Article pubs.acs.org/JPCA
Cite This: J. Phys. Chem. A 2018, 122, 4246−4251
Kinetics of First-Row Transition Metal Cations (V+, Fe+, Co+) with OCS at Thermal Energies Brendan C. Sweeny, Shaun G. Ard,* Nicholas S. Shuman, and Albert A. Viggiano Space Vehicles Directorate, Air Force Research Laboratory, Kirtland Air Force Base, New Mexico 87117, United States ABSTRACT: The temperature-dependent kinetics for reactions of V+, Fe+, and Co+ with OCS are measured using a selected ion flow tube apparatus heated to 300−600 K. All three reactions proceed solely by C−S activation at thermal energies, resulting in metal sulfide cation formation. Previously calculated reaction pathways were employed to inform statistical modeling of these reactions for comparison to the data. As surmised previously, all three reactions at thermal energies require spin crossing, with the Fe+ reaction crossing once circumventing a prohibitive transition state, before crossing again to form ground state products. The Fe+ and Co+ reaction efficiencies increase with energy. For the Co+ reaction, and to a lesser extent the Fe+ reaction, the apparent activation energies are less than the reaction endothermicities, possibly indicating increasing diabatic behavior of the spin crossings with energy. The V+ reaction was well modeled assuming an entirely adiabatic spin crossing, such that the resultant avoided crossing behaves similarly to a tight transition state. The subsequent reaction of VS+ with OCS producing VS2+ is also investigated; the rate-limiting transition state energy derived from statistical modeling is poorly reproduced by quantum calculations using a variety of methods, highlighting the large (1−2 eV) uncertainty in calculated energetics of transition-metal containing species.
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INTRODUCTION Understanding the fundamental behavior of metal sulfides is critical for many applications in biochemistry and in catalysis. At the molecular level, metal sulfides, specifically Fe−S, constitute redox centers in some metalloproteins and are active sites for many enzymes where they can reduce sulfide bonds and initiate radical reactions.1 At the nanoscale, metal sulfide nanostructures provide a unique combination of photoresponse and surface catalytic activity.2 Carbonyl sulfide (OCS) is the most abundant and naturally occurring sulfur containing compound in the atmosphere and plays a significant role in the Earth’s sulfur cycle.3 From a catalytic perspective, OCS is a common intermediate for the synthesis of sulfur containing organic compounds, particularly pesticides. Theoretical treatments of reactions between a variety of metal cations and OCS have been performed.4−6 However, a clear experimental basis for this treatment has been lacking for some metals and the fundamental mechanistic details are only qualitatively understood. Probing metal sulfide reactions in the gas phase provides fundamental kinetic information in a controlled environment that is otherwise prohibitively difficult to attain in the condensed phase, such as the adiabatic behavior of the reaction mechanism. Analyzing reactions in the gas phase allows for the characterization of spin-catalyzed reactions. Evidence of electronic state dependence on reactivity7 lead to the introduction of the concept of two-state reactivity (TSR),8,9 where spin-crossing to a potential energy surface of an excited © 2018 American Chemical Society
electronic state enables access to a lower energy pathway. In many cases, TSR can lower or completely circumvent barriers to product formation. This behavior can be characterized well by probing the temperature-dependent kinetics.8,10,11 Previously, Armentrout, Schwarz, and co-workers concluded that the activation of the weakly bound C−S bond was the preferred pathway for reactions between metal cations (Co+ and Fe+) and OCS.12,13 Furthermore, it was suggested that multiple spin-crossing events were required in the case of Fe+, resulting in a relatively low efficiency compared to Co+ at large reaction energies.12 Here, we expand upon their initial observations with temperature-dependent kinetics for Fe+, Co+, and V+ with OCS at thermal energies. Temperaturedependent kinetics at thermal energies are often a sensitive probe of mechanistic details and can elucidate the effects of spin crossing on the reaction kinetics. The data are compared to results of statistical modeling based on previously calculated reaction coordinates for these systems in order to elucidate further details of the C−S activation by these first row transition metal cations. Received: February 23, 2018 Revised: April 2, 2018 Published: April 2, 2018 4246
DOI: 10.1021/acs.jpca.8b01841 J. Phys. Chem. A 2018, 122, 4246−4251
