Empirical QSPR Correlations

Empirical QSPR Correlations In quantitative structure property relationship (QSPR) methods, physical properties are correlated with molecular descriptors that characterize the molecular and electronic structure of the molecule. Large amounts of experimental data are used to statistically determine the most significant descriptors to be used in the correlation and their contributions. The resultant correlations are simple to apply if the descriptors are available. Descriptors must generally be generated by the user with computational chemistry software, although the DIPPR 801 database now contains a table of molecular descriptors for most of the compounds in it. QSPR methods are often very accurate for specific families of compounds for which the correlation was developed, but extrapolation problems are even more of an issue than with GC methods. 

Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton s equations of motion for a small number (on the order of 103) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the potential energy between molecules to simulate configurations of the molecules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not generally available at this time. 

Organic molecules The Ambrose method is recommended for all three critical properties of hydrocarbons and n-alcohols. The Joback method is recommended for Tc and Pc of all other organic molecules. Fedors method is recommended for Vc of these compounds, but the Joback method can also be used. 

Inorganic molecules The simple correlation Tc = 1.647, is recommended if the normal boiling point is known. Critical pressure Pc is best obtained by extrapolating vapor pressure data to Tc, and Vc is best obtained from a correlation of liquid density extrapolated to Tc. 

Other recent methods including the Wilson-Jasperson (Wilson, G. M., and L.V. Jasperson, Critical Constants Tc, Pc, Estimation Based on Zero, First and Second Order Methods, AIChE Spring Meeting, New Orleans, La., 1996) and Marrero-Pardillo [Marrero-Morejon, J., and E. Pardillo-Fontdevila, AIChE J., 45 (1999) 615] methods have proved to be as good as or better for some classes of compounds than the methods presented here however, their application is more difficult. 

Critical Properties The critical temperature T, pressure P , and volume V of a compound are important, widely used constants. They are important in determining the phase boundaries of a compound and (particularly T and P ) are required input parameters for most thermal and volumetric property calculations of the equilibrium phases using CS or analytical equations of state. Most estimation methods employ weighted group, atom, or bond contributions. 

The critic temperature of a compound is the temperature above which a liquid phase cannot be formed, no matter the pressure of the system. The critical pressure is the vapor pressure of the compound at the critical temperature. The critical volume is the volume occupied by a set amount of a compound (typically 1 mol) at its critical temperature and pressure. 

The critical compressibihty factor Z is determined from the experimental or predicted values of the critical properties by the definition 

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In this section, two types of structure-metal binding ability relationships will be described. The first one concerns empirical linear correlations between equilibrium constants of complexation or extraction and some descriptors. In most cases, these correlations are obtained for relatively small datasets (less than 20 molecules) without any validation. We do not intend to analyze them in detail only their general characteristics will be reported. The second type of relationships were obtained in regular QSPR studies involving the selection of pertinent descriptors from their large initial pools, and the stage of the models, validation on external test set(s). 

Physical properly estimation methods may be classified into six general areas (1) theory and empirical extension of theory, (2) corresponding states, (3) group contributions, (4) computational chemistry, (5) empirical and quantitative structure property relations (QSPR) correlations, and (6) molecular simulation. A quick overview of each class is given below to provide context for the methods and to define the general assumptions, accuracies, and limitations inherent in each. 

A large group of empirical molecular descriptors involves solvent effects on various chemical or physical processes. Because of the complexity of solvent effects, the respective QSAR/QSPR correlation equations are usually multiparametric,... 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

Classes of Estimation Methods Table 1.1.1 summarizes the property estimation methods considered in this book. Quantitative property-property relationships (QPPRs) are defined as mathematical relationships that relate the query property to one or several properties. QPPRs are derived theoretically using physicochemical principles or empirically using experimental data and statistical techniques. By contrast, quantitative structure-property relationships (QSPRs) relate the molecular structure to numerical values indicating physicochemical properties. Since the molecular structure is an inherently qualitative attribute, structural information has first to be expressed as a numerical values, termed molecular descriptors or indicators before correlations can be evaluated. Molecular descriptors are derived from the compound structure (i.e., the molecular graph), using structural information, fundamental or empirical physicochemical constants and relationships, and stereochemcial principles. The molecular mass is an example of a molecular descriptor. It is derived from the molecular structure and the atomic masses of the atoms contained in the molecule. An important chemical principle involved in property estimation is structural similarity. The fundamental notion is that the property of a compound depends on its structure and that similar chemical stuctures (similarity appropriately defined) behave similarly in similar environments. 

The goal of this work is to provide an overview of QSPR studies in metal complexation and extraction and to discuss under which conditions QSPR modeling may become a valuable tool for computer-aided design of new metal binders. Early empirical correlations will be analyzed here only for comparison with regular QSPRs. 

In a broader context, LFER and similar approaches are subsets of correlation analyses. Exner defines correlation analysis as a mathematical treatment starting from experimental data and seeking empirical relationships which can subsequently be interpreted theoretically. Although certainly not restricted to chemistry, correlation analysis has been developed extensively in physical organic chemistry. In addition to LFER, LSER, QSAR, and QSPR involve empirical models and, hence, fall in the category of correlation analysis. 

It is not easy to find successful structure-activity/ property correlations, but the rapid growth of publications dealing with QSAR/QSPR studies clearly demonstrates the progress in this area. To obtain a significant correlation, it is crucial that appropriate descriptors be employed, whether they are theoretical, empirical, or derived from readily available experimental characteristics of the structures. Many descriptors reflect simple molecular properties and thus can provide insight into the physicochemical nature of the activity/ property under consideration. 

There exists a large body of empirical vulnerability data for conventional EM for which numerous researchers have correlated molecular or material properties [102-156]. Of these, a large number of the molecular properties used in the correlations were predicted using semi-empirical or quantum mechanical methods. While many of these are quite useful in identifying potential vulnerability of an EM, they should not be used to justify mechanistic arguments [157,158]. Additionally, as with all QSPR approaches, the predictive capability is strongly dependent on the quality of the empirical information used in the parameterization. Unreliable empirical information used in the parameterization could result in a highly inaccurate tool. For vulnerability, the majority of the empirical data consists of results of drop-... 

This article describes the current capabilities for predicting materials properties using atomistic computational approaches. The focus is on inorganic materials including metals, semiconductors, and insulators in the form of bulk solids, surfaces, and interfaces. Properties of isolated molecules, liquids. and organic polymers are treated as separate entries. Besides a computational approach based on physical laws, materials properties can also be predicted by empirical rules and statistical correlations between chemical composition, bonding topology, and macroscopic properties. These very useful and quick approaches, which include so-called quantitative structure-property relationship (QSPR) methods, are covered in other entries of this encyclopedia (see Quantitative Structure-Property Relationships (QSPR)). 

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