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Review

Computational Studies of Molybdenum-Containing Metal–Sulfur and Metal–Hydride Clusters

by
Nishshanka M. Lakshan
1,
Dinesh C. Aluthge
2 and
W. M. C. Sameera
2,3,*
1
Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH 43210, USA
2
Department of Chemistry, University of Colombo, Colombo 00300, Sri Lanka
3
Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigården 4, SE-412 96 Gothenburg, Sweden
*
Author to whom correspondence should be addressed.
Catalysts 2024, 14(11), 816; https://doi.org/10.3390/catal14110816
Submission received: 30 September 2024 / Revised: 3 November 2024 / Accepted: 5 November 2024 / Published: 13 November 2024
(This article belongs to the Section Catalytic Materials)
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Abstract

:
The development of transition metal clusters is an active area of research in inorganic chemistry, as they can be used as catalysts to perform chemically or biologically relevant reactions. Computational chemistry, employing density functional theory (DFT), plays a key role in rationalizing the electronic structure and properties of transition metal clusters. This article reviews recent quantum chemical studies of Mo3S4M clusters (M = Fe, Co, Ni), their CO- or N2-bound variants, and metal–hydride clusters. The ground state of the cluster systems was computed, and properties such as metal–metal bonding, orbital interactions, fluxional behavior of ligands, spectroscopy, and reaction mechanisms were rationalized and compared with available experimental results. Our research findings evidence that computational studies employing quantum chemical methods can guide experimental researchers to develop novel transition metal clusters for potential applications in catalysis.

1. Introduction

Iron–sulfur clusters are found in living organisms, and they act as catalysts to activate small molecules [1,2,3,4]. For example, the nitrogenase enzyme catalyzes the reduction of N2 into NH3, where metal–sulfur clusters in the active site catalyze nitrogen fixation under ambient conditions (Figure 1a). Due to the importance of NH3 as an industrial feedstock, particularly in fertilizer production, the global demand for it remains high. Thus, the Haber–Bosch process produces over 200 million metric tons of anhydrous ammonia annually. While the Haber–Bosch process is catalytic, it still requires high temperatures and pressures. It is estimated that the Haber–Bosch process is responsible for the consumption of 1–2 percent of the world’s energy supply. With the demand for fixed nitrogen remaining high, there has been significant interest in developing transition metal complexes and clusters as homogeneous catalysts to activate dinitrogen.
The Schrock group developed the first homogeneous catalyst, a mononuclear molybdenum(III)tris(amido)amine complex (Figure 1b) for the reduction of N2 into NH3 [5]. A dinuclear molybdenum–dinitrogen complex, developed by the Nishibayashi group, can also reduce N2 into NH3 (Figure 1c) [6]. The Fe complex of Peters and co-workers (Figure 1d) [7,8,9] can also perform the catalytic conversion of N2 into NH3. The reported homogeneous catalysts for nitrogen fixation are summarized in recent reviews [1,2,3,4].
