CH Activation by a Heavy Metal Cation: Production of H 2 from the Reaction of Acetylene with C 4 H 4 -Os(+) in Gas phase

: While ﬁrst-row transition metal cations, notably Fe(+), catalyze the gas-phase conversion of acetylene to benzene, a distinct path is chosen in systems with Os, Ir, and Rh cations. Rather than losing the metal cation M(+) from the benzene–M(+) complex, as is observed for the Fe(+) system, the heavy metal ions activate CH bonds. The landmark system C 4 H 4 -Os(+) reacts with acetylene to produce C 6 H 4 -Os(+) and dihydrogen. Following our work on isomers of the form C 2n H 2n -Fe(+), we show by DFT modeling that the CH bonds of the metalla-7-cycle structure, C 6 H 6 -Os(+), are activated and deﬁne the gas-phase reaction path by which H 2 is produced. The landmark structures on the network of reaction paths can be used as a basis for the discussion of reactions in which a single Os atom on an inert surface can assist reactions of hydrocarbons. of species evolving from the benzene complex of the osmium cation, OsC 6 H 6 (+), and an isomeric seven-membered unsaturated ring, tracing reaction paths that lead to the evolution of hydrogen gas. The experimental facts [5], based on gas-phase observations of species produced from clusters of acetylene with osmium, revealed no direct structural infor-mation. A more detailed examination of the mass spectrometry data may offer proof of such smaller clusters such as those suggested by our density functional modeling. Contributions: Conceptualization, anal-ysis, C.T., E.A.B. writing—original C.T.; writing— review Z.A. and E.A.B.; visualization, C.T. manuscript.


Introduction
The computational modeling of metal-intermediated catalysis is generally difficult, owing to the structural complexity of the solid structures and surfaces involved in most processes. Some simplification is achieved for systems in which a metal cluster or even a single metal atom is isolated on an inert support [1][2][3][4][5], and further simplification is found in more unusual gas-phase processes involving homogeneous clusters M n (+k) [6][7][8]. The limiting case (n = 1) offers the modeler the easiest task, but complications remain: the charge and the spin states of the metal atom can favor distinct structures and reaction paths.
The experimental studies of single-metal ion catalysis are well established [9][10][11]. The single-metal Fe(+1)-catalyzed transformation of acetylene into benzene is of particular interest. The experimental investigation of the gas-phase, metal-assisted activation of hydrocarbons has employed mass spectrometry (MS) and infrared spectroscopy (IR). MS does not reveal molecular structures but only fragmented masses and associated empirical formulas. IR provides bonding information, but this must be interpreted within a structural model. Computational modeling can fill in gaps, defining equilibrium structures, reaction paths, and transition state geometries. Accordingly, these experimental investigations are often accompanied or supplemented by computational modeling [12]. Recent studies show that several 5d transition metal cations activate small hydrocarbons, producing dihydrogen [13][14][15]. Of these heavy metals, tantalum, tungsten, osmium, iridium, platinum we have chosen to study Osmium, as a congener of the extensively studied iron.
In this report we extend our theoretical investigations to osmium cation reactions with acetylene, which, compared to the modeling of Iron cation systems [16,17], seems to be largely neglected. We hope the structures and energetics we report here can guide the interpretation of the future experimental data on gas-phase systems and single-atom catalytic processes involving a single atom on a surface. The Fe(+) structures we already reported [16] included some that were not studied previously [17]. These are the Fe analogies to 6, 7A and 7B, 8, 12, 13, S1 and S2. Species 6, 7, and 8 are eta-1, eta-2, and eta-3 complexes of Fe(+) with the C 4 H 4 ring. Eta-2 coordination can connect adjacent C atoms (7A) or nonadjacent C atoms (7B). Species 11 may be what Chretien and Salahub [17] call Fe(c-C 4 H 4 )(C 2 H 2 ) cation; in that species Fe participates in a ferro-cyclopentyl ring and a three-membered ferro-cyclopropenyl ring, according to these authors. Structure 12 is called chair and structure 13 is called saddle for easy reference and visualization.
The species studied here include the Os(+) analogs of the C 2n H 2n -Fe(+) structures from reference [16]; that is, 2-15 as shown in Figure 1. interpretation of the future experimental data on gas-phase systems and single-atom catalytic processes involving a single atom on a surface. The Fe(+) structures we already reported [16] included some that were not studied previously [17]. These are the Fe analogies to 6, 7A and 7B, 8, 12, 13, S1 and S2. Species 6, 7, and 8 are eta-1, eta-2, and eta-3 complexes of Fe(+) with the C4H4 ring. Eta-2 coordination can connect adjacent C atoms (7A) or nonadjacent C atoms (7B). Species 11 may be what Chretien and Salahub [17] call Fe(c-C4H4)(C2H2) cation; in that species Fe participates in a ferro-cyclopentyl ring and a three-membered ferro-cyclopropenyl ring, according to these authors. Structure 12 is called chair and structure 13 is called saddle for easy reference and visualization.
The species studied here include the Os(+) analogs of the C2nH2n-Fe(+) structures from reference [16]; that is, 2-15 as shown in Figure 1.

