A norm indexes-based QSPR model for predicting the standard vaporization enthalpy and formation enthalpy of organic compounds

Highlights

• A unified QSPR model was proposed for predicting four thermodynamic properties endpoints.

• The model for four properties endpoints was established with unified norm indexes used.

• Norm indexes could be used to describe the $\Delta H_{\text{v}}^0$, $\Delta H_{\text{f}}^0\left(\text{g}\right)$, $\Delta H_{\text{f}}^0\left(\text{s}\right)$ and $\Delta H_{\text{f}}^0\left(\text{l}\right)$ of organic compounds.

Abstract

As important thermodynamic properties, vaporization enthalpy and formation enthalpy were extensively utilized in the chemical industry process and chemical engineering design, environment and agriculture. Based on the concept of norm index proposed by our group previously, a unified QSPR model was built for predicting four properties endpoints for 14 families of organic compounds. Four thermodynamic properties endpoints, including standard vaporization enthalpy ($\Delta H_{\text{v}}^0$), standard formation enthalpy in gas state ($\Delta H_{\text{f}}^0\left(\text{g}\right)$), standard formation enthalpy in solid state ($\Delta H_{\text{f}}^0\left(\text{s}\right)$) and standard formation enthalpy in liquid state ($\Delta H_{\text{f}}^0\left(\text{l}\right)$), were involved in the same modelling work. This model has satisfactory fitting effect for four properties endpoints with R² of 0.967 for $\Delta H_{\text{v}}^0$, R² of 0.990 for $\Delta H_{\text{f}}^0\left(\text{g}\right)$, R² of 0.989 for $\Delta H_{\text{f}}^0\left(\text{s}\right)$ and R² of 0.987 for $\Delta H_{\text{f}}^0\left(\text{l}\right)$, respectively. Moreover, the results of internal validation, external validation and applicability domain analysis indicated the good stability and robustness of this model. This work not only calculated vaporization enthalpy and formation enthalpy with the same formula, but also covered gas, solid and liquid phases for formation enthalpy. Satisfying results obtained in the present work suggest that this model and norm indexes have good reliability and generalization.

Introduction

The physical and thermodynamic properties of organic compounds play an important role in various chemical industry process and chemical engineering design [[1], [2], [3], [4]], environment and agriculture [[5], [6], [7], [8], [9]]. The vaporization enthalpy ($\Delta$H_v) and the formation enthalpy ($\Delta$H_f) were basic physical properties of organics. $\Delta$H_v is an essential tool for correlating and predicting many physical phenomena, such as vapor pressures [10], surface tension [11], the Hildebrand's and the Hansen's solubility parameters of hydrocarbons [12]. $\Delta$H_f could be used to calculate the equilibrium constants of reaction, and is of great significance in the study of resonance energies, bond energies, nature of chemical bond and other related features [13]. It is necessary to understand the fundamental physicochemical properties of these compounds such as $\Delta$H_v and $\Delta$H_f. Because of the exponential increase in the number of newly synthesized and discovered organic compounds, but the experimental data of most compounds are not measurable, and the data obtained through experimental studies are not only expensive but also time-consuming. Therefore, it is urgent to develop a stable and reliable calculation method to solve these problems.

A great deal of effort has been made in the development of methods for estimating enthalpy over the past decades. The empirical correlation method, the group contribution method (GCM) and the quantitative structure-property relationship (QSPR) method were usually used to calculate $\Delta$H_v and $\Delta$H_f. Estimation of $\Delta$H_v by empirical correlation method, depends on some physicochemical properties including critical properties (T_c, P_c, V_c) and normal boiling point (T_b), as shown in Riedel [14], Chen [15], Alibakhshi [16] and Belghit et al.‘s investigations [17]. In terms of GCM, Benson et al. [[18], [19], [20]] proposed a general method to estimate the thermochemical properties of chemical species on the basis of group additive contributions. Joback and Reid [21] developed the first-order contribution method, which used 41 first-order groups to calculate the $\Delta$H_v and $\Delta$H_f of organics. Constantinou and Gani [22] proposed the second-order contribution method which calculated physicochemical properties including critical properties and $\Delta$H_v and $\Delta$H_f. Interestingly, they all tried to distinguish the isomers of some organic compounds. Jia and Wang [[23], [24], [25], [26]] proposed the positional distributive group contribution method, which could effectively distinguish the organic isomers and was successfully used to predict the critical properties and enthalpy of organic compounds. On the whole, the GCM is simple and general, yet it relies on the contribution values of the groups and could not be applied to new structural classification.

Another way to predict physicochemical properties is to establish a QSPR model from the structure of molecules. QSPR [[27], [28], [29], [30], [31], [32], [33]] is an effective method to link the thermodynamic/physical/chemical properties of organics with their compositions and structures. Recently, several QSPR models for estimating $\Delta$H_v of organic compounds have been proposed. In Abooali and Sobati ‘s investigation [34], a model was built with MLR (Multiple Linear Regression) method for predicting the $\Delta$H_v at T_b of 180 pure refrigerants with R² of 0.96 and AARD of 6.83%. Krasnykh et al. [35] determined the $\Delta H_{\text{v}}^0$ (standard enthalpy of vaporization) of trimethylolpropane and carboxylic acids esters by the transpiration method, and good results were obtained with the relative error less than 2%. In addition, by using MLR method, Sosnowska et al. [28] proposed a QSPR model for estimating the $\Delta H_{\text{v}}^0$ for persistent organic pollutants with good fitting and the external predictive ability (R² = 0.888, $Q_{\text{CV}}^2$ = 0.878). In terms of $\Delta$H_f, based on neural-network method, Hu et al. [36] presented a QSPR model to predict the $\Delta H_{\text{f}}^{\text{0}}$ of 180 organic molecules with good effect. Mercader et al. [37] established a QSPR model to predict $\Delta$H_f of 51 hydrocarbons by using correlation weighting of local invariants in atomic orbital molecular graphs (AOMGs), their model could provide satisfactory results with low average deviation. Furthermore, Vatani et al. [38] predicted the $\Delta H_{\text{f}}^{\text{0}}$ of 1115 compounds based on a multivariate linear genetic algorithm, and during their modelling work, five structural descriptors were calculated and selected from 1664 descriptor libraries.

In this study, the four properties endpoints - structure modelling study was performed with uniform norm descriptors for predicting the enthalpy of organic chemicals. The standard vaporization enthalpy ($\Delta H_{\text{v}}^0$), standard formation enthalpy in gas state ($\Delta H_{\text{f}}^0\left(\text{g}\right)$), standard formation enthalpy in solid state ($\Delta H_{\text{f}}^0\left(\text{s}\right)$) and standard formation enthalpy in liquid state ($\Delta H_{\text{f}}^0\left(\text{l}\right)$) were used as properties endpoints for the same modelling work. Also, the prediction ability of this model was tested by using several validation methods.