Improved Atomic Wave Functions using a Functional Transformation

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Abstract
The accuracy of an atomic wave function is often increased by an adjustment of the overall scale of the wave function. This method of improving a wave function is here generalized by considering a variable scale factor which can be an arbitrary function of the radius This type of variation has the valuable property of leaving all the coefficients in the density matrices invariant so that it is much easier to minimize the energy than it is for most parameters. The new integrals which arise are relatively easy to evaluate. To illustrate the power of the method an application is made to the simplest wave functions for the He isoelectronic sequence. A simple type of variation is found and the results show that a close approximation to the self-consistent-field energies can be obtained from a two-parameter wave function.