Computational Methods
In our work on Fe(+) catalyzed transformation of acetylene into benzene [16] we evaluated the relative performance of Density Functional and Complete Active Space Self-Consistent Field (CASSCF) Hamiltonians. Some states required a multi-configurational wave function for even and qualitatively correct representation. Remarkably, density functional theory (DFT) with the B97XD [18] range-and dispersion-corrected functional, and the aug-cc-pTZV basis [19], offered a surprisingly coherent account of structures and energetics. In view of the effectiveness of density functional theory for FeC6H6 cation, and its relatively modest demands on computational resources, we chose an analogous model for the study of the OsC6H6 cations. Owing to the presence of the heavy metal osmium, we chose the def2-tzvp basis [20,21] which incorporated a pseudopotential representing the 60-electron inner core of the metal; this basis treats all electrons of C and H. For some preliminary calculations we used the pseudopotential, MWB60, and its associated basis functions [21] for Os and def2-tzvp for C and H. All computations were accomplished

Computational Methods
In our work on Fe(+) catalyzed transformation of acetylene into benzene [16] we evaluated the relative performance of Density Functional and Complete Active Space Self-Consistent Field (CASSCF) Hamiltonians. Some states required a multi-configurational wave function for even and qualitatively correct representation. Remarkably, density functional theory (DFT) with the ωB97XD [18] range-and dispersion-corrected functional, and the aug-cc-pTZV basis [19], offered a surprisingly coherent account of structures and energetics. In view of the effectiveness of density functional theory for FeC 6 H 6 cation, and its relatively modest demands on computational resources, we chose an analogous model for the study of the OsC 6 H 6 cations. Owing to the presence of the heavy metal osmium, we chose the def2-tzvp basis [20,21] which incorporated a pseudopotential representing the 60-electron inner core of the metal; this basis treats all electrons of C and H. For some preliminary calculations we used the pseudopotential, MWB60, and its associated basis functions [21] for Os and def2-tzvp for C and H. All computations were accomplished with Gaussian 09 [22] and Gaussian 16 [23]. Full coordinates for structures along the Os dehydrogenation pathways are available from C.T.  Figure 2 displays the Gibbs energies, which are reported in the Gaussian output from computations including a vibrational analysis:

Energetics and Structures for Fe(+)C 6 H 6 Species
with Gaussian 09 [22] and Gaussian 16 [23]. Full coordinates for structures along the Os dehydrogenation pathways are available from C.T. Figure 2 displays the Gibbs energies, which are reported in the Gaussian output from computations including a vibrational analysis: The Gibbs energy is composed of (a) the electronic energy ED computed in the B97XD/def2-tzvp model; (b) Z which is the zero-point vibrational energy; (c) a thermal correction representing the integral of the ideal gas constant-pressure heat capacity, Cp = 5R/2, integrated from lower bound 0 to the standard temperature T; and (d) the entropy term. S is composed of several parts, including a vibrational portion which can be evaluated by use of the vibrational partition function, a spin multiplicity contribution of form k ln(W) for which W is the spin multiplicity, and a translational portion which can be evaluated by the Sackur Tetrode equation, applicable for an ideal gas composed of particles of mass m. All these terms are computed within the Gaussian software [22,23]. Figure 2 shows that the Fe cation has a sextet ground state, as Hund's rule implies. The addition of acetylene to the Fe cation stabilizes the system, but acetylene adducts 2 -4 (that is Fe(HCCH)n for n = 1, 2, and 3) all favor quartet spin. Each addition of an acetylene stabilizes the quartet relative the doublet. The incremental stabilization of the quartet declines as successive acetylenes are added. The sextet is always much more unstable than the quartet (by about 1.4, 2.6, and 3.4 eV for n = 1, 2, and 3) in the series of iron-acetylene adducts. The quartet of species 4 lies at 2.8 eV relative to the reference energy for the quartet, Fe-benzene. The question then is how, in view of the high energies of species 5-9, reaching 6 eV or more, could the Fe(HCCH)3 cationic system rearrange to form Fe(+)-benzene? We must assume that a substantial portion of the original energy (>8 eV relative to Fe -benzene) is retained in the gas phase cluster.

