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Hydrogen Sulfide as a Scavenger of Sulfur Atomic Cation Ryan C. Fortenberry, Tarek Trabelsi, and Joseph S. Francisco J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02923 • Publication Date (Web): 11 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

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The Journal of Physical Chemistry

Hydrogen Sulfide as a Scavenger of Sulfur Atomic Cation Ryan C. Fortenberry,∗,†,‡ Tarek Trabelsi,¶ and Joseph S. Francisco¶ †Georgia Southern University, Department of Chemistry & Biochemistry, Statesboro, GA 30460, U.S.A. ‡University of Mississippi, Department of Chemistry & Biochemistry, University, MS 38677, U.S.A. ¶Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, U.S.A. E-mail: [email protected] Phone: 912-478-7694

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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 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The well-studied hydrogen sulfide molecule is shown here for the first time to form a S−S bond barrierlessly with sulfur atomic cation to produce stable H2 SS+ , a compound for which there is nearly no literature data. Previous work has shown that the reaction of hydrogen sulfide with neutral atomic sulfur will likely only take place at high pressures. Conversely, this work shows that hydrogen sulfide will readily bind with atomic sulfur cation first through the 1 4 A00 state from association of H2 S with S+ (4 S) and then will relax down to the nearly degenerate 1 2 A0 or 1 2 A00 states. S+ (4 S) + H2 S lies 29.5 kcal/mol above the 1 4 A00 H2 SS+ minimum. The 1 4 A00 H2 SS+ minimum in the S−S bond is also directly intersected by the doublet potential energy surface. As the S−S bond shortens in the association, the 1 2 A0 and 1 2 A00 states split falling 33.5 kcal/mol and 26.4 kcal/mol, respectively, below the 1 4 A00 state. Hence, this work is opening the door for novel synthesis of S−S bonds or potential removal of the common H2 S toxin/pollutant through concatenation and subsequent precipitation.

Introduction The ubiquity of hydrogen sulfide in fossil fuel extraction and production combined with its toxic properties and simple structure make any novel H2 S chemistry applicable across the chemical spectrum. H2 S is known to form in nature from biological and even astronomical sources. 1 The recent discovery of S2 H in the interstellar medium 2 has shown that reactions of H2 S with the sulfur atomic cation may produce the S2 H radical in dense ultraviolet photon environments like the Horsehead nebula. The intermediate in the reaction of H2 S + S+ to produce S2 H is hypothesized to be H2 S2 + . The most stable form of this atomic composition, of course, is the hydrogen persulfide cation, HSSH+ , which exists in both cis and trans conformers 3 like the analogous HOOH+ hydrogen peroxide cation. 4,5 However, exploration of the [H2 ,S2 ]·+ potential energy surface (PES) has turned up a novel, third H2 S2 + isomer in the form of H2 S−S+ , 3 depicted in Figure 1a. This isomer is shown to be stable and lie in 2


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the range of 20 kcal/mol above the trans-HSSH+ global minimum. Figure 1: The side-on structure of (a) 1 2 A0 H2 SS+ and (b) the doublet C1 transition state.

a)

b)

Most hydrogen sulfide reactions are initiated with one of the hydrogen atoms and engage in S−H bond cleavage. The H2 S + S+ reaction, on the other hand, should engage directly with the central sulfur atom. Such a direct mechanism for the creation of a S−S bond with H2 S has not been documented. The reaction of hydrogen sulfide with neutral atomic sulfur leading to 1 A0 H2 SS, as well as other channels including SH + SH and hydrogen persuflide, has been explored. 6 However, the formation of the S−S bond in such a H2 SS molecule is believed only to form at high pressures due to a necessary bond S−S bond shortening. 6 The corresponding cation PES appears to have more favorable reaction chemistry.

