Prediction of the transition temperature of bent-core liquid crystals using fuzzy “digital thermometer” model based on artificial neural networks
Introduction
Quantitative structure–property/activity relationship (QSPR/QSAR) models for the prediction of physical properties and biological activities of organic compounds from their molecular structures have been a focus of great attention for a long time (Mu et al., 2007). In recent years, artificial neural networks (ANNs) have opened a new avenue for developing empirical models useful for predicting the performance of the process outside the experimental domain (Olea, 2007). A literature review indicate that QSPR modeling based on ANNs has grown dramatically, suggesting the importance of applications of ANN in molecular modeling (Katritzky et al., 2010). ANNs are useful tools in QSPR studies because a given structure–property relationship is often nonlinear (Yao et al., 2004).
The QSPR models are very important in the field of liquid crystals, since small structural modifications of liquid crystal (LC) molecules can drastically influence their transition temperature. Therefore, the design of molecular structure with desired LC phase temperature, based only on empirical rules, is a very complex task. The QSPR methodology has been successfully applied to predict various physical and chemical properties of LCs Al-Fahemi (2014), Antanasijević et al. (2016a), Gong et al. (2008), Johnson and Jurs (1999), which possess unique physicochemical properties and have wide application in a variety of fields Bahadur (1994), Vicari (2016). Nowadays, bent-core LCs are the most attractive type of these materials due to their promising applications Eremin and Jákli (2013), Takezoe and Takanishi (2006), and their transition temperatures have been the subject of recent QSPR studies Antanasijević et al. (2016b), Antanasijević et al. (2016c). In those studies, the QSPR models with good predictive ability (R2 0.90) based on decision trees, multivariate adaptive regression splines and group method of data handling (GMDH-type) neural network have been proposed for the prediction of five-ring bent-core LCs transition temperatures.
In this study, the transition temperature of bent-core LCs was predicted using general regression neural network (GRNN) with the aim to develop a more accurate model that will allow the estimation of prediction error for each compound. For this purpose, the ANN model with digital output neurons, previously proposed for the transition temperatures of smectic LC compounds by Schroder et al. (1996), has been adapted using fuzzy logic. Since a large number of molecular descriptors can be calculated for each compound, two model-free methods that can take into account both linear and nonlinear relationships, namely the partial mutual information (PMI) and self-organizing maps (SOM) combined with chi square ranking, were applied prior to the model development for the selection of the most relevant subset.
Section snippets
LC dataset
In this study, a dataset (see Table S1 in the supplemental material of the paper (Antanasijević et al., 2016c) that contains the transition temperature values for 243 bent-core LC compounds was utilized for the development and testing of models. This dataset consisted of structurally diverse five-ring aromatic compounds with the transition temperature values in the range from 352.15 to 458.15 K. The same subset of 36 compounds was used for model testing, in order to allow direct comparison with
Performance of models
In the case of FSL-SOM approach, the lowest size SOM output map that had “empty” map unit(s) was 5 5, and the initial pool of 360 2D descriptor was separated into 18 groups (see Table S1. in Supplementary material). After the chi square based ranking was performed, the 18 most significant descriptors were determined (Table 1). The descriptors selected by the PMI method are also given in Table 1, while the short description of descriptors selected by the both approaches is provided in Table 2.
Conclusion
The results reported in this study indicate that ANN model with fuzzy digital output neurons can be successfully used for the simulation of bent-core liquid crystal (LC) compounds physical properties, i.e. transition temperatures, and for the estimation of related prediction error.
The best results ( and MAE 4.81 K) were obtained using standard GRNN model with the 2D descriptors subset determined by PMI-based (partial mutual information) method. Although
Funding
This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Project Nos. 172007 and 172013).
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