Even though several transition metal complexes can convert N2 into NH3, only the Nishibayashi group’s Mo complex shows comparable or higher activity than nitrogenases [6]. Thus, synthetic analogs of the active site of nitrogenases have been developed. There are several reported examples in the literature for synthetic metal–sulfur clusters, often partial analogs of nitrogenase enzyme active site, FeMoco. Mori et al. synthesized a cubane-type Ru-Ir-sulfido cluster that binds dinitrogen (Figure 2a) [10]. Another partial analog with a bridging dinitrogen molecule was reported by Suess and coworkers (Figure 2b) [11]. A recent report by Ohki and coworkers showed the ability of iron–sulfur clusters (Figure 2c,d) to reduce N2 into N(SiMe3)3 [12]. The experimental work in the investigation was complemented by a detailed computational study that is highlighted in this review.
Synthetic metal–hydride clusters can also be used to activate N2 [13]. In general, N2 can be incorporated into mononuclear metal–hydride complexes, but activation of the N–N bond is difficult. On the other hand, multimetallic hydride complexes show N–N bond activation, where the hydride ligands can act as reducing agents and proton sources. For example, in the presence of UV irradiation under N2, a binuclear Fe(II) dihydride complex of the Holland group can release H2 and form an end-on dinitrogen complex (Figure 3a) [14,15]. Ding et al. reported cobalt and nickel hydride complexes containing β-diketiminate-ligands. In the presence of 2.0 equiv. of KBEt3H, their cobalt chloride complex can be converted into a cobalt dihydride complex that can react with N2 under mild conditions to form an end-on bridged dinitrogen complex (Figure 3b) [16]. Hydrogenolysis of a CpXTi(CH2SiMe3) (CpX = C5Me4SiMe3) complex by Shima et al. gives rise to a mixed-valence cluster (CpXTi)3(μ3-H)(μ-H)6 (Figure 3c) [17]. This cluster can react with N2 at room temperature to produce an imido/nitrido complex [(CpXCTi)3(μ3-N)(μ-NH)(μ-H)3].
Quantitative details of the electronic structure of the transition metal clusters and their relation to the properties are essential in developing novel transition metal complexes and clusters to reduce N2 into NH3. In this direction, computational methods, employing density functional theory (DFT), play a major role [18]. Moreover, DFT calculations can rationalize the ground state of the transition metal clusters, determine the quantitative details of the reaction mechanisms, and characterize the short-lived intermediates in the catalytic cycles. Thus, quantum chemical studies guide experimental research to develop novel catalysts to convert N2 into NH3.
Schrock and co-workers proposed the mechanism of the full catalytic cycle for their molybdenum(III)tris(amido)amine complex catalyst (Figure 1b) that invokes stepwise addition of protons and electrons (i.e., Yandulov–Schrock mechanism). The proposed mechanism was validated through computational studies by Cao et al. [19], Magistrato et al. [20], Studt and Tuczek [21], and Reiher and coworkers [22,23,24,25,26,27]. The mechanism of the transformation of N2 into NH3, catalyzed by a dinitrogen-bridged dimolybdenum complex of Nishibayashi and co-workers [6], [{Mo(N2)2(PNP)}2(μ-N2)], (PNP = 2,6-bis(di-tert-butylphosphinomethyl)pyridine), was investigated using computational methods by Batista and coworkers [28] and Yoshizawa and coworkers [29,30]. Further, the proposed mechanism involved the stepwise addition of protons and electrons, where a Mo–N2 intermediate acts as the key active intermediate. Electronic structural and mechanistic studies of the catalytic N2 conversion into NH3 are highlighted in the recent literature [30,31].
This article summarizes the recent progress in computational studies of metal–sulfur clusters and metal–hydride clusters, focusing on the ground state of the clusters and properties such as metal–metal binding, fluxional behavior of ligands, orbital interactions, spectroscopy, and reaction mechanisms. In each section of the article, computational methods were briefly discussed, and the key findings were highlighted.

