In fact, COSMO may be considered as a limiting case of the PCM model, where the dielectric constant is set to infinity.
The geometries of isolated and solvated Fc2CS molecules were optimized with tight convergence thresholds for gradients and displacements (<10 −5 a.u.). The optimized crystal structure of Fc2CS fulfilled a looser convergence threshold for gradients (<10 −3 a.u.).
The values of RMSD between calculated and experimental structures were computed in the VMD 1.9.1 program. The RMSD was defined by the ith atom in the experimental structure, N was equal to 42, wi was a weighting factor for the ith atom (its mass in our case). The RMSD defined above was minimized using the method of Kabsch [S10]. The resulting minimum values of RMSD are presented in Tables 3 and 4. The RMSD values   listed in Tables S4-S6 were calculated using the above formula except i p was either the ith bond length (N = 61) or bond angle (N = 213) or torsion angle (N = 672) and wi was always equal to 1.
For the gas−phase rotamers of Fc2CS, their orbital analysis in terms of NBOs and the topological analyses of their electron density were carried out using their wavefunctions calculated at the PBE-D/QZVP level of theory. These wavefunctions were stored in the respective files generated by Gaussian 09 D.01.
In Subsection 2.3 two levels of theory, that is, PBE-D/TZVP and SCS-MP2/TZVPP, were used to estimate the energy barriers for the rotations of Fc-group and Cp-ring in an isolated Fc2CS molecule. It is important to verify the ability of the two levels to calculate these barriers with reasonable accuracy. Because there are neither experimental nor high-level theoretical estimates of such barriers for Fc2CS, it is necessary to consider some other molecules which manifest structural similarities with Fc2CS and for which accurate rotation barriers are available. In consequence, two molecules are selected. Benzaldehyde is designated as an example of a molecule containing an aromatic ring with the adjacent π-conjugated substituent. Revolving the phenyl ring about the C-C(=O) bond in benzaldehyde roughly resembles the rotation of Fc-group in Fc2CS. Ferrocene can quite naturally be regarded as a model molecule with Cp-ring rotation. The benzaldehyde molecule is optimized in its two conformations; with either flat or perpendicular arrangement of aldehyde group relative to phenyl ring. The ferrocene molecule is optimized in the eclipsed and staggered conformations of its Cp-rings. The optimizations are performed at the PBE-D/TZVP and SCS-MP2/TZVPP levels of theory. Difference in the energies of two conformations defines the rotation barrier for each molecule. The calculated barriers are listed in Table S1. Table S1. Rotation barriers (in kcal mol −1 ) calculated for two model molecules at two levels of theory.

Molecule
PBE-D/TZVP SCS-MP2/TZVPP Benzaldehyde 9.1 7.5 Ferrocene 0.9 2.1 The reference values of rotation barriers are available for both molecules. For benzaldehyde its rotation barrier is estimated to be 7.7 kcal mol −1 [S11]. This is a high-level theoretical value that was recently proven to be correct [S12]. In the case of ferrocene, the rotation barrier of 0.9 kcal mol −1 was deduced from experimental measurements [S13].
The comparison of the calculated barriers (Table S1) with the corresponding reference data reveals that the PBE-D/TZVP level performs excellently for the rotation barrier of ferrocene and it overestimates the rotation barrier of benzaldehyde slightly. For benzaldehyde the barrier calculated at the SCS-MP2/TZVPP level turns out to be in very good agreement with the reference value. Unfortunately, the SCS-MP2/TZVPP level is incapable of reproducing the rotation barrier of ferrocene well. To conclude, the PBE-D/TZVP level affords reliable estimates of rotation barriers for two model molecules and its good performance should be transferred to both kinds of rotation in Fc2CS. The SCS-MP2/TZVPP level should provide reliable barriers only for the rotation of Fc-group in Fc2CS.
In Subsection 2.6 the lattice energy was calculated for the crystal of Fc2CS. The lattice energy (E lattice ) of Fc2CS crystal was defined by the following formula: where E crystal was the energy of the unit cell of Fc2CS, Z was the number of molecules in the unit cell (Z = 4 for Fc2CS) and E molecule was the energy of an isolated Fc2CS molecule in its lowest-energy conformation (that is, rotamer A). The E crystal and E molecule energies were calculated at the PBE-D/SVP level of theory. The effect of k-point sampling scheme on the calculated value of E lattice is established by performing a series of single-point periodic PBE-D/SVP calculations with various k-point sampling schemes. The same crystal structure, previously optimized at the PBE/SVP level, is used in these calculations. The calculated values of E lattice are presented in Table S2. It is evident that the E lattice energy converges very fast and the increase of k-point mesh beyond 5×3×3 does not improve the value of E lattice . Table S2. The lattice energy (E lattice , in kcal mol −1 ) of Fc2CS, calculated using various k-point sampling schemes. k-point mesh E lattice 5 × 3 × 3 -40.9 7 × 5 × 5 -40.9 9 × 7 × 7 -40.9 11 × 9 × 9 -40.9 In Subsection 2.7 the intermolecular interactions occurring in the crystal of Fc2CS were discussed in terms of energetic quantities, such as the interaction energy and its components. The interaction energy (E inter ) within pairs, triples or a four of Fc2CS molecules in the crystal of Fc2CS was determined at the PBE-D/SVP level of theory. From a computational viewpoint, the molecules constituted a cluster for which the total energy was calculated. Thus, the cluster was formed as either a dimer or a trimer or a tetramer, depending on the number of Fc2CS molecules (within the cluster approach, individual Fc2CS molecules can be termed as monomers). The cluster was built using the Fc2CS unit cell optimized at the PBE-D/SVP level. Part of the atoms occupying the optimized unit cell was translated by lattice vectors to generate whole molecules. The tetramer is shown in Figure S3. Trimers (T1-T4, Figure S4) and dimers (D1-D6, Figure S5) were obtained by removing certain molecules from the tetramer.

