The Hydrogen Abstraction Reaction H2S + OH â H2O + SH

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The Hydrogen Abstraction Reaction HS + OH # HO + SH: Convergent Quantum Mechanical Predictions Mei Tang, Xiang-Rong Chen, Zhi Sun, Yaoming Xie, and Henry F. Schaefer J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09563 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 8, 2017

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The Journal of Physical Chemistry

The Hydrogen Abstraction Reaction H2S + OH → H2O + SH: Convergent Quantum Mechanical Predictions Mei Tang,a Xiangrong Chen,a* Zhi Sun,b Yaoming Xie,b and Henry F. Schaefer b* a

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, 610064, China

b

Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States

E-mail: [email protected] (X. C.), [email protected] (H. F. S.)

Abstract:

The hydrogen abstraction reaction H2S + OH → H2O + SH has been studied using

the “gold standard” CCSD(T) method along with the Dunning's aug-cc-pVXZ (up to 5Z) basis sets.

For the reactant (entrance) complex, the CCSD(T) method predicts a HSH···OH

hydrogen-bonded structure to be lowest-lying, and the other lower-lying isomers, including the two-center three-electron hemibonded structure H2S···OH, have energies within 2 kcal/mol. The similar situation is for the product (exit) complex. With the aug-cc-pV5Z single point energies at the aug-cc-pVQZ geometry, the dissociation energy for the reactant complex to the reactants (H2S + OH) is predicted to be 3.37 kcal/mol, and that for the product complex to the products (H2O + SH) is 2.92 kcal/mol.

At the same level of theory, the classical barrier height

is predicted to be only 0.11 kcal/mol.

Thus the OH radical will react promptly with H2S in the

atmosphere.

We have also tested the performance of 29 density functional theory (DFT)

methods for this reaction.

Most of them can reasonably predict the reaction energy, but the

different functional give quite different energy barriers, ranged from -10.3 to +2.8 kcal/mol, suggesting some caution in choosing density functionals to explore the PES of chemical reactions.

1

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1. INTRODUCTION The potential surface for the hydrogen atom abstraction reactions H2O + OH → OH + H2O has been successfully predicted by using the CCSD(T) method,1 which has been called “gold standard” for systems dominated for a single configuration.

Following the study of this simple

and archetypal reaction, the H2S + OH → SH + H2O reaction appears to come next as we seek to understand the mechanisms of reactions of the second-row molecular systems.

In fact,

hydrogen sulfide (H2S) exists in atmospheric, interstellar, and industrial environment, and it has an important impact on the environment, including topics such as acid rain, human health influence, and visibility reduction.2,3

The atmospheric loss process for the toxic H2S is

primarily oxidized by the hydroxyl radical.4

Thus, the reliable theoretical study of the H2S +

OH reaction should be anticipated by the chemistry community. Analogous to the H2O + OH reaction, the H2S + OH reaction should have an analogous reactant complex with a hydrogen bond between H2S and OH.

Indeed, the hydrogen-bonded

adduct HSH…OH has been optimized using the MP2/6-311G** method,5 and later the other hydrogen-bonded adduct H2S···HO was studied by the MP2 and B3LYP methods.6

In 2005,

however, ab initio and DFT investigations reported another kind of complex H2S···OH with a two-center three-electron S···O bond,7 based on experimental evidence for the two-center three-electron adduct of (CH3)2S-OH.

Recently, Alday et al.8 studied such a two-center

three-electron hemibond complex H2S···OH, and examined the electronic structure of the hemibond using the molecular orbital (MO) and natural bond orbital (NBO) analyses.

Alday et

al. attempted to compare the hemibond complex to the hydrogen bond complex which was 2


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optimized with DFT, but they were unable to optimize the hydrogen-bond complex with the CCSD(T)-F12 method.

One of our goals in the present research is to compare the different

complexes associated with this reaction. Although some parts of the potential surface for the H2S + OH → H2O + HS reaction have been theoretically studied before, those results had substantial discrepancies for the barrier height prediction.

In 2003, Mousavipour et al. predicted the barrier in a range from -5.0 to +2.6

kcal/mol with different theoretical methods.9

In 2007, Truhlar et al. adopted several DFT

methods and the MC-QCISD method to predict barrier values -0.24 kcal/mol (M06-2X) to +0.82 (MC-QCISD/3) kcal/mol.10

More recently (2015), a barrier of 0.18 kcal/mol is reported from

the CCSD(T) single point energy at the DFT geometry.11

In this paper, we will re-examine the

potential surface of the H2S + OH → H2O + HS reaction with high-level theoretical methods to provide more reliable structures and energetics.

2. THEORETICAL METHODS The CCSD(T) method12-14 was adopted in the present study to predict potential energy surface (PES) features for the H2S + OH reaction.

The CCSD(T) abbreviation denotes the

coupled cluster single and double excitations method with a perturbative treatment of triple excitations. Dunning's correlation-consistent polarized valence basis sets augmented with diffuse functions were adopted.15-17 used.

For the O and H atoms the standard aug-cc-pVXZ basis sets were

For the S atom an additional set of d functions was added, denoted as aug-cc-pV(X+d)Z, 3



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which has successfully corrected the deficiencies of the standard correlation consistent basis sets on the second-row atoms Al - Cl.18-20

In the text below, we may simply use DZ, TZ, QZ, and

5Z, respectively, to refer to the aug-cc-pVXZ (X = D, T, Q, 5, for O and H) and aug-cc-pV(X+d)Z (for S) basis sets for the sake of brevity.