2. Results and Discussion

2.1. The Electronic Ground State of the Clusters

Typically, transition metal clusters consist of several low-lying spin states. Thus, the first step of a computational study is to optimize the possible spin states starting from the X-ray structure (if available) and determine the ground state. After structure optimization, vibrational frequency calculations must be performed to confirm that the optimized structures are local minima (i.e., no imaginary frequencies). Then, the ground state can be identified by comparing the relative energy of the computed spin states. Ground state optimized structure must be compared with the X-ray structure (if available) and confirmed that they agree.
Ohki and co-workers have developed Mo3S4MCl clusters (M = Fe, Co, Ni, Figure 4a), which were characterized by X-ray diffraction [18]. These clusters can be used as the starting materials to perform catalytic N2 reduction. Here we discuss the electronic structure of Mo3S4FeCl that consists of several spin states, specifically S = 0, 1, and 2. The molecular structures of these spin states were optimized using DFT, as implemented in the ORCA 2.9 program [32]. The scalar relativistic effects with the ZORA Hamiltonian were employed [33]. Two density functionals, specifically B3LYP (20% Hartree–Fock exchange) [34,35] and BP86 (0% Hartree–Fock exchange) [36,37], including empirical dispersion corrections were used [38]. The ZORA-recontracted TZVP and def2-TZVP basis sets [39,40], and def2-TZVP/J auxiliary basis sets were applied for all atoms.
According to B3LYP-D3BJ results, the ground state of Mo3S4FeCl (1) is the S = 1 state, while the S = 0 and S = 2 states are 7.9 and 20.2 kcal mol−1 higher in energy, respectively. The computed spin densities of the S = 1 state [⍴Mo = −0.43, −0.43, −0.43; ⍴Fe = 3.05; ⍴Cl = 0.16] suggested that three unpaired electrons are localized on the Fe, while the unpaired electron in the Mo3S4 unit is antiferromagnetically coupled to the unpaired electrons on the Fe. The computed spin contamination value of the S = 1 ground state is 3.18, which is slightly higher compared to the ideal value (3.00), indicating some spin contamination. When we used the BP86-D3BJ functional, the ground state of 1 is still S = 1. The S = 0 and S = 3 states are 0.03 and 26.6 kcal mol−1 higher in energy. However, the computed spin densities of the S = 1 state [⍴Mo = −0.18, −0.18, −0.18; ⍴Fe = 2.23; ⍴Cl = 0.18] indicated that two unpaired electrons are on the Fe with some partial delocalization of negative spin density on the Mo3S4 unit. The computed <S2> value of 2.31 is higher than the ideal value (2.00), indicating some spin contamination. Based on the computational results, we concluded that the ground state of the Mo3S4FeCl cluster is the triplet state. Even though both B3LYP-D3BJ and BP86-D3BJ functionals confirmed that the ground state of Mo3S4FeCl is S = 1, computed spin density distributions are rather different. This discrepancy comes from the Hartree–Fock exchange of the density functionals. Therefore, the electronic structure and the computed energy gaps between the possible spin states of the transition metal clusters can be affected by the chosen density functional. This study indicated that the chosen density functional has a significant effect on the electronic structure of the Mo3S4FeCl cluster.

2.2. Characterization of Metal–Metal Bonding

X-ray structures of transition metal clusters provide quantitative details of the arrangement of atoms. However, the characterization of metal–metal binding is challenging for experiments. The ground state structure of metal clusters can be computed using DFT, and the metal–metal bonding can be rationalized by inspecting the molecular orbitals in the frontier region, computing Mayer bond indexes [41], and performing quantum theory of atoms in molecules (QTAIMs) analysis [42].
We have reported the X-ray structure of Cp‡2Mo2H8 (Cp‡ = C5H2tBu3) (2, Figure 4a) [43], indicating four Mo-H and four Mo-H-Mo units. A relatively short Mo–Mo bond distance, 2.56 Å, suggests metal–metal bonding. The metal–metal bonding of 2 was determined from computational studies. First, the molecular structure of 2 was optimized using the BP86 functional [36,37], including empirical dispersion corrections [38], as implemented in the ORCA 2.9 program [32]. The ZORA Hamiltonian was employed for scalar relativistic effects [33]. The ZORA-recontracted TZVP and def2-TZVP basis sets [39,40], and def2-TZVP/J auxiliary basis sets were applied for all atoms. According to DFT calculations, the S = 0 is the ground state of 2, and the S = 1 state is 23.2 kcal mol−1 higher compared to the ground state. The positions of the H atoms in the metal coordination spheres of the optimized ground state structure (i.e., four Mo-H and four Mo-H-Mo units) are in agreement with the X-ray structure. Thus, DFT calculations confirmed the positions of Mo-H and two Mo-H-Mo units. Also, the computed Mo-Mo distance (2.54 Å) of the optimized ground state structure is very similar to that of the X-ray structure, 2.56 Å.
The Kohn–Sham frontier molecular orbitals (Figure 5) of the ground state optimized structure of 2 provided some insights into the Mo–Mo bonding. Moreover, the HOMO (177) has σ characters, while the molecular orbitals 172 and 173 have δ and δ* characters, respectively. Thus, the σ2δ2δ*2 configuration indicates a Mo–Mo bond. The computed Mayer bond index (0.92) also suggested a Mo–Mo single bond. The QTAIM confirmed the presence of a bond critical point (BCP). Based on the computed data, we concluded that 2 has the metal–metal single bond character. This study showed that computational methods are very useful in characterizing metal–metal bonding in transition metal clusters.

