  Concentrating on zero temperature Quantum Monte Carlo calculations of
electronic systems, we give a general description of the theory of finite size
extrapolations of energies to the thermodynamic limit based on one and two-body
correlation functions. We introduce new effective procedures, such as using the
potential and wavefunction split-up into long and short range functions to
simplify the method and we discuss how to treat backflow wavefunctions. Then we
explicitly test the accuracy of our method to correct finite size errors on
example hydrogen and helium many-body systems and show that the finite size
bias can be drastically reduced for even small systems.