The geometry optimizations were

carried out with basis sets up to QZ, while the larger 5Z basis sets were used for single-point energies (at the QZ geometries) to refine the energy profile.

The exception is for the isolated

reactants (H2S and OH) and products (H2O + SH), for which the optimized geometries using 5Z basis set are also reported. All the stationary points on the potential surface were characterized by harmonic vibrational frequencies at the same level (up to the QZ basis sets).

The CCSD(T) computations were

performed with the CFOUR program.21 In the present study, density functional theory (DFT) methods were tested, and 29 popular functionals were adopted for the H2S + OH reaction.

Among these DFT functionals, the

MPW1K (proposed in 2000) and M06-2X (proposed in 2008) methods are chosen to carry out more computations, parallel to the CCSD(T) results. This choice is based on the previous studies in which the MPW1K method22 was successfully applied to the H2O + OH reaction1 and the H2O + F reaction.23 The M06-2X method has been recommended by Truhlar et al.24 for main group thermochemistry and noncovalent interactions.

The DFT computations were

carried out using the Gaussian09 program.25

4


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3. RESULTS AND DISCUSSIONS 3.1 Structures and Energies of Stationary Points The stationary points on the CCSD(T) potential energy surface (PES) are outlined in Figure 1, and each point will be discussed below.

TS

Reactants 0.00 0.00 0.00 0.00

H S

O

RC-A -3.25 -3.31 -3.49 -3.55

H +

0.11 0.06 0.18 0.48

H

H

CCSD(T)/aug-cc-pV(5+d)Z CCSD(T)/aug-cc-pV(Q+d)Z CCSD(T)/aug-cc-pV(T+d)Z CCSD(T)/aug-cc-pV(D+d)Z

H

S H

O

H

H S

H

O

H O

H +

S

H S

H

H

H O

-32.48 -32.47 -32.12 -31.63

-29.54 -29.51 -29.13 -28.52

Products

PC-A

Figure 1. The profile of the potential energy surface for the H2S + OH → H2O + SH reaction predicted with the CCSD(T) method. For the 5Z basis set, only single-point computations were performed at the QZ geometry.

3.1.1 Reactants (H2S and OH) For the isolated reactants H2S and OH, the CCSD(T) predicted geometric parameters are convergent with the basis set size and in good agreement with the experimental results.26,27

The

S−H distances in H2S are predicted to be 1.350, 1.339, 1.338, and 1.338 Å, using the CCSD(T) 5



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method along with the DZ, TZ, QZ, and 5Z basis sets, respectively.

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The H−S−H bond angle of

H2S is 92.4°, 92.3°, 92.4°, and 92.4°, respectively (Figure S1 in Supporting Information). Those results are consistent with the experimental structure (1.3356 Å and 92.12°).26 For the OH radical the bond distance is predicted to be 0.980, 0.973, 0.971, and 0.970 Å, with the DZ, TZ, QZ, and 5Z basis sets, respectively (Figure S1 in Supporting Information). These theoretical results are well converged towards the experimental equilibrium separation 0.9697 Å.27 We also used the DFT methods (MPW1K and M06-2X) to obtain results parallel to CCSD(T).

With the M06-2X/aug-cc-pV(T+d)Z method, the S−H distance and the H−S−H

angle in H2S are 1.336 Å and 92.3°, respectively. corresponding values are 1.333 Å and 92.7°.

With the MPW1K functional, the

The O-H distance in the OH radical is predicted to

be 0.972 (M06-2X) and 0.963 (MPW1K) Å.

These two functionals predict reasonable

geometries for H2S and OH, in agreement with the CCSD(T) results.

3.1.2 Reactant (Entrance) Complex For the reactant complex H2S···OH, three isomers with different bonding have been found. One hydrogen-bonded isomer H2S···HO, RC-A at its 2A′ ground state (Figure 2) may correspond to the reactant complex (CP1) for the OH + H2O → H2O + OH reaction.1

However,

since the electronegativity of the S atom is less than that of the O atom, the hydrogen bonding between S and H atoms is weaker.

The dissociation energy of RC-A relative to the reactants

(H2S and OH) is predicted to be ~3.3 kcal/mol (Figure 1), which is notably smaller than the 6


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comparable relative energy (5.7 kcal/mol) of reactant complex (H2O)OH for the OH + H2O reaction.1

The 2A″ state (not included in Figure 2) for RC-A lies above the 2A′ ground state by

only 0.12 kcal/mol (Table 1).

This small difference is understandable because the OH radical

(2Π) has two degenerate components, and the weak interaction with the H2S molecule should not split these two electronic states significantly.

RC-A (2A′)

RC-B (2A′)

RC-C (2A″) Figure 2. The optimized geometries of the reactant complexes. All bond distances are in Å.

Another isomer RC-B has been called the hemibond complex (Figure 2),7,8,11 in which the S and O atoms are thought to share three electrons, making the S-O bond order 0.5. Note that the analogous bonding was also found in the water dimer cation (H2O)2+ and the dihydrogen sulfide dimer cation (H2S)2+, in which a hemi-bond was between two heavy atoms.28-32

The 7



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RC-B complex has only the 2A′ electronic state, with the unpair electron necessarily in the reflection plane.

The nature of the purported two-center three-electron hemibond was

investigated by Alday et al.8

The 2A″ state for RC-B is not a stationary point, since no such a

hemibond exists without the in-plane unpair electron, and it collapses to RC-A (2A″).