Energetics and Structures for Fe(+)C6H6 Species
We did not trace out a full reaction path network for the Fe system, but we can identify some possible landmarks (relative minima in Gibbs energy). If the reaction branches from the quartet of the species 3 cation with an unbound acetylene at 4.0 eV, then the quartets of species 10-14 are within relatively easy reach. We note that all spin states of The Gibbs energy is composed of (a) the electronic energy E D computed in the ωB97XD/def2-tzvp model; (b) Z which is the zero-point vibrational energy; (c) a thermal correction representing the integral of the ideal gas constant-pressure heat capacity, C p = 5R/2, integrated from lower bound 0 to the standard temperature T; and (d) the entropy term. S is composed of several parts, including a vibrational portion which can be evaluated by use of the vibrational partition function, a spin multiplicity contribution of form k ln(W) for which W is the spin multiplicity, and a translational portion which can be evaluated by the Sackur Tetrode equation, applicable for an ideal gas composed of particles of mass m. All these terms are computed within the Gaussian software [22,23]. Figure 2 shows that the Fe cation has a sextet ground state, as Hund's rule implies. The addition of acetylene to the Fe cation stabilizes the system, but acetylene adducts 2-4 (that is Fe(HCCH) n for n = 1, 2, and 3) all favor quartet spin. Each addition of an acetylene stabilizes the quartet relative the doublet. The incremental stabilization of the quartet declines as successive acetylenes are added. The sextet is always much more unstable than the quartet (by about 1.4, 2.6, and 3.4 eV for n = 1, 2, and 3) in the series of iron-acetylene adducts. The quartet of species 4 lies at 2.8 eV relative to the reference energy for the quartet, Fe-benzene. The question then is how, in view of the high energies of species 5-9, reaching 6 eV or more, could the Fe(HCCH) 3 cationic system rearrange to form Fe(+)-benzene? We must assume that a substantial portion of the original energy (>8 eV relative to Fe-benzene) is retained in the gas phase cluster.
We did not trace out a full reaction path network for the Fe system, but we can identify some possible landmarks (relative minima in Gibbs energy). If the reaction branches from the quartet of the species 3 cation with an unbound acetylene at 4.0 eV, then the quartets of species 10-14 are within relatively easy reach. We note that all spin states of species 14 are higher in energy than the quartet of species S1. The quartet and sextet of S2 return upon the reoptimization to the C 2v structure of S1.

Energetics and Structures for Os(+)C 6 H 6 Species
The corresponding Gibbs energy profile for Os(+) species is shown in Figure 3. Once again the sextet is the most stable state of Os(+). As acetylenes are added, the system is stabilized; in this case the doublets are favored. Doublets of species 5, 7A, and 9 are energetically accessible for Os(+) systems, in contrast to the case for Fe(+) systems. Note that, for each system, species 6 seems to be highly energetic and thus unlikely to be populated. In further contrast to the Fe(+) systems, the doublets of Os(+) species 10-14 are all available. The structures 10, 11, and 13 have particularly stable doublets. The Os(+)-benzene ground-state doublet 15 can be formed with ease from species 13.
C 2021, 7, x FOR PEER REVIEW 4 of 16 species 14 are higher in energy than the quartet of species S1. The quartet and sextet of S2 return upon the reoptimization to the C2v structure of S1.

