The electronic Schrödinger equation is the fundamental (quantum mechanical) equation which governs the properties of atoms, molecules, solids and materials. A key feature of this equation is the presence of electronelectron interactions, which account for the fact that the electrons (which provide the "glue" that binds atoms into molecules and solids), repel each other according to a Coulomb potential. This, together with the fact that electrons are fermions (quantum objects such that an exchange of two particles lead to a sign change in the wavefunction), results in an intricate correlated motion of the electrons. It turns out that an accurate description of the chemical bond requires a good, sometimes very good, account of this correlated motion. Unfortunately, the necessary complexity introduced to correlate many electrons is immense, and has been the source of countless (uncontrolled) approximations in quantum chemistry and condensedmatter physics. In many of the most interesting systems, these approximations fail to deliver, in that they do not provide even a qualitatively correct picture of the electronic structure.
The work of my group in the past few years has been to develop a radically new way to approach to the problem posed by correlated electrons. We have developed a new Quantum Monte Carlo approach based on a "Game of Life" concept to the simulation of of electronic systems. In this approach, we simulate a population of walkers of positive and negative sign which live on an abstract lattice called Slater determinant space (which is a space that accounts properly for the fermion nature of electrons). These walkers stochastically procreate, as well as annihilate and die, according to a simple, welldefined, set of rules. For a given chemical system, the Schrodinger Hamiltonian defines the rates at which the walkers die and procreate, but otherwise the rules stay the same for all systems. A computer simulation which repeatedly executes these rules lads to an evolving population of walkers. What is remarkable (and which we have shown explicitly) is that such a simulation can solve the electronic Schrodinger equation, to within systematically improveable approximations, taking full account of the correlated nature of electronic systems. In other words, we have discovered that it is possible to harness the power of a specially designed "Game of Life" to do something very useful, namely to solve electronic Schrodinger equations.
This discovery opens up a huge and very important field of research, as it provides a new way to approach one of the fundamental equations of physical science, and which has already attracted the attention of some of the top researchers in the field, internationally. The purpose of this fellowship is provide me the time and resources to develop these ideas to full, to foster collaborations, and to keep ahead of the competition. The impact of this research may be felt across a broad range of technologically important disciplines, from the molecular physics of transition metal molecules, to the field of transitionmetal oxides, whose electronic structure continue to pose the severest challenge to existing methods.
