# Carbonyl Composition and Electrophilicity in Vaping Emissions of Flavored and Unflavored E-Liquids
## 2 Materials and Methods
### Global Electrophilicity and Local Site Reactivity Calculations  
The global electrophilicity index, \(\omega\), a reactivity parameter introduced by [PERSON] et al. in 1999 describes the stabilization energy of atoms or molecules when they accept an additional electronic charge from the environment [26]. In this study, Gaussian 16W was used to optimize geometries and compute \(\omega\) of interested simple carbonyls (i.e., formaldehyde, acetaldehyde, and benzaldehyde) and \(\alpha\),\(\beta\)-unsaturated carbonyls (i.e., acrolein and _trans_-2-hexenal). Density functional theory was used to optimize the geometry of molecules at the B3 LYP/6-311 + G(d,p) level of theory, and the conductor-like polarizable continuum model (CPCM) was implemented to include water as a solvent. The optimized geometries are shown in Table S1.  
To calculate \(\omega\), chemical potential (\(\mu\)) and chemical hardness (\(\eta\)), which are associated with ionization potential (\(I\)) and electron affinity (\(A\)) [26; 41], were calculated using the finite difference approximation. Ionization potential and electron affinity energies were obtained using energies of compounds in their neutral (charge 0), cationic (charge +1), and anionic (charge \(-1\)) states [42], which were computed using natural population analysis (NPA) in Gaussian 16W. Ionization potential was calculated as \(\mathrm{E_{cation}}-\mathrm{E_{neutral}}\) (Equation (1)), while electron affinity was calculated as \(\mathrm{E_{neutral}}-\mathrm{E_{anion}}\) (Equation (2)). Calculations for chemical potential, chemical hardness, and global electrophilicity index are shown in the following equations [26; 43].  
\[I=E_{cation}-E_{neutral} \tag{1}\]  
\[A=E_{neutral}-E_{anion} \tag{2}\]  
\[\mu=-\frac{I+A}{2} \tag{3}\]  
\[\eta=\frac{I-A}{2} \tag{4}\]  
\[\omega=\frac{\mu^{2}}{2\eta} \tag{5}\]  
In addition to global electrophilicity calculations, the condensed Fukui functions that represent local reactivity at specific sites within a molecule were also calculated. First, Gaussian 16W was used to optimize geometries at the B3 LYP/6-311 + G(d,p) level of theory in water using the CPCM solvation model. Then, the NPA in charges 0, \(-1\), and +1 were calculated in Gaussian 16W. Afterwards, the output values (Table S2) were uploaded into the UCA-FUKUI 1.0 software ([[https://uca-fukui.software.informer.com/1.0/](https://uca-fukui.software.informer.com/1.0/)]([https://uca-fukui.software.informer.com/1.0/](https://uca-fukui.software.informer.com/1.0/)) (accessed on 11 March 2019)) to calculate the condensed Fukui functions (\(f_{k}^{0}\), \(f_{k}^{-}\), \(f_{k}^{+}\), and dual-descriptor) using the finite difference method [44]. The following equations show the condensed Fukui functions for the \(k\)th atom in the molecule.  
\[f_{k}^{-}=q_{k}(N_{0})-q_{k}(N_{0}-1)\,,\text{ for electrophilic attack} \tag{6}\]  
\[f_{k}^{+}=q_{k}(N_{0}+1)-q_{k}(N_{0})\,,\text{ for nucleophilic attack} \tag{7}\]  
\[f_{k}^{0}=\frac{1}{2}\left(f_{k}^{+}+f_{k}^{-}\right)\,,\text{ for neutral (or radical) attack} \tag{8}\]  
\[\text{Dual-descriptor}=f_{k}^{+}-f_{k}^{-} \tag{9}\]  
In the above equations, \(q_{k}(N_{0}-1)\,,q_{k}(N_{0}+1)\,,\) and \(q_{k}(N_{0})\) represent the number of electrons associated with the \(k\)th atom in the molecule, where the total number of the electrons in the molecule is \(N_{0}-1\), \(N_{0}+1\), and \(N_{0}\)[44]. The dual-descriptor is the difference between \(f_{k}^{+}\) and \(f_{k}^{-}\), and it is either >0 or <0 [44; 45; 46]. If the dual-descriptor is >0, it indicates that the reaction site favors a nucleophilic attack, and if the dual-descriptor is <0, an electrophilic attack may be favored [44].