Computational Details All computations in this work rely up the explicitly correlated coupled cluster singles, doubles, and perturbative triples CCSD(T)-F12/aug-cc-pVTZ level of theory 7–11 within the frozen-core approximation and the MOLPRO2015.1 quantum chemistry package. 12 The transition state optimization is undertaken within the Gaussian09 program and the MP2/631+G∗ level of theory. 13–15 Furthermore, a scan of the S−S bond from the CCSD(T)F12/aug-cc-pVTZ optimized geometries with 0.1 ˚ A intervals while the positions of the two hydrogen atoms and other sulfur is fixed for each state. 3



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Additionally, the anharmonic vibrational frequencies are computed for each spin state of H2 SS+ in order to provide accurate, anharmonic zero-point vibrational energy corrections and insights gained from the vibrational structure of H2 SS+ . A fourth-order Taylor series expansion of the potential within the internuclear Hamiltonian (a quartic force field or QFF) is constructed in a standard fashion 16–20 but only utilizing CCSD(T)-F12/aug-cc-pVTZ instead of a composite QFF approach, as is typical, 21 including work on the S2 H radical that ultimately led to its interstellar detection. 22 From the reference geometries, 665 total points are computed based on displacements of the below symmetry-internal coordinates:

S1 (a0 ) = r(S − S)

(1)

1 S2 (a0 ) = √ [r(H1 − S) + r(H2 − S)] 2 1 S3 (a0 ) = √ [6 (H1 − S − S) + 6 (H2 − S − S)] 2 S4 (a0 ) = 6 (H1 − S − H2 ) 1 S5 (a00 ) = √ [r(H1 − S) − r(H2 − S)] 2 1 S6 (a00 ) = √ [6 (H1 − S − S) − 6 (H2 − S − S)]. 2

(2) (3) (4) (5) (6)

Fitting of these points via a least-squares approach with the sum of residuals squared being on the order of 10−17 a.u.2 or less generates the equilibrium geometry that is refit to produce zero gradients. The subsequent force constants are incorporated in second-order vibrational perturbation theory (VPT2) 23–25 through transformations within the INTDER 26 program and evaluation within the SPECTRO 27 program. The vibrationally-averaged (Rα ) geometries, rotational constants, and vibrational frequencies are given in Table 2. MP2/augcc-pVTZ provides the double-harmonic intensities and dipole moments. The S5 and S6 a00 displacements of the 1 2 A00 state are not variationally accessible in the electronic structure computations for the QFF. The symmetry falls from Cs to C1 , and this state is the first excited state. Hence, the electronic wave function for displacements of these coordinates will

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not match that of the other points based on the 1 2 A00 geometry. This leaves only the four totally-symmetric frequencies computed for this state.

Results and Discussion The Nature of H2 SS+ Figure 2: The a) 4a00 , b) 14a0 , and c) 15a0 molecular orbitals.

a)

b)

c)

The geometry of the 1 2 A0 (presumed ground) state of H2 SS+ is optimized followed by geometry optimizations of the low-lying 1 2 A00 and 1 4 A00 states. The highest occupied molecular orbital (HOMO), HOMO-1, and lowest unoccupied molecular orbital (LUMO) are depicted in Figure 2. In the ground 2 A0 state, the 4a00 is the HOMO-1, 14a0 is the HOMO (or, alternatively, singly occupied molecular orbital: SOMO), and 15a0 is the LUMO. These correlate, respectively, with the 3pz , 3px , and 3py atomic orbitals on the terminal sulfur atom. There is no antibonding character in the 4a00 /3pz and little in the 14a0 /3px . These two orbitals also can be thought of as nearly degenerate 3p orbitals. However, the 15a0 /3py is fully antibonding with a 3py /lone pair orbital on the sulfur atom in the H2 S moiety which

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increases its relative energy. The CCSD(T)-F12/aug-cc-pVTZ 1 2 A0 state of H2 SS+ lies 20.8 kcal/mol above the transHSSH+ minimum as shown in Table 1. A preliminary MP2/6-31+G∗ transition state optimization puts the doublet C1 transition state (structure in Figure 1b) barrier at 56.8 kcal/mol, and the relative energy between the two isomers at this level of theory is a comparable 20.5 kcal/mol. Furthermore a CCSD(T)-F12/aug-cc-pVTZ energy at this MP2/631+G∗ transition state geometry reduces the barrier to 48.0 kcal/mol. Hence, the barrier to isomerization is likely ∼30 kcal/mol above ground state H2 SS+ . Consequently, H2 SS+ will not spontaneously isomerize to HSSH+ . Figure 3: The CCSD(T)-F12/aug-cc-pVTZ potential energy curves of the S−S stretch in 1 2 0 A (black), 1 2 A00 (red), and 1 4 A00 (green) H2 SS+ .

