Lanthanides as Catalysts: Guided Ion Beam and Theoretical Studies

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Lanthanides as Catalysts: Guided Ion Beam and Theoretical Studies of Sm+ + COS Peter B. Armentrout, Richard M Cox, Brendan C. Sweeny, Shaun G Ard, Nicholas S. Shuman, and Albert A Viggiano J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09905 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 25, 2017

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The Journal of Physical Chemistry

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Submitted to J. Phys. Chem. A

Lanthanides as Catalysts: Guided Ion Beam and Theoretical Studies of Sm+ + COS P. B. Armentrout,1,* Richard M Cox,1,† Brendan C. Sweeny,2 Shaun G. Ard,2 Nicholas S. Shuman,2 and Albert A. Viggiano2 1

Department of Chemistry, University of Utah, Salt Lake City, UT 84112, USA

2

Air Force Research Laboratory, Space Vehicles Directorate, Kirtland AFB, New Mexico 87117

ABSTRACT: Reactions of samarium cations with carbonyl sulfide are examined using a guided ion beam tandem mass spectrometer and a variable temperature selected ion flow tube apparatus. Formation of SmS+ + CO is observed in both instruments with a kinetic energy and temperature dependence demonstrating a barrierless reaction occurring with an efficiency of 26 ± 9%. Formation of SmO+ + CS is also observed at high kinetic energies and exhibits a threshold determined as 2.81 ± 0.32 eV, substantially higher than expected from known thermochemistry. The potential energy surfaces for these reactions along sextet and octet spin surfaces are also examined theoretically at the MP2 and CCSD(T) levels. The observed barrier for oxidation is shown to likely correspond to the energy of the crossing between surfaces corresponding to the ground state electronic configuration of Sm+ (8F,4f66s1) and an excited surface having two electrons in the valence space (excluding 4f), which are needed to form the strong SmO+ bond. In contrast, the S-CO bond is activated much more readily because this crossing occurs at much lower energies. This result is attributed to the much weaker S-CO bond energy as well as the ability of sulfur to bind effectively at different angles. Although both reactions are spinforbidden, evidence for a more efficient spin-allowed process is also observed in the SmS+ + CO cross section. *Corresponding author: email: [email protected] †

Present address: Pacific Northwest National Laboratory, Richland, WA 99352, USA

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INTRODUCTION Lanthanides are potentially interesting catalysts as the 4f orbitals can potentially act as both sinks and sources for electron density. Because spin-orbit interactions are generally large for such heavy metal systems, conservation of spin is not expected to play an important role in their reactivity, although this aspect of reactivity has rarely been quantified. In order to understand the fundamental limitations associated with the possibility of such catalytic reactions, it is useful to examine whether the transfer of electrons from 4f orbitals into other valence orbitals is facile. This can potentially be examined in detail in the gas phase where complicating effects associated with solvation or solid state interactions cannot occur. An interesting application of lanthanide (Ln) reactivity has recently been explored by the Air Force Research Laboratory (AFRL).1 Ionospheric scintillation, a phenomenon that interferes with satellite communications,1 can potentially be mediated using the chemi-ionization process 1 that takes advantage of the abundance of atomic oxygen in the ionosphere. Ln + O → LnO+ + e–.

(1)

Three releases of samarium (Sm) from sounding rockets in the ionosphere have occurred.2-3 At the time of the atmospheric experiments, the previously reported thermochemistry suggested that reaction 1 was exothermic by ~0.3 eV;4 however, the level of ionization observed was substantially below pre-launch predictions. This disappointing result has subsequently been rationalized on the basis of new thermochemistry for reaction 1 where Ln = Sm.4 This study determined the exothermicity was only 0.08 ± 0.07 eV. Such a low exothermicity means that the reverse recombination reaction can occur with a large fraction of the ambient electrons present, thereby suppressing the plasma density generated. An interesting aspect of this previous work4 was the observation that several oxidants (CO2, COS, and NO) provided misleading thermochemical information. We have recently revisited the CO2 system, reaction 2,5 which is exothermic by 0.27 ± 0.07 eV, Sm+ + CO2 → SmO+ + CO


(2)

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yet exhibits a large barrier of 1.77 ± 0.11 eV. The reverse reaction was also studied, exhibiting a barrier of 2.04 ± 0.13 eV, consistent with the known exothermicity of the forward reaction. Studies also included examination of the thermodynamics of the Sm+(CO2) and OSm+(CO) intermediates, such that a fairly complete potential energy surface (PES) could be constructed from experimental data alone. This PES was compared with high level computations, which established that the observed barrier probably corresponds to the energy of the crossing between surfaces corresponding to the ground state electronic configuration of Sm+ (8F,4f66s1) and an excited surface having two electrons in the valence space (excluding 4f), which are needed to form the strong SmO+ bond. It was also found that the crossing occurred relatively high in energy in part because activation of the CO2 bond requires bending of the molecule. Note that these results indicate that movement of 4f electrons into the valence space needed for bonding is inefficient because the crossing between these diabatic surfaces occurs at elevated energies. COS is isovalent with CO2, such that their behavior is expected to be similar. However, as shown below, two reactions are observed in the present study corresponding to activation of either the CS or the CO bond. Sm+ + COS

→ SmS+ + CO

(3)

→ SmO+ + CS

(4)

The oxidation reaction 4 is shown to exhibit a barrier like that found for CO2, whereas the sulfidation reaction 3 has no barrier. Theory is then used to explore why activation of the two bonds is intrinsically so distinct. Interest in activation of COS by metals6-7 can also be linked to the potential importance in remediation efforts to remove this major sulfur containing compound from the environment.8-10

EXPERIMENTAL AND THEORETICAL METHODS Guided Ion Beam Tandem Mass Spectrometer. The guided ion beam tandem mass spectrometer (GIBMS) used in these studies has been described previously.11 Reactant ions were generated using a direct current discharge flow tube (DC/FT) source,12 in which Ar is ionized in



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a dc electric field of 1.2 – 1.4 kV and the ions then sputter metal cations from a cathode comprising a samarium foil sample. A flow of He/Ar carrier gasses (9:1 mixture at about 0.5 Torr) is used to carry the Sm+ ions down a 1 m long flow tube. Here Sm+ ions undergo ~105 collisions, which nominally thermalizes them. Previous work4-5 indicates that some excited electronic states may persist, so O2 or SO2 gas was also admitted to the flow tube about 15 cm downstream from the ion source. The DC/FT source has previously been shown to produce atomic metal cations with an internal electronic energy distribution that can be characterized by a temperature of 300 – 1100 K.13-17 Thus, 67.8% of Sm+ ions are found in the 8F1/2 ground level at 300 K, and decreases to 21.1% of the ions at 1100 K.18 Given a conservative estimate for the average internal temperature of the Sm+ ions of 700 ± 400 K, the ions have an average internal energy of 0.06 ± 0.05 eV. Sm+ ions were extracted from the source and the heaviest isotope,

154

Sm (22.7%

abundance), was selected using a magnetic momentum analyzer. These reactant ions were decelerated to well-defined kinetic energies, focused into a radiofrequency (rf) octopole ion beam guide,19-21 which acts as an efficient radial trap for the ions without impeding their passage along the axis. The octopole passed through a static gas cell containing the neutral reactant gas at pressures between 0.10 and 0.40 mTorr, which are low enough that reactions occurred under near single collision conditions. Residual reactant and product ions drifted to the end of the octopole, where they were focused into a quadrupole mass filter for mass analysis and counted using a Daly detector.22 Absolute reaction cross sections (uncertainties of ±20%) were determined using a procedure similar to Beer’s Law detailed elsewhere.20 Center-of-mass (CM) frame energies, which are used throughout the remainder of the manuscript, were determined by converting the laboratory ion energies (lab) using ECM = Elab × m/(m + M) where m is the mass of the COS neutral reactant and M is the mass of the samarium cation reactant. A retarding potential analysis in the octopole was used to measure the absolute zero of energy and the full width at half-maximum (FWHM, typically 0.4 – 0.6 eV, lab) of the ion beam.20 The absolute energy scale has an uncertainty of about 0.05 eV (lab), 0.014 eV (CM).


