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Thermochemical and Kinetics of CHSH + H Reactions: The Sensitivity of Coupling the Low and High-Level Methodologies Daniely V. V. Cardoso, Leonardo A. Cunha, Rene Felipe Keidel Spada, Corey A. Petty, Luiz Fernando de Araujo Ferrão, Orlando Roberto-Neto, and Francisco Bolivar Correto Machado J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09272 • Publication Date (Web): 22 Dec 2016 Downloaded from http://pubs.acs.org on December 26, 2016

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The Journal of Physical Chemistry

Thermochemical and Kinetics of CH3SH + H Reactions: The Sensibility of Coupling the Low and High-Level Methodologies Daniely V. V. Cardoso,† Leonardo A. Cunha,† Rene F. K. Spada,‡ Corey A. Petty,† Luiz F. A. Ferrão,† Orlando Roberto-Neto,¶ and Francisco B. C. Machado∗,† †Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12.228-900, São Paulo, Brazil ‡Departamento de Física, Universidade Federal do Espírito Santo, Vitória, 29.075-910, Espírito Santo, Brazil ¶Divisão de Aerotermodinâmica e Hipersônica, Instituto de Estudos Avançados, São José dos Campos, 12.228-001, São Paulo, Brazil E-mail: [email protected] Phone: (+55) 12 3947-5957

1 ACS Paragon Plus Environment


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Abstract The reaction system formed by the methanethiol molecule (CH3 SH) and a hydrogen atom was studied via three elementary reactions, two hydrogen abstractions and the C – S bond cleavage (CH3 SH + H; R1 → CH3 S + H2 ; R2 → CH2 SH + H2 ; R3 → CH3 + SH2 ). The stable structures were optimized with various methodologies of the density functional theory and the MP2 method. Two minimum energy paths for each elementary reaction were built using the BB1K and MP2 methodologies, and the electronic properties on the reactants, products, and saddle points were improved with coupled cluster theory with single, double, and connected triple excitations (CCSD(T)) calculations. The sensibility of coupling the low and high-level methods to calculate the thermochemical and rate constants were analyzed. The thermal rate constants were obtained by means of the improved canonical variational theory (ICVT) and the tunneling corrections were included with the small curvature tunneling (SCT) approach. Our results are in agreement with the previous experimental measurements and the calculated branching ratio for R1 :R2 :R3 is equal to 0.96:0:0.04, with kR1 = 9.64 × 10−13 cm3 molecule−1 s−1 at 298 K.

Introduction In recent years, studies have shown that sulfur organic compounds significantly contribute to climate change by exacerbating acid rain and the greenhouse effect. 1,2 Knowledge of how the elementary reactions occur can help to reduce these effects. The methanethiol (CH3 SH) molecule is a potential candidate as an atmospheric pollutant due to its release into the biosphere through both natural and anthropogenic actions. 3,4 Our research group has previously studied its reaction with oxygen 5 and sulfur 6 atoms, while this work focuses on reaction with a hydrogen atom. The reactions involving hydrogen (H( 2S)) with methanethiol have been the target of both experimental and theoretical investigations with the aim of determining the thermo-


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chemical and kinetic properties. Martin et al. 7 made a kinetic study of the CH3 SH + H reaction at 298 K using electron paramagnetic resonance and mass spectrometric analysis finding a rate constant equal to (2.20 ± 0.20) × 10−12 cm3 molecule−1 s−1 . Wine et al. 8 also experimentally studied the kinetics of this reaction reporting a rate constant equal to (2.01 ± 0.03) × 10−12 cm3 molecule−1 s−1 at 298 K and an Arrhenius equation k = (3.45 ± )cm3 molecule−1 s−1 . Theoretically, Wang et al. 9 studied the same 0.13) × 10−11 exp(− 845±12 T reaction using a dual-level methodology to build the reaction path. The MP2 was used as the low-level and G3(MP2) as the high-level. At 298 K, they reported a rate constant of 2.71 × 10−13 cm3 molecule−1 s−1 and, in a temperature range of 249–405 K, the Arrhenius expression was given by the k = 4.61×10−11 exp(− 834.35 )cm3 molecule−1 s−1 equation. Recently, T Kerr et al. 10 carried out an experimental and theoretical study for this reaction system. Experimentally, an Arrhenius equation for the 296-1007 K temperature range was reported −1

kJ mol as being k = (3.45 ± 0.19) × 10−11 exp(− −6.92±0.16 )cm3 molecule−1 s−1 . They have RT

also used the CVT/SCT methodology to obtain the following modified Arrhenius equation )cm3 molecule−1 s−1 which is valid for the temperature k = (1.46 × 10−16 × T 1.824 exp(− 509 T range between 200-3000 K. In this work, we also carry out a systematic study about the relevance of the low-level methodology in the thermal rate constants of the title reaction. We propose three elementary reaction paths that should be present in the decomposition mechanisms of sulfur containing organic compounds reacting with hydrogen atoms, which are also present in the atmosphere. These paths are the hydrogen abstraction from the thiol group (R1 ), the hydrogen abstraction from the CH3 group (R2 ), and the C – S bond breaking (R3 ), presented below: SP

