Universal mathematical identities in density functional theory: results from three different spin-resolved...

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Reactivity Theory

Background:

• Existing theoretical approaches to conceptual DFT lack unification.
• Spin-polarized density functional theory (SP-DFT) offers a framework for describing spin-dependent electronic properties.
• Understanding chemical reactivity requires robust theoretical tools.

Purpose of the Study:

• To provide a unified and systematic theoretical framework for all common conceptual DFT formulations.
• To derive chemical reactivity indicators within the closed-system, open-system, and density representations of SP-DFT.
• To develop a universal notation for conceptual DFT identities.

Main Methods:

• Derivation of global, local, and nonlocal chemical reactivity indicators within the closed-system representation of SP-DFT.
• Establishment of links between closed-system, open-system, and density representations, including spin-resolved identities.
• Development of a powerful matrix-vector notation for universal representation of DFT identities.

Main Results:

• A unified theoretical framework for conceptual DFT is presented, encompassing existing and new formulations.
• Spin-resolved Berkowitz-Parr and Harbola-Chattaraj-Cedillo-Parr identities are derived.
• A matrix-vector notation is developed, simplifying and unifying various conceptual DFT representations.

Conclusions:

• The developed framework provides a comprehensive understanding of chemical reactions from electron-following and electron-preceding perspectives.
• The [N(alpha),N(beta)] representation is highlighted as potentially more useful than the [N,N(S)] representation for coupled spin and electron transfer reactions.
• The unified approach and universal notation advance the field of conceptual DFT.