Improved quantum theory of many-electron systems. I. Construction of eigenfunctions of Ŝ^2 which satisfy Pauli's principle

A general method of obtaining many-electron wave functions which are eigenfunctions of S-^2 and which also satisfy Pauli's principle is developed. This method is based on the properties of the irreducible units of the group algebra of the symmetric group. Using this method, expansions of the exact wave function are found which will in succeeding articles form the basis of a powerful method of obtaining accurate and quite useful many-electron wave functions for atoms, molecules, and solids.