Energetics and Structures for Os(+)C6H6 Species
The corresponding Gibbs energy profile for Os(+) species is shown in Figure 3. Once again the sextet is the most stable state of Os(+). As acetylenes are added, the system is stabilized; in this case the doublets are favored. Doublets of species 5, 7A, and 9 are energetically accessible for Os(+) systems, in contrast to the case for Fe(+) systems. Note that, for each system, species 6 seems to be highly energetic and thus unlikely to be populated. In further contrast to the Fe(+) systems, the doublets of Os(+) species 10-14 are all available. The structures 10, 11, and 13 have particularly stable doublets. The Os(+)-benzene ground-state doublet 15 can be formed with ease from species 13. If we examine the quartet multiplicity system, which for structure 3 lies only about 0.5 eV higher in energy than the doublet, the passage to the quartets for 5, 10, 11, 12, 13 and especially 14 (for which the quartet is the ground state) are within energetic reach. From 14 only a modest energy investment is needed to liberate H2 and achieve the ground state quartet of S1. We remind the reader, that barring rapid collisional cooling, all the original energy in the system remains in the OsC6H6(+) cluster. If H2 departs the reaction zone, quartet OsC6H4(+) remains, as observed [5].

Comparison of MC6H6 Cation Energetics for M = Fe and Os
There are significant differences between the Fe(+) and Os(+) energy profiles:


A decline is found for both systems in BE as acetylenes are added. However, successive binding energies (BE) of acetylenes are about 50% greater for Os(+) than Fe(+).


The quartet is the ground state of the benzene-Fe(+) complex, consistent with other computational results [20]. The doublet is preferred for the benzene-Os(+) complex.


The energy requirement for expelling benzene and sextet Os(+) from the groundstate, doublet benzene-Os(+) is 3.67 eV, while producing a sextet Fe(+) from the ground-state quartet, benzene-Fe(+), requires 3.08 eV. This inhibits the benzene production for Os(+) relative to Fe(+). If we examine the quartet multiplicity system, which for structure 3 lies only about 0.5 eV higher in energy than the doublet, the passage to the quartets for 5, 10, 11, 12, 13 and especially 14 (for which the quartet is the ground state) are within energetic reach. From 14 only a modest energy investment is needed to liberate H 2 and achieve the ground state quartet of S1. We remind the reader, that barring rapid collisional cooling, all the original energy in the system remains in the OsC 6 H 6 (+) cluster. If H 2 departs the reaction zone, quartet OsC 6 H 4 (+) remains, as observed [5].

Comparison of MC 6 H 6 Cation Energetics for M = Fe and Os
There are significant differences between the Fe(+) and Os(+) energy profiles: • A decline is found for both systems in BE as acetylenes are added. However, successive binding energies (BE) of acetylenes are about 50% greater for Os(+) than Fe(+). This favors the production of C-O binding in the Os system.

•
The quartet is the ground state of the benzene-Fe(+) complex, consistent with other computational results [20]. The doublet is preferred for the benzene-Os(+) complex.

•
Species doublet 14 and doublets S1 and S2 are relatively high in energy for the Fe(+) system, but more accessible in the Os(+) system. This favors H 2 production for the heavy metal cation.

•
The energy requirement for producing H 2 from 14 leaving C 6 H 4 -Os(+) is substantial (0.78 eV) but the elimination product at 2.5 eV is lower in energy than the free benzene and separate Os(+), by 3.3 eV.

Reaction Paths for Extrusion of H 2 from OsC 6 H 6 Cation
It is observed that Os(+) activates the CH bond of acetylene, producing H 2 and leaving an OsC 6 H 4 cation residue [5]. Neither the pathway for H 2 production nor the structure of the residue has yet been defined, so we explored steps in the reaction. We begin with the seven-membered ring (Species 14 of Figure 1) and the complex of Os with benzene (Species 15 of Figure 1). We introduce a new naming scheme, Xn, with labels X = B for bicyclic and X = C for monocyclic species, and with n coding the number of H atoms attached to Os. For n = 1, 2, 3, the number of attached H atoms are 0, 1, and 2. Further descriptors are attached as needed.

