## 2 Methodology
### Computational Protocols Employed to Predict Dielectric Strength  
The dielectric strengths of the designed organic compounds were calculated using four distinct equation-based protocols: (i) POLAR-IE-MW equation (PIM), (ii) reparameterized POLAR-IE-MW equation (re-PIM), (iii) parameterized POLAR-IE-MW-NF equation (PIMN), and (iv) optimized factor equation (OPT). Here, each equation is named to indicate the incorporated factors (i.e., polarizability (POLAR), ionization energy (IE), molecular weight (MW), and new factor (NF)) with or without parameterization. In detail, the PIM (\(E_{PIM}\)), re-PIM (\(E_{re-PIM}\)), PIMN (\(E_{PIMN}\)), and OPT (\(E_{OPT}\)) equations are given as follows:  
\[E_{PIM}=0.0012\alpha^{1}(\epsilon_{i}^{a})^{0.288}(M_{w})^{0.401}, \tag{1}\]  
\[E_{re-PIM}=xa^{y}(\epsilon_{i}^{a})^{z}(M_{w})^{m}, \tag{2}\]  
\[E_{PIMN}=xa^{y}(\epsilon_{i}^{a})^{z}(M_{w})^{m}\theta^{n}, \tag{3}\]  
\[E_{OPT}=xa^{y}(N_{e})^{z}(M_{w})^{m}\Big{(}E_{f}\Big{)}^{n}(V_{m})^{l}, \tag{4}\]  
Figure 1: Schematic flow of the DFT-/equation-based protocol for predicting the dielectric strength of 168 PFC and non-PFC compounds. where \(\alpha\), \(\varepsilon_{i}^{a}\), \(N_{e}\), \(M_{w}\), \(\theta\), \(E_{f}\), and \(V_{m}\) are the polarizability, IE, number of electrons, MW, NF, formation energy, and molar volume, respectively. In particular, \(\theta\) is the number of electrons, HOMO, HOMO-LUMO gap, electronic spatial extent gap, formation energy, or molar volume. Notably, the equations contain parameters (\(x\), \(y\), \(z\), \(m\), \(n\), and \(l\)) to be fitted for the reliable prediction of the dielectric strength. The polarizability and IE of each compound were computed using a DFT modeling approach with the B3 LYP functional and 6-311+G(d,p) basis set, as described in our previous study [21]. The DFT-computed values of these core factors have already been validated for a large set of organic compounds by systematic comparison with their experimental values [21]. Notably, the DFT modeling approach has been widely utilized for the investigation of electrochemical properties of organic compounds [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. An average relative error was computed for each core factor which was predicted by the DFT modeling approach. The relative error of each compound is defined as the deviation of the DFT-calculated value from its experimental value, which is subsequently normalized by the experimental value. The average relative error is therefore the averaged value for the relative errors of 168 PFC and non-PFC compounds. In that sense, the average relative error is a descriptor to determine how accurately the DFT-based modeling approach can predict the core factors. The first equation, PIM, was derived from a parameterized equation developed to accurately predict the dielectric strengths of a selected set of PFC compounds in our previous study [21]. The previous equation was developed using a limited database that did not cover the full range of available PFC compounds and contained no non-PFC compounds [21]. Consequently, PIM was reparameterized to obtain the second equation, re-PIM, with the aim of further advancing this protocol in terms of the quality of the parameters in the equation. A more advanced version of the equation, PIMN, was subsequently developed to overcome the limited combination of original factors (i.e., polarizability, IE, and MW), and was considered critically impactful for dielectric strength predictions in our previous study. This advance was achieved by incorporating a new factor, \(\theta\). The new factors introduced in this study, which included electrical factors (the number of electrons, HOMO, HOMO-LUMO gap, and electronic spatial extent gap), chemical factors (formation energy), and physical factors (molar volume), are discussed in detail in the next section. Figure 2: Classification of organic compounds in the database.