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The Journal of Physical Chemistry A
Table 1. Rate Constants, Reaction Efficiencies, And Higher Order Chemistry Observed for Reactions of Fe+, Co+, and V+ with OCS T (K)
reaction 6
Fe + OCS → FeS + CO
3
Co+ + 1OCS → 5CoS+ + 1CO
+
1
6
+
1
V + 1OCS → 3VS+ + 1CO
5 +
a
300 400 500 600 400 500 600 300 400 500 600
k (10−10 cm3 s−1)
k/kcolla
higher order bimolecular products observed
± ± ± ± ± ± ± ± ± ± ±
0.20 0.21 0.24 0.28 0.02 0.04 0.05 0.36 0.26 0.22 0.22
FeS2+, FeS3+, FeS4+
2.4 2.5 2.7 3.2 0.27 0.41 0.52 4.4 3.1 2.5 2.5
0.6 0.6 0.7 0.8 0.07 0.10 0.13 1.1 0.8 0.6 0.6
CoS2+, CoS3+, CoS4+
VS2+, VS3+, VS4+
kcoll is calculated employing the parametrization theory of Su and Chesnavich.18
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EXPERIMENTAL SECTION All measurements were performed on a variable temperature selected ion flow tube (VT-SIFT) at the Air Force Research Laboratory described in detail previously.14,15 The metal ions studied here, Fe+, Co+, and V+ were formed using a glow discharge rod source based on the design used by Armentrout and also described in detail elsewhere.16 Briefly, approximately 1 std. L min−1 of a 10:1 He to Ar gas mix flowed over a 1/4″ rod of the appropriate metal at approximately 1 Torr. The metal rod was biased between −1 and −4 kV, resulting in a discharge of 10−30 mA between the rod and a 6 cm diameter grounded can surrounding the discharge area. This discharge produces Ar+ which subsequently impacts the metal rod at high energies sputtering neutral and ionic metal species. The ions are then extracted through a biased nose cone into a differentially pumped region and the ion of interest is mass selected using a quadrupole mass filter. The ion is then injected via a Venturi inlet into the flow tube in a 13 std. L min−1 laminar flow of He. Approximately 104−105 collisions thermalize the ions at the temperature of the flow tube (300−600 K) controlled by resistive heating. OCS is introduced 59 cm before the end of the flow tube, which results in reaction times on the order of 3 ms. Remaining reactant ions as well as resultant product ions are extracted through a 3 mm aperture in a rounded nosecone, transported using a rectilinear ion guide and probed with an orthogonal accelerated time-of-flight mass spectrometer. Rate constants are extracted by monitoring the decrease in reactant ion signal as a function of OCS concentration, with complete mass spectra stored at every flow point. Each ion peak is integrated to get the total ion counts. We have found negligible mass discrimination over the ranges relevant to the systems studied here. No evidence of excited state ions was observed, consistent with Armentrout’s finding that ions produced in a source of this type are primarily ground state. Errors in the rate constants are estimated to be ±15% relative and ±25% absolute.15
Co+ + 1OCS → 5CoS+ + 1CO; Δr H0° = 0.19 ± 0.09 eV
3
5
RESULTS AND DISCUSSION The three primary reactions studied here in eqs 1,12 2,12 and 317 Fe+ + 1OCS → 6 FeS+ + 1CO; Δr H0° = 0.06 ± 0.04 eV
+
V + 1OCS → 3 VS+ + 1CO; Δr H0° = − 0.58 ± 0.09 eV
(3)
vary from endothermic (Co+) to thermoneutral (Fe+) and to exothermic (V+) due to the strength of the metal sulfide bond formed. As previously observed at higher translational energies in GIB studies,12 each of these metal cations activates the C−O bond of OCS; however, the strength of O−CS bond (6.88 eV) is such that the metal oxide cation producing channels are all significantly endothermic and cannot occur at thermal energies. The rate constants measured for reactions 1−3 are shown in Table 1. All three metals were found to yield only metal sulfide ions in the primary bimolecular reaction at all temperatures studied. Chemistry of the metal sulfide product ions resulted in further sulfur addition to the ions, with an apparent coordination sphere of 4 for all metals studied. In addition to the bimolecular S addition, some of the secondary reactions involved clustering. Co+ was also observed to cluster with OCS at room temperature, which concealed the slow bimolecular rate for this reaction, precluding a determination of the rate constant. Cations with one or more sulfur additions often showed significant propensity toward clustering with OCS, undermining attempts at quantifying the latter reactions, with the exception of the VS+ + OCS reaction (see below). The reactions of both Fe+ and Co+ with OCS display enhanced efficiency with increasing temperature. Arrhenius plots of these dependencies are shown in Figure 1, along with the apparent activation energies as determined from the fit to the data. The reaction of Fe+ with OCS has an activation energy of 13 ± 10 meV, which agrees within mutual uncertainty with the overall endothermicity of the reaction determined by Armentrout et al. as 60 ± 40 meV.12 The Co+ reaction’s temperature dependence displays an activation energy of 68 ± 15 meV, somewhat smaller than the reaction endothermicity of 190 ± 90 meV. Additional insight into the temperature dependencies can be gained by consideration of the reaction coordinates as calculated elsewhere using the B3LYP functional, see Figure 2.4,5 The Co+ reaction begins on a triplet surface, but must cross over to a quintet surface coupled to ground state CoS+. Spin allowed production of 3CoS+ is calculated to lie over 0.5
