Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory

Area of Science:

• Theoretical Chemistry
• Quantum Chemistry
• Computational Chemistry

Background:

• Conceptual density functional theory (DFT) utilizes reactivity indexes like the Fukui function and hardness/softness to predict molecular behavior.
• These indexes are fundamental linear responses crucial for understanding nucleophilic and electrophilic atomic propensities.

Purpose of the Study:

• To demonstrate the expansion of hardness/softness kernels in isolated systems into eigenmodes.
• To provide physical interpretations for these modes and establish their relationships with other reactivity descriptors.
• To apply these findings to specific kinetic energy functionals and quantum gas models.

Main Methods:

• Expansion of hardness/softness kernels into variational principle eigenmodes (polarization and charging modes).
• Analysis of the properties and relationships of these eigenmodes, including sum rules.
• Application to Thomas-Fermi and von Weizacker kinetic energy functionals.
• Derivation of approximate analytical solutions for a confined free quantum gas.

Main Results:

• Hardness/softness kernels can be decomposed into polarization and charging modes.
• Polarization modes are orthogonal to the Fukui function and relate to densities at constant chemical potential.
• Charging modes involve virtual charge transfers and obey a sum rule, with an established link to the polarizability kernel.
• Approximate analytical solutions for reactivity kernels and the Fukui function were derived for a quantum gas model.

Conclusions:

• The eigenmode expansion provides a novel framework for understanding reactivity in DFT.
• This approach offers insights into the physical interpretation of reactivity indexes.
• The findings facilitate the calculation of hardness kernels from Kohn-Sham orbitals and enable analytical solutions for simplified models.