Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Analytic exchange-correlation kernel formulations are crucial for density functional theory (DFT) perturbation calculations.
• Generalized gradient approximation (GGA) and auxiliary density functional theory (ADFT) are key frameworks in modern computational chemistry.

Purpose of the Study:

• To derive and discuss the working equation for the GGA exchange-correlation kernel within the ADFT framework.
• To extend the formulation to unrestricted approaches and discuss implementation details.
• To compare the performance of analytic kernels with finite difference methods.

Main Methods:

• Development and implementation of an analytic GGA ADFT kernel.
• Utilizing deMon2k software with native or LibXC library functionals.
• Comparison with finite difference calculations for validation.
• Application of auxiliary density perturbation theory for analytic frequency calculations.

Main Results:

• Quantitative agreement between analytic and finite difference calculations.
• Substantial improvement in computational performance with analytic GGA ADFT kernels.
• Similar performance gains observed for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements.

Conclusions:

• Analytic GGA ADFT kernels offer significant computational advantages without sacrificing accuracy.
• The developed method provides a more efficient approach for DFT perturbation calculations.
• This work contributes to advancing computational efficiency in quantum chemistry.