Enthalpy of Formation of CH3SO and CH3SO2: A Difficult Case in Quantum Chemistry

Journal of the Brazilian Chemical Society

Ornellas, Fernando R.¹  Resende, Stella M.¹  Universidade de São Paulo, São Paulo, Brazil¹ 

关键词: thermochemistry;    heat of formation;    enthalpy;    sulfur-reduced compounds;    ab initio;   

DOI  :  10.1590/S0103-50532002000500004

学科分类：化学（综合）

来源: SciELO

【 摘 要 】

The complexity of environmental chemical processes with several reactions occurring simultaneously poses a great challenge to scientists involved in the modelling of reaction cycles. The identification of intermediates and products that can play a significant role in the overall reaction is thus of great relevance. In this context, the availability of thermochemical data is very important in helping to provide information about the stability and reactivity of the chemical species involved and may be decisive in answering questions about endothermicity and feasibility of various atmospheric processes. Theoretically, empirical group additivity methods such as those developed by Benson and co-workers1 provide an easy way to estimate the thermochemistry of gas-phase reactions for species whose thermochemistry has not been measured. However, its weakness lies in its requirement to apply corrections for steric effects that are not always well determined, as well as for groups not experimentally studied. On the other hand, ab initio methods represent today an important tool to generate thermochemical data, but the final accuracy is dependent on the level of calculation used. Procedures such as G2, G2(MP2) and G3 methods have been reported frequently, with accuracies in the range of 1 to 2 kcal mol-1.2-4 The CBS-Q approach gives an accuracy of about 1 kcal mol-1,5 reaching the complete basis set limit and making use of a high level of electronic correlation treatment such as CCSD(T). The use of isodesmic reactions,6 where systematic computational errors may cancel between the right and left sides of a chemical reaction, is also a common useful practice. Besides, molecules containing second row atoms such as sulfur often need a higher theoretical description than molecules containing only first row atoms.7 In the context of atmospheric reactions, the determination of important thermochemical data such as the enthalpy of formation for molecules containing sulfur can thus be a challenge. The sulfur-reduced species H3SO and CH3SO2, derived from the atmospheric decomposition of dimethyl sulfide,8 are excellent examples showing this difficulty. The enthalpy of formation of CH3SO was estimated by Benson as being -16 kcal mol-1,9 and a G2(MP2) calculation by Turecek produced a value of -18.5 kcal mol-1.10 More recently, a calculation at the CCSD(T)/cc-pVTZ level conducted by Resende and De Almeida led to a lower value of -11.9 kcal mol-1.11 To the best of our knowledge, no experimental determination has been reported in the literature. For CH3SO2, there are a number of theoretical investigations. Benson's estimate is -55 kcal mol-1;9 a calculation at the HF/STO-3G level has produced a value of -62.7 kcal mol-1,12 while more recent determinations using the G2 and G2(MP2) methodologies have led to values of -47.6 and -50.4 ± 1 kcal mol-1, respectively.13,14 Resende and De Almeida have obtained -38.9 kcal mol-1,11 and the most recent value, reported by Denis and Ventura,15 using the DFT/6-311+G(3df,2p) level of calculation, is -56.3 ± 2 kcal mol-1. On the experimental side, the only determination reported gives a value of -61.8 ± 1.8 kcal mol-1.16 This variety of results clearly show that the values of the heats of formation for these two sulfur compounds differ considerably depending on the methodology used. Considering the possibility of carrying out calculations at a very high level of description of electronic correlation and the extrapolation of results to the basis set limit, we have reexamined the determination of the heat of formation of these two molecules hoping to unambiguously set a very accurate and definite value, and thus contribute with reliable results for scientists involved with the atmospheric chemistry of sulfur compounds. The reactions used by Resende and De Almeida11 for the determination of the enthalpies of formation of CH3SO and CH3SO2, shown below, were investigated in their own contexts of atmospheric chemistry, and the enthalpies of formation were obtained as an additional information among other thermodynamic data.These reactions are not isodesmic, but are isogyric, which means that the number of unpaired spins is conserved.6 This property raised the expectation that it would lead to reasonable values of the enthalpies of formation, however, a comparison of the results obtained in that study with the ones more recently reported shows a significant difference. An analysis of the possible sources of this difference raises two possibilities: one is the level