Overview of the Reaction Network for the H 2 Extrusion from OsC 6 H 6 Doublet Cation
To provide an overview of the multiple reaction paths, the reaction network is sketched on a globe (Figure 4). We begin with the species B1c, the C 6v complex of Os(+) with benzene) and C1 (1-Osmacyclohept-2,4,6-triene), located on a slice of the sphere, defining a plane perpendicular to the poles and circumscribed by the "Arctic Circle". These OsC 6 H 6 (+) species have each of the six H atoms attached to its own C atom. They appear on the first of four planar slices of the sphere, the "Arctic Circle". The second slice, the "Tropic of Cancer", contains C2 and B2 cis and trans; these species have a single H atom attached to osmium. Reaction paths connecting C1 with C2 and also B1c with B2 cis and trans species are shown by the curved lines. These paths pass through transition states each marked by an asterisk. It is also possible to interconvert C1 with B1c, and C2 with B2 cis and trans; such paths are marked by straight lines passing through transition states marked by X. Similarly, we find C3 and B3 structures with two H atoms connected to osmium on the "Tropic of Capricorn" with analogous reaction paths. Finally, at the "Antarctic Circle" we find species, C4 and B4, which have the formula OsC 6 H 4 (+); the H 2 is extruded.     We explore the reaction paths beginning with the lowest energy structure for the OsC 6 H 6 cation, which is the C 6v complex of Os with benzene with a doublet spin state. We call this "B1 closed" or B1c ( Figure 5). Is there a path from this species allowing the production of H 2 ? Table 1 contains Gibbs energy values in Hartrees and relative Gibbs energies in eV for species that we identify as we progressing through the B-path. The first step must be a H transfer from C to Os. We find a transition state at 2.645 eV for that H transfer. An intrinsic reaction coordinate passing through that transition state from B1c leads to an HOs-C 6 H 5 cation at 1.361 eV. The protonated osmium atom is coordinated (η3) to the C 6 H 5 ring in this structure, which we call "B2 closed" or B2c. This species can pass to the B2 cis lying at 1.734 eV through a transition state at 2.285 eV. A conversion to B2 trans (at 2.380 eV) requires a passage through a TS at 2.039 eV.

Continuation of the B Path toward H2 Extrusion.
The second H transfer passes over a small barrier to produce a structure we call "ortho", B3, with the two Os-H bonds, perpendicular and parallel to the molecule's C6H4 hydrocarbon plane, respectively. (See Figure 6.) The cis and trans isomers of bicyclic H2OsC6H4 are very close in energy to the ortho form; they can be easily interconverted.   B2 cis and B2 trans can be interconverted by the clockwise or anticlockwise twist of the torsion angle C-C-Os-H around an Os-C bond. The lower energy path (with a TS at 2.039 eV) breaks an Os-C bond entirely and detaches the Os atom from the phenyl ring, while the higher energy path (with a TS at 2.202 eV) only weakens the Os-C bond to the hydrogenated alpha C so that the bicyclic nature of the structure is preserved and the Os atom stays above the phenyl plane.
B2 trans, lying at 1.610 eV, need only surmount a small barrier of 0.121 eV to arrive at B3 ortho lying at 1.633 eV. (See Table 1.) Similarly, B2 cis lies at 1.734 eV encounters a

