1 Introduction

The environmentally benign generation of hydrogen via water electrolysis plays a key role in a future hydrogen economy. The most efficient catalyst for the hydrogen evolution reaction (HER) is platinum, but the available supplies of this element are not sufficient to meet the expected demand for large-scale hydrogen production. Molybdenum sulfide (MoS2) based catalysts have the potential to replace platinum as a HER catalyst in electrochemical water splitting [1,2,3,4,5,6,7]. The material is also discussed as a catalyst for methanol synthesis from carbon dioxide and molecular hydrogen [8, 9]. A better understanding of the reaction mechanisms contributes to the targeted optimization of the catalysts.

In industry, MoS2-based catalysts are widely used e.g. in hydrotreating of refined petroleum products [10,11,12,13], as well as a lubricant [14]. For the sulfidation of molybdenum, various sulfur agents may be used, such as hydrogen sulfide (H2S) or organosulfide compounds like dimethyl disulfide (DMDS) [15]. In a previous study the tendency of carbon to become incorporated into MoS2 nanoparticles synthesized from a metallic Mo precursor was investigated [16], with the main focus lying on the possible incorporation of carbon during the sulfidation with organosulfides, namely DMDS and dimethyl sulfide (DMS). Scanning tunneling microscopy showed that the size and shape of the resulting MoS2 clusters were affected by the choice of the sulfiding agent [16]. X-ray photoelectron spectroscopy revealed that when H2S or DMDS was used as a sulfur agent, no carbon was incorporated inside or on the surface of the nanoclusters [16]. However, when using DMS instead, incomplete sulfidation led to some carbon species on poorly crystalline MoS2 phases of non-carbide nature, which disappeared upon annealing [16]. The deficiency of carbon after sulfidation could be explained by DMDS decomposition into DMS and H2S in the presence of H2, as reported by Texier et al. [15]. In the absence of hydrogen, direct extraction of sulfur from DMDS with the formation of DMS as a byproduct has the same effect. DFT calculations were used to investigate the stability of different carbon species (C, CH, CH2) incorporated into MoS2 [16]. The calculations showed that, both for S-edge and Mo-edge, the stability of the substituted species increases from C via CH to CH2 [16]. Further quantum chemical studies addressed Mo10S x species as model systems of planar molybdenum sulfide clusters [17], determined the most stable composition of Mo n S m species [18], or investigated hydrogen evolution from water mediated by Mo3S4− [19].

In the gas phase, MoX n +, X=O, S, n = 1–3, have been studied with a combination of experiment and theory [20] by Schwarz and co-workers. Very recently, the reactions of molybdenum monoxide and dioxide cations with ethanol were addressed by the same group [21, 22]. Structure and thermochemistry of MoSx+ was addressed by Schwarz, Armentrout and co-workers using guided ion beam experiments and Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry in combination with quantum chemistry [23]. Guided ion beam experiments also yielded a wealth of thermochemical data on MoOx+ species interacting with CO and CO2 [24, 25]. Fielicke and co-workers studied the effect of molybdenum doping on the reactivity of metal and metal oxide clusters [26, 27]. Bohme and co-workers established that a gas-phase Mo(C60)4+ complex can be formed in a flow reactor [28]. The same group studied the reactions of Mo+ with heavy water [29], carbon disulfide [30], O2 [31] and N2O [32] as part of a large-scale investigations of periodic trends. Although lying in the thermodynamic window, Mo+ does not catalyze the reduction of N2O by CO [33].

In this work, the formation of MoxSy+ clusters from Mo n + and DMDS is studied to understand the formation of these clusters. For this task an FT-ICR mass spectrometer is used, as it is an excellent tool for the examination of ion–molecule reactions in the gas-phase [34,35,36], including catalytic cycles [37,38,39]. Experiments are complemented by quantum chemical calculations of reactant and product species to test whether the observed product ions are energetically accessible.

2 Experimental Section and Calculations

The reactivity measurements are performed on a modified Bruker/Spectrospin CMS47X FT-ICR mass spectrometer, equipped with a 4.7 T superconducting magnet and an Apex III data station [40, 41]. The ions are generated in a laser vaporization source [42,43,44], which is combined with supersonic expansion. The molybdenum vaporization is achieved by focusing the second harmonic (532 nm) of a 5 ns pulsed Nd:YAG laser with 5–120 mJ per pulse, depending on the desired cluster species. Due to the high boiling point of molybdenum of 4885 K [45], relatively high laser pulse energies had to be used. The produced plasma is rapidly thermalized by a precisely timed helium gas pulse of typically 30 µs, which propagates perpendicularly to the lasers beam path. The gas pulse is produced in the source chamber (10−6–10−4 mbar) by a piezoelectric valve with a backing pressure of about 20 bar. During thermalization cluster formation occurs. The produced (cluster-)ions are entrained by the helium gas carrier and are accelerated and guided by several electrostatic lenses towards the ultrahigh vacuum (UHV) region, with a pressure in the lower 10−10 mbar range without reaction gas. The source gas pulses have no measurable effect on the UHV pressure. The ICR cell is located in the center of the superconducting magnet, where the ions are trapped, mass selected, reacted and detected.