2.3. Fluxional Behavior of Ligands

Atomic-scale chemical events, such as conformational changes in structure and chemical reactions, are very fast processes. Thus, experimental characterizations of such chemical events are challenging for experiments, whereby computational studies become indispensable. NMR is a powerful technique to characterize the fluxional behavior of ligands in transition metal complexes and clusters. For example, the Cp‡2Mo2H2(μ-C6H6) cluster (3, Figure 4a) indicated a fluxional behavior of benzene on the Mo–Mo unit in the NMR spectrum [43]. Complex 3 was formed when a benzene molecule coordinated to the Mo–hydride complex 2 through H2 elimination. DFT calculations were performed to obtain quantitative mechanistic insights for the fluxional behavior of 3, as implemented in the ADF program [44]. The revPBE functional [45], including the empirical dispersion [38], was used. The TZP basis sets were applied for all atoms [40], and the relativistic Scalar ZORA approach used for Mo [46]. The COSMO implicit solvation model was applied [47], where benzene was used as the solvent.
The computed relaxed potential energy surface for the rotation of the benzene unit of 3 is shown in Figure 4b, where the lowest energy structure showed the μ-η2:η2-coordination mode. In this structure, the computed C5-Mo1-Mo2-C2 torsion angle (i.e., the reaction coordinate) of 52.6° is relatively closer to the X-ray structure (47.5°). An isomeric μ-η2:η2-coordination mode of benzene was also found when the C5-Mo1-Mo2-C2 torsion angle was 32.7° (denoted as “perpendicular”), and this structure was about 0.5 kcal/mol higher in energy. The μ-η3:η3-coordination mode (denoted as “parallel”) form is about 1 kcal/mol above the “perpendicular” mode. The computed barrier for going from the “perpendicular” form to the “parallel” form has a barrier of about 1.6 kcal/mol. Therefore, both “parallel” and “perpendicular” modes can be formed at room temperature, indicating the possibility of fluxional behavior of the benzene on the Mo–Mo unit. This is in agreement with the NMR data. This study highlighted the crucial role of computational studies in interpreting puzzling NMR data.

2.4. Intermolecular Interactions

Our goal is to develop transition metal clusters to activate small molecules. For this purpose, the first step is to coordinate small molecules, such as CO or N2 to the transition metal(s) in the cluster. Then, CO or N2 can be converted into other chemicals, such as CH4, CH3OH, and NH3. The coordination of CO (or N2) on the transition metal cluster depends on the interaction energy between CO (or N2) and the transition metal cluster. Thus, quantitative details of the interaction energies are essential in developing CO- or N2-bound transition metal clusters. In this direction, Ohki and co-workers have synthesized CpXL3Mo3S4M(CO) clusters and characterized them by X-ray diffraction, IR, and electrochemical methods [48]. Computational methods were employed to characterize the interaction energy between [CpXL3Mo3S4M] and CO.
An energy decomposition analysis (EDA) [49] together with the natural orbitals for chemical valence (NOCV) [50] was performed to rationalize the interaction energy (ΔEint) between [CpXL3Mo3S4M] and CO of 4 (M = Fe), 5 (M = Co), and 6 (M = Ni). In EDA, ΔEint can be separated into Pauli repulsion (ΔEPauli), electrostatic attraction (ΔEelstat), orbital interactions (ΔEorb), dispersion energy (ΔEdisp), and solvation energy (ΔEsol). EDA-NOCV can separate the ΔEorb further into the orbital interactions, which is very useful in rationalizing chemical bonds. EDA-NOCV was performed for the ground state optimized structures of CpXL3Mo3S4M(CO) using the ADF program [44]. The BP86 [36,37] functional, including empirical dispersion [38], was used. The TZ2P [40] basis sets were applied for all atoms, and the relativistic Scalar ZORA [46] approach was employed for Co, Ni, and Mo. The COSMO method [47], employing tetrahydrofuran solvent, was used as the implicit solvent model.
Numerical data of the EDA-NOCV of CpXL3Mo3S4M(CO) clusters are summarized in Table 1. The computed ΔEint is stronger for the Fe system (101.1 kcal/mol) compared to Co (81.5 kcal/mol) or Ni (77.3 kcal/mol) systems. Thus, CO binding on the Fe system is favorable compared to the Co and Ni systems. In the attractive energy terms, ΔEelstat and ΔEorb are dominant and can overcome the ΔEPauli in all three systems, while the ΔEelstat and ΔEsol are very small. The ΔEelstat and ΔEorb of the Fe system are rather similar, while the ΔEelstat term is relatively strong in both Co and Ni systems. As the ΔEorb term is significant in all three systems, the EDA-NOCV was performed to obtain quantitative insights into the M(d) to π*(CO) back donation and CO to M(d) σ donation. Computed plots of deformation densities are summarized in Figure 6.
The computed orbital interaction energy of the Fe system is −125.8 kcal mol−1, which is stronger compared to the Co (−93.5 kcal/mol) and Ni (−79.8 kcal/mol) systems. In the case of the Co system, the π back donation from Co to π* of CO [orb(1) and orb(2) in Figure 6a, −57.5 kcal mol−1 in total] is dominant compared to the σ donation from CO to Co [orb(3) in Figure 6a, −25.0 kcal mol−1]. Similarly, the π back donation from Ni to π* of CO is dominant [orb(1) and orb(3) in Figure 6b, −50.5 kcal mol−1 in total]. In the case of the Fe system, π back donation from Fe to π* of CO character can be seen in orb(1), orb(2), and orb(3). The computed deformation densities of the Fe system have the strongest ΔEorb (−125.8 kcal/mol). Thus, compared to the Co and Ni systems, the C–O bond of the Fe system is activated, and therefore, the CO reduction would be favorable in this system. Based on the computational results, [CpXL3Mo3S4Fe]CO is our primary target to convert CO into CH4 or CH3OH.

