Exploring Simple, Interpretable, and Predictive QSPR Model of Fullerene C60 Solubility in Organic Solvents

1. Introduction

Fullerene, a highly symmetrical cage-like molecule has specific interaction with organic solvents and its knowledge can provide significant information on the mechanisms of solute-solvent interactions. The fullerenes have defined rigid geometries in distinction to other solutes whose shapes undergo conformational changes. Not only that intramolecular vibrational partition functions may undergo solvent-dependent changes (Prylutskyy et al., 2003). Due to sparingly soluble nature of C₆₀ in major organic solvents, the production cost is still high for this nanomaterial (Shunaev et al., 2015). Therefore, understanding of fullerene’s solubility provides significant feature assisting in purification, extraction, bioavailability, reactivity, and risk assessment of fullerenes. This information is vital due to ample application of carbon nanostructures, such as C₆₀ and its derivatives in diverse aspects of nanotechnology, pharmaceuticals, cosmetic, medicinal chemistry, environmental applications (Cook et al., 2010; Bogatu, & Leszczynska, 2016) and materials science (Gharagheizi & Alamdari, 2008; Sivaraman et al., 2001).

Quantitative structure-property relationship (QSPR) represents a powerful tool for modeling and prediction of physiochemical properties. The QSPR method is defined on the foundation of a mathematical algorithm providing a rational basis for establishing a predictive correlation model. Apart from providing a mathematical correlation, it also enables the exploration of chemical features encoded within parameters (descriptors) (Roy, Kar, & Das, 2015a; Toropova, 2016). Hence, diverse set of descriptors plays a noteworthy role in the recognition as well as analysis of the chemical basis involved in a studied phenomenon. Therefore, reliable QSPR model can offer time and cost-effective measure of C₆₀ solubility values in organic solvents in the absence of experimental data.

A series of investigation for predicting C₆₀ solubility in organic solvents employing QSPR model has been reported in the last 12 years. Liu et al. (2005) generated a linear model as well as a least-squares support vector machine (LSSVM) model for predicting the solubility of C₆₀ in 128 and 122 organic solvents, respectively. Toropov et al. (2007, 2009) demonstrated two kinds of descriptors methods for predicting solubility of C₆₀ in different organic solvents. Same dataset was used to build one-variable model once with the optimal descriptors calculated with simplified molecular input line entry system(SMILES) (Toropov et al., 2007) and in another work with International Chemical Identifier (InChI) (Toropov et al., 2009) with high statistical results. Petrova et al. (2011) depicted successful application of the GA-MLR technique in combination with quantum-chemical and topological descriptors yields reliable four-variable models for 122 organic solvents. One GA-MLR model was developed to predict the fullerene solubility in 36 benzene derivatives by Pourbasheer et al. (2011). Ghasemi et al. (2013) proposed first 3D-QSAR model employing VolSurf based descriptors with SPA-SVM (successive projection algorithm-support vector machine) method to predict C₆₀ solubility in 132 organic solvents with acceptable statistical results. In recent time, Xu et al. (2016) proposed a QSPR model for predicting the solubility of fullerene C₆₀ in 156 diverse organic solvents with the norm indexes.

In this regard, we aimed to find simple, predictive, computationally time-efficient and mechanistically interpretable model to predict the solubility of C₆₀ in the same set of organic solvents considered by Xu et al. (2016). In addition, the study intends to estimate predictive potential of the simple 1D and 2D descriptors to model the solubility of the fullerene C₆₀ in a large number of organic solvents.