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5

A modified line-of-centers model, eq 5, was used to evaluate the kinetic energy dependence of endothermic reaction cross sections.21, 23-24 σ(E) = σ0 Σi gi (E + Ei – E0)n/E

(5)

Here σ0 is an energy-independent scaling factor, E is the relative kinetic energy of the reactants, Ei is the energy of the reactants’ electronic, vibrational, and rotational states having populations gi (Σgi = 1), n is an adjustable parameter controlling the shape of the cross section, and E0 is the 0 K reaction threshold. Eq 5 must be convolved with the kinetic energy distributions of the reactants before comparison to the data.20, 25-27 Parameters of eq 5, σ0, n, and E0, were optimized using a nonlinear least-squares method until they reproduce the experimental cross section. Uncertainties in these parameters were evaluated by modeling several independent data sets using a range of n values, with the threshold energy also including the absolute uncertainties in the internal energies of reactant ions and the absolute kinetic energy scale. VT-SIFT Apparatus. Thermal kinetic measurements were performed on a variable temperature selected ion flow tube (VT-SIFT) at the Air Force Research Laboratory, described in detail previously.28-29 Sm+ was formed using a glow discharge rod source, similar to that described above, and detailed elsewhere.12 Briefly, approximately 1 std. L min-1 of a 10:1 He to Ar gas mix at a pressure of approximately 1 Torr flowed over an iron “boat” containing Sm chips. 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 that surrounds the discharge area. This discharge produces Ar+ that impacts the metal rod at high energies, sputtering neutral and ionic metal species. The ions were then extracted through a biased nose cone into a differentially pumped region and the ion of interest was mass selected using a quadrupole mass filter. The ion was then injected via a Venturi inlet into the flow tube in a 13 std. L min-1 laminar flow of He. Ions undergo approximately 104 – 105 collisions with the He buffer gas, which is thermalized at the temperature of the flow tube (300 – 600 K) controlled by resistive heating. No evidence of excited state Sm+ was observed, as evidenced by the decay of Sm+ being well-described by a single exponential over an order of magnitude at all temperatures. These observations place an



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upper limit of ~10% on the population of excited state species. COS was introduced 59 cm before the end of the flow tube, which resulted in reaction times on the order of 3 ms. Remaining reactant ions as well as resultant product ions were then extracted through a 3 mm aperture in a rounded nosecone, transported using a rectilinear ion guide, and probed with an orthogonal acceleration time-of-flight mass spectrometer. Kinetics were extracted by monitoring the decrease in reactant ion signal as a function of COS concentration, with complete mass spectra stored at every flow point. Each ion peak was integrated to get the total ion counts. We found no significant mass discrimination between reactant and product ions in this system, as evidenced by the total counts being constant as a function of the extent of reaction within statistical scatter. Uncertainties in the rate coefficients are estimated to be ± 15% relative and ± 25% absolute.28 Computational Approach. Theoretical calculations were performed using the Gaussian 09 suite of programs.30 Ground and low-energy states and their bond energies were calculated using the B3LYP,31-32 MP2, and CCSD(T)33-36 levels of theory. For both MP2 and CCSD(T) calculations, all electrons were included in the correlation calculation (utilizing the “full” keyword). Two sets of basis sets were used. In the first, which will be referred to as SDD below, the basis set for Sm was the Stuttgart Dresden (SDD) double zeta basis (12s11p9d8f)/[5s5p4d3f] with a small core (28 electron) effective core potential (ECP).37 This was combined with the def2-TZVPPD basis on O, C and S. MP2/SDD calculations were used to determine vibrational frequencies of all species, which were used (after scaling by 0.989)38 to apply zero-point energy corrections and in modeling the data. The second basis set utilized is referred to as VXZ-DK3 below where X = D, T, and Q. This basis set combined the all-electron cc-pVXZ-DK339 basis set for Sm along with aug-ccpCVXZ-DK basis sets on C, O, and S and uses the 2nd order Douglas-Kroll-Hess Hamiltonian (DKH2).40-41 The basis sets for Sm were obtained from Prof. Kirk A Peterson and those for the lighter atoms were obtained from the EMSL basis set exchange. The procedure of Feller, Dixon, and Nicholas42 was used to perform complete basis set (CBS) extrapolations. This procedure combines the total energies as shown in eq 6,


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7

E[x] = E [∞] + B exp[-(x - 1)] + C exp[-(x - 1)2 ]

(6)

which reduces to eq 7 when D, T, and Q basis sets are used (x = 2, 3, and 4). E [∞] = 1.676755 E[4] – 0.711622 E[3] + 0.034867 E[2]

(7)

Analytic geometry optimization and frequency calculations using the all-electron basis sets and DKH2 Hamiltonian were not available. Instead, to determine the structures, energies, and vibrational frequencies of SmS+ using the VXZ-DK3 basis sets and DKH2 Hamiltonian, the potential energy curves were mapped by performing seven-single point energy calculations for each diatomic near the equilibrium bond length determined from MP2/SDD calculations. The equilibrium bond lengths and minima of the potential energy curves were subsequently deduced from fifth-order polynomial fits with the vibrational frequency extracted using the analysis of Dunham.43 For CO, CS, and COS, structures were ascertained using a similar procedure intrinsic to Gaussian09 at the MP2/VXZ-DK3 level. The SDD basis set was utilized to explore the intermediates and potential energy surfaces (PESs) of the reaction of Sm+ with COS because use of the large all-electron basis sets was impractical. In previous work,5 it was found that B3LYP/SDD calculations were incapable of qualitatively describing the Sm+ + CO2 system, whereas MP2/SDD and CCSD(T)/SDD approaches provided a qualitatively reasonable characterization. Similar results were obtained for a theoretical description of the SmS+ molecule.44 Thus, the MP2/SDD approach coupled with relaxed PES scans of the SSmC and OSmC bond angles were used to examine the PESs for reaction 3 and reaction 4, respectively. Stationary points along this surface were optimized at the MP2/SDD level and verified to have all positive frequencies for intermediates and one imaginary frequency for transition states. Using these geometries, single point energy calculations at the CCSD(T)/SDD level were also conducted for all intermediates and transition states located along the PESs for reaction of Sm+ with COS. Connections between transition states and stable intermediates were verified by intrinsic reaction coordinate (IRC) calculations or relaxed potential energy surface scans in all cases.



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RESULTS Reaction of Sm+ + COS. VT-SIFT studies of the reaction of Sm+ with COS yield the formation of SmS+ + CO in reaction 3. Rate coefficients were determined over a range of 200 – 600 K and are listed in Table 1. Compared to trajectory calculations45 of the collision limit for interaction of ions with polar molecules (for COS, µ = 0.71 D and α = 5.09 Å3),46 this reaction occurs with an efficiency of 20 ± 6% independent of temperature. To our knowledge, this rate coefficient has not previously been reported. GIBMS studies of the reaction of Sm+ and COS yields two products according to reactions 3 and 4, with their kinetic energy dependent cross sections shown in Fig. 1. The cross section for the SmS+ + CO, reaction 3, has a magnitude of 1.4 × 10-14 cm2 at the lowest energy examined (0.025 eV) and declines as the energy increases, indicating an exothermic and barrierless process. Below 0.5 eV, this cross section closely follows the energy dependence expected from trajectory calculations45 with an efficiency of 33 ± 7% independent of energy. This corresponds to a rate coefficient at room temperature of 3.2 ± 0.6 × 10-10 cm3/s. This efficiency is somewhat higher than that observed in the VT-SIFT studies but the values agree within the combined experimental uncertainties for an average value of 26 ± 9%. As the energy increases, the SmS+ cross section reaches a minimum near 0.7 eV before rising until it nearly matches the trajectory cross section in magnitude and behavior from 2 – 4 eV. The cross section begins to drop near 5 eV, presumably because the SmS+ product begins to dissociate, a process that can begin at D0(OC-S) = 3.14 ± 0.02 eV, Table 2.47-49 The cross section for SmO+ + CS, reaction 4, rises from an apparent threshold near 3 eV and reaches a maximum near 9 eV. The latter energy is well above D0(SC-O) = 6.88 ± 0.04 eV, Table 2, which is where the SmO+ product can have enough energy to dissociate. For both reactions, the fact that dissociation occurs above its thermodynamic onset is consistent with much of the available energy being in relative translation of the products or carried away in internal modes of the CS or CO product.


