From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Materials Science

Background:

• Traditional methods for calculating reactivity measures like global hardness and local softness rely on approximations.
• The finite difference approximation is commonly used but has limitations in accuracy.

Purpose of the Study:

• To develop and apply a first-principles method for calculating reactivity measures directly from electron density.
• To validate the new method against conventional approaches and analytical solutions.

Main Methods:

• Utilized a recently derived density gradient theorem and the principle of nearsightedness.
• Calculated local softness s(r) directly from the electron density function.
• Obtained global softness S and Fukui function f(r) by integrating local softness.

Main Results:

• Successfully calculated important reactivity measures, including local softness, Fukui function, and global hardness, directly from first principles.
• Demonstrated an analytical relation between global softness and atomic number (S = σZ⁻²) for hydrogenic orbitals.
• Validated global hardness calculations against the conventional (I - A) finite difference approximation, showing favorable agreement.

Conclusions:

• The new first-principles approach provides accurate reactivity measures, surpassing the limitations of the finite difference approximation.
• The findings offer a more fundamental understanding of chemical reactivity based on electron density.
• The method is applicable to atoms and ions across the first four rows of the periodic table.