Continuation of the B Path toward H 2 Extrusion
The second H transfer passes over a small barrier to produce a structure we call "ortho", B3, with the two Os-H bonds, perpendicular and parallel to the molecule's C 6 H 4 hydrocarbon plane, respectively. (See Figure 6.) The cis and trans isomers of bicyclic H 2 OsC 6 H 4 are very close in energy to the ortho form; they can be easily interconverted.
B2 cis and B2 trans can be interconverted by the clockwise or anticlockwise twist of the torsion angle C-C-Os-H around an Os-C bond. The lower energy path (with a TS at 2.039 eV) breaks an Os-C bond entirely and detaches the Os atom from the phenyl ring, while the higher energy path (with a TS at 2.202 eV) only weakens the Os-C bond to the hydrogenated alpha C so that the bicyclic nature of the structure is preserved and the Os atom stays above the phenyl plane.
B2 trans, lying at 1.610 eV, need only surmount a small barrier of 0.121 eV to arrive at B3 ortho lying at 1.633 eV. (See Table 1.) Similarly, B2 cis lies at 1.734 eV encounters a modest barrier, 0.188 eV on its way to B3 ortho. B3 ortho at 1.633 eV can find its way to B3 trans at 1.590 eV by surmounting a modest barrier of 0.254 eV.
B3 ortho can easily interconvert to an equivalent form B3 ortho. These isomers are separated by a very low barrier (0.054 eV). See Figure 7.
Loss of H 2 from B3 ortho to produce B4 is endothermic by 0.893 eV ( Table 1). The energy to affect the extrusion is available only if the original Os(+):3HCCH cluster is not rapidly cooled in the course of reaction. This is evidently the case for the experimental observation of a very low-pressure gas-phase system [5]. 3.4.4. Overview of the C Reaction Path for H 2 Extrusion from 1-Osma-cyclohepta 2,4,6-triene (C1) An alternative path for hydrogen extrusion may be traced from monocyclic 1-Osmacyclohepta 2,4,6-triene (Species 14 in Figure 1 above). We call this structure C1. Gibbs energies in Hartrees and the relative energies in eV are collected in Table 2. C1 lies at 1.518 eV relative to the C 6v cationic complex of Os with benzene. The first H transfer to Os shown in Figure 9 generates species C2 at 1.236 eV, after passing through a TS at 2.243 eV; that is, over a barrier of 0.725 eV. Table 2. Energetics (ωB97XD/def2-tzvp) for landmarks along the C path for H transfer to polycyclic Os species from the most stable C species of OsC 6 H 6 cation. Species labels and Gibbs energies (G) in Hartrees are reported along with relative Gibbs energies in electron volts (eV). The energy reference point is the energy of the C 6v complex of the Os cation with benzene, OsC 6 H 6 + (see Table 1).  Figure 11 C 2021, 7, x FOR PEER REVIEW 10 of 16 Figure 8. Landmarks for the first proton transfer to Os, which can take place on the cyclic scaffold (the Cyclic Path C, steps C1 to C2). 3. 4. 5. Second H Transfer (C path)

Species
The second H transfer for the C species is shown in Figure 9. The destination C3 (monocyclic H2OsC6H4) can exist in cis and trans forms, which lie 0.715 and 0.974 eV above C2, respectively (See Table 2). The barriers opposing the passage of C2 to C3 cis and trans are large: 1.633 and 1.758 eV, respectively. Although C2 seems accessible, from B2 (see Figure 8. Landmarks for the second proton transfer to Os for the cyclic scaffold (the Cyclic Path C, steps C2 to C3) which may branch to "cis" and "trans" pathways, to cis-H 2 OsC 6 H 4 or trans-H 2 OsC 6 H 4 . Figure 9. Landmarks for the second proton transfer to Os for the cyclic scaffold (the Cyclic Path C, steps C2 to C3) which may branch to "cis" and "trans" pathways, to cis-H2OsC6H4 or trans-H2OsC6H4. 3.4. 6. Can Crossover from C to B Paths Occur? Figure 10 shows the passage from C2 to B2 cis and trans. The barriers are 1.063 and 1.144 eV, respectively (Table 3). This reinforces the notion that C2 may be a trap, from which the system must only retreat.
B3 trans which lies at 1.590 eV is 0.363 eV more stable than B3 cis. The barrier impeding passage from B3 trans to C3 trans is estimated as 1.364 eV, so the crossover to the C path seems quite unlikely.