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Experimental Thermochemistry. Information regarding the SmS+ bond energy is not available in the literature. The exothermic and barrierless reaction 3 observed here indicates that D0(Sm+-S) > D0(OC-S) = 3.14 ± 0.02 eV, although the relative inefficiency may suggest that the exothermicity is not large. In a related study, the BDE for SmS+ was assessed from four independent chemical reactions as D0(Sm+-S) = 3.37 ± 0.09 eV, where the uncertainty is one standard deviation of the mean.44 Notably this value agrees well with the lower limit of 3.14 eV and indicates that reaction 3 is exothermic by only 0.23 ± 0.09 eV. We also modeled the endothermic feature in the SmS+ + CO cross section after first subtracting the trajectory model of the exothermic reactivity (σtraj) scaled to the data at low energies. This analysis leads to a threshold of 0.71 ± 0.08 eV (along with σ0 = 20.6 ± 3.0 Å2 and n = 1.0 ± 0.1). Such a feature can plausibly be assigned to formation of an excited state of the SmS+ product with an excitation energy of 0.94 ± 0.12 eV, as discussed further below. The SmO+ bond energy has recently been reevaluated as 5.725 ± 0.07 eV.4 Given D0(SC-O) = 6.88 ± 0.04 eV, reaction 4 is endothermic by 1.16 ± 0.08 eV. The apparent threshold for reaction 4 is well above this endothermicity. Indeed, analysis of this cross section using eq 5, shown in Figure 1, yields a threshold (E0) of 2.81 ± 0.32 eV (along with σ0 = 0.26 ± 0.16 Å2eV-1 and n = 2.0 ± 0.3), 1.6 ± 0.3 eV higher than expected. Notably, the uncertainties in these modeling parameters are relatively high because modeling the seven different data sets resulted in relatively large variations in the parameters of eq 5 compared with most systems. Indeed, the threshold values varied from 2.35 to 3.29 eV, which is potentially indicative of a system where the onset is not a well characterized asymptotic level. Furthermore, these data were not analyzed in competition with the strongly favored SmS+ + CO channel. Such competition will shift the observed threshold for reaction 4 to higher energies, such that the real threshold energy for formation of SmO+ + CS is lower. An approximate phase space calculation of this effect shows that the shift is on the order of 0.5 eV, effectively moving the thermodynamic threshold down to 2.3 ± 0.4 eV.



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Computational Results. In previous work,5 calculations for SmO+ determined a ground electronic state of 6∆ (possibly 6Φ), in which σ and π bonds are formed using 5d orbitals on Sm (supplying two electrons) and 2p orbitals on O (supplying four electrons) with the remaining five valence electrons being in non-bonding 4f orbitals. Because only five of the seven 4f orbitals are occupied, different occupations of these orbitals lead to many low-lying states. The 6∆/Φ ground state leaves a hole in the σ and δ/φ 4f orbitals, such that the overall valence configuration is designated π4σ2[φ2δ1π2]/ π4σ2[φ1δ2π2], where the 4f orbitals are indicated in square brackets. We recently reevaluated this system using a multireference configuration interaction approach (MRCI), all electron basis sets, and Douglas Kroll Hamiltonian (DK3-MRCI+Q/VTZ-DK3).44 Before corrections for spin-orbit interactions, this analysis indicates that the ground configuration is 6Π (π4σ2[φ2δ2π1]) with 6Σ+ (π4σ2[φ2δ2σ1]) lying only 0.001 eV higher in energy. The 6∆ and 6Φ states are also low-lying, with excitation energies of 0.028 and 0.086 eV, respectively. If these relative energies are empirically corrected for spin-orbit interactions, the ground state returns to 6Φ, with 6∆ only 0.006 eV higher, in agreement with our previous work, with three other states within 0.11 eV.44 This work also presented a comprehensive theoretical evaluation of the analogous SmS+ molecule, including results at the (DK3-MRCI+Q/VTZ-DK3) level.44 Before spin-orbit corrections, the ground state is 6Σ+ (π4σ2[φ2δ2σ1]) with the 6Π (0.016 eV), 6∆ (0.055 eV) and 6Φ (0.097 eV) states continuing to be low-lying. Application of empirical spin-orbit corrections indicates that the ground state is also 6Φ, with five other states within 0.10 eV. Calculations of Overall Thermochemistry. To determine what level of theory could be used to successfully describe the results obtained experimentally, several quantities known in the literature were calculated at several levels of theory. As provided in Table 3, these include the excitation energy of the 6F (4f66s1) state of Sm+ relative to the ground state 8F (4f66s1) (0.188 eV averaged over all SO levels),50 the bond energies of COS (Table 2),51 the SmO+ and SmS+ bond energies,4, 44 and the enthalpies of reactions 3 and 4. It can be seen that all levels of theory do a reasonable job (within 0.05 eV) of predicting the atomic excitation energy. Deviations from


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experiment for D0(OC-S) and D0(O-CS) are more substantial with most MP2 approaches predicting values somewhat higher than experiment. CCSD(T) values are somewhat lower than experiment, but reproduce both experimental values nicely when a complete basis set extrapolation is performed (including a 0.024 eV correction for the spin-orbit splitting of S). For D0(SmO+), the B3LYP/SDD value is well below experiment, MP2/SDD is too high, MP2/VxZDK3 are somewhat low, whereas CCSD(T)/SDD and CCSD(T)/CBS bracket the experimental value within about 0.3 eV. For the weaker D0(SmS+), the same relative trends are observed, but now all theoretical values are lower than experiment, with only MP2/SDD, CCSD(T)/SDD, and CCSD(T)/CBS approaching the correct value. The theoretical enthalpies of reaction 3, ∆rH0(3) = D0(OC-S) – D0(SmS+), are given in Table 3 including empirical spin-orbit corrections. B3LYP/SDD and MP2/VxZ-DK3 results predict the reaction is substantially endothermic, in contrast to the observed exothermicity. In contrast, CCSD(T)/SDD and CCSD(T)/CBS calculations correctly predict an exothermic process. For reaction 4, agreement between experiment and theory is reasonable at the CCSD(T)/ VXZ-DK3 levels with MP2/SDD and CCSD(T)/SDD being slightly low. Overall, the mean absolute deviations between experiment and the various levels of theory shows that the best results are obtained at the CCSD(T)/CBS, CCSD(T)/VQZ, and

CCSD(T)/SDD levels. This comparison demonstrates that the

CCSD(T)/SDD//MP2/SDD approach provides reasonable accuracy at a computationally accessible level for further calculations. Potential Energy Surfaces for SC-O Bond Activation. Potential energy surfaces for interaction of Sm+ and COS along both octet and sextet spin surfaces were calculated at the MP2/SDD level of theory. Nearly all species on these surfaces are planar, such that they can have A′ and A′′ symmetry; however, the distinction between these is generally small as they are associated with different occupations of the 4f orbitals on Sm. Further, this distinction can be removed easily by small deviations from planarity, such that all A′ and A′′ surfaces should mix readily. In the following discussion, energies correspond to the CCSD(T)/SDD//MP2/SDD results in all cases.



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We begin with the surfaces associated with activation of the SC-O bond, reaction 4, as these results parallel those previously described for activation of CO2 by Sm+.5 A schematic of the surfaces is shown in Figure 2, with energies for all stationary points listed in Table 4. Structures of these stationary points are shown in Figure 3 for the octet (part a ) and sextet (part b) spin species. The entrance channel for reaction 4 is associated with potential wells corresponding to linear Sm+(OCS) intermediates for each spin state, lying about 0.8 eV below their respective reactant asymptotes. These parallel the calculated differences in the Sm+ states, which differ only in the coupling between the 6s electron and the six 4f electrons. Because these surfaces both have the same orbital occupations, they behave similarly as the system proceeds along both octet and sextet surfaces. As the COS molecule bends towards the samarium cation, the OSmC angle increases and the energy rises, with the octet and sextet surfaces remaining parallel. Near 27°, the Sm+(OCS) TSs, Table 4 and Figure 3, are reached and correspond to insertion of Sm+ into a OC π bond. These TSs lie ~0.63 eV above the Sm+(OCS) entrance channel complexes. The imaginary frequencies, 1117 and 1438 cm-1 on the octet and sextet surfaces, respectively, correspond largely to a bending motion of the OCS molecule (530 cm-1 in free COS). These TSs lead to intermediates in which Sm+ binds to both an oxygen and carbon, the Sm+(OCS) bent intermediates in Table 4 and Figure 3. These intermediates lie only 0.11 and 0.16 eV below their respective TSs. From these intermediates, the Sm can insert more fully into the CO bond to form OSm+(CS). As this occurs, the energy rises rapidly reaching another transition state near 50° on both spin surfaces, OSm+(CS) TS, Table 4. These TSs lie 1.8 – 2.2 eV above reactants with the sextet states (both 6A′ and 6A′′ versions were located) lying 0.4 and 0.3 eV below the octet state. Their imaginary frequencies, ~430 cm-1, correspond primarily to OCS bond cleavage. These TSs lead to OSm+(CS) excited state (ES) intermediates having OSmC bond angles near 94°, consistent with donation of the CS lone pair of electrons into an empty 5d orbital on Sm. These intermediates lie 0.02 (8A′′) and 0.37 (6A′) eV below the TSs. (An 8A′ ES was also located.) The ES intermediates are high in energy because they correspond to states having a bond order between Sm+ and O of only 2.5. This is clear for the octet because the SmO+


