Electronic wave functions IX. Calculations for the three lowest states of the beryllium atom

The investigation described here has provided wave functions for the lowest S1, P1 and P3 states of the beryllium atom which are more accurate according to the energy test than any wave functions reported previously for these states. The first is an improvement on a previous result by the author, and the other two on results by Hartree & Hartree. The calculations were performed by the poly-detor variational method using exponential functions, and they provided an opportunity to test particular procedures for the choice of elementary functions and detors. The wave functions will be valuable for the calculation of atomic properties, but a simple examination is sufficient to show interesting characteristics such as the occurrence of various types of electronic positional correlation. In the calculation various theorems and formulas were established, and these will be useful for further calculations on the same states and also for calculations on many more complicated atomic states.