Development of three-dimensional descriptors represented by tensors: Free energy of hydration density tensor

In order to describe the degree of interaction of a molecule with its environments by descriptors, several three-dimensional descriptors have been proposed. With the physical properties calculated around a molecule, scalar, vector, and tensor (zeroth, first, and second moments) of the physical properties were calculated and were used as descriptors for calculating the similarity index between the molecules. The tensors contain the information on the spatial distribution of those physical properties around the molecule. Hydration Free Energy Density (HFED) proposed by No et al. was used to calculate HFED tensor. The descriptors were used for the similarity index calculations between substituted benzenes and between lead compounds of HIV-1 protease inhibitors. The substituted benzenes are grouped according to the similarity indices. The grouping seems reasonable from the viewpoint of a chemical sense. The lead fragments of the HIV-1 protease inhibitors have a high similarity among themselves though their chemical formulas are not very similar, the lead fragments are diverse. Although the chemical formulas are diverse, the spatial distribution of the physical properties around the molecules is similar. The descriptors have high discriminating power in the similarity calculation between the molecules.