Table 1. The relative energies (kcal/mol) for the isomers of the reactant complexes. RC-A (2A’)

RC-A (2A”)

RC-B (2A’)

RC-C (2A”)

CCSD(T)/aug-cc-pV(D+d)Z CCSD(T)/aug-cc-pV(T+d)Z CCSD(T)/aug-cc-pV(Q+d)Z CCSD(T)/aug-cc-pV(5+d)Z

0.00 0.00 0.00 0.00

0.09 0.08 0.08 0.08

0.58 0.42 0.20 0.13

1.59 1.67 1.59 1.56

1.93 2.04 1.94 1.91

MPW1K/aug-cc-pV(D+d)Z MPW1K/aug-cc-pV(T+d)Z MPW1K/aug-cc-pV(Q+d)Z MPW1K/aug-cc-pV(5+d)Z

0.00 0.00 0.00 0.00

0.10 0.09 0.09 0.09

0.44 0.57 0.57 0.57

1.92 1.81 1.77 1.77

2.26

a

2.19

a

2.13

a

2.12

a

M06-2X/aug-cc-pV(D+d)Z M06-2X/aug-cc-pV(T+d)Z M06-2X/aug-cc-pV(Q+d)Z M06-2X/aug-cc-pV(5+d)Z

0.00 0.00 0.00 0.00

0.09 0.09 0.09 0.09

-1.28 -1.22 -1.17 -1.17

1.88 1.94 1.90 1.92

1.56

a

1.51

a

1.49

a

1.49

a

Methods

a

RC-C (2A’)

With an imaginary vibrational frequency.

There has been long-standing uncertainty whether the reactant complex is a hemibond structure or a hydrogen-bonded form.

Our CCSD(T) method predicts that these two isomers

(RC-A and RC-B) have very close energies with RC-B marginally higher by 0.58, 0.42, 0.20, and 0.13 kcal/mol with the DZ, TZ, QZ, and 5Z basis sets, respectively (Table 1).

In order to

find the energy barrier between RC-A and RC-B, we scanned the structure energies with respect to the S-H-O angle from 35° to 245° with the CCSD(T)/ang-cc-pV(D+d)Z method.

The 8


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resulting energy curve is seen in Figure 3, and it shows the structure RC-A is lower than RC-B by ~0.5 kcal/mol, and the barrier is only 0.12 kcal/mol from the hemibond (RC-B) side, indicating a very flat potential surface around these two isomers. The third isomer RC-C has a hydrogen bond between the H atom in H2S and the O atom in OH (Figure 2), and it was reported previously.5, 6

This RC-C isomer HSH···OH is analogous

to a reactant complex CP2 (HOH···OH) for the H2O + OH reaction1, and RC-C is higher than the lowest complex CP1 by about 2 kcal/mol.

The RC-C isomer has two electronic states (2A″

and 2A′) with the 2A″ state slightly (0.2 kcal/mol) lower.

The 2A″ state of RC-C lies above

RC-A by 1.59, 1.67, 1.59, 1.56 kcal/mol (Table 1) with DZ, TZ, QZ, and 5Z, respectively.

Figure 3. Potential energy curve between RC-A (2A′) and RC-B (2A′) with the CCSD(T)/aug-cc-pV(D+d)Z method and with the DFT methods.

9



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As a comparison, the DFT (M06-2X and MPW1K) relative energies are also shown in Table 1 and Figure 3. CCSD(T) method.

It is noted that the MPW1K method predicts energies similar to the

On the contrary, the M06-2X method predicts RC-B structure lies lower

than RC-A by ~1.2 kcal/mol.

The potential energy curves predicted by M06-2X and MPW1K

are also shown in Figure 3, which clearly shows the comparison of the two DFT results with CCSD(T).

The different energy ordering was also observed in the study of the water dimer

cation (H2O)2+ system.

The DFT methods, such as M06-2X and B3LYP, predict the hemibond

structure to be the global minimum,28-30 while the high-level ab initio studies predicted that the hydrogen-bonded structure is more stable.31-33 experiment.34

As expected, the later results were supported by

Table 1 shows that the DFT methods predicts some structures with an imaginary

vibrational frequency, although the CCSD(T) method predicts all real frequencies for these isomers.

Most of these imaginary frequencies are around 100i cm-1.

However, we will not go

further to find the DFT minima because the present study focuses on the CCSD(T) results.

In

Section 3.2 below, we will examine more DFT methods to show that the use of DFT methods should be done with caution.

3.1.3 Transition State The structure of transition state (TS) for the H2S + OH → H2O + SH reaction is optimized in the present study with the CCSD(T)/aug-cc-pV(X+d)Z (X = D, T, Q) methods, and it lies above the reactants (H2S and OH) by 0.48, 0.18, and 0.06 kcal/mol, respectively.

The single

point energy with the 5Z basis sets makes the relative energy to be 0.11 kcal/mol.

This is 10


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comparable with the MCG3/3 barrier height (0.4 kcal/mol) reported by Truhlar et al. in their 2013 paper.10

This barrier is also very close to the reported Arrhenius activation energy (0.3

kcal/mol),35 although one should be cautious about equating the Arrhenius activation energy to the barrier height. This transition state is confirmed with the vibrational analysis.

There is one (and only one)

imaginary vibrational frequency (914i, 879i, or 871i cm-1 predicted by DZ, TZ, or QZ basis sets, respectively), corresponding to the S···H···O asymmetric stretching mode, which leads to the HSH···OH complex on one side and the HS···HOH complex on other side. Our optimized geometry of the TS with the CCSD(T) method is shown in Figure 4.

