Vibrational spectroscopy of metal methanesulfonates: M = Na, Cs, Cu, Ag, Cd

In this work, we have used a combination of vibrational spectroscopy (infrared, Raman and inelastic neutron scattering) and periodic density functional theory to investigate six metal methanesulfonate compounds that exhibit four different modes of complexation of the methanesulfonate ion: ionic, monodentate, bidentate and pentadentate. We found that the transition energies of the modes associated with the methyl group (C–H stretches and deformations, methyl rock and torsion) are essentially independent of the mode of coordination. The SO3 modes in the Raman spectra also show little variation. In the infrared spectra, there is a clear distinction between ionic (i.e. not coordinated) and coordinated forms of the methanesulfonate ion. This is manifested as a splitting of the asymmetric S–O stretch modes of the SO3 moiety. Unfortunately, no further differentiation between the various modes of coordination: unidentate, bidentate etc … is possible with the compounds examined. While it is likely that such a distinction could be made, this will require a much larger dataset of compounds for which both structural and spectroscopic data are available than that available here.


Introduction
Metal methanesulfonates (M(CH 3 SO 3 )x · nH 2 O) are compounds of interest because of the role they play as catalysts for numerous reactions in organic synthesis including (but not limited to) Mannich, Biginelli reaction, esterification and tetrahydropyranylation of alcohols and phenols [1] (figure 1). This is due to their low toxicity, low cost and low reactivity with air and water [2].
Although these substances are rarely found naturally, some forms can be found in the sea as a result of methanesulfonic acid (CH 3 SO 3 H) being produced and emitted by marine phytoplankton (via the oxidation of dimethyl sulfide). This then undergoes chemical reactions with the cations present in sea salt e.g. Mg 2+ , K + , Ca 2+ and Na + , to form their respective metal methanesulfonate salts [3,4]. The natural methods through which these salts form mean that they are vital to exploring the past were converged to better than |0.0035| eV Å −1 . After geometry optimization, the vibrational spectra were calculated in the harmonic approximation using density functional perturbation theory [17]. This procedure generates the vibrational eigenvalues and eigenvectors, which allows visualization of the modes within Materials Studio (http://accelrys.com/products/collaborative-science/bioviamaterials-studio/) and is also the information needed to calculate the INS spectrum using either the programs ACLIMAX [18] or AbINS [19]. We emphasize that the transition energies have not been scaled.

Results and discussion
In this section, we will first provide a complete assignment for Cs(CH 3 SO 3 ) based on a periodic DFT calculation. We will then use this to assign the internal modes of the methanesulfonate ion in the other materials. Figure 2 shows the INS, Raman and infrared spectra of Cs(CH 3 SO 3 ). Table 1 lists the transition energies and assignments, which are based on visualization of the modes from the CASTEP calculation. In the electronic supplementary material, table S2 lists all of the calculated modes with their assignments. Cs(CH 3 SO 3 ) crystallizes in the orthorhombic space group Pnma (no. 62) with four formula units in the primitive cell [20], thus there are 108 modes in total comprising 3 acoustic modes, 21 optic translational modes of the ions, together with 12 librational and 72 internal modes of the methanesulfonate ion. A complete factor group analysis is given in the electronic supplementary material, table S2. The methanesulfonate ion is on a general position, however it has C 3v symmetry within the accuracy of the analysis. Assuming For a centrosymmetric molecule in the gas phase the rule of mutual exclusion (no coincidences in the infrared and Raman spectra) is strictly valid. In the solid state, this is only rigorously true for a centrosymmetric molecule in a crystal that crystallizes in a centrosymmetric system and has only one molecule in the primitive cell. A classic example is K 2 [PtCl 6 ], which crystallizes in a cubic space group and the [PtCl 6 ] 2− ion occupies an octahedral site [21]. For a centrosymmetric crystal with two molecules in the unit cell, the vibrations form in-phase and out-of-phase pairs; this is the factor group splitting and arises from interactions between the molecules. In the limit that the interaction is zero, the inphase and out-of-phase pairs are accidentally degenerate. If one mode is Raman active and the other is infrared active, then even though it is a centrosymmetric system, the modes will occur at the same transition energy in both spectra. It is the degree of coupling between the species that determines the        difference in the transition energies in the two forms of spectroscopy. This is explored in more detail in the electronic supplementary material, figure S1 and table S2. In the present case, although the structure is centrosymmetric, the factor group splitting is small, even though there are four molecules in the unit cell, meaning that modes occur at similar energies in both sets of spectra. There is no evidence for symmetry-breaking in this system, as has been found for other alkali metal compounds [22,23].

