**Quantum Mechanical Approaches for Piezoelectricity Study in Perovskites**

Edilson Luiz C. de Aquino, Marcos Antonio B. dos Santos, Márcio de Souza Farias, Sady S. da Silva Alves, Fábio dos Santos Gil, Antonio Florêncio de Figueiredo, José Ribamar B. Lobato, Raimundo Dirceu de P. Ferreira, Oswaldo Treu-Filho, Rogério Toshiaki Kondo and José Ciríaco Pinheiro

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http://dx.doi.org/10.5772/62696

#### **Abstract**

In this chapter, we show the procedures we have been used to theoretically investi‐ gate 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 molecu‐ lar 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 BaTiO3 and LaTiO3 may have piezoelectric properties caused by electrostatic interactions.

**Keywords:** basis sets, theoretical methods, quantum mechanical approaches, piezo‐ electricity, perovskites

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