The

geometrical parameters for this structure are convergent with respect to the size of the basis sets. Compared with the previous studies, our geometrical parameters are quite different from the earlier theoretical studies with the MP2 method by Wilson et al.5 in 1994 and by Mousavipour et al. in 2003.9

In References 5 and 9, the H···O distance (1.377 Å) is shorter than the S···H

distance (1.416 or 1.417 Å).

However, we predict that the S···H distance of 1.402 Å is shorter

than the H···O distance of 1.483 Å (with the QZ basis sets, Figure 4), and our result is coincident with Hammond’s postulate.

Our predicted S-H-O bond angle is 137.5° (QZ), which is also

different from the value of 148.82° obtained at the MP2/6-311++G(3df,3pd) level of theory.9 Our dihedral angle τ(H-S-H-O) is predicted to be 70.8° (QZ), while it was previously reported as 150.9°.5

However, the present results are in good agreement with those reported by Truhlar et

al. in 2013,10 in which the geometry for this transition state was optimized with four DFT methods (M06-2X, MPW1K, BB1K, MPWB1K) and the MC-QCISD method. 11



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1.483 CCSD(T)/aug-pV(Q+d)Z 1.480 CCSD(T)/aug-pV(T+d)Z 1.474 CCSD(T)/aug-pV(D+d)Z

1.402 1.403 1.416 1.339 S 1.340 92.2° 1.351 92.0° 92.2° H

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H

O

137.5° 139.1° 102.4° 139.9° 102.2° 102.7°

(H-S-H-O) = 70.8° 70.7° 71.5°

H

0.970 0.973 0.979

(S-H-O-H) = 38.6° 38.3° 40.3°

Figure 4. Three optimized geometries of the transition state TS.

All bond distances are in Å.

With the two Truhlar DFT (M06-2X and MPW1K) methods using the aug-cc-pV(T+d)Z basis set, we find the energy barrier is predicted to be -0.5 kcal/mol (M06-2X) or +0.7 kcal/mol (MPW1K).

The TS structure has the corresponding S-H bond distance of 1.399 Å and O-H

distance of 1.459 Å and the S-H-O bond angle is predicted to be 138.4° with M06-2X method. These geometrical parameters agree with the CCSD(T) results.

3.1.4 Product (Exit) Complex As for the reactant complex (Section 3.1.2), we found three isomers for the product complex (H2O…HS, Figure 5), and their energies are within 1 kcal/mol of each other.

The

hydrogen-bonded structure H2O…HS (PC-A) at its 2A′ electronic state is of the lowest energy, while its 2A″ state has slightly higher energy (0.3 kcal/mol, Table 2).

The 2-center 3-electron

hemibond H2O…SH (PC-B) also has a 2A′ ground state, lying above PC-A by less than 1 kcal/mol (Table 2).

Similar to the reactant complexes, the 2A″ state of PC-B is not a stationary 12


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point, but collapses to the 2A″ state of PC-A.

There is another hydrogen-bonded structure

HOH…SH (PC-C) with nearly degenerate energy to PC-A.

The 2A′ state and the 2A″ state of

PC-C have similar energies, and they lie above PC-A by less than 0.3 kcal/mol (Table 2).

PC-A (2A′)

PC-B (2A′)

PC-C (2A″)

Figure 5. Optimized geometries of the product complexes. All bond distances are in Å.

The product complex isomers have much lower energies than the reactant complexes.

The

lowest isomer PC-A (2A′) lies below the reactants (H2S and OH) by about 32 kcal/mol (Figure 1). Relative to the isolated products (H2O and SH), the dissociation energy of the 2A′ product complex PC-A is 3.1, 3.0, and 3.0 kcal/mol predicted by the DZ, TZ, and QZ, respectively. The single-point energy with 5Z basis set at the QZ geometry is predicted to be 2.9 kcal/mol. 13



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Table 2.

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Relative energies (kcal/mol) for the isomers of the product complexes. PC-A (2A’)

PC-A (2A”)

PC-B (2A’)

PC-C (2A”)

PC-C (2A’)


0.00 0.00 0.00 0.00

0.25 0.23 0.25 0.25

0.91 0.75 0.76 0.74

0.10 0.16 0.26 0.29

0.29 0.26 0.25 0.26

MPW1K/aug-cc-pV(D+d)Z MPW1K/aug-cc-pV(T+d)Z MPW1K/aug-cc-pV(Q+d)Z MPW1K/aug-cc-pV(5+d)Z

0.00 0.00 0.00 0.00

0.25 0.23 0.23 0.23

0.85 0.84 0.87 0.86

0.25 0.21 0.24 0.23

−b −b −b −b

M06-2X/aug-cc-pV(D+d)Z M06-2X/aug-cc-pV(T+d)Z M06-2X/aug-cc-pV(Q+d)Z M06-2X/aug-cc-pV(5+d)Z

0.00a 0.00a 0.00a 0.00

0.26

-0.56 -0.62 -0.62 -0.58

-0.17 -0.14 -0.12 -0.14

−b

Methods

a b

0.22 0.23 0.23

− −c −c

With a small imaginary vibrational frequency. Collapsed to PC-A. c Collapsed to PC-B.

Table 2 also lists the results from the parallel computations with the DFT (MPW1K and M06-2X) methods.

It can be seen that the relative energies from the MPW1K method are close

to the CCSD(T) results except that the PC-C (2A′) structure is not a stationary point, but collapses to PC-A.

The M06-2X method predicts a different energy order, in that the PC-B and

PC-C structures are lower than PC-A, although the energy differences are very small, within 1 kcal/mol.

