Stable, Fast, and Accurate Kohn-Sham Matrix Reconstruction in Gaussian Basis for Open-Shell Molecular and...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Conventional inverse Kohn-Sham Density Functional Theory (KS-DFT) methods face numerical challenges.
• Projecting real-space potentials onto limited Gaussian basis sets can lead to inefficient self-consistent-field (SCF) optimizations.

Purpose of the Study:

• To present a robust density matrix penalization method for finite basis KS matrix reconstruction.
• To overcome the limitations of existing inverse KS-DFT approaches in Gaussian basis representations.

Main Methods:

• Constructing a matrix-represented auxiliary KS Hamiltonian.
• Defining density matrix mismatch in a Löwdin-orthogonalized basis for basis rotation invariance.
• Analytically deriving the penalty Hamiltonian matrix contribution in the original Gaussian basis.

Main Results:

• The method demonstrates robust and efficient SCF optimization across various systems.
• Progressively tightening penalty strengths drive density matrix and real-space density into near machine precision agreement.
• Achieves substantially smaller density deviations compared to conventional Zhao-Morrison-Parr (ZMP) calculations.

Conclusions:

• The developed method offers a stable, fast, and accurate route for finite basis KS matrix reconstruction.
• Establishes a practical framework for density-matrix-based inverse reconstruction in Gaussian basis electronic structure calculations.