1 CH3 SH + H −−→ CH3 S + H2

SP

2 CH3 SH + H −−→ CH2 SH + H2

SP

3 CH3 SH + H −−→ CH3 + SH2


(R1 ) (R2 ) (R3 )


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To characterize the stationary points (reactants, products, and saddle points (SP)) and to build the reaction paths, the methododology used should adequately describe the isolated systems and the breaking/making of chemical bonds processes. In order to minimize computational effort, the dual-level methodology 11 is often applied. As the name suggests, this approach employs two methods, a low-level methodology to compute all points properties along the reaction path, and a high-level methodology to improve the stationary points properties of the surface. In this work, the high-level methodology used to determine the energetic properties of the reaction was the coupled cluster with single, double and quasiperturbative treatment of the triple excitations (CCSD(T)), 12 and the density functional theory (DFT) and the second-order Møller-Plesset perturbation theory (MP2) 13 were employed as the low-level method. Several DFT functionals were tested in order to find the most reliable for the CH3 SH + H reactions. In previous works, we have employed the dual-level methodology to calculate accurately the properties of several chemical reactions. 5,6,14–18 In this work, with the experience gained from previous research, a rigorous analysis was carried out regarding the coupling of the low and high-level methods, in particular when calculating the thermochemical properties, and subsequent rate constant calculations. We have analyzed in which conditions this coupling can generate artificial tunneling and variational effects in the calculated rate constants. Based on these analysis, we are confident that the rate constants reported herein are trustworthy for usage in mechanism simulations involving the R1 –R3 elementary reactions.

Methodology The stationary structures (reactants, products and saddle point (SP)) of the CH3 SH + H reaction paths were optimized and identified via vibrational analysis, and the zero-point energies (ZPE) were obtained. The energetic properties calculated were the classical barrier (V ‡ , defined as the electronic energy difference between the saddle point and the reactants),


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the adiabatic barrier (∆VaG,‡ , V ‡ + ∆ZP E ‡ ), the energy of the reaction (∆E, electronic energy difference between products and reactants), and the enthalpy of the reaction at 0 K (∆H0◦ , ∆E + ∆ZP E). In this study, several DFT methods (BB1K, 19 M06-2X, 20,21 BMK, 22 CAM-B3LYP, 23 B3LYP, 24,25 WB97-X 26 and BH&HLYP 27 ) were employed as well as MP2. 13 These calculations were carried out with the aug-cc-pVXZ (X=D, T and Q) 28,29 basis set for the carbon and hydrogen atoms. As recommended in the literature, 30–33 high exponent d functions were included in the sulfur basis set, generating the aug-cc-pV(X+d)Z basis set. We use the notation aXdZ (X = D, T and Q) to denote the combination of the aug-cc-pVXZ (C and H) and aug-cc-pV(X+d)Z (S) basis sets. For the MP2 approach, the 6-311+G(d,p) basis set 34 was used. To check if the SP’s connect the reactants to the products of the hydrogen abstractions and C – S bond cleavage, intrinsic reaction coordinate (IRC) 35 calculations were performed using the BB1K/aTdZ methodology. In order to improve the electronic properties (∆E and V ‡ ), calculations with CCSD(T) with the aTdZ and aQdZ basis set were carried out using geometries optimized with the BB1K and MP2 methods, and the results were extrapolated to the complete basis set (CBS) limit using the method introduced by Halkier et al. 36 From now on, the single-point CCSD(T)/CBS results will be denoted as our best results and will be used as a benchmark value for the other methods used in this study. The T1 diagnostic was calculated to verify the reliability of the CCSD(T) calculations. According to Lee and Taylor, 37 a T1 diagnostic value higher than 0.02 indicates a certain multireference character for the system. However, Rienstra-Kiracofe et al. 38 argued that if the T1 diagnostic value is lower than 0.044, the system is well described with single reference methods. The reaction rate constants were calculated with the improved canonical variational theory (ICVT). 39,40 For that, the electronic (Vmep ) and adiabatic (VaG ) paths were calculated



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using the dual-level methodology, 11 using BB1K and MP2 methods as low-level for the electronic calculations of potential energy surface and CCSD(T)/CBS as the high-level calculations at the selected points. This approach for the calculation of the kinetic properties is known as variational transition state theory with interpolated single point energies (VTSTISPE). 11 The tunneling corrections were included with the small curvature tunneling (SCT) 41 method. The electronic structure calculations were carried out using the Gaussian 09 package 42 and the chemical kinetics results were obtained with the Polyrate 2008 program. 43 The Vmep and VaG surfaces were obtained with the Gaussrate 2009 package, 44 which interfaces the Gaussian and Polyrate programs.

