*Advanced Applications of Hydrogen and Engineering Systems in the Automotive Industry*


#### **Table 2.**

*Calculated total electronic energy (Eo), Hcorr, Gcorr, and the zero-point vibrational energies (ZPE) at the M06-2X/6-31g(d) level (in hartree).*



*Quantum Calculations to Estimate the Heat of Hydrogenation Theoretically DOI: http://dx.doi.org/10.5772/intechopen.93955*

*Limit energies were obtained using the web page http://sf.anu.edu.au/* �*vvv900/cbs/#ref\_3 [36]. <sup>a</sup> M06-2X/cc-pVDZ//M06-2X/6-31g(d) level. b M06-2X/cc-pVTZ//M06-2X/6-31g(d) level.*

*c*

*cc-pV(TD)Z extrapolated level.*

#### **Table 3.**

*Computed CCSD(T)/ccpVXZ energies at the M06-2X/6-31g(d) geometries, where X = D, T, as well as extrapolated values by the Eq. (2) (in hartree).*

(T)/cc-pVXZ energies computed at the M06-2X/6-31g(d) geometries, where X = D, T. **Table 3** also shows extrapolated values by the Eq. (2) (denoted *E*∞).

It is noted from **Table 3** that the cc-pV(DT)Z extrapolated level yield electronic energies for all reactants and products less than CCSD(T)/cc-pVDZ and CCSD (T)/cc-pVTZ levels, and it is expected that the calculations of the hydrogenation enthalpies by cc-pV(DT)Z extrapolated level are compatible with the experimental values.

#### *3.2.2 Enthalpies of hydrogenation at 298.15 K in gas phase*

The usual way to calculate enthalpies of reaction is to calculate heats of formation, and take the appropriate sums and difference (Eq. (3)).

$$
\Delta\_{\text{hyd}}H^{\text{o}}(\text{298}) \sum\_{\text{products}} \Delta\_f H^{\text{o}}(\text{298}) - \sum\_{\text{reactans}} \Delta\_f H^{\text{o}}(\text{298}) \tag{3}
$$

However, since Gaussian program provides the sum of electronic and thermal enthalpies, there is a short cut: namely, to simply take the difference of the sums of these values for the reactants and the products. This works since the number of atoms of each element is the same on both sides of the reaction, therefore all the atomic information cancels out, and you need only the molecular data. For example, using the information in **Table 2** (or **Table 3** for energies), the enthalpy of reaction can be calculated simply by Eq. (4):

$$
\Delta\_{\text{hyd}}H\_{298}^{0} = \sum \left( E\_0 + H\_{\text{corr}} \right)\_{\text{products}} - \sum \left( E\_0 + H\_{\text{corr}} \right)\_{\text{reactants}} \tag{4}
$$

*E*<sup>0</sup> can represent either *E*DZ, *E*TZ, *E*QZ or *E*<sup>∞</sup> keeping the calculated *H*corr value at M06-2X/6-31g(d) level is fixed. The calculated enthalpies of hydrogenation are


*b CCSD(T)/cc-pVTZ//M06-2X/6-31g(d) level.*

*d NIST-JANAF thermo-chemical tables.*

#### **Table 4.**

*Difference between experimental and calculation values of standard enthalpies of hydrogenation of some unsaturated hydrocarbons in the gas phase at 298.15 K (in kJ Mol*�*<sup>1</sup> ).*

*c cc-pV(TD)Z extrapolated level.*

*Quantum Calculations to Estimate the Heat of Hydrogenation Theoretically DOI: http://dx.doi.org/10.5772/intechopen.93955*


**Table 5.**

*Statistical parameters for all used methods to calculate hydrogenation enthalpies. (in kJ Mol–<sup>1</sup> ).*

#### **Figure 1.**

*Calculated versus experimental hydrogenation enthalpy* Δ*H*<sup>0</sup> hydð Þ *<sup>298</sup>*, *15K* , *kJ mol*�*<sup>1</sup>* h i *of 29 hydrocarbons.*

reported in **Table 4**, along with the experimental values. **Table 5** shows statistical parameters for all used computational methods. **Figure 1** shows a linear analysis of the best calculated results in terms of experimental results.

Our best theoretical estimates of the enthalpies of hydrogenation are based on basis set limit extrapolation calculations, when the pair cc-pVDZ and cc-pVTZ are used, and the mean absolute deviation (MAD) between experimental and calculated values is 1.5 kJ mol�<sup>1</sup> (**Table 5**). The enthalpies of hydrogenation of some alkenes (12 compounds) have been calculated at the HF, B3LYP, M06, MP2, G3, G4, CBS-QB3, CBS-APNO, and W1BD levels and, in the case of the first four methods, using a variety of basis sets up to aug-ccpVTZ [37], and it is found that the MAD decreases gradually from the first to the last method (18.4–4.2 kJ mol�<sup>1</sup> ). Moreover, Rogers et al. [38–40] calculated the hydrogenation enthalpy at 298.15 K for reactions involving cyclic and acyclic C4 (20 reactions), cyclic C5 (23 reactions) and C6 (24 reactions) hydrocarbons using the G2 and G2(MP2) ab initio methods, and it is found that the MAD is about 3.3, 3.7 and 5.0 kJ �<sup>1</sup> , respectively.
