## 3 Results and Discussion
### Validation of Vaporisation Enthalpies Using Structure-Property Relationships
#### 3.3.5 Quantum Chemistry: Theoretical Enthalpies of Formation of Iso-Propyl- and Tert-Butyl-Benzenes  
Since experimental data are not available for all alkylbenzenes of interest for this work, especially not for crowded tert-butylbenzenes, they were calculated using quantum chemistry (QC). Are the high-level methods G3 MP2 and G4 good enough to accurately calculate the gas-phase formation enthalpies of large molecules such as tri- and tetra-tert-butylbenzenes? It is common practice to test QC methods against a set of reliable experimental data. There are fourteen reliable gas-phase formation enthalpies of di- and tri-alkyl substituted benzenes (see Table 8) that might help answer this question. This data set was utilized to validate the results of the composite methods G3 MP2 and G4. The most stable conformers for each alkylbenzene were found using a computer code named CREST (conformer-rotamer ensemble sampling tool) [60] and optimised with the B3 LYP/6-3 lg(d,p) method [61]. The energies \(E_{0}\) and the enthalpies \(H_{298}\) of the most stable conformers were calculated using the G3 MP2 and G4 methods implemented in the Gaussian 16 Software. The enthalpies, \(H_{298}\), from the output files were converted into the _theoretical_ gas-phase enthalpies of formation alkylbenzenes using an atomisation (AT) reaction [62], as well as using the _well-balanced reactions_ (WBR) given in Table S12. The comparison of the G3 MP2 results from the atomisation reaction with the experimental results is given in Table S13. The comparison of the G4 results from the atomisation reaction with the experimental results is given in Table S14. It was found that the enthalpies of formation calculated using AT are slightly but systematically more negative for both methods. Such a feature of AT reactions is known [63], but this disadvantage can be easily removed by correcting the calculated results. The latter correction was derived from the correlation between experimental enthalpies of formation and the \(\Delta_{\text{f}}H_{\text{m}}^{\text{o}}\)(g, AT)-values directly calculated via atomisation reaction. The following correction equations were derived:  
\[\text{for G3 MP2 }\Delta_{\text{f}}H_{\text{m}}^{\text{o}}(\text{g})\text{AT}_{ \text{corr}}/\text{kJ.mol}^{-1}=0.9749\ \times\ \Delta_{\text{f}}H_{\text{m}}^{\text{o}}(\text{g},\ \text{AT})+7.3\ \text{with}\ R^{2}=0.9995 \tag{11}\] \[\text{for G4 }\Delta_{\text{f}}H_{\text{m}}^{\text{o}}(\text{g})\text{AT}_{ \text{corr}}/\text{kJ.mol}^{-1}=0.9614\ \times\ \Delta_{\text{f}}H_{\text{m}}^{\text{o}}(\text{g},\ \text{AT})+2.6\ \text{with}\ R^{2}=0.9996 \tag{12}\]  
The data used to develop these equations are given in Table S12 for G3 MP2 and in Table S13 for G4. The _theoretical_\(\Delta_{\text{f}}H_{\text{m}}^{\text{o}}\)(g)\({}_{\text{theor}}\)-values of alkylbenzenes \"corrected\" in this way for both methods agree well with the values derived from the well-balanced reactions given in Table S12. For the sake of brevity, all quantum chemical results are summarized in Table 10.  
Since the results from the G3 MP2 and G4 methods agree well, the _theoretical_ average values, \(\Delta_{\rm f}H_{\rm m}^{\rm o}(\mathfrak{g})_{\rm theor}\), were calculated in Table 10, column 6 for all alkylbenzenes and these values were used for comparison with the experimental results in Table 8, column 5. As can be seen from Table 8, the theoretical results agree, within experimental uncertainties, with the reliable experimental enthalpies of formation. Such good agreement could convince that the QC results for the tri- and tetra-tert-butylbenzenes can be considered reliable. However, from our experience, the QC results for large molecules with 20-25 \"heavy\" atoms should be viewed with caution. For this reason we decided to examine the applicability of the QC results for 1,2-di-tert-butylbenzene, 1,2,4-tri-tert-butylbenzene and 1,2,4,5-tetra-tert-butylbenzene, where the experimental enthalpies of formation in the condensed state are available from the literature [57; 64; 65].