Test of the Polarized Orbital Method: H−

The polarized-orbital method and many of the common variations and approximations of this approach are tested in a computation of the binding energy of the negative hydrogen ion ${\mathrm{H}}^{\ensuremath{-}}$. It is found that if a trial wave function for ${\mathrm{H}}^{\ensuremath{-}}$ is constructed from a distorted atomic wave function in which the first-order perturbed orbital is simply added to the undistorted atomic function, the result is a very poor approximation (binding energy -0.0094 Ry). However, if the trial function is modified, as suggested by Drachman, with the introduction of an additional independent function multiplying the perturbed orbital, the result is quite good, the binding energy being -0.0544 Ry. For comparison, the exact value (due to Pekeris) is -0.0555 Ry.