A generalized formula for the energies of alternant molecular orbitals. II. Heteronuclear molecules

Using the method of alternant molecular orbitals ( AMO ), it is shown that the energies of AMOS ( E k σ ) for an arbitrary heteronuclear alternant system, having a singlet ground state, are connected with the energies of MOS ( e k ( k ) ) obtained by means of the conventional Hartree–Fock ( HF ) method ( SCF ‐ LCAO ‐ MO ‐ PPP ) via the formula:\documentclass{article}\pagestyle{empty}\begin{document}$$ E_{k\sigma } = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}\left( {e_k + e_{\bar k} + \delta _{1,k\sigma } } \right) \pm \sqrt {\left( {\frac{{e_k - e_{\bar k} }}{2} + \delta _{2,k\sigma } } \right)^2 + \delta _{3,k\sigma }^2 } $$\end{document}In the general case, the determination of the correlation corrections δ i , k σ is connected with the solving of a complicated system of integral equations, which is considerably simplified if the Hubbard approximation is accepted for the electron interaction. The energy spectrum of a chain with two atoms in the elementary cell ( AB ) n is considered as an example. It is shown that if nontrivial solutions exist (δ i , k σ ≠ 0), the correlation correction for AMOS of different spin are different (δ i , k σ ≠ δ i , k β ), from which it follows, that the width of the energy gap Δ E ∞ for AMOS with different spin is different: Δ E ∞,α ≠ Δ E ∞,β .