Numerically stable optimized effective potential method with standard Gaussian basis sets

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Electronic Structure Theory

Background:

• Optimized Effective Potential (OEP) methods are crucial for accurate electronic structure calculations.
• Standard OEP methods often face numerical stability issues, limiting their applicability.
• Gaussian basis sets are widely used but require careful handling in OEP calculations.

Purpose of the Study:

• To present a numerically stable Optimized Effective Potential (OEP) method utilizing Gaussian basis sets.
• To enable the use of standard Gaussian basis set libraries in OEP calculations.
• To demonstrate the method's applicability for both exchange and correlation potentials.

Main Methods:

• A novel sequence of preprocessing steps for auxiliary basis sets, Kohn-Sham response functions, and OEP equation components.
• Representation of potentials via charge densities and their electrostatic potentials.
• Application of the method to exact exchange-only Kohn-Sham calculations for atoms and molecules using specific Gaussian basis sets (aux-cc-pwCVXZ, aux-cc-pVDZ/mp2fit, aux-cc-pVTZ/mp2fit).

Main Results:

• Achieved numerically stable and physically reasonable exchange potentials.
• Demonstrated convergence of results with increasing orbital basis set quality.
• Successfully applied the method to calculate correlation potentials within the direct random phase approximation.

Conclusions:

• The developed preprocessing technique significantly improves the numerical stability of OEP calculations with Gaussian basis sets.
• The method is versatile, applicable to both exchange and correlation potentials, and beneficial for calculating effective potentials from electron densities.
• This work provides a robust framework for advanced electronic structure calculations in computational and quantum chemistry.