The scan of the S−S bond stretch is given in Figure 3. The black line is clearly the lowest and corresponds to the 1 2 A0 state. However, the red 1 2 A00 state lies only a few kcal/mol above the ground state, precisely 7.1 kcal/mol as given in Table 1. The PES in 6


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this coordinate begins to converge for both states as the S−S bond length gets to 2.5 ˚ A and longer. The reason is quite simple in that these are simply different occupations of otherwise degenerate 3p orbitals in the S+ cation. As shown above with the MOs in Figure 2, close to H2 S, the occupation of these two matters due to the antibonding character present in the HOMO/SOMO. Further away, the occupation does not matter since the relative positioning of the 3p orbitals becomes irrelevant. Table 1: The Reaction/Excitation Energiesa (in kcal/mol) for H2 SS+ Processes. CCSD(T)-F12b CCSD(T) MRCISD MRCISD(+Q) 2 + 2 0 + 1 Bg trans-HSSH → 1 A H2 SS 20.8 20.1 + 4 2 0 + H2 S + S ( S) → 1 A H2 SS -63.0 -61.2 -63.9 H2 S+ + S(3 P ) → 1 2 A0 H2 SS+ -66.7 -66.3 -66.0 + 2 2 0 + H2 S + S ( D) → 1 A H2 SS -110.8 -110.7 -105.4 -29.5 -29.8 -27.8 H2 S + S+ (4 S) → 1 4 A00 H2 SS+ 1 2 A00 H2 SS+ → 1 2 A0 H2 SS+ -7.1 -6.6 -6.0 -6.0 4 00 + 2 0 + -33.5 -31.4 -31.6 -30.9 1 A H2 SS → 1 A H2 SS a All computations utilize the aug-cc-pVTZ basis set except for MP2/6-31+G∗ . b Including the zero-point vibrational energy from Table 1.

At 2.7 ˚ A, the doublet potential energy surface crosses the quartet nearly at the same position as the optimum bond length in 1 4 A00 H2 SS+ . The quartet state is lower in energy at bond lengths longer than its equilibrium due to the orbital occupation of the lone S+ atom. H2 S does not contribute to the overall molecular term in the pure doublet and quartet surfaces since H2 is closed shell leaving all such unpaired electron arrangements largely dependent upon the sulfur atomic cation. Neutral sulfur is (3 P ) in its ground state like oxygen, but once it is ionized, the ground state term becomes S+ (4 S) like phosphorus or nitrogen. The excitation energy for the S+ (2 D) ← S+ (4 S) is computed here, again with CCSD(T)-F12/augcc-pVTZ, to be 47.9 kcal/mol where experiment is close to this value at 42.47 kcal/mol. 28 However, the key and most promising aspect of this study is that 1 4 A00 H2 SS+ is a fully stable minimum. Association of the S+ cation to H2 S is downhill with an energy gain of 29.5 kcal/mol (Table 1). Hence, ground state sulfur atomic cation appears to be able to bond with hydrogen sulfide in the gas phase. Then, the molecule can phosphoresce the 33.5 7