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(8Σ, π4σ1[φ2δ2π2]) state lies ~2 eV above the 6Φ ground state.5 The sextet state is comparable, differing only in how the six 4f electrons are coupled to the singly occupied bonding sigma orbital. These ES intermediates can readily lose CS to form the associated state of SmO+, which are well above the ground state, Figure 2. Linear versions of the OSm+(CS) intermediates were looked for but never converged and are expected to have imaginary frequencies. Ground state (GS) SmO+ has a triple bond that requires two 5d electrons on Sm+. Thus, from the ES intermediates, one of the 4f electrons must switch to the bonding orbitals, which cannot occur for the octet states. This OSm+(CS) GS intermediate lies well below the ES intermediates and 0.36 eV below reactants, Figure 2. Its structure is similar to the OSm+(CS) ES intermediate with a OSmC bond angle of 99°, but a distinctly shorter SmO bond, 1.764 Å versus 2.106 Å for the sextet ES, Figure 3. Loss of the CS ligand can lead directly to the ground state SmO+(6Φ) + CS(1Σ+) products, 0.82 eV above reactants at this level of theory (0.98 eV after spin-orbit corrections for the Sm+ reactant and SmO+ product, Table 3). To understand how the GS and ES surfaces must interact, relaxed potential energy surface scans along both surfaces were conducted in the region where they should cross. Figure 4 shows that as OC bond length (or equivalently, the OSmC angle) decreases for the GS intermediate, the energy increases rapidly. This behavior occurs partly because this surface diabatically correlates with a reactant Sm+(4f55d2) excited state, which lies above the Sm+(8F,4f66s1) GS by about 2.35 eV experimentally.52 Figure 4 also shows the sextet surface starting from the Sm+(OCS) bent intermediate and proceeding to the OSm+(CS) TS. The apparent surface crossing found corresponds to that between diabatic sextet surfaces associated with 4f66s1 and 4f55d2 configurations, although it can be realized that the “crossing” shown in Figure 4 does not relate directly to where these surfaces interact as only the OC bond length is the same. Other bond lengths and bond angles differ. We tried to explore this crossing in more detail by calculating energies using the same geometries along one surface but altering the orbital occupation. For both surfaces, such calculations always collapsed to the lower energy configuration, such that a “true” crossing point could not be located. In analogy with the results



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for this crossing point located in the Sm+ + CO2 reaction, the true crossing point should be at higher energies than the apparent crossing point in Figure 4. It is conceivable that Sm+ can also form SmO+ by breaking the SmO+-CS bond in the Sm+(OCS) intermediate. This pathway was not explored here because examination of this process in the analogous Sm+ + CO2 reaction showed that this process is considerably higher in energy than the pathways analogous to those shown in Figures 2 and 4.5 Potential Energy Surfaces for OC-S Bond Activation. Potential energy surfaces for interaction of Sm+ and COS along both octet and sextet spin surfaces were calculated at the MP2/SDD level of theory with single point energies at the CCSD(T)/SDD level. These surfaces are shown in Figure 5 for activation of the OC-S bond, with energies for all stationary points listed in Table 5. Structures of these stationary points are shown in Figure 6 for the octet (part a) and sextet (part b) spin species, respectively. In contrast to the interactions of Sm+ with the oxygen end of the COS molecule (or with CO2), the Sm+(SCO) adducts have a side-on geometry with a SmSC bond angle of 95°, Figure 6 (~26° for ∠SSmC, Table 5) for both the octet and sextet species. Again these intermediates are separated by an energy comparable to the splitting between the atomic states. A linear complex of the sextet state was located computationally but has two degenerate imaginary frequencies (52 cm-1) in the bending motion collapsing to the side-on geometry. Along the octet surface, reaction proceeds over Sm+(SCO) TSsb in which the samarium inserts into the SC π bond, forming the Sm+(SCO) bent intermediate. The TS is nearly isoenergetic with the reactants, whereas the bent intermediate lies 0.24 eV below the reactants and slightly above the Sm+(SCO) side intermediate. The Sm+(SCO) bent intermediate can also be formed from Sm+(OCS) bent by passing over Sm+(OCS) TSbb, which lies 0.015 eV below the reactants on the octet surface. This is marginally the lowest energy pathway for forming the Sm+(SCO) bent intermediate. Along the octet surface, Sm+(SCO) bent can pass over SSm+(CO) TS (0.11 eV above reactants), in which the CS bond is broken, leading to the SSm+(CO) intermediate (0.19 eV below reactants). This species has a SSmC bond angle of 83° suggesting that the CO ligand is donating into an empty


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15

5d orbital on the Sm+ cation. From the SSm+(CO) intermediate, loss of CO is straightforward and leads to the SmS+(8Φ) + CO products, calculated to lie 0.53 eV above the reactants. Note that the product asymptote is the rate-limiting step along the octet surface. Along the sextet surface, a pathway parallel to that of the octet surface can be followed throughout the reaction. For this pathway, the bent intermediate lies below the comparable octet intermediate (by 0.04 eV), as do the SSm+(CO) TS (by 0.18 eV), SSm+(CO) intermediate (by 0.04 eV), and the product asymptote (by 0.13 eV). Note that the product formed via this pathway is an excited sextet state of SmS+ having an electron configuration analogous to the octet surface, i.e., π3σ2[φ1δ2π2σ1] in which only one valence electron on Sm+ participates in the bonding, consistent with diabatic correlation with the 6s14f6 configurations of the low-lying states of Sm+. Because these intermediates correlate with an excited state of the products, they are labeled using ES to distinguish them from the pathway forming ground state (GS) products. An alternative pathway between the Sm+(SCO) side and bent intermediates was also located along the sextet surface. Here, the samarium cation begins to interact with both the sulfur and oxygen atoms by passing over Sm+(SCO) TSsq, which connects to a planar intermediate having a quadrilateral geometry in which there are both Sm-S and Sm-O bonds. This Sm+(SCO) quad intermediate lies 0.73 eV below GS reactants (0.87 eV below sextet reactants). From this intermediate, the bent SCO molecule rotates out of the plane to move the carbon towards the samarium center at TSqb, which lies 0.14 eV above reactants and is essentially isoenergetic with the sextet state of TSsb. TSqb leads to the Sm+(SCO) bent intermediate. As for the pathway yielding SmO+ + CS, formation of ground state SmS+ + CO products requires correlation with an excited state of Sm+ having two valence electrons in the 5d orbitals. Interaction of the sextet Sm+(5d24f5) (2.35 eV higher than the Sm+(8F) GS)52 with COS forms the Sm+(SCO) bent (GS) intermediate, lying 0.56 eV above ground state reactants. This passes over a barrier at SSm+(CO) TS (GS) lying 0.33 eV higher in energy to form the SSm+(CO) GS intermediate, which is the global minimum along all surfaces at -1.00 eV below reactants. Loss



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16

of CO from this species readily forms the SmS+(6Φ) GS, with a calculated exothermicity of 0.19 eV (exothermic by 0.09 eV after SO corrections, Table 3). Again the GS and ES surfaces must cross one another, which could be qualitatively characterized by relaxed potential energy surface scans in the region where crossing should occur. Figure 7 shows that as the SC bond length (or equivalently, the SSmC angle) decreases for the GS intermediate, the energy increases rapidly as the system approaches the SSm+(CO) TS (GS). (Two surfaces are shown corresponding to the intrinsic reaction coordinate from this TS and to a scan of the SC bond distance starting at the GS intermediate.) Again this rapid increase in energy results because this surface diabatically correlates with the Sm+(4f55d2) excited state reactant lying 2.35 eV above the Sm+ (8F) ground state.52 Figure 7 also shows the sextet surface starting from the Sm+(OCS) bent intermediate, proceeding to the OSm+(CS) TS, and then to the SSm+(CO) ES intermediate. The apparent surface crossings found between the GS and ES surfaces correspond to those between diabatic sextet surfaces associated with 4f66s1 and 4f55d2 configurations. Again the “crossings” shown in Figure 7 do not correspond to where these surfaces interact because they only share a common SC bond length and no other molecular dimensions. Because these surfaces do not have any symmetry or spin constraints that differentiate them, a “true” crossing point could not be located. Nevertheless, Figure 7 shows that the crossing seam lies below the energy of the reactants, which is consistent with the experimental observation that reaction 3 occurs with no barrier. This is also shown qualitatively in Figure 5.

DISCUSSION As for reactions of Sm+ with CO2, Sm+ reacts with COS to form the SmO+ product with a threshold measured to be considerably above the endothermicity of process 4. In contrast, activation of the weaker CS bond in reaction 3 exhibits no barriers. It is important to point out that both reactions 3 and 4 are formally spin-forbidden because Sm+ ions have an octet ground state, COS, CO, and CS have singlet states, and SmO+ and SmS+ have sextet spin ground states.


