Neural Network Based Temperature-Dependent Quantitative Structure Property Relations (QSPRs) for Predicting Vapor Pressure of Hydrocarbons Denise Yaffe and Yoram Cohen* Department of Chemical Engineering, University of California, Los Angeles, Los Angeles, California 90095-1592 Received September 28, 2000 A neural network based quantitative structure-property relationship (QSPR) was developed for the vapor pressure-temperature behavior of hydrocarbons based on a data set for 274 compounds. The optimal QSPR model was developed based on a 7-29-1 back-propagation neural network architecture using valance molecular connectivity indices ( 1  v , 3  v , 4  v ), molecular weight, and temperature as input parameters. The average absolute errors in vapor pressure predictions for the test, validation, and overall data sets were 8.2% (0.036 log P units or 23.2 kPA), 9.2% (0.039 log P units or 26.8 kPA), and 10.7% (0.046 log P units or 31.1 kPA), respectively. The performance of the QSPR for temperature-dependent vapor pressure, which was developed from a simple set of molecular descriptors, displayed accuracy of better than or well within the range of other available estimation methods. INTRODUCTION Vapor pressure is an important property in many practical applications. Vapor pressures are commonly used for as- sessing the mass distribution of chemicals in the environment, designing chemical processes, and calculating other physi- cochemical properties. With vapor pressure data, air-water partition coefficients, enthalpy of vaporizations, rates of evaporation, and flash points can be estimated. The greatest difficulty and uncertainty arises when vapor pressures are being determined for chemicals of low volatility (vapor pressures below 1 Pa). Experimental vapor pressure data are abundant for low molecular weight hydrocarbons. However, reliable experimental vapor pressure data are scarce for most compounds with normal boiling points over 200 °C. As a complement to experimental vapor pressure data, numerous correlations for estimating vapor pressures have been proposed. Most vapor pressure estimation equations are either empirical or are based on equations-of-state or on the Clausius-Clapeyron equation. The Clapeyron, Lee-Kesler, Riedel, Frost-Kalkwarf-Thodos, Riedel-Plank-Miller, and Thek-Stiel are equations based on corresponding-state rela- tionships developed from critical temperature and pressure data. These equations are applicable for mostly light mo- lecular weight, nonpolar compounds with vapor pressures above 1.33 kPa. 1 The above approaches rely on knowledge of at least one critical property, boiling point, or melting point temperature. Unfortunately, boiling points and melting points as well as critical properties are often lacking, especially for heavy hydrocarbons with many being thermally unstable in the critical region. Quantitative structure-property relationship (QSPR) is an alternative approach for estimating vapor pressure. The premise of QSPR is that physicochemical properties can be correlated with molecular structural characteristics (geometric and electronic) expressed in terms of appropriate molecular descriptors. 2 Various studies have reported on the use of electronic (i.e., dipole moments, hydrogen bonding param- eters), lipophilic (i.e., partition coefficients), and topological (i.e., molecular connectivity indices and other geometric parameters) descriptors as well as other molecular parameters (e.g., molar volume, parachor, and molar refractivity) for correlating structural parameters with physicochemical prop- erties. QSPR development involves the selection of molecular descriptors to satisfactorily characterize different sets of compounds and the application of algorithms, such as partial least-squares or artificial neural networks to build the QSPR model. 3-15 Partial least-squares regression methods require a priori specification of the analytical form of the QSPR model. As an alternative, neural networks (NNs) have gained popularity in recent years as a technique for developing quantitative structure-property relationship (QSPR) models. The advantage of NNs over the regression analysis methods is their inherent ability to incorporate nonlinear relationships between the structures of compounds and their physical properties. 13-16 The primary goal of the present study is to investigate the potential applicability of neural network/temperature-de- pendent QSPR models to predict vapor pressure as a function of temperature. Specifically, we demonstrate the approach for hydrocarbons ranging from four to 12 carbon atoms. We select a back-propagation neural network system since it is especially suitable for mapping complex nonlinear relation- ships that may exist between model output (i.e., physico- chemical properties) and model inputs (i.e., molecular descriptors). Currently, vapor pressure QSPRs that have been proposed are limited to predicting vapor pressure at a constant temperature. For example, Katritzky et al., 10 using a QSPR approach, proposed a five-descriptor linear correlation model for predicting vapor pressures of 411 compounds at 25 °C. The above author reported a standard vapor pressure (atm) * Corresponding author phone: (310)825-8766; fax: (310)477-3868; e-mail: yoram@ucla.edu. 463 J. Chem. Inf. Comput. Sci. 2001, 41, 463-477 10.1021/ci000462w CCC: $20.00 © 2001 American Chemical Society Published on Web 02/21/2001