3.1.5 Products H2O and HS The geometric parameters for products (SH and H2O) predicted by the CCSD(T) method (Figure S2 in Supporting Information) are in excellent agreement with experiment.27,37

With 14


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the largest basis set (5Z), the S-H distance in SH radical is 1.3421 Å, while the experimental measurement is 1.3409 Å.27

The predicted O-H distance and H-O-H angle in H2O are 0.9584 Å

and 104.43°, respectively, in excellent agreement with the experimental determination of 0.9578 Å and 104.48°.36 The CCSD(T) energy change for the exothermic reaction H2S + OH → H2O + SH is 28.5, 29.1, 29.5, and 29.5 kcal/mol predicted with the DZ, TZ, QZ, and 5Z basis sets, respectively (Figure 1), which is close to the experimental reaction heat, 28 kcal/mol.37

As a comparison,

Truhlar et al. have reported the energy of reaction to be 30.9 kcal/mol (MC-QCISD/3) or 31.4 kcal/mol (MCG3/3//MC-QCISD/3),10 and Zhang et al. reported it to be 27.4 kcal/mol with the CCSD(T)//BH&HLYP method.11

Our obtained exothermicity is between the values reported by

Truhlar et al. and Zhang et al. As for the DFT results, the exothermicity is predicted to be 26.5 kcal/mol with the MPW1K method and the aug-cc-pV(T+d)Z basis set, and it is 29.7 kcal/mol with the M06-2X method. The S−H distance in SH radical is 1.336 Å and 1.339 Å with the MPW1K and M06-2X methods, respectively, in good agreement with the experimental results.

The DFT geometry of H2O is

also close to experiment.

3.2 Energetics of DFT Methods Density functional theory (DFT) is commonly-used tool for theoretical chemistry nowadays, and the newer functionals are proposed continually.

Since various DFT methods are

constructed with different strategies, they may predict different results for particular problems.1,23 15



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Page 16 of 33

Thus, it is worth comparing the performance of different DFT functionals, applied in the H2S + OH → H2O + SH reaction. In the present study, we adopted 29 functionals with aug-cc-pV(T+d)Z basis sets to investigate the H2S + OH → H2O + SH reaction,

Table 3 lists the energies of all stationary

points for this reaction predicted from the 29 DFT methods. methods38-69 are provided in the last column of the table.

References to the various DFT

For comparison, the CCSD(T) results

are also included at the bottom of Table 3. Most DFT methods predict the energy of reaction in a reasonable range from -25.9 to -31.4 kcal/mol, indicating that they are well designed to treat the geniune minima.

However,

different DFT methods predict very different relative energy for the transition state (TS) in a large range from -10.3 to +2.8 kcal/mol.

Five of the methods predict positive barriers, whereas

the other 24 DFT functionals predict the negative barriers.

Similar to the cases of the H2O +

OH reaction and H2O + F reaction,1,23 the Hartree-Fock (H-F) component in the functional plays an important role in predicting the energy barrier. The DFT methods with larger fractions of H-F exchange generally yield higher barriers.

For instance, a barrier of 2.8 kcal/mol for this

reaction is found using BH&HLYP functional (with 50% H-F component).

The pure DFT

method BP86 (with zero H-F component) yields an erroneous and very negative barrier of -10.3 kcal/mol.

The most popular B3LYP functional predicts a notably too low relative energy for

transition state (-3.9 kcal/mol) and the entrance complex (-6.8 kcal/mol).

This suggests

cautions in choosing density functionals to explore the PESs of chemical reactions.

16


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Table 3 Relative energies (in kcal/mol) for the stationary points on the potential energy surface for the H2S + OH reaction predicted by 29 DFT methods along with the aug-cc-pV(T+d)Z basis sets. The most reliable CCSD(T)/5Z results are reported on the last line for comparison. Methods BH&HLYP M06HF MPW1K BB1K MPWKCIS1K

MPWB1K M06-2X M05-2X wB97 BMK wB97X M05 wB97XD CAM-B3LYP mPW1PW91 M06 B3PW91 PBE0 B3LYP HSEh1PBE B98 TPSS1KCIS MPW3LYP TPSSh M06L MPW1KCIS VSXC BLYP BP86 CCSD(T)/5Z a

H2S+OH 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Reactant complex -2.3 -3.4 -2.5 -3.3 -2.8 -3.8 -4.7 -5.0 -5.1 -4.5 -5.2 -5.8 -5.1 -5.5 -5.5 -6.9 -6.1 -6.3 -6.8 -6.5 -7.1 -7.3 -7.5 -7.4 -8.1 -8.2 -10.6 -11.4 -12.4 -3.3

TS 2.8 1.6 0.7 0.3 0.1 -0.1 -0.5 -1.1 -1.1 -1.2 -1.6 -1.7 -1.9 -2.3 -2.8 -3.0 -3.4 -3.7 -3.9 -3.9 -4.2 -4.4 -4.6 -4.6 -5.1 -5.8 -7.1 -9.2 -10.3 0.1

Barrier of TS from RC 5.1 5.0 3.2 3.6 2.9 3.7 4.3 3.9 4.0 3.3 3.6 4.1 3.3 3.2 2.7 3.9 2.7 2.7 2.9 2.6 2.9 2.8 3.0 2.8 3.0 2.5 3.5 2.2 2.1 3.5

Exit complex -27.6 -33.8 -28.1 -28.6 -29.2 -29.1 -33.1 -33.1 -32.2 -31.6 -31.9 -32.1 -31.2 -31.6 -29.8 -32.9 -30.0 -30.5 -30.7 -30.5 -31.7 -28.8 -31.4 -28.2 -29.3 -31.8 -34.0 -32.6 -33.4 -32.5