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DOI: 10.1021/acs.jpca.8b01841 J. Phys. Chem. A 2018, 122, 4246−4251
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interplay between sextet and quartet surfaces has been observed in reactions of FeO + with both H 2 and CH 4 . 10,19,20 Interestingly, in both cases it was determined that the initial crossing behaves adiabatically, having little kinetic effect. The second crossing was found to have both adiabatic (spincrossing) and diabatic (spin-conserving) components leading to production of both ground and excited state products.10,21 In the present experiments at thermal energies, any diabatic component is significantly hindered energetically and thus likely to lower reaction efficiency as the complex dissociates back to reactants. Armentrout has observed an increase in diabatic behavior with increased translational energy for several systems.12,17 If that were the case here, the increased reactivity with increasing energy would be mitigated by the increased diabaticity of the spin crossings, manifesting as apparent activation energies smaller than expected from Arrhenius behavior with a known endothermic barrier, such as observed here. Theoretical treatment of spin crossing is not trivial by any means, however for the reactions of Fe+ and Co+ with OCS they may prove paramount in understanding the temperature dependencies of these reactions. In contrast to the Fe+ and Co+ reactions, the reaction of V+ with OCS displays a negative dependence with temperature. This is a common behavior in exothermic ion−molecule reactions where the rate limiting transition state lies below the reactant energy.22 As temperature increases, the entropic preference of returning to reactants becomes increasingly dominant over the energetic preference of crossing the transition state. As with the Co+ reaction, this reaction is not spin allowed and a crossing from the quintet surface associated with ground state vanadium cation to the triplet surface associated with ground state VS+ is required for reaction at thermal energies. Distinct from the other reactions discussed here, the crossing from the quintet to triplet surfaces takes place prior to the transition state on the quintet surface, while the transition state on the triplet surface occurs prior to the crossing. The reaction coordinate offers a pathway to products around the transitions states, i.e. the rate limiting step is the crossing probability and not passage over either of the transition states. It is interesting that the apparent effect on the overall reaction efficiency of passing through this curve crossing leads to a negative temperature dependence similar to that expected for a reaction in which the efficiency is controlled by a submerged tight transition state. For further insight, we apply statistical modeling methods, described in detail elsewhere,23 to reproduce the observed rate constants. The crossing point described elsewhere at the B3LYP/6-311+G(d) level was identified and a normal-mode analysis performed. Calculating the potential along five identified real vibrational modes shows that the crossing point structure is at an energetic minimum along each, and that a harmonic approximation of the frequency is reasonable. A single identified imaginary frequency does not lie at an energetic maximum, this not being a stationary point, but appears to lie directly along the reaction coordinate leading to the actual transition state. Since the imaginary frequency is not used in the statistical calculations, we attempt to treat this crossing point as though it were a tight transition state within the rigid Rice−Ramsperger−Kassel−Marcus (RRKM) framework. This leads to the modeled fit to the experimental rate constants shown in Figure 3. While perhaps fortuitous, this treatment, without adjustment of the calculated energetics or frequencies, reasonably reproduces both the magnitude and
Figure 1. Rate constants for the reactions of Fe+ and Co+ with OCS as a function of inverse temperature. Arrhenius fits to the data result in apparent activation energies as shown.
