Notes on Hartree-Fock Theory and Related Topics

Abstract

The numerical challenges encountered when addressing electronic structure problems from first principles in computational quantum chemistry are humbling. Solving the Schrödinger equation for a large molecular system amounts to handling sets of second-order differential or integro-differential equations, often with thousands of variables. Indeed, the large number of particles that have to be treated in a quantum-mechanical description of a chemical system is certainly one of the greatest obstacles to quantum chemistry. The equations may have millions of singularities, and an accuracy of a few parts per billion is usually required. While a lot of sophisticated method development has been devoted to this problem with spectacular progress in the last couple of decades, the current state of the art nevertheless leaves both room and need for improvement. Many problems where a theoretical-computational approach could have an immense potential would require a quantitative description of extended molecular systems, i.e., molecules in the range 102--104 atoms.