of the calculation, and the other is the choice of the reactions used. Pushing the calculation to a very high level of theory is the alternative to identify the sources of inaccuracies in the first calculation and, therefore, to provide more accurate values for the enthalpies of formation of CH3SO and CH3SO2. Since the rationale behind the use of isodesmic reactions is the cancelation of computational errors between the two sides of a reaction, the minimization of these errors by means of a choice of a theoretical method where the complete basis set limit is reached and where a high level of electronic correlation is included in the calculation of the energies of the species involved can bypass the need of using this type of reactions. Under this circumstance, reactions 1 and 2 can be used to obtain accurate values for the enthalpies of formation of CH3SO and CH3SO2.   Calculations All calculations were carried out using the Gaussian package of programs.17 The MP2/cc-pVTZ level of theory was used for the optimizations of the five species involved in reactions 1 and 2. Harmonical frequencies were also determined at this level. The complete basis set limit was reached through the procedure developed and tested by Dunning and co-workers18 using single point calculations at the MP2/cc-pVDZ and MP2/cc-pVQZ levels of theory. This approach states that the dependence on basis set of several molecular properties, as the stabilization energy, is well represented by a simple exponential function of the formwhere n is the index of the basis set, and B, c, and A∞ are adjustable parameters, with A∞ being the asymptotic limit for the function. The limiting value of this function provides an estimate of the complete basis set (CBS) limit. In our calculation, n ranged from 2 to 4, and the function extrapolated was the energy for every stationary point at the MP2 level. Since all species are radicals, and spin contamination could be relevant in these systems, the respective projected values were used. Single point calculations also were conducted at the CCSD(T)/cc-pVTZ level of theory, aiming to include electronic correlation effects in a more accurate form. Recourse to the additivity approximation2,19 also made possible the prediction of more accurate values for the energies through the relation:  Results and Discussion The calculated energy values are given in Table 1. Figure 1 displays the geometrical parameters of the molecules considered in this work. It is interesting to note that the species CH3SO2 has the two oxygen atoms staggered with one hydrogen of CH3, which is in agreement with the findings of Davis,20 and Frank and Turecek,14 but different from the result reported by McKee.21 From the reaction energies listed also in Table 1, one can notice the significant variation in these values as one goes from the double-zeta to the complete basis set limit. At the MP2 level, it amounts to -22.5 kcal mol-1, and shows the influence of the basis set size on this property. On the other hand, electronic correlation turns out to be more important for reaction 2 than for reaction 1. The variation in energy from PMP2 to CCSD(T) is 2.9 kcal mol-1 for reaction 1 and 6.8 kcal mol-1 for reaction 2. The influence of the triples contributions on the CCSD values is also slightly greater for reaction 2 than for reaction 1.   The nuclear contributions to the enthalpy are 0.18 and -0.11 kcal mol-1, respectively, for reactions 1 and 2, leading therefore to a theoretical reaction enthalpy of -44.43 kcal mol-1 for reaction 1, and -33.07 kcal mol-1 for reaction 2, at the CCSD(T)/CBS level of theory. With the values of 9.8 and 6.51 kcal mol-1 for the standard heat of formation of CH3SCH2O and CH3CH2O2, determined previously by Resende and De Almeida,11,23 and the most recent value for CH3S reported in the literature, 31.04 ± 0.42 kcal mol-1, determined by photodissociation spectroscopy,22 the enthalpy of formation of CH3SO can be calculated as -16.7 kcal mol-1, using reaction 1. From this value and reaction 2, the CH3SO2 enthalpy of formation will be -53.1 kcal mol-1. These results are shown in Table 2, together with existing experimental and theoretical values. The value calculated in this work for the enthalpy of formation of CH3SO is in excellent agreement with Benson's estimate, being both about 2 kcal mol-1 smaller than the theoretical estimate of Turecek.10 As discussed above, basis set size effects are quite significant for this system, and in the G2 (MP2) methodology used in Turecek's work it corresponds to the 6-311+G(3df,2p) basis set. From Table 1, the variation in energy for reaction 1 is about 6 kcal mol-1, as one moves from the cc-pVTZ basis set to the complete basis set limit. This difference should be smaller for the reaction used by Turecek, since it is isodesmic, but it can explain the observed differences. In the

【 授权许可】

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