Figure 2. Calculated reaction coordinates for metal cations and OCS:4−6 (A) Co+ + OCS; (B) Fe+ + OCS; (C) V+ + OCS. Orange and blue represent low and high spin states, respectively. Energy values adapted from refs 4−6.
eV above the ground state, and thus not likely to be contributing at these energies. The Fe+ reaction is spin allowed, as both Fe+ and FeS+ have sextet ground states. However, as surmised by Armentrout, Schwarz, and co-workers without the benefit of quantum chemical calculations, the reactant intermediate complex has a quartet ground state.12 Thus, the purely adiabatic pathway for this reaction involves a spin crossing in the vicinity of the reactant intermediate, which allows for circumvention of an energetically prohibitive transition state on the sextet surface. This is followed by another spin crossing in the vicinity of the product intermediate to form ground state products. This 4248
DOI: 10.1021/acs.jpca.8b01841 J. Phys. Chem. A 2018, 122, 4246−4251
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Figure 4. VS+ + OCS experimental rate constants with fit from statistical modeling (see text).
Figure 3. V+ + OCS experimental rate constants with fit from statistical modeling (see text). Error bars represent the 15% relative uncertainty between temperatures.
path using statistical theory (Figure 4) while treating the TS energy as an adjustable parameter suggests that an energy of −0.4 ± 0.2 eV relative to reactants is consistent with the experimental results. This brings about the question as to whether an error of 1 eV in the calculated energy is reasonable. The reported energy was calculated at the B3LYP level using the DZVP basis set on V and TZVP basis set on all other atoms. A recent survey of density functional methods on firstrow transition metal bond energies27 reports mean average deviations of about 0.3−0.6 eV, which translates to a 2σ uncertainty of 1−2 eV.28 The B3LYP functional specifically has an uncertainty of ∼1.5 eV, suggesting that it is reasonable for the calculated TS energy to have been overestimated and that the reaction path is correct. To illustrate this point, we have calculated both the TS energy and the reasonably well-known VS+ 0K bond dissociation energy (BDE)17,25 using a variety of functionals as well as the MP2 and B2PLYP methods with the 6-311++G(d,p) and def2-TZVP basis sets using the Gaussian 09 software. The resulting scatter plot (Figure 5) shows that the uncertainties are indeed quite large, no method is particularly reliable, and that there is a general bias for methods
temperature dependence of the experimental data. This suggests that the surfaces may be strongly coupled and the spin crossing behaving purely adiabatically, with the energetic maximum along the adiabatic path acting as a de facto stationary point and rate-limiting submerged transition state. While most of the higher order chemistry observed for reactions 1−3 was obscured by competition with tertiary association channels, reaction 424,25 VS+ + OCS → VS2+ + CO; Δr H0° = − 0.75 ± 0.11 eV
(4)
was observed without this ambiguity. The rate constants for this reaction are listed in Table 2, and shown in Figure 4. Table 2. Rate Constants and Reaction Efficiencies Observed for the Reaction of VS+ with OCS 3
reaction
T (K)
VS+ + 1OCS → 3VS2+ + 1CO
300 400 500 600
k (10−10 cm3s−1)
k/kcolla
± ± ± ±
0.49 0.24 0.23 0.19
5.4 2.6 2.4 2.0
1.9 0.9 0.8 0.7
a
kcoll is calculated employing the parametrization theory of Su and Chesnavich18
The magnitude and temperature dependence of reaction 4 is very similar to that of reaction 3. The uncertainties attributed to these rate constants (±25% relative and ±35% absolute) are larger than those for the primary reaction rates due to their higher order nature. Unlike reaction 3, which requires crossing from the quintet to triplet surface, reaction 4 is calculated to take place entirely on the triplet surface.26 Two different pathways were calculated leading to two different isomers of VS2+, although only one isomer is calculated to be energetically accessible at thermal energies. Production of this isomer is limited by a three-centered transition state, calculated to lie 0.59 eV above the reactant energy, too large a barrier to be consistent with the observed reaction efficiencies. Reasonable explanations are either that an alternative, lower energy, reaction path exists and was not identified, or that the reaction path is correct, but the calculated energy of the TS is significantly overestimated. Modeling the reported reaction
