O Estado Sólido: Descrição Cristalográfica e Cálculos sob Condições Periódicas de Contorno

Resumo

The properties of solid-state systems are governed by chemical bonds and, mainly, by the intermolecular
interactions responsible for the stability of compounds. To understand the correlation between structure and
properties, theoretical calculations in solid-state systems are invaluable tools. In this context, knowledge
of the crystal system and its symmetry plays a crucial role in the initial step of such calculations. In
this work, we describe the fundamental concepts of crystalline solids, symmetry elements, unit cells,
density functional theory (DFT), and periodic boundary conditions. From a crystallographic standpoint,
the most symmetric unit cell is usually selected, regardless of its size, which can complicate theoretical
calculations. However, it is often possible to define a smaller unit cell that represents the same crystal
packing, thereby reducing computational cost. For this reason, a primitive unit cell is generally chosen
for theoretical calculation inputs, where translation is the only symmetry operation explicitly employed
to simulate periodic systems. By establishing a conceptual bridge between crystallographic symmetry and
periodic electronic-structure calculations, this work provides a didactic and integrative perspective that
facilitates the interpretation of solid-state properties. Such an approach supports practical applications
in areas such as semiconductor engineering, heterogeneous catalysis, energy storage, and the rational
design of metal–organic frameworks (MOFs), emphasizing the scientific and educational relevance of
combining experimental and theoretical methods in solid-state chemistry.
Keywords: Solid-state; symmetry; DFT calculations.