A comparison between the local-energy method and the variation principle

In order to compare the local-energy method with the variation principle as an optimization technique, numerical results are given for the ground states of the hydrogen molecule ion and the helium atom. Although the optimum wave functions obtained from the two methods are very similar, expectation values of various operators are given more accurately by the variation-principle functions. Conditions are discussed under which the local-energy method could be superior to the variation principle as an optimization technique.