Figure 5. Calculated zero-point corrected VS+ 0K BDE and the energy of the rate-limiting TS relative to reactants in the VS+ + OCS reaction using the indicated methods with either the 6-311G++(d,p) (red) or def2-TZVP (black) basis sets. Experimentally derived values (solid red lines) and uncertainties (dashed red lines) are indicated. 4249
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to overestimate the TS energy in this case, less so with the TZVPP basis set than with 6-311++G(d,p). We note that the uncertainties in the calculated BDE appear compatible with the uncertainties in first-row transition metal BDEs reported elsewhere,27 and that the uncertainties in the calculated TS energy appear to be of a similar magnitude.
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CONCLUSION We have presented the temperature-dependent rate constants of C−S activation of OCS by first row transition metal cations Fe+, Co+, and V+. The room temperature efficiencies of the reaction are primarily an effect of the metal sulfide bond strength of the formed metal sulfide cation, VS+ > FeS+ > CoS+. As previously identified, all three systems require spin crossing for thermal reaction, as the spin allowed products for the V+ and Co+ systems are energetically inaccessible, and the spin allowed Fe+ reaction requires two spin crossings as the transition state on the ground state sextet surface lies significantly above reactant energies. Both the Fe+ and Co+ reactions display increased efficiency with energy, consistent with the slight endothermicity of these reactions. Arrhenius fits to the data, however, result in apparent activation energies smaller than their respective reaction endothermicities, possibly indicating increasing ineffectiveness of the required spin crossing with increased energy. The V+ reaction displayed a negative temperature dependence, consistent with a purely adiabatic spin crossing which was well modeled, allowing the spin crossing to effectively function as a tight transition state. Detailed calculations on these systems, specifically in the vicinity of these curve crossings, would greatly inform the interpretation of these temperature dependent data, as well as advance the understanding of the kinetic role of spin crossings in reactions such as this. However, the spin-allowed reaction of VS+ highlights the caution required with computation on these systems. The reaction was well modeled with a transition state energy significantly lower than previously calculated. Further calculations employing a variety of common methods and basis sets found substantial variance on both this transition state energy, as well as the well-known V−S+ bond energy. Clearly, continued computational development as well as more experimental data from a range of systems are needed for comparison and to develop a detailed understanding of the fundamental reaction mechanisms for transition metal systems.
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Article
AUTHOR INFORMATION
Corresponding Author
*(S.G.A.)
[email protected]. ORCID
Brendan C. Sweeny: 0000-0001-5066-417X Nicholas S. Shuman: 0000-0002-0274-2644 Albert A. Viggiano: 0000-0002-8638-2446 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Air Force Office of Scientific Research (AFOSR-16RVCOR276). B.C.S. is supported by the National Research Council Research Associateship Program. S.G.A. is supported through the Institute for Scientific Research of Boston College under Contract No. FA9453-10-C-0206. 4250
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