Criteria of Goodness for Approximate Wave Functions

The relations between the root-mean-square error of an approximate ground state wave function, the energy error, and the root-mean-square local energy deviation are exhibited and discussed. Computations of these quantities for helium wave functions containing errors of different character and magnitude are presented, and are shown to indicate that the errors in wave functions of the Hylleraas type are of increasingly short range character as these functions are made more flexible. The form of variational process which will give a wave function most satisfactory for a given purpose is discussed with illustrative computations relating to the diamagnetic susceptibility of He. It is found that the energy error associated with a wave function may be a comparatively unsatisfactory criterion of goodness.