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Experimentally, it is not possible to ascertain whether this condition limits the efficiency of the reaction, although spin and angular momentum seem unlikely to be good quantum numbers for such a heavy metal system. In that regard, the reactions can occur on ground state Ω = 1/2 surfaces throughout. Although theoretical explorations of this lanthanide chemistry are impeded by the need to consider high spin states, a result of many non-bonding 4f electrons, use of the CCSD(T)/SDD//MP2/SDD approach provides reasonably quantitative agreement between experiment and theory, as quantified in Table 3. The theoretical surfaces show that the octet and sextet surfaces in the entrance channel parallel one another closely such that strong interactions between these surfaces of different spin seem likely. Overall, there are three experimental observations that need to be explained: a) the ~ 2.3 ± 0.4 eV barrier to reaction 4, b) the exothermicity of reaction 3 with no temperature dependence in its rate coefficient, and c) the high energy feature observed for SmS+ + CO formation starting near 0.71 ± 0.08 eV. In our previous exploration of the reaction of Sm+ with CO2, the barrier to formation of SmO+ + CO, measured to be 1.77 ± 0.11 eV, was assigned to the crossing point between the two sextet surfaces correlating to ground state reactants (having six 4f electrons) and ground state products (having five 4f electrons), where the latter diabatically correlates with an Sm+ reactant lying 2.35 eV above the ground state reactant. There, a more explicit calculation of the crossing point between these two sextet surfaces was possible and found to be in agreement with the experimental threshold energy once spin-orbit corrections were applied. A direct comparison of the SmO+ product cross sections in the two systems shows that the CO2 reactant leads to a much larger SmO+ cross section (by over an order of magnitude) and lower apparent threshold (by ~1.5 eV). Indeed, the SmO+ cross section in the CO2 system has a comparable magnitude to the SmS+ cross section observed here above about 5 eV. This observation clearly indicates that the cross section for reaction 4 is limited by competition with the much more favorable reaction 3. Thus, the onset observed for reaction 4 is shifted by competition with reaction 3, making the measured 2.3 ± 0.4 eV threshold corrected approximately for this competition the value that should be compared with theory. Nevertheless, even this threshold remains comparable to the 2.35 eV



Page 18 of 46

18

excitation energy associated with the Sm+ excited state that diabatically leads to the ground state products. It seems likely that the origins of this barrier are identical in the CO2 and COS systems, and this is indicated qualitatively in Figure 2, where the crossing point between sextet surfaces is located at the lower limit of the experimentally measured value. It might also be realized that excited states of SmO+ can be formed at higher energies, but no distinct evidence for such pathways is evident in the experimental cross section. For reaction 3, Figure 5 shows that a likely pathway is interaction of Sm+(8F) with COS along the octet potential energy surface eventually forming the Sm+(SCO) bent intermediate. The PES shows a transition state, Sm+(SCO) TSsb, that is essentially isoenergetic with the reactants, but this can be avoided by forming the bent intermediate from the slightly more stable Sm+(OCS) bent intermediate of Figure 2 via TSbb, which lies 0.015 eV below reactants. One can also imagine forming Sm+(SCO) bent directly from reactants by bringing the Sm+ from the side of the COS molecule with no barrier whatsoever. Once at the octet bent intermediate, the sextet surface is nearly parallel and slightly lower in energy, such that coupling between the two spin surfaces could occur readily. From here, there is a crossing between the sextet ES and GS surfaces, which must occur at energies below the reactant asymptote (as indicated qualitatively in Figure 5). This forms the SSm+(CO) GS intermediate, which easily loses CO to form the ground state SSm+ (6Φ) + CO products. The fact that no temperature dependence is observed in the rate coefficient for this reaction (or equivalently that the kinetic energy dependence follows the collision cross section energy dependence, Figure 1) but the reaction is only 26% efficient is unusual. The temperature (kinetic energy) dependence indicates that there is no barrier along the potential energy surface exceeding the energy of the reactant asymptote. The low efficiency of the reaction, 20 – 33 %, is consistent with an initially formed reagent undergoing back reaction to reform reactants upon most collisions; however, typically such reactions show a negative temperature dependence because the back reaction is entropically favored by its loose transition state. A similar flat temperature dependence was observed in the reaction of Fe+ + N2O53 and found to be a result of cancelling positive and negative dependences in competing diabatic and


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19

adiabatic pathways, but this is unlikely to be the case here. More likely, the OC-S reaction coordinate provides no kinetic hindrance and the low efficiency is instead a result of entrance channel effects controlling whether Sm+(OCS) or Sm+(SCO) is initially formed. In this regard, it is useful to realize that the Sm+(OCS) (8∆) intermediate (0.82 eV below reactants) is substantially lower in energy than the Sm+(SCO) side (8A′′) intermediate (0.31 eV below reactants) or Sm+(SCO) bent (8A′′) intermediate (0.24 eV below reactants), such that the intermediates leading to CS bond activation are populated less than that leading to CO activation. (For an intermediate having 0.82 eV of internal energy, an equilibrium population of these three intermediates is approximately 49%, 26%, and 24%.) As suggested by a reviewer, a complicating possibility is related to the efficiency of the couplings between the octet surfaces of the reactants with the comparable sextet surfaces in the entrance channel or between ground and excited sextet surfaces after S-CO insertion. If there are such non-adiabatic effects here, then the efficiency of the reactions could be suppressed although some dependence on the temperature/kinetic energy might still be expected. Estimating the efficiencies of such couplings is inherently difficult, as previously discussed for coupling of quartet and sextet surfaces in the reactions of Fe+ + propane54-55 and in the doublet and quartet surfaces in the reactions of Ti+ + CH3OH.56 In particular, the latter case shows that simple spin-orbit coupling calculations do not always provide a quantitative approximation of the likelihood of coupling between surfaces of different spin. Finally, the high energy feature observed in the SmS+ cross section, Figure 1, can probably be attributed to the spin-allowed formation of SmS+ (8Γ) + CO. The approximate threshold measured for the high-energy feature in the SmS+ cross section is 0.71 ± 0.08 eV. This can be compared favorably to the calculated value for the spin-allowed asymptote of 0.53 eV at the CCSD(T)/SDD level (0.85 eV, MP2/SDD), Table 5, (0.60 eV including SO corrections). Thus, even though spin should not be a particularly good quantum number, the conservation of spin apparently allows reaction 3 to occur with enhanced probability at higher kinetic energies. It



Page 20 of 46

20

is also possible that other excited states of SmS+ (e.g., the excited 6Φ) might contribute at these energies, but why these would lead to a distinct cross section feature is not obvious. It is also useful to qualitatively consider the shapes of these surfaces. Interaction of Sm+(4f66s1) with COS (in either the octet or sextet spin state) is initially attractive as a consequence of the ion-dipole interaction, but no covalent coupling can occur unless the COS molecule bends appreciably such that a radical site on the oxygen or sulfur center begins to develop. Because the polarizability of S is higher than that of O and the OC-S bond is weaker than the SC-O bond, radical character is more easily developed on the sulfur center. In either case, this interaction eventually leads to the high energy OSm+(CS) ES and SSm+(CO) ES species because Sm+(4f66s1) can only form a single covalent bond. In contrast, shifting one of the 4f orbitals to a 5d orbital makes it available for bonding, greatly increasing the strength of the SmX+ species (where X = O or S) and leading to the sextet OSm+(CS) GS and SSm+(CO) GS intermediates, which easily lose the CX ligand to form SmO+(6Φ) + CS and SmS+(6Φ) + CO ground state products. Because the energy of the Sm+(4f55d2) state is so high, 2.35 eV above the Sm+(4f64s1) ground state,52 the crossings between the ES and GS sextet surfaces can be relatively high as well (as in the case of the activation of the SC-O bond), whereas the stronger covalent interaction with the sulfur end of the molecule and weaker OC-S bond allows the crossing to occur at much lower energy.

ACKNOWLEDGEMENTS This material is based upon work supported by the Air Force Office of Scientific Research under AFOSR Award Nos. FA9550-16-1-0095 (PBA) and AFOSR-16RVCOR02. The authors thank Professor Kirk A. Peterson for providing the all-electron basis sets for Sm. We thank the Center of High Performance Computing at the University of Utah for the generous allocation of computer time and the Extreme Science and Engineering Discovery Environment (XSEDE), Grant No. TG-CHE170012, for allocations on the regular, large, and extreme shared memory nodes at the Pittsburgh Supercomputing Center (PSC) at Carnegie Mellon University and


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allocations on the computer nodes at the San Diego Supercomputing Center (SDSC) at University of California San Diego.



