# Density Functional Theory (DFT) Based¶

The Hohenberg-Kohn theorem assures us that a system’s ground-state electron density contains all the information necessary to compute all of its observable properties. Moreover, the mathematical framework of density-functional theory (DFT) provides a rich framework for deriving chemically intuitive concepts to compute conceptual properties of chemical systems, even though those properties are rarely observable.

Unlike the framework of conceptual DFT (which is focused on reactivity), the DFT-based descriptive tools are primarily used to elucidate molecule’s electronic structure and binding, though some of them are relevant to chemical reactivity as well. At the most fundamental level, the electron density and its derivatives are of the most fundamental importance. At the next level, various energetic quantities associated with DFT have a leading role; these include the electrostatic potential, the kinetic energy density and various approximations thereto, etc. Suitably chosen linear combinations of these quantities have proven conceptual significance, as do several of the “intermediate quantities” that are commonly used in developing new density functionals in DFT.

Note

DFT-based tools can be computed in a spin resolved or non-spin resolved manner. Specifically, you can initialize the DFTBased class with spin=”a”, spin=”b”, spin=”s”, or spin=”ab” to use \(\alpha\), \(\beta\), \(\alpha - \beta\) or \(\alpha + \beta\) electron density, respectively. For simplicity, we do not specify the spin in mathematical formulas that follows.