Knowledge Bank

Analytical expressions for atomic-wave functions are necessary in quantitative LCAO molecular-orbital calculations. Unless calculations are made to determine the best form of the atomic-wave function in the molecular orbital, the best procedure appears to be the use of self-consistent field atomic orbitals. The $Slater1$ hydrogen-like atomic orbitals, which have been used in most instances, do not closely approximate the SCF atomic orbitals. We have therefore undertaken to find analytical empirical formulae for atomic-wave functions which more closely approximate SCF atomic orbitals when calculations have been made, and which therefore may be thought to be also more accurate than the Slater functions where such calculations do not exist.