H2O+HS -25.9 -31.4 -26.5 -27.0 -27.6 -27.0 -29.7 -29.8 -28.3 -29.5 -28.2 -29.1 -28.4 -29.4 -27.9 -29.3 -28.4 -28.1 -28.7 -27.9 -28.9 -26.4 -28.7 -25.6 -25.3 -29.6 -28.0 -29.8 -30.0 -29.5

HF%

Ref

50 100 42.8 42 41 44 54 56 LCa 42 LCa 28 LCa

38 39 22 40 41 42 24 44 45 43 45 47 46 48 49,50 24 50,51

19-65

25 27 20 25 20 25 21.98 13 21.8 10 0 15 0 0 0

52-54

51 55-61

62 63 42,49 64 65 41 66 67,68 68,69

For the LC methods, the percentage of H-F component varies with the long-range corrections. Table 3 shows that those functionals with the H-F component of 40 – 54% predict the

energy barrier close to the CCSD(T) results (± 0.6 kcal/mol).

Among those functionals, the 17



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Page 18 of 33

MPW1K method was reported to predict the best energy barriers for the H2O + OH reaction and the H2O + F reaction.1,23 The M06-2X method has been recommended for kinetics by Truhlar et al.24

Thus, we have chosen these two functionals along with the cc-pV(T+d)Z basis sets to

study all structures as shown in Tables 1 and 2, and discussed in Section 3.1. In fact, Truhlar and co-workers have systematically evaluated the DFT performance for prediction of transition state geometries and barrier heights.70 similar trend.

Our results in Table 3 show a

In the present paper we have provided another case for which B3LYP tends to

underestimate barriers, whereas the BB1K and MPWB1K predict good barrier height for the H2S + OH reaction. Turhlar et al. also reported benchmark computations of the transition state geometries and barrier heights.71-73

One of their goals was to give reasonably accurate energetics using the

least expensive levels of theory, including the strategy of performing high-level single-point energies at the geometries from the best functionals.

In this connection, we have listed in Table

S4 (Supporting Information) the different geometries of the transition states optimized by the 29 DFT methods.

These 29 geometries are in reasonable agreement, since the CCSD(T)

single-point energies (Table S5 in Supporting Information) are in a narrow range (± 0.5 kcal/mol). Using two extreme cases in Table 3 (BH&HLYP and BP86), the barrier heights predicted by the CCSD(T) single-point energies are -0.0 and -0.2 kcal/mol, respectively, which are much better than those (+2.8 and -10.3 kcal/mol) in Table 3.

Considering that the reliability of

CCSD(T)/CBS for thermochemical kinetics is in the neighborhood 0.4 kcal/mol,74 this single-point strategy should be applicable. 18


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3.3 Vibrational Frequencies and ZPVE Corrections Table 4 displays the harmonic vibrational frequencies and zero-point vibrational energies (ZPVEs) for all the stationary points in the H2S + OH reaction predicted with the CCSD(T) method.

Our results predicted by the CCSD(T) method along with the QZ basis sets are in

excellent agreement with the available experimental harmonic vibrational frequencies for the reactants (H2S and OH) and products (H2O and SH).27,75

The largest deviation is only 5 cm-1

for all the vibrational frequencies for H2O, H2S, and the OH radical, while for the SH radical the deviation is somewhat larger, which is 12 cm-1 (2700 cm-1 vs 2712 cm-1). As mentioned above, the imaginary vibrational frequency of the transition state is predicted to be 914i, 879i, and 871i cm-1 with the DZ, TZ, and QZ basis sets, respectively. From Table 4, it is shown that the ZPVE correction for the reactants (H2S and OH) using three basis sets (DZ, TZ, and QZ) is in a small range (from 14.74 to 14.88 kcal/mol), while the ZPVE correction for the products (H2O and SH) is from 17.17 to 17.33 kcal/mol.

Thus, the

ZPVE corrections decreases the exothermicity by 2.43 (DZ), 2.41 (TZ), or 2.45 (QZ) kcal/mol, and ∆H, the energy of reaction with QZ basis set, becomes -27.06 kcal/mol (QZ), which is close to the experimental results of 28 kcal/mol.37 The ZPVE correction for the reactant complex (RC-A) is ~1.5 kcal/mol, and the relative energy of RC-A after the ZPVE correction becomes -1.8, -1.6, and -1.4 kcal/mol (DZ, TZ, and QZ, respectively).

Similarly, the relative energy of the product complex is reduced to -27.8,

-28.4, and -28.6 kcal/mol (DZ, TZ, and QZ, respectively) after ZPVE corrections. 19



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Page 20 of 33

Table 4. Harmonic vibrational frequencies (ω in cm-1) and ZPVEs (in kcal/mol) for the stationary points of the H2S + OH reaction with the CCSD(T) method. Relative energies are given with and without zero-point vibration energy (ZPVE) corrections (in kcal/mol). The experimental harmonic vibrational frequencies (ω, in cm-1) for the reactants and products are also listed for comparison. ZPVE

∆ZPVE

∆E

∆EZPVE

Vibrational Frequencies ω CCSD(T)/aug-cc-pV(D+d)Z

H2S + OH

14.74

0.00

0.00

0.00

2726

2705

1198

(H2S);

3684

(OH)

