Green's function quantum Monte Carlo (GF QMC) simulations of fermionic ensembles require the definition of a so-called spectral parameter W to yield trustworthy estimates of the fully correlated ground state energy E. In the present work we discuss the influence of the shift parameter, W, on the convergence behaviour of GF QMC simulations. As model systems we have considered some π molecules which are studied in the framework of the Pariser–Parr–Pople (PPP) Hamiltonian. The influence of the W parameter on the convergence of the GF QMC simulations in many-electron systems with an odd number of electronic permutations within one spin direction exceeds the influence observed in systems without such odd permutations. They do not occur in polyenes and Huckel annulenes with an electron count of (4n + 2) (n = 0, 1, 2…). The GF QMC technique adopted as a computational tool has been developed to study π molecules with fermionic sign problems owing to odd electronic interchanges within one spin direction.
We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair-correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range
rs=0.5--20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair-correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies.