Numerical Calculations of Electric Response Properties Using the Bubbles and Cube Framework.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical physics

Background:

• Calculating the response of electronic orbitals to external fields is crucial in quantum chemistry.
• Existing methods may face limitations in accuracy or computational efficiency for complex systems.

Purpose of the Study:

• To develop and validate a fully numerical method for computing the response of Hartree-Fock orbitals to external electric fields.
• To assess the method's accuracy by comparing calculated polarizabilities with literature values.

Main Methods:

• Utilized Green's function methods for iterative numerical integration of the Helmholtz kernel to optimize Hartree-Fock orbitals.
• Applied iterative numerical integration of the Sternheimer equation's Helmholtz kernel for orbital response calculation.
• Expanded orbitals using atom-centered functions (bubbles) and numerical tensorial local basis functions on a 3D grid.

Main Results:

• Successfully implemented a fully numerical approach for calculating orbital response to electric fields.
• Calculated polarizabilities for Helium (He), molecular Hydrogen (H2), and Ammonia (NH3) using the developed method.
• Obtained results that show good agreement with existing literature values, validating the method's accuracy.

Conclusions:

• The developed numerical method provides an accurate and efficient way to compute the response of Hartree-Fock orbitals to external electric fields.
• The method is suitable for calculating molecular polarizabilities and can be extended to other properties.
• This work contributes to advancing computational methods in quantum chemistry.