Quantum-Mechanical Study of the F 1Πu and f 3Πu States of He2

A quantum‐mechanical study of the two states, $F^1{\Pi }_u$ and $f^3{\Pi }_u$ of the helium molecule is made using the valence‐bond method with configuration interaction. A procedure for constructing valence‐bond functions which give good energy values in the entire range of internuclear distances is described. The wave‐function used for each calculation is a 49‐term function of the generalized valence‐bond type. The basis for the ${}^1{\Pi }_u$ state is a set of Slater‐type orbitals, while the one for the ${}^3{\Pi }_u$ state contains both Slater and elliptic‐type orbitals. Vibrational levels and spectropscopic constants are calculated and the results suggest the existence of more vibrational levels than have hitherto been observed for both states, the spectroscopic constants being in excellent agreement with experiment. The existence of maxima in the potential curves of both states is confirmed to be due to the avoidance of crossings of curves of the same group theoretical species.