Results and Discussion The equilibrium structures of the stationary points involved in the R1 , R2 , and R3 reaction paths are presented in Figure 1 with some selected bond lengths and angles calculated with the BB1K/aTdZ and MP2/6-311+G(d,p) methodologies and, for the reactants and products, experimentally measured values are also presented. 45–48 The optimized geometries are available in the Supporting Information. The results for the stable geometries are in good agreement with the experimental values, differing by no more than 0.018 Å (C – S bond in CH3 SH and CH3 S molecules) and 3.5◦ (H – C – S angle in CH3 S molecule). The calculated harmonic frequencies (Table 1) are in good agreement with the experimental measurements of fundamental frequencies, differing by around 5%, which is the expected difference between harmonic and the fundamental frequencies. The largest deviation occurs for the third mode of CH3 S molecule (12% lower than the experiment). The intrinsic reaction coordinate calculations confirm the connection of the saddle points to reactants and products, and all transition states have only one imaginary frequency. The imaginary frequency plays an important role in the chemical kinetics calculations, and should be calculated ac-


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curately, 49 since it is related to the curvature of the potential energy surface around the SP. When the value for the imaginary mode is too high, the barrier becomes narrower, which may lead to artificially enhanced tunneling effects, as will be explained in the following discussion. We have shown previously that the BB1K method produces imaginary frequencies for the transition states that are sufficiently close to the CCSD(T) calculations. 16,17,50

Figure 1: Equilibrium geometries of the R1 , R2 , and R3 reactional paths with selected bond lengths (Å) and angles (degrees) calculated with BB1K/aTdZ (first line) and MP2/6311+G(d,p) (second line) and experimental values (between parenthesis). To verify if a multireference method is required for a reliable characterization of these structures, the T1 diagnostic was calculated with the CCSD/aQdZ methodology at the optimized geometries obtained with the BB1K/aTdZ and MP2/6-311+G(d,p) approaches (Table 2). The highest T1 diagnostic value is for the CH2 SH molecule (0.019), and it is still below the limits proposed by Lee and Taylor 37 (0.02) and Rienstra-Kiracofe et al. 38 (0.044). Since the barrier height is the main factor that leads to reliable rate constants, several DFT (BB1K, M06-2X, BMK, CAM-B3LYP, B3LYP, WB97X and BH&HLYP) and the MP2 7 ACS Paragon Plus Environment


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Table 1: Harmonic frequencies (cm−1 ) calculated with the BB1K/aTdZ and MP2/6311+G(d,p) methodologies and theoretical and experimental values found on the literature.

System CH3 SH

CH3 S

CH2 SH

CH3

H2 S

H2

SP1 SP2 SP3 a

BB1K MP2 Exp. 51 BB1K MP2 Exp. 52 BB1K MP2 Theor. 53,a BB1K MP2 Exp. 52 BB1K MP2 Exp. 54 BB1K MP2 Exp. 47 BB1K MP2 BB1K MP2 BB1K MP2

3213 3200 3000 3188 3182 3375 3361 3153 3360 3366 3184 2806 2806 2626 4484 4534 4403 3214 3193 3256 3243 3226 3219

3212 3197 3000 3161 3160 2960 3245 3228 3033 3359 3366 3184 2793 2793 2615

3120 3100 2931 3081 3074 2706 2783 2812 2604 3173 3173 3002 1218 1218 1183

2779 2808 2597 1493 1491 1496 1432 1463 1389 1429 1446 1383

1511 1498 1475 1399 1400

3206 3191 3163 3142 3217 3204

3118 3094 2779 2805 3118 3090

1743 1494 1489 1674 2800 2837

1508 1464 1436 1447 1499 1476

Frequencies 1497 1380 1472 1411 1430 1335 1352 876 1384 895 1313 882 799 875 820 817 769 514 455 580

1094 1116 1051 1428 1446 1383

1491 1436 1287 1267 1489 1466

1376 1404 1277 1234 1344 1336

1119 1127 1074 762 758 727 368 388 423

991 1008 976 657 630 586 144 248 272

816 832 803

750 754 708

285 247

1099 1120 1115 1128 1122 1183

991 1008 986 1006 949 929

846 898 847 867 870 921

753 754 789 789 693 737

441 584 542 548 498 608

214 276 328 324 287 411

136 136 266 251 187 200

The values were obtained with the MP2/6-31G* method. 53

Table 2: T1 diagnostic values for the species involved in R1 , R2 and R3 paths.

