4.2. Calculation of Molecular Descriptors

The ISIDA fragment descriptor, which is also realized as the substructure molecular fragment (SMF) descriptor, is defined as the number of topological fragments of the molecular structure. There are two main classes of molecular subgraphs: (I) “sequences” and (II) “augmented atoms.” The “sequences” means the shortest path of two atoms connected by chemical bonds. There are three types of “sequences,” which are performed as atom types (A), bond types (B), and atom and bond types (AB). For each type of sequence, the minimal and maximal lengths of the path are defined as n_min and n_max, respectively. In this study, the length of the sequence corresponds to n_min = 2 and n_max = 8. The selected atoms with their environment are defined as “augmented atoms,” which also includes neighbor atom and bond types (AB), atom types (A), or bond types (B).

Since ILs are composed of anions and cations, it is necessary to calculate descriptors for cations and anions separately. The detailed descriptor calculation process is performed as follows: first, the 2D chemical structures of each cation and anion were drawn using MarvinSketch (version 15.6.29.0) and optimized based on the clean in 2D method. Structure data files (SDF) including two cations and three anions were then, respectively, imported into EdiSDF, a program of the ISIDA system, to generate SDF records of cations and anions. The described SMF descriptors were generated by the SMF module of the ISIDA system.

The mixture descriptor for the IL mixture was developed by combining the descriptors of diverse cations and anions separately. The 12 proposed formulas that take into account their respective mole fractions were used to calculate mixed-cation descriptors and mixed-anion descriptors³⁴ (Table 3). Then, descriptors for constituted species were concatenated to describe the structure of the multiple-ion system.³⁵

Since ILs consist of cations and anions, their thermal stability and the character of the cations and anions are intimately connected. Thus, not only the structural characteristics of ions should be taken into account, but also the contribution of interaction is indispensable. The molecular structure can be intuitively represented by the SMF module, while the interactions between the cations and anions cannot be represented because of the limitation of the software. Considering the diverse associations that possibly exist in a multiple-ion system of IL mixtures, the descriptors based on the norm index were proposed to describe each cation–anion interaction of imidazolium IL mixtures in this work.

First, the 3D structure of each cation and anion was achieved by Chemdraw (version 14), with the optimization based on the MM2 module (the class 1 Allinger molecular mechanics program). For further optimization, the Gaussian (version GaussView 6.0.16) was employed to carry out density functional theory (DFT) M06-2X functional calculation on the basis of 6-311+G (d,p). Then, the optimized molecular structures were characterized by the matrix norm index.³³

The calculation process of distance matrices and property matrices is shown as follows:

n is the path between atoms i and j.

is the Euclidean spatial distance between atoms i and j.

where AW, Ra, EN, MW, AQ, and BD are atom weight, atom radius, electronegativity, molecular weight, atom charge, and branching degree, respectively.

Then, the distance matrices and the property matrices are combined as CM matrices, which are calculated as follows:

where m = 1, 2, 3, 4, and 5, which correspond to matrices MP₁ to MP₅. Furthermore, the three norm indexes are defined in eqs 12–14:

where p and q represent the number of rows and columns of matrix CM, respectively. is the eigenvalue of the matrix, and the is defined as the Hermite matrix of the matrix.

Considering that the thermal stability is related to the various interactions of the binary IL system, the descriptors for multiple cation–anion interactions are further proposed based on the original calculation for single ILs,^29,33 which are defined as follows:

In this study, all the four interaction descriptors , , , and were proposed to represent the cation–anion interactions individually, and then all those descriptors were concatenated to describe the characteristics of multiple-interaction system, where w = 1, 2, and 3, corresponding to norm(CM,1), norm(CM,2), and norm(CM,3), and CF and AF refer to the mass fractions of the cations and anions, respectively. The , and , refer to the norm indexes of matrices calculated from the cations and anions, individually.