2.5. Determination of Oxidation States

Mössbauer spectroscopy is a powerful tool to characterize the oxidation state of Fe in transition metal clusters. The isomer shift (δ) and quadrupole splitting (ΔEQ) are two parameters measured in Mössbauer spectroscopy. The δ is the key parameter to determine the oxidation state of Fe, as the δ is sensitive to the charge density at the Fe nucleus. The quadrupole splitting (ΔEQ) is sensitive to the coordination environment. Thus, Mössbauer spectroscopy is a powerful method for characterizing Fe-containing transition metal clusters. DFT can be used for calculating the Mössbauer data (i.e., δ and ΔEQ) of Fe, and computed data are very useful in interpreting conflicting or puzzling experimental results.
Ohki and co-workers have synthesized and spectroscopically characterized three cubic clusters, Cp*3Mo3S4Fe-N2-FeS4Mo3Cp*3 (7, Figure 2c), CpXL3Mo3S4Fe-N2 (8, Figure 2d), and CpXL3Mo3S4Fe-N2(SiPh3) (9, Figure 7a) [12], where N2 is coordinated to Fe. 57Fe Mössbauer data were collected from experiments and calculations to obtain some insights into the oxidation state of Fe. The low-lying spin states of 7–9 were calculated using DFT implemented in the ORCA program [32]. The BP86 is the functional, [36,37] including empirical dispersion, ref. [38] was used. The ZORA scalar relativistic method [33], the ZORA-def2-TZVP basis sets, and SARC/J auxiliary basis sets were applied for all atoms [39,40]. The conductor-like continuum polarization model (C-PCM) was used as the implicit solvent model [51], where tetrahydrofuran was used as the solvent. Mössbauer parameters, specifically δ and ΔEQ were calculated using the B3LYP [34,35] functional as implemented in the ORCA program [32]. The CP(PPP) basis sets were used for Fe [52], and DKH-def2-TZVP [53] basis sets were applied for the remaining atoms. For the isomer-shift calculations, α = 0.1706325, β = 0.33226751, and C = 23615 values were employed [54].
The experimental δ values of the CpR3Mo3S4FeCl clusters (CpR = Cp*, CpL, CpXL) are 0.55–0.56 mm s−1, which are typical for Fe(II). Thus, the oxidation state of Fe in 6–7 seems Fe2+ but slightly reduced compared to CpR3Mo3S4FeCl clusters. To understand this trend, δ values of 7–9 were computed using DFT. The computed ground states of clusters 7–9 were closed-shell singlet, S = 0. Optimized ground state structures are in agreement with the X-ray structures. Mössbauer parameters were calculated starting from the X-ray structures and also from the optimized ground state (S = 0) structures. Calculated δ values of the X-ray structures are in agreement with the experimental data (Table 2). The experimental or computed δ values are compatible with the Fe2+ oxidation state of Fe but are slightly reduced. This study indicated the importance of quantum chemical calculations in determining the oxidation state of the iron in transition metal clusters.