System BB1K geometry SP1 0.013 SP2 0.017 SP3 0.015 CH3 SH 0.010 CH2 SH 0.019 CH3 S 0.012 CH3 0.009 H2 S 0.010 H2 0.006 H 0.000

MP2 geometry 0.015 0.017 0.016 0.010 0.019 0.012 0.009 0.010 0.006 0.000

calculations were compared to the CCSD(T) classical barrier values and also to the previous results obtained with the G3(MP2) 55 and CCSD(T) levels of theory. 9 These results are presented in Table 3 for R1 , R2 , and R3 reactions. Our most correlated and best results (CCSD(T)/CBS//BB1K/aTdZ and CCSD(T)/CBS//


866i 1668i 1518i 1846i 536i 712i

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Table 3: Adiabatic barrier (∆VaG,‡ ) in kcal mol−1 for R1 , R2 and R3 . Method BB1K/aDdZ BB1K/aTdZ M06-2X/aTdZ BMK/aTdZ CAM-B3LYP/aTdZ BH&HLYP/aTdZ B3LYP/aTdZ WB97X/aTdZ MP2/6-311+G(d,p) G3(MP2)//MP2/6-311+G(d,p) 9 CCSD(T)/6-311++G(2df,2p)//MP2/6-311+G(d,p) 9 CCSD(T)/CBS//BB1K/aTdZ CCSD(T)/CBS//MP2/6-311+G(d,p)

R1 R2 1.96 7.77 2.23 8.02 2.87 9.25 2.71 9.56 0.16 5.07 1.03 6.93 0.03 3.14 4.41 9.42 6.18 14.50 1.87 9.02 2.08 9.67 2.17 8.74 1.75 8.84

R3 4.16 3.84 4.43 4.32 1.64 3.04 0.68 6.16 11.52 4.24 5.36 3.71 3.32

MP2/6-311+G(d,p)) suggests that the adiabatic barriers are in the range of 1.75–2.17 kcal mol−1 , 8.74–8.84 kcal mol−1 and 3.32–3.71 kcal mol−1 for R1 , R2 and R3 , respectively. The previous results 9 are in this range for R1 , but differ by about 1 and 2 kcal mol−1 for R2 and R3 , respectively. Among the DFT and the MP2 calculations, the BB1K approach (for both basis sets) gives better agreement with the CCSD(T) results, with differences of around 1 kcal mol−1 followed by the BMK and M06-2X functionals. The CAM-B3LYP, B3LYP, and BH&HLYP underestimate the barrier height while the WB97X and MP2 methods overestimate the barrier. The thermochemical properties for the BB1K functional, MP2, and CCSD(T) methods, as well as experimental measurements are presented in Table 4. The full set of results are found in the Supporting Information. For the reaction enthalpy (∆H0◦ , Table 4), the CCSD(T)/CBS results are within the experimental range estimates for all reaction paths. The BB1K functional also yields better results than the MP2 method, when compared to the CCSD(T) values, with BB1K/aTdZ being the best approach. For the adiabatic barrier (∆VaG,‡ ), the MP2 method, as expected, overestimates the barrier height (as pointed above), and the BB1K method differ from the highly-correlated results by less than 1 kcal mol−1 . As discussed above, we have also shown



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Table 4: Thermochemistry of CH3 SH + H system for the three reaction paths obtained with various methods and available experimental data (kcal mol−1 ).

Method BB1K/aDdZ BB1K/aTdZ MP2/6-311+G(d,p) CCSD(T)/CBS//BB1K CCSD(T)/CBS//MP2 Experimental 56

V‡ 2.67 3.00 7.05 2.94 2.62

R1 ∆VaG,‡ 1.96 2.23 6.18 2.17 1.75

∆E -14.76 -16.56 -14.55 -17.03 -17.04

∆H0◦ -15.18 -16.87 -14.76 -17.34 -17.25 -17.67 – -16.67

Method BB1K/aDdZ BB1K/aTdZ MP2/6-311+G(d,p) CCSD(T)/CBS//BB1K CCSD(T)/CBS//MP2 Experimental 56

V‡ 9.32 9.61 15.83 10.33 10.17

R2 ∆VaG,‡ 7.77 8.02 14.50 8.74 8.84

∆E -4.70 -6.50 -1.12 -7.19 -7.11

∆H0◦ -7.57 -9.46 -3.71 -10.15 -9.70 -12.87 – -8.87

Method BB1K/aDdZ BB1K/aTdZ MP2/6-311+G(d,p) CCSD(T)/CBS//BB1K CCSD(T)/CBS//MP2 Experimental 53,56,57

V‡ 3.26 2.94 10.14 2.81 1.94

R3 ∆VaG,‡ 4.16 3.84 11.52 3.71 3.32

∆E -14.95 -15.37 -12.23 -16.54 -16.50

∆H0◦ -15.73 -16.21 -12.96 -17.38 -17.23 -18.50 – -16.50

previously that BB1K usually provides accurate thermochemical results for hydrogen abstraction reactions. 16,17,50 Also, in a recent review, Peverati and Truhlar 58 have shown the excellent performance of BB1K for 76 barrier heights with comparable results to more recent functionals, such as M06-2X, 20 M08-SO, 59 M08-HX, 59 and MN12-SX 60 . Both the aTdZ and aDdZ basis sets are suitable to perform the Vmep and VaG calculations, since the difference between the calculated barriers is only 0.33 kcal mol−1 . However, the aDdZ base has a computational cost one order of magnitude lower than aTdZ. We used the BB1K/aDdZ methodology to calculate the energies and harmonic frequencies along the reaction paths, correcting the frequencies at the stable points (reactants, products and SP’s) with the BB1K/aTdZ values, and improving the electronic properties (∆E and V ‡ ) with the CCSD(T)/CBS//BB1K/aTdZ results. This surface will be referred to as DLB (duallevel with BB1K) from now on. In order to study the variational effect and the tunneling 10 ACS Paragon Plus Environment

