# Ali Alavi

## Quantum Monte Carlo approach to the full configuration interaction problem

Location: Hörsaal A (1.3.14)Time: Monday, October 25, 2010, 14 h s.t. |

The full configuration interaction (FCI) method describes the many-electron wavefunction of an atom, molecule or even solid in terms of a linear superposition of all Slater determinants constructible from a one-particle basis. It provides the fullest possible description of the correlation within the available basis, but remains all but intractable to achieve in practice, owing to the factorially growing size of the Hilbert space of the problem.

We have recently developed a quantum Monte Carlo technique of sampling the FCI space, by propagating an annihilating population of positive and negative walkers according to set of rules designed to mimic the imaginary-time Schrodinger equation. The key feature is this method is walker annihilation, which enables the exact many-electron wavefunction to spontaneously emerge via a self-organisation of the walkers onto the significant determinants, which the algorithm itself locates as the simulation proceeds.

The method is able to yield the FCI energy, to within controllable statistical bounds, for very sizeable Hilbert spaces (exceeding 10^{16} determinants). A remarkable aspect of the new method is the scaling with number of electrons. I will show that, although it remains exponential, the exponent in the exponential is small. Several applications will be shown: the electron affinities and ionisation potentials, all-electron binding curve of F2, and a 54-electron uniform electron gas in three-dimensional periodic boundaries. Future perspectives of the method are also discussed.

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