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22 REFERENCES (1) Shuman, N. S.; Hunton, D. E.; Viggiano, A. A. Ambient and Modified Atmospheric Ion Chemistry: From Top to Bottom. Chem. Rev. 2015, 115, 4542-4570. (2) Caton, R. G.; Pedersen, T. R.; Groves, K. M.; Hines, J.; Cannon, P. S.; Jackson-Booth, N.; Parris, R. T.; Holmes, J. M.; Su, Y.-J.; Mishin, E. V., et al. Artificial Ionospheric Modification: The Metal Oxide Space Cloud Experiment. Radio Science 2017, 52, 539-558. (3) Bernhardt, P. A.; Siefring, C. L.; Briczinski, S. J.; Viggiano, A.; Caton, R. G.; Pedersen, T. R.; Holmes, J. M.; Ard, S.; Shuman, N.; Groves, K. M. A Physics-based Model for the Ionization of Samarium by the MOSC Chemical Releases in the Upper Atmosphere. Radio Science 2017, 52, 559-577. (4) Cox, R. M.; Kim, J.; Armentrout, P. B.; Bartlett, J.; VanGundy, R. A.; Heaven, M. C.; Ard, S. G.; Melko, J. J.; Shuman, N. S.; Viggiano, A. A. Evaluation of the Exothermicity of the Chemi-ionization Reaction Sm + O → SmO+ + e–. J. Chem. Phys. 2015, 142, 134307. (5) Armentrout, P. B.; Cox, R. M. Potential Energy Surface for Reaction of Sm+ + CO2 → SmO+ + CO: Guided Ion Beam and Theoretical Studies. Phys. Chem. Chem. Phys. 2017, 19, 11075-11088. (6) Wang, L.; He, W.; Yu, Z. Transition-metal Mediated Carbon–sulfur Bond Activation and Transformations. Chem. Soc. Rev. 2013, 42, 599–621. (7) Jiang, X.-F.; Huang, H.; Chai, Y.-F.; Lohr, T. L.; Yu, S.-Y.; Lai, W.; Pan, Y.-J.; Delferro, M.; Marks, T. J. Hydrolytic Cleavage of Both CS2 Carbon–sulfur Bonds by Multinuclear Pd(II) Complexes at Room Temperature. Nat Chem 2017, 9, 188-193. (8) Sze, N. D.; Ko, M. K. W. CS2 and COS in the Stratospheric Sulphur Budget. Nature 1979, 280, 308–310. (9) Turco, R. P.; Whitten, R. C.; Toon, O. B.; Pollack, J. B.; Hamill, P. OCS, stratospheric aerosols and climate. Nature 1980, 283, 283-285. (10) Notholt, J.; Kuang, Z.; Rinsland, C. P.; Toon, G. C.; Rex, M.; Jones, N.; Albrecht, T.; Deckelmann, H.; Krieg, J.; Weinzierl, C., et al. Enhanced Upper Tropical Tropospheric COS: Impact on the Stratospheric Aerosol Layer. Science 2003, 300, 307-310. (11) Loh, S. K.; Hales, D. A.; Lian, L.; Armentrout, P. B. Collision-Induced Dissociation of Fen+ (n = 2 - 10) with Xe: Ionic and Neutral Iron Cluster Binding Energies. J. Chem. Phys. 1989, 90, 5466-5485.


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24 (26) Armentrout, P. B., Thermochemical Measurements by Guided Ion Beam Mass Spectrometry. In Adv. Gas Phase Ion Chem., Adams, N.; Babcock, L. M., Eds. JAI Press: Greenwich, Connecticut, 1992; Vol. 1, pp 83-119. (27) Lifshitz, C.; Wu, R. L. C.; Tiernan, T. O.; Terwilliger, D. T. Negative Ion-molecule Reactions of Ozone and Their Implications on the Thermochemistry of O3-. J. Chem. Phys. 1978, 68, 247-260. (28) Viggiano, A. A.; Morris, R. A.; Dale, F.; Paulson, J. F.; Giles, K.; Smith, D.; Su, T. Kinetic Energy, Temperature, and Derived Rotational Temperature Dependences for the Reactions of Kr+(2P3/2) and Ar+ with HCl. J. Chem. Phys. 1990, 93, 1149-1157. (29) Melko, J. J.; Ard, S. G.; Shuman, N. S.; Pedder, R. E.; Taormina, C. R.; Viggiano, A. A. Coupling an Electrospray Source and a Solids Probe/Chemical Ionization Source to a Selected Ion Flow Tube Apparatus. Rev. Sci. Instrum. 2015, 86, 084101. (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al., Gaussian 09, Revision A.02. Gaussian 09, Revision A.02 ed.; Gaussian Inc.: Pittsburgh, PA, 2009. (31) Becke, A. D. Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. (32) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. (33) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479483. (34) Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J. Non-iterative Fifth-order Triple and Quadruple Excitation Energy Corrections in Correlated Methods. Chem. Phys. Lett. 1990, 165, 513-522. (35) Scuseria, G. E.; Lee, T. J. Comparison of Coupled-cluster Methods Which Include the Effects of Connected Triple Excitations. J. Chem. Phys. 1990, 93, 5851-5855. (36) Crawford, T. D.; Stanton, J. F. Investigation of an Asymmetric Triple-Excitation Correction for Coupled-Cluster Energies. Int. J. Quantum Chem. 1998, 70, 601-611. (37) Dolg, M.; Stoll, H.; Preuss, H. Energy-Adjusted Ab Initio Pseudopotentials for the Rare Earth Elements. J. Chem. Phys. 1989, 90, 1730-1734.


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25 (38) Foresman, J. B.; Frisch, A. E., Exploring Chemistry with Electronic Structure Methods. 2nd ed.; Gaussian, Inc.: Pittsburgh, PA, 1996. (39) Lu, Q.; Peterson, K. A. Correlation consistent basis sets for lanthanides: The atoms La–Lu J. Chem. Phys. 2016, 145, 054111. (40) Douglas, M.; Kroll, N. M. Quantum Electrodynamical Corrections to the Fine Structure of Helium. Ann. Phys. (N. Y.) 1974, 82, 89-155. (41) Reiher, M.; Wolf, A. Exact Decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess Transformation up to Arbitrary Order. J. Chem. Phys. 2004, 121, 1094510956. (42) Feller, D.; Dixon, D. A.; Nicholas, J. B. Binding Enthalpies for Alkali Cation−Benzene Complexes Revisited. J. Phys. Chem. A 2000, 104, 11414-11419. (43) Dunham, J. L. The Energy Levels of a Rotating Vibrator. Phys. Rev. 1932, 41, 721-731. (44) Armentrout, P. B.; Demireva, M.; Peterson, K. A. Guided Ion Beam and Theoretical Studies of the Bond Energy of SmS+. J. Chem. Phys. 2017, 147, 214307. (45) Su, T.; Chesnavich, W. J. Parameterization of the Ion-polar Molecule Collision Rate Constant by Trajectory Calculations. J. Chem. Phys. 1982, 76, 5183-5185. (46) Spackman, M. A. Accurate Prediction of Static Dipole Polarizabilities with Moderately Sized Basis Sets. J. Phys. Chem. 1989, 93, 7594-7603. (47) Goos, E.; Burcat, A.; Ruscic, B. Extended Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables; ANL-05/20 and TAE 960 Technion-IIT, Aerospace Engineering, and Argonne National Laboratory, Chemistry Division: 2016. (accessed August 2017). (48) Prinslow, D. A.; Armentrout, P. B. Collision-Induced Dissociation of CS2+. Heat of Formation of the CS Radical. J. Chem. Phys. 1991, 94, 3563-3567. (49) Eland, J. H. D.; Berkowitz, J. Dissociative Photoionization of Carbon Disulphide and Carbonyl Sulphide. J. Chem. Phys. 1979, 70, 5151-5156. (50) Martin, W. C.; Zalubas, R.; Hagan, L. Atomic Energy Levels - The Rare Earth Elements. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. (U.S.) 1978, 60, 1. (51) NIST Computational Chemistry Comparison and Benchmark Database, NIST Standard Reference Database Number 101, Release 17b, September 2015, Editor: Russell D. Johnson III; http://cccbdb.nist.gov/



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26 (52) Gibson, J. K. Role of Atomic Electronics in f-Element Bond Formation: Bond Energies of Lanthanide and Actinide Oxide Molecules. J. Phys. Chem. A 2003, 107, 7891-7899. (53) Ushakov, V. G.; Troe, J.; Johnson, R. S.; Guo, H.; Ard, S. G.; Melko, J. J.; Shuman, N. S.; Viggiano, A. A. Statistical Modeling of the Reactions Fe+ + N2O → FeO+ + N2 and FeO+ + CO → Fe+ + CO2. Phys. Chem. Chem. Phys. 2015, 17, 19700-19708. (54) Schultz, R. H.; Armentrout, P. B. Nonadiabatic Behavior of a Transition Metal System: Exothermic Reactions of Fe+(6D,4F) and Propane. J. Phys. Chem. 1987, 91, 4433-4435. (55) Schultz, R. H.; Elkind, J. L.; Armentrout, P. B. Electronic Effects in C-H and C-C Bond Activation: State-specific Reactions of Fe+(6D, 4F) with Methane, Ethane and Propane. J. Am. Chem. Soc. 1988, 110, 411-423. (56) Sweeny, B. C.; Ard, S. G.; McDonald, D. C.; Martinez, O.; Viggiano, A. A.; Shuman, N. S. Discrepancy Between Experimental and Theoretical Predictions of the Adiabaticity of Ti+ +CH3OH. Chem. Eur. J. 2017, 23, 11780-11783.