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correction effect in the rate constants, we also carried out the chemical kinetic calculations with another surface, built with the MP2/6-311+G(d,p) methodology as the low-level and the CCSD(T)/CBS//MP2/6-311+G(d,p) methodology as the high-level, which we refer to as DLM (dual-level with MP2). Both surfaces are presented in Figure 2. Analyzing the Vmep obtained with DLB and DLM methodologies for the reaction path R2 (Figure 3), it is observed that the curvature for DLM is narrower than the DLB, mostly because the saddle point obtained with the MP2 method has a higher imaginary frequency. Although both surfaces have similar heights, there is a larger flattening of the MP2 low-level surface, compared with the high-level correction (DLM). The value of the barrier decreases from 15.83 to 10.17 kcal mol−1 . On the other hand, the low-level BB1K and DLB potential energy surfaces are in close agreement, since the barrier height difference between these two methods is within the chemical accuracy of 1 kcal mol−1 . Also, as the corrected barriers are practically equal for both surfaces, a larger tunneling is expected in the DLM surface. 40

40

DLB

20 10 0 −10 −20 −1

DLM

30

Energy [kcal/mol]

30

Energy [kcal/mol]

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R1 Vmep

R1 VaG

R2 Vmep

R2 VaG

R3 Vmep

R3 VaG

−0.8

−0.6

−0.4

−0.2

20 10 0 −10

0

0.2

0.4

0.6

0.8

−20 −1

1

R1 Vmep

R2 VaG

R2 Vmep

R2 VaG

R3 Vmep

R3 VaG

−0.8

−0.6

s [(amu)1/2 Å)]

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

s [(amu)1/2 Å)]

Figure 2: Vmep and VaG calculated with the dual-level (DL) methodology, using BB1K (DLB) and MP2 (DLM) as the low-level methods. The electronic properties were improved with the CCSD(T)/CBS methodology. These surfaces were used to calculate the thermal rate constants with the TST and ICVT methodologies and, for the latter, the tunneling corrections were applied with the SCT approach. The results are presented in Tables 5 (R1 ), 6 (R2 ) and 7 (R3 ). It is worth noticing that symmetry factors and chirality do not contribute to the computation of the rate constants for any of the reaction paths studied. The rotational symmetry numbers 11 ACS Paragon Plus Environment


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Figure 3: Miminum energy paths, Vmep , calculated for the R2 reaction path with the duallevel methodology using two different low-levels: BB1K (DLB) and MP2 (DLM). were calculated according to Fernández-Ramos et al. 61 considering the point group of the hydrogen atom (C∞v ), CH3 SH (Cs ), SP1 (Cs ), SP2 (C1 ) and SP3 (C1 ), leading to symmetry numbers equal to 1 for all reaction paths. However, it should be pointed out we assumed that there are three equivalent hydrogen atoms on the methyl group and the rate constants for the R2 reaction path are multiplied by three. Table 5: Rate constants (cm3 molecule−1 s−1 ) for the R1 reaction path. T (K) 200 298 350 400 500 600 800 1000 1200 2000 3000

TST DLB 1.1×10−13 7.7×10−13 1.5×10−12 2.4×10−12 5.0×10−12 8.6×10−12 1.9×10−11 3.3×10−11 5.0×10−11 1.5×10−10 3.4×10−10

ICVT DLM 2.5×10−13 1.2×10−12 1.9×10−12 2.8×10−12 5.0×10−12 7.7×10−12 1.5×10−11 2.4×10−11 3.5×10−11 9.7×10−11 2.1×10−10

DLB 6.5×10−14 6.1×10−13 1.2×10−12 2.1×10−12 4.7×10−12 8.3×10−12 1.9×10−11 3.3×10−11 5.0×10−11 1.5×10−10 2.8×10−10

DLM 1.5×10−13 8.9×10−13 1.6×10−12 2.4×10−12 4.3×10−12 7.0×10−12 1.4×10−11 2.3×10−11 3.4×10−11 9.6×10−11 1.5×10−10

ICVT/SCT DLB DLM 1.8×10−13 2.2×10−13 9.6×10−13 1.0×10−12 −12 1.7×10 1.8×10−12 −12 2.8×10 2.6×10−12 −12 5.6×10 4.6×10−12 −12 9.4×10 7.3×10−12 −11 2.0×10 1.4×10−11 −11 3.4×10 2.4×10−11 −11 5.1×10 3.4×10−11 −10 1.5×10 9.7×10−11 −10 2.9×10 1.4×10−10