Second H Transfer (C Path)
The second H transfer for the C species is shown in Figure 8. The destination C3 (monocyclic H 2 OsC 6 H 4 ) can exist in cis and trans forms, which lie 0.715 and 0.974 eV above C2, respectively (See Table 2). The barriers opposing the passage of C2 to C3 cis and trans are large: 1.633 and 1.758 eV, respectively. Although C2 seems accessible, from B2 (see below) it would not be feasible to advance further along the C path. 3.4.6. Can Crossover from C to B Paths Occur? Figure 10 shows the passage from C2 to B2 cis and trans. The barriers are 1.063 and 1.144 eV, respectively (Table 3). This reinforces the notion that C2 may be a trap, from which the system must only retreat.  We explored the possibility of the interconversion of the residues B4 and C4 (Table  3). We found that the barrier for the passage of C4 (at 3.214 eV) to B4 (at 2.530 eV) was modest, only 0.256 eV. However, the reverse path would have to surmount a barrier of 0.960 eV. Therefore, we see no opportunity for the crossover to the C path from the B path at this stage. 3.4.7. Extrusion of H2 from OsC6H6 (+) If in fact C3 cis and trans species were to be formed, the endothermicity for H2 extrusion ( Figure 11) would be 1.263 eV for C3 cis and 1.004 eV for C3 trans ( Table 2).
The passage from B3 ortho to B4 and H2 (Table 1), and also the passage from C3 cis to C4 and H2, ( Table 2) do not admit a description of transition states. The potential energy curve for the production of H2 from B3 ortho is smoothly uphill with no hint of a transition state. The dissociation from C3 cis is likewise uphill without a transition state. Overcoming the energy cost requires that the reactive cluster is not rapidly cooled. This need may well be met in a low-pressure gas, but this is less likely in a condensed phase.   3.470 B3 trans which lies at 1.590 eV is 0.363 eV more stable than B3 cis. The barrier impeding passage from B3 trans to C3 trans is estimated as 1.364 eV, so the crossover to the C path seems quite unlikely.
We explored the possibility of the interconversion of the residues B4 and C4 (Table 3). We found that the barrier for the passage of C4 (at 3.214 eV) to B4 (at 2.530 eV) was modest, only 0.256 eV. However, the reverse path would have to surmount a barrier of 0.960 eV. Therefore, we see no opportunity for the crossover to the C path from the B path at this stage. 3.4.7. Extrusion of H 2 from OsC 6 H 6 (+) If in fact C3 cis and trans species were to be formed, the endothermicity for H 2 extrusion ( Figure 11) would be 1.263 eV for C3 cis and 1.004 eV for C3 trans ( Table 2).
The passage from B3 ortho to B4 and H 2 (Table 1), and also the passage from C3 cis to C4 and H 2 , (Table 2) do not admit a description of transition states. The potential energy curve for the production of H 2 from B3 ortho is smoothly uphill with no hint of a transition state. The dissociation from C3 cis is likewise uphill without a transition state. Overcoming the energy cost requires that the reactive cluster is not rapidly cooled. This need may well be met in a low-pressure gas, but this is less likely in a condensed phase. C 2021, 7, x FOR PEER REVIEW 13 of 16 Figure 11. Landmarks for the extrusion of H2 from cationic H2OsC6H4 cis and trans C3 and from B4.

Discussion
We located landmarks on the reaction paths producing H2 from OsC6H6 cationic species. While we must assume that the reactive cluster has abundant energy to affect the extrusion of dihydrogen, the potential surface must still favor a particular flow. We distinguished the B paths (in which the reacting species are bicyclic 6.1.0 rings) from the C paths (in which the species are monocyclic seven-membered rings) and also allowed the possibility of crossover. Figures 12 and 13 show what we consider to be the most significant of the many possible passages from B1c to H2 and a residue, either B4 or C4.

Discussion
We located landmarks on the reaction paths producing H 2 from OsC 6 H 6 cationic species. While we must assume that the reactive cluster has abundant energy to affect the extrusion of dihydrogen, the potential surface must still favor a particular flow. We distinguished the B paths (in which the reacting species are bicyclic 6.1.0 rings) from the C paths (in which the species are monocyclic seven-membered rings) and also allowed the possibility of crossover. Figures 12 and 13 show what we consider to be the most significant of the many possible passages from B1c to H 2 and a residue, either B4 or C4.