MP2/ 6-31+G∗ 20.5 -43.0 -52.1 -110.6 -23.6 -6.8 -19.5


kcal/mol (1.45 eV or 853 nm) energy and collapse to the exceptionally stable H2 SS+ 2 A0 ground state. Falling to the slightly higher 1 2 A00 state is also possible and will give off 26.4 kcal/mol in energy (1083 nm). These relative energies are corroborated with CCSD(T)/aug-cc-pVTZ, MRCISD/augcc-pVTZ, and MRCISD(+Q)/aug-cc-pVTZ computations 29,30 in Table 1, and the PES is confirmed by similar scans with MRCISD(+Q)/aug-cc-pVTZ (given in Figure S1 of the supplemental information, SI). The difference in any of the methods with CCSD(T)-F12/augcc-pVTZ is always less than 5.0 kcal/mol if not 1.0 kcal/mol indicating that the CCSD(T)F12 results are valid especially in comparison to both the “gold standard” quantum chemical method in CCSD(T)/aug-cc-pVTZ. 31 The T1 diagnostics at the minima are all less than the worrisome 0.02 value 32 with most less than 0.015. The MRCI computations treat the 10 lowest-energy orbitals for any of the H2 SS+ species as doubly occupied with the remaining valence orbitals treated as active orbitals. Even the MP2/6-31+G∗ computations are in quantitative agreement for the doublet values and are in semi-quantitative agreement for the quartet values. Regardless, the methods are consistent lending credence to the inferences made herein. Most likely, the doublet character for dissociation of H2 SS+ will not be conserved at the dissociation limit. While the doublet PES dissociation energy is 110.8 kcal/mol, the MRCISD(+Q)/aug-cc-pVTZ scan in Figure S1 indicates that 2 B1 H2 S+ and S(3 P ) will be be the final products of breaking the S−S bond in 1 2 A0 or 12 A00 H2 SS+ . The ionization potentials of H2 S+ and S(3 P ) are nearly identical at 10.457 eV and 10.360 eV, respectively, from standards, indicating that favorable electron occupations within dissociation are more important than ionization energies. Hence, the dissociation energy of 1 2 A0 H2 SS+ is most likely 66.7 kcal/mol from Table 1.

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Table 2: The CCSD(T)-F12/aug-cc-pVTZ Zero-Point (Rα ) Geometries, Vibrational Frequencies (Intensitiesa in Parentheses), and Spectroscopic Constants for 1 2 A0 , 1 2 A00b , and 1 4 A00 H2 SS+ . 1 2 A0 1 2 A00 1 4 A00 r0 (S−S) ˚ A 2.021 102 2.104 191 2.767 212 1.363 523 1.356 000 1.350 132 r0 (H−S) ˚ A 6 (H−S−S) 104.213 97.566 92.045 101.104 92.520 90.887 τ (H−S−S−H) A0 cm−1 4.980 520 4.795 621 4.755 494 0.240 517 0.223 855 0.131 842 B0 cm−1 0.237 767 0.222 988 0.131 513 C0 cm−1 µD 3.22 3.11 1.75 00 −1 ω1 (a ) cm H−S antisymm. stretch 2617.5 (82) 2613.5 (74) 2676.8 (34) ω2 (a0 ) cm−1 H−S symm. stretch 2691.7 (66) 2585.9 (78) 2661.8 (45) 0 −1 ω3 (a ) cm H−S−S symm. bend 1211.2 (12) 1150.2 (5) 1194.1 (1) 00 −1 ω4 (a ) cm H−S−S antisymm. bend 796.0 (0) 802.2 (6) 441.9 (1) ω5 (a0 ) cm−1 in-plane S bend 751.6 (5) 788.6 (4) 431.1 (39) 482.5 (1) 480.9 (1) 242.6 (23) ω6 (a0 ) cm−1 S−S stretch 4168.4 – 3770.6 Zero-Point cm−1 00 −1 2495.1 – 2563.8 ν1 (a ) cm H−S antisymm. stretch 0 −1 ν2 (a ) cm H−S symm. stretch 2479.7 2518.2 2550.1 ν3 (a0 ) cm−1 H−S−S symm. bend 1169.3 1118.4 1170.8 00 −1 769.3 – 421.5 ν4 (a ) cm H−S−S antisymm. bend 0 −1 ν5 (a ) cm in-plane S bend 724.2 782.4 409.0 ν6 (a0 ) cm−1 S−S stretch 472.4 474.7 237.4 a The double-harmonic intensities (in km/mol) and dipole moments are from MP2/aug-cc-pVTZ. b 00 The a vibrational states are not producible in the QFF. See text for discussion.

