A direct method to transform between expansions in the configuration state function and Slater determinant bases.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Transforming wave functions between Slater determinants (SD) and configuration state functions (CSF) is crucial in quantum chemistry.
• Existing methods often involve large transformation matrices and extensive computational resources.

Purpose of the Study:

• To introduce a novel, efficient algorithm for wave function transformation between SD and CSF bases.
• To significantly reduce the computational cost and time required for these transformations.

Main Methods:

• A new algorithm modifies expansion coefficients during electron spin-coupling, avoiding large, single many-electron transformations.
• The genealogical coupling scheme is employed for the transformation process.

Main Results:

• The algorithm drastically reduces the number of operations compared to previous methods.
• Demonstrated efficiency with a transformation for 30 unpaired electrons and singlet spin: 150x10^6 SD coefficients to 10x10^6 CSF coefficients in 1 minute.

Conclusions:

• The novel algorithm offers a highly efficient solution for wave function transformations in quantum chemistry.
• This method presents a significant advancement, reducing a multi-year computation to minutes.