The thermochemistry of alkanethiols and thioethers. Estimation of the enthalpies of formation of 1,3-dithiapropane and 1,3,5-trithiapentane

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Introduction
The structure and energetics of molecules are fundamental concepts in Chemistry, the energy associated with a particular structure being related to the constituent atoms, and the corresponding bonds and angles that form the molecular framework. 1Thermodynamic data such as the enthalpies of formation are often helpful in the understanding of the conformational and reactivity trends exhibited by the molecules.][3] Several empirical methods have been applied to the calculation of enthalpies of formation of hydrocarbons and alkane derivatives.The simplest procedures for calculating values for standard enthalpies of formation assume that enthalpies of atomization of compounds may be represented by a sum of contributions from the constituent bonds.Sophisticated procedures require a large number of parameters and so less elaborate, more generally applicable, procedures are required.The three most commonly used are those due to Laidler, 4 Allen 5,6 and Benson. 7,8In the Laidler bond additivity approach, 4 values for some bond energies are allowed to depend on the environments of the bonds.The Allen group increment method 5,6 assumes constant values for bond energies, but also includes contributions from molecular fragments.The Benson group additivity scheme 7,8 does not use bond energies and instead assumes that enthalpies of formation or atomization can be represented by contributions from different types of molecular fragments.The unified scheme of Cox and Pilcher, 2 which consolidates the Allen, Benson and Laidler methods, is more sophisticated and has been applied almost exclusively to simple hydrocarbons.
More recently, the Pedley method 9 that allows bond-energy terms to vary among a number of specific environments, and the additive bond-energy scheme of Smith 10,11 that includes geminal H−H terms have been developed.
In this work we have carried out a study on the thermochemistry of alkanethiols and thioethers.Relationships between the enthalpies of formation of alkanes, alkanethiols, and thioethers are discussed with the purpose of deriving different group interconversion contributions that permit the estimation of unknown ∆ f H 0 m (g) values for alkanethiols and thioethers from known values of alkanes.We have also carried out a theoretical study at the G2(MP2), G2, and G3 levels, calculating the enthalpies of formation of two compounds, 1,3dithiapropane and 1,3,5-trithiapentane, and comparing them with the values previously estimated.