DMDS vapor is introduced into the UHV via a leak valve at a constant background pressure in the range of (6–8) × 10−9 mbar. The liquid sample is degassed by several freeze–pump–thaw cycles. Broadband and single frequency resonant excitation are used to isolate the species of interest. Stable ion signal conditions were obtained for Mo n +, n = 1–3, and their reactions with DMDS were monitored by taking mass spectra at delays from 0.0 to 25.0 s. Since ion accumulation in the cell takes 2 s, some reaction products are already present at 0 s reaction delay. Typically, 20 experiment cycles are run at each reaction delay for signal averaging. Kinetic analysis is performed assuming pseudo-first order kinetics. Due to the large number of intermediates and products, only peaks that exceeded a relative intensity of 2% at any time during the first 4 s were taken into account for data evaluation, to keep the fits manageable. After calibration of the measured pressures and correcting for ion-gauge sensitivity [46], pressure-independent rate coefficients are obtained as described in detail before [47]. The uncertainty in pressure measurement is the dominant contribution to the experimental error of the rate coefficients, which is typically 25–30%. Branching ratios are more accurate, since they depend only on the error of the pseudo-first order rate coefficients. Their error depends on the overall signal-to-noise level of the experiment and is estimated to ± 2–3% in the present study.

Since natural molybdenum has a broad isotopic distribution, isotopically enriched 92Mo (STB Isotope Germany GmbH) was used. Metallic powder of 700 mg 92Mo with ≥ 99.9% enrichment was pressed and sintered into a solid target disk. DMDS (≥ 99.0%, Sigma-Aldrich) was used without further purification.

Structure and energetics of relevant species along the reaction path were calculated using density functional theory (DFT), employing the M06-L functional [48] along with the def2TZVP basis set [49]. For species containing molybdenum atoms, various possible conformations were used as a starting point for optimization, with spin multiplicities up to heptuplet. In total, more than 450 initial optimization points of different structure or spin multiplicity were considered for 26 non-trivial molybdenum-containing species studied in the present work. Only the most stable structures are dealt further. The stability of the wavefunction was tested in every local minimum. Frequency calculations were performed to verify the absence of imaginary frequencies, zero-point energy is included in all reported energies. No scaling was applied to the calculated frequencies.

See Supporting Information (SI) for the complete parameter matrices containing all calculated absolute reaction rates, as well as optimized structures and benchmarking of the computational method with respect to other DFT functionals and higher-level methods.

3 Results and Discussion

3.1 Monomer Mo+

Due to the vast variety of products being formed in competing reactions, the reaction kinetics were fitted only for the first 4.0 s. The kinetic diagram showing the time dependent relative intensities of the parent ion (Mo+) and its product ions is depicted in Fig. 1. In total 39 reaction channels were used to describe the time profile of the measured data. Since the precursors of secondary and higher order products cannot be unambiguously identified on the basis of the kinetics data, the main focus here lies on the first reaction step. The reactions and rate coefficients for the first reaction step are listed in Table 1. These results are robust with respect to the sequence of secondary and higher-order reactions chosen for the fit. The reaction energies were calculated only for products that, for stoichiometric reasons, can be formed from Mo+ and one DMDS molecule.

Fig. 1
figure 1

Kinetic fit of Mo+ with DMDS during first 4 s of the reaction at pDMDS = 5.9(2) × 10−9 mbar. The graph has been split into a primary and b secondary products

Full size image
Table 1 Rate coefficients and reaction energies for the first step of the suggested reaction sequence of Mo+ with DMDS during the first 4.0 s
Full size table

At the early stage of the reaction, the primary products MoS2+, MoS2CH+ and MoS2CH3 are the most dominant, with branching ratios of 24, 20 and 12%, respectively (see reactions 1.5, 1.7 and 1.9 in Table 1). The remaining products are produced with branching ratios of 5–8%. In the kinetic model used for the fit, the DMDS cation is formed by charge transfer from higher order products such as MoS+, MoSCH2+ and MoSCH3+ (see Table S1). The data at longer times suggest that charge transfer products, in particular C2H6S2+ and C2H5S+, are efficiently formed throughout the reaction sequence, most likely from multiple precursors.