Cs(CH 3 SO 3 )
The spectra illustrate the complementarity of the three techniques. INS has no symmetry-based selection rules [24], however there is a strong 'propensity' rule that motions that involve displacement of hydrogen dominate the spectrum. This is dramatically shown by the strongest mode in the INS spectrum at approximately 270 cm −1 , which is assigned to the torsion about the C-S bond. The computational study (electronic supplementary material, table S4) confirms that this mode has essentially zero intensity in both the infrared and Raman spectrum, but as a consequence of the large amplitude hydrogen motion, it is very strong in the INS spectrum. It is also notable that only the methyl modes (torsion, rock, deformations) have significant intensity in the INS spectrum. This demonstrates that the coupling between the CH 3 and SO 3 moieties in the ion is weak. By contrast, the strongest modes in the infrared and Raman spectra are motions of the SO 3 moiety. . It can be seen that for the INS and Raman spectra the agreement is almost quantitative in terms of both transition energy and relative intensity. For the infrared spectrum, the intensity agreement is poorer, which is a consequence of the use of the same band width for all of the calculated modes; inspection of the experimental spectrum shows that this is not the case. Nonetheless, it is clear that the calculation has provided a reliable basis for the spectral assignment and this will be used for the other salts. Figure 4 shows the INS, Raman and infrared spectra of Na(CH 3 SO 3 ). The similarities to those of the Cs salt are striking, except for the greater intricacy of the Na spectra. The structure of the Na salt is complex with 20 formula units in the primitive cell [25]. The very large number of optic modes (537) means that it is not possible to calculate the Raman spectrum in a reasonable time. However, as figure 5 shows, the calculated INS spectrum is in excellent agreement with the experimental spectrum. In the electronic supplementary material, figure S4 compares the observed and calculated infrared spectra. Table 1 lists the observed bands and their assignments.

Cu, Cd and Ag methanesulfonates
In contrast to the simple ionic bonding present in the alkali metal salts, the structures of the Cu [26], Cd [27] and Ag [28] compounds are more diverse and more complex. The Cu compound has square planar  For the Cd compound, the Cd atom is located at the inversion centre of an octahedron with the O atoms of two water molecules at the apices and the O atoms belonging to four methanesulfonato groups in the horizontal plane. The Cd atoms are bridged by the methanesulfonato groups, so forming parallel infinite chains running along the b axis. The Ag complex has an even more elaborate structure. There is no distinct molecule; the methanesulfonato groups act as pentacoordinating ligands. Thus, each Ag atom is at the centre of a very distorted trigonal bipyramid. Figure 6 shows the three structures, which exhibit monodentate, bidentate and pentadentate coordination, respectively, of the methanesulfonato ligand.
The INS spectra of the Cu, Cd and Ag materials (including the D 2 O isotopomers for Cu and Cd) are shown in figure 7. As with the alkali metal salts (figures 3 and 5 and table 1) the features assigned to modes of the methyl group dominate the spectra and show a remarkable constancy in position (table 2). This is consistent with the methyl groups not being involved in the bonding; in all three examples they project into vacant space in the structure. The modes due to the coordinated water molecules in the Cu and Cd compounds give rise to librational modes in the 400-900 cm −1 region [29][30][31]. These are relatively weak and are readily assigned because they are shifted and much weaker in the D 2 O-containing samples.   figure S5). For the alkali metal salts, the spectra are consistent with local C 3v symmetry, the degenerate modes only show a small or no splitting. This is not the case here; the asymmetric S-O stretch mode is both strongly perturbed and is downshifted with respect to the M = Na and Cs salts. It can be seen that the degeneracy of the S-O asymmetric stretch is lifted and two modes appear. (For the Cd salt, this manifests as a broadening of the band; compare the width of the symmetric and asymmetric S-O stretches.) Unfortunately, there is no apparent correlation between the degree of splitting and the type of coordination as there is, for example, with carbonate complexes [32].

Conclusion
At the outset of this work, it was hoped that the mode of coordination of the methanesulfonate ion would show characteristic patterns in the vibrational spectra. These could then be used as a fingerprint for the type of coordination, as found for other ions, e.g. nitrite, sulfate and carbonate [32]. We have studied six compounds that exhibit four different modes of coordination. We found that the transition energies of the modes associated with the methyl group (C-H stretches and deformations, methyl rock and torsion) are essentially independent of the mode of coordination. The SO 3 modes in the Raman spectra also show little variation. In the infrared spectra, there is a clear distinction between ionic (i.e. not coordinated) and coordinated forms of the methanesulfonate ion. This is manifested as a splitting of the asymmetric S-O stretch modes of the SO 3 moiety. Unfortunately, no further differentiation between the various modes of coordination, unidentate, bidentate etc. . . . , is possible with the compounds examined. While it is likely that such a distinction could be made, this will require a much larger dataset of compounds for which both structural and spectroscopic data is available than that used here. Data accessibility. The data which underpin this work are available via TopCat, the ISIS Facility's open access online data repository at: https://data.isis.stfc.ac.uk/doi/investigation/88613665.