Full Configuration Interaction Quantum Monte Carlo: from Molecules to Materials

The fundamental equation governing the properties of atoms, molecules and materials is the many-electron Schr\ odinger equation, whose solution gives the energy of the system under consideration, by solving for the correlated motions of the constituent electrons. Accounting for this correlation has proven to be both essential for useful modelling of materials, as well as extremely difficult to calculate. In this proposal, we will develop a radically new approach to this problem based an algorithm which propagates an evolving distribution of walkers which inhabit an abstract space of states (Slater determinants) which are able to account for this correlation.The algorithm is a remarkably simple set of rules (but specially devised), akin to a Game of Life. This algorithm has been shown by the PI to work efficiently for isolated molecules, extending the range of FCI-level calculations by many orders of magnitude. The proposal here is to extend FCIQMC for an infinitely repeating system, which can be used to model a material such as diamond or graphite. This extension requires the method to be extended in a fundamental way, to allow for complex rather than purely real walkers. A method to do this is proposed in the Case for Support. If successful, this method could transform the field of modelling of materials, in that it would give access, for the first time, a way to compute the correlation energy without the imposition of uncontrolled approximations. In developing experience with this new technique, we hope one day to be able to solve some of the problems posed by the rapidly developing field of correlated materials, which have so far proven impervious to existing methods.

The academic impact of this proposal should be the take-up of the new method by both theoreticians and experimentalists interested in systems for which the current methods (both in quantum chemistry and in density-functional theory) fail. These, I envisage, will be primarily in strongly correlated systems (both molecules and solids). How will this impact be achieved? Apart from publications (which we will do our best to get into high impact journals), I hope both to develop collaborations with interested parties (for example with other code-developing groups, who can interface their code with ours, thereby giving rise to an enhanced capability of both codes), and also with experimentalists wishing to address specific systems), as well as by holding workshops and tutorials (for example hosted by CECAM) in which the method is disseminated. From an economic and societal perspective, the impact of this project must inevitably be viewed in the long-term . I truly believe that the potential this new method has is huge, in that it could help generate unbiased wavefunctions for strongly correlated materials; the insights garnered by analysing such wavefunction could unlock the mysteries behind these very difficult - but technologically very promising - materials. Of course, a method which can yield high accuracy solutions to many-electron Schrodinger equations will undoubtedly have applications in a large number of systems, with an impact that is impossible to gauge - but the upside is immense.