Discussion
We located landmarks on the reaction paths producing H2 from OsC6H6 cationic species. While we must assume that the reactive cluster has abundant energy to affect the extrusion of dihydrogen, the potential surface must still favor a particular flow. We distinguished the B paths (in which the reacting species are bicyclic 6.1.0 rings) from the C paths (in which the species are monocyclic seven-membered rings) and also allowed the possibility of crossover. Figures 12 and 13 show what we consider to be the most significant of the many possible passages from B1c to H2 and a residue, either B4 or C4.    Figure 12 shows the possible evolution from B1c. We had little choice in the first step but to produce B2c and then B2 cis, even though the passage was endothermic by 1.734 eV and surmounted a barrier of 2.52 eV. B2 cis can interconvert easily to the slightly more stable B2 trans at 1.610 eV, facing a barrier of 0.355 eV.
B2 cis or trans could form B3 ortho by overcoming the small barriers of 0.188 eV or 0.105 eV. Then, B3 ortho can generate B4 and H2 at a cost of 0.897 eV. B2 cis or trans could cross over to the much more stable C2 (1.236 eV), opposed by perhaps surmountable barriers of 0.555 eV or 0.688 eV, respectively. Figure 13 shows that from there it is uphill to C3 cis or trans at 1.951 or 2.21 eV, over high barriers of 0.918 or 0.784 eV. The production of C4 and H2 requires 1.263 eV from C3 cis or 1.004 eV from C3 trans.
We conclude then that a likely reaction path is B1c to B2c to B2 cis; followed by the possible isomerization to B2 trans and production of B3 ortho. If C1 is populated the system could find its way to C2, which could then convert to B2 and continue along the path already described.
How can we discern any features of the paths actually followed? C2 and B2 trans may be the longest-lived intermediate species for the systems with a single H transfer, and C3 cis and B3 ortho among systems for systems with a second H transfer would have very different IR spectra. Likewise, the residues from H2 extrusion, C4 and B4, would have very different IR spectra. While the experimental challenges would be considerable, distinguishing some aspects of the reaction net may be possible.

Conclusions
Using density functional methods, we have evaluated the energies and structures of species evolving from the benzene complex of the osmium cation, OsC6H6 (+), and an isomeric seven-membered unsaturated ring, tracing reaction paths that lead to the evolution of hydrogen gas. The experimental facts [5], based on gas-phase observations of species produced from clusters of acetylene with osmium, revealed no direct structural information. A more detailed examination of the mass spectrometry data may offer proof of such smaller clusters such as those suggested by our density functional modeling.  Figure 12 shows the possible evolution from B1c. We had little choice in the first step but to produce B2c and then B2 cis, even though the passage was endothermic by 1.734 eV and surmounted a barrier of 2.52 eV. B2 cis can interconvert easily to the slightly more stable B2 trans at 1.610 eV, facing a barrier of 0.355 eV.
B2 cis or trans could form B3 ortho by overcoming the small barriers of 0.188 eV or 0.105 eV. Then, B3 ortho can generate B4 and H 2 at a cost of 0.897 eV.
B2 cis or trans could cross over to the much more stable C2 (1.236 eV), opposed by perhaps surmountable barriers of 0.555 eV or 0.688 eV, respectively. Figure 13 shows that from there it is uphill to C3 cis or trans at 1.951 or 2.21 eV, over high barriers of 0.918 or 0.784 eV. The production of C4 and H 2 requires 1.263 eV from C3 cis or 1.004 eV from C3 trans.
We conclude then that a likely reaction path is B1c to B2c to B2 cis; followed by the possible isomerization to B2 trans and production of B3 ortho. If C1 is populated the system could find its way to C2, which could then convert to B2 and continue along the path already described.
How can we discern any features of the paths actually followed? C2 and B2 trans may be the longest-lived intermediate species for the systems with a single H transfer, and C3 cis and B3 ortho among systems for systems with a second H transfer would have very different IR spectra. Likewise, the residues from H 2 extrusion, C4 and B4, would have very different IR spectra. While the experimental challenges would be considerable, distinguishing some aspects of the reaction net may be possible.

Conclusions
Using density functional methods, we have evaluated the energies and structures of species evolving from the benzene complex of the osmium cation, OsC 6 H 6 (+), and an isomeric seven-membered unsaturated ring, tracing reaction paths that lead to the evolution of hydrogen gas. The experimental facts [5], based on gas-phase observations of species produced from clusters of acetylene with osmium, revealed no direct structural information. A more detailed examination of the mass spectrometry data may offer proof of such smaller clusters such as those suggested by our density functional modeling.
This work deals with the evolution of dihydrogen from acetylene by the simplest possible process involving single-heavy-atom catalysis. The details of the structure of intermediate species presented here may find their counterparts in single-atom catalysis, involving graphene and solid-state surfaces, adding depth to the description of practical conversion processes.