In a previous article, we used Hartree-Fock (HF) theory to study the piezoelectricity in BaTiO₃. In this paper, we applied the Douglas-Kroll-Hess second order scalar relativistic method to investigate the possible piezoelectric properties in the perovskite YFeO₃ structure, which has not yet been studied experimentally. The 30s20p13d and 31s21p17d Gaussian basis sets for the Fe (⁵D) and Y (²D) atoms, respectively, were built with the Generator Coordinate HF method. After contraction to [13s7p5d] and [13s8p7d], in combination with the 20s14p/6s4p basis set for the O (³P) atom from literature, they had their quality evaluated using calculations of the total and the orbital energies for the ²FeO⁺¹ and ¹YO⁺¹ fragments. The dipole moment, the total energy, and the total atomic charges in YFeO₃ in C(s) space group were calculated. The results and the analysis lead us to believe that the perovskite YFeO₃ does not present piezoelectric properties.

Molecular electrostatic potential (MEP) and pattern recognition (PR) were used to draw potentially active pentamidine derivatives against Trypanosome brucei rhodesiense (T. b. rhodesiense). PR models: Principal Component Analysis, PCA model; Hierarchical Cluster Analysis, HCA model; K-Nearest Neighbor, KNN model; Soft Independent Modeling of Class Analogy, SIMCA model; and Stepwise Discriminant Analysis, SDA model, were built by reducing the dimensionality of a data matrix to twenty-eight pentamidine derivatives and allowed the compounds to be classified into two classes: more active and less active, according to their degrees of activity against T. b. rhodesiense. The study outlined that the properties HOMO (highest occupied molecular orbital) energy, VOL (molecular volume), and ASA_P (water accessible surface area of all polar (½qi½³0. 2) atoms) are the most relevant for the construction of the models. The key structural features required for biological activity investigated through MEP were used as guidelines in the design of thirteen new compounds, which were evaluated by PR models as more active or less active against T. b. rhodesiense. The application of PR models indicated nine promising compounds (29, 30, 31, 32, 33, 36, 37, 39, and 40) for synthesis and biological assays.

Artemisinins tested against W-2 strains of malaria falciparum are investigated with molecular electrostatic potential (MEP), in an attempt to identify key features of the compounds that are necessary for their activities, as well as to investigate likely interactions with the receptor in a biological process and to use that information to propose new molecules. In order to discover the best geometry involving the ligand-receptor complexes (heme) studied and help in the proposition of the new derivatives, molecular simulations of interactions between the most negative charged region around the peroxide and heme locates (the ones around the Fe 2+ ion) were carried out. In addition, PCA (principal components analysis), HCA (hierarchical cluster analysis), SDA (stepwise discriminant analysis), and KNN (K-nearest neighbor) multivariate models were employed to investigate which descriptors are responsible for the classification between the higher and lower antimalarial activity of the compounds, and also this information was used to propose new potentially active molecules. The information accumulated in studies of MEP, molecular docking, and multivariate analysis supported the proposal of new structures with potential antimalarial activities.

In this chapter, firstly, we briefly review aspects of the approximation of quantum chemistry, molecular electrostatic potential (MEP), and chemometrics techniques, which are accredited as important tools in the development of chemical science and are frequently used in the study and design of bioactive compounds. Ultimately, we use MEP and pattern recognition (PR) techniques as tools to design nitrofuran compounds with biological activity against Trypanosoma cruzi (T. cruzi). PR models (PCA, HCA, KNN, SDA, and SIMCA) were constructed and demonstrated that 23 nitrofurans can be classified into two classes or groups: more active and less active according to their degrees of activity against T. cruzi. Properties such as charge on the N atom of the nitro group (QN1); the difference between the highest occupied molecular orbital (HOMO) energy and the lowest unoccupied molecular orbital (LUMO) energy (GAP energy); molecular representation of structure based on electron diffraction code of signal 5, unweighted (Mor05u); and Moriguchi water-octanol partition coefficient (MlogP) are responsible for the classification into more active and less active studied nitrofurans. It is interesting to notice that these properties represent three distinct classes of interactions between the nitrofurans and the biological receptor: electronic (QN1 and GAP energy), steric (Mor05u), and hydrophobic (MlogP). The results of the application of PR models on the validation set evidenced two nitrofuran compounds (compounds 25 and 30) as more promising for synthesis and biological assays, which in the future can be used to validate our PR models.

In this chapter, we show the procedures we have been used to theoretically investigate the piezoelectric effects in perovskites. The construction of extended basis sets using the generator coordinate Hartree-Fock (GCHF) method is shown, as well as the strategies used to contract extended basis sets and to evaluate their quality in molecular calculations. Besides, we show adequate procedures to choice polarization and diffuse functions to best represent the studied crystal. In addition, we also discuss conditions under which GCHF basis sets and standard basis sets from literature can be used to theoretical investigation of piezoelectricity in perovskites. We finalize the chapter presenting and discussing the results for investigations of piezoelectricity with standard basis sets for barium and lanthanum titanates. To conclude, we present evidences that BaTiO 3 and LaTiO 3 may have piezoelectric properties caused by electrostatic interactions.