## 2 Materials and Methods
### Vaporization Thermodynamics of Alkyl-Quinolines and Alkyl-Pyridines
#### 3.3.3 Validation Using the Group-Additivity Principles: \"Centerpiece Approach\"  
In series of our recent papers [46; 47] we are developing a so-called \"centerpiece\" approach, which is closely related to the conventional group-additivity (GA) methods [48; 49]. In the GA methods, the enthalpy of a molecule of interest is collected from small groups (or \"Lego bricks\") with well-defined energetic contributions. In contrast, the idea of this \"centerpiece\" approach is to select a potentially large \"core\" molecule that may mimic the structure of the molecule of interest, but the selected \"core\" molecule has the well-established thermodynamic properties. Various substituents can be attached (or subtracted) to this \"centerpiece\" in different positions. The visualization of the \"centerpiece\" approach for ethyl-quinolines is given in Figure 2.  
For the calculation, e.g., the enthalpy of vaporization of 2-ethyl-quinoline, a similarly shaped unsubstituted quinoline can be taken as a possible \"centerpiece\" with a reliable experimental \(\Delta_{1}^{\mathrm{g}}H_{\mathrm{m}}^{\mathrm{O}}(298.15\) K)-value (see Table 2). It is obvious that quinoline rings already bear the main energetic contribution to the vaporization enthalpy due to the interactions of aromatic rings in the liquid phase. Such a specific contribution is unique to the quinoline as the \"centerpiece\" molecule and cannot be captured by any other method. This special feature of the \"centerpiece\" approach significantly increases the reliability of the property prediction for similarly shaped molecules, e.g., ethyl-quinolines. In order to estimate the vaporization enthalpy of 2-ethyl-quinoline, we use the well-known \(\Delta_{1}^{\mathrm{g}}H_{\mathrm{m}}^{\mathrm{O}}(298.15\) K)-value of quinoline as the \"centerpiece\", and add the contribution for the ethyl-substituent as it shown in Figure 2. The contribution for the ethyl group can be easily derived as the difference between vaporization enthalpy of 2-, 3-, or 4-ethyl-pyridine and enthalpy of vaporization of unsubstituted pyridine (see Figure 2). To validate the \"centerpiece\" approach for quinoline derivatives, we calculated enthalpies of vaporization of 2-ethyl-quinoline, 3-ethyl-quinoline, and 4-ethyl-quinoline (see Table 2, labeled as GA) and these values agree within \(\pm 1\) kJ-mol\({}^{-1}\) with results derived from other methods. 3.4 Validation Using the Correlation with the Number of C-Atoms (N\({}_{\mathrm{C}}\)) in the Alkyl Chain  
The final check to establish the internal consistency of the experimental results evaluated in Table 3 for alkyl-pyridines is to correlate the \(\Delta_{1}^{\mathrm{g}}H_{\mathrm{m}}^{\mathrm{o}}(298.15\) K)-values with the number of C-atoms (\(N_{\mathrm{C}}\)) in the alkyl chain. As a rule, the simple linear correlation type is observed in all homologous series regardless of the functional group attached to the alkyl chain [50]. In addition, for the alkyl-substituted pyridines the \(\Delta_{1}^{\mathrm{g}}H_{\mathrm{m}}^{\mathrm{o}}(298.15\) K) correlates with \(N_{\mathrm{C}}\) = 0-4 as follows:  
Figure 2: Calculation of vaporization enthalpies, \(\Delta_{1}^{\mathrm{g}}H_{\mathrm{m}}^{\mathrm{o}}(298.15\) K), of ethyl-substituted quinolines using the “centerpiece approach”.