RC-A

16.32

1.58

-3.37

-1.79

3610

2721

2700

1198

448

337

148

146

111

TS

15.27

0.53

0.48

1.01

3697

2708

1692

1100

721

333

251

181

914i

PC-A

18.35

3.61

-31.44

-27.83

3903

3785

2667

1638

364

223

109

78

72

H2O + HS

17.17

2.43

-28.52

-26.09

3905

3787

1638

(H2O);

2682

(SH)

3718

(OH)

CCSD(T)/aug-cc-pV(T+d)Z H2S + OH

14.84

0.00

0.00

0.00

2731

2716

1211

(H2S);

RC-A

16.40

1.56

-3.16

-1.60

3636

2728

2713

1209

451

342

143

140

114

TS

15.42

0.58

0.18

0.76

3725

2718

1748

1110

720

327

256

179

879i

PC-A

18.35

3.51

-31.75

-28.24

3917

3809

2669

1645

351

202

109

77

60

H2O + HS

17.25

2.41

-29.13

-26.72

3920

3811

1646

(H2O);

2693

(SH)

3739

(OH)

330

139

136

111

CCSD(T)/aug-cc-pV(Q+d)Z H2S + OH

14.88

0.00

0.00

0.00

2738

2722

1212

(H2S);

RC-A

16.40

1.52

-2.96

-1.44

3654

2734

2719

1210

TS

15.52

0.64

0.06

0.70

3744

2725

1786

1112

721

326

258

181

871i

PC-A

18.37

3.49

-32.06

-28.57

3939

3830

2675

1648

347

195

109

74

30

H2O + HS

17.33

2.45

-29.51

-27.06

3941

3831

1650

(H2O);

2700

(SH)

440

Experimental results H 2S

a

OH

b

H 2O HS a

2733

2722

1215 3738

a

3943

3832

1649

b

2712 b

Ref. 75; Ref. 27. The ZPVE correction increases the barrier height by ~0.6 kcal/mol, the barrier height after

the ZPVE corrections would be 1.0, 0.8, and 0.7 kcal/mol (DZ, TZ, and QZ, respectively).

If

we apply the ZPVE corrections from QZ basis sets onto the 5Z single-point energies, then the best estimation for the relative energies for the RC, TS, PC, and products (H2O + HS) will be 20


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-1.73, 0.75, -28.99, and -27.09 kcal/mol, respectively.

3.4 The Effect of the Additional d Function on the Sulfur Atom. In 1995, Bauschlicher and Partridge found that the atomization energy of SO2, among the 55 G2 molecules, is the most sensitive to basis set.18

The aug-cc-pVTZ basis set is found to

perform significantly less well, because of lack of a tight d function.

In 1998, Martin and Uzan

reported that by adding a single high-exponent d function to the standard cc-pVnZ (n = 3, 4, 5) basis sets, convergence is greatly accelerated for the second-row compounds.19

Thus, Dunning,

Peterson, and Wilson20 suggested their newly constructed cc-pV(X+d)Z basis sets for the second-row elements, and this is what we have used in the present study. Here we test how the additional d functions effect the energy barrier and the isomerization energies for the sulfur-containing structures studied in this paper.

Table 5 lists the CCSD(T)

relative energies of the stationary points for the H2S + OH → H2O + SH reaction with two sets of basis functions: the first is the original aug-cc-pVXZ basis set, and the second is the basis set with the additional d functions on the S atom.

Table 5 shows that the two kinds of basis sets

predict almost the same relative energies for the reactant complex (RC-A) with the difference less than 0.07 kcal/mol.

For the transition state (TS), the basis sets with additional d functions

predict slight higher relative energies by 0.02 – 0.29 kcal/mol.

For the product complex (PC-A)

and the products, the differences are somewhat larger, the relative energies are predicted to be higher by 0.07 – 1.02 kcal/mol, but the differences decrease when the size of the basis set increases.

21



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Table 5. Comparison of the relative energies of the stationary points for the reaction of H2S + OH → H2O + SH predicted by the CCSD(T)/cc-pVXZ (X = D, T, Q) method and by the basis sets with the additional set of d functions on the S atom. Methods CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pV5Z CCSD(T)/aug-cc-pV(D+d)Z CCSD(T)/aug-cc-pV(T+d)Z CCSD(T)/aug-cc-pV(Q+d)Z CCSD(T)/aug-cc-pV(5+d)Z

Reactants 0.00 0.00 0.00 0.00

RC-A -3.57 -3.49 -3.32 -3.18

TS 0.19 0.03 -0.03 0.09

PC-A -32.65 -32.67 -32.79 -32.53

Products -29.49 -29.65 -29.81 -29.59

0.00 0.00 0.00 0.00

-3.55 -3.49 -3.31 -3.25

0.48 0.18 0.06 0.11

-31.63 -32.12 -32.47 -32.48

-28.52 -29.13 -29.51 -29.54

Table 6. Comparison of the relative energies for the different structures of the reactant complex and those of the product complex predicted by the CCSD(T)/cc-pVXZ (X = D, T, Q) method and by the basis sets with the additional set of d functions on the S atom. Methods

RC-A (2A’) RC-B (2A’)

RC-C (2A”)

PC-A (2A’) PC-B (2A’)

PC-C (2A”)

CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pV5Z

0.00 0.00 0.00 0.00

0.58 0.43 0.21 0.05

1.59 1.69 1.58 1.48

0.00 0.00 0.00 0.00

0.94 0.76 0.77 0.74

0.12 0.18 0.27 0.28


0.00 0.00 0.00 0.00

0.58 0.42 0.20 0.13

1.59 1.67 1.59 1.56

0.00 0.00 0.00 0.00

0.91 0.75 0.76 0.74

0.10 0.16 0.26 0.29

In Table 6, we report similar comparisons for the relative energies of the isomers for the reactant complex and the product complex.

