Extending Conceptual DFT to Fourth Order: From Quartic Curvature to Third-Order Fukui Response

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Conceptual density functional theory (DFT) provides tools to understand chemical reactivity.
• Existing descriptors often capture linear responses, limiting insights into complex electronic behaviors.

Purpose of the Study:

• To extend conceptual DFT to fourth-order energy derivatives.
• To introduce and investigate new quantum reactivity descriptors: quartic curvature (λ) and third-order Fukui function (f(3)(r)).
• To explore nonlinear aspects of electronic reactivity and molecular stability.

Main Methods:

• Development of a direct computational methodology for fourth-order descriptors.
• Finite-difference approximations of frontier orbital energies to calculate global descriptor λ.
• Derivation of the local descriptor f(3)(r) from the third-order response of electron density.

Main Results:

• The quartic curvature (λ) quantifies chemical hardness curvature, indicating electronic stability under charge changes.
• The third-order Fukui function (f(3)(r)) maps regions sensitive to charge transfer.
• Application to push-pull organic molecules and open-shell systems revealed differences in charge transfer and delocalization.

Conclusions:

• Fourth-order conceptual DFT descriptors offer chemically meaningful insights beyond the harmonic approximation.
• These advanced tools capture nonlinear reactivity and electronic stability.
• The study validates the utility of higher-order descriptors for understanding complex molecular systems.