Spectroscopic Details As previously shown in the scan from Figure 3, the doublet and quartet geometries given in Table 2 differ notably in the S−S bond length. The occupation of the 15a0 antibonding 3py orbital (Figure 2c) in the 1 4 A00 state increases the bond length from 2.021 ˚ A in the 1 2

A0 state to 2.767 ˚ A in the quartet. The bond angles and dihedral in both of the A00 states

are close to 90.0◦ as is expected for third-row atoms where hybridization is not as common as in second-row atoms. 33–35 This also highlights that the MOs on the terminal carbon are behaving in the 3p-like fashion as suggested in the scan. Each of these three states exhibit near-prolate behavior in the rotational constants, and the longer S−S bond in the 1 4 A00 9



state almost halves the nearly degenerate B and C constants as compared to those in the two doublet states. The fundamental anharmonic vibrational frequencies are also provided in Table 2. The states all exhibit similar frequency and intensity magnitudes for similar atomic motions except for the three lowest-frequencies of the 1 4 A00 state. Each of these are heavily influenced by the elongated S−S bond in some way reducing their frequencies. Most notably from these vibrational computations is that for the 1 2 A0 state, the ν6 = 28 vibrational energy equals that of the excitation energy into or out of the 1 4 A00 state. While this overtone level should be put within a 25-30 quanta window due to accuracy reduction of the overtones, 36 vibrational progression can also be modeled instead of pure electronic collapse from the excited 1 4 A00 state to the 1 2 A0 state. The quanta for the 1 2 A00 state are reduced to 20-25 for such behavior, and the reduction in ν6 for the 1 4 A00 state will require nearly triple such quanta for it to dissociate with pure vibrational excitation. Granted, there is likely notable spin-orbit couplings between the doublet states and even these two states and the 1 4 A00 state. Hence, the photophysics will be intertwined to some extent. Regardless, each of these three spin states of H2 SS+ are further confirmed to be stable and possess a downhill pathway for association of a sulfur atomic cation to hydrogen sulfide. Additionally, the close proximity of the two doublet states and similar fundamental vibrational frequencies implies that electronic-vibrational (E-V) energy transfer could be taking place as the vibrational transitions of the two electronic surfaces interact with one another.

Conclusions This work showcases that S+ will bind with H2 S likely spontaneously in the gas phase. Recent astrochemical models have shown that H2 S in icy grains could be a reservoir of interstellar sulfur 37 indicating that collisions between hydrogen sulfide and the abundant sulfur atomic cation 38 are common in both the condensed and gas phases. As a result, concatenation of

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S−S bonds in space can begin with these two fairly ubiquitous interstellar species. Other environments where hydrogen sulfide and sulfur atomic cation are common, such as the Earth’s atmosphere and fossil fuel plumes, will likely produce similar behavior. Scavenging sulfur and potentially even other atomic cations (such as sodium and magnesium) by the common hydrogen sulfide molecule can now be further explored. The subsequent increase in the molecular density would reduce the volatility of hydrogen sulfide-related species making them easier to analyze and separate in various physical environments.

Supplemental Information The SI contains Figure S1 which is an additional scan of the S−S bond with the hydrogen sulfide coordinates fixed for each of the three spin states investigated. This is done with MRCISD(+Q)/aug-cc-pVTZ.

Acknowledgements RCF wishes to acknowledge support from NASA grant NNX17AH15G issued through the Science Mission Directorate as well as Prof. Nathan J. DeYonker of the University of Memphis for help in setting up the MRCI computations and pointing out the low-lying nature of the 1 2 A00 state. The WebMO graphical user interface 39 is utilized for visualizing the MOs in Figures 1 and 2.

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Hydrogen Sulfide as a Scavenger of Sulfur Atomic Cation - The

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