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The application of first principles electronic structure calculations involves solving the Schrödinger equation for many-electron systems to analyze various substances and calculate physical quantities. When dealing with electronic systems, it is often simply referred to as "first principles calculations." The term "first principles electronic structure calculations" or "first principles calculations" specifically refers, in a narrow sense, to calculations imposed with periodic boundary conditions, such as in the case of crystalline solids, surfaces, and interfaces. In the field of chemistry, calculations for molecules under isolated boundary conditions are generally termed "ab initio calculations."

However, in this article, both are broadly referred to as "first principles calculations."

First principles calculations are widely used in industrial research and development. Literally executing the approach of "solving the Schrödinger equation for many-electron systems" is almost impossible in practical terms, so first principles calculations based on density functional theory (DFT) are realistically performed. As there is already a wealth of information on the basics of DFT, it will be omitted here.

While the foundational theory of DFT remains an advanced research topic, actual applied calculations using package software such as OpenMX, Quantum ESPRESSO, VASP, and GAUSSIAN are active. DFT serves as a pragmatic simulation tool and has a very broad range of applications, making it applicable to almost anything in materials science.

Below is a list of physical properties and analyzable phenomena (in part) that can be obtained through DFT-based first principles calculations, which are deemed useful in various fields. It is hoped that this provides hints on the versatility of DFT in addressing diverse aspects of materials science.