Comment on the Luken-Sinanoǧlu paper "Theory of atomic structures including electron correlation. V. Excited states not lowest of their symmetry and oscillator strengths in neutral and singly ionized atoms"

A recent paper by Luken and Sinanoǧlu (Phys. Rev. A 13 1293, 1976) has criticized some of our work and contains material on excited states and oscillator strengths. We suggest that satisfaction of upper boundedness via the Hylleraas-Undheim-MacDonald theorem is neither a sufficient nor a necessary condition for obtaining reasonably accurate oscillator strengths. Our method for truncated Hamiltonian matrices which chooses the root which minimizes the energy as well as the correlation overlap $〈\frac{X}{X}〉$ in fact yielded upper bounds and did not suffer a "variational collapse." We point out that for excited valence states embedded in Rydberg or continuum series, the $f$ values are very sensitive to (a) choice of basis sets and (b) Relative position of diagonal matrix elements. The Ni ${}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}\to 2s2p^4 {}_{}{}^4{}_{}{}^{}P$, Bi ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2s2p^2 {}_{}{}^2{}_{}{}^{}S$, Ci $2p^2 {}_{}{}^3{}_{}{}^{}P\to 2s2p^3 {}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ transitions serve as examples.