Supplementary
The energies of individual molecules constituting a given n-mer (n = di, tri, tetra) were subtracted from the energy of the entire n-mer in order to obtain E inter . Both the n-mer and the individual molecules exhibited their geometries taken from the optimized unit cell of Fc2CS crystal. In order to remove the basis-set superposition error from the values of E inter , the counterpoise correction proposed by Boys and Bernardi [S14] was employed.
An important issue in calculating interaction energies between molecules is the quality of the basis set applied. SVP is a basis set of modest size and it does not include diffuse functions. To assess the reliability of the SVP basis set in predicting E inter between Fc2CS molecules, E inter for one selected dimer (denoted as D1 in Figure S5) was calculated using PBE-D combined with three orbital basis sets of increasing size: SVP, TZVP and aug-cc-pVDZ [S15]. Only the aug-cc-pVDZ basis set covered a set of diffuse functions. The calculations involved the following numbers of primitive Gaussians: 1624, 2714 and 4032, respectively. The calculated values of E inter are listed in Table S3. The magnitude of E inter at the PBE-D/SVP level is reduced by ca. 5%, compared to the E inter value obtained from PBE-D/aug-cc-pVDZ. The reduction of E inter at PBE-D/SVP level turns out to be surprisingly small despite the moderate size of SVP and the lack of diffuse functions. It should be stressed that the size of the aug-cc-pVDZ basis set is twice and half as large as that of SVP. Thus, the SVP basis set provides a reasonable compromise between accuracy and computational cost. Based on the successful validation of PBE-D/SVP for E inter in D1, it can be assumed that this level of theory is able to predict E inter in other n-mers reliably. Table S3. Interaction energy and its LMOEDA components between two Fc2CS molecules of dimer D1. The dimer is shown in Figure S5. All energies are given in kcal mol −1 . The calculated E inter energy was also analyzed in more detail using two partitioning schemes. First, the E inter energy of each dimer was partitioned into several terms according to the LMOEDA method. Electrostatic terms, such as nuclear-nuclear, 1-electron and 2-electrons electrostatic interactions, were grouped into the electrostatic component (E elst ). The polarization component (E pol ) included orbital relaxation effects. The dispersion component (E disp ) was composed of the correlation term and the dispersion term calculated using Grimme's empirical dispersion correction included in the PBE-D density functional. Finally, exchange and repulsion terms were joined together into the exchange-repulsion component (E exch-rep ).

Basis set
The four components calculated using PBE-D and different basis sets are appended to Table S3. It is clear that the percentage shares of E elst , E pol and E disp are practically insensitive to the basis set used.
Second, the many-body analysis was performed for the E inter energy of the tetramer shown in Figure S3 to estimate the strength of individual interactions between the Fc2CS molecules occupying the unit cell of Fc2CS crystal. According to this analysis, E inter of a cluster possessing four molecular fragments (i, j, k, l) can be partitioned into its two-, three-and four-body contributions ( where i, j, k, l indicate individual monomers in the tetramer; Etot(i), Etot(i,j), Etot(i,j,k) and Etot (i,j,k,l) denote the total energies of given monomer, dimer, trimer and tetramer, respectively. The two-body contribution to E inter expresses the sum of the interaction energies for all pairs of Fc2CS molecules constituting the tetramer. The three-body contribution to E inter covers the three-body effects on the interaction energies of all trimers formed within the tetramer.

Supplementary Section S2. Additional tables and figures
Supplementary Table S4. RMSD (in Å) in bond lengths for the optimized geometry of an isolated Fc2CS molecule relative to the corresponding bond lengths of the reference molecular geometry extracted from the XRD crystal structure of Fc2CS. Supplementary Table S7. Selected geometrical parameters extracted from the optimized structure of an isolated Fc2CS molecule and from the XRD structure of Fc2CS crystal. The numbering of atoms corresponds to that shown in Figure S2. Bond lengths are given in Å and angles are in °.  Table S8. Distance (d, in Å) between atoms linked by a bond path and selected QTAIM parameters (ρ,  2 ρ, H, DI, in a.u.) at the critical point on the bond path for rotamers A-C in the gas phase. The numbering of atoms linked by a bond path is explained in Figure S2.  Figure S5.  Figure S2. 2 Percentage share of each attractive component with respect to the total attraction is given in parentheses. Table S10. Distances between two C1 atoms belonging to different molecules (d inter C1···C1, in Å), the interaction energy between the molecules and its two-and three-body

Supplementary
body 3 E , in kcal mol −1 ) for trimers T1-T4 extracted from the optimized unit cell of Fc2CS. The trimers are shown in Figure S4. 1 Numbering of atoms is explained in Figure S2.