OptOrbFCI-CD: Combining optimal orbital selection and Cholesky decomposition for accurate and efficient full configuration interaction

Full configuration interaction (FCI) remains an indispensable method for strongly correlated electronic structure calculations due to its high accuracy, but its steeply scaling computational cost limits applications with large basis sets. We propose an improved optimal orbital selection algorithm for full configuration interaction with Cholesky decomposition (OptOrbFCI-CD) that significantly enhances computational efficiency without sacrificing accuracy in large basis set calculations. The computational complexities of the algorithm are systematically analyzed before and after applying Cholesky decomposition, demonstrating significant time reduction for large systems. Numerical results for H4 molecules are presented, validating the algorithm’s effectiveness across varying basis set sizes. Our findings suggest that although the energy continues to decrease with increasing basis set size, the convergence rate progressively slows without reaching full saturation. The improved algorithm exhibits strong potential for scaling to larger systems while maintaining an optimal balance between computational cost and accuracy.