As a rule of thumb of kinetics, it is known that at room temperature, an increase of 1 kcal mol−1 in the barrier height leads to a reaction rate constant approximately 10 times lower. In addition, a high imaginary frequency associated with a low reduced mass indicates 12 ACS Paragon Plus Environment

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Table 6: Rate constants (cm3 molecule−1 s−1 ) for the R2 reaction path. T (K)

TST DLB 1.2×10−20 1.7×10−17 1.6×10−16 7.8×10−16 7.9×10−15 3.9×10−14 3.2×10−13 1.3×10−12 3.3×10−12 3.1×10−11 1.2×10−10

200 298 350 400 500 600 800 1000 1200 2000 3000

ICVT DLM 9.0×10−21 1.4×10−17 1.3×10−16 6.5×10−16 6.7×10−15 3.4×10−14 2.8×10−13 1.1×10−12 2.9×10−12 2.7×10−11 1.1×10−10

DLB 1.0×10−20 1.5×10−17 1.4×10−16 7.1×10−16 7.3×10−15 3.7×10−14 3.1×10−13 1.2×10−12 3.2×10−12 3.0×10−11 1.2×10−10

DLM 2.5×10−21 1.0×10−17 1.0×10−16 5.4×10−16 5.8×10−15 3.0×10−14 2.6×10−13 1.1×10−12 2.7×10−12 2.6×10−11 1.0×10−10

ICVT/SCT DLB DLM 7.7×10−18 1.1×10−17 3.1×10−16 3.7×10−16 −15 1.3×10 1.4×10−15 −15 3.8×10 4.0×10−15 −14 2.2×10 2.1×10−14 −14 7.8×10 7.3×10−14 −13 4.7×10 4.2×10−13 −12 1.6×10 1.4×10−12 −12 3.9×10 3.4×10−12 −11 3.2×10 2.8×10−11 −10 1.2×10 1.1×10−10

Table 7: Rate constants (cm3 molecule−1 s−1 ) for the R3 reaction path. T (K) 200 298 350 400 500 600 800 1000 1200 2000 3000

TST DLB 1.3×10−15 2.9×10−14 7.9×10−14 1.7×10−13 4.9×10−13 1.0×10−12 3.0×10−12 6.0×10−12 1.0×10−11 3.5×10−11 8.1×10−11

ICVT DLM 2.8×10−15 4.2×10−14 9.8×10−14 1.8×10−13 4.6×10−13 8.7×10−13 2.1×10−12 3.9×10−12 6.1×10−12 1.9×10−11 4.0×10−11

DLB 1.1×10−15 2.6×10−14 7.0×10−14 1.5×10−13 4.2×10−13 9.0×10−13 2.5×10−12 4.9×10−12 7.6×10−12 2.2×10−11 4.5×10−11

DLM 2.6×10−16 8.8×10−15 2.6×10−14 5.7×10−14 1.8×10−13 3.8×10−13 1.0×10−12 2.0×10−12 3.2×10−12 1.0×10−11 2.2×10−11

ICVT/SCT DLB DLM 2.9×10−15 4.2×10−16 4.0×10−14 1.1×10−14 −14 9.6×10 3.0×10−14 −13 1.9×10 6.4×10−14 −13 4.9×10 1.9×10−13 −12 1.0×10 4.0×10−13 −12 2.6×10 1.1×10−12 −12 5.0×10 2.0×10−12 −12 7.8×10 3.3×10−12 −11 2.2×10 1.0×10−11 −11 4.5×10 2.2×10−11

a high tunneling factor at low temperatures, whereas a low imaginary frequency indicates a relatively flat potential energy surface around the saddle point, in which variational effects can play a major role. Combining these considerations alongside with the barrier height being the sensitivity of the reaction rate constant to the temperature, one can qualitatively interpret the trends presented in table 5, 6 and 7 in the light of energetics and imaginary frequencies of the studied reaction paths at each dual-level methodology. Analyzing the results of energetics for the R1 reaction path, one would expect that the rate constant would be slightly more sensible to temperature changes using the DLB methodology (due to a barrier 0.4 kcal mol−1 higher) when compared to DLM. On the other



