It was clear early-on that grid based techniques, run into a computational bottleneck. Because electrons clump close to the point charge nuclei, they are usually described by central-distribution analytic functions, e.g. ). For multi-atom (multi-centered) molecules, Roothaan suggested using Linear Combinations of Atomic Orbitals (LCAO or Molecular Orbitals MO), to model this kind of electron amplitude distribution. This is the basis-function ansatz. Pople (and others) developed and promoted Gaussian-function Basis Sets (GBS) for rapid integration and manipulation. He popularized this approach with his Quantum Chemistry code Gaussian. Gaussian-functions are used because they are popular well-behaved central-distribution, which have analytic integrals (unlike the analytic Slater functions). Within the given basis-set, the Schrödinger equation becomes the Configuration Interaction (CI) equation. Despite the challenge of solving even the Boron atom above, these innovations have allowed for routine large-scale ab initio 3 simulations of proteins, with 10,000+ basis-functions. For a recent implementation see . Appendix A discusses a few different kinds of basis-sets and how to obtain them from online databases. Before we discuss details of an Self-Consistent-Field (SCF) calculations lets describe these atomic/molecular integrals.