Coulomb-hole summations and energies for GW calculations with limited   number of empty orbitals: a modified static remainder approach
  Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self energy. We propose a scheme to reduce the summation over empty states by the use of a modified static-remainder approximation, which is simple to implement and yields accurate self energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals. 
Jack Deslippe and Georgy Samsonidze and Manish Jain and Marvin L.   Cohen and Steven G. Louie
cond-mat.mtrl-sci