Results and Discussion
The known enthalpies of formation 9 in the gas phase, ∆ f H 0 m (g), of alkanes, alkanethiols and thioethers, have been collected in Table 1.As it is well known, 2,[12][13][14][15][16][17] the values of the thermodynamic properties of a homologous series, Y−(CH 2 ) m −H, show a monotonic, often linear, dependence on m.Prosen, Johnson and Rossini, 13 proposed the general relation: where A is a constant peculiar to the end group Y; B is a constant for all normal alkyl series, independent of Y; and δ is a term which has a small finite value for lower members, being largest for m = 0, and becomes zero for higher members, beginning near m = 4. B values of -20.71, -20.62 and -20.53 kJ mol -1 have been obtained by us for n-alkanes, 1-alkenes and 1alkynes, respectively, using the experimental data available in the literature. 9However, for 1alkanols, B has a value of -20.13 kJ mol -1 .The reason for the different methylene increment in 1-alkanols is not well understood. 11In 1-alkanethiols a B value of -(20.80 ± 0.18) kJ mol -1 is obtained, indicating that their behavior is similar to that generally observed, but different to that of 1-alkanols.A value of -4.95 kcal mol -1 (-20.71kJ mol -1 ) was obtained by Good and DePrater 18 using the data between 1-butanethiol and 1-decanethiol.An interesting way in which data may be examined is via calculations of energies for converting one group, such as methyl or methylene, to another.Group interconversion is more satisfactory that replacement of a hydrogen by a functional group since nonbonded interactions will cancel to some extent in the former case but not in the latter. 16ollowing the ideas of Stull et al., 19 Wiberg et al., 15 and Slayden and Liebman, 12 we can describe the energetics of alkanethiols and thioethers defining the quantities: The variation of the ∆∆ f H o m values for alkanethiols is small.Not taking into account the conversion from ethane to methanethiol, where a CH 3 group attached to another CH 3 group is converted to SH, we obtain a mean value of 57.8 ± 1.1 kJ mol -1 , using 18 data points.In the case of thioethers, the ∆∆ f H o m values present a wider range of values and the four compounds with higher deviations have not been taken into account in the calculation of the mean value, 63.2 ± 2.3 kJ mol -1 (obtained using 13 data points ] values calculated above, it is now possible to estimate the enthalpies of formation of different alkanethiols or thioethers.We have first applied this method to the calculation of ∆ f H 0 m (g) for the alkanethiols and thioethers used in the derivation of the ∆∆ f H o m values.The results are collected in Table 2.The average deviation is 0.8 kJ mol -1 for alkanethiols, and 1.9 kJ mol -1 for thioethers.
A further step in the process of proving the validity of our predictions is to calculate ∆ f H 0 m (g) values for a series of compounds containing the sulfide and/or thiol groups, and not used in the derivation of the ∆∆ f H o m values.Nine compounds have been found in the literature: cyclopentanethiol, cyclohexanethiol, cyclopentyl methyl sulfide, 3,5-dithiaheptane, 3,6dithiaoctane, and four alkanedithiols: 1,4-dithiabutane, 1,5-dithiapentane, 1,6-dithiahexane, and 1,7-dithiaheptane.The calculated ∆ f H 0 m (g) values for all of these compounds are collected in Table 3.As it can be seen, a very good agreement is obtained between the experimental and calculated ∆ f H 0 m (g) values.Finally, we have calculated the enthalpies of formation of two compounds with unknown ∆ f H 0 m (g) value: a dithiol, With the purpose of checking the accuracy of the estimated enthalpies of formation of the above mentioned two compounds, we have also carried out a theoretical study, calculating their enthalpies of formation at the G2(MP2), G2 and G3 levels.These methods have been previously used by us [21][22][23][24][25][26][27][28][29] for the calculation of the enthalpies of formation of different compounds containing S atoms: thiirane, 21 thiane, 21,22 1,3-and 1,4-dithiane, 21 1,3,5-trithiane, 22 2-and 3thiophenecarboxylic acids, 23 thiane sulfoxide and thiane sulfone, 24 1,3-dithiane sulfone, 26 and 1,3-dithiane sulfoxide. 27In all the cases, a good agreement between experimental and theoretical results was obtained.
The most stable conformers of both studied compounds are in gauche, gauche conformation (anomeric effect) as it is well known 30,31 in the case of HSCH 2 SH.To our knowledge, there is not any conformational study in the literature for HSCH 2 SCH 2 SH.The MP2(FULL)/6-31G(d)-optimized structures are drawn in Figure 1.
Calculated energies at 0 K, and enthalpies at 298 K, for 1,3-dithiapropane and 1,3,5trithiapentane are given in Table 4.In standard Gaussian-n theories, theoretical enthalpies of formation are calculated through atomization reactions ( 5) and (6).We have detailed this method in previous studies. 32,33 4 S 2 (g) → C(g) + 4 H(g) + 2 S(g) C 2 H 6 S 3 (g) → 2 C(g) + 6 H(g) + 3 S(g) Raghavachari et al. 34 have proposed to use a standard set of isodesmic reactions, the "bond separation reactions", 35 to derive the theoretical enthalpies of formation.This method has been detailed in previous studies. 32,33 bond separation reactions for 1,3-dithiapropane and 1,3,5-trithiapentane are, respectively: C 2 H 6 S 3 (g) + 2 CH 4 (g) + H 2 S(g) → 4 CH 3 SH(g) The ∆ f H o m calculated values, at the G2(MP2), G2 and G3 levels, using both atomization and isodesmic bond separation reactions, are shown in Table 5.The averages of the values calculated at the different Gn levels from atomization and bond separation isodesmic reactions, 16.3 and 27.7 kJ mol -1 , for 1,3-dithiapropane and 1,3,5-trithiapentane, respectively, are in reasonable agreement with the values previously estimated in this work, 10.9 and 31.9 kJ mol -1 , respectively, within the uncertainties associated to Gaussian-n methods.This method has been detailed in ref 24
The scheme of G3 theory is similar to that of G2, but the MP2 single-point energy calculation is performed with a new basis set, referred to as G3large that includes core correlation.So, G3 is effectively at the QCISD(T,full)/G3large level, making certain

Table 1 .
Experimental enthalpies of formation a of alkanes, alkanethiols and thioethers, used in this work, and calculated 2 → S,(g)] values, for alkanethiols and thioethers, respectively.All values in kJ mol -1

Table 3 .
Calculated ∆ f H 0 m (g) values for a series of sulfur compounds, using the ∆∆ f H o m [CH 3 → SH,(g)] and ∆∆ f H o m [CH 2 → S,(g)] values calculated in this work.All values in kJ mol -1 a Values taken from ref 9, unless otherwise noted b Value taken from ref 20.

Table 5 .
Calculated enthalpies of formation for the studied compound at the G2(MP2), G2 and G3 levels using both atomization and bond separation isodesmic reactions.All values in kJ mol-1 a Value obtained from atomization reaction including spin-orbit and bond additivity corrections.