Extending the Scope of Conceptual Density Functional Theory with Second Order Analytical Methodologies

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Conceptual density functional theory (DFT) is a key tool for understanding chemical reactivity.
• Previous studies predominantly used finite difference methods to compute response functions.
• Second-order response functions and their extensions are gaining importance in DFT.

Purpose of the Study:

• To develop and extend an analytical approach for computing second-order response functions in DFT.
• To provide a complete set of analytically computable second-order properties.
• To compare analytical hardness with Parr-Pearson hardness and assess density functional approximations (DFAs).

Main Methods:

• Analytical computation of hardness, Fukui function, softness kernel, and hardness matrix.
• Utilizing the Berkowitz-Parr relation and Parr and Liu's functional expansion.
• Numerical study of the perturbation expansion of the energy functional up to second order.

Main Results:

• Highlighted differences between analytical hardness and Parr-Pearson absolute chemical hardness.
• Demonstrated the analytical Fukui function's advantage in handling charged systems and fractional occupations.
• Confirmed Kohn's Nearsightedness principle via the softness kernel and supported Nalewajski's charge sensitivity analysis with the hardness matrix.
• Introduced a new energy decomposition and validated perturbation expansion energies against DFA calculations.

Conclusions:

• The analytical approach provides accurate and insightful chemical reactivity measures.
• This method aids in evaluating the (de)localization error of DFAs.
• The study validates the convergence and utility of perturbation expansion in reactivity studies.