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hand, tunneling effects would play a major role on the computation of rate constants using the DLM methodology for this reaction path. This larger tunneling could increase even more the DLM rate constants at low temperatures, however since the barrier heights (around 2 kcal mol−1 ) are considerably close to the average thermal energy (around 0.5 kcal mol−1 at 298 K), a relatively large fraction of molecules has enough energy to bypass the barrier and thermal transmission is more prominent than tunneling, even at low temperatures. For the R2 reaction path, the high-level corrections to the barrier height are in close agreement (8.74 kcal mol−1 and 8.84 kcal mol−1 , respectively for DLB and DLM). Moreover, due to the high imaginary frequency for both methods (relatively higher in DLM), one would expect a major contribution of tunneling effects and a minor contribution of variational effects on the computation of the reaction rates for this path. Hence, it is expected that for the whole temperature range the rate constants calculated at DLM and DLB methodologies should be in close agreement with each other. Finally, for the R3 reaction path, one should first notice that this path involves the breaking of the C-S bond of methanethiol. Therefore, a higher mass is being displaced and tunneling effects are minimal to the rate constants for this path. Given this, at low temperatures, the difference of about 0.4 kcal mol−1 between the DLB and DLM barrier heights would be one of the main factors that explain the difference between the rate constants calculated with both methods, and qualitatively, in a first analysis, it should have the same behavior as R1, with DLB relatively lower than DLM. At higher temperatures, DLB should be closer or surpass DLM. However, the DLM surface for this reaction path presents a large displacement of the maximum in the adiabatic surface when compared to the electronic one, which is effectively computed as a variational effect and therefore, DLM rate constants of R3 are much lower than DLB. Quantitatively, the ratio between the ICVT and TST rate constants gives the variational effect on each reaction path. The ratio of rate constants calculated with the DLB surfaces at 298 K are equal to 0.78 for R1 and 0.89 for both R2 and R3 , while for the DLM surface


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these ratios are equal to 0.78 (R1 ), 0.77 (R2 ) and 0.21 (R3 ). The DLM values, specially for R3 , seems to be too low, and should be caused by artificial variational effects due to poor choice of methodologies for the dual-level approach. For R3 , the electronic barrier estimated by the MP2/6-311+G(d,p) is equal to 10.14 kcal mol−1 l while the CCSD(T)/CBS//MP2/6311+G(d,p) value is 1.94 kcal mol−1 . Using these two values in the dual-level methodology, the electronic barrier at R3 decreases by 8.20 kcal mol−1 and the electronic surface becomes flatter. In this context, the MP2/6-311+G(d,p) ZPE variation along the reaction path is enough to unnaturally shift the maximum of the VaG to around 0.5[(amu)1/2 ] Å (Figure 2). The problems associated with the shifting of the VaG maximum in the reaction coordinate and the difference of the reaction coordinates themselves between the low and high-level methodologies were discussed previously in the literature. 62–65 On the other hand, the electronic barrier (V ‡ ) of the DLB surface of R3 is equal to 3.26 kcal mol−1 and 2.81 kcal mol−1 at the at the BB1K/aDdZ and CCSD(T)/CBS//BB1K/aTdZ levels of theory, respectively. Thus, we find that using DFT at the low-level yields better agreement with the high-level. Furthermore, using DFT displaces the maximum of the VaG surface by less than 0.1 [(amu)1/2 ] Å compared do the saddle point position. We can attribute the differences in the shifts of the VaG maximums to the variational effect’s contribution to the two surfaces. This larger shift from DLM leads to a higher variational effect, necessarily causing lower rate constants. Despite the CCSD(T)/CBS//MP2/6-311+G(d,p) method predicting a lower adiabatic barrier than CCSD(T)/CBS//BB1K/aTdZ (3.32 and 3.71 kcal mol−1 , respectively), the ICVT calculated rate constants for R3 at all temperatures considered have lower values on the DLM surface, rather than DLB. This strongly indicates that for the cases considered, the BB1K functional as the low-level leads to more reliable surfaces than the MP2 methodology. One can calculate the contribution of tunneling effects by taking the ratio of the ICVT/CST and ICVT rate constants. At 298 K, we find these to be 1.59 (R1 ), 20.52 (R2 ), and 1.53 (R3 ) for the DLB surfaces, and 1.16 (R1 ), 35.14 (R2 ), and 1.22 (R3 ) for the DLM surfaces.