Structures of possible association and reaction products are shown in Fig. 2a. When Mo+ and CH3SSCH3 interact, there is up to 4.7 eV of energy released (as calculated at the M06-L/def2TZVP level of theory). This energy is redistributed among the internal degrees of freedom of the cluster and leads to dissociation of various bonds, leading to the observed reaction products. The high reaction energy also explains why the association product is not observed among the reactions products, since a large number of strongly exothermic reaction channels make radiative association [50] impossible. The majority of dissociation reactions are calculated to be substantially exothermic; however, the fastest reactions are not necessarily the most exothermic ones. This might be rationalized by kinetic effects, or entropic barriers might prevent the ion from reorganization. At the same time, different neutral reaction products might be formed than the ones assumed in Table 1, e.g. 2 CH3· instead of C2H6, leading to less exothermic reactions. There is one reaction that is slightly endothermic (reaction 1.2, ΔE = 0.01) where we might expect that the excess energy is supplied by the kinetic energy of the trapped ions.

Fig. 2
figure 2

a–c Left: initial complexes obtained after the reaction of Mo n + and CH3SSCH3, n = 1–3, along with energy ΔE (in eV) relative to the separated reactants. Right: ions obtained after dissociation of the initial complex as included in Tables 1, 2, 3 as well as neutral MoS2C2H6. d Selected ions arising during secondary reactions and their relative energy E (in eV). All structures were optimized at the M06-L/def2TZVP level of theory, spin multiplicities S are given for each ion. Color code: molybdenum—blue; sulfur—orange; carbon—green; hydrogen—white

Full size image
Table 2 Rate coefficients for the suggested reaction sequence of Mo2+ with DMDS during the first 4.0 s of the reaction
Full size table
Table 3 Rate coefficients for the suggested reaction sequence of Mo3+ with DMDS during the first 4.0 s of the reaction
Full size table

From a structural perspective, molybdenum tends to form as many bonds with heavy atoms as possible, as shown also in previous studies on charged and neutral Mo x S y clusters [18, 19, 51]. Already for the association product, the structure containing two Mo–C and two Mo–S bonds was found to be the most stable one (see Fig. 2a). This is also true for ions produced in subsequent reactions that form as many bonds of molybdenum with heavy atoms as possible (see below). There were, on the other hand, no structures with the metal center inserting into C–H bonds found among the most stable isomers. This is perfectly in line with studies by Armentrout on the activation of alkanes by Mo+, where only endothermic reactions were observed [52,53,54].

A qualitative analysis of the mass spectra for reaction delay until t r  = 20.0 s reveals that these products continue to react with DMDS until the final products are formed. The molybdenum containing products are shown in Fig. 3, where the most dominant ones are MoS5C2H6+, MoS4C3H9+ and MoS5C3H9+. It is worth mentioning that neither pure MoSx+ nor MoCxHy+ species were present as final products. Combining the general reaction pattern with theoretical calculations on geometry optimization at the M06-L/def2TZVP level suggests the formation of up to five Mo–S bonds together with Mo–C bonds, see Fig. 2d. This may be expected, since molybdenum is known to form a rich variety of sulfides [45]. However, the most intense final product is the charge transfer product SC2H5+. Other intense charge transfer products are S2C2H6+, S3C3H9+, SC2H3+ and S2C3H7+; their intensities are 88, 53, 41 and 20%, respectively, relative to SC2H5+ with 100%.

Fig. 3
figure 3

Mass spectrum of Mo+ with DMDS after a reaction delay of 20.0 s showing the final products of the reaction (pDMDS = 5.9(2) × 10−9 mbar). Intensities are given relative to the most abundant product SC2H5+

Full size image

3.2 Dimer Mo2 +

Again, due to the vast variety of simultaneous reactions with different intermediates reacting through competing reaction channels, only the first 4.0 s of the reaction were analyzed with a kinetics fit. The kinetic model was developed iteratively by choosing stoichiometrically allowed and chemically reasonable reaction pathways and testing the quality of the fit. In Fig. 4 the time dependent relative intensities of the parent and product ions are shown. Due to the many intermediates which had to be taken into account, the graph is split in primary and higher order products. The primary reactions are listed in Table 2. A total of 46 different reaction channels were used in the kinetic model. At this high number of different reaction channels, the chosen model is not the only possibility, and secondary reactions cannot be assigned unambiguously. Therefore, only the first step, Mo2+ + CH3SSCH3, is discussed in more detail. The reactions 2.1, 2.4 and 2.6 are dominant, consistent with the tendency of molybdenum to directly extract sulfur from DMDS. All reactions included in Table 2 are again calculated to be exothermic.

