## 2 Materials and Methods
### Calculated Mass-Energy Profiles  
Each mass-energy profile consists of a series of pairs of \(m/z\) values and energies necessary for the formation of the respective ions. Semiempirical methods such as RM1 and PM7, as well as functional B3 LYP, are currently used to calculate the activation energy descriptors of molecular fragmentation in EI-MS, since the fragmentation is an intramolecular transformation. Any other QC method can be used to generate these descriptors because the mining algorithm removes any energy profile that does not provide the maximum docking score. The mass-energy profiles calculated in a previous paper with _HyperChem_ 8.0.10, _MOPAC_2012, and _Gaussian_ 09 software were used (Tables A1-A4) [11; 12; 13; 14]. They correspond to structures **1**-5 from Figure 1. In these profiles, the strings of the calculated and experimental energy descriptors correspond to the ionic masses in ascending order. In this QSFR-based technique, the calculated energy descriptors were enthalpies and Gibbs energies of ion formation (\(\Delta_{\beta}H_{ion}\) or \(\Delta_{\beta}G_{ion}\)) and enthalpies and Gibbs energies of fragmentation (\(\Delta_{\beta}H_{frag}\) or \(\Delta_{\beta}G_{frag}\)), respectively. They were calculated with Equations (1) and (2), respectively:  
\[\Delta_{\beta}H_{frag}=\Delta_{\beta}H\;(\text{I}_{i}^{+})+\Sigma\Delta_{ \beta}H\;(\text{F}_{i})-\Delta_{\beta}H\;(\text{M}), \tag{1}\]  
\[\Delta_{\beta}G_{frag}=\Delta_{\beta}G\;(\text{I}_{i}^{+})+\Sigma\Delta_{ \beta}G\;(\text{F}_{i})-\Delta_{\beta}G\;(\text{M}), \tag{2}\]  
where \(\Delta_{\beta}H\;(\text{I}_{i}^{+})\) is the formation enthalpy of the resulted fragmentation ion, \(\Sigma\Delta_{\beta}H\;(\text{F}_{i})\) is the sum of the formation enthalpies of accompanying fragments, and \(\Delta_{\beta}H\;(\text{M})\) is the molecular enthalpy of candidate structure. The meanings are similar for \(\Delta_{\beta}G\)[11]For ease of reference, they were also assigned the following acronyms: DAG (**diacetone-D-glucose**) (**1**), DAM (**diacetone-D-mann**ose**) (**2**), DAG**al (**diacetone-D-galc**ose**) (**3**), DAF (**diacetone-D-fructose**) (**4**), and DAS (**diacetone-L-sorbose**) (**5**). Through the perspective of the \"Lock and Key\" concept, the calculated profiles represent the keys. Each of them contains five of the seven \"pins\" representing the primary ion energies used in the analysis, possibly obtained from the candidate structures **1-5** in the mass spectrometer (Table 1). The absence of some energy values from the calculated profiles indicates differences in primary fragmentations between the candidate structures. Thus, the ions at \(m/z\) 245, \(m/z\) 187, and \(m/z\) 127 had calculated energies for all structures (**1-5**). This is because each of them could fragment into those ions by losing methyl, hydroxyl and/or one or two molecules of acetone (Table 1, Figure 1). Instead, several cells in Tables A1-A4 contain the letter \"a\" for \"absent\" because the candidate structures could not form the respective primary ions. Thus, the ions at \(m/z\) 229 and \(m/z\) 171 appeared only for structures **3-5** because they explicitly contain the -CH\({}_{2}\)OH group, which the other structures (**1** and **2**) do not contain (Figure 1, Tables 1 and A1-A4). Similarly, the ions at \(m/z\) 159 and \(m/z\) 101 appeared only for structures **1** and **2**, as they explicitly contain the -C\({}_{5}\)H\({}_{9}\)O\({}_{2}\) group, which the other structures (**3-5**) do not contain (Figure 1, Tables 1 and A1-A4) [11]. Primary ions result from the cleavage of a single chemical bond from the molecular structure, accompanied or not by the elimination of some small molecules. Their formation requires small fragmentation energies compared to those of ions that are formed after multiple molecular cleavages. If primary ions with the same \(m/z\) originate from different molecular structures, they will need different energies for their formation.