2.6. Reaction Mechanisms

The mechanism of a reaction provides a detailed atomic-scale picture of the chemical events. Modern computational methods, employing DFT, can be used as a powerful tool to compute reaction mechanisms [55,56]. DFT can rationalize the intermediates and transition states of the reaction mechanisms. Thus, the reaction barriers for the individual chemical steps of the mechanism, including the rate-determining step, can be computed. We have reported the mechanism of the full catalytic cycle of the silylation of N2 catalyzed by hydride clusters, (C5Me4R)Mo(PMe3)(H)(μ-H)3FeCp∗ (R = Me, H) (10, Figure 7b) [57]. In this mechanistic study, the (C5Me4R)Mo(PMe3)(H)(μ-H)3FeCp∗ cluster (10) was used as the catalyst to convert N2 into N(SiMe3)3. According to DFT calculations, the closed-shell singlet state, i.e., S = 0, is the ground state of 10. Starting from the ground state of 10, the free energy profile of the mechanism was computed. The BP86 is functional [36,37], which includes Grimme’s dispersion and Becke-Johnson damping [38], as implemented in the Gaussian16 program [58]. The SDD [59,60] basis sets were used for Fe and Mo. The def2-TZVP basis sets were applied for the other atoms [40]. The polarizable continuum model (PCM) [61] was applied, where THF was used as the solvent.
The computed free energy profile is shown in Figure 8. The first step of the mechanism is the reaction between a Me3Si radical and the Mo-H of 10 (=12b), giving rise to 2I1. After that, N2 coordination occurs at the Mo site with a free energy barrier of 9.8 kcal mol−1, while N2 coordination at the Fe site is a further 8.4 kcal mol−1 higher in energy. Then, two Me3Si radicals react with the Mo-N2 unit in a step-wise manner through low free energy barriers to form the intermediate 2I4. The third Me3Si radical reacts with the proximal nitrogen atom of 2I4 to form 1I5′. After that, Na atoms in solution react with 1I5′, giving rise to Na[(Me3Si)NN(SiMe3)2], which will ultimately convert into N(SiMe3)3. As the 2I1 is recovered, the next catalytic cycle can be started. The rate-determining step is the third SiMe3 radical attack (i.e., 2I4 → 1TS4′ → 2I5′) that has a free energy barrier of 12 kcal mol−1. Thus, the catalytic cycle can operate under mild conditions. This study indicated the importance of quantum chemical calculations in determining the reaction mechanisms.

3. Conclusions

Transition metal clusters are challenging to characterize from experimental studies alone. In this direction, computational methods, employing DFT, play a crucial role. This article summarized recent progress in calculating the electronic structure and properties of Mo3S4M clusters (M = Fe, Co, Ni), their CO- or N2-bound variants, and metal–hydride clusters. Moreover, low-lying spin states of transition metal clusters were computed, and the properties, such as metal–metal bonding, orbital interactions, spectroscopy (e.g., IR, Mössbauer), and reaction mechanisms were rationalized. Computed data explained the puzzling experimental results. Thus, computational studies, employing DFT, can guide experimental researchers to characterize novel transition metal clusters and tune them to convert small molecules such as CO and N2 into other chemicals.

Funding

This work was partly supported by JSPS KAKENHI [grant numbers JP19K03940 (to WMCS), JP21H05416 (to WMCS)].

Data Availability Statement

No new data were created or analyzed in this study.

Acknowledgments

Thanks to supercomputing resources at the Institute for Chemical Research, Kyoto University (Japan). We thank Yasuhiro Ohki and Kazuki Tanifuji (Kyoto University in Japan) for useful discussions.

Conflicts of Interest

The authors declare no conflict of interest.

