An Algorithm for computing Three- and Four-Body Density Matrices from CASCI Wavefunction and AI-Assisted Code Optimization

Three- and four-body density matrices in the active space are required for second-order n-electron valence perturbation theory (NEVPT2) following complete active-space configuration interaction (CASCI) calculations. We developed an algorithm to generate these computationally demanding quantities by extending the π-CASCI program, which is based on the graphical symmetric group approach (GSGA). A manually written prototype was subsequently optimized through AI-assisted code optimization, resulting in substantially improved performance.