Description:

Implement exact analytical overlap integrals for Slater-Type Orbitals (STO) to provide a "ground truth" mode alongside the current Gaussian (GTO) approximation. Users can select between maximum speed (GTO) and theoretical exactness (STO).

Tasks:

• STO Math Implementation

  • Implement exact overlap integral formulas for STOs in math/shielding.rs.
  • Implement exact Coulomb integral calculation based on overlap.

• Configuration & CLI

  • Add IntegralMode enum (GTO/STO) to SolverOptions.
  • Wire CLI argument --mode <gto|sto> (Default: GTO).
  • Dispatch correct integral method in build_invariant_system.

• Validation & Benchmarks

  • Add regression tests ensuring STO stability.
  • Benchmark STO vs GTO performance impact.
  • Verify STO results.