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Catalysts 14 00816 g001
Figure 1. (a) Active site FeMo-cofactor of the Mo-nitrogenase. (b–d) Transition metal complexes that convert N2 into NH3.
Figure 1. (a) Active site FeMo-cofactor of the Mo-nitrogenase. (b–d) Transition metal complexes that convert N2 into NH3.
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Figure 2. Synthetic metal sulfur clusters reported in the literature for N2 reduction.
Figure 2. Synthetic metal sulfur clusters reported in the literature for N2 reduction.
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Figure 3. Multimetallic hydride complexes developed by (a) Holland group [14,15], (b) Ding et al. [16], and (c) Shima et al. [17] for N–N bond activation.
Figure 3. Multimetallic hydride complexes developed by (a) Holland group [14,15], (b) Ding et al. [16], and (c) Shima et al. [17] for N–N bond activation.
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Figure 4. (a) Cubic Mo3S4MCl clusters (M = Fe, Co, Ni), (b) computed relaxed potential energy surface for the rotation of the C6H6 of 3, where the C5-Mo1-Mo2-C2 torsion angle as the reaction coordinate.
Figure 4. (a) Cubic Mo3S4MCl clusters (M = Fe, Co, Ni), (b) computed relaxed potential energy surface for the rotation of the C6H6 of 3, where the C5-Mo1-Mo2-C2 torsion angle as the reaction coordinate.
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Figure 5. Kohn–Sham frontier molecular orbitals of the S = 0 state optimized structure of Cp‡2Mo2H8.
Figure 5. Kohn–Sham frontier molecular orbitals of the S = 0 state optimized structure of Cp‡2Mo2H8.
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Figure 6. Plots of the deformation densities of (a) 4 (M = Fe), (b) 5 (M = Co), and (c) 6 (M = Ni). The “v” is the eigenvalues of the deformation densities.
Figure 6. Plots of the deformation densities of (a) 4 (M = Fe), (b) 5 (M = Co), and (c) 6 (M = Ni). The “v” is the eigenvalues of the deformation densities.
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Figure 7. (a) N2 bound CpXL3Mo3S4Fe cluster (9) and (b) (C5Me4H)Mo(PMe3)(H)(μ-H)3FeCp* (10).
Figure 7. (a) N2 bound CpXL3Mo3S4Fe cluster (9) and (b) (C5Me4H)Mo(PMe3)(H)(μ-H)3FeCp* (10).
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Figure 8. Free energy profile of the catalytic silylation of N2 by 10.
Figure 8. Free energy profile of the catalytic silylation of N2 by 10.
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Table 1. Numerical data of EDA-NOCV. Energies are in kcal/mol.
Table 1. Numerical data of EDA-NOCV. Energies are in kcal/mol.
(4, M = Fe)(5, M = Co)(6, M = Ni)
∆Eint−101.1−81.5−77.3
∆EPauli196.9170.5149.6
∆Eelstat−130.2−122.0−115.3
∆Eorb−125.8−93.5−79.8
∆Edisp−9.26−10.5−7.1
∆Esol−32.8−26.0−24.7
Table 2. Computed and experimental Mössbauer parameters of 7, 8, and 9.
Table 2. Computed and experimental Mössbauer parameters of 7, 8, and 9.
Transition Metal ClusterIsomer-Shift (mm s−1)
X-RayOptimizedExperimental
70.46, 0.460.35, 0.350.48
80.390.260.40
90.260.140.26
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Lakshan, N.M.; Aluthge, D.C.; Sameera, W.M.C. Computational Studies of Molybdenum-Containing Metal–Sulfur and Metal–Hydride Clusters. Catalysts 2024, 14, 816. https://doi.org/10.3390/catal14110816

AMA Style

Lakshan NM, Aluthge DC, Sameera WMC. Computational Studies of Molybdenum-Containing Metal–Sulfur and Metal–Hydride Clusters. Catalysts. 2024; 14(11):816. https://doi.org/10.3390/catal14110816

Chicago/Turabian Style

Lakshan, Nishshanka M., Dinesh C. Aluthge, and W. M. C. Sameera. 2024. "Computational Studies of Molybdenum-Containing Metal–Sulfur and Metal–Hydride Clusters" Catalysts 14, no. 11: 816. https://doi.org/10.3390/catal14110816

APA Style

Lakshan, N. M., Aluthge, D. C., & Sameera, W. M. C. (2024). Computational Studies of Molybdenum-Containing Metal–Sulfur and Metal–Hydride Clusters. Catalysts, 14(11), 816. https://doi.org/10.3390/catal14110816

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