Quantitative structure–activity ? property relationships (QSAR ? QSPR),the essential tools in chemometrics and medicinal chemistry, are mathematical equations relating chemical structure to a wide variety of chemical and biological properties ? activities Recently, a new class of electronic descriptors, called quantum topology molecular similarity (QTMS) indices introduced by O'Brein and Popelier , has been shown to be successful in a variety of QSAR and QSPR calculations. The theory behind the calculation of QTMS indices uses the idea of theory of 'atoms in molecules' (AIM), pioneered by Bader to specify the electronic information in a molecular system. This theory is deeply rooted in quantum mechanics, and can be used to enhance chemical insight through ab initio wave functions. It has been demonstrated that QTMS offers a reliable alternative to electronic parameters and has delivered excellent QSARs of environmental, biological and industrial interest. In QTMS methodology, a set of electronic features is calculated for each chemical bond in the molecule. Therefore, one of the most important features of QTMS in bond critical point (BCP) space is the ability to make two-dimensional information about molecules. In this method, multiple bonds are mentioned in each molecule, and for each bond multiple descriptor, there will be a two-dimensional matrix corresponding to each molecule. In other words, for a series of molecules sharing a common structural backbone, QTMS theory produces a matrix of descriptors instead of a vector of descriptors in traditional QSAR. For a parent molecule with n chemical bonds, QTMS will calculate a descriptor data matrix of (n · m) dimension, where m is the number of QTMS descriptors calculated for each chemical bond. To handle the QTMS indices for QSAR ? QSPR studies, Popelier et al. unfold the data in a single row vector for each molecule or reduce the dimension of QTMS data matrix into a single score vector by means of principal component analysis (PCA). Therefore, they used first-order calibration methods to derive structure–activity ? property relationships.
