Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory

Abstract

In conceptual density functional theory, reactivity indexes as the Fukui function, the global hardness/softness, and hardness/softness kernels are fundamental linear responses extensively studied to predict the nucleophilic and electrophilic propensities of atoms in molecules. We demonstrate that the hardness/softness kernels of an isolated system can be expanded in eigenmodes, solutions of a variational principle. These modes are divided into two groups: the polarization modes and the charging modes. The eigenvectors of the polarization modes are orthogonal to the Fukui function and can be interpreted as densities induced at a constant chemical potential. The charging modes of an isolated system are associated with virtual charge transfers weighted by the Fukui function and obey an exact nontrivial sum rule. The exact relation between these charging eigenmodes and those of the polarizability kernel is established. The physical interpretation of the modes is discussed. Applications of the present findings to the Thomas–Fermi and von Weizacker kinetic energy functionals are presented. For a confined free quantum gas, described by the von Weizacker kinetic energy functional, we succeed to derive an approximate analytical solution for the Fukui function and for hardness/softness and polarizability kernels. Finally, we indicate how numerical calculations of the hardness kernel of a molecule could be performed from the Kohn–Sham orbitals.

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“…Comp2 might have limited cellular penetration and lower binding affinity to target biomolecules due to its pronounced electronegativity. Comp3, which is characterized by pronounced hardness and polarizability, might react with external agents, which could affect its specificity for target cells 62,63 . Comp5 might be less effective against tumours and more susceptible to metabolic elimination due to its stability and lower reactivity 64 .…”

“…Comp3, which is characterized by pronounced hardness and polarizability, might react with external agents, which could affect its specificity for target cells. 62 , 63 Comp5 might be less effective against tumours and more susceptible to metabolic elimination due to its stability and lower reactivity. 64 Notably, pharmacokinetic analysis revealed Comp3 to be the most suitable and least toxic, underscoring the importance of integrating quantum descriptors with biological data for holistic evaluation.…”

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