Cohesive energy of silicon by the Green’s-function Monte Carlo method

The total energy of diamond-structure silicon is calculated by a fixed-node Green's-function Monte Carlo method using a pseudo-Hamiltonian to eliminate the core electrons. This demonstrates the feasibility of calculating properties of solids with the quantum Monte Carlo method, since the statistical error for a supercell of 64 atoms is 0.02 eV/atom. The agreement with experiment, although good, is limited by the accuracy of the pseudo-Hamiltonian. We find that the correlation energy is improved over a variational pair-product trial function by 0.34 eV/atom in the solid compared with 0.21 eV in the free atom.