Fig. 4
figure 4

Kinetic fit of Mo2+ with DMDS during the first 4.0 s of the reaction at pDMDS = 7.6(7) × 10−9 mbar. For the sake of clarity, the graph has been split in products containing up to two (a) or up to five (b) sulfur atoms respectively

Full size image

The addition of CH3SSCH3 to Mo2+ is again considerably exothermic (up to − 5.9 eV, see Fig. 2b). DMDS tends to dissociate on the ion, forming a rhombic Mo2S2 core with CH3 groups attached to Mo atoms. The product ions form a high number of Mo–S and Mo–C bonds, similar to the case of Mo+. Predicted structural patterns are close to the ones calculated for neutral Mo x S y gas phase compounds [18].

For reaction delays higher than 4.0 s, the acquired mass spectra were analyzed qualitatively, revealing that after a reaction time of approximately t r  = 19.0 s the dimer is completely converted to the products shown in Fig. S1. Clearly the most abundant products are Mo2S6C3H9+, Mo2S7C3H9+ and Mo2S8C3H9+. Again, no pure MozSx+ nor MozCxHy+ were found as final products. In the low mass region, charge transfer products were found. These were identified as SC2H5+, S2C2H6+ (ionized DMDS) and S3C3H9+; their intensities relative to the most intensive Mo2S8C3H9+ peak are 29, 19 and 11%, respectively.

3.3 Trimer Mo3 +

For the first 4.0 s, the reaction proceeds smoothly, as shown in Fig. 5. Since Mo2+ is a product of the reaction, as shown in the mass spectrum in Fig S2, a large number of species can be observed as secondary products. Interestingly, two oxide species Mo2O+ and Mo3S2O+ are observed, suggesting that some of the species present might be capable of dehydrogenating water, which is likely to be present in traces in the vacuum system. The kinetic fit, Fig. 5, shows that the oxides are not primary products of Mo3+ + CH3SSCH3. The first step of the reaction kinetics was modelled as shown in Table 3. Calculated reaction energies are all exothermic.

Fig. 5
figure 5

Kinetic fit of Mo3+ with DMDS during first 4.0 s of the reaction at pDMDS = 6.8(5) × 10−9 mbar

Full size image

Molybdenum trimer Mo3+ is predicted to be cyclic, in agreement with previous calculations on neutral systems [18]. The trimer unit is also kept during optimization for complexes with sulfur or carbon atoms, with the association product having a sandwich structure with a Mo3S2 core and two CH3 groups attached to Mo atoms, analogous to the association product of Mo2+ and DMDS (see Fig. 2c), with the reaction energy of − 7.0 eV. It is interesting to note that the only reaction that does not produce a Mo3-containing ion, reaction 3.1 resulting in Mo2+ + CH3Mo(S2)CH3, is with ΔE = − 0.98 eV only mildly exothermic, but has almost 50% branching ratio. This indicates that during the formation of the association product, the initial insertion of a Mo center into the S–S bond releases sufficient energy to liberate Mo2+.

Interestingly, no charge transfer products were found in the acquired mass spectra. This might be due to the relatively high noise level in the Mo3+ experiment, which leads to small intensities of secondary products of Mo2+ in the first 4 s of the reaction, below the noise level.

4 Conclusions

Despite the vast variety of product ions forming, the early stage of each reaction was analyzed for all molybdenum cluster cations examined. Reasonable reaction schemes with realistic reaction rates in the order of 10−10 cm3 s−1 were found. Charge transfer reactions forming mixed SxCyHz+ clusters were observed only for the monomer and dimer in later stages of the reaction; in fact, charge transfer product ions became the dominant products in the monomer kinetics after longer times. At higher reaction delays, the dominant molybdenum containing product ions had the form Mo x S y (CH3) z + with x = 1, 2, y > x and z = 2, 3. Supported by theoretical calculations, it can be assumed that these products consist of two or three methyl groups binding on the sulfided molybdenum cluster. The trimer was found to be relatively unstable, since a dissociative reaction channel was observed producing the fragment ion Mo2+ at a high rate of (5.3 ± 1.5) × 10−10 cm3 s−1. Albeit not being final products, pure MoxSy+ product ions were observed for all examined species, illustrating the strong tendency of molybdenum to form sulfides by direct extraction of sulfur from DMDS.

In accordance with literature [16], the high sulfidation potential of DMDS can be confirmed. However, also a high yield of CxHy species incorporated in the product clusters is observed. According to the calculated energetics from the literature [16], the binding energy of CHy species incorporated in MoS2 increases from C via CH and CH2 to CH3. This trend is qualitatively reflected in the product distribution, where MopSqCx+ species are very rare.