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Note that the tunneling contribution for the R2 reaction path is higher than for R1 and R3 . However, the higher ratio of the DLM surface could contain a excess of tunneling contributions due to a flattening of 5.66 kcal mol−1 at SP2 . The coupling between the low and high-level for the DLB surface is appreciably better since the DLB surface is shifted by only 0.72 kcal mol−1 . The relative narrowness of the DLM is clear when compare the imaginary frequencies of the R2 calculated by MP2 (1841i cm−1 ) and BB1K (1518i cm−1 ). To evaluate which method exhibits saddle point frequencies closest to the CCSD(T), we perform optimization and frequency calculations for the saddle point of R1 with BB1K, MP2, and CCSD(T) using the aDdZ basis set. The imaginary frequencies of the saddle point were equal to 805i cm−1 , 1622i cm−1 and 1186i cm−1 for BB1K, MP2, and CCSD(T) methods, respectively. The BB1K frequency underestimates the CCSD(T) frequency by 32%, while the MP2 is 37% higher than the CCSD(T) reference. This behavior was observed previously in the literature for hydrogen abstraction reactions. 16 Therefore, the DLB surface should be closer to a high-level surface than DLM. Considering all the above results, one can conclude that the best methodology is the ICVT/SCT approach with the DLB surface. Since the proposed mechanism consists of parallel reactions (i.e., the most important path is the one that has the highest rate constant), the results also emphasize the importance of R1 among the studied ones, through the entire temperature range. The rate constants of this path are 9.7 × 10−13 at 298 K and 2.0 × 10−11 at 800 K. This reaction path is followed by R3 , presenting rate constant values of 4.0 × 10−14 (298 K) and 2.6×10−12 (800 K). Lastly, the rate constant results for R2 are 1.0×10−16 (298 K) and 1.6 × 10−13 (800 K). The branching ratio for R1 to R3 are equal to 0.96:0:0.04 at 298 K and 0.87:0:0.12 at 800 K. For higher temperatures, R1 remains predominant, but R2 becomes competitive to R3 for temperatures higher than 1500 K (Figure 4), both contributing around 10% up to 3000 K. Finally, Figure 5 shows the total rate constants obtained at the ICVT/SCT level of theory using both DLB (5a) and DLM (5b) surfaces, alongside with previous experimental


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1 0.9

Branching ratios

0.8 0.7 0.6

kR1 / kT kR2 / kT kR3 / kT

0.5 0.4 0.3 0.2 0.1 0

0

500

1000

1500

2000

2500

3000

Temperature (K)

Figure 4: Thermal rate constant branching ratios calculated considering the ICVT/SCT values for the R1 –R3 reaction paths. and theoretical data. While Kerr et al. 10 experimental data agrees very well with Wine et al. 8 (around 2 ×10−12 cm3 molecule−1 s−1 at 298 K), their variational transition state theory rate constants are about half the value of the measured data (0.87 ×10−12 cm3 molecule−1 s−1 at 298 K), as the ICVT/SCT total rate constant reported in the present study (around 1.0 ×10−12 cm3 molecule−1 s−1 at 298 K). We believe that this factor of 2 is close to the limit of transition state derived methodologies using highly correlated surfaces, and most of the remaining error is possibly due to attributing the flow from the reactants to products by a minimum energy path instead of a complete surface. 10 -10

10 -10

ICVT/SCT Exp. Ref.[66] Exp. Ref.[10] Exp. Ref.[8] Teo. Ref.[10]

10 -11

k (cm3 molecule−1 s−1 )

k (cm3 molecule−1 s−1 )

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


10 -12

10 -13 0.5

1.0

1.5

2.0

2.5

3.0

3.5

1000T (K ) −1

−1

4.0

4.5

10 -11

10 -12

10 -13 0.5

5.0

ICVT/SCT Exp. Ref.[66] Exp. Ref.[10] Exp. Ref.[8] Teo. Ref.[10]

1.0

(a) DLB

1.5

2.0

2.5

3.0

3.5

1000T−1 (K−1 )

4.0

4.5

5.0

(b) DLB

Figure 5: Arrhenius plots using DLB and DLM surfaces. The experimental results presented as the red curve were obtained by Amano et al. 66



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Conclusions The reaction enthalpies at 0 K, barrier heights, and thermal rate constants for the CH3 SH + H reaction were computed using several DFT approximations, the MP2 and CCSD(T) methodologies. The reaction path presenting the lower adiabatic barrier is the hydrogen abstraction reaction from the thiol group (R1 ), followed by the C – S bond break (R3 ), and the hydrogen abstraction from the methyl group (R2 ). The thermal rate constants were also calculated at the TST, ICVT and ICVT/SCT levels of theory. The dual-level approach was employed to build the Vmep and VaG surfaces. The CCSD(T)/CBS results were used as the high-level and the BB1K and the MP2 methods were selected for the low-level. When MP2 was used, we found that the surface predicts high values of tunneling and variational effects, which seems to be overestimated. This is due to the mismatch between the low-level and the high-level energetics results, which is observed by the difference of the barrier height values for the MP2 and CCSD(T) methods. However, using BB1K as low-level the agreement with CCSD(T) results are better and therefore, the tunneling and variational effects should be more reliable. Analyzing the thermal rate constants, the R1 reaction path is clearly the predominant at low temperatures, followed by R3 and R2 . The branching ratios at 298 K are equal to 0.96:0.00:0.04 for the R1 –R3 reaction paths, respectively, demonstrating that the hydrogen abstraction from the thiol group is the main reaction path of this reaction system.

Acknowledgement The authors acknowledge the research and fellowship support of the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under Process Nos. 2014/25734-0, 2014/241556, 2014/14470-1 and 2012/11857-7, and to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Process No. 304914/2013-4.


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Supporting Information Available The following files are available free of charge. This work includes Supporting Information containing cartesian coordinates (in Å) for all stationary geometries, a complete list of the calculated thermochemistry data, along side with overall rate constants, Arrhenius plots and activation energies using DLB and DLM surfaces.

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