Ground state of excitonic molecules by the Green’s-function Monte Carlo method

The biexciton bound complex of two electrons and two holes is equivalent to the hydrogen molecule with different masses0 and it can be treated in the same way as the hydrogen molecule by QMC methods. For equal electron and proton masses the complex is equivalent to a positronium molecule. The authors applied simple diffusion QMC with importance sampling to calculate ground-state energies of biexcitons for a range of electron-to-hole mass ratios a= me/mh. The full four-body problem was treated with positive and negative charges of unity interacting with Coulomb potentials. Since the ground state is nodeless, the problem of nodes does not occur, and the importance sampling function was taken as a simple product of electron-electron and hole-hole Jastrow functions with exponential terms. The results gave energies considerably lower than variational estimates and better agreement with experimental measurements for several crystalline materials. The limiting behavior as a -+ 0 was found in excellent agreement with the exact result.