Quantum Monte Carlo meets Quantum Chemistry

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 electron-electron 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 condensed-matter 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, well-defined, 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 leads 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 transition-metal oxides, whose electronic structure continue to pose the severest challenge to existing methods.

Electronic structure theory is fundamental to the understanding of many physical and chemical systems, because key properties (such the total energy) are determined by the quantum mechanics of the (many) electrons that move in field generated by the nuclei of the system.

Modelling systems in which the electronic structure plays a crucial role, therefore, requires us to solve quantum mechanical (i.e. in essence the Schrödinger) equations for the electrons. Unfortunately, these equations are extremely difficult to solve, because it is necessary to account for the correlated nature of electrons in molecules. Approximations, therefore, need to be made and in many systems of great interest (for example those containing the 3d elements), these can be too severe.

Methods that can improve upon the approximations needed to make the quantum mechanical equations tractable, therefore, are of fundamental interest, and indeed constitute a very important area of research. The impact to society and the economy which progress in this field constitutes is immense, because the range of systems which it addresses so diverse. Examples can be taken from the field of catalysis, to the design of materials to store e.g. hydrogen, to how metal centres in enzymes work.

In this proposal, we will be developing a new method to solve to high (and systematically improvable) accuracy the full configuration-interaction (FCI) equations of a molecule, i.e. the quantum mechanical equations expressed in a Slater determinant basis. FCI wavefunctions are the most flexible and least biased way to solve the many-electron Schrödinger equation, but are out of reach of conventional methods for systems with more than a few electrons.

Our method combines ideas from two fields: quantum chemistry and quantum Monte Carlo. We shown in our work of the past two years that it is capable of solving problems hitherto out of reach from conventional (and very well established) methods of either field. The method has generated much interest internationally from leading theoretical groups. Our intention is to develop this method so that it can widely applied to systems for which the current methods to do not work well. In particular, it holds great promise in its applications to solids, where configuration interaction methods have never been successfully employed. In this way, we hope to be able to obtain totally new insights into the nature of electron correlation in extended systems.

This proposal also has a significant educational/training element to it, given that two PhD students and one postdoc will be employed on this grant. They will have the opportunity to contribute to the development this very promising methodology, and like my other students who have been involved on this project, will undoubtedly be in demand upon finishing their work. Their exposure to working at the cutting edge of an exciting and emerging technique, and interacting with other leading groups, will help develop them into fully-fledged researchers in their own right. This will be very helpful for their careers, and also constitutes an important and concrete societal impact.