The results show that the isomerization energies are

not sensitive for the additional d functions on the S atom.

The differences of the isomerization

energies predicted by the two types of basis sets are almost the same, within 0.08 kcal/mol. 22


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4. CONCLUSIONS We have investigated the stationary points on the potential energy surface for the H2S + OH → H2O + HS reaction using the "gold standard" CCSD(T) method with basis sets up to aug-cc-pV(5+d)Z. 1. Analogous to the previously studied H2O + OH reaction, there exist both reactant complexes and product complexes.

However, the binding energies for these

complexes are much smaller (e.g., 3.4 kcal/mol for H2S···HO vs. 5.7 kcal/mol for H2O···HO) than those of the H2O + OH reaction.

This is due to the weaker hydrogen

bonding between the S atom and the H atom than that between the O atom and the H atom. 2.

For the reactant complex, there are three isomers: two with hydrogen bonding (like H2O + OH) and one with what has been called7,8 a 2-center 3-electron hemibond. These isomers have energies within 2 kcal/mol.

3. The product complex also has three distinct structures, analogous to the reactant complex.

These isomers have nearly degenerate energies (within 1 kcal/mol).

4. The CCSD(T) classical barrier height is predicted to be 0.11 kcal/mol (relative to the reactants H2S + OH) based on the 5Z single-point energies at the QZ geometries. most reliable ZPVE corrected barrier height is 0.75 kcal/mol.

The

It is clear that the OH

radical will react promptly with H2S in the atmosphere. 5. Different DFT methods predict quite different barrier height for the H2S + OH reaction, 23



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Page 24 of 33

although most of them can predict reasonable reaction energies.

Those functionals

with the 40% H-F component predict the barrier height close to the CCSD(T) result. The 2000 MPW1K method of Truhlar did especially well.

This was also true for the

H2O + OH reaction and the H2O + F reaction. 6. The additional set of d basis functions on the sulfur atom changes the relative energies of the stationary points for the H2S + OH reaction.

But the energy changes are not

large (less than 1 kcal/mol).

Supporting Information The optimized geometries of the reactants H2S and OH (Figure S1), the optimized geometries of the products H2O and SH (Figure S2), the optimized geometries (Z-matrix) of the entrance complex (Table S1), the optimized geometries (Z-matrix) of the transition state TS (2A) (Table S2), the optimized geometries (Z-matrix) of the product (exit) complex (Table S3), and complete author lists of References 21 and 25.

Acknowledgments This work was supported by the NSAF Joint Fund set up by the National Natural Science Foundation of China and the Chinese Academy of Engineering Physics (Grants U1430117).

At

the University of Georgia this research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Computational and Theoretical Chemistry (CTC) Program, Grant DE-SC0015512.

24


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Reference (1) Gao, A.; Li, G.; Peng, B.; Xie, Y.; Schaefer, H. F. The Symmetric Exchange Reaction OH + H2O → H2O + OH: Convergent Quantum Mechanical Predictions. J. Phys. Chem. A 2016, 120, 10223-10230. (2) Graedel, T. E. The Homogeneous Chemistry of Atmospheric Sulfur. Rev. Geophy. Space Phys. 1977, 15, 421–428. (3) Koziel, J. A.; Baek, B. H.; Spinhirne J. P., Parker, D. B. Ambient Ammonia and Hydrogen Sulfide Concentrations at A Beef Cattle Feedlot in Texas; 2004 ASAE Annual Meeting Ottawa, Ontario, Canada, 2004. (4) Jaeschke, W.; Claude, H.; Herrmann, J. Sources and Sinks of Atmospheric H2S. J. Geophy. Res. 1980, 85, 5639–5644. (5) Wilson, C.; Hirst, D. M. Reaction of H2S with OH and A Study of the HSO and SOH Isomers High-Level Ab Initio Calculations. J. Chem. Soc. Faraday Trans. 1994, 90, 3051-3059. (6) Wang, B. S.; Hou, H.; Gu, Y. S. Theoretical Study of the Hydrogen Bonded Structures between H2S and OH Radical. J. Mol. Struct. 2000, 505, 241–246. (7) Uchimaru, T.; Tsuzuki, S.; Sugie, M.; Tokuhashi, K.; Sekiya, A. A Theoretical Study on the Strength of Two-Center Three-Electron Bond in (CH3)2S–OH and H2S–OH Adducts. Chem. Phys. Lett. 2005, 408, 216–220. (8) Alday, B.; Johnson, R.; Li, J.; Guo, H. Hemibond Complexes between H2S and Free Radicals (F, Cl, Br, and OH). Theor. Chem. Acc. 2014, 133, 1540-1545. (9) Mousavipour, S. H.; Namdar-Ghanbari, M. A.; Sadeghian, L. A Theoretical Study on the Kinetics of Hydrogen Abstraction Reactions of Methyl or Hydroxyl Radicals with Hydrogen Sulfide. J. Phys. Chem. A 2003, 107, 3752-3758. (10) Ellingson, B. A.; Truhlar, D. G. Explanation of the Unusual Temperature Dependence of the Atmospherically Important OH + H2S →H2O + HS Reaction and Prediction of the Rate Constant at Combustion Temperatures. J. Am. Chem. Soc. 2007, 129, 12765-12771. 25



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The Hydrogen Abstraction Reaction H2S + OH â H2O + SH

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The Hydrogen Abstraction Reaction H2S + OH â H2O + SH