Numerical solution of Schrödinger’s equation in polyatomic molecules

We have developed a fully numerical, basis-set-free algorithm for solution of the Schrödinger single-particle equation in polyatomic molecules. As a test of the algorithm, the Hartree–Fock energy of H+3 is computed and compared with previous momentum-space benchmarks. The present calculations are the first successful basis-set-free calculations in coordinate space on a polyatomic molecular system.