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27

Table 1. Rate coefficients and reaction efficiencies determined for reaction 3 by the VT-SIFT technique. T (K)

k3 (10-10 cm3 s-1)a

k3/ktraj b

200

2.0 ± 0.5

0.19 ± 0.05

300

2.2 ± 0.5

0.22 ± 0.05

400

2.1 ± 0.5

0.22 ± 0.05

500

1.9 ± 0.5

0.20 ± 0.05

600

1.7 ± 0.4

0.19 ± 0.05

a

Relative uncertainties are ±15%.

b

Collision rate coefficients calculated using the trajectory method of ref. 45.



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Table 2. Literature thermochemistry a ∆fH0

∆fH298

(kJ/mol)

(kJ/mol)

-141.8 ± 2.0

-141.7

CO

-113.813 ± 0.17

-110.53

CS

275.3 ± 3.8a,b

278.5

273.2 ± 1.3 c

276.5

C

711.4 ± 0.6

716.9

O

246.844 ± 0.002

249.229

S

274.92 ± 0.25

277.17

Compound

COS

a

Ref. 47.

b

Ref. 48.

c

Ref. 49.


Page 29 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


29

Table 3. Theoretical results at several levels of theory compared with experimental values. All values in eV. Approach Exp

Basis set E(Sm+, 6F) D0(OC-S)d

0.188

3.14 ±

B3LYP

MP2

MP2

MP2

MP2

MP2

CCSD(T)

CCSD(T)

CCSD(T)

CCSD(T)

CCSD(T)

SDDa

SDDa

VDZb

VTZb

VQZb

CBSc

0.189

0.180

0.196

0.197

0.194

0.192

0.143

0.153

0.163

0.163

0.163

3.387

3.008

3.358

3.468

3.531

2.990

2.631

2.969

3.079

3.142

3.225

2.212

2.365

2.544

2.661

3.079

2.531

2.828

3.041

3.176

0.162

0.796

0.993

0.924

0.870

-0.089

0.100

0.141

0.038

-0.034

7.380

7.009

7.355

7.469

7.534

6.749

6.345

6.736

6.862

6.934

6.324

5.260

5.335

5.326

5.318

5.769

5.099

5.379

5.417

5.432

1.056

1.749

2.020

2.143

2.216

0.980

1.246

1.357

1.445

1.502

0.28

0.50

0.60

0.61

0.62

0.14

0.42

0.26

0.18

0.16

3.248

0.02 + e

D0(SmS )

3.37 ±

2.601

0.09

∆rH0(3)d,e

-0.23 ±

0.647

0.09 D0(O-CS)

6.88 ±

7.061

0.04 D0(SmO+)f

5.725 ±

4.286

0.07

∆rH0(4)f

1.16 ±

2.775

0.08 MADg

0.71

a

SDD basis set and ECP on Sm, def2-TZVPPD on O, C, and S.

b

cc-pVXZ-DK3 on Sm and aug-cc-pCVXZ-DK on O, C, and S.

c

Complete basis set extrapolations as described in text.

d

All theoretical values include a spin-orbit correction for S of 0.024 eV, see text.

e

All theoretical values include a spin-orbit correction for SmS+, Sm+, and S of 0.123 eV,

see ref. 44. f

All theoretical values include a spin-orbit correction for SmO+ and Sm+ of 0.163 eV, see

ref. 5. g

Mean absolute deviations from experimental values.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 30 of 46

30 Table 4. Energies, zero point energies, bond distances, and bond angles for stationary states calculated along the potential energy surface for activation of the CO bond in COS by Sm+ a MP2/SDD

ZPE

CCSD(T)/SDD

Erel

r(Sm-O)

r(Sm-C)

∠OSmC

(Eh)

(Eh)b

(Eh)

(eV)c

(Å)

(Å)

(°)

-1167.709681

0.009128

-1167.735001

0.000, 0.000

-1167.703083

0.009128

-1167.729744

0.180, 0.143

Sm+(OCS) (8∆)

-1167.742693

0.009940

-1167.765897

-0.876, -0.819

2.432

3.622

0

(6∆)

-1167.735045

0.09903

-1167.759850

-0.669, -0.655

2.439

3.629

0

Sm+(OCS) TS (8A′′)

-1167.711426

0.007863 (1105i)

-1167.740833

-0.082, -0.193

2.265

2.691

27

(6A′′)

-1167.702885

0.007783 (1422i)

-1167.734726

0.148, -0.029

2.252

2.757

26

Sm+(OCS) bent (8A′′)

-1167.717639

0.008833

-1167.745935

-0.225, -0.306

2.239

2.458

31

(6A′′)

-1167.712284

0.008866

-1167.741697

-0.078, -0.189

2.213

2.495

31

Sm+(OCS) TSbb (8A′′)

-1167.708153

0.008427 (123i)

-1167.734843

0.023, -0.015

2.519

2.288

29

(6A′′)

-1167.698072

0.008077 (110i)

-1167.727588

0.287, 0.173

2.556

2.283

29

OSm+(CS) TS (8A′′)

-1167.600503

0.006398 (428i)

-1167.650113

2.897, 2.236

2.116

2.661

50

(6A′)

-1167.604489

0.006482 (428i)

-1167.666570

2.790, 1.790*

2.084

2.654

50

(6A′′)

-1167.601916

0.006437 (436i)

-1167.662438

2.859, 1.901*

2.085

2.648

50

OSm+(CS) GS (6A)d

-1167.727592

0.011759

-1167.751043

-0.412, -0.361

1.764

2.675

99

OSm+(CS) ES (8A′′)

-1167.616965

0.010356

-1167.654888

2.556, 2.213

1.985

2.741

93

(8A′)

-1167.612334

0.010782

-1167.651736

2.694, 2.311

2.124

2.736

93

Species (state) Sm+ + COS (8F1/2 + 1Σ+) (6F1/2 + 1Σ+)


Page 31 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


31

(6A′) SmO+ + CS (8Σ− + 1Σ+)

-1167.614169

0.010085

-1167.683636

2.625, 1.424*

2.106

-1167.568941

0.004331

-1167.611708

3.699, 3.224

2.082

2.745

(6∆ + 1Σ+) -1167.672780 0.005037 -1167.700885 0.893, 0.817 1.729 a Geometries and vibrational frequencies calculated at the MP2/SDD level with single point energy calculations using the CCSD(T)/SDD approach. Values for octet and sextet species are indicated in roman and italics font, respectively. b

Zero point energy after scaling by 0.989. Imaginary frequencies in cm-1 are included in parentheses.

c

In most cases, it can be seen that the MP2 and CCSD(T) values are similar, but in a few (marked by *), the differences are appreciable. This is attributed to mixing in the lower energy configuration in the CCSD(T) calculations.

d

This state has a OSmCS dihedral angle of 1.4°. A planar 6A′′ state lies 0.005 eV higher in energy.


95

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 32 of 46

32 Table 5. Energies, zero point energies, bond distances, and bond angles for stationary states calculated along the potential energy surface for activation of the CS bond in COS by Sm+ a MP2/SDD

ZPE

CCSD(T)/SDD

Erel

r(Sm-S)

r(Sm-C)

∠SSmC

(Eh)

(Eh)b

(Eh)

(eV)

(Å)

(Å)

(°)

-1167.709681

0.009128

-1167.735001

0.000, 0.000

-1167.703083

0.009128

-1167.729744

0.180, 0.143

Sm+(SCO) side (8Α′′)

-1167.723078

0.009363

-1167.746493

-0.358, -0.306

3.137

3.630

26

(8Α′)

-1167.722354

0.009354

-1167.745576

-0.339, -0.282

3.140

3.632

26

(6Α′′)

-1167.715724

0.009353

-1167.740520

-0.158, -0.144

3.170

3.668

25

Sm+(SCO) TSsb (8A′)

-1167.704427

0.007784 (1544i)

-1167.733682

0.106, -0.001

2.806

2.939

32

(6A)

-1167.704171

0.007461 (2417i)

-1167.728066

0.105, 0.143

2.828

3.012

32

Sm+(SCO) TSsq (6A)

-1167.713714

0.009121 (61i)

-1167.737784

-0.110, -0.076

2.659

2.048

39

Sm+(SCO) quad (6A)

-1167.730043

0.008389

-1167.761071

-0.574, -0.729

2.731

2.662

36

Sm+(SCO) TSqb (6A)

-1167.698564

0.007939 (165i)

-1167.728577

0.270, 0.142

2.910

2.298

33

Sm+(SCO) bent

(8A′′)

-1167.721356

0.008995

-1167.743880

-0.319, -0.243

2.683

2.531

38

ES (6A′′)

-1167.716015

0.008971

-1167.745069

-0.177, -0.278

2.663

2.574

38

GS (6A′′)

-1167.679237

0.009153

-1167.714169

0.829, 0.568

2.728

2.021

36

(8A′′)

-1167.696780

0.007252 (306i)

-1167.729059

0.300, 0.111

2.600

2.614

52

GS (6A′)

-1167.676381

0.008787 (181i)

-1167.701785

0.897, 0.895

2.659

2.048

39

ES (6A′)

-1167.698021

0.007175 (315i)

-1167.735604

0.264, -0.070

2.584

2.615

51

Species (state) Sm+ + COS (8F1/2 + 1Σ+) (6F1/2 + 1Σ+)

SSm+(CO) TS


Page 33 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


33

SSm+(CO)

(8A′)

-1167.704932

0.007158

-1167.739876

0.073, -0.188

2.608

2.737

83

GS (6A′)

-1167.740369

0.007079

-1167.770500

-0.869, -1.000

2.239

2.570

80

ES (6A′)

-1167.705313

0.007071

-1167.741164

0.063, -0.224

2.607

2.735

83

SmS+ + CO (8Γ + 1Σ+)

-1167.674686

0.005498

-1167.711907

0.853, 0.530

2.583

(6Φ + 1Σ+)

-1167.704237

0.006021

-1167.738811

0.064, -0.188

2.214

(6Φ + 1Σ+) -1167.678220 0.005497 -1167.716514 0.757, 0.404 2.586 a Geometries and vibrational frequencies calculated at the MP2/SDD level with single point energy calculations using the CCSD(T)/SDD approach. Values for octet and sextet species are indicated in roman and italics font, respectively. b

Zero point energy after scaling by 0.989. Imaginary frequencies in cm-1 are included in parentheses.



Page 34 of 46

34 Figure Captions Figure 1. Cross sections for the reaction between Sm+ and COS as a function of energy in the center-of-mass (lower x-axis) and laboratory (upper x-axis) frames: part a, logarithmic energy scale; part b, linear energy scale. The solid black line shows the collision cross section calculated using the trajectory model of ref. 45. The dashed blue line shows the model cross section given by eq 5, and the solid blue line is this model convoluted over the experimental energy distributions.

Figure 2. Reaction coordinate diagram for activation of the CO bond of COS by Sm+ calculated at the CCSD(T)/SDD//MP2/SDD level of theory (energies listed in Table 4). Red and blue lines indicate surfaces of sextet and octet spin, respectively. The thick horizontal line with error bars indicates the experimentally determined threshold energy for reaction 4. The red dashed line connects the OSm+(CS) GS with its diabatic source, the excited Sm+(4f55d2) + COS reactants and indicates that the crossing between sextet surfaces is likely to occur in the vicinity of the activation of the CO bond, see text.

Figure 3. Structures of intermediates and transition states along the potential energy surfaces for activation of the OC bond of COS by of Sm+ calculated at the MP2/SDD level of theory. Energies are given in Table 4. Species with octet spin are in part a and those with sextet spin are in part b.

Figure 4. Relaxed potential energy surface scans at the MP2/SDD level along the GS (dotted line) and ES (solid line) sextet surfaces for CO bond activation of COS by Sm+.


Page 35 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


35

Figure 5. Reaction coordinate diagram for activation of the CS bond of COS by Sm+ calculated at the CCSD(T)/SDD//MP2/SDD level of theory (energies listed in Table 5). Red and blue lines indicate surfaces of sextet and octet spin, respectively. Thick horizontal lines with error bars indicate experimentally determined energies for the reaction 3 exothermicity (red) and high energy feature (blue). The red dashed line connects the SSm+(CO) GS with its diabatic source, the excited Sm+(4f55d2) + COS reactants (off-scale, see Figure 2).

Figure 6. Structures of intermediates and transition states along the potential energy surfaces for activation of the SC bond of COS by Sm+ calculated at the MP2/SDD level of theory. Energies are given in Table 5. Species with octet spin are in part a and those with sextet spin are in part b.

Figure 7. Relaxed potential energy surface scans at the MP2/SDD level along the GS (dotted lines) and ES (solid line) sextet surfaces for CS bond activation of COS by Sm+. The two GS surfaces were obtained from the IRC of the SSm+(CO) TS (GS) (upper line) and a scan of the SC distance starting from the SSm+(CO) GS intermediate and going near the TS.



36

Energy (eV, Lab) 0.1

1

10

2

cm )

1000 Trajectory

Cross Section (10

-16

100 SmS+

10 1

Sm+ + COS SmO+

0.1 0.01 0.1

1

10

Energy (eV, CM) Energy (eV, Lab)

2

cm )

0

Cross Section (10

-16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 46

10

20

30

40

Sm+ + COS

100

Trajectory

10

SmS+

1 0.1 SmO+

0.01 0

2

4

6

8

10

Energy (eV, CM) Figure 1 ACS Paragon Plus Environment

Page 37 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


37

Figure 2



Page 38 of 46

38

1.22 159

2.265 2.432

27° 2.691

1.190 1.530 +

8

Sm (OCS) ∆

1.546

+

8

Sm (OCS) TS A’’

2.239 31°

1.26 147°

2.458 +

1.577

29° 2.288

50°

1.222 164° 1.587

3.192 + 8 Sm (OCS) TSbb A’’

124°

2.661

8

Sm (OCS) bent A’’

2.519

2.080

2.116

+

1.483 8

OSm (CS) TS A’’

1.985 93°

1.48

2.74 +

8

OSm (CS) (ES) A’’

Figure 3a


Page 39 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


39

1.221

2.439

1.190 1.530 +

6

Sm (OCS) ∆

2.252 26° 2.757 +

159° 1.541 6

Sm (OCS) TS A’’

2.213 31° 2.495 +

1.274 145°

2.070

2.084 50° 2.654

1.576

125°

1.484 OSm (CS) TS A’

6

Sm (OCS) bent A’’

+

6

1.764

2.106 1.487

95°

2.675

2.745 +

1.479

99° +

6

6

OSm (CS) (GS) A

OSm (CS) (ES) A’

1.226 163°

2.60 28° 2.297

1.597

3.148 6 Sm (OCS) TSbb A’’ +


Figure 3b


40

3

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 46

OSm+(CS) TS

2

1

0

+

OSm (CS) GS

+

-1

Sm (OCS) bent

1.0

1.5

2.0

2.5

3.0

OC bond length (A)

Figure 4


3.5

Page 41 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


41

Figure 5 ACS Paragon Plus Environment


Page 42 of 46

42

1.579

2.806

78°

1.613 162°

95

3.13

2.93 1.148 +

+

8

Sm (SCO) side A’’

2.683 38° 2.531 +

8

Sm (SCO) TSsb A’

2.280

2.600

1.695 143°

122°

52° 2.614

1.181

+

8

1.136 8

SSm (CO) TS A’’

Sm (SCO) bent A’’

2.608 83°

1.129

2.737 +

8

SSm (CO) (ES) A’ Figure 6a ACS Paragon Plus Environment

Page 43 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


43

1.579 1.155

1.562

3.321

174°

95° 3.170

1.169

49° +

3.268

6

Sm (SCO) side A

+

6

Sm (SCO) TSsq A

1.619 2.828 32° 3.012 +

162°

1.669 133°

2.731

1.243

64°

1.141 6

Sm (SCO) TSsb A’

2.285 +

6

Sm (SCO) quad A

2.663

1.719

1.695 2.750

140°

38° 2.574 1.179 + 6 Sm (SCO) bent (ES) A’’

136° 1.209

37° 25° 2.854 +

6

Sm (SCO) TSqb A

Figure 6b



Page 44 of 46

44

2.663

1.719

2.728

36° 2.021 2.436

140°

38° 2.574

1.179 6 Sm (SCO) bent (ES) A’’

1.615

+

+

6

Sm (SCO) bent (GS) A′′

2.243

2.584 51° 2.615

122°

1.656 2.659 39°

1.138

+

SSm (CO) TS (ES) A’

2.607

+

6

SSm (CO) TS (GS) A’

2.239 1.129

2.735 +

156° 1.226

2.048

6

83°

170° 1.241

1.130

80° 2.570

6

SSm (CO) (ES) A’


+

6

SSm (CO) (GS) A’

Figure 6c

Page 45 of 46

45

SSm+(CO) TS (GS)

0.5

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


+

SSm (CO) TS (ES)

0.0 SSm+(CO) ES

-0.5 Sm+(SCO) bent

-1.0 +

SSm (CO) GS

1.5

2.0

2.5

3.0

3.5

SC bond distance (A) Figure 7 Figure 6



46

TOC Graphic

2

cm )

Sm+ + COS

-16

collision limit

SmS+ (efficient)

Cross Section (10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 46

SmO+ (excess barrier) 0

2

4

6

8

Energy (eV)


10

Lanthanides as Catalysts: Guided Ion Beam and Theoretical Studies

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